ALBERT

Description: We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of non-autonomous Hamiltonian vector fields.

Description: We consider the Schur–Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$ . We show that the infinite-dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I $_\infty$ , II, and III. A key result is an approximation theorem that can be seen as an approximate multivariate analogue of Kadison's Carpenter Theorem.

Description: We study the rate of convergence to zero of the tail entropy of $C^\infty$ maps. We give an upper bound of this rate in terms of the growth in $k$ of the derivative of order $k$ and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to $C^r$ $(r\geqslant 2)$ robustly non- $h$ -expansive dynamical systems.

Description: Let ${{\mathscr {C}}}^0_{{{\mathfrak {g}}}}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'({{\mathfrak {g}}})$ and let $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of type $A_{\infty }$ . In this paper, we investigate the relationship between the categories ${{\mathscr {C}}}^0_{A_{N-1}^{(1)}}$ and ${{\mathscr {C}}}^0_{A_{N-1}^{(2)}}$ by constructing the generalized quantum affine Schur–Weyl duality functors ${\mathcal {F}}^{(t)}$ from $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ to ${{\mathscr {C}}}^0_{A_{N-1}^{(t)}}\ (t=1,2)$ .

Description: We present new constructions of complex and $p$ -adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.

Description: We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross–Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton with zero speed.

Description: Let $k$ and $n$ be positive even integers. For a cuspidal Hecke eigenform $h$ in the Kohnen plus space of weight $k-n/2+1/2$ for $\varGamma _0(4),$ let $I_n(h)$ be the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift of $h$ in the space of cusp forms of weight $k$ for ${\rm Sp}_n({{\bf{Z}}}),$ and $f$ be the primitive form of weight $2k-n$ for ${\rm SL}_2({{\bf{Z}}})$ corresponding to $h$ under the Shimura correspondence. We then express the ratio $\displaystyle {\langle I_n(h), I_n(h) \rangle / \langle h, h \rangle }$ of the period of $I_n(h)$ to that of $h$ in terms of special values of certain $L$ -functions of $f$ . This proves the conjecture proposed by Ikeda concerning the period of the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift.

Description: Although copepods have been considered tolerant against the direct influence of the ocean acidification (OA) projected for the end of the century, some recent studies have challenged this view. Here, we have examined the direct impact of short-term exposure to a pCO 2 / pH level relevant for the year 2100 ( pH NBS , control: 8.18, low pH : 7.78), on the physiological performance of two representative marine copepods: the calanoid Acartia grani and the cyclopoid Oithona davisae . Adults of both species, from laboratory cultures, were preconditioned for four consecutive days in algal suspensions ( Akashiwo sanguinea ) prepared with filtered sea water pre-adjusted to the targeted pH values via CO 2 bubbling. We measured the feeding and respiratory activity and reproductive output of those pre-conditioned females. The largely unaffected fatty acid composition of the prey offered between OA treatments and controls supports the absence in the study of indirect OA effects (i.e. changes of food nutritional quality). Our results show no direct effect of acidification on the vital rates examined in either copepod species. Our findings are compared with results from previous short- and long-term manipulative experiments on other copepod species.

Description: We analyzed the genetic structure of the radiolarian morphospecies Larcopyle buetschlii from the surface to deep waters (up to 2000 m) in the Japan Sea using the internal transcribed spacer (ITS) regions of ribosomal RNA genes. Each individual had several ITS variants, but these polymorphisms show no vertical phylogeographic structure, suggesting a single biological species. Its rapid clonal reproduction suggested by high ITS variation likely plays a pivotal role in maintaining its wide vertical distribution.

Description: Phronima sedentaria is a hyperiid amphipod that diel migrates into a pronounced oxygen minimum zone (OMZ) in the Eastern Tropical North Pacific. In this study, oxygen consumption and lactate production were measured in P. sedentaria to estimate the aerobic and anaerobic contributions to total metabolism under conditions that mimic its day- (1% oxygen, 10°C) and night-time (20% oxygen, 20°C) habitat. When exposed to hypoxia and low temperature, the total metabolism of P. sedentaria was depressed by 78% compared with normoxic conditions. The metabolic enzymes citrate synthase (CS) and lactate dehydrogenase (LDH) were also measured as indicators of aerobic and anaerobic metabolism, and compared with specimens collected from the California Current and the North Atlantic to assess potential adaptations to low oxygen. LDH activity was not significantly different between regions. Significant differences in CS activity may be due to variation in food availability. Climate change is predicted to increase surface temperatures and cause the expansion of OMZs. This will result in vertical compression of the night-time range for P. sedentaria and is likely to have the same impact on other diel migrators. Habitat compression will reduce zooplankton contribution to carbon cycling and alter oceanic ecology, including predator–prey interactions.

Description: Many phytoplankton exploit phosphorus (P) from organic sources when dissolved inorganic P (DIP) is depleted. This process is, however, rarely considered in ecological and biogeochemical models. We present a mechanistic model describing explicitly the ability of phytoplankton to use dissolved organic P (DOP) when DIP is limiting, by synthesizing alkaline phosphatase (AP) that releases DIP from DOP. This model, applicable to any phytoplankton species expressing AP, is here specifically developed for the colony-forming Phaeocystis globosa. It describes the main processes related to P metabolism, including DIP transport, intracellular accumulation and assimilation. Model behaviour is explored in DIP-limiting batch-type conditions for different DOP ranging between 0 and 1.5 mmol P m –3 . Simulations show that the DOP-derived DIP increases the maximum biomass reached and extends the period of net growth. The magnitude of the enhanced biomass production is controlled by the DOP initially present as well as the released DOP, the latter being recycled by lysis of P. globosa cells. We also present a simplified model version derived from the mechanistic model, which involves fewer state variables and parameters. The latter is directly usable in both variable (quota-type) and fixed stoichiometry descriptions of phytoplankton growth.

Description: Zooplankton diel vertical migration (DVM) is often explained as a balance between predator avoidance and resource acquisition. However, recent studies suggest that ultraviolet radiation (UV) may also be important in driving zooplankton DVM in some systems. Williamson et al. ( Williamson et al ., 2011 ) proposed the "transparency-regulator hypothesis," which integrates UV into our current understanding of the drivers of DVM and predicts that the relative roles of UV and visual predation pressure will vary systematically across a gradient of lake transparency. To assess this hypothesis, we conducted in situ mesocosm experiments in five different lakes: two lakes without fish and three lakes with fish that spanned a range of UV and visible light transparency. We used an open-bottomed mesocosm design that allowed for the direct manipulation of UV that did not constrain visual predators or the amplitude or timing of natural migrations. Consistent with the transparency-regulator hypothesis, we found that UV is an important driver of Daphnia DVM in highly UV transparent lakes with and without fish but not in low transparency systems. Our results also suggest that UV and visual predation pressure may interact in systems of intermediate transparency.

Description: Competition for resources can lead to species exclusion. However, this exclusion may be avoided if species show differential adaptation to physical environment. Empirical studies on competition are difficult when species are phylogenetically close and have complex life cycles. This is the case of B. plicatilis and B. manjavacas , two cryptic rotifer species differing in their salinity niches and in life-history traits related to sex and diapause. These differences have been suggested to promote the stable co-occurrence observed in natural populations of these species. However, in a previous empirical study, the outcome of competition between both species was always exclusion. Here, we theoretically explored the effect of complex life-history traits and salinity fluctuations on the long-term competitive outcome of B. plicatilis and B. manjavacas . We developed a model and simulated ecological scenarios combining different growing period lengths, levels of crossed induction of sex between species and salinity regimes. Results show that a fluctuating salinity regime, an intermediate length of growing season and a low level of crossed induction of sex are essential conditions to take into account to explain coexistence.

Description: Colonization of new habitats through dispersal of phytoplankton cysts might be limited, if resident populations outcompete invaders during germination. We reciprocally transferred Gonyostomum semen (Raphidophyceae) cysts from three lakes into native and foreign waters originating from the respective habitats. Germination rate and germling growth were impacted by water origin, but there was no preference for native water. Gonyostomum semen 's ability to germinate in different conditions might explain its expansion in northern Europe.

Description: Measuring zooplankton biomass and physiological rates is of paramount importance in biological oceanography in order to assess the role of this community in, e.g. carbon fluxes. Classical methods (incubations) are very time-consuming and cannot match the frequency of physical and chemical measurements. Attempting to solve this, a variety of methods (e.g. egg production, RNA/DNA ratio or enzyme activities) have been developed over the last decades. These methods also show uncertainties and hitherto only incubation methods have been widely accepted. Predictive equations relating physiological processes and body weight (bw) and temperature are a rough alternative, normally used to ascertain the role of these organisms in the oceanic ecosystem. However, using imaging systems and empirical relationships to determine bw allows the application of physiological models to each individual, obtaining reliable estimates for taxonomic groups and size classes. In this study, we developed predictive equations suitable for growth and respiration estimations in subtropical regions. In addition, biomass and physiological rates assessed from empirical equations in combination with an image-based system (ZooImage) were compared with standard and enzymatic methods, respectively. We observed a consistent agreement between methodologies, the former resulting in an inexpensive and faster procedure for the appraisal of biomass and community carbon fluxes at large spatial and temporal scales.

Description: Carbon-specific prey clearance and ingestion rates of 1.5-mm tentaculate larvae of the ctenophore Mnemiopsis leidyi increased linearly between 6 and 25°C but declined between 25 and 30°C. Both absolute (length) and carbon-specific growth rate increased linearly with increasing temperature. The latter was 0.87 d –1 at 25°C. Extremely low or negative growth rates observed at 6 and 30°C help define the thermal limits to population growth of this successful biological invader.

