Chains of large gaps between primes

Let $p_n$ denote the $n$-th prime, and for any $k \geq 1$ and sufficiently large $X$, define the quantity $$G_k(X) := \max_{p_{n+k} \leq X} \min( p_{n+1}-p_n, \dots, p_{n+k}-p_{n+k-1} ),$$ which measures the occurrence of chains of $k$ consecutive large gaps of primes. Recently, with Green and Konyagin, the authors showed that $$G_1(X) \gg \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for sufficiently large $X$. In this note, we combine the arguments in that paper with the Maier matrix method to show that $$G_k(X) \gg \frac{1}{k^2} \frac{\log X \log \log X\log\log\log\log X}{\log \log \log X}$$ for any fixed $k$ and sufficiently large $X$. The implied constant is effective and independent of $k$.Comment: 16 pages, no figure

Content, cost and context: a framework for understanding human signaling systems

Humans frequently perform extravagant and seemingly costly behaviors, such as widely sharing hunted resources, erecting conspicuous monumental structures, and performing dramatic acts of religious devotion. Evolutionary anthropologists and archeologists have used signaling theory to explain the function of such displays, drawing inspiration from behavioral ecology, economics, and the social sciences. While signaling theory is broadly aimed at explaining honest communication, it has come to be strongly associated with the handicap principle, which proposes that such costly extravagance is in fact an adaptation for signal reliability. Most empirical studies of signaling theory have focused on obviously costly acts, and consequently anthropologists have likely overlooked a wide range of signals that also promote reliable communication. Here, we build on recent developments in signaling theory and animal communication, developing an updated framework that highlights the diversity of signal contents, costs, contexts, and reliability mechanisms present within human signaling systems. By broadening the perspective of signaling theory in human systems, we strive to identify promising areas for further empirical and theoretical work

Evolutionary connectionism: algorithmic principles underlying the evolution of biological organisation in evo-devo, evo-eco and evolutionary transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions

Integrating personality research and animal contest theory: aggressiveness in the green swordtail <i>Xiphophorus helleri</i>

&lt;p&gt;Aggression occurs when individuals compete over limiting resources. While theoretical studies have long placed a strong emphasis on context-specificity of aggression, there is increasing recognition that consistent behavioural differences exist among individuals, and that aggressiveness may be an important component of individual personality. Though empirical studies tend to focus on one aspect or the other, we suggest there is merit in modelling both within-and among-individual variation in agonistic behaviour simultaneously. Here, we demonstrate how this can be achieved using multivariate linear mixed effect models. Using data from repeated mirror trials and dyadic interactions of male green swordtails, &lt;i&gt;Xiphophorus helleri&lt;/i&gt;, we show repeatable components of (co)variation in a suite of agonistic behaviour that is broadly consistent with a major axis of variation in aggressiveness. We also show that observed focal behaviour is dependent on opponent effects, which can themselves be repeatable but were more generally found to be context specific. In particular, our models show that within-individual variation in agonistic behaviour is explained, at least in part, by the relative size of a live opponent as predicted by contest theory. Finally, we suggest several additional applications of the multivariate models demonstrated here. These include testing the recently queried functional equivalence of alternative experimental approaches, (e. g., mirror trials, dyadic interaction tests) for assaying individual aggressiveness.&lt;/p&gt

Bayesian modeling of recombination events in bacterial populations

Background: We consider the discovery of recombinant segments jointly with their origins within multilocus DNA sequences from bacteria representing heterogeneous populations of fairly closely related species. The currently available methods for recombination detection capable of probabilistic characterization of uncertainty have a limited applicability in practice as the number of strains in a data set increases. Results: We introduce a Bayesian spatial structural model representing the continuum of origins over sites within the observed sequences, including a probabilistic characterization of uncertainty related to the origin of any particular site. To enable a statistically accurate and practically feasible approach to the analysis of large-scale data sets representing a single genus, we have developed a novel software tool (BRAT, Bayesian Recombination Tracker) implementing the model and the corresponding learning algorithm, which is capable of identifying the posterior optimal structure and to estimate the marginal posterior probabilities of putative origins over the sites. Conclusion: A multitude of challenging simulation scenarios and an analysis of real data from seven housekeeping genes of 120 strains of genus Burkholderia are used to illustrate the possibilities offered by our approach. The software is freely available for download at URL http://web.abo.fi/fak/ mnf//mate/jc/software/brat.html

