Stability and bifurcations of equilibria in a delayed Kirschner–Panetta model

In this paper, a delay differential equation model of immunotherapy for tumor-immune response is presented. The dynamics that interplays between the three model factors, namely, effector cells, tumor cells and interleukin-2 is studied and the quantitative analysis is performed. We estimate the length of delay to preserve the stability of an equilibrium state of biological significance. The impact of delay in the immunotherapy with interleukin-2, especially, at different antigenicity levels, is discussed, along with the scenarios under which the tumor remission can be prolonged.     

On Sharma-Swarup algorithm for time minimising transportation problems

In this note, the fallacy in the method given by Sharma and Swarup, in their paper on time minimising transportation problem, to determine the setS _hkof all nonbasic cells which when introduced into the basis, either would eliminate a given basic cell (h, k) from the basis or reduce the amountx _hkis pointed out.     

初发系统性红斑狼疮患者调节性T细胞和Th17细胞的检测及意义

目的：观察初发系统性红斑狼疮（SLE）患者外周血调节性T细胞（Treg）和Th17细胞的变化,探讨其临床意义。方法检测15例初发SLE患者（活动组11例,非活动组5例）及10例健康对照者（对照组）的外周血CD4＋CD25highTreg、Th17细胞占CD4＋的比例,分析两种细胞的比率与疾病活动指数（SLEDAI）的相关性。结果初发SLE患者外周血CD4＋CD25highTreg和Th17细胞的比例与对照组相比,差异无统计学意义（P＞0.05）,与SLEDAI无相关性（均P＞0.05）。CD4＋CD25highT细胞与Th17细胞的比率在活动组患者下降尤为明显（P＜0.05）,且与SLEDAI呈明显的负相关（P＜0.05）。结论初发的活动性SLE患者外周血Treg与Th17细胞的比率明显下降,并与疾病活动密切相关,两群细胞的失衡可能在SLE发病机制中起重要的作用。     

On 321-Avoiding Permutations in Affine Weyl Groups

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type A _{n – 1} by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for a 321-avoiding element of W (considered as a Coxeter group) may be obtained from each other by repeated applications of short braid relations.Using Shi's characterization of the Kazhdan–Lusztig cells in the group W, we use our main result to show that the fully commutative elements of W form a union of Kazhdan–Lusztig cells. This phenomenon has been studied by the author and J. Losonczy for finite Coxeter groups, and is interesting partly because it allows certain structure constants for the Kazhdan–Lusztig basis of the associated Hecke algebra to be computed combinatorially.We also show how some of our results can be generalized to a larger group of permutations, the extended affine Weyl group associated to GL _n ()     

Orbits of Groups Generated by Transvections over F<Subscript>2</Subscript>

Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. n particular, we compute orbits that are in bijection with connected components of real double Bruhat cells in semisimple groups, extending results of M. Gekhtman, B. Shapiro, M. Shapiro, A. Vainshtein and A. Zelevinsky.The author’s research was supported in part by Andrei Zelevinsky’s NSF grant #DMS-0200299.     

Global dynamics of delay‐distributed HIV infection models with differential drug efficacy in cocirculating target cells

In this paper, we investigate the dynamical behaviors of three human immunodeficiency virus infection models with two types of cocirculating target cells and distributed intracellular delay. The models take into account both short‐lived infected cells and long‐lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of infection is given by bilinear and saturation functional responses in the first and second models, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. We have derived the basic reproduction number R₀ for the three models. For the first two models, we have proven that the disease‐free equilibrium is globally asymptotically stable (GAS) when R₀≤1, and the endemic equilibrium is GAS when R₀>1. For the third model, we have established a set of sufficient conditions for global stability of both equilibria of the model. We have checked our theoretical results with numerical simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal two-layer selection policy for a flexible manufacturing system

This paper deals with the selection problem in a manufacturing system. The manufacturing system consists of a flexible manufacturing cellC ₀ which feedsM flexible manufacturing cellsC _1i ,i=1, ...,M. In addition, each cellC _1i ,i=1, ...,M, is feeding several production lines. Sufficient conditions on optimal feedback selection policies for theM+1 flexible manufacturing cells are derived. These selection policies maximize the probability of the system output reaching some demand before any of the system buffers is being overflowed. A numerical study is conducted.     

Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.     

Polygonal invariant curves for a planar piecewise isometry

We investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number of transitive components. The union of all periodic components is an invariant pentagon with unequal sides. Transitive components are invariant curves on which the dynamics are conjugate to a transitive interval exchange. The restriction of the map to the invariant pentagonal region is the first known piecewise isometric system for which there exist an infinite number of periodic components but the only aperiodic points are on the boundary of the region. The proofs are based on exact calculations in a rational cyclotomic field. We use the system to shed some light on a conjecture that PWIs can possess transitive invariant curves that are not smooth.

     

太阳能小屋设计的问题解析

就2012年“高教社杯”全国大学生数学建模竞赛B题“太阳能小屋的设计”的背景作了介绍,针对该问题提出一种启发式算法的求解方法,虽然不能保证得到的结果是最优解,但至少还是比较好的可行解。在分析和求解过程中,针对学生在赛题试卷中出现的问题作了简要的说明。     

Machine interference in automated cells

This paper presents a simulation and an analytical modeling of the machine interference problem in manufacturing cells. Each machine experiences two types of stoppage which are to be served by a robot. Several combinations of the distributions of the stoppages, service distributions, and service disciplines are studied. We determine the optimal number of machines assigned to the robot under different operating conditions such that the expected total cost of the manufacturing cell is minimized.This research is based on Mr. Norton's M.S. thesis, which was conducted at Rutgers.     

Cellular homology of real flag manifolds

Let ${\mathbb{F}}_{\Theta }=G∕P_{\Theta }$ be a generalized flag manifold, where $G$ is a real non-compact semi-simple Lie group and $P_{\Theta }$ a parabolic subgroup. A classical result says the Schubert cells, which are the closure of the Bruhat cells, endow ${\mathbb{F}}_{\Theta }$ with a cellular CW structure. In this paper we exhibit explicit parametrizations of the Schubert cells by closed balls (cubes) in ${\mathbb{R}}^n$ and use them to compute the boundary operator $\partial$ for the cellular homology. We recover the result obtained by Kocherlakota [1995], in the setting of Morse Homology, that the coefficients of $\partial$ are 0 or $\pm 2$ (so that ${\mathbb{Z}}_2$-homology is freely generated by the cells). In particular, the formula given here is more refined in the sense that the ambiguity of signals in the Morse–Witten complex is solved.     

Differential equations related to the Williams-Bjerknes tumour model

We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which spreads through an epithelial basal layer modeled onI ⊂ Z ². The solution of this problem is a familyp = (p _i(t)), where eachp _i(t)could be considered as an approximation to the probability that the cell situated ati is cancerous at timet. We prove that this problem has a unique solution, it is defined on [0, +∞[, and, for some relevant situations, lim_t→∞ P _i(t) = 1 for alli ∈ I. Moreover, we study the expected number of cancerous cells at timet.     

Left cells containing a fully commutative element

Let W be a finite or an affine Coxeter group and W_c the set of all the fully commutative elements in W. For any left cell L of W containing some fully commutative element, our main result of the paper is to prove that there exists a unique element (say w^L) in L∩W_c such that any z∈L has the form z=xw^L with ?(z)=?(x)+?(w^L) for some x∈W. This implies that L is left connected, verifying a conjecture of Lusztig in our case.     