Description: We have supplemented available, concurrent measurements of fresh weight ( W , g) and body carbon (C, g) (46 individuals, 14 species) and nitrogen (N, g) (11 individuals, 9 species) of marine gelatinous animals with data obtained during the global ocean MALASPINA 2010 Expedition (totalling 267 individuals and 33 species for the W versus C data; totalling 232 individuals and 31 species for the N versus C data). We then used those data to test the allometric properties of the W versus C and N versus C relationships. Overall, gelatinous organisms contain 1.13 ± 1.57% of C (by weight, mean ± SD) in their bodies and show a C:N of 4.56 ± 2.46, respectively, although estimations can be improved by using separate conversion coefficients for the carnivores and the filter feeders. Reduced major axis regression indicates that W increases isometrically with C in the carnivores (cnidarians and ctenophores), implying that their water content can be described by a single conversion coefficient of 173.78 gW(g C) –1 , or a C content of 1.17 ± 1.90% by weight, although there is much variability due to the existence of carbon-dense species. In contrast, W increases more rapidly than C in the filter feeders (salps and doliolids), according to a power relationship W = 446.68C 1.54 . This exponent is not significantly different from 1.2, which is consistent with the idea that the watery bodies of gelatinous animals represent an evolutionary response towards increasing food capture surfaces, i.e. a bottom-up rather than a top-down mechanism. Thus, the available evidence negates a bottom-up mechanism in the carnivores, but supports it in the filter feeders. Last, N increases isometrically with C in both carnivores and filter feeders with C:N ratios of 3.89 ± 1.34 and 4.38 ± 1.21, respectively. These values are similar to those of compact, non-gelatinous organisms and reflect a predominantly herbivorous diet in the filter feeders, which is confirmed by a difference of one trophic level between filter feeders and carnivores, according to stable N isotope enrichment data.

Description: I explored mortality estimation for stage-structured populations, building on previous work that applied vertical life-table methods to populations of copepods. A new Bayesian approach for estimating mortality rates accounts for uncertainties in stage duration and number counted by stage, which have not been fully incorporated into previous analyses. This method assumes that mortality is similar among similar life stages. Results using simulated data show that realistic values of the standard deviation of stage duration and number of individuals counted result in reliable mortality estimates, though with wide confidence intervals. This uncertainty obscures variation in estimated mortality between successive stages and can also obscure bias due to violation of underlying assumptions such as that of a stable stage distribution. More importantly, the uncertainty calls into question many previous mortality estimates across pairs of life stages that do not account for these sources of uncertainty. The method was applied to an introduced population of the brackish-water cyclopoid copepod Limnoithona tetraspina in the San Francisco Estuary. Despite the uncertainties, results were interpretable: mortality was highest in nauplii and lowest in adults, probably because of high vulnerability of nauplii to invertebrate predators and low vulnerability of adults to fish predation.

Description: The strong La Niña of 2010–2011 provided an opportunity to investigate the ecological impacts of El Niño-Southern Oscillation on coastal plankton communities using the nine national reference stations around Australia. Based on remote sensing and across the entire Australian region 2011 (La Niña) was only modestly different from 2010 (El Niño) with the average temperature declining 0.2%, surface chlorophyll a up 3% and modelled primary production down 14%. Other changes included a poleward shift in Prochlorococcus and Synechococcus . Along the east coast, there was a reduction in salinity, increase in nutrients, Chlorophytes and Prasinophytes (taxa with chlorophyll b , neoxanthin and prasinoxanthin). The southwest region had a rise in the proportion of 19-hexoyloxyfucoxanthin; possibly coccolithophorids in eddies of the Leeuwin Current and along the sub-tropical front. Pennate diatoms increased, Ceratium spp. decreased and Scrippsiella spp. increased in 2011. Zooplankton biomass declined significantly in 2011. There was a reduction in the abundance of Calocalanus pavo and Temora turbinata and increases in Clausocalanus farrani , Oncaea scottodicarloi and Macrosetella gracilis in 2011. The changes in the plankton community during the strong La Niña of 2011 suggest that this climatic oscillation exacerbates the tropicalization of Australia.

Description: Jellyfish are effective predators on mesozooplankton and release large amounts of dissolved organic matter. Nevertheless, jellyfish initiated trophic cascades and bottom-up influences impacting lower trophic levels have received limited attention. We conducted a mesocosm experiment to quantify simultaneous top-down and bottom-up effects of a common jellyfish, Cyanea capillata , in a natural plankton community during autumn. Treatments were 0, 2 or 5 jellyfish per 2.5 m 3 mesocosm, four replicates each, with initial additions of inorganic nutrients. Primary and bacterial production, species abundance and composition of several trophic levels and nutrient and carbon dynamics were followed during the 8-day experiment. Multivariate statistics and generalized additive mixed modelling were applied to test whether jellyfish carbon concentration (0–1.26 mg jellyC L –1 ) in the mesocosms affected the variables monitored. Unexpected negligible predatory impact of jellyfish on mesozooplankton was observed, potentially related to jellyfish senescence. Community compositions of bacteria, phytoplankton and mesozooplankton changed with time, but did not differ between treatments. However, nutrient regeneration by jellyfish was evident, and jellyfish had a positive impact on total and specific bacterial production, total primary production and the 〉10 µm chlorophyll a fraction. Bottom-up influences from abundant jellyfish could thus stimulate productivity in nutrient depleted autumnal surface waters.

Description: The feeding ecology of Blackfordia virginica was evaluated concurrently with their ecophysiological condition in a temperate estuary. The diet of B. virginica is composed not only of metazooplankton, as commonly observed for other jellyfish species, but also of phytoplankton, ciliates and detritus. This feeding behavior might explain their good nutritional condition and sustainable growth during bloom peaks, when zooplankton abundance has already decreased significantly.

Description: The pelagic dynamics of the cosmopolitan scyphozoan Aurelia sp . was investigated in three French Mediterranean lagoons, Thau, Berre and Bages-Sigean, which harbour resident populations. The annual cycles showed a common univoltine pattern in all lagoons where the presence of pelagic stages in the water column lasted ~8 months. Field observations showed a release of ephyrae in winter time followed by pronounced growth between April and July, when individuals reached the largest sizes, before disappearing from the water column. Maximum abundance of ephyrae and medusae were registered in Thau. Medusae abundance attained a maximum of 331 ind 100 m –3 in Thau, 18 ind 100 m –3 in Berre and 7 ind 100 m –3 in Bages-Sigean lagoons. Temperature and zooplankton abundance appeared as leading factors of growth, where Bages-Sigean showed the population with higher growth rates (2.66 mm day –1 ) and maximum size (32 cm), followed by Thau (0.57–2.56 mm day –1 ; 22.4 cm) and Berre (1.57–2.22 mm day –1 ; 17 cm). The quantification of environmental windows used by the species showed wider ranges than previously reported in the Mediterranean Sea, which suggests a wide ecological plasticity of Aurelia spp. populations in north-western Mediterranean lagoons.

Description: Two lobate ctenophores, Bolinopsis infundibulum and Mnemiopsis leidyi , occur in the North Sea. Stomach contents of field-collected B. infundibulum were recorded and clearance rates for cladocerans and copepods calculated. In starvation experiments, daily body carbon losses of 2.2 and 1.2% and total carbon content losses of 76 and 63% were observed for B. infundibulum (after 68 days) and M. leidyi (after 67 days), respectively.

Description: The ctenophore Mnemiopsis leidyi is characterized by high growth rates and a large reproductive capacity. However, reproductive dynamics are not yet well understood. Here, we present laboratory data on food-dependent egg production in M. leidyi and egg hatching time and success. Further, we report on the reproduction of laboratory-reared and field-caught animals during starvation. Our results show that the half-saturation zooplankton prey concentration for egg production is reached at food levels of 12–23 µgC L –1 , which is below the average summer food concentration encountered in invaded areas of northern Europe. Furthermore, starved animals continue to produce eggs for up to 12 days after cessation of feeding with high overall hatching success of 65–90%. These life history traits allow M. leidyi to thrive and reproduce in environments with varying food conditions and give it a competitive advantage under unfavourable conditions. This may explain why recurrent population blooms are observed and sustained in localized areas in invaded northern Europe, where water exchange is limited and zooplankton food resources are quickly depleted by M. leidyi . We suggest that these reproductive life history traits are key to its invasion success.

Description: Surface-dwelling colonies of Velella velella occur throughout tropical to cold-temperate oceans of the world and sometimes are stranded in masses along hundreds of kilometers of beaches. Large-scale blooms in the Western Mediterranean Sea in 2013 and 2014 allowed the study of diet, prey digestion times and predation rates. Gastrozooid content analyses showed that 59% of the 769 identified prey were euphausiid larvae (calytopsis and furcilia) captured at night. Copepods (41%), fish eggs (2.2%) and larvae (0.5%) were captured both at day and night. Digestion times at ambient temperature (~17°C) of calytopsis, furcilia and copepods were estimated to be 〉6.5, 4.4 and 3.9 h, respectively. Estimated prey consumption was substantially lower in 2014 than in 2013 (41 vs. 75 prey day –1 colony –1 ). Velella velella and other gelatinous species bloomed in the Mediterranean Sea and the northeastern Atlantic and Pacific oceans in 2013 and 2014. Because of the wide distribution of V. velella colonies, their mass occurrences, potential importance as predators and competitors of fish, additional production from symbiotic zooxanthellae and stranding on beaches, they could be important in open-ocean carbon cycling and in transport of pelagic production to landmasses.

