Survival probabilities in time-dependent random walks

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical life-time of the walkers is found to decrease with an increment of the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.Comment: 4 pages, 3 figure

Survival Probabilities of History-Dependent Random Walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter \mu reaches a critical value \mu_c. For strong positive correlations, \mu > \mu_c, the survival probability is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in time (chain length).Comment: 3 pages, 2 figure

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

Brain microRNAs among social and solitary bees

Evolutionary transitions to a social lifestyle in insects are associated with lineage-specific changes in gene expression, but the key nodes that drive these regulatory changes are unknown. We examined the relationship between social organization and lineage-specific microRNAs (miRNAs). Genome scans across 12 bee species showed that miRNA copy-number is mostly conserved and not associated with sociality. However, deep sequencing of small RNAs in six bee species revealed a substantial proportion (20–35%) of detected miRNAs had lineage-specific expression in the brain, 24–72% of which did not have homologues in other species. Lineage-specific miRNAs disproportionately target lineage-specific genes, and have lower expression levels than shared miRNAs. The predicted targets of lineage-specific miRNAs are not enriched for genes with caste-biased expression or genes under positive selection in social species. Together, these results suggest that novel miRNAs may coevolve with novel genes, and thus contribute to lineage-specific patterns of evolution in bees, but do not appear to have significant influence on social evolution. Our analyses also support the hypothesis that many new miRNAs are purged by selection due to deleterious effects on mRNA targets, and suggest genome structure is not as influential in regulating bee miRNA evolution as has been shown for mammalian miRNAs

The Drosophila Gene CheB42a Is a Novel Modifier of Deg/ENaC Channel Function

Degenerin/epithelial Na+ channels (DEG/ENaC) represent a diverse family of voltage-insensitive cation channels whose functions include Na+ transport across epithelia, mechanosensation, nociception, salt sensing, modification of neurotransmission, and detecting the neurotransmitter FMRFamide. We previously showed that the Drosophila melanogaster Deg/ENaC gene lounge lizard (llz) is co-transcribed in an operon-like locus with another gene of unknown function, CheB42a. Because operons often encode proteins in the same biochemical or physiological pathway, we hypothesized that CHEB42A and LLZ might function together. Consistent with this hypothesis, we found both genes expressed in cells previously implicated in sensory functions during male courtship. Furthermore, when coexpressed, LLZ coprecipitated with CHEB42A, suggesting that the two proteins form a complex. Although LLZ expressed either alone or with CHEB42A did not generate ion channel currents, CHEB42A increased current amplitude of another DEG/ENaC protein whose ligand (protons) is known, acid-sensing ion channel 1a (ASIC1a). We also found that CHEB42A was cleaved to generate a secreted protein, suggesting that CHEB42A may play an important role in the extracellular space. These data suggest that CHEB42A is a modulatory subunit for sensory-related Deg/ENaC signaling. These results are consistent with operon-like transcription of CheB42a and llz and explain the similar contributions of these genes to courtship behavior

On the Necessary Memory to Compute the Plurality in Multi-Agent Systems

We consider the Relative-Majority Problem (also known as Plurality), in which, given a multi-agent system where each agent is initially provided an input value out of a set of $k$ possible ones, each agent is required to eventually compute the input value with the highest frequency in the initial configuration. We consider the problem in the general Population Protocols model in which, given an underlying undirected connected graph whose nodes represent the agents, edges are selected by a globally fair scheduler. The state complexity that is required for solving the Plurality Problem (i.e., the minimum number of memory states that each agent needs to have in order to solve the problem), has been a long-standing open problem. The best protocol so far for the general multi-valued case requires polynomial memory: Salehkaleybar et al. (2015) devised a protocol that solves the problem by employing $O(k 2^k)$ states per agent, and they conjectured their upper bound to be optimal. On the other hand, under the strong assumption that agents initially agree on a total ordering of the initial input values, Gasieniec et al. (2017), provided an elegant logarithmic-memory plurality protocol. In this work, we refute Salehkaleybar et al.'s conjecture, by providing a plurality protocol which employs $O(k^{11})$ states per agent. Central to our result is an ordering protocol which allows to leverage on the plurality protocol by Gasieniec et al., of independent interest. We also provide a $\Omega(k^2)$-state lower bound on the necessary memory to solve the problem, proving that the Plurality Problem cannot be solved within the mere memory necessary to encode the output.Comment: 14 pages, accepted at CIAC 201

The gut microbiome defines social group membership in honey bee colonies

In the honey bee, genetically related colony members innately develop colony-specific cuticular hydrocarbon profiles, which serve as pheromonal nestmate recognition cues. Yet, despite high intracolony relatedness, the innate development of colony-specific chemical signatures by individual colony members is largely determined by the colony environment, rather than solely relying on genetic variants shared by nestmates. Therefore, it is puzzling how a nongenic factor could drive the innate development of a quantitative trait that is shared by members of the same colony. Here, we provide one solution to this conundrum by showing that nestmate recognition cues in honey bees are defined, at least in part, by shared characteristics of the gut microbiome across individual colony members. These results illustrate the importance of host-microbiome interactions as a source of variation in animal behavioral traits

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Self-Gravitating Strings In 2+1 Dimensions

We present a family of classical spacetimes in 2+1 dimensions. Such a spacetime is produced by a Nambu-Goto self-gravitating string. Due to the special properties of three-dimensional gravity, the metric is completely described as a Minkowski space with two identified worldsheets. In the flat limit, the standard string is recovered. The formalism is developed for an open string with massive endpoints, but applies to other boundary conditions as well. We consider another limit, where the string tension vanishes in geometrical units but the end-masses produce finite deficit angles. In this limit, our open string reduces to the free-masses solution of Gott, which possesses closed timelike curves when the relative motion of the two masses is sufficiently rapid. We discuss the possible causal structures of our spacetimes in other regimes. It is shown that the induced worldsheet Liouville mode obeys ({\it classically}) a differential equation, similar to the Liouville equation and reducing to it in the flat limit. A quadratic action formulation of this system is presented. The possibility and significance of quantizing the self-gravitating string, is discussed.Comment: 55 page