arXiv subjects

Chuang Xu

Publications and source records attributed to Chuang Xu.

At least 37 records · Page 2Linked to original sources

arXiv2023

The asymptotic tails of limit distributions of continuous time Markov chains

This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity nor moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth-death processes. The approach together with the identities easily extends to discrete time Markov chains.

math.PR↗

arXiv2023

Implementation and performances of the IPbus protocol for the JUNO Large-PMT readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a large neutrino detector currently under construction in China. Thanks to the tight requirements on its optical and radio-purity properties, it will be able to perform leading measurements detecting terrestrial and astrophysical neutrinos in a wide energy range from tens of keV to hundreds of MeV. A key requirement for the success of the experiment is an unprecedented 3% energy resolution, guaranteed by its large active mass (20 kton) and the use of more than 20,000 20-inch photo-multiplier tubes (PMTs) acquired by high-speed, high-resolution sampling electronics located very close to the PMTs. As the Front-End and Read-Out electronics is expected to continuously run underwater for 30 years, a reliable readout acquisition system capable of handling the timestamped data stream coming from the Large-PMTs and permitting to simultaneously monitor and operate remotely the inaccessible electronics had to be developed. In this contribution, the firmware and hardware implementation of the IPbus based readout protocol will be presented, together with the performances measured on final modules during the mass production of the electronics.

physics.ins-det↗

arXiv2023

Classification and threshold dynamics of stochastic reaction networks

Stochastic reaction networks (SRNs) provide models of many real-world networks. Examples include networks in epidemiology, pharmacology, genetics, ecology, chemistry, and social sciences. Here, we model stochastic reaction networks by continuous time Markov chains (CTMCs) and pay special attention to one-dimensional mass-action SRNs (1-d stoichiometric subspace). We classify all states of the underlying CTMC of 1-d SRNs. In terms of (up to) four parameters, we provide sharp checkable criteria for various dynamical properties (including explosivity, recurrence, ergodicity, and the tail asymptotics of stationary or quasi-stationary distributions) of SRNs in the sense of their underlying CTMCs. As a result, we prove that all 1-d endotactic networks are non-explosive, and positive recurrent with an ergodic stationary distribution with Conley-Maxwell-Poisson (CMP)-like tail, provided the state space of the associated CTMCs consists of closed communicating classes. In particular, we prove the recently proposed positive recurrence conjecture in one dimension: Weakly reversible mass-action SRNs with 1-d stoichiometric subspaces are positive recurrent. The proofs of the main results rely on our recent work on CTMCs with polynomial transition rate functions.

math.PR↗

arXiv2023

Mass testing of the JUNO experiment 20-inch PMTs readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose, large size, liquid scintillator experiment under construction in China. JUNO will perform leading measurements detecting neutrinos from different sources (reactor, terrestrial and astrophysical neutrinos) covering a wide energy range (from 200 keV to several GeV). This paper focuses on the design and development of a test protocol for the 20-inch PMT underwater readout electronics, performed in parallel to the mass production line. In a time period of about ten months, a total number of 6950 electronic boards were tested with an acceptance yield of 99.1%.

physics.ins-det↗

arXiv2022

Validation and integration tests of the JUNO 20-inch PMTs readout electronics

The Jiangmen Underground Neutrino Observatory (JUNO) is a large neutrino detector currently under construction in China. JUNO will be able to study the neutrino mass ordering and to perform leading measurements detecting terrestrial and astrophysical neutrinos in a wide energy range, spanning from 200 keV to several GeV. Given the ambitious physics goals of JUNO, the electronic system has to meet specific tight requirements, and a thorough characterization is required. The present paper describes the tests performed on the readout modules to measure their performances.

