Compositional bisimulation metric reasoning with Probabilistic Process Calculi

We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of non-expansiveness) captures the essential nature of compositional reasoning and allows now also to reason compositionally about recursive processes. We characterize the distance between probabilistic processes composed by standard process algebra operators. Combining these results, we demonstrate how compositional reasoning about systems specified by continuous process algebra operators allows for metric assume-guarantee like performance validation

Alterations to the Gastrointestinal Microbiome Associated with Methamphetamine Use among Young Men who have Sex with Men.

Methamphetamine (MA) use is a major public health problem in the United States, especially among people living with HIV (PLWH). Many MA-induced neurotoxic effects are mediated by inflammation and gut microbiota may play a role in this process, yet the effects of MA on the microbiome have not been adequately explored. Therefore, we performed 16S rRNA gene sequencing on rectal swab samples from 381 men who have sex with men, 48% of whom were PLWH and 41% of whom used MA. We compared microbiome composition between MA users and non-users while testing for potential interactions with HIV and controlling for numerous confounders using inverse probability of treatment weighting. We found that MA use explained significant variation in overall composition (R2 = 0.005, p = 0.008) and was associated with elevated Finegoldia, Parvimonas, Peptoniphilus, and Porphyromonas and reduced Butyricicoccus and Faecalibacterium, among others. Genera including Actinomyces and Streptobacillus interacted with HIV status, such that they were increased in HIV+ MA users. Finegoldia and Peptoniphilus increased with increasing frequency of MA use, among others. In summary, MA use was associated with a microbial imbalance favoring pro-inflammatory bacteria, including some with neuroactive potential and others that have previously been associated with poor HIV outcomes

Linear Distances between Markov Chains

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results

Fixed-point Characterization of Compositionality Properties of Probabilistic Processes Combinators

Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127

Characterizing Intrinsic Compositionality in Transformers with Tree Projections

When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems like human languages? There is an apparent tension between compositional accounts of human language understanding, which are based on a restricted bottom-up computational process, and the enormous success of neural models like transformers, which can route information arbitrarily between different parts of their input. One possibility is that these models, while extremely flexible in principle, in practice learn to interpret language hierarchically, ultimately building sentence representations close to those predictable by a bottom-up, tree-structured model. To evaluate this possibility, we describe an unsupervised and parameter-free method to \emph{functionally project} the behavior of any transformer into the space of tree-structured networks. Given an input sentence, we produce a binary tree that approximates the transformer's representation-building process and a score that captures how "tree-like" the transformer's behavior is on the input. While calculation of this score does not require training any additional models, it provably upper-bounds the fit between a transformer and any tree-structured approximation. Using this method, we show that transformers for three different tasks become more tree-like over the course of training, in some cases unsupervisedly recovering the same trees as supervised parsers. These trees, in turn, are predictive of model behavior, with more tree-like models generalizing better on tests of compositional generalization.Comment: Fixed title and metadat

NetCoMi: network construction and comparison for microbiome data in R

MOTIVATION Estimating microbial association networks from high-throughput sequencing data is a common exploratory data analysis approach aiming at understanding the complex interplay of microbial communities in their natural habitat. Statistical network estimation workflows comprise several analysis steps, including methods for zero handling, data normalization and computing microbial associations. Since microbial interactions are likely to change between conditions, e.g. between healthy individuals and patients, identifying network differences between groups is often an integral secondary analysis step. Thus far, however, no unifying computational tool is available that facilitates the whole analysis workflow of constructing, analysing and comparing microbial association networks from high-throughput sequencing data. RESULTS Here, we introduce NetCoMi (Network Construction and comparison for Microbiome data), an R package that integrates existing methods for each analysis step in a single reproducible computational workflow. The package offers functionality for constructing and analysing single microbial association networks as well as quantifying network differences. This enables insights into whether single taxa, groups of taxa or the overall network structure change between groups. NetCoMi also contains functionality for constructing differential networks, thus allowing to assess whether single pairs of taxa are differentially associated between two groups. Furthermore, NetCoMi facilitates the construction and analysis of dissimilarity networks of microbiome samples, enabling a high-level graphical summary of the heterogeneity of an entire microbiome sample collection. We illustrate NetCoMi's wide applicability using data sets from the GABRIELA study to compare microbial associations in settled dust from children's rooms between samples from two study centers (Ulm and Munich). AVAILABILITY R scripts used for producing the examples shown in this manuscript are provided as supplementary data. The NetCoMi package, together with a tutorial, is available at https://github.com/stefpeschel/NetCoMi. CONTACT Tel:+49 89 3187 43258; [email protected]. SUPPLEMENTARY INFORMATION Supplementary data are available at Briefings in Bioinformatics online

Design Environments for Complex Systems

The paper describes an approach for modeling complex systems by hiding as much formal details as possible from the user, still allowing verification and simulation of the model. The interface is based on UML to make the environment available to the largest audience. To carry out analysis, verification and simulation we automatically extract process algebras specifications from UML models. The results of the analysis is then reflected back in the UML model by annotating diagrams. The formal model includes stochastic information to handle quantitative parameters. We present here the stochastic -calculus and we discuss the implementation of its probabilistic support that allows simulation of processes. We exploit the benefits of our approach in two applicative domains: global computing and systems biology

Compositionality for Quantitative Specifications

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations

Scalable methods for computing state similarity in deterministic Markov Decision Processes

We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong theoretical guarantees on differences in optimal behaviour. Unfortunately, their computation is expensive and requires a tabular representation of the states, which has thus far rendered them impractical for large problems. In this paper we present a new version of the metric that is tied to a behavior policy in an MDP, along with an analysis of its theoretical properties. We then present two new algorithms for approximating bisimulation metrics in large, deterministic MDPs. The first does so via sampling and is guaranteed to converge to the true metric. The second is a differentiable loss which allows us to learn an approximation even for continuous state MDPs, which prior to this work had not been possible.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20