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  • Springer  (77,797)
  • Wiley  (15,981)
  • 1980-1984  (59,712)
  • 1965-1969  (28,969)
  • 1925-1929  (5,097)
  • 1984  (59,712)
  • 1965  (28,969)
  • 1925  (5,097)
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  • 1980-1984  (59,712)
  • 1965-1969  (28,969)
  • 1925-1929  (5,097)
Year
  • 1
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    Unknown
    Die Geschichte der Antarktisforschung (1984)
    Springer
    In:  EPIC3Naturwissenschaften, Springer, 71(12), pp. 599-608, ISSN: 0028-1042
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    Publication Date: 2014-06-04
    Repository Name: EPIC Alfred Wegener Institut
    Type: Article , notRev
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  • 2
    Electronic Resource
    Electronic Resource
    Comment on biomass diversity in ecology (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 967-969 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462083
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  • 3
    Electronic Resource
    Electronic Resource
    Physik der Selbstorganization und Evolution (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 971-972 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462084
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  • 4
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    Announcements (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 973-974 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462085
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  • 5
    Electronic Resource
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    Random selection—A simple model based on linear birth and death processes (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 11-17 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Linear birth and death processes are used to derive simple expressions for sequential extinction times and gene fixation probabilities in asexual populations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463720
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  • 6
    Electronic Resource
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    On the measurement of shapes (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 1-10 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We are here concerned with the functionf which assigns to each pointP of an object the numberf(P) which is the shortest distance fromP to the border. This function appears in various guises in diverse biological studies. The functionf(P) is itself a measure of shape—or more precisely, an infinite set of measures, one for each point (and hence, in view of its geometric definition, usually in a form inconvenient for use). Thus in this paper we sought a reasonable representative of this infinite set of measures, namely themean of the numbersf(P) asP ranges over all points of the entity. Computability studies are developed for various classes of shapes. For example, (1) the mean for a lamina bounded by a polygon circumscribable about a circle of radiusr isr/3; (2) the mean for a domain bounded by a polyhedron circumscribable about a sphere of radiusr isr/4. The transition from pointwise to piecewisef(P), especially in the non-convex case, requires working with inequalities.
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    URL: http://dx.doi.org/10.1007/BF02463719
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  • 7
    Electronic Resource
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    Traveling bands of chemotactic bacteria in the context of population growth (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 19-40 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model for traveling bands of motile and chemotactic bacteria in the presence of cell growth and death is examined. It is found that asymptotic traveling wave solutions exist in the absence of chemotaxis, due to the balance of growth, death and random motility. Thus random motility confers the ecological advantage of population propagation through migration into nutrient-rich regions. The presence of chemotaxis amplifies this advantage by moving more cells into higher nutrient concentration regions, resulting in larger and faster bands. Therefore there seem to be two types of traveling bands that can be attained by chemotactic bacteria in the presence of growth and death: (1) these growth/death/motility bands; and (2) pure chemotactic ‘Keller-Segel'-type bands. Comparison to experimental observations by Chapman in 1973 indicate that the latter seem to be formed. The relationship between these two types of solution is at present uncertain. The growth/death/motility bands may have relevance on longer time or distance scales characteristic of microbial ecological systems.
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    URL: http://dx.doi.org/10.1007/BF02463721
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  • 8
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    A mathematical model of the pathological functional state of the oxygen transport system (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 115-125 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Based on the principle of minimum power, a mathematical model of the pathological functional state of the oxygen transport system is presented. The model is used to determine the optimal functional parameters of the oxygen transport system in hyperthyroidism, anemia and hypertension. Theoretical results are compared with clinical data.
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    URL: http://dx.doi.org/10.1007/BF02463725
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  • 9
    Electronic Resource
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    Stability in an insect-pathogen model incorporating age-dependent immunity and seasonal host reproduction (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 139-153 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A modified SIRS model is developed as a framework for the study of epizootiological dynamics in an insect-pathogen system. Linearized stability analysis reveals that the system with one immune and one susceptible host class can exhibit stable, periodic or unstable behavior depending on model parameters. In general, high pathogenicity, short pathogen propagule lifespan and high host reproductive rate are stabilizing influences. Pathogen transmissibility and propagule production/host do not influence local stability. The effect of seasonal host reproduction is studied because most insect hosts are seasonal in temperate climates. The basic stability dependence on model parameters holds except as modified by the length of the reproduction interval. The results of this study are compared with the recent work of Anderson and May.
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    URL: http://dx.doi.org/10.1007/BF02463727
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  • 10
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    Random predator-prey interactions in a varying environment: Extinction or survival (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 175-184 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The random predator-prey type interactions of the population species in a random varying environment have been investigated. The Fokker-Planck equation for the transition probability, corresponding to the stochastic differential equations established from Lotka-Volterra equations by the introduction of randomness and variability, has been integrated in the form of a path integral. The transition probabilities for extinction or survival of one or several species have been approximately evaluated and investigated.
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    URL: http://dx.doi.org/10.1007/BF02463729
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  • 11
    Electronic Resource
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    Coexistence of two microbial populations competing for a renewable resource in a non-predator-prey system (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 155-174 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract If two microbial populations compete for a single resource in a homogeneous environment with time invariant inputs they cannot coexist indefinitely if the resource competed for is not renewed by biological activity within the system. Mathematical studies have shown that in a predator-prey system, where the resource (prey) is self-renewing, the two competitors (predators) can coexist in a limit cycle. This suggests that if the resource competed for is renewed by biological activity within the system coexistence can occur in any microbial system provided that it exhibits the same features as, but without being, a predator-prey one. A food chain involving commensalism, competition and amensalism is presented here. Two subcases are considered. It is only when maintenance effects are taken into account that coexistence, in limit cycles, can occur for this system. Limit cycle solutions for the system are demonstrated with the help of computer simulations. Some necessary conditions for coexistence are presented, as are some speculations regarding the possible physical explanations of the results.
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    URL: http://dx.doi.org/10.1007/BF02463728
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  • 12
    Electronic Resource
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    Adaptive regulation of wall shear stress optimizing vascular tree function (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 127-137 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm2), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.
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    URL: http://dx.doi.org/10.1007/BF02463726
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  • 13
    Electronic Resource
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    Population dynamics with age- and time-dependent birth and death rates (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 185-185 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02463730
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  • 14
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    A unifying concept for the amino acid code (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 187-203 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The structure of the genetic code is related to a Gray code, which is a plausible theoretical model for an amino acid code. The proposed model implies that the most important factor in shaping the code was the effects of mistakes in translation, not effects of mutations. Another possible implication is that the preservation of stiffness and flexibility at appropriate places in a protein chain is as important in protein structure as the appropriate placement of hydrophilic (external) and hydrophobic (internal) residues. Other results are a simple conceptualization of the relationships among the 20 amino acids and their relations to their codons. The detailed relationships are summarized in the following ‘similarity alphabet’: ala, thr, gly, pro, ser; asp, asn, glu, gln, lys; his, arg, trp, tyr, phe; leu, met, ile, val, cys; (ATGPS DNEQK HRWYF LMIVC in the one-letter code). This alphabet falls into four groups of amino acids: small, external, large, internal. The approximate relation of the groups to their codons is expressed as: the first base of a codon controls size—a purine means a small amino acid, a pyrimidine means large; the middle base controls cloisterednes—purine means external, pyrimidine means internal. These relationships express the minimum change principle upon which the code appears to be founded.
