Search

Levels of selection and multilevel evolutionary processes are essential concepts in evolutionary theory, and yet there is a lack of common mathematical models for these core ideas. Here, we propose a unified mathematical framework for formulating and optimizing multilevel evolutionary processes and genetic algorithms over arbitrarily many levels based on concepts from category theory and population genetics. We formulate a multilevel version of the Wright-Fisher process using this approach, and we show that this model can be analyzed to clarify key features of multilevel selection. Particularly, we derive an extended multilevel probabilistic version of Price's Equation via the Kantorovich Monad, and we use this to characterize regimes of parameter space within which selection acts antagonistically or cooperatively across levels. Finally, we show how our framework can provide a unified setting for learning genetic algorithms (GAs), and we show how we can use a Variational Optimization and a multi-level analogue of coalescent analysis to fit multilevel GAs to simulated data., Comment: 18 pages, 3 figures

A major challenge in near-term quantum computing is its application to large real-world datasets due to scarce quantum hardware resources. One approach to enabling tractable quantum models for such datasets involves compressing the original data to manageable dimensions while still representing essential information for downstream analysis. In classical machine learning, variational autoencoders (VAEs) facilitate efficient data compression, representation learning for subsequent tasks, and novel data generation. However, no model has been proposed that exactly captures all of these features for direct application to quantum data on quantum computers. Some existing quantum models for data compression lack regularization of latent representations, thus preventing direct use for generation and control of generalization. Others are hybrid models with only some internal quantum components, impeding direct training on quantum data. To bridge this gap, we present a fully quantum framework, $\zeta$-QVAE, which encompasses all the capabilities of classical VAEs and can be directly applied for both classical and quantum data compression. Our model utilizes regularized mixed states to attain optimal latent representations. It accommodates various divergences for reconstruction and regularization. Furthermore, by accommodating mixed states at every stage, it can utilize the full-data density matrix and allow for a "global" training objective. Doing so, in turn, makes efficient optimization possible and has potential implications for private and federated learning. In addition to exploring the theoretical properties of $\zeta$-QVAE, we demonstrate its performance on representative genomics and synthetic data. Our results consistently indicate that $\zeta$-QVAE exhibits similar or better performance compared to matched classical models.

We present an operational semantics for the language MeTTa.

Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning algorithms are treated on a par with models as stochastic programs. Here, we offer a framework for representing and learning flexible PAC-Bayes bounds as stochastic programs using DPP-based methods. In particular, we show that DPP techniques may be leveraged to derive generalization bounds that draw on the compositionality of DPP representations. In turn, the bounds we introduce offer principled training objectives for higher-order probabilistic programs. We offer a definition of a higher-order generalization bound, which naturally encompasses single- and multi-task generalization perspectives (including transfer- and meta-learning) and a novel class of bound based on a learned measure of model complexity. Further, we show how modified forms of all higher-order bounds can be efficiently optimized as objectives for DPP training, using variational techniques. We test our framework using single- and multi-task generalization settings on synthetic and biological data, showing improved performance and generalization prediction using flexible DPP model representations and learned complexity measures., Comment: 19 pages, 2 figures

We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. This allows our approach to provide a convenient means of deriving synthetic denotational semantics for various type systems. Particularly, we derive bisimulations for pure type systems (PTS), and probabilistic dependent type systems (PDTS). We discuss further the relationship of PTS to non-well-founded set theory, and demonstrate the feasibility of our approach with an implementation of a bisimulation proof in a Guarded Cubical Type Theory type checker., Comment: 18 pages, 3 figures

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences., Comment: 22 pages, 3 figures, Perspective

A variety of methods have been proposed for interpreting nodes in deep neural networks, which typically involve scoring nodes at lower layers with respect to their effects on the output of higher-layer nodes (where lower and higher layers are closer to the input and output layers, respectively). However, we may be interested in picking out a prioritized collection of subsets of the inputs across a range of scales according to their importance for an output node, and not simply a prioritized ranking across the inputs as singletons. Such a situation may arise in biological applications, for instance, where we are interested in epistatic effects between groups of genes in determining a trait of interest. Here, we outline a flexible framework which may be used to generate multiscale network interpretations, using any previously defined scoring function. We demonstrate the ability of our method to pick out biologically important genes and gene sets in the domains of cancer and psychiatric genomics., Comment: Machine Learning for Health (ML4H) Workshop at NeurIPS 2018 arXiv:1811.07216

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated expression of modules (and module groups) of functionally related genes across the genome. Coregulation can also arise through the physical association of multi-gene complexes through chromosomal looping, which are then transcribed together. We present a general formalism for modeling coregulation rules in the framework of Random Boolean Networks (RBN), and develop specific models for transcription factor networks with modular structure (including module groups, and multi-input modules (MIM) with autoregulation) and multi-gene complexes (including hierarchical differentiation between multi-gene complex members). We develop a mean-field approach to analyse the stability of large networks incorporating coregulation, and show that autoregulated MIM and hierarchical gene-complex models can achieve greater stability than networks without coregulation whose rules have matching activation frequency. We provide further analysis of the stability of small networks of both kinds through simulations. We also characterize several general properties of the transients and attractors in the hierarchical coregulation model, and show using simulations that the steady-state distribution factorizes hierarchically as a Bayesian network in a Markov Jump Process analogue of the RBN model., Comment: 21 pages, 3 figures

We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). Our estimators generalize those typically used to calculate these statistics on point process data, allowing them to be calculated on RMs which assign continuous values to spatial regions, for instance to model protein intensity. The clustering index (H*) compares Ripley's H function calculated empirically to its distribution under complete spatial randomness (CSR), leading us to consider CSR null hypotheses for RMs which are not point-processes when generalizing this statistic. We thus consider restricted classes of completely random measures which can be simulated directly (Gamma processes and Marked Poisson Processes), as well as the general class of all CSR RMs, for which we derive an exact permutation-based H* estimator. We establish several properties of the estimators, including bounds on the accuracy of our general Ripley K estimator, its relationship to a previous estimator for the cross-correlation measure, and the relationship of our generalized H* estimator to previous statistics. To test the ability of our approach to identify spatial patterning, we use Fluorescent In Situ Hybridization (FISH) and Immunofluorescence (IF) data to probe for mRNA and protein subcellular localization patterns respectively in polarizing mouse fibroblasts on micropattened cells. We observe correlated patterns of clustering over time for corresponding mRNAs and proteins, suggesting a deterministic effect of mRNA localization on protein localization for several pairs tested, including one case in which spatial patterning at the mRNA level has not been previously demonstrated., Comment: 17 pages, 2 figures

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions., Comment: 15 pages

We have investigated the influence of electric field on tin whisker growth. Sputtered tin samples were exposed to electron radiation, and were subsequently found to have grown whiskers, while sister control samples did not exhibit whisker growth. Statistics on the whisker properties are reported. The results are considered encouraging for substantiating an electrostatic theory of whisker growth, and the technique offers promise for investigating early stages of whisker growth in general and establishing whisker-related accelerated life testing protocols., Comment: 4 pages, 5 figures