physics.ins-det↗

arXiv2022

Dark Energy from the Fifth Dimension

After extending the Regge-Teitelboim formulation of gravity to include the case where the background embedding space is not flat, we examine the dynamics of the four-dimensional $k=0$ Robertson-Walker (RW) manifold embedded in various five-dimensional backgrounds. We find that when the background is five-dimensional de Sitter space, the RW manifold undergoes a transition from a de-accelerating phase to an accelerating phase. This occurs before the inclusion of matter, radiation or cosmological constant sources, and thus does not require a balance of different components. We obtain a reasonable two-parameter fit of this model to the Hubble parameter data.

gr-qc↗

arXiv2022

Cosmic acceleration in Regge-Teitelboim gravity

The Regge-Teitelboim formulation of gravity, which utilizes dynamical embeddings in a background space, effectively introduces source terms in the standard Einstein equations that are not attributable to the energy-momentum tensor. We show that for a simple class of embeddings of the Robertson-Walker metric, these source terms naturally generate cosmic acceleration.

gr-qc↗

arXiv2021

Structural classification of continuous time Markov chains with applications

This paper is motivated by examples from stochastic reaction network theory. The $Q$-matrix of a stochastic reaction network can be derived from the reaction graph, an edge-labelled directed graph encoding the jump vectors of an associated continuous time Markov chain on the invariant space $\mathbb{N}^d_0$. An open question is how to decompose the space $\mathbb{N}^d_0$ into neutral, trapping, and escaping states, and open and closed communicating classes, and whether this can be done from the reaction graph alone. Such general continuous time Markov chains can be understood as natural generalizations of birth-death processes, incorporating multiple different birth and death mechanisms. We characterize the structure of $\mathbb{N}^d_0$ imposed by a general $Q$-matrix generating continuous time Markov chains with values in $\mathbb{N}^d_0$, in terms of the set of jump vectors and their corresponding transition rate functions. Thus the setting is not limited to stochastic reaction networks. Furthermore, we define structural equivalence of two $Q$-matrices, and provide sufficient conditions for structural equivalence. Examples are abundant in applications. We apply the results to stochastic reaction networks, a Lotka-Volterra model in ecology, the EnvZ-OmpR system in systems biology, and a class of extended branching processes, none of which are birth-death processes.

math.PR↗

arXiv2021

Vlasov equations on digraph measures

Many science phenomena are described as interacting particle systems (IPS). The mean field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution of a PDE, the Vlasov Equation (VE). Yet, many applications demand IPS coupled on networks/graphs. It is interesting to know, how the limit of a sequence of digraphs associated with the IPS influences the macroscopic MFL. This paper studies VEs on a generalized digraph, regarded as limit of a sequence of digraphs, which we refer to as a digraph measure (DGM) to emphasize that we work with its limit via measures. We provide well-posedness and discretization of the solution of the VE by empirical distributions supported on solutions of an IPS via ODEs coupled on a sequence of digraphs converging to the given DGM. Our result extends existing results on one-dimensional Kuramoto-type networks coupled on dense graphs. Here we allow the underlying digraphs to be not necessarily dense which include many interesting graphical structures such that stars, trees and rings, which have been frequently used in many sparse network models in finance, telecommunications, physics, genetics, neuroscience, and social sciences. A key contribution of this paper is a nontrivial generalization of Neunzert's in-cell-particle approach for all-to-all coupled indistinguishable IPS with global Lipschitz continuity in Euclidean spaces to distinguishable IPS on heterogeneous digraphs with local Lipschitz continuity, via a measure-theoretic viewpoint. The approach together with the metrics is different from the known techniques in $L^p$-functions using graphons and their generalization via harmonic analysis of locally compact Abelian groups. Finally, to demonstrate the wide applicability, we apply our results to various models in higher-dimensional Euclidean spaces in epidemiology, ecology, and social sciences.

math.AP↗

arXiv2021

Full classification of dynamics for one-dimensional continuous time Markov chains with polynomial transition rates

