ALBERT

Description: Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

Description: By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but discover a problem that remains open.

Description: We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

Description: Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \(S_{CS}^\kappa\), \(\kappa\) is some parameter. Instead of making sense of the path integral over the space of \(\mathfrak{g}\)-valued smooth 1-forms on \(S^2 \times S^1\), we use the Segal Bargmann transform to define the path integral over \(B_i\), the space of \(\mathfrak{g}\)-valued holomorphic functions over \(\mathbb{C}^2 \times \mathbb{C}^{i-1}\). This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \(C(B_1^{\times^4} \times B_2^{\times^2}, \mathbb{C})\) and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \(\mathbb{R}^3\). We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \(\kappa\). The second half of the article concentrates on taking \(\kappa\) goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \(SU(N)\) and \(SO(N)\). In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \(SU(N)\) and a Conway type skein relation in the case of \(SO(N)\). By imposing quantization condition on the charge of the link \(L\), we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of \(\mathbb{R}^3\).

Description: We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

Description: Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286; 563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the (286; 563)-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).

Description: Applications of fractional time derivatives in physics and engineering require the existence of nontranslational time automorphisms on the appropriate algebra of observables. The existence of time automorphisms on commutative and noncommutative C*-algebras for interacting many-body systems is investigated in this article. A mathematical framework is given to discuss local stationarity in time and the global existence of fractional and nonfractional time automorphisms. The results challenge the concept of time flow as a translation along the orbits and support a more general concept of time flow as a convolution along orbits. Implications for the distinction of reversible and irreversible dynamics are discussed. The generalized concept of time as a convolution reduces to the traditional concept of time translation in a special limit.

Description: We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.

Description: This article is devoted to the study of the ASARCO demolition seismic data. Two different classes of modeling techniques are explored: First, mathematical interpolation methods and second statistical smoothing approaches for curve fitting. We estimate the characteristic parameters of the propagation medium for seismic waves with multiple mathematical and statistical techniques, and provide the relative advantages of each approach to address fitting of such data. We conclude that mathematical interpolation techniques and statistical curve fitting techniques complement each other and can add value to the study of one dimensional time series seismographic data: they can be use to add more data to the system in case the data set is not large enough to perform standard statistical tests.

Description: Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained by the Dirac-method as well as results from other methods, specifically in connection with evolution-like equations ruled by square-root operators, that we will address to as relativistic evolution equations.

Description: Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom), dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone and the various uses of psi in maths and physics; they arrive at dessins d’enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell’s theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.

Description: The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established. We prove that the Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras having a properly uniformly bounded approximate unit and not necessarily m-convex. Based on these results the K-regularity property for quasi-stable Frechet algebras having a properly uniformly bounded approximate unit is established.

Description: We investigate various scenarios for ending the San Francisco MSM (men having sex with men) HIV/AIDS epidemic (1978–1984). We use our previously developed model and explore changes due to prevention strategies such as testing, treatment and reduction of the number of contacts. Here we consider a “what-if” scenario, by comparing different treatment strategies, to determine which factor has the greatest impact on reducing the HIV/AIDS epidemic. The factor determining the future of the epidemic is the reproduction number R0; if R0 〈 1, the epidemic is stopped. We show that treatment significantly reduces the total number of infected people. We also investigate the effect a reduction in the number of contacts after seven years, when the HIV/AIDS threat became known, would have had in the population. Both reduction of contacts and treatment alone, however, would not have been enough to bring R0 below one; but when combined, we show that the effective R0 becomes less than one, and therefore the epidemic would have been eradicated.

Description: This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2) for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3) per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N) and a computational cost of O(N logN) per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

Description: Extending Eilenberg–Mac Lane’s cohomology of abelian groups, a cohomology theory is introduced for commutative monoids. The cohomology groups in this theory agree with the pre-existing ones by Grillet in low dimensions, but they differ beyond dimension two. A natural interpretation is given for the three-cohomology classes in terms of braided monoidal groupoids.

Description: The Aharonov-Vaidman gauge additively transforms the mean energy of a quantum mechanical system into a weak valued system energy. In this paper, the equation of motion of this weak valued energy is used to provide a mathematical statement of an extended 1st Law of Thermodynamics that is applicable to the mean energy of a closed quantum system when the mean energy is expressed in the Aharonov-Vaidman gauge, i.e., when the system’s energy is weak valued. This is achieved by identifying the generalized heat and work exchange terms that appear in the equation of motion for weak valued energy. The complex valued contributions of the additive gauge term to these generalized exchange terms are discussed and this extended 1st Law is shown to subsume the usual 1st Law that is applicable for the mean energy of a closed quantum system. It is found that the gauge transformation introduces an additional energy uncertainty exchange term that—while it is neither a heat nor a work exchange term—is necessary for the conservation of weak valued energy. A spin-1/2 particle in a uniform magnetic field is used to illustrate aspects of the theory. It is demonstrated for this case that the extended 1st Law implies the existence of a gauge potential ω and that it generates a non-vanishing gauge field F. It is also shown for this case that the energy uncertainty exchange accumulated during the evolution of the system along a closed evolutionary cycle C in an associated parameter space is a geometric phase. This phase is equal to both the path integral of ω along C and the integral of the flux of F through the area enclosed by C.

Description: The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alpha}\) is the Riemann–Liouville fractional derivative of order \(\alpha \in (0,1)\), \(\gamma>0\) and \(f\) is an \(X\)-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic flows. Well-posedness is proven, and a subordination identity is obtained relating the solution operator of the considered problem and the \(C_{0}\)-semigroup, generated by the operator \(A\). As an example, the Rayleigh–Stokes problem for a generalized second-grade fluid is considered.

Description: This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

Description: We address the recently posed question as to whether the nonlocality of a single member of an entangled pair of spin 1 / 2 particles can be shared among multiple observers on the other wing who act sequentially and independently of each other. We first show that the optimality condition for the trade-off between information gain and disturbance in the context of weak or non-ideal measurements emerges naturally when one employs a one-parameter class of positive operator valued measures (POVMs). Using this formalism we then prove analytically that it is impossible to obtain violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality by more than two Bobs in one of the two wings using unbiased input settings with an Alice in the other wing.

Description: A smooth function of the second moments of N continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously to a single continuous variable. New uncertainty relations are obtained for multi-partite systems that allow one to distinguish entangled from separable states. We also investigate the geometry of the “uncertainty region” in the N ( 2 N + 1 ) -dimensional space of moments. It is shown to be a convex set, and the points on its boundary are found to be in one-to-one correspondence with pure Gaussian states of minimal uncertainty. For a single degree of freedom, the boundary can be visualized as one sheet of a “Lorentz-invariant” hyperboloid in the three-dimensional space of second moments.

Description: This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustness of the technique implemented on the chosen chaotic system.

Description: In this paper, we consider the time-dependent Schrödinger equation: i ∂ ψ ( x , t ) ∂ t = 1 2 ( − Δ ) α 2 ψ ( x , t ) + V ( x ) ψ ( x , t ) , x ∈ R , t > 0 with the Riesz space-fractional derivative of order 0 〈 α ≤ 2 in the presence of the linear potential V ( x ) = β x . The wave function to the one-dimensional Schrödinger equation in momentum space is given in closed form allowing the determination of other measurable quantities such as the mean square displacement. Analytical solutions are derived for the relevant case of α = 1 , which are useable for studying the propagation of wave packets that undergo spreading and splitting. We furthermore address the two-dimensional space-fractional Schrödinger equation under consideration of the potential V ( ρ ) = F · ρ including the free particle case. The derived equations are illustrated in different ways and verified by comparisons with a recently proposed numerical approach.

Description: The rate of change of any function versus its independent variables was defined as a derivative. The fundamentals of the derivative concept were constructed by Newton and l’Hôpital. The followers of Newton and l’Hôpital defined fractional order derivative concepts. We express the derivative defined by Newton and l’Hôpital as an ordinary derivative, and there are also fractional order derivatives. So, the derivative concept was handled in this paper, and a new definition for derivative based on indefinite limit and l’Hôpital’s rule was expressed. This new approach illustrated that a derivative operator may be non-linear. Based on this idea, the asymptotic behaviors of functions were analyzed and it was observed that the rates of changes of any function attain maximum value at inflection points in the positive direction and minimum value (negative) at inflection points in the negative direction. This case brought out the fact that the derivative operator does not have to be linear; it may be non-linear. Another important result of this paper is the relationships between complex numbers and derivative concepts, since both concepts have directions and magnitudes.

