On the tractability of the Brownian Bridge algorithm

ON SOME CLASSES OF BI-UNIVALENT FUNCTIONS

A checking test for a monotone read-once function f depending essentially on all its n variables is a set of vectors M distinguishing f from all other monotone read-once functions of the same variables. We describe an inductive procedure for obtaining individual lower and upper bounds on the minimal number of vectors T(f) in a checking test for any function f. The task of deriving the exact value of T(f) is reduced to a combinatorial optimization problem related to graph connectivity. We show that for almost all functions f expressible by read-once conjunctive or disjunctive normal forms, T(f) ~n / ln n. For several classes of functions our results give the exact value of T(f).

In [9], the notion of c-differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from the technique of higher order differential cryptanalysis, in this paper we propose the notion of higher order c-derivatives and differentials and investigate their properties. Additionally, we consider how several classes of functions, namely the multiplicative inverse function and the Gold function, perform under higher order c-differential uniformity.

Have decidual natural killer (dNK) cells a different microRNA (miRNA or miR) expression pattern compared to NK cells circulating in the peripheral blood (pb) of healthy pregnant women in the first trimester of gestation? dNK cells have a unique miRNA profile, showing exclusive expression of a set of miRNAs and significant up- or down-regulation of most of the miRNAs shared with pbNK cells. dNK cells differ from pbNK cells both phenotypically and functionally, and their origin is still debated. Many studies have indicated that miRNAs regulate several important aspects of NK cell biology, such as development, activation and effector functions. Decidua basalis and peripheral blood specimens were collected from women (n = 7) undergoing voluntary termination of gestation in the first trimester of pregnancy. dNK and pbNK cells were then highly purified by cell sorting. miRNAs expression was analysed by quantitative RT-PCR (qRT-PCR)-based arrays using RNA purified from freshly isolated and highly purified pbNK and dNK cells. Results from arrays were validated by qRT-PCR assays. The bioinformatics tool ingenuity pathway analysis (IPA) was applied to determine the cellular network targeted by validated miRNAs and the correlated biological functions. Herein, we identified the most differentially expressed miRNAs in NK cells isolated from peripheral blood and uterine decidua of pregnant women. We found that 36 miRNAs were expressed only in dNK cells and two miRNAs only in pbNK cells. Moreover, 48 miRNAs were commonly expressed by both NK cell preparations although at different levels: 28 were upregulated in dNK cells, while 15 were downregulated compared to pbNK cells. Validation of a selected set (n = 11) of these miRNAs confirmed the differential expression of nine miRNAs: miR-10b and miR-214 expressed only in dNK cells and miR-200a-3p expressed only in pbNK cells; miR-130b-3p, miR-125a-5p, miR-212-3p and miR-454 were upregulated while miR-210-3p and miR-132 were downregulated in dNK cells compared to pbNK cells. IPA network analysis identified a single network connecting all the miRNAs as well as their significant involvement in several classes of functions: 'Organismal injury, Reproductive system disease, Inflammatory disease' and 'Cellular development'. These miRNAs target molecules such as argonaute 2, tumour protein p53, insulin and other genes that belong to the same network and significantly influence cell differentiation and pregnancy. In the present study, the cellular network and biological functions modulated by miRNAs differentially expressed in dNK and pbNK cells were identified by IPA considering only molecules and relationships that were with confidence 'experimentally observed' in leucocytes. The decidual and pbNK cells that were analysed here are a heterogeneous population and further study will help to disentangle whether there are differences in miRNA production by the different subsets of NK cells. This is the first study describing a different miRNA expression profile in dNK cells compared to matched pbNK cells during the first trimester of pregnancy. Our findings improved the body of knowledge on dNK cell biology and strongly suggest further investigation into the roles of miRNAs that are differentially expressed in human dNK compared to pbNK cells. Our results suggest that specific miRNAs can modulate dNK cell origin and functions, highlighting a potential role of this miRNA signature in human development and diseases. This work was supported by grants from the Istituto Pasteur, Fondazione Cenci Bolognetti, the European NoE EMBIC within FP6 (Contract number LSHN-CT-2004-512040), Istituto Italiano di Tecnologia, and Ministero dell'Istruzione, dell'Università e della Ricerca (Ricerche Universitarie), and from Università Politecnica delle Marche. There are no conflicts of interest to declare.

The delay of circuits whose inputs have specified arrival times

Many voting systems consist of a set of players who can form coalitions; a winning coalition is one that can pass a measure. The winning and losing coalitions can be given by several classes of functions, including switching functions, threshold functions, weighted voting systems, and simple games. We define a zonotope T n T_n related to these functions and describe its coordinates in terms of a measure of voting power. We also give a voting interpretation of the coordinates of the derived zonotope T ¯ n \bar {T}_n .

