Stochastic modeling of carcinogenesis by state space models: a new approach

In this paper, we have developed some state space models for carcinogenesis involving multievent models and multiple pathways models. In these state space models, the stochastic system models are stochastic models of carcinogenesis expressed in terms of stochastic differential equations, whereas the observation models are statistical models based on the observed number of detectable preneoplastic lesions per individual over time and the observed number of detectable cancer tumors per individual over time. In this paper, we have applied some of the theories to some animal papillomas data from some initiation-promotion experiments on skin cancer in mice to estimate some unknown parameters. For this data set we have obtained excellent fit by a model with three piece-wise intervals.     

Generalized type I invexity and duality in multiobjective variational problems

In this paper, we introduce new classes of generalized V-type I invex functions for variational problems and consider a multiobjective variational problem (VP). A number of sufficiency results are established using Lagrange multiplier conditions under various types of generalized V-type I invexity requirements. Duality results are obtained for Mond-Weir type duals under the above generalized V-type I invexity assumptions and their generalizations.     

具有迷向S曲率Randers度量的几何意义

Riemann流形上的Zermelo航行为Randers度量提供了一个简洁而且清晰的几何背景．在这个背景下D．Bao，C．Robles和Z．Shen对于具有常旗曲率的Randers度量进行了完全分类．这篇论文中，我得到了判定具有特殊曲率性质的Randers度量的两个充分必要条件．从这两个条件出发，我得到了迷向S曲率的Randers度量的几何意义和一系列推论，并且构造了具有迷向S曲率Randers度量的新例子．最后，在Zermelo航行的背景下研究了Berwald型的Raiders度量．     

A system of steady-state boundary layer equations for a dilatantous medium

The existence of a solution of a system of equations that arise in the hydrodynamics of a Newtonian liquid is proved, and a number of properties of this solution are studied. It is established that the rate of propagation of the perturbations is finite under particular conditions. The uniqueness of the solution where the rate of propagation of the perturbations is finite is demonstrated.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 89–108, 1989.     

The death-mutation model of carcinogenesis

Multistage models of carcinogenesis that include death and mutation of target cells at risk for cancer, but do not include cell division, may be appropriate for cancers in which clonal expansion arises downstream of the rate-determining step toward carcinogenesis. Such models are simpler than clonal expansion models, so when they are appropriate, they should be used. The purpose of this paper is to illustrate how linear systems theory applies to these death-mutation models of carcinogenesis.     

Long-term dynamics of chromosomal instability in cancer: A transition probability model

A stochastic model of chromosomal instability has been previously developed which has included one adjustable parameter—the probability of a segregation error. Using computer simulations, we have previously analyzed this model and were able to reproduce a short-term dynamics of chromosome copy number distributions in clones of cancer cells. In a short run, segregation errors provide a continuous production of deviant cells with increasing variation of cell karyotypes, which depends upon the rate of segregation errors. In the long-term observations, many tumors and cancer cell lines have been observed to maintain a stable, although abnormal, distribution of chromosome number for hundreds of cell generations. This phenomenon of “stability within instability” presents an interesting paradox, which could be addressed mathematically. However, this would require modeling of long term growth of tumor cell clones for hundreds of generations, which has far exceeded capabilities of modern computer systems. In this study, we have analyzed asymptotic behavior of our model using a semianalytical approach. A transition probability matrix was derived analytically and implemented in a recursive algorithm for computational experiments. Using this transition probability model, the expected frequencies of chromosome copy number have been calculated under various initial and boundary conditions. We have also tested several alternative models, which describe various mechanisms of errors in segregation of chromosomes, and found conditions for stabilization of distribution of chromosomes copy numbers over a large number of cell generations. Stable clonal frequencies were estimated which are independent of initial conditions, i.e., chromosome copy numbers in the initiator cells. These stable distributions were, however, dependent on the model assumptions regarding particular mechanism of errors in segregation of chromosomes. Thus, our modeling results have suggested a possible connection between the form of stable distribution of chromosome numbers in tumors and the underlying mechanism of errors in segregation of chromosomes. This new analytical approach allows us to overcome technical impairments and limitations of computer simulation, and, for the first time, provides mathematical insight into long-term evolution of chromosome numerical changes in human tumors.     