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    URL: http://dx.doi.org/10.1007/BF02460068
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  • 15
    Electronic Resource
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    Concentration-dependent diffusion coefficient and dissipative structures (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 269-282 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theoretical study of the Brusselator model with non-uniform distribution of component A and a concentration-dependent diffusion coefficient has been performed. Numerical simulation reveals that a variable diffusion coefficient alters the bifurcation pattern and the stability properties of the steady-state as well as periodic solutions. A simple approximate method, based on one-point collocation, has been proposed to analyze the bifurcation phenomena for the case of fixed boundary conditions and low system size.
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    URL: http://dx.doi.org/10.1007/BF02460074
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  • 16
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    Cuttrees in the topological analysis of branching patterns (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 283-294 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees.
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    URL: http://dx.doi.org/10.1007/BF02460075
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  • 17
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    Capillary operators (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 247-268 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL p[0,∞], (1〈-p〈-∞). A discussion is included of theL p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O K (relating extravascular concentration to intravascular) and K a, k (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O K ‖ p 〈-1, ‖K a, k ‖ p 〈-1), isotone, linear operators onL p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL p) is derived, whereP n (a) is the Poisson probabilitye −a a n /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖Ok‖=‖Ka,k‖p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.
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  • 18
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    Long-term memory modules (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 295-326 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract One particular kind of structure offers possible explanations, for long-term memory, efficient consolidation of stored information from the environment, clustering of data strings and multimodal functioning. It is a possible model for pieces of neural structure and its use offers a uniform method for both studying and constructing an extensive class of mechanisms.
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    URL: http://dx.doi.org/10.1007/BF02460076
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  • 19
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    Properties of levenshtein metrics on sequences (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 327-332 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Levenshtein dissimilarity measures are used to compare sequences in application areas including coding theory, computer science and macromolecular biology. In general, they measure sequence dissimilarity by the length of a shortest weighted sequence of insertions, deletions and substitutions required, to transform one sequence into another. Those Levenshtein dissimilarity measures based on insertions and deletions are analyzed by a model involving valuations on a partially ordered set. The model reveals structural relationships among poset, valuation and dissimilarity measure. As a consequence, certain Levenshtein dissimilarity measures are shown to be metrics characterized by betweenness properties and computable in terms of well-known measures of sequence similarity.
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    URL: http://dx.doi.org/10.1007/BF02460077
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  • 20
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    Announcement (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 337-337 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    URL: http://dx.doi.org/10.1007/BF02460079
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  • 21
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    Commensalism of methane-producing and motile aerobic bacteria in certain freshwater wetlands (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 333-336 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is pointed out that the methane flux measured experimentally for certain ponds and swamps is quantitatively consistent with a commensal dependence of Methanobacteria on O2-chemotactic motile aerobic bacteria. The Methano species is thereby shielded from oxygen and provided with carbon dioxide for the anaerobic production of methane.
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    URL: http://dx.doi.org/10.1007/BF02460078
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  • 22
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    Persistence in stochastic food web models (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 357-370 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A sufficient condition is given for stochastic boundedness persistence of a top predator in generalized Lotka-Volterra-type stochastic food web models in arbitrary bounded regions of state space. The main result indicates that persistence in the corresponding deterministic system is preserved in the stochastic system if the intensities of the random fluctuations are not too large.
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    URL: http://dx.doi.org/10.1007/BF02462011
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  • 23
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    Evolution of cannibalism in an age-structured population (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 371-377 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract One of Bobisud's models for the evolution of cannibalism is reanalyzed by applying the method of finding evolutionarily stable strategies (or ESS's). It is demonstrated that ‘no cannibalism’ never will be an ESS if the initial rate of cannibalism is too large. It is further demonstrated that individual selection may even result in the evolution of cannibalism during food abundance. Some empirical case studies are briefly discussed in relation to this model.
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    URL: http://dx.doi.org/10.1007/BF02462012
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  • 24
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    An algorithm to equiprobably generate all directed trees withk labeled terminal nodes and unlabeled interior nodes (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 379-387 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A computer algorithm is presented which equiprobably generates any member of the set of all directed trees withk labeled terminal nodes and unlabeled interior nodes. The algorithm requires roughlyk 2 /2 storage locations. The one-time initialization requiresO(k 2 ) time, while generating each tree requiresO(k) time.
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  • 25
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    Pattern recognition in several sequences: Consensus and alignment (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 515-527 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The comparison of several sequences is central to many problems of molecular biology. Finding consensus patterns that define genetic control regions or that determine structural or functional themes are examples of these problems. Previously proposed methods, such as dynamic programming, are not adequate for solving problems of realistic size. This paper gives a new and practical solution for finding unknown patterns that occur imperfectly above a preset frequency. Algorithms for finding the patterns are given as well as estimates of statistical significance.
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    Pattern recognition in genetic sequences by mismatch density (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 501-514 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new development is introduced here in the use of dynamic programming in finding pattern similarities in genetic sequences, as was first done by Needleman and Wunsch (1969). A condition of pattern similarity is defined and an algorithm is given which scans any set of similarities and screens out those which fail to meet the condition. When the set to be scanned contains every pair of segments, one from each of two given sequences of lengthsm andn (i.e. every possible location for a pattern similarity), then it completes the scan in a number of computational steps proportional tom·n, leaving those pairs of segments which satisfy the similarity condition. The algorithm is based on the concept of match density, as suggested by Goad and Kanehisa (1982).
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    URL: http://dx.doi.org/10.1007/BF02459499
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    Distinguished words in data sequences: Analysis and applications to neural coding and other fields (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 529-543 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper concerns sequences of letters in which certain “distinguished” words are of interest. Such sequences arise as data in numerous fields including genetics and neuroscience. A probability distribution is given for the number of occurrences of a chosen word in a randomized sequence of letters. Such words are considered “favored” if they occur more than expected at random. Favored words have been discovered in nerve impulse trains and may reflect a neural coding scheme.
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    URL: http://dx.doi.org/10.1007/BF02459501
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    Searching the protein sequence database (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 545-552 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract As the volume of protein sequence data grows, rapid methods for searching the protein sequence database become of primary importance. Rigorous comparison of sequences is obtained with the well-known dynamic programming algorithms. However, these algorithms are not rapid enough to use for routinely searching the entire database. In this paper we discuss some methods that can be used for rapid searches.
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    URL: http://dx.doi.org/10.1007/BF02459502
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    Algorithms for computing evolutionary similarity measures with length independent gap penalties (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 553-566 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We give algorithms for computing the extent of similarity between two or three sequences of letters. The similarity measures we consider include a penalty for inserting gaps within the sequence in order to enhance similarity. The magnitude of the penalty for gaps is assumed to be independent of their size in order to accommodate certain biological applications. Our algorithm for three sequence comparisons, which is based on solving a system of recursive equations, improves upon the efficiency of existing methods. Although the system of recursive equations utilized by the algorithm is quite complicated as it stands, it has none the less been simplified by appeal to combinatorial considerations.
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  • 30
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    Line geometries for sequence comparisons (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 567-577 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Well-known dynamic programming algorithms exist for comparing two finite sequences inO(N 2) time and storage, whereN is the common sequence length. Extensions to the comparison ofM finite sequences requireO((2N) M) time and storage, making such algorithms difficult even forM=3. A simple generalization of the sequences makes it possible to obtain some results about the geometry of sequence alignments. These ideas suggest heuristic approaches to problems of comparing several sequences. IfM sequences are known to be related by a binary tree, they can be aligned inO(MN 2) time andO(N 2+NM) storage.
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    The uniqueness of protein sequences. Uniqueness diagrams for the Dayhoff file—1984 (1984)
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    Bulletin of mathematical biology 46 (1984), S. 661-672 
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    Notes: Abstract Protein sequences of the Dayhoff databank of 1984 have been analyzed to evaluate the occurrences of the 400 dipeptides and 8000 tripeptides. Expected values and standard deviations for the di- and tripeptides were determined by Monte Carlo and binomial approximation. A condensed format containing this information, labeled a uniqueness diagram, is presented and made available in the form of a microfiche.
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    The characteristics method applied to the study of muscle dynamics (1984)
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    Bulletin of mathematical biology 46 (1984), S. 827-844 
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    Notes: Abstract In two-state sliding filament models of muscle contraction a partial differential equation must be solved to find the cross-bridge distribution functionn(x, t). In this paper the analytical form of this function is obtained by integration along the characteristic line and special cases are presented in which the explicit expression forn(x, t) can be completely determined. These analytical solutions provide a direct mathematical connection between the microscopic contraction parameters contained in the kinetic theories and macroscopic muscle dynamics and are thus used to investigate what parameters influence the transient contractile tension in typical experimental conditions. The results of this investigation are consistent with relevant aspects of muscle physiology.
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    Beyond the binary case in random nets (1984)
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    Bulletin of mathematical biology 46 (1984), S. 845-857 
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    Notes: Abstract Experiments on random binary, ternary, etc. (P=2, 3,…, 10) switching nets are reported. Behavioral cycle lengths are examined as functions of output variety,P, input connectance,K, and net size,N. Overall, output variety appears an influential, well-behaved net property. Strong, but well-behaved interactions appear among net variables. In high connectance nets, median cycle length grows approx. asP N/2. Other factors constant, one-connected nets show the shortest cycles, and connectance effects appear to converge asymptotically aroundN. Data for cycle length as a function of net size suggest a concavity not compatible with the Kauffman “square root law” (Kauffman, 1969). Evidence of a positive relationship between cycle length and run-in length is found in two-input nets; weaker evidence is obtained that in higher connectance nets this relationship becomes negative in sign. The “modular complexity” ofP〉2 nets is examined briefly.
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    Influence of landscape on the spread of an infection (1984)
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    Bulletin of mathematical biology 46 (1984), S. 869-877 
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    Notes: Abstract The influence of topographical situation on the spread of infection is studied. The investigation is based on a multigroup model. The population under consideration is thought to be divided into subpopulations living in regions that are separated from each other by natural barriers (mountains). Infection is carried from one region to another by migrating infectives. Migration is possible only along the river system so that the structure of the epidemiological network is that of a symmetric tree. The results allow comparison of the velocity of propagation of the epidemic for different geographical situations and allow quantification of the “channel-effect”, according to which mountainous regions are channels rather than barriers to the spread of an epidemic.
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    Compartmental systems and generating functions (1965)
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    Bulletin of mathematical biology 27 (1965), S. 49-63 
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    Notes: Abstract Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation. From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model. From the graph it is possible to calculate the transfer generating function between any two connected nodes, the mean permanence time in a given node, the mean transit time between two nodes, and their precursor-successor order.
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    On the competitive exclusion principle (1965)
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    Bulletin of mathematical biology 27 (1965), S. 85-89 
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    Notes: Abstract The Competitive Exclusion Principle, formulated by V. Volterra (Memorie del R. Comitato Talassografico Italiano,131, 1–142, 1927) for a number of species competing for a common ecological niche, is extended to a number of species competing for many ecological niches.
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    Periodic and aperiodic phases of circulatory mixing (1965)
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    Bulletin of mathematical biology 27 (1965), S. 65-70 
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    Notes: Abstract A modification is presented of an earlier theory of the mixing of dye following injection into the circulation. Approximate theoretical relations are given for the concentration of dye in the right heart and in the aorta following right atrial injection. It is shown that when the probability distribution of transit times around the circulation has a prolonged tail, mixing waves are now inscribed about a quasi-exponential relation. Later in time the relation levels off to a uniform asymptotic concentration corresponding to an equilibrium volume of dilution.
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    Cooperative specific adsorption of ions at charged sites in an electric field (1965)
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    Bulletin of mathematical biology 27 (1965), S. 91-104 
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    Notes: Abstract The adsorption of two cations at the anionic sites of a polymer (e.g., such as a protein) in an electric fields is discussed, taking into account cooperative interaction of the cations mediated through the backbone of the polymer. The calculation of the grand partition function explicitly considers the vacant negative sites of the polymer. As in the case without cooperative interaction, the problem reduces to the determination of the largest eigenvalue of asymmetric matrices. The weights of the different neighbor configurations are determined. Approximate formulae for the grand partition function and for those weights are derived. The formal analogy of these cooperative phenomena and those occurring in quantum (bio)chemistry is pointed out exemplifying an earlier suggestion about the basis of quantum biology.
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    A proposed mechanism for the sol-gel transformation (1965)
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    Bulletin of mathematical biology 27 (1965), S. 105-112 
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    Notes: Abstract The transformation from gel to sol in cell cytoplasm is treated as the transition from a lattice of macromolecules linked by Ca++ ions to a random distribution of the macromolecules. The transition is a cooperative process, whose probability is expressed in terms of the theory of runs. The process is related to cell metabolism by the assumption that available Ca++ concentration is regulated by metabolically produced endogenous chelating agents.