Description: In the paper, the authors find three new identities of the Catalan-Qi numbers and provide alternative proofs of two identities of the Catalan numbers. The three identities of the Catalan-Qi numbers generalize three identities of the Catalan numbers.

Description: We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included.

Description: Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more noncommuting reference bases respects uncertainty like relations for a given state of single and bipartite quantum systems. In the case of bipartite systems, we find that the presence of entanglement may tighten the above relation. Further, we find an upper bound on the sum of the relative entropies of coherence of bipartite quantum states in two noncommuting reference bases. Moreover, we provide an upper bound on the absolute value of the difference of the relative entropies of coherence calculated with respect to two incompatible bases.

Description: Although versions of Poisson’s Summation Formula (PSF) have already been studied extensively, there seems to be no theorem that relates discretization to periodization and periodization to discretization in a simple manner. In this study, we show that two complementary formulas, both closely related to the classical Poisson Summation Formula, are needed to form a reciprocal Discretization-Periodization Theorem on generalized functions. We define discretization and periodization on generalized functions and show that the Fourier transform of periodic functions are discrete functions and, vice versa, the Fourier transform of discrete functions are periodic functions.

Description: In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order.

Description: The purpose of this paper is to present a consistent mathematical framework that shows how the EPR (Einstein. Podolsky, Rosen) phenomenon fits into our view of space time. To resolve the differences between the Hilbert space structure of quantum theory and the manifold structure of classical physics, the manifold is taken as a partial representation of the Hilbert space. It is the partial nature of the representation that allows for action at a distance and the failure of the manifold picture.

Description: For many scientific calculations, particularly those involving empirical data, IEEE 32-bit floating-point arithmetic produces results of sufficient accuracy, while for other applications IEEE 64-bit floating-point is more appropriate. But for some very demanding applications, even higher levels of precision are often required. This article discusses the challenge of high-precision computation, in the context of mathematical physics, and highlights what facilities are required to support future computation, in light of emerging developments in computer architecture.

Description: This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.

Description: The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials. Expansions in terms of orthogonal polynomials are very common in many applications. While the connection problem may be solved by directly computing the change–of–basis matrix, this approach is computationally expensive. A recent approach to solving the connection problem involves the use of the spectral connection matrix, which is a matrix whose eigenvector matrix is the desired change–of–basis matrix. In Bella and Reis (2014), it is shown that for the connection problem between any two different classical real orthogonal polynomials of the Hermite, Laguerre, and Gegenbauer families, the related spectral connection matrix has quasiseparable structure. This result is limited to the case where both the source and target families are one of the Hermite, Laguerre, or Gegenbauer families, which are each defined by at most a single parameter. In particular, this excludes the large and common class of Jacobi polynomials, defined by two parameters, both as a source and as a target family. In this paper, we continue the study of the spectral connection matrix for connections between real orthogonal polynomial families. In particular, for the connection problem between any two families of the Hermite, Laguerre, or Jacobi type (including Chebyshev, Legendre, and Gegenbauer), we prove that the spectral connection matrix has quasiseparable structure. In addition, our results also show the quasiseparable structure of the spectral connection matrix from the Bessel polynomials, which are orthogonal on the unit circle, to any of the Hermite, Laguerre, and Jacobi types. Additionally, the generators of the spectral connection matrix are provided explicitly for each of these cases, allowing a fast algorithm to be implemented following that in Bella and Reis (2014).

Description: In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are compared with those presented in this paper. By using the Bernstein characterization theorem we find the conditions under which the even moments are non-negative.

Description: In this paper, we have presented a family of fourth order iterative methods, which uses weight functions. This new family requires three function evaluations to get fourth order accuracy. By the Kung–Traub hypothesis this family of methods is optimal and has an efficiency index of 1.587. Furthermore, we have extended one of the methods to sixth and twelfth order methods whose efficiency indices are 1.565 and 1.644, respectively. Some numerical examples are tested to demonstrate the performance of the proposed methods, which verifies the theoretical results. Further, we discuss the extraneous fixed points and basins of attraction for a few existing methods, such as Newton’s method and the proposed family of fourth order methods. An application problem arising from Planck’s radiation law has been verified using our methods.

Description: In this paper, sufficient conditions are given to investigate the existence of mild solutions on a semi-infinite interval for first order semi linear impulsive neutral functional differential evolution inclusions with infinite delay using a recently developed nonlinear alternative for contractive multivalued maps in Frechet spaces due to Frigon combined with semigroup theory. The existence result has been proved without assumption of compactness of the semigroup. We introduced a new phase space for impulsive system with infinite delay and claim that the phase space considered by different authors are not correct.

Description: We consider two principal bundles of embeddings with total space E m b ( M , N ) , with structure groups D i f f ( M ) and D i f f + ( M ) , where D i f f + ( M ) is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: B ( M , N ) = E m b ( M , N ) / D i f f ( M ) and B + ( M , N ) = E m b ( M , N ) / D i f f + ( M ) from the various properties described, an adequate group seems to be a group of Fourier integral operators, which is carefully studied. It is the main goal of this paper to analyze this group, which is a central extension of a group of diffeomorphisms by a group of pseudo-differential operators which is slightly different from the one developped in the mathematical litterature e.g. by H. Omori and by T. Ratiu. We show that these groups are regular, and develop the necessary properties for applications to the geometry of B ( M , N ) . A case of particular interest is M = S 1 , where connected components of B + ( S 1 , N ) are deeply linked with homotopy classes of oriented knots. In this example, the structure group of the tangent space T B + ( S 1 , N ) is a subgroup of some group G L r e s , following the classical notations of (Pressley, A., 1988). These constructions suggest some approaches in the spirit of one of our previous works on Chern-Weil theory that could lead to knot invariants through a theory of Chern-Weil forms.

Description: We propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for fixed type Barrier options, and apply the Mellin transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of Lévy processes numerically. Finally, the algorithm for computing numerically is presented with results for a set of Lévy processes.

Description: The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given.

Description: In this manuscript, we define generalized Kincses-Totik type contractions within the context of metric space and consider the existence of a fixed point for such operators. Kincses-Totik type contractions extends the renowned Banach contraction mapping principle in different aspects. First, the continuity condition for the considered mapping is not required. Second, the contraction inequality contains all possible geometrical distances. Third, the contraction inequality is formulated for some iteration of the considered operator, instead of the dealing with the given operator. Fourth and last, the iteration number may vary for each point in the domain of the operator for which we look for a fixed point. Consequently, the proved results generalize the acknowledged results in the field, including the well-known theorems of Seghal, Kincses-Totik, and Banach-Caccioppoli. We present two illustrative examples to support our results. As an application, we consider an Ulam-stability of one of our results.

Description: We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximating the derivative in Newton’s iteration using a rational linear function. Unlike the existing methods of a similar nature, the scheme of the new method is easy to remember and can also be implemented for systems of nonlinear equations. The applicability of the method is demonstrated on some practical as well as academic problems of a scalar and multi-dimensional nature. In addition, to check the efficacy of the new technique, a comparison of its performance with the existing techniques of the same order is also provided.

Description: In this short note we give an elementary description of the linear part of the minimal free resolution of a Stanley-Reisner ring of a simplicial complex Δ . Indeed, the differentials in the linear part are simply a compilation of restriction maps in the simplicial cohomology of induced subcomplexes of Δ . Along the way, we also show that if a monomial ideal has at least one generator of degree 2, then the linear strand of its minimal free resolution can be written using only ± 1 coefficients.

Description: In this paper, we propose a branch-and-bound algorithm to solve exactly the minimum vertex cover (MVC) problem. Since a tight lower bound for MVC has a significant influence on the efficiency of a branch-and-bound algorithm, we define two novel lower bounds to help prune the search space. One is based on the degree of vertices, and the other is based on MaxSAT reasoning. The experiment confirms that our algorithm is faster than previous exact algorithms and can find better results than heuristic algorithms.

Description: We present fixed points results of multivalued Prešić type k-step iterative mappings satisfying generalized weakly contraction conditions in metric spaces. An example is presented to support the main result proved herein. The stability of fixed point sets of multivalued Prešić type weakly contractive mappings are also established. Global attractivity result for the class of matrix difference equations is derived as application of the result presented herein. These results generalize and extend various comparable results in the existing literature.