First passage probability distributions in Markov models and the HIV incubation distribution under treatment

In this paper, I derive some first passage probability distributions for some continuous time Markov chains. By using these results, I then derive some exact HIV incubation distributions under treatment by anti-viral drugs such as AZT under some general conditions. It is shown that under some special conditions, these distributions are mixtures of generalized Gamma distributions.     

Ethnic Preferences,Social Distance Dynamics,and Residential Segregation: Theoretical Explorations Using Simulation Analysis∗

In this paper I consider theories of residential segregation that emphasize social distance and ethnic preference dynamics. I argue that these theories are more compelling than many critics have supposed, and I conclude that they deserve to be considered more carefully. I then use simulation methodology to assess the potential impact of social distance and ethnic preference dynamics on ethnic segregation under certain theoretically interesting conditions. Based on the results from the simulation analyses, I offer three conclusions: (1) status preferences and status dynamics have the capacity to produce high levels of status segregation but do not produce high levels of ethnic segregation under the specified simulation conditions; (2) ethnic preferences can, under certain theoretically interesting conditions specified in these simulations, produce high levels of ethnic segregation in the absence of housing discrimination; and (3) ethnic preferences and social distance dynamics can, when combined with status preferences, status dynamics, and demographic and urban-structural settings common in American cities, produce highly stable patterns of multi-group segregation and hyper-segregation (i.e., high levels of ethnic segregation on multiple dimensions) of minority populations. Based on these model-based theoretical explorations I speculate that the persistence of segregation in recent decades may have been overdetermined, that is, it may have been sustained by multiple sufficient causes including not only discrimination, but also social distance and preference dynamics. This raises the possibility that reductions in housing discrimination may not necessarily lead to large declines in ethnic segregation in the short run because social distance and preference dynamics may be able to sustain ethnic segregation at surprisingly high levels in the absence of housing discrimination.     

The Size of a Maximum Subgraph of the Random Graph with a Given Number of Edges

Doklady Mathematics - We have proven that the maximum size k of an induced subgraph of the binomial random graph $$G(n,p)$$ with a given number of edges $$e(k)$$ (under certain conditions on this...     

Bifurcation and forced symmetry breaking in Hamiltonian systems

We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold. In particular we study the persistence of an initial relative equilibrium subjected to this forced symmetry breaking. We see that, under certain nondegeneracy conditions, an estimate can be made on the number of bifurcating relative equilibria. To cite this article: F. Grabsi et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Block designs admitting regular automorphisms

This paper treats a class of combinatorial designs which are essentially partially balanced incomplete block designs with two associate classes and with the additional feature that there are constants s and t so that for any treatment-block pair (x, B), the number of first associates of x in the block B is s or t depending on whether x ? B or x ? B. We obtain necessary and sufficient conditions that a P.B.I.B.D. should have this feature and obtain generalizations of earlier results on triangular and L₂ (n) P.B.I.B.D.'s. Finally, we consider two graphs naturally associated with quasi symmetric P.B.I.B.D.'s having this special feature determine their spectra, and investigate the conditions under which they are strongly regular.     

On the necessity of the solvable conditions of the typical boundary value problems for quasilinear hyperbolic systems

Some solvable conditions have been derived to ensure the existence and the uniqueness of the C^∞solution for the typical boundary problem on a local angular region for quasilinear hyperbolic systems in two variables[1]. These solvables conditions mean that, under the formulation of the typical boundary problem, the all order derivatives of the solution can be determined uniquely at the vertex. The main purpose of this paper is to show that these solvable conditions are also necessary. In other words, if these solvable conditions fail to hold, then the boundary value problem will either have no solution or have infinite number of solutions.     