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    Kinetic criteria of solid state mechanisms in biology (1965)
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    Bulletin of mathematical biology 27 (1965), S. 113-118 
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    Notes: Abstract Kinetic criteria for solid state physical mechanisms of electron and ion transport in biological systems are summarized, and the mechanisms are discussed. A reaction which is rate-limited by electron or ion transport across a particle or membrane in accord with Ohm's law will show first order kinetics, with an hyperbolic relationship between rate constant and the sum of substrate plus product. Larger initial substrate concentrations produce smaller rate constants, thus giving the appearance of substrate inhibition. Examples are cytochrome oxidase and peroxidase, and pyruvate carboxylase. Ohmic transport mechanisms may be caused by electron conduction or superconduction through protein, by electron conduction through water, or by conduction of ions through membranes. A reaction which is rate-limited by charge transport across an activation energy barrier at an interface in accord with a logarithmic voltage-current law will show reaction kinetics conforming to the Elovich equation, and will have the appearance of a pair of simultaneous first order processes. Examples include decay of photogenerated free radicals in eye melanin particles and in photosynthetic particles of bacteria, and sodium and potassium ion transport across cell surfaces. The logarithmic voltage-current law may be regarded as an empirical relationship describing behavior of interfaces, justified by extensive experimental data on many types of interfaces, or it may be derived theoretically for individual cases from statistical mechanical and/or solid state physical considerations.
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    Analysis of some effects of aortic smooth muscle onin vivo aortic pressure curves (1965)
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    Bulletin of mathematical biology 27 (1965), S. 119-130 
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    Notes: Abstract When aortic pressure curves were predicted previously on the basis of a newly developed model of visco-elastic properties of the aorta, it was necessary to use published viscoelastic constants. These were usually obtained from longitudinal strips of blood vessels long removed from the animal, and therefore probably containing deteriorated smooth muscle. The predicted curves had the same form as actual tracings, substantiating the analysis somewhat, but the pressure levels were low. These low levels, if due to inadequate visco-elastic constants, could be attributed to the use of longitudinal rather than circumferential segments as well as to the use of segments with deteriorated muscle. The present analysis uses data collected by the author testing circumferential viscoelastic properties of fourteen different aortic regions in a way suggested by the author's model of an aortic wall. Moreover, the constants were measured on segments containing muscle relaxed by EDTA solutions and on similar segments containing muscle contracted by neosynephrine. These visco-elastic constants were used in the author's nonlinear differential equation of motion of the aortic wallin vivo to predictin vivo pressure curves. The predicted curves were low in any given aortic region if relaxed constants were used, but at normal levels with contracted constants. In fact, pressure curves predicted using constants obtained from aortic segments containing contracted muscle resembled actual tracings in form and pressure levels. Even the observed variations in the form of the systolic pressure curve down the aorta were predicted by this analysis.
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    Biological similarity relative to allometric quantities (1965)
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    Bulletin of mathematical biology 27 (1965), S. 131-133 
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    Notes: Abstract It is an empirical finding that an allometric quantity with dimensional exponents α, β and γ relative to mass, length, and time, respectively, has a value for its allometric exponentb satisfying the relation $$\tfrac{1}{3}(3\alpha + \beta + {\gamma \mathord{\left/ {\vphantom {\gamma 2}} \right. \kern-\nulldelimiterspace} 2}) \leqslant b \leqslant \tfrac{1}{3}(3\alpha + \beta + \gamma ).$$ A theoretical derivation is given of this double inequality using only the fact of constant density and the plausible assumption that metabolic rate is a dominant allometric quantity.
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    The entropy of a continuous distribution (1965)
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    Bulletin of mathematical biology 27 (1965), S. 135-143 
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    Notes: Abstract C. Shannon's definition (Bell System Technical Journal,27, 379–423, 1948) of the entropy of a continuous distribution is dimensionally incorrect and does not have the same significance as the corresponding definition in the discrete case. A new definition is proposed: this modified entropy is more like the entropy of a discrete distribution in one way, in another more like Shannon's “transmission rate.” The ideas are illustrated by reference to Wright's study of the hereditary influence on the coat pattern of the guinea pig.
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    Theorems on random evolution (1965)
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    Bulletin of mathematical biology 27 (1965), S. 145-150 
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    Notes: Abstract In the following paper, a possible mode of evolution is described which differs from the traditional modes in not being selective in the Darwinian sense.
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    Information theory and genetics (1965)
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    Bulletin of mathematical biology 27 (1965), S. 177-181 
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    Notes: Abstract A description of the kinds of systems susceptible to information theoretical analysis is given. By means of an example, certain common fallacies in the application of communication theory to biology are illustrated. The entropy-information analogy is discussed. *** DIRECT SUPPORT *** A01E2109 00008
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    A note on equivalent mathematical models (1965)
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    Bulletin of mathematical biology 27 (1965), S. 161-175 
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    Notes: Abstract A mathematical model of a process contains parameters supposedly characterizing the system which manifests the process. If the parameters are statistically distributed in a population of such systems, the process manifested by the entire population will in general be described by a different mathematical model. Thus a choice is always at hand between two or more mathematical models, depending on which parameters (if any) are assumed to be distributed and, if so, how. Examples of such alternative interpretations are given for mathematical models of some behavioral processes.
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    Superimposed random coding of stimulus-response connections (1965)
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    Bulletin of mathematical biology 27 (1965), S. 191-202 
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    Notes: Abstract The problem of economically linking a large number of stimuli with a large number of potential responses is considered to resemble a problem of efficient retrieval of documents (the responses) on the basis of their characterization by descriptors (the stimuli to which the responses are appropriate). In this retrieval problem, a method whereby the codes for descriptors are random positions in a coding field, and whereby codes for all applicable descriptors are superimposed in the same field, seems to be the simplest way of avoiding serious difficulties of retrieval. After a review of this method, the possibility is considered that very simple neural mechanisms could embody the essential features of the method. The aim of the discussion is to learn whether very simple structures and patterns of reinforcement would be adequate to carry out useful information processing in the brain, and to show some conceivable functions of simple neural networks which the experimenter might keep in mind. The discussion also shows how the structure of a simple “perceptron”-like network is suggested by the requirements of a retrieval task.
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    Studies on the electroretinogram. II. Model of an a-wave regenerator mechanism (1965)
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    Bulletin of mathematical biology 27 (1965), S. 223-233 
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    Notes: Abstract A model is proposed to relate the regeneration of the ERGa-wave after partial light adaptation to the level of the light adaptation. The model assumes that thea-wave amplitude is a function of some reactive substance associated with ana-wave generator. The maximuma-wave amplitude occurs when the eye is fully dark adapted, and thea-wave generator initiator concentration is at a maximum. Thea-wave generator initiator concentration can be decreased by interacting with a product of the rhodopsin-light energy reaction, and increased by removal of this inhibitor. The removal of the inhibitor depends upon the isomerization of the all-trans-retinene to the 11-cis form. An excess of inhibitory material overa-wave generator initiator would cause a delay in the appearance of thea-wave until the excess inhibitory material is removed. This delay is a linear function of the logarithm of the adapting energy. The agreement of this model with the experimental ERG data is very good.