Description: Several hypotheses exist that describe phytoplankton spring blooms in temperate and subpolar oceans: the critical depth, shoaling mixed layer (ML), critical turbulence, onset of stratification and disturbance-recovery hypotheses. These theories appear to be mutually exclusive and none of them describe the annual cycle of phytoplankton biomass. Here, we present a model of the annual cycle in phytoplankton that recognizes that phytoplankton are not always mixed throughout the so-called ML, and that it is important to distinguish between the surface biomass and depth-integrated phytoplankton. Once these important distinctions are made, the annual cycles and blooms in surface and depth-integrated phytoplankton can be described straightforwardly in terms of the physical drivers and biotic responses.

Description: Impacts of climate change on marine ecosystems have become increasingly apparent during the past decades. In consequence, it is necessary to study how these alterations can affect the habitat and population dynamics of key organisms. Here we used a video plankton recorder (VPR) to investigate the effect of climate-induced habitat changes on the copepod Pseudocalanus acuspes , a key species in the Baltic Sea. The VPR allowed the observation of reproducing copepod females, identified by attached egg sacs, usually lost during traditional net sampling. We compared the small-scale distribution of our target species during non-inflow and inflow periods. Our study showed a large increase in the availability of suitable habitat after the inflow event due to improved oxygen and salinity conditions. Furthermore, increased copepod abundance and a deeper and wider vertical distribution was apparent. Applying a new approach to estimate in situ egg production rates from VPR-derived images revealed no changes. However, we observed increased offspring survival with improved hydrographic conditions pointing toward the importance of salinity and oxygen for the population dynamics of Baltic P. acuspes . Our observations illustrate the strong impact that climate change can have on the habitat of key marine ecosystem species, important for overall ecosystem dynamics.

Description: Research on nutrient controls of planktonic productivity tends to focus on a few standard fractions of inorganic or total nitrogen (N) and phosphorus (P). However, there is a wide range in the degree to which land-derived dissolved organic nutrients can be assimilated by biota. Thus, in systems where such fractions form a majority of the macronutrient resource pool, including many boreal inland waters and estuaries, our understanding of bacterio- and phytoplankton production dynamics remains limited. To adequately predict aquatic productivity in a changing environment, improved standard methods are needed for determining the sizes of active (bioavailable) pools of N, P and organic carbon (C). A synthesis of current knowledge suggests that variation in the C:N:P stoichiometry of bioavailable resources is associated with diverse processes that differentially influence the individual elements across space and time. Due to a generally increasing organic nutrient bioavailability from C to N to P, we hypothesize that the C:N and N:P of bulk resources often vastly overestimates the corresponding ratios of bioavailable resources. It is further proposed that basal planktonic production is regulated by variation in the source, magnitude and timing of terrestrial runoff, through processes that have so far been poorly described.

Description: Understanding the factors that regulate the abundance, size structure and community structure of cladocerans is an important goal of aquatic ecologists. While both top-down and bottom-up factors help to structure cladoceran communities, there may be interactions between these factors. We conducted a mesocosm study to determine how alien large-bodied Daphnia , zebra mussels and fish affected cladoceran community and size structure. We found that large-bodied Daphnia reduced algal resources and the fecundity of smaller bodied cladocerans. Fish removed the large-bodied Daphnia magna from the mesocosms and shifted the cladoceran community to a smaller body size. Fish also appeared to promote increases in cladoceran diversity through the coexistence of several smaller bodied taxa. In contrast, zebra mussels increased cyanobacteria and helped to promote the success of the alien Daphnia , but reduced the biomass of small-bodied cladocerans. Zebra mussels reduced the carbon (C):phosphorus (P) ratio of the phytoplankton in the mesocosms which may have favored the relatively P-limited Daphnia . Combined, our results highlight the complex interactions of multiple factors that help to regulate cladoceran community and size structure.

Description: In freshwater systems, Daphnia has been demonstrated to show adaptive responses following the light–dark cycle. The adjustment of these responses to the change of day and night is probably transmitted via the hormone melatonin. The rate-limiting enzyme in melatonin synthesis is the arylalkylamine N-transferase (AANAT). We identified three genes coding for insect-like AANATs in Daphnia , of which we measured the gene expression in an ecologically relevant light–dark cycle. We demonstrated that Daphnia 's insect-like AANAT gene expression oscillated in a daily manner, and that the highest peak of expression after the onset of darkness was followed by a peak of melatonin production at midnight. Moreover, we could show an oscillation of endogenous melatonin synthesis in Daphnia . In most organisms, melatonin synthesis is due to rhythmic expression of genes of the circadian clock, since transcription of aanat s is directly linked to a circadian transcription factor. We could demonstrate that putative clock genes and insect-like AANAT genes of Daphnia were equally expressed. Therefore, we propose that melatonin synthesis is coupled to the expression of Daphnia clock genes, and that insect-like AANATs of crustaceans have a similar function as AANATs of vertebrates: The initiation of melatonin synthesis. In future studies with Daphnia , it will be necessary to take the time of day into account since melatonin concentrations might influence stress responses.

Description: It has been hypothesized that terrestrial particulate organic matter (t-POM) makes important contributions to Daphnia production in some lakes. We conducted a series of feeding experiments to explore the fatty acid responses in Daphnia to diets comprised of different terrestrial resources (i.e. Alnus rubra , Phragmites australis , Betula nana and Betula pendula ) and mixed diets with terrestrial and phytoplankton ( Scenedesmus or Cryptomonas ) resources. When fed 100% phytoplankton, Daphnia had very similar ( r 2 〉 0.80) fatty acid profiles to their diets, whereas Daphnia that consumed t-POM diets had weak correlations ( r 2 = 0.002–0.56) with the corresponding diet sources. Unusual 16 carbon chain polyunsaturated fatty acids (16:26, 16:33 and 16:43), linoleic acid (18:26) and α-linolenic acid (18:33) were diagnostic fatty acids for Scenedesmus and Daphnia that consumed this alga. Stearidonic acid (18:43) and eicosapentaenoic acid (20:53) were diagnostic for Cryptomonas and Daphnia that consumed this diet. All of the t-POM resources were characterized by a high content of saturated fatty acids (SAFA; 79 ± 12%), especially the diagnostic long-chain SAFA (20:0, 22:0, 24:0, 26:0, 28:0). Daphnia that consumed t-POM assimilated very little of these terrestrial biomarkers, but the shorter chain SAFA 16:0 and 18:0 were very prevalent in juvenile and adult Daphnia that consumed terrestrial plant matter. The -3:-6 ratios were distinctive between terrestrial (0.3–1.6) and phytoplankton resources (3–15), and this ratio in Daphnia was strongly associated with their diets ( r 2 = 0.88). These results suggest that Daphnia , and perhaps zooplankton in general, preferentially retain algae-derived 3 fatty acids, and low -3:-6 ratios in Daphnia indicate a mainly terrestrial diet or poor nutritional condition.

Description: In order to trace community dynamics and reticulate evolution in hybrid species complexes, long-term comparative studies of natural populations are necessary. Such studies require the development of tools for fine-scale genetic analyses. In the present study, we developed species-diagnostic SNP-based markers for hybridizing freshwater crustaceans: the multispecies Daphnia longispina complex. Specifically, we took advantage of transcriptome data from a key species of this hybrid complex, the annotated genome of a related Daphnia species and well-defined reference genotypes from three parental species. Altogether eleven nuclear loci with several species-specific SNP sites were identified in sequence alignments of these reference genotypes from three parental species and their interspecific hybrids. A PCR-RFLP assay was developed for cost-efficient large population screening by SNP-based genotyping. Taxon assignment by RFLP patterns was nearly perfectly concordant with microsatellite genotyping across several screened populations from Europe. Finally, we were able to amplify two short regions of these loci in formaldehyde-preserved samples dating back to the year 1960. The species-specific SNP-based markers developed here provide valuable tools to study hybridization over time, including the long-term impact of various environmental factors on hybridization and biodiversity changes. SNP-based genotyping will finally allow eco-evolutionary dynamics to be revealed at different time scales.

Description: A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product $\mathcal S^2\times \mathcal S^2$ of two copies of the Hilbert–Schmidt classes into the trace class $\mathcal S^1$ is established in terms of linear Schur multipliers acting on the space $\mathcal S^\infty $ of all compact operators. Using this formula, we resolve Peller's problem on Koplienko–Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function $f$ with a bounded second derivative, a self-adjoint (unbounded) operator $A$ and a self-adjoint operator $B\in \mathcal S^2$ such that \[ f(A+B)-f(A)-\left.\frac{d}{dt}(f(A+tB))\right\vert_{t=0}\notin \mathcal S^1. \]

Description: Let $\mu $ be a probability measure on $ \mathbb R^n$ with a bounded density $f$ . We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann–Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu $ , any marginal $\pi _E(\mu )$ , or a small perturbation thereof, satisfies a nearly optimal small-ball probability.