Description: The Foundation Fighting Blindness leads a collaborative effort among patients and families, scientists, and the commercial sector to drive the development of preventions, treatments, and cures for inherited retinal diseases (IRDs). When the nonprofit was established in 1971, it sought the knowledge and insights of leaders in the retinal research field to guide its research funding decisions. While the Foundation’s early investments focused on gaining a better understanding of the genetic causes of IRDs, its portfolio of projects would come to include some of the most innovative approaches to saving and restoring vision, including gene replacement/augmentation therapies, gene editing, RNA modulation, optogenetics, and gene-based neuroprotection. In recent years, the Foundation invested in resources such as its patient registry, natural history studies, and genetic testing program to bolster clinical development and trials for emerging genetic therapies. Though the number of clinical trials for such therapies has surged over the last decade, the Foundation remains steadfast in its commitment to funding the initiatives that hold the most potential for eradicating the entire spectrum of IRDs.

Description: A conspicuous cell-shape phenotype known as “screwy” was reported to result from mutations at two or three uncharacterized loci in the ciliate Paramecium tetraurelia. Here, we describe a new screwy mutation, Spinning Top, which appeared spontaneously in the cross of an unrelated mutant with reference strain 51. The macronuclear (MAC) genome of the Spinning Top mutant is shown to lack a ~28.5-kb segment containing 18 genes at the end of one chromosome, which appears to result from a collinear deletion in the micronuclear (MIC) genome. We tested several candidate genes from the deleted locus by dsRNA-induced silencing in wild-type cells, and identified a single gene responsible for the phenotype. This gene, named Spade, encodes a 566-aa glutamine-rich protein with a C2HC zinc finger. Its silencing leads to a fast phenotype switch during vegetative growth, but cells recover a wild-type phenotype only 5–6 divisions after silencing is stopped. We analyzed 5 independently-obtained mutant alleles of the Sc1 locus, and concluded that all of them also lack the Spade gene and a number of neighboring genes in the MAC and MIC genomes. Mapping of the MAC deletion breakpoints revealed two different positions among the 5 alleles, both of which differ from the Spinning Top breakpoint. These results suggest that this MIC chromosome region is intrinsically unstable in strain 51.

Description: Extracellular vesicles (EVs) have received increasing attention over the last two decades. Initially, they were considered as just a garbage disposal tool; however, it has progressively become clear that their protein, nucleic acid (namely miRNA and mRNA), and lipid contents have signaling functions. Besides, it has been established that cells release different types of vesicular structures for which characterization is still in its infancy. Many stress conditions, such as hypoxia, senescence, and oncogene activation have been associated with the release of higher levels of EVs. Further, evidence has shown that autophagic–lysosomal pathway abnormalities also affect EV release. In fact, in neurodegenerative diseases characterized by the accumulation of toxic proteins, although it has not become clear to what extent the intracellular storage of undigested materials itself has beneficial/adverse effects, these proteins have also been shown to be released extracellularly via EVs. Lysosomal storage disorders (LSDs) are characterized by accumulation of undigested substrates within the endosomal–lysosomal system, due either to genetic mutations in lysosomal proteins or to treatment with pharmacological agents. Here, we review studies investigating the role of lysosomal and autophagic dysfunction on the release of EVs, with a focus on studies exploring the release of EVs in LSD models of both genetic and pharmacological origin. A better knowledge of EV-releasing pathways activated in lysosomal stress conditions will provide information on the role of EVs in both alleviating intracellular storage of undigested materials and spreading the pathology to the neighboring tissue.

Description: Previous study has demonstrated that the riboflavin treatment promoted the early ripening of the ‘Kyoho’ grape berry. However, the molecular mechanism causing this was unclear. In order to reveal the regulation mechanism of riboflavin treatment on grape berry development and ripening, the different berry developmental stages of the ‘Kyoho’ berry treated with 0.5 mmol/L of riboflavin was sampled for transcriptome profiling. RNA-seq revealed that 1526 and 430 genes were up-regulated and down-regulated, respectively, for the comparisons of the treatment to the control. TCseq analysis showed that the expression patterns of most of the genes were similar between the treatment and the control, except for some genes that were related to the chlorophyll metabolism, photosynthesis–antenna proteins, and photosynthesis, which were revealed by the enrichment analysis of Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG). The differentially expressed genes and weighted gene co-expression network analysis (WGCNA) analysis identified some significantly differentially expressed genes and some hub genes, including up-regulation of the photosynthesis-related ELIP1 and growth and development-related GDSL; and down-regulation of the oxidative stress-related ATHSP22 and berry softening-related XTH32 and GH9B15. The results suggested that the riboflavin treatment resulted in the variations of the expression levels of these genes, and then led to the early ripening of the ‘Kyoho’ berry.

Description: The taxonomical identification merely based on morphology is often difficult for ancient remains. Therefore, universal or specific PCR amplification followed by sequencing and BLAST (basic local alignment search tool) search has become the most frequently used genetic-based method for the species identification of biological samples, including ancient remains. However, it is challenging for these methods to process extremely ancient samples with severe DNA fragmentation and contamination. Here, we applied whole-genome sequencing data from 12 ancient samples with ages ranging from 2.7 to 700 kya to compare different mapping algorithms, and tested different reference databases, mapping similarities and query coverage to explore the best method and mapping parameters that can improve the accuracy of ancient mammal species identification. The selected method and parameters were tested using 152 ancient samples, and 150 of the samples were successfully identified. We further screened the BLAST-based mapping results according to the deamination characteristics of ancient DNA to improve the ability of ancient species identification. Our findings demonstrate a marked improvement to the normal procedures used for ancient species identification, which was achieved through defining the mapping and filtering guidelines to identify true ancient DNA sequences. The guidelines summarized in this study could be valuable in archaeology, paleontology, evolution, and forensic science. For the convenience of the scientific community, we wrote a software script with Perl, called AncSid, which is made available on GitHub.

Description: Taenia pisiformis is a tapeworm causing economic losses in the rabbit breeding industry worldwide. Due to the absence of genomic data, our knowledge on the developmental process of T. pisiformis is still inadequate. In this study, to better characterize differential and specific genes and pathways associated with the parasite developments, a comparative transcriptomic analysis of the larval stage (TpM) and the adult stage (TpA) of T. pisiformis was performed by Illumina RNA sequencing (RNA-seq) technology and de novo analysis. In total, 68,588 unigenes were assembled with an average length of 789 nucleotides (nt) and N50 of 1485 nt. Further, we identified 4093 differentially expressed genes (DEGs) in TpA versus TpM, of which 3186 DEGs were upregulated and 907 were downregulated. Gene Ontology (GO) and Kyoto Encyclopedia of Genes (KEGG) analyses revealed that most DEGs involved in metabolic processes and Wnt signaling pathway were much more active in the TpA stage. Quantitative real-time PCR (qPCR) validated that the expression levels of the selected 10 DEGs were consistent with those in RNA-seq, indicating that the transcriptomic data are reliable. The present study provides comparative transcriptomic data concerning two developmental stages of T. pisiformis, which will be of great value for future functional studies on the regulatory mechanisms behind adult worm pathogenesis and for developing drugs and vaccines against this important parasite.

Description: Background: Genomes are non-randomly organized within the interphase nucleus; and spermatozoa are proposed to have a unique hairpin-loop configuration, which has been hypothesized to be critical for the ordered exodus of the paternal genome following fertilization. Recent studies suggest that the hairpin-loop model of sperm chromatin organization is more segmentally organized. The purpose of this study is to examine the 3D organization and hairpin-loop configurations of chromosomes in human spermatozoa. Methods: Three-color sperm-fluorescence in-situ hybridization was utilized against the centromeres, and chromosome p- and q-arms of eight chromosomes from five normozoospermic donors. Wide-field fluorescence microscopy and 3D modelling established the radial organization and hairpin-loop chromosome configurations in spermatozoa. Results: All chromosomes possessed reproducible non-random radial organization (p 〈 0.05) and formed discrete hairpin-loop configurations. However, chromosomes preferentially formed narrow or wide hairpin-loops. We did not find evidence to support the existence of a centralized chromocenter(s) with centromeres being more peripherally localized than one or both of their respective chromosome arms. Conclusion: This provides further evidence to support a more segmental organization of chromatin in the human sperm nucleus. This may be of significance for fertilization and early embryogenesis as specific genomic regions are likely to be exposed, remodeled, and activated first, following fertilization.