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    On the quantitative relationship between survival rate of larvae and their food supply (1965)
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    Bulletin of mathematical biology 27 (1965), S. 215-222 
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    Notes: Abstract The survival rate of fishes in their earlier stages of development and the influencing factors present one of the most fundamental problems of fish population dynamics. After I. Hjort's (Cons. L.'explor. Ner.,20, 3–228, 1914) work, there have been many investigators in this field and there is no doubt about the very important role of ova and larvae mortality in the fate of a given fish generation. Less clear are the ideas concerning factors determining the high mortality of fishes in their earlier stages of development; especially the factor of food supply of larvae during the period of transition to exogenic nutrition. The value of this factor has been estimated differently from different points of view. For example, R. J. H. Beverton and S. J. Holt (On the Dynamics of Exploited Fish Population, 1957) have given to the food supply factor its deserved importance. On the other hand, T. V. Dekhnik (Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960;Ibid.,14, 222–243, 1961) has proved in her investigations that at least for pelagic larvae of Black Sea fishes there is an excessive amount of food, and that therefore food cannot play an important role in larva survival. Not wanting to stop to review the literature of the problem (see Dekhnik,Trudy Sevastopolskoi Biologicheskoi Stantsii,13, 216–244, 1960), we will only remark that the problem as a whole needs further investigation. Not only new data are needed, but also methods for following up analysis have to be worked out.
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    Learning fluctuations and hysteresis phenomena (1965)
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    Bulletin of mathematical biology 27 (1965), S. 253-259 
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    Notes: Abstract The investigation described here is anexperimental one which brings to light some new facts and confirms others already reported. They partly concern the hysteresis phenomena handled by N. Rashevsky (Mathematical Biophysics, 1960) and partly provide a point of departure for future biophysical research to be undertaken by biomathematicians.
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    An analysis of aortic pressure curves taking into account visco-elastic properties of the aorta and variations in peripheral resistance (1965)
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    Bulletin of mathematical biology 27 (1965), S. 27-52 
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    Notes: Abstract The aortic pressure curve necessarily reveals the mechanical properties of the aorta and peripheral resistance as well as of the dynamics of blood flow. The present study uses a reasonable model of visco-elastic properties of the aorta, a reasonable form for variations in peripheral resistance and blood flow to predict an aortic pressure tracing. Numerical values of constants measured experimentally were available in the published literature. These were used in the nonlinear differential equations of motion of the system under analysis. The equations yielded to piece-wise solution, giving the aortic circumference and the aortic pressure as functions of time. The form of both curves resembles clinical tracings, but numerical values of circumference were higher and of pressure lower thanin vivo. The discrepancies between predicted and clinical curves may reveal certain inadequacies in published measurements on visco-elastic constants. These measurements have been made on longitudinal rather than circumferential strips often containing dead rather than living muscle. The discrepancies, therefore, indicate specific gaps in our knowledge of aortic behaviorin vitro. The suggested model of the system aided in the design of experiments which could supply data necessary to substantiate or to revise the model.
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    The venous circulation (1965)
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    Bulletin of mathematical biology 27 (1965), S. 373-377 
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    Notes: Abstract Some aspects of the circulation through the veins remain unexplained. The pressure gradient which ordinarily exists across a large vein, for example, is much greater than that necessary to maintain the same flow through a rigid tube of identical diameter (Brecher, 1956; Starling and Evans, 1962). During inspiration, blood flow through the thoracic portion of the inferior vena cava increases markedly, while that through the distal abdominal portion does not change. Furthermore, an active source of pressure drop in the chest is necessary to maintain venous flow. For the open chest the pressure drop occurs mainly during ventricular contraction, while in the closed chest it is produced chiefly by inspiration. The present study indicates that the high distensibility of the veins accounts in significant degree for the behavior characteristic of the venous circulation.
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    A logical model for growth and differentiation in multi-celled organisms (1965)
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    Bulletin of mathematical biology 27 (1965), S. 379-387 
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    Notes: Abstract This paper is an attempt to provide a logical model for the process of growth and differentiation in a multi-cellular organism. More specifically it is intended to show how genetic information relating to macroscopic structure and coded in the form of a logical tree could be progressively embodied in the organism as it develops by repeated division from a single cell. The aim is to establish biological analogies rather than mathematical interest, and reproduction, adaption, and the coordinating action of hormones are discussed within the general logical framework.
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    A mathematical model of the urethra (1965)
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    Bulletin of mathematical biology 27 (1965), S. 407-415 
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    Notes: Abstract Models having the form of surfaces of revolution may be used to represent the urethra under pre-voiding pressure. From such models are derived formulas for calculating muscle tension from the shape of a urethragram.
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    Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors (1965)
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    Bulletin of mathematical biology 27 (1965), S. 389-406 
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    Notes: Abstract The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1965)
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    Bulletin of mathematical biology 27 (1965), S. 431-434 
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    Notes: Abstract The sensitivity and “specificity” of measurements for the determination of transferates are enhanced by the use of an additional radiotracer, serving to trace the unlabelled substance. This method presents advantages mostly in systems outside their steady state but only exeptionally in steady state systems.
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    Analysis of tracer experiments V: Integral equations of perturbation-tracer analysis (1965)
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    Bulletin of mathematical biology 27 (1965), S. 417-429 
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    Notes: Abstract An integral equation approach to perturbation-tracer analysis in steady-state multicompartment systems is formulated. The theory is developed for δ function perturbation and tracer inputs and extended to the case of continuous small perturbations and continuous tracer inputs. It is shown that the first order dependence of the initial entry function can then be expressed by means of an integral equation: $$B_1 (t) = \int_{t_2 = - \infty }^\infty {\int_{t_1 = - \infty }^\infty {P(t_1 )T(t_2 )B_1 (t - t_2 ,t_1 - t_2 )dt_1 dt_2 } } $$ whereB 1(t) is the first order initial entry function for the tracer material,P(t1) the perturbation function.T(t 2) is the tracer input function, andB 1(t−t 2 ,t 1 −t 2 ) is a continuous function of two variables characterizing the first order perturbation-tracer response of the system.
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    Correlation “waves” in brain-like structures (1965)
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    Bulletin of mathematical biology 27 (1965), S. 435-447 
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    Notes: Abstract A correspondence is established between a tangible model of brain structure (and function) and a system of observer-observed interactions. The observed quantities are “stimuli” in the form of signal amplitude distributions in a mass of neuron-like units; the observer is a set of neurons (not circumscribed in a local region) in which a distributed parameter mirrors the stimulus history of the set, i.e., represents a “memory”. Utilizing the theory of the Perceptron, a contemporary brain model, it is demonstrated that large systems composed of many observer-observed interactions exhibit quantum mechanical behavior on a “macroscopic” scale. This behavior entails wave-like phenomena and the need of applying the superposition mechanics to system information content calculations.
