arXiv subjects

Benjamin Allen

Publications and source records attributed to Benjamin Allen.

29 records · Page 2Linked to original sources

arXiv2017

Programmable Molecular Composites of Tandem Proteins with Graphene-Oxide for Efficient Bimoprh Actuators

The rapid expansion in the spectrum of two-dimensional (2D) materials has driven the efforts of research on the fabrication of 2D composites and heterostructures. Highly ordered structure of 2D materials provides an excellent platform for controlling the ultimate structure and properties of the composite material with precision. However, limited control over the structure of the adherent material and its interactions with highly ordered 2D materials results in defective composites with inferior performance. Here, we demonstrate the successful synthesis, integration, and characterization of hybrid 2D material systems consisting of tandem repeat (TR) proteins inspired by squid ring teeth and graphene oxide (GO). The TR protein layer acts as a unique programmable molecular spacer between GO layers. As an application, we further demonstrate thermal actuation using bimorph molecular composite films. Bimorph actuators made of molecular composite films (GO/TR) can lead to energy efficiencies 18 times higher than regular bimorph actuators consisting of a GO layer and a TR protein layer (i.e., conventional bulk composite of GO and TR). Additionally, molecular composite bimorph actuators can reach curvature values as high as 1.2 cm-1 by using TR proteins with higher molecular weight, which is 3 times higher than conventional GO and TR composites.

cond-mat.soft↗

arXiv2016

Evolutionary dynamics on any population structure

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class which suggests there is no efficient algorithm. Whether there exists a simple solution for weak selection was unanswered. Here we provide, surprisingly, a general formula for weak selection that applies to any graph or social network. Our method uses coalescent theory and relies on calculating the meeting times of random walks. We can now evaluate large numbers of diverse and heterogeneous population structures for their propensity to favor cooperation. We can also study how small changes in population structure---graph surgery---affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

q-bio.PE↗

arXiv2016

The limits of weak selection and large population size in evolutionary game theory

Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the wN limit, in which weak selection is applied before the large population limit, and the Nw limit, in which the order is reversed. Formal mathematical definitions of the Nw and wN limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the Nw and wN limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

q-bio.PE↗

arXiv2016

Critical shear rate and torque stability condition for a particle resting on a surface in a fluid flow

We advance a quantitative description of the critical shear rate $\dot{γ_c}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane experimental apparatus which enables measurement of $\dot{γ_c}$ over a wide range of particle Reynolds number $Re_p$ from $10^{-3}$ to $1.5 \times 10^3$. The condition to dislodge the particle is found to be consistent with the torque balance condition, which { yields a lower $\dot{γ_c}$ compared with} force balance because of the torque component due to drag about the particle center. The data for $Re_p < 0.5$ is in good agreement with analytical calculations of the drag and lift coefficients in the $Re_p \rightarrow 0$ limit. For higher $Re_p$, where analytical results are unavailable, the hydrodynamic coefficients are found to approach a constant for $Re_p > 1000$. We show that a linear combination of the hydrodynamic coefficients found in the viscous and inertial limits can describe the observed $\dot{γ_c}$ as a function of the particle and fluid properties.

cond-mat.soft↗

arXiv2016

Evolution of worker policing

Workers in insect societies are sometimes observed to kill male eggs of other workers, a phenomenon known as worker policing. We perform a mathematical analysis of the evolutionary dynamics of policing. We investigate the selective forces behind policing for both dominant and recessive mutations for different numbers of matings of the queen. The traditional, relatedness-based argument suggests that policing evolves if the queen mates with more than two males, but does not evolve if the queen mates with a single male. We derive precise conditions for the invasion and stability of policing alleles. We find that the relatedness-based argument is not robust with respect to small changes in colony efficiency caused by policing. We also calculate evolutionarily singular strategies and determine when they are evolutionarily stable. We use a population genetics approach that applies to dominant or recessive mutations of any effect size.

q-bio.PE↗

arXiv2016

Assortment and the evolution of cooperation in a Moran process with exponential fitness

