Class Of Chains Research Articles

Symmetry-enforced planar nodal chain phonons in non-symmorphic materials

Nodal chains in which two nodal rings connect at one point were recently discovered in non-symmorphic electronic systems and then generalized to symmorphic phononic systems. In this work, we identify a new class of planar nodal chains in non-symmorphic phononic systems, where the connecting rings lie in the same plane. The constituting nodal rings are protected by mirror symmetry, and their intersection is guaranteed by the combination of time-reversal and non-symmorphic twofold screw symmetry. The connecting points are fourfold degenerate while those in previous works are twofold degenerate. We found 8 out of 230 space groups that can host the proposed planar nodal chain phonons. Taking wurtzite GaN (space group No. 186) as an example, the planar nodal chain is confirmed by first-principles calculations. The planar nodal chains result in two distinct classes of drumhead surface states on the [10(–1)0] and the [0001] surface Brillouin zones. Our finding reveals a class of planar nodal chains in non-symmorphic phononic systems, expanding the catalog of topological nodal chains and enriching the family of topological surface states.

An almost sure invariance principle for some classes of non-stationary mixing sequences

In this note we (in particular) prove an almost sure invariance principle (ASIP) for non-stationary and uniformly bounded sequences of random variables which are exponentially fast ϕ-mixing. The obtained rate is of order o(Vn14+δ) for an arbitrary δ>0, where Vn is the variance of the underlying partial sums Sn. For certain classes of inhomogeneous Markov chains we also prove a vector-valued ASIP with similar rates.

Discrete self-similar and ergodic Markov chains

The first aim of this paper is to introduce a class of Markov chains on Z+ which are discrete self-similar in the sense that their semigroups satisfy an invariance property expressed in terms of a discrete random dilation operator. After showing that this latter property requires the chains to be upward skip-free, we first establish a gateway intertwining relation between the semigroup of such chains and the one of spectrally negative self-similar Markov processes on R+. As a by-product, we prove that each of these Markov chains, after an appropriate scaling, converge in the Skorohod metric to the associated self-similar Markov process. By a linear perturbation of the generator of these Markov chains, we obtain a class of ergodic Markov chains which are nonreversible. By means of intertwining relations and their strengthened interweaving versions, we derive several deep analytical properties of such ergodic chains, including the description of the spectrum, the spectral expansion of their semigroups and the study of their convergence to equilibrium in the Φ-entropy sense as well as their hypercontractivity property.

Recurrence of a class of quantum Markov chains on trees

The problem of recurrence for quantum Markov chains on trees (QMCT), is more subtle than for 1D quantum Markov chains (QMC); it involves infinitely many rays due to the exponential growth of ramifications on the Cayley trees and their relevant constraints. We study criteria for recurrence of QMCT based on the correlations functions and boundary conditions. These represent a bridge between recurrence and phase transitions. Furthermore, we illustrate our results through an Ising model with competing interactions.

Extreme value statistics of positive recurrent centrally biased random walks

We consider the extreme value statistics of centrally-biased random walks with asymptotically-zero drift in the ergodic regime. We fully characterize the asymptotic distribution of the maximum for this class of Markov chains lacking translational invariance, with a particular emphasis on the relation between the time scaling of the expected value of the maximum and the stationary distribution of the process.

A new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains

Abstract In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov–Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition steps. An example of a class of processes is provided to point that such estimates considering several transition steps may be applicable when one transition can not guarantee any convergence. Moreover, a better estimate can be obtained for a higher number of transitions steps. A law of large numbers is presented for a class of ergodic nonlinear Markov chains with finite state space that may serve as a basis for nonparametric estimation and other statistics.

Non-Bayesian Social Learning on Random Digraphs With Aperiodically Varying Network Connectivity

In this article, we study non-Bayesian social learning on random directed graphs and show that under mild connectivity assumptions, all the agents almost surely learn the true state of the world asymptotically in time if the sequence of the associated weighted adjacency matrices belongs to Class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {P}^*$</tex-math></inline-formula> (a broad class of stochastic chains that subsumes uniformly strongly connected chains). We show that uniform strong connectivity, while being unnecessary for asymptotic learning, ensures that all the agents’ beliefs converge to a consensus almost surely, even when the true state is not identifiable. We then provide a few corollaries of our main results, some of which apply to the variants of the original update rule, such as inertial non-Bayesian learning and learning via diffusion and adaptation. Others include the extensions of known results on social learning. We also show that if the network of influences is balanced in a certain sense, then asymptotic learning occurs almost surely even in the absence of uniform strong connectivity.

The utility of serum amylase as a prognostic marker in multiple myeloma.

Ectopic production of amylase by tumor cells is known since 1951. Elevated amylase in multiple myeloma (MM) was first described in 1988. It has been postulated that translocation of chromosome 1, where amylase gene is situated, is responsible for ectopic production from the malignant plasma cells. Anecdotal reports have shown hyperamylasemia in MM to be associated with extensive bone disease, rapid progression, and shorter survival. Serum amylase estimation is a ubiquitous test. This prospective study was conducted to ascertain the degree of elevated amylase, its clinical utility, and implications in MM patients. In an 18-month period, all consenting patients with newly diagnosed or relapsed MM were tested for serum amylase levels. The study excluded patients with elevated lipase, abnormal creatinine clearance, and evidence of intestinal obstruction or perforation. Patients with amylase value >100 U/L were designated to have "elevated amylase level" for the purpose of this study. We enrolled 58 patients with MM, of which 29.3% (n = 17) were found to have elevated serum amylase levels. The median age of patients with elevated amylase was 65 years. The male-to-female ratio was 1.9:1. There was no statistical association between age, gender, type of heavy chain class, light chain, or high-risk cytogenetics. Among patients with the International Staging System (ISS), Stages I, II, and III, 20.8% (n = 5), 31.3% (n = 5), and 41.2% (n = 7) were noted to have elevated amylase levels. A statistically significant association was noted between the presence of extramedullary disease (EMD) and elevated amylase level (P = 0.028). Higher mortality (29.4% versus 17%) and shorter mean survival of (30.2 ± 3.3 months versus 51.7 + 4.9 months) were recorded in patients with elevated amylase levels in comparison to those with normal levels. Elevated serum amylase level in MM is indicative of advanced ISS stage, the presence of EMD, higher risk of mortality, and shorter survival. Serum amylase can be used as a cost-effective tool in myeloma management.

Comparison of Effective Bandwidth Estimation Methods for Data Networks

The purpose of this work is to apply techniques to estimate the Effective Bandwidth, from traffic traces, for the Generalized Markov Fluid Model in data networks. This model is assumed because it is versatile in describing traffic fluctuations. The concept of Effective Bandwidth proposed by Kelly is used to measure the channel occupancy of each source. Since the estimation techniques we will use require prior knowledge of the number of clustering clusters, the Silhouette algorithm is used as a first step to determine the number of classes of the modulating chain involved in the model. Using that optimal number of clusters, the Kernel Estimation and Gaussian Mixture Models techniques are used to estimate the model parameters. After that, the performance of the proposed methods is analyzed using simulated traffic traces generated by Markov Chain Monte Carlo algorithms.

Deviation inequalities for stochastic approximation by averaging

We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization.

Symmetry-Resolved Entanglement Entropy in Critical Free-Fermion Chains

The symmetry-resolved Rényi entanglement entropy is the Rényi entanglement entropy of each symmetry sector of a density matrix rho . This experimentally relevant quantity is known to have rich theoretical connections to conformal field theory (CFT). For a family of critical free-fermion chains, we present a rigorous lattice-based derivation of its scaling properties using the theory of Toeplitz determinants. We consider a class of critical quantum chains with a microscopic U(1) symmetry; each chain has a low energy description given by N massless Dirac fermions. For the density matrix, rho _A, of subsystems of L neighbouring sites we calculate the leading terms in the large L asymptotic expansion of the symmetry-resolved Rényi entanglement entropies. This follows from a large L expansion of the charged moments of rho _A; we derive mathrm {tr}(mathrm {e}^{mathrm {i}alpha Q_A} rho _A^n)~=~a mathrm {e}^{mathrm {i}alpha langle Q_Arangle } (sigma L)^{-x}(1+O(L^{-mu })), where a, x and mu are universal and sigma depends only on the N Fermi momenta. We show that the exponent x corresponds to the expectation from CFT analysis. The error term O(L^{-mu }) is consistent with but weaker than the field theory prediction O(L^{-2mu }). However, using further results and conjectures for the relevant Toeplitz determinant, we find excellent agreement with the expansion over CFT operators.

SHLD1 is dispensable for 53BP1-dependent V(D)J recombination but critical for productive class switch recombination

SHLD1 is part of the Shieldin (SHLD) complex, which acts downstream of 53BP1 to counteract DNA double-strand break (DSB) end resection and promote DNA repair via non-homologous end-joining (NHEJ). While 53BP1 is essential for immunoglobulin heavy chain class switch recombination (CSR), long-range V(D)J recombination and repair of RAG-induced DSBs in XLF-deficient cells, the function of SHLD during these processes remains elusive. Here we report that SHLD1 is dispensable for lymphocyte development and RAG-mediated V(D)J recombination, even in the absence of XLF. By contrast, SHLD1 is essential for restricting resection at AID-induced DSB ends in both NHEJ-proficient and NHEJ-deficient B cells, providing an end-protection mechanism that permits productive CSR by NHEJ and alternative end-joining. Finally, we show that this SHLD1 function is required for orientation-specific joining of AID-initiated DSBs. Our data thus suggest that 53BP1 promotes V(D)J recombination and CSR through two distinct mechanisms: SHLD-independent synapsis of V(D)J segments and switch regions within chromatin, and SHLD-dependent protection of AID-DSB ends against resection.

Mathematical Modeling and Optimal Control for a Class of Dynamic Supply Chain: A Systems Theory Approach

Dynamic supply chains (SC) are important to reduce inventory, enable the flow of materials, maximize profits, and minimize costs. This research work presents a capacity–inventory management model via system dynamics for a dynamic supply SC, applying model-based optimal control techniques. In the context of high-volume manufacturing (HVM) that present low variability and predictable demand, for mathematical modeling purposes, a set of coupled first-order ordinary differential equations, with an analogy from the mixing problem, is presented, which relates capacity and inventory levels, taking into account a production rate at each node of interaction. The application of ordinary differential equations via the mixing problem (or compartmental analysis) is important based on the idea of a balance between the influx and outflux of raw material along the supply chain. A proper literature review on optimal control for supply chains is analyzed. The mathematical model introduced is presented in a linear time-invariant (LTI) state-space formulation. Stability analysis for the dynamic serial SC is presented, and a sensitivity analysis is also conducted for the capacity and production rate parameters considering the effects of variations in parameters along the SC. An energy-based optimal control is also developed with proper simulations.

The Tamari block lattice: An order on saturated chains in the Tamari lattice

In this article we define a partially-ordered set on equivalence classes of maximal chains of an interval of the Tamari lattice, which we call the Tamari Block Poset. We prove this is a graded lattice. Along the way we discuss some useful characterizations of its elements. In conclusion we define explicit maps between our work and the Higher Stasheff-Tamari orders in dimensions two and three.

Universal finite-size amplitude and anomalous entangment entropy of $z=2$ quantum Lifshitz criticalities in topological chains

We consider Lifshitz criticalities with dynamical exponent z=2z=2 that emerge in a class of topological chains. There, such a criticality plays a fundamental role in describing transitions between symmetry-enriched conformal field theories (CFTs). We report that, at such critical points in one spatial dimension, the finite-size correction to the energy scales with system size, LL, as \sim L^{-2}∼L−2, with universal and anomalously large coefficient. The behavior originates from the specific dispersion around the Fermi surface, \epsilon \propto \pm k^2ϵ∝±k2. We also show that the entanglement entropy exhibits at the criticality a non-logarithmic dependence on l/Ll/L, where ll is the length of the sub-system. In the limit of l\ll Ll≪L, the maximally-entangled ground state has the entropy, S(l/L)=S_0+(l/L)\log(l/L)S(l/L)=S0+(l/L)log(l/L). Here S_0S0 is some non-universal entropy originating from short-range correlations. We show that the novel entanglement originates from the long-range correlation mediated by a zero mode in the low energy sector. The work paves the way to study finite-size effects and entanglement entropy around Lifshitz criticalities and offers an insight into transitions between symmetry-enriched criticalities.

Normalizers of chains of discrete p-toral subgroups in compact Lie groups

In this paper we study the normalizer decomposition of a compact Lie group G using the information of the fusion system F of G on a maximal discrete p-toral subgroup. We prove that there is an injective map from the set of conjugacy classes of chains of F-centric, F-radical discrete p-toral subgroups to the set of conjugacy classes of chains of p-centric, p-stubborn continuous p-toral subgroups. The map is a bijection when π0(G) is a finite p-group. We also prove that the classifying space of the normalizer of a chain of discrete p-toral subgroups of G is mod p equivalent to the classifying space of the normalizer of the corresponding chain of p-toral subgroups.

Genome-wide DNA methylation profiles of autism spectrum disorder.

