Class Of Chains Research Articles

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364].

On the rate of convergence for a class of Markovian queues with group services

There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function is not applicable here. This approach gives sharp bounds for the situation of essentially non-negative matrix of the corresponding system, but in our case it does not hold. Here we use the method of differential inequalities to obtaining bounds on the rate of convergence to the limiting characteristics for the class of finite Markovian queueing models. We obtain bounds on the rate of convergence and compute the limiting characteristics for a specific non-stationary model too. Note the results can be successfully applied for modeling complex biological systems with possible single births and deaths of a group of particles.

The role of B7 family members in the generation of Immunoglobulin.

Ig is a Y-shaped protein produced by plasma cells and exerts multiple functions in humoral immunity. There are five groups of Igs including IgA, IgD, IgE, IgG, and IgM, which differ in their heavy chain class. The primary function of Igs includes the neutralization of extrinsic pathogens, agglutination of foreign cells for phagocytosis, precipitation of soluble antigens in serum, and complement fixation. The B cells activated by antigen(s) can differentiate into antibody-producing cells that are called plasma cells and usually matured in the germinal center (GC). Follicular T helper (Tfh) cells crosstalk with antigen-presenting cells and play a crucial role in the development of the GC. Moreover, Tfh cells regulate trafficking through the GC to allow formative interaction with GC B cells that ultimately results in affinity maturation, B-cell memory, and Ig class switching. The B7 family is a series of number of structurally related membrane proteins that bind with a specific receptor to deliver costimulatory or co-inhibitory signals that regulate the activation of T cells in GC. Here, we review and summarize the recent advance of the effects of B7 family members on Ig production and relative diseases.

Adiabatic Eigenstate Deformations as a Sensitive Probe for Quantum Chaos

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

CtIP-mediated DNA resection is dispensable for IgH class switch recombination by alternative end-joining

To generate antibodies with different effector functions, B cells undergo Immunoglobulin Heavy Chain (IgH) class switch recombination (CSR). The ligation step of CSR is usually mediated by the classical nonhomologous end-joining (cNHEJ) pathway. In cNHEJ-deficient cells, a remarkable ∼25% of CSR can be achieved by the alternative end-joining (Alt-EJ) pathway that preferentially uses microhomology (MH) at the junctions. While A-EJ-mediated repair of endonuclease-generated breaks requires DNA end resection, we show that CtIP-mediated DNA end resection is dispensable for A-EJ-mediated CSR using cNHEJ-deficient B cells. High-throughput sequencing analyses revealed that loss of ATM/ATR phosphorylation of CtIP at T855 or ATM kinase inhibition suppresses resection without altering the MH pattern of the A-EJ-mediated switch junctions. Moreover, we found that ATM kinase promotes Alt-EJ-mediated CSR by suppressing interchromosomal translocations independent of end resection. Finally, temporal analyses reveal that MHs are enriched in early internal deletions even in cNHEJ-proficient B cells. Thus, we propose that repetitive IgH switch regions represent favored substrates for MH-mediated end-joining contributing to the robustness and resection independence of A-EJ-mediated CSR.

Perfect quantum state transfer on diamond fractal graphs

In the quest for designing novel protocols for quantum information and quantum computation, an important goal is to achieve perfect quantum state transfer for systems beyond the well-known one- dimensional cases, such as 1D spin chains. We use methods from fractal analysis and probability to find a new class of quantum spin chains on fractal-like graphs (known as diamond fractals) which support perfect quantum state transfer and which have a wide range of different Hausdorff and spectral dimensions. The resulting systems are spin networks combining Dyson hierarchical model structure with transverse permutation symmetries of varying order.