Description: In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

Description: This paper characterizes the retailer’s loss aversion by introducing a loss aversion coefficient and proposes a new loss aversion utility function for the retailer. To hedge against the risk arising from the uncertain market demand, we use the Conditional Value-at-Risk (CVaR) measure to quantify the potential risks and obtain the optimal order quantity for the retailer to maximize the CVaR objective of loss aversion utility. It is shown that that the optimal order quantity for a retailer to maximize the expected loss aversion utility is smaller than expected profit maximizing (EPM) order quantity in the classical newsvendor model, which can help to explain decision bias in the newsvendor model. This study shows that the optimal order quantity with the CVaR objective can decrease in retail price under certain conditions, which has never occurred in the newsvendor literature. With the optimal order quantity under the CVaR objective, it is proved that the retailer’s expected loss aversion utility is decreasing in the confidence level. This confirms the fact that high return means high risk, while low risk comes with low return. Based on the results, several management insights are suggested for the loss-averse newsvendor model.

Description: As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Description: Increasing evidence suggests that overlapping genes are much more common in eukaryotic genomes than previously thought. These different-strand overlapping genes are potential sense–antisense (SAS) pairs, which might have regulatory effects on each other. In the present study, we identified the SAS loci in the equine genome using previously generated stranded, paired-end RNA sequencing data from the equine chorioallantois. We identified a total of 1261 overlapping loci. The ratio of the number of overlapping regions to chromosomal length was numerically higher on chromosome 11 followed by chromosomes 13 and 12. These results show that overlapping transcription is distributed throughout the equine genome, but that distributions differ for each chromosome. Next, we evaluated the expression patterns of SAS pairs during the course of gestation. The sense and antisense genes showed an overall positive correlation between the sense and antisense pairs. We further provide a list of SAS pairs with both positive and negative correlation in their expression patterns throughout gestation. This study characterizes the landscape of sense and antisense gene expression in the placenta for the first time and provides a resource that will enable researchers to elucidate the mechanisms of sense/antisense regulation during pregnancy.

Description: In this work, we consider the general class of difference equations (covered many equations that have been studied by other authors or that have never been studied before), as a means of establishing general theorems, for the asymptotic behavior of its solutions. Namely, we state new necessary and sufficient conditions for local asymptotic stability of these equations. In addition, we study the periodic solution with period two and three. Our results essentially extend and improve the earlier ones.

Description: This study considers an asset-liability optimization model based on constraint robustness with the chance constraint of capital to risk assets ratio in a safety-first framework under the condition that only moment information is known. This paper aims to extend the proposed single-objective capital to risk assets ratio chance constrained optimization model in the literature by considering the multi-objective constraint robustness approach in a modified safety-first framework. To solve the optimization model, we develop a deterministic convex counterpart of the capital to risk assets ratio robust probability constraint. In a consolidated risk measure of variance and safety-first framework, the proposed distributionally-robust capital to risk asset ratio chance-constrained optimization model guarantees banks will meet the capital requirements of Basel III with a likelihood of 95% irrespective of changes in the future market value of assets. Even under the worst-case scenario, i.e., when loans default, our proposed capital to risk asset ratio chance-constrained optimization model meets the minimum total requirements of Basel III. The practical implications of the findings of this study are that the model, when applied, will provide safety against extreme losses while maximizing returns and minimizing risk, which is prudent in this post-financial crisis regime.

Description: In this paper, a mathematical model based on the one-parameter Mittag-Leffler function is proposed to be used for the first time to describe the relation between the unemployment rate and the inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a power function in the model definition. Considering that the ordinary as well as generalised Mittag-Leffler function behave between a purely exponential function and a power function it is natural to implement it in the definition of the model used to describe the relation between the data representing the Phillips curve. For the modelling purposes the data of two different European economies, France and Switzerland, were used and an “out-of-sample” forecast was done to compare the performance of the Mittag-Leffler model to the performance of the power-type and exponential-type model. The results demonstrate that the ability of the Mittag-Leffler function to fit data that manifest signs of stretched exponentials, oscillations or even damped oscillations can be of use when describing economic relations and phenomenons, such as the Phillips curve.

Description: By using the Kolmogorov-Arnold-Moser (KAM) theory, we investigate the stability of two elliptic equilibrium points (zero equilibrium and negative equilibrium) of the difference equation t n + 1 = α t n + β t n 2 − t n − 1 , n = 0 , 1 , 2 , … , where are t − 1 , t 0 , α ∈ R , α ≠ 0 , β 〉 0 . By using the symmetries we find the periodic solutions with some periods. Finally, some numerical examples are given to verify our theoretical results.

Description: The mean-shift method is a convenient mode-seeking method. Using a principle of the sample mean over an analysis window, or kernel, in a data space where samples are distributed with bias toward the densest direction of sample from the kernel center, the mean-shift method is an attempt to seek the densest point of samples, or the sample mode, iteratively. A smaller kernel leads to convergence to a local mode that appears because of statistical fluctuation. A larger kernel leads to estimation of a biased mode affected by other clusters, abnormal values, or outliers if they exist other than in the major cluster. Therefore, optimal selection of the kernel size, which is designated as the bandwidth in many reports of the literature, represents an important problem. As described herein, assuming that the major cluster follows a Gaussian probability density distribution, and, assuming that the outliers do not affect the sample mode of the major cluster, and, by adopting a Gaussian kernel, we propose a new mean-shift by which both the mean vector and covariance matrix of the major cluster are estimated in each iteration. Subsequently, the kernel size and shape are updated adaptively. Numerical experiments indicate that the mean vector, covariance matrix, and the number of samples of the major cluster can be estimated stably. Because the kernel shape can be adjusted not only to an isotropic shape but also to an anisotropic shape according to the sample distribution, the proposed method has higher estimation precision than the general mean-shift.

Description: Childhood acute lymphoblastic leukemia (ALL) peaks around age 2–4, and in utero genetic epigenetic mother-fetus crosstalk might tune ALL onset during childhood life. Folate genes variably interact with vitamin status on ALL risk and prognosis. We investigated DHFR and MTHFR gene variants in 235 ALL children and their mothers to disclose their role in determining ALL onset age and survival. Pyrosequence of DHFR 19bp ins/del (rs70991108; W/D), MTHFR C677T (rs1801133; C〉T), and MTHFR A1298C (rs1801131; A〉C) was assessed in children and in 72% of mothers for dyad-analysis comparison. DHFR DD-children had delayed ALL onset compared to WW-children (7.5 ± 4.8 vs. 5.2 ± 3.7 years; P = 0.002) as well as MTHFR 1298 CC-children compared to AA-children (8.03 ± 4.8 vs. 5.78 ± 4.1 years; P = 0.006), and according to the strong linkage disequilibrium between MTHFR 677 T-allele and 1298C-allele, MTHFR TT-children showed early mean age of onset though not significant. Offspring of MTHFR 677 TT-mothers had earlier ALL onset compared to offspring of 677 CC-mothers (5.4 ± 3.3 vs. 7 ± 5.3 years; P = 0.017). DHFR/MTHFR 677 polymorphism combination influenced onset age by comparing DD/CC vs. WW/TT children (8.1 ± 5.7 vs. 4.7 ± 2.1 years; P = 0.017). Moreover, mother-child genotype combination gave 5.5-years delayed onset age in favor of DD-offspring of 677 CC-mothers vs. WW-offspring of 677 TT-mothers, and it was further confirmed including any D-carrier children and any 677 T-carrier mothers (P = 0.00052). Correction for multiple comparisons maintained statistical significance for DHFR ins/del and MTHFR A1298C polymorphisms. Unexpectedly, among the very-early onset group (〈2.89 years; 25th), DD-genotype inversely clustered in children and mothers (4.8% vs. 23.8% respectively), and accordingly ALL offspring of homozygous DD-mothers had increased risk to have early-onset (adjusted OR (odds ratio) = 3.08; 1.1–8.6; P = 0.03). The opposite effect DHFR promoter variant has in tuning ALL onset-time depending on who is the carrier (i.e., mother or child) might suggest a parent-origin-effect of the D-allele or a two-faced epigenetic role driven by unbalanced folate isoform availability during the in-utero leukemogenesis responsible for the wide postnatal childhood ALL latency.

Description: In this paper, we establish generalized Suzuki-simulation-type contractive mapping and prove fixed point theorems on non-Archimedean quasi modular metric spaces. As an application, we acquire graphic-type results.

Description: In this study we introduce several new Ostrowski-type inequalities for both left and right sided fractional integrals of a function g with respect to another function ψ . Our results generalized the ones presented previously by Farid. Furthermore, two illustrative examples are presented to support our results.

