Checking the validity of truncating the cumulant hierarchy description of a small system

We analyze the behavior of the first few cumulant in an array with a small number of coupled identical particles. Desai and Zwanzig (J. Stat. Phys., {\bf 19}, 1 (1978), p. 1) studied noisy arrays of nonlinear units with global coupling and derived an infinite hierarchy of differential equations for the cumulant moments. They focused on the behavior of infinite size systems using a strategy based on truncating the hierarchy. In this work we explore the reliability of such an approach to describe systems with a small number of elements. We carry out an extensive numerical analysis of the truncated hierarchy as well as numerical simulations of the full set of Langevin equations governing the dynamics. We find that the results provided by the truncated hierarchy for finite systems are at variance with those of the Langevin simulations for large regions of parameter space. The truncation of the hierarchy leads to a dependence on initial conditions and to the coexistence of states which are not consistent with the theoretical expectations based on the multidimensional linear Fokker-Planck equation for finite arrays

Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

Kernel Approximation on Manifolds II: The L∞L_{\infty}-norm of the L2L_2-projector

This article addresses two topics of significant mathematical and practical interest in the theory of kernel approximation: the existence of local and stable bases and the L_p--boundedness of the least squares operator. The latter is an analogue of the classical problem in univariate spline theory, known there as the "de Boor conjecture". A corollary of this work is that for appropriate kernels the least squares projector provides universal near-best approximations for functions f\in L_p, 1\le p\le \infty.Comment: 25 pages; minor revision; new proof of Lemma 3.9; accepted for publication in SIAM J. on Math. Ana

Синтез нечетких систем автоматического управления генетическими алгоритмами по векторным критериям в среде MATLAB

Задачи многокритериального параметрического синтеза систем управления сведены к задачам оптимизации векторных целевых функций, решение которых позволяет удержать процесс синтеза систем в допустимой области. Для оптимизации векторных целевых функций систем автоматического управления модифицированы бинарный и непрерывный генетические алгоритмы. Показана эффективность применения модифицированных генетических алгоритмов для синтеза систем управления путем оптимизации векторных целевых функций. Рассмотрение задач синтеза линейных и нечетких ПИД регуляторов показало, что в задаче синтеза нечеткого регулятора определяется вектор переменных параметров большей размерности, а в модели системы управления вместо линейных уравнений применяются нелинейные уравнения с использованием системы нечеткого вывода

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Temperature-driven single-valley Dirac fermions in HgTe quantum wells

We report on temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and temperature range from 2 K to 150 K, clearly indicate a change of the band-gap energy with temperature. The quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At the critical temperature of 90 K, the merging of inter- and intra-band transitions in weak magnetic fields clearly specifies the formation of gapless state, revealing the appearance of single-valley massless Dirac fermions with velocity of $5.6\times10^5$ m$\times$s$^{-1}$. For both quantum wells, the energies extracted from experimental data are in good agreement with calculations on the basis of the 8-band Kane Hamiltonian with temperature-dependent parameters.Comment: 5 pages, 3 figures and Supplemental Materials (4 pages

On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems

Cyclin A1 and P450 aromatase promote metastatic homing and growth of stem-like prostate cancer cells in the bone marrow

Bone metastasis is a leading cause of morbidity and mortality in prostate cancer (PCa). While cancer stem-like cells have been implicated as a cell of origin for PCa metastases, the pathways which enable metastatic development at distal sites remain largely unknown. In this study, we illuminate pathways relevant to bone metastasis in this disease. We observed that cyclin A1 (CCNA1) protein expression was relatively higher in PCa metastatic lesions in lymph node, lung, and bone/bone marrow. In both primary and metastatic tissues, cyclin A1 expression was also correlated with aromatase (CYP19A1), a key enzyme that directly regulates the local balance of androgens to estrogens. Cyclin A1 overexpression in the stem-like ALDHhigh subpopulation of PC3M cells, one model of PCa, enabled bone marrow integration and metastatic growth. Further, cells obtained from bone marrow metastatic lesions displayed self-renewal capability in colony forming assays. In the bone marrow, Cyclin A1 and aromatase enhanced local bone marrow-releasing factors, including androgen receptor, estrogen and matrix metalloproteinase MMP9 and promoted hte metastatic growth of PCa cells. Moreover, ALDHhigh tumor cells expressing elevated levels of aromatase stimulated tumor/host estrogen production and acquired a growth advantage in the presence of host bone marrow cells. Overall, these findings suggest that local production of steroids and MMPs in the bone marrow may provide a suitable microenvironment for ALDHhigh PCa cells to establish metastatic growths, offering new approaches to therapeutically target bone metastases

Pseudomonas aeruginosa biofilm is a potent inducer of phagocyte hyperinflammation

OBJECTIVE: Pseudomonas aeruginosa effectively facilitate resistance to phagocyte killing by biofilm formation. However, the cross talk between biofilm components and phagocytes is still unclear. We hypothesize that a biofilm provides a concentrated extracellular source of LPS, DNA and exopolysaccharides (EPS), which polarize neighbouring phagocytes into an adverse hyperinflammatory state of activation. METHODS: We measured the release of a panel of mediators produced in vitro by murine neutrophils and macrophages exposed to various biofilm components of P. aeruginosa cultures. RESULTS: We found that conditioned media from a high biofilm-producing strain of P. aeruginosa, PAR5, accumulated high concentrations of extracellular bacterial LPS, DNA and EPS by 72 h. These conditioned media induced phagocytes to release a hyperinflammatory pattern of mediators, with enhanced levels of TNF-α, IL-6, IL12p40, PGE2 and NO. Moreover, the phagocytes also upregulated COX-2 and iNOS with no influence on the expression of arginase-1. CONCLUSIONS: Phagocytes exposed to biofilm microenvironment, called by us biofilm-associated neutrophils/macrophages (BANs/BAMs), display secretory properties similar to that of N1/M1-type phagocytes. These results suggest that in vivo high concentrations of LPS and DNA, trapped in biofilm by EPS, might convert infiltrating phagocytes into cells responsible for tissue injury without direct contact with bacteria and phagocytosis