Description: Let $\pi :X\to \mathbb {P}^1_{\mathbb {Q}}$ be a non-singular conic bundle over $\mathbb {Q}$ having $n$ non-split fibres and denote by $N(\pi ,B)$ the cardinality of the fibres of Weil height at most $B$ that possess a rational point. Serre showed in 1990 that a direct application of the large sieve yields \[ N(\pi,B)\ll B^2(\log B)^{-n/2} \] and raised the problem of proving that this is the true order of magnitude of $N(\pi ,B)$ under the necessary assumption that there exists at least one smooth fibre with a rational point. We solve this problem for all non-singular conic bundles of rank at most 3. Our method comprises the use of Hooley neutralisers, estimating divisor sums over values of binary forms, and an application of the Rosser–Iwaniec sieve.

Description: We associate a dimer algebra $A$ to a Postnikov diagram $D$ (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian ${\rm Gr}(k,n)$ . We show that $A$ is isomorphic to the endomorphism algebra of a corresponding Cohen–Macaulay module $T$ over the algebra $B$ used to categorify the cluster structure of ${\rm Gr}(k,n)$ by Jensen–King–Su. It follows that $B$ can be realised as the boundary algebra of $A$ , that is, the subalgebra $eAe$ for an idempotent $e$ corresponding to the boundary of the disc. The construction and proof uses an interpretation of the diagram $D$ , with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus.

Description: We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$ -planes in $n$ -space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective–injective object is Geiss–Leclerc–Schröer's category Sub $Q_k$ , which categorifies the coordinate ring of the big cell in this Grassmannian.

Description: We develop a way of seeing a complete orientable hyperbolic 4-manifold $ {\mathcal {M}}$ as an orbifold cover of a Coxeter polytope $ {\mathcal {P}} \subset \mathbb {H}^4$ that has a facet colouring. We also develop a way of finding a totally geodesic sub-manifold $ {\mathcal {N}}$ in $ {\mathcal {M}}$ , and describing the result of mutations along $ {\mathcal {N}}$ . As an application of our method, we construct an example of a complete orientable hyperbolic 4-manifold $ {\mathcal {X}}$ with a single non-toric cusp and a complete orientable hyperbolic 4-manifold ${\mathcal {Y}}$ with a single toric cusp. Both $ {\mathcal {X}}$ and $ {\mathcal {Y}}$ have twice the minimal volume among all complete orientable hyperbolic 4-manifolds.

Description: The covariogram $g_{K}$ of a convex body $K$ in $ \mathbb {R}^n$ is the function that associates to each $x\in \mathbb {R}^n$ the volume of the intersection of $K$ with $K+x$ . Determining $K$ from the knowledge of $g_K$ is known as the Covariogram Problem. It is equivalent to determining the characteristic function $1_K$ of $K$ from the modulus of its Fourier transform $\widehat {{1_K}}$ in $ \mathbb {R}^n$ , a particular instance of the Phase Retrieval Problem. We connect the Covariogram Problem to two aspects of the Fourier transform $\widehat {{1_K}}$ seen as a function in $\mathbb {C}^n$ . The first connection is with the problem of determining $K$ from the knowledge of the zero set of $\widehat {{1_K}}$ in $\mathbb {C}^n$ . To attack this problem T. Kobayashi studied the asymptotic behavior at infinity of this zero set. We obtain this asymptotic behavior assuming less regularity on $K$ and we use this result as an essential ingredient for proving that when $K$ is sufficiently smooth and in any dimension $n$ , $K$ is determined by $g_K$ in the class of sufficiently smooth bodies. The second connection is with the irreducibility of the entire function $\widehat {{1_K}}$ . This connection also shows a link between the Covariogram Problem and the Pompeiu Problem in integral geometry.

Description: Let $\varphi :X\to S$ be a morphism between smooth complex analytic spaces and let $f=0$ define a free divisor on $S$ . We prove that if the deformation space $T^1_{X/S}$ of $\varphi $ is a Cohen–Macaulay $\mathcal {O}_X$ -module of codimension 2, and all of the logarithmic vector fields for $f=0$ lift via $\varphi $ , then $f\circ \varphi =0$ defines a free divisor on $X$ ; this is generalized in several directions. Among applications we recover a result of Mond–van Straten, generalize a construction of Buchweitz–Conca, and show that a map $\varphi :\mathbb {C}^{n+1}\to \mathbb {C}^n$ with critical set of codimension 2 has a $T^1_{X/S}$ with the desired properties. Finally, if $X$ is a representation of a reductive complex algebraic group $G$ and $\varphi $ is the algebraic quotient $X\to S=X\!{/\!/} G$ with $X\!{/\!/} G$ smooth, then we describe sufficient conditions for $T^1_{X/S}$ to be Cohen–Macaulay of codimension 2. In one such case, a free divisor on $\mathbb {C}^{n+1}$ lifts under the operation of ‘castling’ to a free divisor on $\mathbb {C}^{n(n+1)}$ , partially generalizing work of Granger–Mond–Schulze on linear free divisors. We give several other examples of such representations.

Description: Let $M^n$ be a compact manifold of dimension $n$ with free $T^k$ -action. We consider collapsings of $M$ on $N=M/T^k$ such that the sectional curvature and diameter of $M$ satisfy $|K(M)|\leq a$ and $ {\rm diam}(M) 〈 d$ , and give examples of collapsings for all $k$ such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of $M$ are bounded above by $c(M)\cdot \hbox {inj}(M)^{2k}$ . Moreover, we prove that the first non-zero eigenvalue of Laplacian acting on 1-forms of all principal $T^k$ -bundle $M$ over $N$ is bounded below by $c(n,a,d,N)\cdot {\rm Vol}(M)^2$ and $c\cdot \hbox {inj}(M)^{2k}$ when $M$ collapses on $N$ .

Description: We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types A and à . This entails showing that the minimal elements of the positive semiring of these cluster algebras form a linear basis over the integers for the cluster algebra.

Description: We prove that strongly F -regular and F -pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F -injective singularities fail to satisfy even the most basic Bertini-type results.

Description: This is the second of a pair of papers on the Delta-group structure on the braid and mapping class groups of a surface. We obtain a description of the homotopy groups of these Delta-groups and generalize to an arbitrary surface the Berrick–Cohen–Wong–Wu exact sequence relating the Brunnian braid groups of the 2-sphere to its homotopy groups. We prove a similar result for Brunnian mapping class groups.

Description: We construct a geometric realization of the Khovanov–Lauda–Rouquier algebra R associated with a symmetric Borcherds–Cartan matrix A = ( a ij ) i , j I via quiver varieties. As an application, if a ii != 0 for any i I , we prove that there exists a one-to-one correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of U A – (g) (respectively, V A ( )) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, R ).

Description: The purpose of this paper is to study the nature of quasi-invariant measures for finitely generated non-discrete subgroups of Diff ( S 1 ). For this, we apply ideas involving the closure of these groups to find out that the regularity of the measure depends on a ‘measurable version’ of well-known problems concerning stable self-intersection of Cantor sets. As applications, we prove that every d -quasiconformal probability measure for a non-solvable and non-discrete group must be absolutely continuous. Concerning singular quasi-invariant measures, it is also proved that their associated Hausdorff measures must either be zero or of infinite mass, a result contrasting with the case of dynamically defined Cantor sets and also applicable to the examples of singular stationary measures constructed by Kaimanovich and Le Prince. As a further application of our methods, a theorem of rigidity for measurable conjugations between groups as above is obtained.

Description: We study the space of period polynomials associated with modular forms of integral weight for finite-index subgroups of the modular group. For the modular group, this space is endowed with a pairing, corresponding to the Petersson inner product on modular forms via a formula of Haberland, and with an action of Hecke operators, defined algebraically by Zagier. We generalize Haberland's formula to (not necessarily cuspidal) modular forms for finite-index subgroups, and we show that it conceals two stronger formulas. We extend the action of Hecke operators to period polynomials of modular forms, we show that the pairing on period polynomials appearing in Haberland's formula is nondegenerate, and we determine the adjoints of Hecke operators with respect to it. We give a few applications for 1 ( N ): an extension of the Eichler–Shimura isomorphism to the entire space of modular forms; the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms, which are independent of the period relations; and an explicit formula for Fourier coefficients of Hecke eigenforms in terms of their period polynomials, generalizing the Coefficient theorem of Manin.

Description: We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2 (5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.

Description: Let U R d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f : U -〉 R can be approximated by real analytic convex functions, uniformly on all of U . We also show that C 0 -fine approximation of convex functions by smooth (or real analytic) convex functions on R d is possible in general if and only if d = 1. Nevertheless, for d ≥ 2, we give a characterization of the class of convex functions on R d which can be approximated by real analytic (or just smoother) convex functions in the C 0 -fine topology. It turns out that the possibility of performing this kind of approximation is not determined by the degree of local convexity or smoothness of the given function, but by its global geometrical behaviour. We also show that every C 1 convex and proper function on U can be approximated by C convex functions in the C 1 -fine topology, and we provide some applications of these results, concerning prescription of (sub-)differential boundary data to convex real analytic functions, and smooth surgery of convex bodies.

Description: Let $G$ be a compact connected Lie group, or more generally a path connected topological group of the homotopy type of a finite CW-complex, and let $X$ be a rational nilpotent $G$ -space. In this paper, we analyze the homotopy type of the homotopy fixed point set $X^{hG}$ , and the natural injection $k\colon X^G\hookrightarrow X^{hG}$ . We show that if $X$ is elliptic, that is, it has finite-dimensional rational homotopy and cohomology, then each path component of $X^{hG}$ is also elliptic. We also give an explicit algebraic model of the inclusion $k$ based on which we can prove, for instance, that for $G$ a torus, $\pi _* (k)$ is injective in rational homotopy but, often, far from being a rational homotopy equivalence.

Description: We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.