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    Mathematical models for cellular systems. The von foerster equation. Part II (1965)
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    Bulletin of mathematical biology 27 (1965), S. 449-471 
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    Notes: Abstract This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly.
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    Mathematical models of nonuniform intrapulmonary gas distribution (1965)
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    Bulletin of mathematical biology 27 (1965), S. 473-476 
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    Notes: Summary Mathematical models of nonuniform gas distribution in the lungs which assume a two-chambered lung to be ventilated through a third chamber, i.e. a common dead space, have led to diverging results. A breath-by-breath analysis of such a system results in a two-exponential solution whereas a continuous ventilation analysis gives a three-exponential solution. This is caused by the different assumptions made in the two models about the composition of dead space gas. In the breath-by-breath analysis one assumes that theN 2 content of the dead space is zero at the end of inspiration. In the continuous ventilation model one assumes that theN 2 content in the dead space is unknown at all instants during the breathing cycle. No physical significance should be attached to any chamber in this type of analysis. The continuous ventilation model provides a more general solution than the cyclical ventilation model, because the former treats the common dead spaces as an independent unknown.
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    On the electrocardiographic field equation (1965)
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    Bulletin of mathematical biology 27 (1965), S. 493-495 
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    The representation of organisms in terms of predicates (1965)
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    Bulletin of mathematical biology 27 (1965), S. 477-491 
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    Notes: Abstract The different approaches to relational biology developed by N. Rashevsky and R. Rosen consider essentially binary relations between various components of biological functions of the organism. Actually an organism is represented by a set of differentn-ary relations. The present paper is an attempt to outline a possible approach to this more realistic situation. Inasmuch asn-ary relation is ann-place predicate, it is attempted to describe the basic known properties of an organism in terms ofn-place predicates, in which the variables represent the different “components” of the organism. Some possible forms of such predicates are discussed and some general properties of systems of such predicates are studied. It is shown that if the organism is described by predicates of the type discussed here, statements can be derived about the conditions “of reestablishability” of different components. Conclusions similar to those obtained previously by R. Rosen are reached now on a very different basis. A description of the process of cell differentiation in multicellular organisms in terms of predicates studied here is briefly outlined. A comparison of similarities and differences between the approach and Rosen’s description of organisms in terms of the theory of categories is made.
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    Temporal organization in cells (1965)
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    Bulletin of mathematical biology 27 (1965), S. 497-500 
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    29th National Meeting of the Operations Research Society of America (1965)
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    Bulletin of mathematical biology 27 (1965), S. 503-503 
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    Harold A. White March 4, 1933–July 27, 1965 Obituary notice (1965)
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    Bulletin of mathematical biology 27 (1965), S. 501-502 
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    High-speed recursive digital filter realization (1984)
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    Circuits, systems and signal processing 3 (1984), S. 267-294 
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    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Pipeline techniques have been successfully applied to speeding up processing in both general- and special-purpose digital computers. Application of these techniques to nonrecursive (FIR) filters has been suggested and is quite straightforward. Application to recursive (IIR) filters has not previously been shown. In this paper, the technique for applying pipeline techniques to recursive filters is shown and the advantages and disadvantages of the technique are discussed. Using these techniques, recursive digital filters operating at hitherto impossibly high rates can be designed.
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    A Hybrid system for the reconstruction of a smooth function from its samples (1984)
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    Circuits, systems and signal processing 3 (1984), S. 295-314 
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    Notes: Abstract The long-standing problem of reconstructing a function from its samples is considered again. Assuming a sequence of oversampled values, a set of appropriate idealized reconstruction filters can be defined, which do not suffer from instability or slow convergence. The realization — a cascade of a nonrecursive digital filter, D/A-converter, and a fixed/analog smoothing filter — demands the design of the digital filter for the increase of the sampling rate. The design of this nonrecursive filter is the purpose of this paper. Approximations in the frequency as well as in the time domain are presented.
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    Power system transient stability analysis: Formulation as nearly Hamiltonian systems (1984)
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    Circuits, systems and signal processing 3 (1984), S. 105-122 
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    Notes: Abstract In this paper we formulate power systems as nonlinear nearly Hamiltonian systems. Using the invariance principle for ordinary differential equations, necessary and sufficient conditions for asymptotic stability are established and a new method of estimating the domain of attraction of the stable equilibrium point is developed. The present results constitute a novel approach to stability analysis and involve the following three steps: a. Given a system with dissipation, the stability of its equilibrium is ascertained by determining the stability of the associated conservative system. b. Attractivity of the stable equilibrium of the entire system (with dissipation) is determined from the system topology. c. An estimate of the domain of attraction of the asymptotically stable equilibrium is obtained by making use of results obtained in (a) and (b). The stability criterion developed in this paper sheds new light on the mechanism of instability in power systems and it provides analytical verification to the concept of the potential-energy boundary surface (PEBS). The PEBS is a hypersurface which makes up a part of the boundary of the domain of attraction of the stable equilibrium in a power system. The existence and properties of the PEBS have thus far been deduced primarily via simulations and heuristic methods.
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    On line-free and flicker-free television reproduction (1984)
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    Circuits, systems and signal processing 3 (1984), S. 161-176 
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    Notes: Abstract In conventional television systems, picture scanning in vertical and temporal directions is usually very defective with regard to the sampling theorem. In this paper some deficiencies such as aliasing, line-structure distortion, line flickering, and large-area flickering are investigated with regard to their dependence on the inter-lacedpicture-scanning process. The three-dimensional reconstruction filtering of the sampled picture is especially analyzed with respect of the viewer's perception. Furthermore, it will be shown that in connection with a new concept of picture scanning published earlier [1], [2], a flat-field reproduction without any 25/30-Hz flicker can be achieved by vertical filtering only. This is true even though the final reproduction by the monitor is performed with interlace. The vertical filtering can then be optimized in the sense of maximum picture sharpness and resolution with negligible ringing as well. Practical results are given in this paper.
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    Design of recursive digital filters for the selection or rejection of a particular velocity in seismic signals (1984)
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    Circuits, systems and signal processing 3 (1984), S. 177-191 
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    Notes: Abstract In this paper a new type of “velocity-selecting/rejecting filter” which passes or stops a particular event in a seismic signal is proposed. The velocity-selecting filter is based on a time-space band-pass filter with sharp passband for a particular direction, and similarly, the velocity-rejecting filter is based on a time-space band-stop filter. A technique for designing such filters, in terms of an infinite-impulse-response (IIR) filter, is presented, in which a rotated version of separable filter is used. Finally, numerical examples are included to illustrate the design theory.
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    Memoryless state feedback control for nonlinear systems (1984)
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    Circuits, systems and signal processing 3 (1984), S. 347-359 
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    Generalized Schur-Coleski factorization with applications to image processing (1984)
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    Circuits, systems and signal processing 3 (1984), S. 315-325 
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    Notes: Abstract A special type of factorization for operators defined on partially ordered Hilbert resolution spaces is considered. The main result includes, as a particular case, the classical Schur-Coleski triangular factorization. Connections with stochastic optimization and image-processing problems are established.