Description: In this case study we successfully teamed the PDQeX DNA purification technology developed by MicroGEM, New Zealand, with the MinION and MinIT mobile sequencing devices developed by Oxford Nanopore Technologies to produce an effective point-of-need field diagnostic system. The PDQeX extracts DNA using a cocktail of thermophilic proteinases and cell wall-degrading enzymes, thermo-responsive extractor cartridges and a temperature control unit. This closed system delivers purified DNA with no cross-contamination. The MinIT is a newly released data processing unit that converts MinION raw signal output into nucleotide base called data locally in real-time, removing the need for high-specification computers and large file transfers from the field. All three devices are battery powered with an exceptionally small footprint that facilitates transport and setup. To evaluate and validate capability of the system for unbiased pathogen identification by real-time sequencing in a farmer’s field setting, we analysed samples collected from cassava plants grown by subsistence farmers in three sub-Sahara African countries (Tanzania, Uganda and Kenya). A range of viral pathogens, all with similar symptoms, greatly reduce yield or destroy cassava crops. Eight hundred (800) million people worldwide depend on cassava for food and yearly income, and viral diseases are a significant constraint to its production. Early pathogen detection at a molecular level has great potential to rescue crops within a single growing season by providing results that inform decisions on disease management, use of appropriate virus-resistant or replacement planting. This case study presented conditions of working in-field with limited or no access to mains power, laboratory infrastructure, Internet connectivity and highly variable ambient temperature. An additional challenge is that, generally, plant material contains inhibitors of downstream molecular processes making effective DNA purification critical. We successfully undertook real-time on-farm genome sequencing of samples collected from cassava plants on three farms, one in each country. Cassava mosaic begomoviruses were detected by sequencing leaf, stem, tuber and insect samples. The entire process, from arrival on farm to diagnosis, including sample collection, processing and provisional sequencing results was complete in under 3 h. The need for accurate, rapid and on-site diagnosis grows as globalized human activity accelerates. This technical breakthrough has applications that are relevant to human and animal health, environmental management and conservation.

Description: The term linkeropathies (LKs) refers to a group of rare heritable connective tissue disorders, characterized by a variable degree of short stature, skeletal dysplasia, joint laxity, cutaneous anomalies, dysmorphism, heart malformation, and developmental delay. The LK genes encode for enzymes that add glycosaminoglycan chains onto proteoglycans via a common tetrasaccharide linker region. Biallelic variants in XYLT1 and XYLT2, encoding xylosyltransferases, are associated with Desbuquois dysplasia type 2 and spondylo-ocular syndrome, respectively. Defects in B4GALT7 and B3GALT6, encoding galactosyltransferases, lead to spondylodysplastic Ehlers-Danlos syndrome (spEDS). Mutations in B3GAT3, encoding a glucuronyltransferase, were described in 25 patients from 12 families with variable phenotypes resembling Larsen, Antley-Bixler, Shprintzen-Goldberg, and Geroderma osteodysplastica syndromes. Herein, we report on a 13-year-old girl with a clinical presentation suggestive of spEDS, according to the 2017 EDS nosology, in whom compound heterozygosity for two B3GAT3 likely pathogenic variants was identified. We review the spectrum of B3GAT3-related disorders and provide a comparison of all LK patients reported up to now, highlighting that LKs are a phenotypic continuum bridging EDS and skeletal disorders, hence offering future nosologic perspectives.

Description: Brazil is an important player when it comes to biofuel and agricultural production. The knowledge of the price relationship between these markets has increasing importance. This paper adopts several tools, namely the Bai–Perron test of breakpoints, the Johansen cointegration test and the vector error correction model exploited by the orthogonal impulse response and the forecast error variance decomposition, for investigating the price transmission among the ethanol and the main Brazil’s agricultural commodities (sugar, cotton, arabica coffee, robusta coffee, live cattle, corn and soybean). The data series cover the period from January 2011 up to December 2018. The results suggest a stronger price transmission from the ethanol commodity to the agricultural commodities, rather than the opposite situation.

Description: We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag–Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.

Description: In this article, we make a detailed study of some mathematical aspects associated with a generalized Lévy process using fractional diffusion equation with Mittag–Leffler kernel in the context of Atangana–Baleanu operator. The Lévy process has several applications in science, with a particular emphasis on statistical physics and biological systems. Using the continuous time random walk, we constructed a fractional diffusion equation that includes two fractional operators, the Riesz operator to Laplacian term and the Atangana–Baleanu in time derivative, i.e., a A B D t α ρ ( x , t ) = K α , μ ∂ x μ ρ ( x , t ) . We present the exact solution to model and discuss how the Mittag–Leffler kernel brings a new point of view to Lévy process. Moreover, we discuss a series of scenarios where the present model can be useful in the description of real systems.

Description: This research paper proposes a derivative-free method for solving systems of nonlinear equations with closed and convex constraints, where the functions under consideration are continuous and monotone. Given an initial iterate, the process first generates a specific direction and then employs a line search strategy along the direction to calculate a new iterate. If the new iterate solves the problem, the process will stop. Otherwise, the projection of the new iterate onto the closed convex set (constraint set) determines the next iterate. In addition, the direction satisfies the sufficient descent condition and the global convergence of the method is established under suitable assumptions. Finally, some numerical experiments were presented to show the performance of the proposed method in solving nonlinear equations and its application in image recovery problems.

Description: The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

Description: Research on longevity and healthy aging promises to increase our lifespan and decrease the burden of degenerative diseases with important social and economic effects. Many aging theories have been proposed, and important aging pathways have been discovered. Model organisms have had a crucial role in this process because of their short lifespan, cheap maintenance, and manipulation possibilities. Yeasts, worms, fruit flies, or mammalian models such as mice, monkeys, and recently, dogs, have helped shed light on aging processes. Genes and molecular mechanisms that were found to be critical in simple eukaryotic cells and species have been confirmed in humans mainly by the functional analysis of mammalian orthologues. Here, we review conserved aging mechanisms discovered in different model systems that are implicated in human longevity as well and that could be the target of anti-aging interventions in human.

Description: In this paper, we introduce the concept of a n 0 -order weighted pseudo Δ n 0 δ -almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q-difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ n 0 δ -almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.

Description: In this paper, based on the very recent work by Nandal et al. (Nandal, A.; Chugh, R.; Postolache, M. Iteration process for fixed point problems and zeros of maximal monotone operators. Symmetry 2019, 11, 655.), we propose a new generalized viscosity implicit rule for finding a common element of the fixed point sets of a finite family of nonexpansive mappings and the sets of zeros of maximal monotone operators. Utilizing the main result, we first propose and investigate a new general system of generalized equilibrium problems, which includes several equilibrium and variational inequality problems as special cases, and then we derive an implicit iterative method to solve constrained multiple-set split convex feasibility problem. We further combine forward-backward splitting method and generalized viscosity implicit rule for solving monotone inclusion problem. Moreover, we apply the main result to solve convex minimization problem.

Description: Symmetrical lupoid onychodystrophy (SLO) is characterized by inflammation of the nail bed and nail sloughing that causes affected dogs considerable pain. Disease etiology remains unclear, although an autoimmune component is suspected. A genome-wide association study on Bearded Collies revealed regions of association on canine chromosomes (CFA) 12 and 17. The large region of association on CFA12 likely consists of two smaller linked regions, both of which are also linked to the dog leukocyte antigen (DLA) class II genes. Dogs homozygous for the alternate allele at the top CFA12 SNP also carried two DLA class II risk haplotypes for SLO, and this locus explained most of the increased risk for disease seen throughout the CFA12 region of association. A stronger peak was seen on CFA17 when analysis was done solely on dogs that carried DLA class II risk haplotypes for SLO. The majority of SLO dogs carried a homozygous alternate genotype on CFA12 and at least one CFA17 risk haplotype. Our findings offer progress toward uncovering the genetic basis of SLO. While the contribution of the CFA17 region remains unclear, both CFA12 and CFA17 regions are significantly associated with SLO disease expression in the Bearded Collie and contain potential candidate genes for this disease.