This paper provides full classification of dynamics for continuous time Markov chains (CTMCs) on the non-negative integers with polynomial transition rate functions. Such stochastic processes are abundant in applications, in particular in biology. More precisely, for CTMCs of bounded jumps, we provide necessary and sufficient conditions in terms of calculable parameters for explosivity, recurrence vs transience, certain absorption, positive recurrence vs null recurrence, and implosivity. Simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions as well as existence and non-existence of moments of hitting times are also obtained. Similar simple sufficient conditions for the aforementioned dynamics together with their opposite dynamics are established for CTMCs with unbounded jumps. The results generalize respective criteria for birth-death processes by Karlin and McGregor in the 1960s. Finally, we apply our results to stochastic reaction networks, an extended class of branching processes, a general bursty single-cell stochastic gene expression model, and population processes, none of which are birth-death processes. The approach is based on a mixture of Lyapunov-Foster type results, semimartingale approach, as well as estimates of stationary measures.

math.PR↗

arXiv2021

Continuum Limits for Adaptive Network Dynamics

Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamical behavior. Even though adaptivity can improve the modelling of collective phenomena, it often complicates the analysis of the corresponding mathematical models significantly. For non-adaptive systems, a possible way to tackle this problem is by passing to so-called continuum or mean-field limits, which describe the system in the limit of infinitely many nodes. Although fully adaptive network dynamic models have been used a lot in recent years in applications, we are still lacking a detailed mathematical theory for large-scale adaptive network limits. For example, continuum limits for static or temporal networks are already established in the literature for certain models, yet the continuum limit of fully adaptive networks has been open so far. In this paper we introduce and rigorously justify continuum limits for sequences of adaptive Kuramoto-type network models. The resulting integro-differential equations allow us to incorporate a large class of co-evolving graphs with high density. Furthermore, we use a very general measure-theoretical framework in our proof for representing the (infinite) graph limits, thereby also providing a structural basis to tackle even larger classes of graph limits. As an application of our theory, we consider the continuum limit of an adaptive Kuramoto model directly motivated from neuroscience and studied by Berner et al.~in recent years using numerical techniques and formal stability analysis.

math.DS↗

arXiv2021

Fiber decomposition of deterministic reaction networks with applications

Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology, genetics, epidemiology, and social sciences. In this chapter we propose a new type of decomposition of RNs, called fiber decomposition. Using this decomposition, we establish lifting of mass-action RNs preserving stationary properties, including multistationarity and absolute concentration robustness. Such lifting scheme is simple and explicit which imposes little restriction on the reaction networks. We provide examples to illustrate how this lifting can be used to construct RNs preserving certain dynamical properties.

q-bio.MN↗

arXiv2020

Asymptotic commutativity of quantized spaces: the case of $\mathbb{CP}^{p,q}$

We present a procedure for quantizing complex projective spaces $\mathbb{CP}^{p,q}$, $q\ge 1$, as well as construct relevant star products on these spaces. The quantization is made unique with the demand that it preserves the full isometry algebra of the metric. Although the isometry algebra, namely $su(p+1,q)$, is preserved by the quantization, the Killing vectors generating these isometries pick up quantum corrections. The quantization procedure is an extension of one applied recently to Euclidean $AdS_2$, where it was found that all quantum corrections to the Killing vectors vanish in the asymptotic limit, in addition to the result that the star product trivializes to pointwise product in the limit. In other words, the space is asymptotically anti-de Sitter making it a possible candidate for the $AdS/CFT$ correspondence principle. In this article, we find indications that the results for quantized Euclidean $AdS_2$ can be extended to quantized $\mathbb{CP}^{p,q}$, i.e., noncommutativity is restricted to a limited neighborhood of some origin, and these quantum spaces approach $\mathbb{CP}^{p,q}$ in the asymptotic limit.