体外扩增人NK细胞及其对白血病细胞杀伤作用的研究

目的通过体外扩增人NK细胞的方法，探讨扩增后NK细胞对K562和HL60白血病细胞株的体外杀伤作用及机制。方法抽取5例健康志愿者外周血，分离单个核细胞（PBMC），与基因修饰K562细胞共同培养，采用流式细胞仪检测NK细胞的表型，铬51释放法测定NK细胞对白血病细胞的杀伤率。结果基因修饰K562细胞在体外刺激NK细胞扩增202倍；扩增后NK细胞对白血病细胞K562、HL60的杀伤率分别为77.1%、61.2%（效/靶比为8∶1），扩增前NK细胞对K562、HL60杀伤率分别为39.0%、35.4%；扩增后NK细胞表面活化受体NKG2D、NKp30和NKp44表达增强；这些活化受体特异抗体能部分抑制扩增后NK细胞的抗白血病作用。结论基因修饰K562细胞刺激NK细胞有效扩增，扩增后NK细胞杀伤白血病细胞作用明显增强，扩增后NK细胞表面部分活化受体上调可能为扩增后NK细胞抑制白血病作用增强的分子机制，NK细胞治疗在白血病中有潜在的应用前景。     

Stability Analysis of the Cambridge Ring

A ring of I cells rotates past I queues, carrying customers from their origins to their destinations. The system is modelled as a Markov chain, and the exact ergodicity conditions are given. They are shown to depend on the precise travel lengths distributions, that is, not only on their means. Ergodicity is proven through the stability analysis of the associated fluid limits. The arrivals distributions, which in the ergodicity conditions appear only through their means, are more subtly involved in the fluid limits behaviour, in that they determine the probabilities of random bifurcations that occur infinitely often in a simple system of I=2 queues.     

Multi-degree cyclic scheduling of a no-wait robotic cell with multiple robots

This paper addresses cyclic scheduling of a no-wait robotic cell with multiple robots. In contrast to many previous studies, we consider r-degree cyclic (r > 1) schedules, in which r identical parts with constant processing times enter and leave the cell in each cycle. We propose an algorithm to find the minimal number of robots for all feasible r-degree cycle times for a given r (r > 1). Consequently, the optimal r-degree cycle time for any given number of robots for this given r can be obtained with the algorithm. To develop the algorithm, we first show that if the entering times of r parts, relative to the start of a cycle, and the cycle time are fixed, minimizing the number of robots for the corresponding r-degree schedule can be transformed into an assignment problem. We then demonstrate that the cost matrix for the assignment problem changes only at some special values of the cycle time and the part entering times, and identify all special values for them. We solve our problem by enumerating all possible cost matrices for the assignment problem, which is subsequently accomplished by enumerating intervals for the cycle time and linear functions of the part entering times due to the identification of the special values. The algorithm developed is shown to be polynomial in the number of machines for a fixed r, but exponential if r is arbitrary.     

Numerical Simulation of Red Blood Cell Suspensions Behind a Moving Interface in a Capillary

Computational modeling and simulation are presented on the motion of red blood cells behind a moving interface in a capillary. The methodology is based on an immersed boundary method and the skeleton structure of the red blood cell (RBC) membrane is modeled as a spring network. As by the nature of the problem, the computational domain is moving with either a designated RBC or an interface in an infinitely long two-dimensional channel with an undisturbed flow field in front of the computational domain. The tanking-treading and the inclination angle of a cell in a simple shear flow are briefly discussed for the validation purpose. We then present and discuss the results of the motion of red blood cells behind a moving interface in a capillary, which show that the RBCs with higher velocity than the interface speed form a concentrated slug behind the moving interface.     

Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models

We consider the problem of scheduling operations in a robotic cell processing a single part type. Each machine in the cell has a one-unit input buffer and a one-unit output buffer. The machines and buffers are served by one single gripper robot. The domain considered is free-pickup cells with additive inter-machine travel time. The processing constraints specify the cell to be a flow shop. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes throughput. Bufferless robotic cells have been studied extensively in the literature. However, the few studies of robotic cells with output buffers at each machine have shown that the throughput can be improved by such a configuration. We show that there is no throughput advantage in providing machine input buffers in addition to output buffers. The equivalence in throughput between the two models has significant practical implications, since the cost of providing additional buffers at each machine is substantial.