Description: In 1990 in Griswold, Connecticut, archaeologists excavated a burial found in a “skull and crossbones” orientation. The lid of the 19th century coffin had brass tacks that spelled “JB55”, the initials of the person lying there and age at death. JB55 had evidence of chronic pulmonary infection, perhaps tuberculosis. It is possible that JB55 was deemed a vampire due to his disease, and therefore had to be “killed” by mutilating his corpse. In an attempt to reveal the identity of JB55, DNA testing was performed. Ancestry informative single nucleotide polymorphism (SNP) analysis using the Precision ID Ancestry Panel indicated European ancestry. A full Y-chromosomal short tandem repeat (Y-STR) profile was obtained, belonging to haplogroup R1b. When the Y-STR profile was searched in the publicly accessible FamilyTreeDNA R1b Project website, the two closest matches had the surname “Barber”. A search of historical records led to a death notice mentioning John Barber, whose son Nathan Barber was buried in Griswold in 1826. The description of Nathan Barber closely fits the burial of “NB13,” found near JB55. By applying modern forensic DNA tools to a historical mystery, the identity of JB55 as John Barber, the 19th century Connecticut vampire, has been revealed.

Description: Neurofibromatosis type 1 (NF1) is an autosomal dominant disease with complete penetrance but high variable expressivity. NF1 is caused by loss-of-function mutations in the NF1 gene, a negative regulator of the RAS-MAPK pathway. The NF1 gene has one of the highest mutation rates in human disorders, which may explain the outbreak of independent de novo variants in the same family. Here, we report the co-occurrence of pathogenic variants in the NF1 and SPRED1 genes in six families with NF1 and Legius syndrome, using next-generation sequencing. In five of these families, we observed the co-occurrence of two independent NF1 variants. All NF1 variants were classified as pathogenic, according to the American College of Medical Genetics and Genomics and the Association for Molecular Pathology (ACMG-AMP) guidelines. In the sixth family, one sibling inherited a complete deletion of the NF1 gene from her mother and carried a variant of unknown significance in the SPRED1 gene. This variant was also present in her brother, who was diagnosed with Legius syndrome, a differential diagnosis of NF1. This work illustrates the complexity of molecular diagnosis in a not-so-rare genetic disease.

Description: Recently, we reported a novel therapeutic probiotic-derived protein, p8, which has anti-colorectal cancer (anti-CRC) properties. In vitro experiments using a CRC cell line (DLD-1), anti-proliferation activity (about 20%) did not improve after increasing the dose of recombinant-p8 (r-p8) to 〉10 μM. Here, we show that this was due to the low penetrative efficiency of r-p8 exogenous treatment. Furthermore, we found that r-p8 entered the cytosol through endocytosis, which might be a reason for the low penetration efficiency. Therefore, to improve the therapeutic efficacy of p8, we tried to improve delivery to CRC cells. This resulted in endogenous expression of p8 and increased the anti-proliferative effects by up to 2-fold compared with the exogenous treatment (40 μM). Anti-migration activity also increased markedly. Furthermore, we found that the anti-proliferation activity of p8 was mediated by inhibition of the p53-p21-Cyclin B1/Cdk1 signal pathway, resulting in growth arrest at the G2 phase of the cell cycle. Taken together, these results suggest that p8 is toxic to cancer cells, shows stable expression within cells, and shows strong cancer suppressive activity by inducing cell cycle arrest. Therefore, p8 is a strong candidate for gene therapy if it can be loaded onto cancer-specific viruses.

Description: The automatic identification of rock type in the field would aid geological surveying, education, and automatic mapping. Deep learning is receiving significant research attention for pattern recognition and machine learning. Its application here has effectively identified rock types from images captured in the field. This paper proposes an accurate approach for identifying rock types in the field based on image analysis using deep convolutional neural networks. The proposed approach can identify six common rock types with an overall classification accuracy of 97.96%, thus outperforming other established deep-learning models and a linear model. The results show that the proposed approach based on deep learning represents an improvement in intelligent rock-type identification and solves several difficulties facing the automated identification of rock types in the field.

Description: Circadian rhythms are biological rhythms with a period of approximately 24 h. While canonical circadian clock genes and their regulatory mechanisms appear highly conserved, the evolution of clock gene families is still unclear due to several rounds of whole genome duplication in vertebrates. The spotted gar (Lepisosteus oculatus), as a non-teleost ray-finned fish, represents a fish lineage that diverged before the teleost genome duplication (TGD), providing an outgroup for exploring the evolutionary mechanisms of circadian clocks after whole-genome duplication. In this study, we interrogated the spotted gar draft genome sequences and found that spotted gar contains 26 circadian clock genes from 11 families. Phylogenetic analysis showed that 9 of these 11 spotted gar circadian clock gene families have the same number of genes as humans, while the members of the nfil3 and cry families are different between spotted gar and humans. Using phylogenetic and syntenic analyses, we found that nfil3-1 is conserved in vertebrates, while nfil3-2 and nfil3-3 are maintained in spotted gar, teleost fish, amphibians, and reptiles, but not in mammals. Following the two-round vertebrate genome duplication (VGD), spotted gar retained cry1a, cry1b, and cry2, and cry3 is retained in spotted gar, teleost fish, turtles, and birds, but not in mammals. We hypothesize that duplication of core clock genes, such as (nfil3 and cry), likely facilitated diversification of circadian regulatory mechanisms in teleost fish. We also found that the transcription factor binding element (Ahr::Arnt) is retained only in one of the per1 or per2 duplicated paralogs derived from the TGD in the teleost fish, implicating possible subfuctionalization cases. Together, these findings help decipher the repertoires of the spotted gar’s circadian system and shed light on how the vertebrate circadian clock systems have evolved.

Description: In this paper, we establish a new q-integral identity, the result is then used to derive two q-integral inequalities of Simpson-type involving strongly preinvex functions. Some special cases of the obtained results are also considered, it is shown that several new and previously known results can be derived via generalized strongly preinvex functions and quantum integrals.

Description: The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.

Description: We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.

Description: Cryptomeria fortunei, also known as the Chinese cedar, is an important timber species in southern China. The primary component of its woody tissues is lignin, mainly present in secondary cell walls. Therefore, continuous lignin synthesis is crucial for wood formation. In this study, we aimed to discover key genes involved in lignin synthesis expressed in the vascular cambium of C. fortunei. Through transcriptome sequencing, we detected expression of two genes, 4CL and CCoAOMT, known to be homologous to enzymes involved in the lignin synthesis pathway. We studied the function of these genes through bioinformatics analysis, cloning, vascular cambium expression analysis, and transgenic cross-species functional validation studies. Our results show that Cf4CL and CfCCoAOMT do indeed function in the pathway of lignin synthesis and likely perform this function in C. fortunei. They are prime candidates for future (gene-editing) studies aimed at optimizing C. fortunei wood production.

Description: The epithelium represents the first and most extensive line of defence against pathogens, toxins and pollutant agents in humans. In general, pathogens have developed strategies to overcome this barrier and use it as an entrance to the organism. Entamoeba histolytica, Naegleria fowleri and Acanthamoeba spp. are amoebae mainly responsible for intestinal dysentery, meningoencephalitis and keratitis, respectively. These amoebae cause significant morbidity and mortality rates. Thus, the identification, characterization and validation of molecules participating in host-parasite interactions can provide attractive targets to timely intervene disease progress. In this work, we present a compendium of the parasite adhesins, lectins, proteases, hydrolases, kinases, and others, that participate in key pathogenic events. Special focus is made for the analysis of assorted molecules and mechanisms involved in the interaction of the parasites with epithelial surface receptors, changes in epithelial junctional markers, implications on the barrier function, among others. This review allows the assessment of initial host-pathogen interaction, to correlate it to the potential of parasite invasion.

Description: The Van der Pol oscillator is investigated by the parameter control method. This method only needs to control one parameter of the Van der Pol oscillator by a simple periodic function; then, the Van der Pol oscillator can behave chaotically from the stable limit cycle. Based on the new Van der Pol oscillator with variable parameter (VdPVP), some dynamical characteristics are discussed by numerical simulations, such as the Lyapunov exponents and bifurcation diagrams. The numerical results show that there exists a positive Lyapunov exponent in the VdPVP. Therefore, an encryption algorithm is designed by the pseudo-random sequences generated from the VdPVP. This simple algorithm consists of chaos scrambling and chaos XOR (exclusive-or) operation, and the statistical analyses show that it has good security and encryption effectiveness. Finally, the feasibility and validity are verified by simulation experiments of image encryption.