High-dimensional integrals occur in a variety of areas, including mathematical finance. In the classical settings, multivariate integration problems suffer from the curse of dimensionality. To vanquish the curse of dimensionality, one may shrink the function class. Here, we use weighted function spaces, in which groups of variables are associated with weights, in order to capture the different importance of each group of variables. For practical applications, the principal difficulty is then in choosing the ‘right’ weights for a given problem or a class of problems. We work in weighted reproducing kernel Hilbert spaces (with ‘general’ rather than ‘product’ weights). We first present a principle to find the good weights for a given problem. This general approach is then applied to a simplified high-dimensional problem from finance, in which the dimension is the number of discrete timesteps for a price of a risky asset which follows geometric Brownian motion. The second focus of this paper is on the dimension reduction techniques, such as the Brownian bridge (BB) and the principal component analysis (PCA). It turns out that the behaviour of the model problem is dramatically improved when quasi-Monte Carlo method is used in conjunction with the dimension reduction techniques: if the right weights are used in every case, then the integration error can be bounded independently of the dimension, whereas without BB or PCA the error bound depends exponentially on the dimension. Finally, for this model problem we show how to construct shifted lattice rules which, when used in conjunction with BB or PCA, yield integration errors converging as O(n−3/4+δ) or O(n−1+δ) (for arbitrary small δ > 0), respectively, independently of the dimension. Thus, in both cases well-designed algorithms can avoid the curse of dimensionality, with PCA having an advantage over BB with respect to the proved order of convergence.

We consider the eigenvalue problem associated with the Dunkl-type differential operator (in which the reflection operator R is involved)in the context of supersymmetric quantum mechanical models. By solving this eigenvalue problem with the help of known exactly solvable potentials, we construct several classes of functions satisfying certain orthogonality relations. We call them the Dunkl-supersymmetric (Dunkl-SUSY) orthogonal functions. These functions can be expressed in terms of the classical orthogonal polynomials. The key feature of these functions is that they appear by pairs, i.e. Qn(x) and Qn(−x) are both the eigenfunctions of . A general formulation of the Dunkl-SUSY orthogonal polynomials is also presented.

Let varGamma (x) denote the classical Euler gamma function. The logarithmic derivative psi (x)=[ln varGamma (x)]'=frac{varGamma '(x)}{ varGamma (x)}, psi '(x), and psi ''(x) are, respectively, called the digamma, trigamma, and tetragamma functions. In the paper, the authors survey some results related to the function [psi '(x)]^{2}+ psi ''(x), its q-analogs, its variants, its divided difference forms, several ratios of gamma functions, and so on. These results include the origins, positivity, inequalities, generalizations, completely monotonic degrees, (logarithmically) complete monotonicity, necessary and sufficient conditions, equivalences to inequalities for sums, applications, and the like. Finally, the authors list several remarks and pose several open problems.

Medical Therapy for Heart Failure With Reduced Ejection Fraction: The CHAMP-HF Registry

In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and the variance reduction that can be achieved with stratified sampling. We first put the emphasis on the consistency of quantization for partitioning the state space in stratified sampling methods in both finite and infinite-dimensional cases. We show that the proposed quantization-based strata design has uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for other Gaussian processes such as Brownian bridge or Ornstein–Uhlenbeck processes. We derive in detail the case of Ornstein–Uhlenbeck processes. We also study the balance between the algorithmic complexity of the simulation and the variance reduction factor.

Relaxation of multidimensional variational problems with constraints of general form

The least-squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001) is a method for Monte Carlo valuation of the price of American options. We use quasi-random sequences to generate asset prices which follow geometric Brownian motions, and obtain a significant increase in the rate of convergence of American min-puts and American-Bermuda-Asian calls. Using the Brownian-bridge formula, we present a method for reducing the memory requirements from O(N x M x d) to O(Nd log(M)) for quasi-random sequences, where N is the number of paths, M is the number of timesteps and d is the number of assets, for example, in a min-put.

Recent results by Toda, Vinay, Damm, and Valiant have shown that the complexity of the determinant is characterized by the complexity ofcounting the number ofaccepting computations ofa nondeterministic logspace-bounded machine. (This class of functions is known as #L) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of theorem of Jung, showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.

These lecture notes present an extensive review of the factorization theory of matrix functions relative to a curve with emphasis on the developments of the last 20–25 years. The classes of functions considered range from rational and continuous matrix functions to matrix functions with almost periodic or even semi almost periodic entries. Also included are recent results about explicit factorization based on the state space method from systems theory, with examples from linear transport theory. Related applications to Riemann-Hilbert boundary value problems and the Fredholm theory of various classes of singular integral operators are described too. The applications also concern inversion of singular integral operators of different types, including Wiener-Hopf and Toeplitz operators.