Weighted voting, threshold functions, and zonotopes

ON SOME CLASSES OF BI-UNIVALENT FUNCTIONS

Consider a situation with n agents or players, where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not (losing). A simple game can be viewed as a monotone boolean function. The dimension of a simple game is the smallest positive integer d such that the simple game can be expressed as the intersection of d threshold functions, where each threshold function uses a threshold and n weights. Taylor and Zwicker have shown that d is bounded from above by the number of maximal losing coalitions. We present two new upper bounds both containing the Taylor-Zwicker bound as a special case. The Taylor-Zwicker bound implies an upper bound of (n choose n/2). We improve this upper bound significantly by showing constructively that d is bounded from above by the cardinality of any binary covering code with length n and covering radius 1. This result supplements a recent result where Olsen et al. showed how to construct simple games with dimension |C| for any binary constant weight SECDED code C with length n. Our result represents a major step in the attempt to close the dimensionality gap for simple games.

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.

On the tractability of the Brownian Bridge algorithm

The delay of circuits whose inputs have specified arrival times

In this paper, the structure of the set of threshold functions and complexity problems are considered. The notion of the signature of a threshold function is defined. It is shown that if a threshold function essentially depends on all of its variables, then the signature of this function is unique. The set of threshold functions is partitioned into classes with equal signatures. A theorem characterizing this partition is proved. The importance of the class of monotone threshold functions is emphasized. The complexity of transferring one threshold function specified by a linear form into another is examined. It is shown that in the worst case this transfer would take exponential time. The structure of the set of linear forms specifying the same threshold function is also examined. It is proved that for any threshold function this set of linear forms has a unique basis in terms of the operation of addition of linear forms. It is also shown that this basis is countable.

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.

In this paper we shall present two types of sufficient conditions under which a switching function can be represented by a threshold gate, i. e., a threshold function, with n variables for an arbitrary positive integer n. In deriving these sufficient conditions, a new concept called an orientating vector is introduced in this paper and it will play an important role in our discussion since it gives an insight into the structure of a threshold gate. We shall begin with notations and preliminaries in Section 2. In Section 3, we shall introduce the notion of orientating vectors in terms of which we give the sufficient conditions for threshold functions. Indeed, an orientating vector can be used to classify the set of all the input vectors Ix), x(2), ••• , x(2n)} into two subsets where one is a set of true (i. e., on) vectors and the other a set of false (i. e., off) vectors. If we arrange all input vectors in an inverse lexical order (see Kitagawa [3]), then, for any p, 1 p_27', a classification of all the input vectors into the two sets Ix), x(2) x(1 and fx(p+1) x(p+2), x(271)1 represents a threshold function as stated in Proposition 3.2. In Section 4, it is described that the combination of two sufficient conditions turn out to be necessary so far as p in the above classification is not greater than 4. This is the reason why the combination of these two sufficient conditions amounts to be necessary and sufficient so far as n is not greater than 3 as given in Section 5. Our results can be compared with the notion of 2-asummability due to Elgot [2] and Chow [1] which gives the necessary and sufficient condition that a switching function is a threshold function when n in not greater than 8. It is noted that the results of this paper can be used to get all the possible digraphs associated with dynamical behaviors of the neuronic equation

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

The Role of the Weighted Voting System in Investments in Local Public Education: Evidence from a New Historical Database

Apoptotic proteins play key roles in understanding the mechanism of programmed cell death. Knowledge about the subcellular localization of apoptotic protein is constructive in understanding the mechanism of programmed cell death, determining the functional characterization of the protein, screening candidates in drug design, and selecting protein for relevant studies. It is also proclaimed that the information required for determining the subcellular localization of protein resides in their corresponding amino acid sequence. In this work, a new biological feature, class pattern frequency of physiochemical descriptor, was effectively used in accordance with the amino acid composition, protein similarity measure, CTD (composition, translation, and distribution) of physiochemical descriptors, and sequence similarity to predict the subcellular localization of apoptosis protein. AdaBoost with the weak learner as Random-Forest was designed for the five modules and prediction is made based on the weighted voting system. Bench mark dataset of 317 apoptosis proteins were subjected to prediction by our system and the accuracy was found to be 100.0 and 92.4%, and 90.1% for self-consistency test, jack-knife test, and tenfold cross validation test respectively, which is 0.9% higher than that of other existing methods. Beside this, the independent data (N151 and ZW98) set prediction resulted in the accuracy of 90.7 and 87.7%, respectively. These results show that the protein feature represented by a combined feature vector along with AdaBoost algorithm holds well in effective prediction of subcellular localization of apoptosis proteins. The user friendly web interface "APSLAP" has been constructed, which is freely available at http://apslap.bicpu.edu.in and it is anticipated that this tool will play a significant role in determining the specific role of apoptosis proteins with reliability.

Protein location prediction using atomic composition and global features of the amino acid sequence