hep-th↗

arXiv2020

Dynamics of continuous time Markov chains with applications

This paper contributes an in-depth study of properties of continuous time Markov chains (CTMCs) on non-negative integer lattices $\N_0^d$, with particular interest in one-dimensional CTMCs with polynomial transitions rates. Such stochastic processes are abundant in applications, in particular in biology. We characterize the structure of the state space of general CTMCs on $\N_0^d$ in terms of the set of jump vectors and their corresponding transition rate functions. For CTMCs on $\N_0$ with polynomial transition rate functions, we provide threshold criteria in terms of easily computable parameters for various dynamical properties such as explosivity, recurrence, transience, certain absorption, positive/null recurrence, implosivity, and existence and non-existence of moments of hitting times. In particular, simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions are obtained, and the few gap cases are well-illustrated by examples. Subtle differences in conditions for different dynamical properties are revealed in terms of examples. Finally, we apply our results to stochastic reaction networks, an extended class of branching processes, a general bursty single-cell stochastic gene expression model, and population processes which are not birth-death processes.

math.PR↗

arXiv2019

Distributional asymptotics mod 1 of $(\log_bn)$

This paper studies the distributional asymptotics of the slowly changing sequence of logarithms $(\log_bn)$ with $b\in\mathbb{N}\setminus\{1\}.$ It is known that $(\log_bn)$ is not uniformly distributed modulo one, and its omega limit set is composed of a family of translated exponential distributions with constant $\log b.$ An improved upper estimate $\left(\sqrt{\log N}/N\right)$ is obtained for the rate of convergence with respect to (w.r.t.) the Kantorovich metric on the circle, compared to the general results on rates of convergence for a class of slowly changing sequences in the author's companion in-progress work. Moreover, a sharp rate of convergence $\left(\log N/N\right)$ w.r.t. the Kantorovich metric on the interval $[0,1]$, is derived. As a byproduct, the rate of convergence w.r.t. the discrepancy metric (or the Kolmogorov metric) turns out to be $\left(\log N/N\right)$ as well, which verifies that an upper bound for this rate derived in [Y. Ohkubo and O. Strauch, Distribution of leading digits of numbers, Unif. Distrib. Theory, $\textbf{11}$ (2016), no.1, 23--45.] is sharp.

math.NT↗

arXiv2019

Best finite constrained approximations of one-dimensional probabilities

This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are prescribed. Necessary and sufficient optimality conditions are established, and the rate of convergence (as the number of atoms goes to infinity) is discussed. In view of emerging mathematical and statistical applications, special attention is given to the case of best uniform approximations (i.e., all atoms having equal weight). The approach developed in this paper is elementary; it is based on best approximations of (monotone) $L^r$-functions by step functions, and thus different from, yet naturally complementary to, the classical Voronoi partition approach.

math.PR↗

arXiv2018

Signature change in matrix model solutions

Various classical solutions to lower dimensional IKKT-like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature change is found to be a common feature of these manifolds when quadratic and cubic terms are included in the bosonic action. In fact, a single manifold may exhibit multiple signature changes. Regions with Lorentzian signature may serve as toy models for cosmological space-times, complete with cosmological singularities, occurring at the signature change. The singularities are resolved away from the commutative limit. Toy models of open and closed cosmological space-times are given in two and four dimensions. The four dimensional cosmologies are constructed from non-commutative complex projective spaces, and they are found to display a rapid expansion near the initial singularity.

hep-th↗

arXiv2018

The asymptotics of purely atomic one-dimensional Levy approximations

For arbitrary Borel probability measures on the real line, necessary and sufficient conditions are presented that characterize best purely atomic approximations relative to the classical Levy probability metric, given any number of atoms, and allowing for additional constraints regarding locations or weights of atoms. The precise asymptotics (as the number of atoms goes to infinity) of the approximation error is identified for the important special cases of best uniform (i.e., all atoms having equal weight) and best (unconstrained) approximations, respectively. When compared to similar results known for other probability metrics, the results for Levy approximations are more complete and require fewer assumptions.

math.PR↗