Description: A notion of tangential thickness of a manifold is introduced. An extensive calculation within the class of lens and fake lens spaces leads to a classification of such manifolds with thickness 1, 3 or 2 $k$ , for $k\geq 1$ . On the other hand, calculations of tangential thickness in terms of the dimension of the manifold and the rank of the fundamental group show very interesting and quite surprising correlations between these invariants.

Description: Extending a classical result of Widom from 1969, polynomials with small supremum norms are constructed for a large family of compact sets $\Gamma$ : their norm is at most a constant times the theoretical lower limit ${{\rm cap}}(\Gamma )^n$ , where ${{\rm cap}}(\Gamma )$ denotes logarithmic capacity. The construction is based on a discretization of the equilibrium measure, and the polynomials have the additional property that outside the given set $\Gamma$ they increase as fast as possible, namely as ${{\rm cap}}(\Gamma )^n\exp (ng_{ \overline {{{}C}}\setminus \Gamma }(z))$ , with the Green's function with pole at infinity in the exponent. This latter fact allows us to use these polynomials as building blocks in constructing Dirac delta-type polynomials around corners: if a compact set $K$ has a corner at some point $z_0$ , then Dirac delta-type polynomials (fast decreasing polynomials) peaking at $z_0$ are polynomials $P_n(z)$ with $P_n(z_0)=1$ that decrease as $|P_n(z)|\prec \exp (-n^ \beta |z-z_0|^ \gamma )$ on the set $K$ as $z$ moves away from $z_0$ . The possible $(\beta , \gamma )$ pairs are completely described in turn of the angle $\alpha \pi$ at $z_0$ ( $\beta \lt 1$ and $\gamma \ge \beta /(2- \alpha )$ or $\beta =1$ and $\gamma 〉 \beta /(2- \alpha )$ ). As application of these fast decreasing polynomials sharp Nikolskii- and Markov-type inequalities are proved for Jordan domains with corners. The paper uses distortion properties of conformal maps, potential theoretic techniques as well as the theory of weighted logarithmic potentials.

Description: We consider for every $n\in \mathbb {N}$ an algebra $\mathcal {A}_{n}$ of germs at $0\in \mathbb {R}^{n}$ of continuous real-valued functions, such that we can associate to every germ $f\in \mathcal {A}_{n}$ a (divergent) series $\mathcal {T}(f)$ with non-negative real exponents, which can be thought of as an asymptotic expansion of $f$ . We require that the $\mathbb {R}$ -algebra homomorphism $f\mapsto \mathcal {T}(f)$ be injective (quasianalyticity property). In this setting, we prove analogue results to Denef and van den Dries’ quantifier elimination theorem and Hironaka's rectilinearization theorem for subanalytic sets.

Description: Suppose that $F(x)\in \mathbb {Z}[\![x]\!]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$ for an integer $b\geq 2$ . In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers. In particular, we prove that $F(1/b)$ cannot be a Liouville number. If, in addition, $F(x)$ is regular, we show that $F(1/b)$ is either rational or transcendental, and in the latter case that $F(1/b)$ is an $S$ -number or a $T$ -number in Mahler's classification of real numbers.

Description: We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class of $p$ -adic integrals under non-degeneracy conditions with respect to associated Newton polytopes. Our techniques prove to be especially useful for the computation of topological zeta functions associated with algebras, resulting in the first systematic investigation of their properties.

Description: We give a bordism-theoretic characterization of those closed almost contact $(2q{+ }1)$ -manifolds (with $q\geq 2$ ) that admit a Stein fillable contact structure. Our method is to apply Eliashberg's $h$ -principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected almost contact 7-manifold with torsion-free second homotopy group is Stein fillable. We also discuss the Stein fillability of exotic spheres and examine subcritical Stein fillability.

Description: Casson-type invariants emerging from Donaldson theory over certain negative-definite four-manifolds were recently suggested by Teleman. These are defined by an algebraic count of points in a zero-dimensional moduli space of flat instantons. Motivated by the cobordism programme of proving Witten's conjecture, we use a moduli space of ${\rm PU}(2)$ Seiberg–Witten monopoles to exhibit an oriented one-dimensional cobordism of the instanton moduli space to the empty space. The Casson-type invariant must therefore vanish.

Description: The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter $\lambda$ . It is shown that there is a threshold value $\lambda _* 〉 0$ of the voltage parameter such that no radially symmetric stationary solution exists for $\lambda 〉 \lambda _* $ , while at least two such solutions exist for $\lambda \in (0,\lambda _* )$ . Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when $\lambda 〉 \lambda _* $ .

Description: Prey size selectivity in piscivorous fish larvae is important to both aquaculture and fisheries science, but laboratory experiments are few. We analyzed selective foraging in Atlantic bluefin tuna larvae ( Thunnus thynnus ) using two larval fish prey species. The experiments revealed that selective foraging of prey sizes differed among bluefin tuna predator sizes (15–25 mm SL) and prey species, bonito ( Sarda sarda ) and seabream ( Sparus aurata ). The observed pattern suggest a general preference for small bonito prey larvae but large seabream prey. Thus, prey size alone is not the only trait responsible for size selectivity in piscivorous fish larvae.

Description: Using a unique 50-year high-resolution time series of daily kom-fyke catches, long-term patterns of scyphomedusae in the western Dutch Wadden Sea were analysed and related to changes in environmental conditions [eutrophication in the 1980s–1990s and recent climate change (increased water temperature)] in the area. Over the years, species composition and general pattern of appearance has remained the same: the first species that occurred in spring was Aurelia aurita , followed by Cyanea lamarckii / C. capillata. Chrysaora hysoscella and Rhizostoma octopus occurred from June to July onwards. All species appeared earlier in recent decades and first appearance and peak occurrence of A. aurita was in part inversely related to previous winter seawater temperature. Last occurrence of C. hysoscella was related to summer seawater temperature and the species is present longer in recent decades. Phenological relationships might have been decoupled since the seasonality of the phytoplankton bloom did not change. All species showed large inter-annual abundance fluctuations, with prolific years followed by sparse years. Peak catches of the coastal species A. aurita occurred in the late 1970s–early 1990s when eutrophication peaked, however, without a significant relationship with total nitrogen input into the area. Unlike for phenology, the patterns of mean abundance of any species did not show a relationship to climate change in the area. This might imply that population regulating mechanisms do not operate during the planktonic phase but during the sessile demersal polyp stages.

Description: In situ fluorometers are the optimal means of providing high-frequency estimates of phytoplankton communities. However, they may be subjected to measurement biases originating from variations in the physiological states of cells, the use of spectral fluorescence signatures (SFS) defined on the basis of inappropriate phytoplankton groups and the lack of linear independence between selected sets of SFS. We assessed correction procedures for measurement biases in mono and mixed cultures of five freshwater phytoplankton species. We investigated the impacts of total Chl a levels, the lack of linear independence between SFS and varying physiological states on the accuracy of the Chl a estimates that were provided by the FluoroProbe (bbe Moldaenke GmbH, Germany). The use of species-specific SFS allowed for the correction of quantification and classification biases. In some cases, the procedure led to a lack of linear independence between SFS, which significantly reduced estimation accuracies. A convenient method to evaluate linear independence between SFS is provided. Differences in the physiological states of phytoplankton cultures following light pre-acclimation and/or N-starvation appeared to be species specific. Light pre-acclimation led to an underestimation of biomass (up to –28.5%) through fluorescence quenching. The responses of the phytoplankton cultures to N-starvation varied depending on the species (from –40.3 to +336% biases in Chl a quantification). Overall, the application of appropriate corrective measures increased data accuracy. However, optimal data reliability can only be achieved by estimating phytoplankton community composition and associated environmental conditions.

Description: Cyanobacteria are the primary taxa responsible for freshwater harmful algal blooms (HABs), with several genera capable of producing potent intracellular toxins and off-flavor compounds. There is considerable growing interest in methods to rapidly quantify cyanobacteria in water samples. Past studies have demonstrated poor correlations between phycocyanin in vivo fluorescence and cyanobacterial cell densities. We conducted a series of laboratory experiments aimed at refining a protocol that uses benchtop fluorometry to measure the cyanobacterial pigment, phycocyanin, to accurately estimate cyanobacterial biovolume. In our study, we found strong correlations between phycocyanin concentration and cyanobacterial biovolume (but not for cell densities) both within and across ponds, which varied widely in productivity and algal diversity. Thus, benchtop fluorometry of phycocyanin is a viable method for water resource managers to quickly estimate cyanobacterial biovolume.

Description: Several dinoflagellate species in the genus Blastodinium are gut parasites of marine planktonic copepods. However, there is only limited information on the occurrence and infection frequencies of Blastodinium spp. in the field and almost no information on the functional impact on their hosts. We report upon the effects of Blastodinium sp . infection on Calanus finmarchicus from the northeastern Atlantic coast off southern Norway during April 2013 and 2014. Up to 58% of C. finmarchicus were infected near the coast, while 〈5% were infected several kilometers offshore. Ingestion rates of infected females were below detection limits and significantly lower than uninfected females. Blastodinium sp . -infected females showed characteristic symptoms of starvation, including lower respiration rates (implying a lower metabolic rate), production of smaller and fewer fecal pellets and significantly fewer eggs than uninfected females. A few females in this study were able to void the infection, however the extended period of starvation is likely to have longer-term repercussions on egg production rates well after the copepod clears the infection. The degree to which the infection affects C. finmarchicus recruitment depends on the extent of the spatial distribution of the infection. Monitoring of parasitic infection during routine field surveys will be required in order to clarify this.