We aimed to identify differentially methylated genes and related signaling pathways in autism spectrum disorder (ASD). First, the DNA methylation profile in the brain samples (GSE131706 and GSE80017) and peripheral blood samples (GSE109905) was downloaded from the Gene Expression Omnibus database (GEO) dataset, followed by identification of differentially methylated genes and functional analysis. Second, the GSE109905 data set was used to further validate the methylation state and test the ability to diagnose disease of identified differentially methylated genes. Third, expression measurement of selected differentially methylated genes was performed in whole blood from an independent sample. Finally, protein-protein interaction (PPI) network of core differentially methylated genes was constructed. Totally, 74 differentially methylated genes were identified in ASD, including 38 hypermethylated genes and 36 hypomethylated genes. 15 differentially methylated genes were further identified after validation in the GSE109905 data set. Among these, major histocompatibility complex (HLA)-DQA1 was involved in the molecular function of myosin heavy chain class II receptor activity; HLA-DRB5 was involved in the signaling pathways of cell adhesion molecules, Epstein-Barr virus infection and antigen processing and presentation. In the PPI analysis, the interaction pairs of HLA-DQA1 and HLA-DRB5, FMN2 and ACTR3, and CALCOCO2 and BAZ2B were identified. Interestingly, FMN2, BAZ2B, HLA-DRB5, CALCOCO2 and DUSP22 had a potential diagnostic value for patients with ASD. The expression result of four differentially methylated genes (HLA-DRB5, NTM, IL16 and COL5A3) in the independent sample was consistent with the integrated analysis. Identified differentially methylated genes and enriched signaling pathway could be associated with ASD.

Algorithms for Queueing Systems with Reneging and Priorities Modeled as Quasi-Birth-Death Processes

We consider a Markovian multiserver queueing system with two customer classes, preemptive priorities, and reneging. We formulate this system as an infinite level-dependent quasi-birth-death process (LDQBD). We introduce an algorithm that endogenously truncates the level and calculates lower and upper bounds on stationary probabilities of this LDQBD such that the gap between the bounds can be any desired amount. Our algorithm can be applied to any LDQBD for which the rate matrices become elementwise nonincreasing above some level. This appears to be the first algorithm that provides bounds on stationary probabilities for an infinite-level LDQBD. To obtain these bounds, the algorithm first obtains lower and upper bounds on the rate matrices of the LDQBD using a novel method, which can be applied to any LDQBD. We then extend this algorithm to approximate performance measures of the system of interest and calculate exact lower and upper bounds for those that can be expressed as probabilities, such as the probability that an incoming low-priority customer will wait. We generate a wide range of instances with up to 100 servers and compare the solution times and accuracy of our algorithm with two existing algorithms. These numerical experiments indicate that our algorithm is faster than the other two algorithms for a given accuracy requirement. We investigate the impact of changing service rates on the proportion of low-priority customers served and their wait time, and we demonstrate how ignoring one of these measures can possibly mislead decision makers. Summary of Contribution: We contribute to operations research by modeling a practically important queueing system and developing an algorithm to accurately compute performance measures for that system. We also contribute to computer science by providing error and complexity analysis for the algorithm to solve a broad class of two-dimensional Markov chains with infinite state space.

From the Bernoulli factory to a dice enterprise via perfect sampling of Markov chains

Given a p-coin that lands heads with unknown probability p, we wish to produce an f(p)-coin for a given function f:(0,1)→(0,1). This problem is commonly known as the Bernoulli factory and results on its solvability and complexity have been obtained in (ACM Trans. Model. Comput. Simul. 4 (1994) 213–219; Ann. Appl. Probab. 15 (2005) 93–115). Nevertheless, generic ways to design a practical Bernoulli factory for a given function f exist only in a few special cases. We present a constructive way to build an efficient Bernoulli factory when f(p) is a rational function with coefficients in R. Moreover, we extend the Bernoulli factory problem to a more general setting where we have access to an m-sided die and we wish to roll a v-sided one; that is, we consider rational functions between open probability simplices. Our construction consists of rephrasing the original problem as simulating from the stationary distribution of a certain class of Markov chains—a task that we show can be achieved using perfect simulation techniques with the original m-sided die as the only source of randomness. In the Bernoulli factory case, the number of tosses needed by the algorithm has exponential tails and its expected value can be bounded uniformly in p. En route to optimizing the algorithm we show a fact of independent interest: every finite, integer valued, random variable will eventually become log-concave after convolving with enough Bernoulli trials.

Limit theorems for chains with unbounded variable length memory which satisfy Cramer condition

We consider a class of variable length Markov chains with a binary alphabet in which context tree is defined by adding finite trees with uniformly bounded height to the vertices of an infinite comb tree. Such type of Markov chain models the spike neuron patterns and also extends the class of persistent random walks. The main interest is the limiting properties of the empirical distribution of symbols from the alphabet. We obtain the strong law of large numbers, central limit theorem, and exact asymptotics for large and moderate deviations. The presence of an intrinsic renewal structure is the subject of discussion in the literature. Proofs are based on the construction of a renewals of the chain and the applying corresponding properties of the compound (or generalized) renewal processes.