Simulation Game Outcomes: A Multilevel Examination of Knowledge Sharing Norms, Transactive Memory Systems, and Individual Learning Goal Orientations

Background. Because computer-based simulation games are widely used in university classrooms, it is important to investigate factors which can lead to effective student team performance and positive individual outcomes. Aim. This correlational study aimed to examine the effects of knowledge sharing norms, transactive memory systems, and individual learning goal orientations on game outcomes. Method. The setting for this study was an undergraduate logistics and supply chain class. The class uses a serious simulation game which is designed to realistically mimic the business transactions within an enterprise resource planning system (ERP). Cross-sectional surveys captured individual learning goal orientations. After multiple rounds of simulation game play, subsequent surveys captured student reactions, perceptions of knowledge sharing behaviors, and transactive memory systems. Results. Two sets of analyses were conducted using a sample of 100 undergraduates performing in 42 teams. At the group-level, OLS regression results suggest that, while there was no effect on objective team performance, knowledge sharing norms enhanced perceptions of team performance, and this effect was mediated through the development of transactive memory systems. For individual-level outcomes, multilevel results suggest that knowledge sharing norms were positively related to satisfaction with the team, but not satisfaction with the task. However, transactive memory systems were positively related both satisfaction with the team and satisfaction with the task. Individual learning goal orientation was positively related to satisfaction with the task but not satisfaction with the team. Conclusion. Our findings suggest that learning goal orientations and norms for knowledge sharing are linked to positive outcomes of team-based simulation game learning activities. Because learning goal orientations are malleable and norms for knowledge sharing can be encouraged, these factors are within the influence of the instructor. As such, they should be nurtured and developed through the active encouragement of experimentation, exploration, and communication between team members.

Bioconversion From Docosahexaenoic Acid to Eicosapentaenoic Acid in the Marine Bacterium Shewanella livingstonensis Ac10.

Eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), which belong to the same class of long chain ω-3 polyunsaturated fatty acids (PUFAs), are present in marine γ-proteobacteria. In contrast to their de novo biosynthesis that has been intensively studied, their metabolic fates remain largely unknown. Detailed information regarding bacterial ω-3 PUFA metabolism would be beneficial for understanding the physiological roles of EPA/DHA as well as the industrial production of EPA, DHA, and other PUFAs. Our previous studies revealed that the EPA-producing marine bacterium Shewanella livingstonensis Ac10 produces EPA from exogenous DHA independently of de novo EPA biosynthesis, indicating the presence of an unidentified metabolic pathway that converts DHA into EPA. In this study, we attempted to reveal the molecular basis for the bioconversion through both in vivo and in vitro analyses. Mutagenesis experiments showed that the gene disruption of fadH, which encodes an auxiliary β-oxidation enzyme 2,4-dienoyl-CoA reductase, impaired EPA production under DHA-supplemented conditions, and the estimated conversion rate decreased by 86% compared to that of the parent strain. We also found that the recombinant FadH had reductase activity toward the 2,4-dienoyl-CoA derivative of DHA, whereas the intermediate did not undergo β-oxidation in the absence of the FadH protein. These results indicate that a typical β-oxidation pathway is responsible for the conversion. Furthermore, we assessed whether DHA can act as a substitute for EPA by using an EPA-less and conversion-deficient mutant. The cold-sensitive phenotype of the mutant, which is caused by the lack of EPA, was suppressed by supplementation with EPA, whereas the DHA-supplementation suppressed it to a lesser extent. Therefore, DHA can partly substitute for, but is not biologically equivalent to, EPA in S. livingstonensis Ac10.

Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions

We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation governing the time evolution of the system's density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, whose main features are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, whose decay rate $u$ should scale as $u\sim t_s^{-\kappa}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $\kappa = z/(y_\mu+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_\mu$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.

The Sierpiński gasket as the Martin boundary of a non-isotropic Markov chain

In 2012 Lau and Ngai, motivated by the work of Denker and Sato, gave an example of an isotropic Markov chain on the set of finite words over a three letter alphabet, whose Martin boundary is homeomorphic to the Sierpi\'nski gasket. Here, we extend the results of Lau and Ngai to a class of non-isotropic Markov chains. We determine the Martin boundary and show that the minimal Martin boundary is a proper subset of the Martin boundary. In addition, we give a description of the set of harmonic functions.

On discrete-time semi-Markov processes

In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop a discrete-time counterpart of such a theory and to show relationships and differences with respect to the continuous time case. We present a class of discrete-time semi-Markov chains which can be constructed as time-changed Markov chains and we obtain the related governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.

Mucosa-associated lymphoid tissue (MALT) lymphoma developing in ectopic mediastinal thyroid tissue: a case report

BackgroundNormally located in the neck, ectopic mediastinal thyroid tissue consists of very rare ectopic thyroid tissue that does not connect to the thyroid gland. A patient with mucosa-associated lymphoid tissue (MALT) lymphoma that has developed in mediastinal thyroid tissue, to our best knowledge, has not been previously reported.Case presentationA 67-year-old woman presented with a superior mediastinal mass that was revealed by chest computed tomography (CT), an optional examination she hoped, during a medical checkup. Contrast-enhanced CT scan performed in our hospital for close examination confirmed the presence of a 2 × 1.3 cm poorly enhanced mass anterior to the trachea during the arterial phase. Magnetic resonance imaging depicted low signal intensity on T1-weighted images and high signal intensity on T2-weighted images. I-131 meta-iodobenzylguanidine did not accumulate in the mass. Serum levels of interleukin-2 receptor, catecholamine, and anti-acetylcholine receptor antibody were within the normal range. The mass was resected through a transverse neck incision for the diagnosis and treatment. The histopathological diagnosis of the specimen was ectopic mediastinal thyroid tissue associated with MALT lymphoma and chronic thyroiditis. Immunoglobulin heavy chain class switch recombination was identified. Fine-needle aspiration biopsy of the cervical thyroid showed chronic thyroiditis but not lymphoma. The patient’s postoperative thyroid function was normal. To date, the patient’s recovery has been uneventful, and she is being monitored without further treatment.ConclusionWe treated the patient with MALT lymphoma that developed in ectopic mediastinal thyroid tissue. This novel case illustrates a new differential diagnosis associated with ectopic mediastinal thyroid tissue.

Onsager's Scars in Disordered Spin Chains.

We propose a class of nonintegrable quantum spin chains that exhibit quantum many-body scars even in the presence of disorder. With the use of the so-called Onsager symmetry, we construct scarred models for arbitrary spin quantum number S. There are two types of scar states, namely, coherent states associated with an Onsager-algebra element and one-magnon scar states. While both of them are highly excited states, they have area-law entanglement and can be written as a matrix product state. Therefore, they explicitly violate the eigenstate thermalization hypothesis. We also investigate the dynamics of the fidelity and entanglement entropy for several initial states. The results clearly show that the scar states are trapped in a perfectly periodic orbit in the Hilbert subspace and never thermalize, whereas other generic states do rapidly. To our knowledge, our model is the first explicit example of disordered quantum many-body scarred models.

Universality and quantum criticality in quasiperiodic spin chains

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems and disordered ones as well. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization-group transformation. These discrete sequences are therefore fixed points of a functional renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP

In this article we study the relation between the eigenstates of open rational spin Heisenberg chains with different boundary conditions. The focus lies on the relation between the spin chain with diagonal boundary conditions and the spin chain with triangular boundary conditions as well as the class of spin chains that can be brought to such form by certain similarity transformations in the physical space. The boundary driven symmetric simple exclusion process (open SSEP) belongs to the latter. We derive a transformation that maps the eigenvectors of the diagonal spin chain to the eigenvectors of the triangular chain. This transformation yields an essential simplification for determining the states beyond half-filling. It allows to first determine the eigenstates of the diagonal chain through the Bethe ansatz on the fully excited reference state and subsequently map them to the triangular chain for which only the vacuum serves as a reference state. In particular the transformed reference state, i.e. the fully excited eigenstate of the triangular chain, is presented at any length of the chain. It can be mapped to the steady state of the open SSEP. This results in a concise closed-form expression for the probabilities of particle distributions and correlation functions in the steady state. Further, the complete set of eigenstates of the Markov generator is expressed in terms of the eigenstates of the diagonal open chain.