Description: Assuming the generalized Riemann hypothesis, we prove a quantitative estimate for the number of simple zeros on the critical line for $L$ -functions attached to classical holomorphic newforms.

Description: In this paper, we consider a $\mathbb {Q}$ -Fano $3$ -fold weighted complete intersection of codimension $2$ in the $85$ families listed in Iano-Fletcher's list and determine which cycle is a maximal center or not. For each maximal center, we construct either a birational involution which untwists the maximal singularity or a Sarkisov link centered at the cycle to another explicitly described Mori fiber space. As a consequence, nineteen families are proved to be birationally rigid and the remaining $66$ families are proved to be birationally non-rigid.

Description: Suppose that a sequence of numbers $x_n$ (a ‘signal’) is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi _n$ , where $\xi _n$ is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space ${\mathscr {X}}$ of possible signals. Is it possible to fully recover the transmitted signal from its noisy version? Is it possible to at least detect that a non-zero signal was transmitted? In this paper, we consider the case in which signals are infinite sequences and the recovery or detection are required to hold with probability 1. We provide conditions on the space ${\mathscr {X}}$ for checking whether detection or recovery are possible. We also analyze in detail several examples including spaces of Fourier transforms of measures, spaces with fixed amplitudes and the space of almost periodic functions. Many of our examples exhibit critical phenomena, in which a sharp transition is made from a regime in which recovery is possible to a regime in which even detection is impossible.

Description: In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to the Dynkin case, we find out that the intersection of semi-stable subcategories may not be semi-stable. However, only a finite number of exceptions occur, and we give a description of these subcategories. Moreover, one can attach a simplicial fan in $\mathbb {Q}^n$ to any acyclic quiver $Q$ , and this simplicial fan allows one to completely determine the canonical presentation of any element in $\mathbb {Z}^n$ . This fan has a nice description in the Dynkin and Euclidean cases: it is described using an arrangement of convex codimension-1 subsets of $\mathbb {Q}^n$ , each such subset being indexed by a real Schur root or a set of quasi-simple objects. This fan also characterizes when two different stability conditions give rise to the same semi-stable subcategory.

Description: The $j$ -multiplicity plays an important role in the intersection theory of Stückrad–Vogel cycles, while recent developments confirm the connections between the $\epsilon$ -multiplicity and equisingularity theory. In this paper, we establish, under some constraints, a relationship between the $j$ -multiplicity of an ideal and the degree of its fiber cone. As a consequence, we are able to compute the $j$ -multiplicity of all the ideals defining rational normal scrolls. By using the standard monomial theory, we can also compute the $j$ - and $\epsilon$ -multiplicity of ideals defining determinantal varieties: The found quantities are integrals which, quite surprisingly, are central in random matrix theory.

Description: Let $\pi : X \to Y$ be a morphism of projective varieties and suppose that $\alpha $ is a pseudo-effective numerical cycle class satisfying $\pi _{*}\alpha =0$ . A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha $ is a limit of classes of effective cycles contracted by $\pi $ . We establish new cases of the conjecture for higher codimension cycles. In particular, we prove a strong version when $X$ is a fourfold and $\pi $ has relative dimension 1.

Description: Let $R$ be a group of prime order $r$ that acts on the $r'$ -group $G$ , let $RG$ be the semidirect product of $G$ with $R$ , let ${\mathbb {F}}$ be a field and $V$ be a faithful completely reducible $\mathbb {F}[{RG}]$ -module. Trivially, $C_{G}({R})$ acts on $C_{V}({R})$ . Let $K$ be the kernel of this action. What can be said about $K$ ? This question is considered when $G$ is soluble. It turns out that $K$ is subnormal in $G$ or $r$ is a Fermat or half-Fermat prime. In the latter cases, the subnormal closure of $K$ in $G$ is described. Several applications to the theory of automorphisms of soluble groups are given.

Description: The mono-epi (ME) exact structure on the morphisms of an exact category $(\mathcal {A}; \mathcal {E})$ is introduced and used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and Wakamatsu's Lemma for an exact category. Salce's Lemma establishes a bijective correspondence $\mathcal {I} \mapsto \mathcal {I}^{\perp }$ between the class of special precovering ideals of $(\mathcal {A}; \mathcal {E})$ and that of its special preenveloping ideals. ME-extensions of morphisms are used to define an extension $\mathcal {I} \diamond \mathcal {J}$ of ideals. Christensen's Lemma asserts that the class of special precovering (respectively, special preenveloping) ideals is closed under products and extensions and that the bijective correspondence of Salce's Lemma satisfies $(\mathcal {I} \mathcal {J})^{\perp } = \mathcal {J}^{\perp } \diamond \mathcal {I}^{\perp }$ and $(\mathcal {I} \diamond \mathcal {J})^{\perp } = \mathcal {J}^{\perp } \mathcal {I}^{\perp }.$ Wakamatsu's Lemma asserts that if a covering ideal $\mathcal {I}$ is closed under ME-extensions, then it is a special precovering ideal. As an application, it is proved that if $G$ is a finite group and $\Phi $ is the ideal of phantom morphisms in the category $k[G]$ - $\rm Mod,$ then $\Phi ^{n-1}$ is the object ideal generated by projective modules, where $n$ is the nilpotency index of the Jacobson radical $J.$ If $R$ is a semiprimary ring, with $J^n =0,$ then $\Phi ^n$ is generated by projective modules. For a right coherent ring $R$ over which every cotorsion left $R$ -module has a coresolution of length $n$ by pure injective modules, $\Phi ^{n+1}$ is generated by flat modules.

Description: We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics.

Description: Let $P_{n}(x)= \sum _{i=0}^n \xi _i x^i$ be a Kac random polynomial where the coefficients $\xi _i$ are i.i.d. copies of a given random variable $\xi $ . Our main result is an optimal quantitative bound concerning real roots repulsion. This leads to an optimal bound on the probability that there is a real double root. As an application, we consider the problem of estimating the number of real roots of $P_n$ , which has a long history and in particular was the main subject of a celebrated series of papers by Littlewood and Offord from the 1940s. We show, for a large and natural family of atom variables $\xi $ , that the expected number of real roots of $P_n(x)$ is exactly $({2}/{\pi }) \log n +C +o(1)$ , where $C$ is an absolute constant depending on the atom variable $\xi $ . Prior to this paper, such a result was known only for the case when $\xi $ is Gaussian.

Description: The goal of this article was to study the Iwasawa theory of an abelian variety $A$ that has complex multiplication by a complex multiplication (CM) field $F$ that contains the reflex field of $A$ , which has supersingular reduction at every prime above $p$ . To do so, we make use of the signed Coleman maps constructed in our companion article [Kâzım Büyükboduk and Antonio Lei, ‘Integral Iwasawa theory of motives for non-ordinary primes’, 2014, in preparation, draft available upon request] to introduce signed Selmer groups as well as a signed $p$ -adic $L$ -function via a reciprocity conjecture that we formulate for the (conjectural) Rubin–Stark elements (which is a natural extension of the reciprocity conjecture for elliptic units). We then prove a signed main conjecture relating these two objects. To achieve this, we develop along the way a theory of Coleman-adapted rank- $g$ Euler–Kolyvagin systems to be applied with Rubin–Stark elements and deduce the main conjecture for the maximal $\mathbb {Z}_p$ -power extension of $F$ for the primes failing the ordinary hypothesis of Katz.

Description: We introduce a notion of rough paths on embedded submanifolds and demonstrate that this class of rough paths is natural. On the way, we develop a notion of rough integration and an efficient and intrinsic theory of rough differential equations (RDEs) on manifolds. The theory of RDEs is then used to construct parallel translation along manifold-valued rough paths. Finally, this framework is used to show that there is a one-to-one correspondence between rough paths on a $d$ -dimensional manifold and rough paths on $d$ -dimensional Euclidean space. This last result is a rough path analogue of Cartan's development map and its stochastic version which was developed by Eells and Elworthy and Malliavin.

Description: We show that several important normal subgroups $\Gamma $ of the mapping class group of a surface satisfy the following property: any free, ergodic, probability measure-preserving action $\Gamma \curvearrowright X$ is stably $OE$ -superrigid. These include the central quotients of most surface braid groups and most Torelli groups and Johnson kernels. In addition, we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice-embeddings. Using these results in combination with previous results from Chifan–Ioana–Kida [‘ $W^*$ -superrigidity for arbitrary actions of central quotients of braid groups’, Math. Ann. 361 (2015) 925–959], we deduce that any free, ergodic, probability measure-preserving action of almost any surface braid group is stably $W^*$ -superrigid, that is, it can be completely reconstructed from its von Neumann algebra.

Description: Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting contractions on a finite-dimensional Hilbert space and studying their joint generalized eigenspaces. Non-tangential regularity of rational functions on the polydisk is also studied. One result states that rational inner functions on the polydisk have non-tangential limits at every point of the $n$ -torus. An algebraic characterization of higher non-tangential regularity is given. We also make some connections with the earlier material and prove that rational functions on the bidisk which are square integrable on the two-torus are non-tangentially bounded at every point. Several examples are provided.

