Fundamental polytopes of metric trees via parallel connections of matroids

We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. In this paper we consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.Comment: 20 pages, 2 Figures, 1 Table. Exposition improved, references and new results (last section) adde

Stationary distributions and condensation in autocatalytic CRN

We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first give explicitly product-form steady-state distributions for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency. Examples of interest in statistical mechanics (inclusion process), life sciences and robotics (collective decision making in ant and robot swarms) are provided. The product-form nature of the steady-state then enables the study of condensation in particle systems that are generalizations of the inclusion process.Comment: 25 pages. Some typos corrected, shortened some part

Impossibility results on stability of phylogenetic consensus methods

We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, "consensus" tree (say, a species tree). Various stability criteria have been explored in this context, seeking to model desirable consistency properties of consensus methods as the experimental data is updated (e.g., more taxa, or more trees, are mapped). However, such stability conditions can be incompatible with some basic regularity properties that are widely accepted to be essential in any meaningful consensus method. Here, we prove that such an incompatibility does arise in the case of extension stability on binary trees and in the case of associative stability. Our methods combine general theoretical considerations with the use of computer programs tailored to the given stability requirements

An algebraic approach to product-form stationary distributions for some reaction networks

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative ergodic CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.Comment: Accepted for publication in SIAM Journal on Applied Dynamical System

Stationary distributions and condensation in autocatalytic reaction networks

We investigate a broad family of stochastically modeled reaction networks by looking at their stationary distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first explicitly give product-form stationary distributions for a class of mostly non-weakly-reversible autocatalytic reaction networks of arbitrary deficiency. We provide examples of interest in statistical mechanics (inclusion process), life sciences, and robotics (collective decision making in ant and robot swarms). The product-form nature of the stationary distribution then enables the study of condensation in particle systems that are generalizations of the inclusion process

Bacteremia During the First Year After Solid Organ Transplantation: An Epidemiological Update.

BACKGROUND There are limited contemporary data on the epidemiology and outcomes of bacteremia in solid organ transplant recipients (SOTr). METHODS Using the Swiss Transplant Cohort Study registry from 2008 to 2019, we performed a retrospective nested multicenter cohort study to describe the epidemiology of bacteremia in SOTr during the first year post-transplant. RESULTS Of 4383 patients, 415 (9.5%) with 557 cases of bacteremia due to 627 pathogens were identified. One-year incidence was 9.5%, 12.8%, 11.4%, 9.8%, 8.3%, and 5.9% for all, heart, liver, lung, kidney, and kidney-pancreas SOTr, respectively (P = .003). Incidence decreased during the study period (hazard ratio, 0.66; P < .001). One-year incidence due to gram-negative bacilli (GNB), gram-positive cocci (GPC), and gram-positive bacilli (GPB) was 5.62%, 2.81%, and 0.23%, respectively. Seven (of 28, 25%) Staphylococcus aureus isolates were methicillin-resistant, 2/67 (3%) enterococci were vancomycin-resistant, and 32/250 (12.8%) GNB produced extended-spectrum beta-lactamases. Risk factors for bacteremia within 1 year post-transplant included age, diabetes, cardiopulmonary diseases, surgical/medical post-transplant complications, rejection, and fungal infections. Predictors for bacteremia during the first 30 days post-transplant included surgical post-transplant complications, rejection, deceased donor, and liver and lung transplantation. Transplantation in 2014-2019, CMV donor-negative/recipient-negative serology, and cotrimoxazole Pneumocystis prophylaxis were protective against bacteremia. Thirty-day mortality in SOTr with bacteremia was 3% and did not differ by SOT type. CONCLUSIONS Almost 1/10 SOTr may develop bacteremia during the first year post-transplant associated with low mortality. Lower bacteremia rates have been observed since 2014 and in patients receiving cotrimoxazole prophylaxis. Variabilities in incidence, timing, and pathogen of bacteremia across different SOT types may be used to tailor prophylactic and clinical approaches

Stationary distributions via decomposition of stochastic reaction networks

We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of stochastic reaction networks are only known in some cases. We analyze class properties of the underlying continuous-time Markov chain of CRNs under the operation of join and examine conditions such that the form of the stationary distributions of a CRN is derived from the parts of the decomposed CRNs. The conditions can be easily checked in examples and allow recursive application. The theory developed enables sequential decomposition of the Markov processes and calculations of stationary distributions. Since the class of processes expressible through such networks is big and only few assumptions are made, the principle also applies to other stochastic models. We give examples of interest from CRN theory to highlight the decomposition.Comment: 21 pages, exposition improve

Fast reactions with non-interacting species in stochastic reaction networks

We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction