Bifurcation into functional niches in adaptation

One of the central questions in evolutionary biology concerns the dynamics of adaptation and diversification. This issue can be addressed experimentally if replicate populations adapting to identical environments Call be investigated in detail. We have studied 501 such replicas Using digital organisms adapting to at least two fundamentally different functional niches (survival strategies) present in the same environment: one in which fast replication is the way to live, and another where exploitation of the environment's complexity leads to complex organisms with longer life spans and smaller replication rates. While these two modes of survival are closely analogous to those expected to emerge in so-called r and K selection scenarios respectively, the bifurcation of evolutionary histories according to these functional niches occurs in identical environments, under identical selective pressures. We find that the branching occurs early, and leads to drastic phenotypic differences (in fitness, sequence length, and gestation time) that are permanent and irreversible. This study confirms an earlier experimental effort using microorganisms, in that diversification can be understood at least in part in terms of bifurcations on saddle points leading to peak shifts, as in the picture drawn by Sewall Wright

Parametric inference in the large data limit using maximally informative models

Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a representation R of that signal which is then observed through a noisy measurement M. From a large number of signals and measurements, we wish to infer the "filter" that maps S to R. However, the standard method for solving such problems, likelihood-based inference, requires perfect a priori knowledge of the "noise function" mapping R to M. In practice such noise functions are usually known only approximately, if at all, and using an incorrect noise function will typically bias the inferred filter. Here we show that, in the large data limit, this need for a pre-characterized noise function can be circumvented by searching for filters that instead maximize the mutual information I[M;R] between observed measurements and predicted representations. Moreover, if the correct filter lies within the space of filters being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the Data Processing Inequality. It is important to note that maximizing mutual information will typically leave a small number of directions in parameter space unconstrained. We term these directions "diffeomorphic modes" and present an equation that allows these modes to be derived systematically. The presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space, one that is obscured by standard likelihood-based inference.Comment: To appear in Neural Computatio

Correct ordering in the Zipf-Poisson ensemble

We consider a Zipf--Poisson ensemble in which X_i\sim\poi(Ni^{-\alpha}) for $\alpha>1$ and $N>0$ and integers $i\ge 1$. As $N\to\infty$ the first $n'(N)$ random variables have their proper order $X_1>X_2>...>X_{n'}$ relative to each other, with probability tending to 1 for $n'$ up to $(AN/\log(N))^{1/(\alpha+2)}$ for an explicit constant $A(\alpha)\ge 3/4$. The rate $N^{1/(\alpha+2)}$ cannot be achieved. The ordering of the first $n'(N)$ entities does not preclude $X_m>X_{n'}$ for some interloping $m>n'$. The first $n"$ random variables are correctly ordered exclusive of any interlopers, with probability tending to 1 if $n"\le (BN/\log(N))^{1/(\alpha+2)}$ for $B<A$. For a Zipf--Poisson model of the British National Corpus, which has a total word count of $100{,}000{,}000$, our result estimates that the 72 words with the highest counts are properly ordered

Chiral plasmons without magnetic field

Plasmons, the collective oscillations of interacting electrons, possess emergent properties that dramatically alter the optical response of metals. We predict the existence of a new class of plasmons -- chiral Berry plasmons (CBPs) -- for a wide range of two-dimensional metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electron-electron interactions yields chiral plasmonic modes at zero magnetic field. The CBP modes are confined to system boundaries, even in the absence of topological edge states, with chirality manifested in split energy dispersions for oppositely directed plasmon waves. We unveil a rich CBP phenomenology and propose setups for realizing them, including in anomalous Hall metals and optically-pumped 2D Dirac materials. Realization of CBPs will offer a new paradigm for magnetic field-free, sub-wavelength optical non-reciprocity, in the mid IR-THz range, with tunable splittings as large as tens of THz, as well as sensitive all-optical diagnostics of topological bands.Comment: 10 pgs, 3 fg

Energy-driven Drag at Charge Neutrality in Graphene

Coulomb coupling between proximal layers in graphene heterostructures results in efficient energy transfer between the layers. We predict that, in the presence of correlated density inhomogeneities in the layers, vertical energy transfer has a strong impact on lateral charge transport. In particular, for Coulomb drag it dominates over the conventional momentum drag near zero doping. The dependence on doping and temperature, which is different for the two drag mechanisms, can be used to separate these mechanisms in experiment. We predict distinct features such as a peak at zero doping and a multiple sign reversal, which provide diagnostics for this new drag mechanism.Comment: 6 pgs, 3 fg

Hierarchical modeling of molecular energies using a deep neural network

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over hierarchical terms. These terms are generated from a neural network--a composition of many nonlinear transformations--acting on a representation of the molecule. HIP-NN achieves state-of-the-art performance on a dataset of 131k ground state organic molecules, and predicts energies with 0.26 kcal/mol mean absolute error. With minimal tuning, our model is also competitive on a dataset of molecular dynamics trajectories. In addition to enabling accurate energy predictions, the hierarchical structure of HIP-NN helps to identify regions of model uncertainty

Methane cracking over cobalt molybdenum carbides

The catalytic behaviour of Co3Mo3C, Co6Mo6C, Co3Mo3N and Co6Mo6N for methane cracking has been studied to determine the relationship between the methane cracking activity and the chemical composition. The characterisation of post-reaction samples showed a complex phase composition with the presence of Co3Mo3C, α-Co and β-Mo2C as catalytic phases and the deposition of different forms of carbon during reaction

Finito: A Faster, Permutable Incremental Gradient Method for Big Data Problems

Recent advances in optimization theory have shown that smooth strongly convex finite sums can be minimized faster than by treating them as a black box "batch" problem. In this work we introduce a new method in this class with a theoretical convergence rate four times faster than existing methods, for sums with sufficiently many terms. This method is also amendable to a sampling without replacement scheme that in practice gives further speed-ups. We give empirical results showing state of the art performance