Evolutionary Games with Affine Fitness Functions: Applications to Cancer

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com, http://dx.doi.org/10.1007/s13235-011-0029-

(De)synchronization of advanced visual information and ball flight characteristics constrains emergent information–movement couplings during one-handed catching

Advance visual information of a projection action and ball flight information is important for organizing dynamic interceptive actions like catching. However, how the central nervous system (CNS) manages the relationship between advance visual information and emerging ball flight information in regulating behavior is less well understood. Here, we sought to examine the extent that advance visual information to the CNS constrains regulation of catching actions by synchronizing and desynchronizing its relationship with ball trajectory characteristics. Novel technology was used to present video footage of an actor throwing a ball at three different speeds, integrated with information from a real ball projected by a machine set to the three speeds. The technology enabled three synchronized and six desynchronized conditions between advance visual information and subsequent ball flight trajectories. Catching performance, kinematic data from the catching hand and gaze behaviors were recorded. Findings revealed that desynchronization of video images of ball projection shaped emergent catching behaviors. Footage of slower throws, paired with faster ball projection speeds, caused catching performance decrements. Timing in early phases of action was organized by the CNS to match the advance visual information presented. In later phases, like the grasp, ball flight information constraints adapted and regulated behaviors. Gaze behaviors showed increased ball projection speed resulted in participants tracking the ball for a smaller percentage of ball flight. Findings highlighted the role of the two visual systems in perception and action, implicating the importance of coupling advanced visual information and ball flight to regulate emergent movement coordination tendencies during interceptive behaviors

Aurora kinase A drives the evolution of resistance to third-generation EGFR inhibitors in lung cancer.

Although targeted therapies often elicit profound initial patient responses, these effects are transient due to residual disease leading to acquired resistance. How tumors transition between drug responsiveness, tolerance and resistance, especially in the absence of preexisting subclones, remains unclear. In epidermal growth factor receptor (EGFR)-mutant lung adenocarcinoma cells, we demonstrate that residual disease and acquired resistance in response to EGFR inhibitors requires Aurora kinase A (AURKA) activity. Nongenetic resistance through the activation of AURKA by its coactivator TPX2 emerges in response to chronic EGFR inhibition where it mitigates drug-induced apoptosis. Aurora kinase inhibitors suppress this adaptive survival program, increasing the magnitude and duration of EGFR inhibitor response in preclinical models. Treatment-induced activation of AURKA is associated with resistance to EGFR inhibitors in vitro, in vivo and in most individuals with EGFR-mutant lung adenocarcinoma. These findings delineate a molecular path whereby drug resistance emerges from drug-tolerant cells and unveils a synthetic lethal strategy for enhancing responses to EGFR inhibitors by suppressing AURKA-driven residual disease and acquired resistance

Evolvable Neuronal Paths: A Novel Basis for Information and Search in the Brain

We propose a previously unrecognized kind of informational entity in the brain that is capable of acting as the basis for unlimited hereditary variation in neuronal networks. This unit is a path of activity through a network of neurons, analogous to a path taken through a hidden Markov model. To prove in principle the capabilities of this new kind of informational substrate, we show how a population of paths can be used as the hereditary material for a neuronally implemented genetic algorithm, (the swiss-army knife of black-box optimization techniques) which we have proposed elsewhere could operate at somatic timescales in the brain. We compare this to the same genetic algorithm that uses a standard ‘genetic’ informational substrate, i.e. non-overlapping discrete genotypes, on a range of optimization problems. A path evolution algorithm (PEA) is defined as any algorithm that implements natural selection of paths in a network substrate. A PEA is a previously unrecognized type of natural selection that is well suited for implementation by biological neuronal networks with structural plasticity. The important similarities and differences between a standard genetic algorithm and a PEA are considered. Whilst most experiments are conducted on an abstract network model, at the conclusion of the paper a slightly more realistic neuronal implementation of a PEA is outlined based on Izhikevich spiking neurons. Finally, experimental predictions are made for the identification of such informational paths in the brain