Description: Retinol binding protein 4 (RBP4), mainly secreted by the liver and adipocytes, is a transporter of vitamin A. RBP4 has been shown to be involved in several pathophysiological processes, such as obesity, insulin resistance, and cardiovascular risk. Reports have indicated the high expression levels of RBP4 in cystic follicles. However, the role of RBP4 in mammalian follicular granulosa cells (GCs) remains largely unknown. To illustrate the molecular pathways associated with the effects of RBP4 on GCs, we used high-throughput sequencing to detect differential gene expression in GCs overexpressing RBP4. A total of 113 differentially expressed genes (DEGs) were identified in RBP4-overexpressing GCs, and they included 71 upregulated and 42 downregulated genes. The differential expressions of the top 10 DEGs were further confirmed by real-time quantitative polymerase chain reaction. Pathway analysis indicated that the DEGs are mostly involved in oxidative phosphorylation, Parkinson’s disease, non-alcoholic fatty liver disease, Huntington’s disease, cardiac muscle contraction, Alzheimer’s disease, fatty acid biosynthesis, AMP-activated protein kinase signaling pathway, and insulin signaling pathway. Genes in these pathways should be useful for future studies on GCs. Altogether, the results of our study establish a framework for understanding the potential functions of RBP4 in porcine GCs.

Description: Radial basis function-based quasi-interpolation performs efficiently in high-dimensional approximation and its applications, which can attain the approximant and its derivatives directly without solving any large-scale linear system. In this paper, the bivariate multi-quadrics (MQ) quasi-interpolation is used to simulate two-dimensional (2-D) Burgers’ equation. Specifically, the spatial derivatives are approximated by using the quasi-interpolation, and the time derivatives are approximated by forward finite difference method. One advantage of the proposed scheme is its simplicity and easy implementation. More importantly, the proposed scheme opens the gate to meshless adaptive moving knots methods for the high-dimensional partial differential equations (PDEs) with shock or soliton waves. The scheme is also applicable to other non-linear high-dimensional PDEs. Two numerical examples of Burgers’ equation (shock wave equation) and one example of the Sine–Gordon equation (soliton wave equation) are presented to verify the high accuracy and efficiency of this method.

Description: Context-aware video recommender systems (CAVRS) seek to improve recommendation performance by incorporating contextual features along with the conventional user-item ratings used by video recommender systems. In addition, the selection of influential and relevant contexts has a significant effect on the performance of CAVRS. However, it is not guaranteed that, under the same contextual scenario, all the items are evaluated by users for providing dense contextual ratings. This problem cause contextual sparsity in CAVRS because the influence of each contextual factor in traditional CAVRS assumes the weights of contexts homogeneously for each of the recommendations. Hence, the selection of influencing contexts with minimal conflicts is identified as a potential research challenge. This study aims at resolving the contextual sparsity problem to leverage user interactions at varying contexts with an item in CAVRS. This problem may be investigated by considering a formal approximation of contextual attributes. For the purpose of improving the accuracy of recommendation process, we have proposed a novel contextual information selection process using Soft-Rough Sets. The proposed model will select a minimal set of influencing contexts using a weights assign process by Soft-Rough sets. Moreover, the proposed algorithm has been extensively evaluated using “LDOS-CoMoDa” dataset, and the outcome signifies the accuracy of our approach in handling contextual sparsity by exploiting relevant contextual factors. The proposed model outperforms existing solutions by identifying relevant contexts efficiently based on certainty, strength, and relevancy for effective recommendations.

Description: Potassium (K) is one of the most important mineral nutrients for wheat. In this study, the effects of low K (LK) treatments and the quantitative trait loci (QTLs) for K, calcium (Ca), and magnesium (Mg) use efficiency traits, both at the seedling and maturity stages of wheat, were investigated. The set of “Tainong 18 × Linmai 6” recombinant inbred lines (RILs) were used to identify the QTLs under different K treatments using hydroponic culture and field trials. The majority of K concentrations and content-related traits at seedling and maturity stages decreased with reduced K supply, but the K use efficiency-related traits increased. In contrast, with reduced K supply, the contents of Ca and Mg increased, while the Ca and Mg use efficiency decreased. A total of 217 QTLs for seedling traits and 89 QTLs for adult traits were detected. Four relatively high-frequency QTLs (RHF-QTLs) and 18 QTL clusters (colocation of QTLs for more than two traits) were detected. Eight clusters were detected for K-, Ca-, and Mg-related traits simultaneously. This means that these traits might be controlled by the same QTL. In addition, we highlight that 4B might be an important chromosome regulating the nutrition of K, Ca, and Mg in wheat. The 4B chromosome and four hot QTL clusters, which located 45 QTLs, might be important potential targets for further investigation.

Description: Identifying associations between lncRNAs and diseases can help understand disease-related lncRNAs and facilitate disease diagnosis and treatment. The dual-network integrated logistic matrix factorization (DNILMF) model has been used for drug–target interaction prediction, and good results have been achieved. We firstly applied DNILMF to lncRNA–disease association prediction (DNILMF-LDA). We combined different similarity kernel matrices of lncRNAs and diseases by using nonlinear fusion to extract the most important information in fused matrices. Then, lncRNA–disease association networks and similarity networks were built simultaneously. Finally, the Gaussian process mutual information (GP-MI) algorithm of Bayesian optimization was adopted to optimize the model parameters. The 10-fold cross-validation result showed that the area under receiving operating characteristic (ROC) curve (AUC) value of DNILMF-LDA was 0.9202, and the area under precision-recall (PR) curve (AUPR) was 0.5610. Compared with LRLSLDA, SIMCLDA, BiwalkLDA, and TPGLDA, the AUC value of our method increased by 38.81%, 13.07%, 8.35%, and 6.75%, respectively. The AUPR value of our method increased by 52.66%, 40.05%, 37.01%, and 44.25%. These results indicate that DNILMF-LDA is an effective method for predicting the associations between lncRNAs and diseases.

Description: If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) − f ( a ) = f ′ ( η ) ( η − a ) , then the point η is called a Flett’s mean value point of f in [ a , b ] . The concept of Flett’s mean value points can be generalized to the 2-dimensional Flett’s mean value points as follows: For the different points r ^ and s ^ of R × R , let L be the line segment joining r ^ and s ^ . If a partially differentiable function f : R × R → R and an intermediate point ω ^ ∈ L satisfy f ( ω ^ ) − f ( r ^ ) = ω ^ − r ^ , f ′ ( ω ^ ) , then the point ω ^ is called a 2-dimensional Flett’s mean value point of f in L. In this paper, we will prove the Hyers–Ulam stability of 2-dimensional Flett’s mean value points.

Description: The goal of this research is to extend and investigate an improved approach for calculating the weighted Moore–Penrose (WMP) inverses of singular or rectangular matrices. The scheme is constructed based on a hyperpower method of order ten. It is shown that the improved scheme converges with this rate using only six matrix products per cycle. Several tests are conducted to reveal the applicability and efficiency of the discussed method, in contrast with its well-known competitors.

Description: We consider a differential game of fisheries in a fan-like control structure of the type “supervisor—several agents”. The dynamics of the controlled system is described by a non-linear differential equation model which is identified on the Azov Sea data. An averaging by two spatial coordinates is conducted. Different information structures of the game are generated by the control methods of compulsion (supervisor restricts the feasible strategies of agents) and impulsion (she exerts an impact to their payoff functionals). Both Stackerlberg and inverse Stackelberg games are considered. For the numerical investigation we use a discretization of the initial model and the method of qualitatively representative scenarios in simulation modeling.

Description: We reported changes in the co-regulated mRNA expression in iron walnut (Juglans sigillata) in response to soil pH treatments and identified mRNAs specific to acidic soil conditions. Phenotypic and physiological analyses revealed that iron walnut growth was greater for the pH 4–5 and pH 5–6 treatments than for the pH 3–4 and pH 6–7 treatments. A total of 2768 differentially expressed genes were detected and categorized into 12 clusters by Short Time-series Expression Miner (STEM). The 994 low-expression genes in cluster III and 255 high-expression genes in cluster X were classified as acid-responsive genes on the basis of the relationships between phenotype, physiology, and STEM clustering, and the two gene clusters were analyzed by a maximum likelihood (ML) evolutionary tree with the greatest log likelihood values. No prominent sub-clusters occurred in cluster III, but three occurred in cluster X. The Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis indicated that acid-responsive genes were related primarily to arginine biosynthesis and the arginine/proline metabolism pathway, implying that polyamine accumulation may enhance iron walnut acid stress tolerance. Overall, our results revealed 1249 potentially acid-responsive genes in iron walnut, indicating that its response to acid stress involves different pathways and activated genes.