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    Iteration and functional expansions (1984)
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    Circuits, systems and signal processing 3 (1984), S. 409-417 
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    Notes: Abstract In a recent paper on nonlocal expansions necessary and sufficient conditions are given under whichf −1 has a generalized power series expansion, whenf is an invertible locally Lipschitz map between certain general subsets of a complex Banach space. Here we establish the validity of a conceptually interesting algorithm for obtaining the expansion. Basically, we show that a certain contraction mapping iteration generates iteratesℐ 1,ℐ 2,... such that eachℐ k yields all of the terms of the generalized power series expansion off −1 up to order (k + 1), assuming merely that the expansion off −1 exists. An earlier different result along related lines is mentioned.
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    Generating nonorthogonal bases for signal representation (1984)
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    Circuits, systems and signal processing 3 (1984), S. 447-475 
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    Notes: Abstract The representation of functions in a basis function expansionz(t)= ∑k=1/∞=,a k〉 x k (t) is straightforward when the basis functionsx k (t) are orthogonal. There has been very little work up to this time in determining how to use nonorthogonal bases in signal representation. On the other hand, applications in data compression and signal synthesis often require using specific tailor-made bases. Presented here is a method for constructing very general nonorthogonal bases. Orthogonality has often been used to show that a basis spans the set of functions of interest and to calculate the coefficients of the representation. In this paper, both of these fundamental aspects are addressed for nonorthogonal bases. A new basis {y k (t)} is obtained by performing a linear transformation on a known existing basis {x k (t)}. This transformation is constructed such that the coefficients of signal representation on the new basis are readily found. Then, a useful and sufficient condition is placed upon the new basis such that representations converge. The fundamental methods are applied to the standard examples of signal representation. The complex sinusoids, the Rademacher functions, the orthogonal polynomials, and the decaying exponentials are used as the original basis {x k (t)} from which a new basis {y k (t)} is generated. Two examples are given to illustrate general applications: one in signal synthesis and one in signal analysis.
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    Steady-state diffusion through a finite pore into an infinite reservoir: An exact solution (1965)
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    Bulletin of mathematical biology 27 (1965), S. 57-65 
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    Notes: Abstract An outline is given of an analysis that leads to an exact solution for the problem of steady-state diffusion through a finite thick pore into an infinite region surrounding the mouth of the pore. From this exact formula a simple expression for the flux is derived. This expression approximates the flux with a relative error of less than 3.42 per cent independently of the ratiol/a wherel is the length of the pore anda its radius. If desired, more accurate expressions for the flux can be obtained from the exact solution.
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    The single file model for the diffusion of ions through a membrane (1965)
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    Bulletin of mathematical biology 27 (1965), S. 79-86 
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    Notes: Abstract The model proposed by A. L. Hodgkin and R. D. Keynes (Jour. of Physiol.,128, 61–88, 1955) for the diffusion of potassium through the nerve membrane is extended to cover an arbitrary number of species of ions with charges not necessarily the same. One type of interference is also investigated.
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    On the theory of the cardiovascular system (1965)
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    Bulletin of mathematical biology 27 (1965), S. 71-83 
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    Notes: Abstract Most theoretical studies of the circulation have focussed on the transmission line properties of arteries. Only a small number of papers have dealt with the circulation as a closed (lumped) system with two pumps connected by the lesser and greater circulation (Beneken, inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Defares,et al., inCirculatory Analog Computers, No. Holland Publ. Co., Amsterdam, 1963; Grodins,Quart. Rev. of Biology,34, 93, 1959; Guyton,Cardiac Output and its Regulation, Saunders Publ. Co., New York, 1963). F. W. Cope's recent studies in this journal (Bull. Math. Biophysics,22, 19, 1960;23, 337, 1961;24, 137, 1962) deal with essentially the same questions, although here the circuit is not “closed”. We have attempted to extend the analysis of the areflex (closed) circulation. The complete study is reported elsewhere (Defares,et al., Acta Physiol, et Parmac. Neerl., 1963).
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    Equations of heat distribution within the body (1965)
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    Bulletin of mathematical biology 27 (1965), S. 67-78 
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    Notes: Abstract A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.
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    Determination of equilibrium constants and maximum binding capacities in complexIn vitro systems: I. The mammillary system (1965)
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    Bulletin of mathematical biology 27 (1965), S. 87-98 
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    Notes: Abstract It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.
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    Southern Regional Graduate Summer Session in Statistics at Oklahoma State University (1965)
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    Bulletin of mathematical biology 27 (1965), S. 111-111 
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    Important announcement to our contributors and readers (1965)
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    Bulletin of mathematical biology 27 (1965), S. 113-113 
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    A theory of ion transport across cell surfaces by a process analogous to electron transport across liquid-solid interfaces (1965)
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    Bulletin of mathematical biology 27 (1965), S. 99-109 
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    Notes: Abstract A kinetic theory of ion transport across cell surfaces has been developed in a form analogous to the kinetic theory of electron transport across solid-liquid interfaces of biological particles. The ionic theory is based on the observation that, at least in one instance, the voltage-current behavior for ion conduction across a cell surface is describable by the Tafel equation, in analogy to the conduction of electrons across solid-liquid interfaces. The theory predicts that the kinetics of ion transport across cell surfaces should conform to the Elovich rate equation, which is shown to be true for various experimental data.
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    Letter to the editor (1965)
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    Bulletin of mathematical biology 27 (1965), S. 114-114 
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    Mathematical development of a physical model of some visco-elastic properties of the aorta (1965)
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    Bulletin of mathematical biology 27 (1965), S. 115-115 
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    A biographical sketch of Nicolas Rashevsky (1965)
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    Bulletin of mathematical biology 27 (1965), S. 3-4 
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    A letter read to professor Rashevsky at a dinner in his honor December 11, 1964 (1965)
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    Bulletin of mathematical biology 27 (1965), S. 5-10 
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    Some comments on re-estalishability (1965)
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    Bulletin of mathematical biology 27 (1965), S. 11-14 
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    Notes: Abstract The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an (ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958.
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    Model studies of blood-glucose regulation (1965)
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    Bulletin of mathematical biology 27 (1965), S. 21-37 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A simplified, linearized model of the system regulating blood-glucose concentrations is reviewed. This model, which predicts a damped sine wave response to an oral glucose load, lumps the large number of kinetic parameters into a much smaller number which can, at least in part, characterize the human glucose regulatory system. The predictions based on the model are compared with measurements of blood-glucose and blood-insulin concentrations during the oral glucose-tolerance test. Various other conditions are simulated and their implications are discussed in terms of the mathematical model used.