Description: We propose a construction of a tensor exact category $\mathcal {F}_X^m$ of Artin–Tate motivic sheaves with finite coefficients $\mathbb {Z}/m$ over an algebraic variety $X$ (over a field $K$ of characteristic prime to $m$ ) in terms of étale sheaves of $\mathbb {Z}/m$ -modules over $X$ . Among the objects of $\mathcal {F}_X^m$ , in addition to the Tate motives $\mathbb {Z}/m(j)$ , there are the cohomological relative motives with compact support $\mathcal {M}_{cc}^m(Y/X)$ of varieties $Y$ quasi-finite over $X$ . Exact functors of inverse image with respect to morphisms of algebraic varieties and direct image with compact supports with respect to quasi-finite morphisms of varieties $Y\longrightarrow X$ act on the exact categories $\mathcal {F}_X^m$ . Assuming the existence of triangulated categories of motivic sheaves $\mathcal {D}\mathcal {M}(X,\mathbb {Z}/m)$ over algebraic varieties $X$ over $K$ and a weak version of the ‘six operations’ in these categories, we identify $\mathcal {F}_X^m$ with the exact subcategory in $\mathcal {D}\mathcal {M}(X,\mathbb {Z}/m)$ consisting of all the iterated extensions of the Tate twists $\mathcal {M}_{cc}^m(Y/X)(j)$ of the motives $\mathcal {M}_{cc}^m(Y/X)$ . An isomorphism of the $\mathbb {Z}/m$ -modules ${\rm Ext}$ between the Tate motives $\mathbb {Z}/m(j)$ in the exact category $\mathcal {F}_X^m$ with the motivic cohomology modules predicted by the Beilinson–Lichtenbaum étale descent conjecture (recently proved by Voevodsky, Rost et al. ) holds for smooth varieties $X$ over $K$ if and only if the similar isomorphism holds for Artin–Tate motives over fields containing $K$ . When $K$ contains a primitive $m$ -root of unity, the latter condition is equivalent to a certain Koszulity hypothesis, as shown in our previous paper [Positselski, ‘Mixed Artin–Tate motives with finite coefficients’, Mosc. Math. J. 11 (2011) 317–402].

Description: We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let $X$ be an arithmetic scheme (scheme of finite type over $\textbf {Z}$ ), and for a prime $p$ let $\zeta _{X_p}(s)$ be the local factor of its zeta function. We present an algorithm that computes $\zeta _{X_p}(s)$ for a single prime $p$ in time $p^{1/2+o(1)}$ , and another algorithm that computes $\zeta _{X_p}(s)$ for all primes $p 〈 N$ in time $N \log ^{3+o(1)} N$ . These generalise previous results of the author from hyperelliptic curves to completely arbitrary varieties.

Description: We undertake a systematic study of asymptotically hereditarily aspherical (AHA) groups, the class of groups introduced by Tadeusz Januszkiewicz and the second author as a tool for exhibiting exotic properties of systolic groups. We provide many new examples of AHA groups, also in high dimensions. We relate the AHA property with the topology at infinity of a group, and deduce in this way some new properties of (weakly) systolic groups. We also exhibit an interesting property of boundaries at infinity for a few classes of AHA groups.

Description: We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli space ${\overline {\mathcal M}}_{g,n}$ of stable genus $g$ curves with $n$ ordered marked points. In particular, we prove that codimension 2 boundary strata are extremal and exhibit extremal boundary strata of higher codimension. We also show that the locus of hyperelliptic curves with a marked Weierstrass point in ${\overline {\mathcal M}}_{3,1}$ and the locus of hyperelliptic curves in ${\overline {\mathcal M}}_4$ are extremal cycles. In addition, we exhibit infinitely many extremal codimension 2 cycles in ${\overline {\mathcal M}}_{1,n}$ for $n\geq 5$ and in ${\overline {\mathcal M}}_{2,n}$ for $n\geq 2$ .

Description: Knowledge of copepod in situ diet is critical for accurate assessment of trophic linkages and transfer efficiencies of the marine food web but is limited due to technical challenges. Here we report, using a recently developed eukaryote-universal copepod-excluding ectobiotic ciliate-blocking protocol, to investigate the natural diets of the copepods Temora turbinata , Subeucalanus subcrassus and Canthocalanus pauper in coastal waters in Sanya Bay, China. Analysis of the resultant 18S rDNA clone libraries revealed diverse diet composition for all the three copepod species, with 11 prey species for C. pauper , 9 for T. turbinata and 9 for S. subcrassus . The ingested materials included land plants, green algae, Metazoa, Euglenozoa and Rhizaria, although species numbers from each of these lineages differed. Broussonetia sp. (land plant), which might have been ingested in the form of pollen or fresh detritus were common among all three copepods, and accounted for a significant proportion (〉55%) of the clones sequenced. These results suggest that copepods in Sanya coastal waters might use terrigenous detritus as supplementary food sources when phytoplankton production is limited. However, the significance of the plant detritus as a nutrition source of these copepods remains to be determined by analyzing carbon-based proportion and digestion/assimilation rate of the ingested plant materials.

Description: Predation is considered an important source of mortality for plankton, but documenting variation in planktonic predation, particularly across interacting environmental cycles, remains logistically difficult, thus our understanding remains limited. To test for the combined effects of prey life history stage, diel or light level phase (including crepuscular periods) and seasonal upwelling on the risk of predation, we deployed tethered adult and larval brine shrimp Artemia franciscana using dock-based plankton tethering units (PTUs). Risk was higher overall during upwelling, but life history stage also interacted with season. There was no seasonal difference in risk for adults. Larvae were at significantly lower risk of predation during non-upwelling than during upwelling. Larvae were also at lower risk during non-upwelling than were adults during either season. During upwelling, there was no significant difference in risk between the two prey categories. With respect to the diel cycle, dusk was safer than daytime. For larvae, the diel pattern in risk remained consistent across seasons while risk for adults at night was slightly lower during upwelling than during non-upwelling. Variation in planktonic predation risk across diel and seasonal cycles differs for different life history stages and thus, generalizations fail to capture the complexity of interactions between factors.

Description: Protistan grazers and viruses are major agents of mortality in marine microbial communities with substantially different implications for food-web dynamics, carbon cycling and diversity maintenance. While grazers and viruses are typically studied independently, their impacts on microbial communities may be complicated by direct and indirect interactions of their mortality effects. Using a modification of the seawater dilution approach, we quantified growth and mortality rates for total phytoplankton and picophytoplankton populations ( Prochlorococcus , Synechococcus , picoeukaryotes) at four contrasting sites in the California Current Ecosystem. Grazing mortality was significant in 10 of 15 cases, while viral effects were significant for 2 cases. Nonetheless, mortality estimates for the entire phytoplankton community based on chlorophyll a were 38 ± 13% higher when viral effects were included, relative to grazing alone. Mortality estimates for picophytoplankton varied in space and among groups. We also explored a potential methodological constraint of this method and hypothesize that heterotrophic bacteria may be affected by the dilution of their growth-sustaining substrates. For all picophytoplankton, estimates of grazing and viral mortality were inversely related within and across experiments. Indirect interactions among grazers and viruses may be important to consider if there are tradeoffs in the grazing and virus resistance strategies of prey/host cells.

Description: Dispersal of native species from the regional pool can recover invaded communities to a pre-invaded state by supplementing declining populations or providing resistant species. However, dispersal may also exacerbate the negative effects of an invader. Introduced species can open or create new niche space, which could facilitate the establishment of competitors or predators that previously could not succeed in the uninvaded local community. To investigate the interaction between dispersal and invasion by a non-native consumer, we conducted a field mesocosm experiment that introduced zebra mussels into native zooplankton communities. Regional zooplankton were collected and added to both invaded and uninvaded communities. In uninvaded communities, zooplankton dispersal reduced cladoceran diversity by ~40%, rotifer abundance by ~65% and copepod nauplii abundance by ~80%. In invaded communities, dispersal increased cladoceran diversity by ~60%, but also further exacerbated the negative effects of zebra mussels on rotifer abundance. This experiment illustrates the potential for dispersal to both positively and negatively affect local communities, and how these effects may change with disturbance and the taxa or community metric of study.

Description: Pulse amplitude-modulated (PAM) fluorometry was used to obtain rapid light curves (RLCs) for phytoplankton from small Canadian lakes of varying water clarity, including metalimnetic communities from two clear lakes. RLCs were measured before and after exposure to a number of experimental spectra containing ultraviolet radiation (UVR) and photosynthetically active radiation (PAR). Photochemical (qP) and non-photochemical (NPQ) quenching during RLCs were positively and significantly correlated with recent in situ light history, but the maximum quantum efficiency of Photosystem II (α) and maximum relative rate of electron transport (rETR max ) were not. rETR max and α were diminished by experimental exposures to UVR and/or high PAR, but significantly less so in phytoplankton from brighter environments. UVR exposures diminished the inducible (photoprotective) NPQ of most epilimnetic phytoplankton. Both the inducible and total (photoprotective + photoinhibitory) NPQ of metalimnetic phytoplankton were stimulated by spectral exposures. Our results are the first obtained from natural communities of freshwater phytoplankton to show that aspects of PSII photophysiology (as inferred from RLCs) vary according to in situ light history.

Description: Inducible defenses are a common phenotypically plastic response to a heterogeneous predation risk. Once induced, these defenses cannot only lose their benefit, but even become costly, should the predator disappear. Consequently, some organisms have developed the ability to reverse their defensive traits. However, despite extensive research on inducible defenses, reports on reversibility are rare and mostly concentrate on defensive behavior. In our study, we investigated the reversibility of morphological defenses in the freshwater crustacean Daphnia barbata . This species responds to Notonecta glauca and Triops cancriformis with two distinctively defended morphotypes. Within the numerous defensive traits, we found both trait- and predator-specific reversibility. Body torsion and tail-spine-related traits were highly reversible, whereas helmet-related traits remained stable, suggesting different physiological constraints. However, in general, we found the defenses against Triops mostly reversible, while Notonecta -induced defenses were persistent and grew further, even in the absence of a predator.