T cell activation: Kinetic proofreading,serial engagement and cell adhesion

There is a fundamental difference in complexity between signaling initiated by ligands on the surface of one cell binding to receptors on the surface of another cell and ligands in solution binding to these receptors. The fact that two cells must approach each other and form a number of intercellular bonds of different types, all within the restricted geometry of the intercellular contact region, introduces the possibility of complex spatio-temporal dynamics of surface receptors that is not present otherwise. Mathematical modelling of these dynamics is in its early stages. However, useful tools have emerged. The purpose of this paper is to describe some of these mathematical tools, indicating their strengths and shortcomings, and suggest some directions for future theoretical studies.     

Large deviations and stochastic flows of diffeomorphisms

Summary Previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold M are extended and then applied to the analysis of the Lyapunov exponents of a stochastic flow of diffeomorphisms of M. An approximation argument relates these results to the behavior near the diagonal Δ in M ² of the associated two point motion. Finally it is shown, under appropriate non-degeneracy conditions, that the two-point motion is ergodic on M ²-Δ if the top Lyapunov exponent is positive. At the period when this research was initiated, both authors where guests of the I.M.A. in Minneapolis. The first author was at Aberdeen University, Scotland when this article was prepared. Throughout the period of this research, the second author has been partially supported by N.S.F. grant DMS-8611487 and ARO grant DAAL03-86-K-171     

ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES

In [1], C. Brezinski raised three unsolved questions in studing multivariable Pade-iype approximation, and the convergence of multivariable Pade-iype approximants under the general conditions is one of them. We have only seen in [2] that the convergence of the mullivariable Fade-type approximants is discussed for a kind of functions defined by Stieltjes integrations under some special conditions. However, the general convergence theorem has not been seen so far. In this paper, some error formulae of bivariate Fade-type approximants in in-legral form are given. By virtue of them, a number of convergence theorems of bivariate Pade-iype approximants are proved under general conditions.     

Modeling and analysis of the latent period of osteosarcomas induced by incorporated Pu: The role of immune responses

This paper considers the utility of a stochastic model of carcinogenesis, proposed earlier by Yakovlev and Polig, in quantitative analysis of the incidence of radiation-induced osteosarcomas in beagels injected with various amounts of ²³⁹Pu. The original version of the model failed to provide a good fit to our experimental data. The model has been generalized by incorporating a simple mechanism of lesion elimination, which is likely to be mediated by the immune system. Two versions of the model were developed: the first version ( Model 1 ) assumed malignant cells to be a target for the immune attack, while in Model 2 initiated cells were assumed to be such a target. Model 2 was rejected by the likelihood ratio test, thereby indicating that the competing model provides a more plausible explanation of the experimental data. Since in experiments with incorporated radionuclides the dose rate varies with time, dose-rate effects cannot be observed directly, and one must rely on mathematical models. The results of our numerical experiments show that, depending on the time of observation, both the direct and the inverse dose-rate effects may manifest themselves even at a fixed total dose level.     

Orphan-Free Anisotropic Voronoi Diagrams

We describe conditions under which an appropriately defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.     

环与剩余类环的同调维数

Ｓａｎｄｏｍｉｅｒｓｋｉ Ｆ．Ｌ,Ｓｍａｌｌ Ｌ．Ｗ,和 Ｆｉｅｌｄｓ Ｋ．Ｌ．［１－２］在“幂零”条件下研究了环与约化环的同调维数．然而对一些环（如交换 Ｖｏｎ Ｎｅｕｍａｎｎ正则环）,“幂零’的条件是不成立的．因此,在本文中我们考虑非“幂零”条件下（如Ｒ（Ｒ／Ｉ）（（Ｒ／Ｉ）Ｒ）是Ｒ－投身的或Ｒ（Ｒ／Ｉ）Ｒ是Ｒ－平坦的）,环与约化环的同调维数．