Description: Prostate cancer is the fifth leading cause of male cancer death worldwide. Although docetaxel chemotherapy has been used for more than fifteen years to treat metastatic castration resistant prostate cancer, the high inter-individual variability of treatment efficacy and toxicity is still not well understood. Since prostate cancer has a high heritability, inherited biomarkers of the genomic signature may be appropriate tools to guide treatment. In this review, we provide an extensive overview and discuss the current state of the art of pharmacogenomic biomarkers modulating docetaxel treatment of prostate cancer. This includes (1) research studies with a focus on germline genomic biomarkers, (2) clinical trials including a range of genetic signatures, and (3) their implementation in treatment guidelines. Based on this work, we suggest that one of the most promising approaches to improve clinical predictive capacity of pharmacogenomic biomarkers in docetaxel treatment of prostate cancer is the use of compound, multigene pharmacogenomic panels defined by specific clinical outcome measures. In conclusion, we discuss the challenges of integrating prostate cancer pharmacogenomic biomarkers into the clinic and the strategies that can be employed to allow a more comprehensive, evidence-based approach to facilitate their clinical integration. Expanding the integration of pharmacogenetic markers in prostate cancer treatment procedures will enhance precision medicine and ultimately improve patient outcomes.

Description: This paper proposes a model of the dynamics of credit contagion through non-performing loans on financial networks. Credit risk contagion is modeled in the context of the classical SIS (Susceptibles-Infected-Susceptibles) epidemic processes on networks but with a fundamental novelty. In fact, we assume the presence of two different classes of infected agents, and then we differentiate the dynamics of assets subject to idiosyncratic risk from those affected by systemic risk by adopting a SIIS (Susceptible-Infected1-Infected2-Susceptible) model. In the recent literature in this field, the effect of systemic credit risk on the performance of the financial network is a hot topic. We perform numerical simulations intended to explore the roles played by two different network structures on the long-term behavior of assets affected by systemic risk in order to analyze the effect of the topology of the underlying network structure on the spreading of systemic risk on the structure. Random graphs, i.e., the Erdös–Rényi model, are considered “benchmark” network structures while core-periphery structures are often indicated in the literature as idealized structures, although they are able to capture interesting, specific features of real-world financial networks. Moreover, as a matter of comparison, we also perform numerical experiments on small-world networks.

Description: Amaryllidaceae alkaloids (AAs) have multiple biological effects, which are of interest to the pharmaceutical industry. To unleash the potential of Amaryllidaceae plants as pharmaceutical crops and as sources of AAs, a thorough understanding of the AA biosynthetic pathway is needed. However, only few enzymes in the pathway are known. Here, we report the transcriptome of AA-producing paperwhites (Narcissus papyraceus Ker Gawl). We present a list of 21 genes putatively encoding enzymes involved in AA biosynthesis. Next, a cDNA library was created from 24 different samples of different parts at various developmental stages of N. papyraceus. The expression of AA biosynthetic genes was analyzed in each sample using RT-qPCR. In addition, the alkaloid content of each sample was analyzed by HPLC. Leaves and flowers were found to have the highest abundance of heterocyclic compounds, whereas the bulb, the lowest. Lycorine was also the predominant AA. The gene expression results were compared with the heterocyclic compound profiles for each sample. In some samples, a positive correlation was observed between the gene expression levels and the amount of compounds accumulated. However, due to a probable transport of enzymes and alkaloids in the plant, a negative correlation was also observed, particularly at stage 2.

Description: Plant growth responds to various environmental and developmental cues via signaling cascades that influence gene expression at the level of transcription and pre-mRNA splicing. Alternative splicing of pre-mRNA increases the coding potential of the genome from multiexon genes and regulates gene expression through multiple mechanisms. Serine/arginine-rich (SR) proteins, a conserved family of splicing factors, are the key players of alternative splicing and regulate pre-mRNA splicing under stress conditions. The rice (Oryza sativa) genome encodes 22 SR proteins categorized into six subfamilies. Three of the subfamilies are plant-specific with no mammalian orthologues, and the functions of these SR proteins are not well known. The clustered regularly interspaced short palindromic repeats (CRISPR)/CRISPR-associated protein 9 (Cas9) system is a genome engineering tool that cleaves the target DNA at specific locations directed by a guide RNA (gRNA). Recent advances in CRISPR/Cas9-mediated plant genome engineering make it possible to generate single and multiple functional knockout mutants in diverse plant species. In this study, we targeted each rice SR locus and produced single knockouts. To overcome the functional redundancy within each subfamily of SR genes, we utilized a polycistronic tRNA-gRNA multiplex targeting system and targeted all loci of each subfamily. Sanger sequencing results indicated that most of the targeted loci had knockout mutations. This study provides useful resource materials for understanding the molecular role of SR proteins in plant development and biotic and abiotic stress responses.

Description: Whole-genome sequences of four EMS (ethyl methanesulfonate)-induced eggplant mutants were analyzed to identify genome-wide mutations. In total, 173.01 GB of paired-end reads were obtained for four EMS-induced mutants and (WT) wild type and 1,076,010 SNPs (single nucleotide polymorphisms) and 183,421 indels were identified. The most common mutation type was C/G to T/A transitions followed by A/T to G/C transitions. The mean densities were one SNP per 1.3 to 2.6 Mb. The effect of mutations on gene function was annotated and only 7.2% were determined to be deleterious. KEGG (Kyoto Encyclopedia of Genes and Genomes) pathway analysis showed 10 and 11 genes, which were nonsynonymous mutation or frameshift deletion in 48-5 and L6-5 involved in the anthocyanin biosynthesis or flavone and flavonol biosynthesis. QRT-PCR results showed that only the Sme2.5_06210.1_g00004.1, which was annotated as UFGT (Flavonoid galactosidase transferase), expression significantly decreased in the L6-5 mutant compared with the WT. Also, the Sme2.5_06210.1_g00004.1 expression was lower in the colorless eggplant compared with colorful eggplant in the natural eggplant cultivar. These results suggest that Sme2.5_06210.1_g00004.1 may play a key role in eggplant anthocyanin synthesis.

Description: Oilseed rape (Brassica napus) is the second largest oilseed crop worldwide. As an architecture component of B. napus, thickness of pod canopy (TPC) plays an important role in yield formation, especially under high-density cultivation conditions. However, the mechanisms underlying the regulation of TPC remain unclear. RNA and microRNA (miRNA) profiling of two groups of B. napus lines with significantly different TPC at the bolting with a tiny bud stage revealed differential expressions of numerous genes involved in nitrogen-related pathways. Expression of several nitrogen-related response genes, including ASP5, ASP2, ASN3, ATCYSC1, PAL2, APT2, CRTISO, and COX15, was dramatically changed in the thick TPC lines compared to those in the thin TPC lines. Differentially expressed miRNAs also included many involved in nitrogen-related pathways. Expression of most target genes was negatively associated with corresponding miRNAs, such as miR159, miR6029, and miR827. In addition, 12 (including miR319, miR845, and miR158) differentially expressed miRNAs between two plant tissues sampled (stem apex and flower bud) were identified, implying that they might have roles in determining overall plant architecture. These results suggest that nitrogen signaling may play a pivotal role in regulating TPC in B. napus.

Description: In this study, we analyzed the effects of breed, diet energy source, and their interaction on adipose tissue transcriptome in growing Iberian and Duroc pigs. The study comprised 29 Iberian and 19 Duroc males, which were kept under identical management conditions except the nutritional treatment. Two isoenergetic diets were used with 6% high oleic sunflower oil (HO) or carbohydrates (CH) as energy sources. All animals were slaughtered after 47 days of treatment at an average live weight of 51.2 kg. Twelve animals from each breed (six fed each diet) were employed for ham subcutaneous adipose tissue RNA-Seq analysis. The data analysis was performed using two different bioinformatic pipelines. We detected 837 and 1456 differentially expressed genes (DEGs) according to breed, depending on the pipeline. Due to the strong effect of breed on transcriptome, the effect of the diet was separately evaluated in the two breeds. We identified 207 and 57 DEGs depending on diet in Iberian and Duroc pigs, respectively. A joint analysis of both effects allowed the detection of some breed–diet interactions on transcriptome, which were inferred from RNA-Seq and quantitative PCR data. The functional analysis showed the enrichment of functions related to growth and tissue development, inflammatory response, immune cell trafficking, and carbohydrate and lipid metabolism, and allowed the identification of potential regulators. The results indicate different effects of diet on adipose tissue gene expression between breeds, affecting relevant biological pathways.