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    URL: http://dx.doi.org/10.1007/BF02477259
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    On compartmentalization (1965)
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    Bulletin of mathematical biology 27 (1965), S. 15-19 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The notion of a compartment is discussed in terms of the Markovian process. From the stochastic matrix (the elements of which are state transition probabilities between different states of a particle of a chemical element), one may find a (generally) nonstochastic matrix; the elements of this second matrix are probabilities that, starting from some initial state, the particle will reach another seleced state (W. Feller, 1962,An Introduction to Probability Theory). Forming equivalence classes of states it can be shown that the equivalence classes based on an equivalence relation, which holds for the elements of the above-mentioned nonstochastic matrix, are essential for the notion of a compartment. From this procedure it is also obvious that a rigorous definition of a physically realizable compartment is impossible. Some conclusions on the practical use of compartmental analysis are drawn.
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    On the use of the Von Foerster equation for the solution and generalization of a problem studied by S. A. Tyler and R. Baserga (1965)
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    Bulletin of mathematical biology 27 (1965), S. 39-48 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a population of cells labeled with a single injection of tritiated thymidine at timet=0, it is assumed that a constant fraction, 1−z, of the cells which are potentially able to divide fail to do so, and that the cells which do divide all have identical generation time,D. Death and emigration of cells are neglected. In mitosis, the partitioning of label among the two daughter cells is supposed to follow the binomial probability law. Using the formalism developed by H. Von Foerster the fraction of labeled cells in the total population is computed as a function oft, the time after injection of label. Ift is an integral multiple ofD the results coincide with those of S. A. Tyler and R. Baserga.
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    Development of structure in a society with a dominance relation when new members are added successively (1965)
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    Bulletin of mathematical biology 27 (1965), S. 151-160 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A society with a dominance relation is considered to be built up by starting with a small society and adding new members in succession. As each member is added he engages in contests with each of the older members to determine the dominance relation between them. The probability that the older member dominates is considered to depend on the size of the society and linearly on the older members score. A recurrence relation for the hierarchy index is derived. The approach of the society to a hierarchical structure is considered for various special cases of this probability. Reasonable assumptions concerning this dominance probability are shown to lead to structures close to the hierarchy. If the new member dominates all the older ones below a certain rank, and is dominated by all those above this rank, then the hierarchy will persist if it is the initial structure, or the structure will tend to hierarchy as the size increases, if it is not the initial structure.
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    URL: http://dx.doi.org/10.1007/BF02477272
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    Theory of hemoglobin facilitated oxygen transport (1965)
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    Bulletin of mathematical biology 27 (1965), S. 183-190 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transport of oxygen in a hemoglobin-saturated medium is theoretically investigated using classical transport theory. It is found that all the chemical complexes can be expressed as a single function of oxygen pressure. A potential difference together with apH shift is predicted to occur across the medium.
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    Notes on magnetic actions upon the nervous system (1965)
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    Bulletin of mathematical biology 27 (1965), S. 203-214 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Several physical effects (magnetomotive force on ions, magnetic induction of electrical field, magnetic changes of inductance) are quantitatively analyzed in an attempt to attain an insight on how externally applied static magnetic fields influence the activity of the neuron and the Nervous System as a whole or in part. The possible magnetic action on shifting excited zones of the axon appears as most promising for prediction and interpretation of measurable effects. Magnetic fields may modify nervous functions by multiplication and addition of very small biophysical effects.
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    Molecular set theory: II. An aspect of the biomathematical theory of sets (1965)
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    Bulletin of mathematical biology 27 (1965), S. 235-251 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.
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    Man/machine interaction in adaptively controlled experimental conditions (1965)
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    Bulletin of mathematical biology 27 (1965), S. 261-273 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Systems in which a human subject interacts with an adaptive control mechanism through display and response facilities are examined. A cybernetic model is discussed, together with supporting experimental data.
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    Computer simulation of stem-cell kinetics (1965)
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    Bulletin of mathematical biology 27 (1965), S. 275-290 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Computer simulation of the stem-cell system has been motivated by a desire to provide a device which may assist the experimenter in his development of complex research strategies in the rapidly developing investigative fields that relate to erythropoiesis and granulopoiesis. A simulation program, written in FORTRAN II for the IBM-7094, is being developed with the requirements of flexibility and broad applicability in mind. The biological model for which it originally was developed differs from those previously advanced by visualizing differentiation into the erythrocytic and granulocytic series as occurring during the post-mitotic phase of a stem cell's growth, the cell's susceptibility to erythropoietic and granulopoietic stimuli varying as its biochemical development unfolds. One might test this model by attempting to demonstrate an asymmetrical interference between erythropoietic and granulopoietic challenges to the stem-cell system. A method for establishing an initial stable configuration of the model is presented. The simulation of the introduction of exogenous erythropoietic stimuli is described. And there is a brief description of the feedback mechanism employed to stabilize the size of the stem-cell population.
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    A note on visual integrative mechanisms (1965)
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    Bulletin of mathematical biology 27 (1965), S. 305-310 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a system as complex and as effective as the eye, the cooperative interaction of different mechanisms may be taken as axiomatic. With this as a starting point, various visual phenomena are considered, such as short term memory, eye movements, and flicker fusion. Simple data on mean values lend support to the proposition that the spatial and temporal characteristics of these phenomena are matched with one another. The significance of this for a mechanism of vision is discussed.
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    Matrix algebra of a generalized linear stochastic model. Nonconfluent and general confluent cases (1965)
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    Bulletin of mathematical biology 27 (1965), S. 311-315 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Matrix algebra is the natural tool for the study of linear stochastic models with many parameters. Complete solutions are given for the nonconfluent and the general confluent cases. It is shown that the axiomatics of a generalized linear stochastic model are naturally described within the framework of the linear algebra in an Euclidean space.
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    Properties of solution of the diffusion-reaction equation (1965)
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    Bulletin of mathematical biology 27 (1965), S. 291-303 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An arbitrary set of chemical reactions is considered to occur among chemical speciesX i . In a closed uniform reaction system certain linear combinations of the concentrations of theX i are constants. The general construction of all such linear combinations with non-negative coefficients is given in terms of the molecular formulae for theX i . It is shown that to each such linear combination there corresponds another which is a harmonic function when the reactions take place in an open spatially distributed stationary reaction system of arbitrary shape. Under the usual boundary conditions these harmonic functions are constants. With some restrictions upon the diffusion and permeability coefficients these constants are evaluated. This evaluation is the basis for relations between the total concentration of a given chemical group (e.g., the sum of the concentrations of a free molecule, or ion, and its various bound forms) in the reaction system, and in the surrounding medium. The bearing of these relations on apparent active transport is noted and illustrated.
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    Analysis of tracer experiments: VI. Determination of partitioned initial entry functions (1965)
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    Bulletin of mathematical biology 27 (1965), S. 329-332 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the partitioned initial entry functions previously introduced in multicompartment analysis can be directly and uniquely determined from the experimental data.
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    URL: http://dx.doi.org/10.1007/BF02477288
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