Code Blue: Nurse Cells Can Resuscitate Lymphocyte Receptors in Nurse Shark Thymus by Secondary Rearrangement

Abstract The thymus is the most conserved primary lymphoid organ present, in some form, in mammals to all the way back in lamprey. It is composed of a densely-packed outer cortex and an exiguous inner medulla. The thymus functions to provide a microenvironment conducive to T lymphocyte maturation and receptor repertoire formation. Sharks are situated at a pivotal location in evolutionary immunology. They are the oldest vertebrates to have similar adaptive immune characteristics to mammals. Shark lymphocyte antigen receptors are diversified by V(D)J recombination via RAG and heavy chain class switch recombination catalyzed by AID. Somatic hypermutation occurs in both B and T cell antigen receptors of shark, mediated by AID as well. Shark T cell receptors also employ antibody-like NARTCR and IgHV components. Looking at the oldest lymphoid tissue in the oldest vertebrate ancestor with adaptive characteristics similar to mammals will yield important information on the evolution of the adaptive immune response as it relates to T lymphocytes. Nurse cells are cortical thymic epithelial cells that play an important role in selection of functional T cells during the maturation process. Nurse cells have been shown, in mice, to surround non-functional T cells in order to allow them to reconfigure their receptors and attempt selection another time via RAG and/or AID. Through the use of immunohistochemistry and in situ hybridization, we will investigate whether nurse cells provide a microenvironment for shark thymocyte receptor revision in sharks as in mammals.

On a class of birth-death processes with time-varying intensity functions

In this paper, we investigate on a class of time-inhomogeneous birth-death chains obtained by applying the composition method to two time-inhomogeneous double-ended chains. Then, we consider the corresponding restricted birth-death process, with zero reflecting boundary. Finally, starting from the restricted process, we construct a time-inhomogeneous BD chain symmetric with respect to zero-state. We obtain closed form expressions for the transition probabilities and for the conditional moments; furthermore, the first-passage-time problem is also taken in consideration. Finally, various numerical computations are performed for periodic intensity functions.

Maladies des chaînes lourdes

In most plasma cell disorders, monoclonal proteins have a structure similar to normal molecules but in abnormal amounts. Heavy chain disease (HCD) is a rare pathology defined by the presence of a monoclonal immunoglobulin (Ig) of abnormal structure, consisting only of an incomplete fragment of the heavy chain (truncated) and devoid of light chains, remarkable for the frequency of associated immunological or haematological diseases.Abnormal lymphocytes or plasma cells secrete the different types of heavy chains (alpha [α], gamma [γ], mu [μ] or delta [δ]) without light chains. The majority of heavy chain proteins are fragments of their normal counterparts with internal deletions of variable length. These deletions seem to result from structural mutations.There are 4 types of MCL according to the Ig heavy chain class produced by clonal cells: α, γ, μ or δ. The clinical presentation is closer to that of lymphoma than to multiple myeloma.The diagnosis of HCD and related diseases is based on the histological study of affected tissues and the analysis of serum or urine. The histological analysis with immunostaining shows a positive monoclonal population for a heavy chain, but negative for the two kappa (κ) and lambda (λ) light chains.The frequency of detection of the monoclonal peak is variable and depends on the type of HCD. The prognosis of these diseases is very variable from one patient to another and the treatment is not standardized.

A paradox for expected hitting times

We prove a counterintuitive result concerning the expected hitting/absorption time for a class of Markov chains. The “paradox” already shows itself in the following elementary example that is suitable for undergraduate teaching: Batman and the Joker perform independent discrete-time random walks on the vertices of a square until they meet, starting from opposite vertices. Batman always moves (and clockwise and anticlockwise steps are equally likely), while the Joker remains still on any given step with probability On average the Joker survives for twice as long by staying still with arbitrarily small but positive probability (in the limit as ) than by always moving (when q = 0).

On obtaining sharp bounds of the rate of convergence for a class of continuous-time Markov chains

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of convergence for such class of Markov chains.