Description: Marine phytoplankton are a taxonomically and functionally diverse group of organisms that are key players in the most important biogeochemical cycles. Phytoplankton taxa show different resource utilization strategies (e.g. nutrient-uptake rates and cellular allocation) and traits. Therefore, acknowledging this diversity is crucial to understanding how elemental cycles operate, including the origin and dynamics of elemental ratios. In this paper, we focus on trait-based models as tools to study the role of phytoplankton diversity in the stoichiometric phenomenology observed in the laboratory and in the open ocean. We offer a compilation of known empirical results on stoichiometry and summarize how trait-based approaches have attempted to replicate these results. By contrasting the different ecological and evolutionary approaches available in the literature, we explore the strengths and limitations of the existing models. We thus try to identify existing gaps and challenges, and point to potential new directions that can be explored to fill these gaps. We aim to highlight the potential of including diversity explicitly in our modeling approaches, which can help us gain important knowledge about changes in local and global stoichiometric patterns.

Description: Highly intermittent spatial variability of phytoplankton is observed ubiquitously in marine ecosystems, especially when measurements are performed at the micro-scale level. Therefore, theoretical developments and new modelling tools are required to understand the observed small-scale vertical structure and its relationship to ecosystem behaviour. Nearly all current ecosystem models are formulated entirely based on the mean field approximation, ignoring sub-grid scale variability. Even if such approximation may be reasonable for meso-scales (and above), it cannot account for micro-scale dynamics, which may also impact macroscopic properties at the larger scale. To consider intermittency of variables in plankton ecosystem models, we apply a newly developed modelling approach called the closure approach. Detailed simulations were conducted, combining fluid-dynamics of the 1D water column with the nutrient-phytoplankton closure ecosystem model for application to a site in the northern North Sea. Compared with a control model, which does not account for such intermittency, the closure model produced substantially different spatio-temporal patterns of mean phytoplankton biomass and growth rate, which depended on the overall level of variability. In this study, we (i) seek to explore the effects of sub-scale variability coupled with physical transport and (ii) begin to address the yet unresolved question of how to consistently model the advection and diffusion of the variances and co-variances used to represent sub-scale variability in the closure approach. Our results suggest that it may be necessary to account explicitly for the intermittent distribution of plankton and nutrients, even in large-scale biogeochemical models.

Description: Seawater viscosity is influenced by temperature as well as through excretion of exopolymers by some plankton. We examined the role of viscosity on the movement patterns and sensory abilities of the dinoflagellate Heterocapsa triquetra , manipulating the viscosity of seawater to simulate a 10 ± 1.5°C temperature change. In a second treatment, we seeded the water with microbeads to examine swimming behaviours in the presence of a mechanical stimulus. Increased viscosity reduced distances between conspecifics 4.7-fold and increased distances between protists and microbeads by 3.4-fold. Increased viscosity also affected other aspects of motility, with an overall reduction in swimming speed of 2.0- and 7.0-fold for treatments with and without mechanical stimuli. Higher viscosities were associated with upward vertical migration, in both the presence and absence of microbeads. Cells were highly sensitive to disturbances to the velocity field, by as little as 1.5%, and different approach distances of H. triquetra to conspecifics over mechanical stimuli suggest sensory capacity to distinguish types of particles. Mediation of motility and migratory behaviours through viscosity implies ramifications for the distribution of protists and their encounters with resources, predators and conspecifics triggered by events such as temperature changes and phytoplankton bloom events.

Description: In this paper, we consider the so-called Toda System in planar domains under Dirichlet boundary condition. We show the existence of continua of solutions for which one component is blowing-up at a certain number of points. The proofs use singular perturbation methods.

Description: According to the celebrated Jaworski theorem, a finite-dimensional aperiodic dynamical system $(X,T)$ embeds in the one-dimensional cubical shift $([0,1]{}^{\mathbb {Z}},\hbox {shift})$ . If $X$ admits periodic points (still assuming $\dim (X) 〈 \infty $ ), then we show in this paper that periodic dimension $\hbox {perdim}(X,T) 〈 {d}/{2}$ implies that $(X,T)$ embeds in the $d$ -dimensional cubical shift $(([0,1]^{d})^{\mathbb {Z}},\hbox {shift})$ . This verifies a conjecture by Lindenstrauss and Tsukamoto for finite-dimensional systems. Moreover, for an infinite-dimensional dynamical system, with the same periodic dimension assumption, the set of periodic points can be equivariantly immersed in $(([0,1]^{d})^{\mathbb {Z}},\hbox {shift})$ . Furthermore, we introduce a notion of markers for general topological dynamical systems, and use a generalized version of the Bonatti–Crovisier tower theorem, to show that an extension $(X,T)$ of an aperiodic finite-dimensional system whose mean dimension obeys $\hbox {mdim}(X,T) 〈 {d}/{16}$ embeds in the $(d+1)$ - cubical shift $(([0,1]^{d+1})^{\mathbb {Z}},\hbox {shift})$ .

Description: Beauville surfaces are an important kind of algebraic surfaces introduced by Catanese. They are rigid surfaces of general type defined over number fields. We prove that, for any $\sigma \in \mathrm {Gal}(\bar {\mathbb Q}/{\mathbb Q})$ different from the identity and the complex conjugation, there is a Beauville surface $S$ such that $S$ and its Galois conjugate $S^{\sigma }$ have non-isomorphic fundamental groups. This in turn easily implies that the action of $\mathrm {Gal}(\bar {\mathbb Q}/{\mathbb Q})$ on the set of isomorphism classes of Beauville surfaces is faithful. These results were conjectured by Bauer, Catanese and Grunewald, and immediately imply that $\mathrm {Gal}(\bar {\mathbb Q}/{\mathbb Q})$ acts faithfully on the connected components of the moduli space of surfaces of general type, a result due to the above-mentioned authors. These results on Beauville surfaces heavily depend on the fact that the absolute Galois group acts faithfully on regular dessins, a result that we prove in this paper. Moreover, we show the stronger result that the action is faithful on the set of quasiplatonic (or triangle) curves of any given hyperbolic type.

Description: It is elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are left inverses to complex geodesics. In the present article, we show that the same property holds for a three-point Pick problem on polydiscs, that is, the solution may be expressed in terms of 3-complex geodesics. Using this idea, we are able to obtain formulas and a uniqueness theorem for solutions of extremal problems. In particular, we determine a class of rational inner functions that solve the interpolation problem. Possible extensions and further investigations are also discussed.

Description: We prove that connected higher-rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces ${\mathcal E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as well. This generalizes the result of Lafforgue asserting that ${\rm SL}(3,\mathbb {R})$ has strong property (T) with respect to Hilbert spaces and the more recent result of the second-named author asserting that ${\rm SL}(3,\mathbb {R})$ has strong property (T) with respect to a certain larger class of Banach spaces. For the generalization to higher-rank groups, it is sufficient to prove strong property (T) for ${\rm Sp}(2,\mathbb {R})$ and its universal covering group. As consequences of our main result, it follows that for $X \in {\mathcal E}_{10}$ , connected higher-rank simple Lie groups and their lattices have property ( $\hbox {F}_X$ ) of Bader, Furman, Gelander and Monod, and that the expanders constructed from a lattice in a connected higher-rank simple Lie group do not admit a coarse embedding into $X$ .

Description: We study the action of ${\rm Gal}(\overline {\mathbb {Q}}/\mathbb {Q})$ on the category of Belyĭ functions (finite étale covers of $\mathbb {P}^1_{{\overline {\mathbb {Q}}}}\setminus \{0,1,\infty \}$ ). We describe a new combinatorial ${\rm Gal}(\overline {\mathbb {Q}}/\mathbb {Q})$ -invariant for Belyĭ functions whose monodromy cycle types above 0 and $\infty $ are the same. We use a version of our invariant to prove that ${\rm Gal}(\overline {\mathbb {Q}}/\mathbb {Q})$ acts faithfully on the set of Belyĭ functions whose monodromy cycle types above 0 and $\infty $ are the same; the proof of this result involves a version of Belyĭ's Theorem for meromorphic functions of odd degree. Using our invariant, we obtain that for all $k 〈 2^{\sqrt {\frac {2}{3}}}$ and all positive integers $N$ , there exists a positive integer $n \le N$ such that the set of degree $n$ Belyĭ functions of a particular rational Nielsen class must split into at least $\Omega (k^{\sqrt {N}})$ Galois orbits.

Description: In this paper, we find approximate solutions of certain Riemann–Hilbert boundary value problems for minimal surfaces in $\mathbb {R}^n$ and null holomorphic curves in $\mathbb {C}^n$ for any $n\ge 3$ . With this tool in hand, we construct complete conformally immersed minimal surfaces in $\mathbb {R}^n$ which are normalized by any given bordered Riemann surface and have Jordan boundaries. We also furnish complete conformal proper minimal immersions from any given bordered Riemann surface to any smoothly bounded, strictly convex domain of $\mathbb {R}^n$ which extend continuously up to the boundary; for $n\ge 5,$ we find embeddings with these properties.

Description: We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over $\mathbb {Z}_p^d$ -extensions of function fields ramifying at a finite set of places.