We study the evolution of cooperation in a finite population interacting according to a simple model of like-with-like assortment. Evolution proceeds as a Moran process, and payoffs from the underlying cooperator-defector game are translated to positive fitnesses by an exponential transformation. These evolutionary dynamics can arise, for example, in a nest-structured population with rare migration. The use of the exponential transformation, rather than the usual linear one, is appropriate when interactions have multiplicative fitness effects, and allows for a tractable characterization of the effect of assortment on the evolution of cooperation. We define two senses in which a greater degree of assortment can favour the evolution of cooperation, the first stronger than the second: (i) greater assortment increases, at all population states, the probability that the number of cooperators increases, relative to the probability that the number of defectors increases; and (ii) greater assortment increases the fixation probability of cooperation, relative to that of defection. We show that, by the stronger definition, greater assortment favours the evolution of cooperation for a subset of cooperative dilemmas: prisoners' dilemmas, snowdrift games, stag-hunt games, and some prisoners' delight games. For other cooperative dilemmas, greater assortment favours cooperation by the weak definition, but not by the strong definition. Our results hold for any strength of selection.

q-bio.PE↗

arXiv2014

The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure

Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the mutation rate, $u$, at which they arise in individuals: $K=u$. This identity enables genetic sequence data to be used as a "molecular clock" to estimate the timing of evolutionary events. While the molecular clock is known to be perturbed by selection, it is thought that $K=u$ holds very generally for neutral evolution. Here we show that asymmetric spatial population structure can alter the molecular clock rate for neutral mutations, leading to either $K u$. Deviations from $K=u$ occur because mutations arise unequally at different sites and have different probabilities of fixation depending on where they arise. If birth rates are uniform across sites, then $K \leq u$. In general, $K$ can take any value between 0 and $Nu$. Our model can be applied to a variety of population structures. In one example, we investigate the accumulation of genetic mutations in the small intestine. In another application, we analyze over 900 Twitter networks to study the effect of network topology on the fixation of neutral innovations in social evolution.

q-bio.PE↗

arXiv2014

An Information-Theoretic Formalism for Multiscale Structure in Complex Systems

We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information theory. In the interest of flexibility we allow information to be quantified using any function, including Shannon entropy and Kolmogorov complexity, that satisfies certain fundamental axioms. Using these axioms, we formalize the notion of a dependency among components, and show how a system's structure is revealed in the amount of information assigned to each dependency. We explore quantitative indices that summarize system structure, providing a new formal basis for the complexity profile and introducing a new index, the "marginal utility of information". Using simple examples, we show how these indices capture intuitive ideas about structure in a quantitative way. Our formalism also sheds light on a longstanding mystery: that the mutual information of three or more variables can be negative. We discuss applications to complex networks, gene regulation, the kinetic theory of fluids and multiscale cybernetic thermodynamics.

cond-mat.stat-mech↗

arXiv2014

Stiffening solids with liquid inclusions

From bone and wood to concrete and carbon fibre, composites are ubiquitous natural and engineering materials. Eshelby's inclusion theory describes how macroscopic stress fields couple to isolated microscopic inclusions, allowing prediction of a composite's bulk mechanical properties from a knowledge of its microstructure. It has been extended to describe a wide variety of phenomena from solid fracture to cell adhesion. Here, we show experimentally and theoretically that Eshelby's theory breaks down for small liquid inclusions in a soft solid. In this limit, an isolated droplet's deformation is strongly size-dependent with the smallest droplets mimicking the behaviour of solid inclusions. Furthermore, in opposition to the predictions of conventional composite theory, we find that finite concentrations of small liquid inclusions enhance the stiffness of soft solids. A straight-forward extension of Eshelby's theory, accounting for the surface tension of the solid-liquid interface, explains our experimental observations. The counterintuitive effect of liquid-stiffening of solids is expected whenever droplet radii are smaller than an elastocapillary length, given by the ratio of the surface tension to Young's modulus of the solid matrix.

cond-mat.soft↗

arXiv2014

Optional games on cycles and complete graphs

We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by adopting loner strategies. Optional games lead to relaxed social dilemmas. Here we explore the interaction between spatial structure and optional games. We find that increasing the number of loner strategies (or equivalently increasing mutational bias toward loner strategies) facilitates evolution of cooperation both in well-mixed and in structured populations. We derive various limits for weak selection and large population size. For some cases we derive analytic results for strong selection. We also analyze strategy selection numerically for finite selection intensity and discuss combined effects of optionality and spatial structure.

q-bio.PE↗

arXiv2008

The Category-Theoretic Arithmetic of Information

We highlight the underlying category-theoretic structure of measures of information flow. We present an axiomatic framework in which communication systems are represented as morphisms, and information flow is characterized by its behavior when communication systems are combined. Our framework includes a variety of discrete, continuous, and, conjecturally, quantum information measures. It also includes some familiar mathematical constructs not normally associated with information, such as vector space dimension. We discuss these examples and prove basic results from the axioms.

math.CT↗