Testing Monotone Read-Once Functions

Disjunctive and conjunctive normal forms of pseudo-Boolean functions

ON SOME CLASSES OF BI-UNIVALENT FUNCTIONS

We consider the problem of efficiently indexing Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) Boolean expressions over a high-dimensional multi-valued attribute space. The goal is to rapidly find the set of Boolean expressions that evaluate to true for a given assignment of values to attributes. A solution to this problem has applications in online advertising (where a Boolean expression represents an advertiser's user targeting requirements, and an assignment of values to attributes represents the characteristics of a user visiting an online page) and in general any publish/subscribe system (where a Boolean expression represents a subscription, and an assignment of values to attributes represents an event). All existing solutions that we are aware of can only index a specialized sub-set of conjunctive and/or disjunctive expressions, and cannot efficiently handle general DNF and CNF expressions (including NOTs) over multi-valued attributes. In this paper, we present a novel solution based on the inverted list data structure that enables us to index arbitrarily complex DNF and CNF Boolean expressions over multi-valued attributes. An interesting aspect of our solution is that, by virtue of leveraging inverted lists traditionally used for ranked information retrieval, we can efficiently return the top-N matching Boolean expressions. This capability enables emerging applications such as ranked publish/subscribe systems [16], where only the top subscriptions that match an event are desired. For example, in online advertising there is a limit on the number of advertisements that can be shown on a given page and only the "best" advertisements can be displayed. We have evaluated our proposed technique based on data from an online advertising application, and the results show a dramatic performance improvement over prior techniques.

The problem is the transformation of a conjunctive normal form (CNF) into a minimized (for the inclusion operator) disjunctive normal form (DNF) and vice versa. This operation is called the unionist product. For a CNF (resp. DNF), one pass of the unionist product provides the prime implicants (resp. implicates); two passes provide the prime implicates (resp. implicants). An algorithm built upon the classical Davis and Putnam procedure is presented for calculating, without the explicit minimization for the inclusion, this unionist product.

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

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 .

We describe the problem of mining set valued rules in large relational tables containing categorical attributes taking a finite number of values. Such rules allow for an interval of possible values to be selected for each attribute in condition instead of a single value for association rules, while conclusion contains a projection of the data restricted by the condition onto a target attribute. An example of such a rule might be “if HOUSEHOLDSIZE = {Two OR Tree} AND OCCUPATION={Professional OR Clerical} THEN PAYMENT_METHOD = {CashCheck (Max=249, Sum=4952) OR DebitCard (Max=175, Sum=3021)} WHERE Confidence=85%, Support=10%.}” We use an original conceptional and formal framework for representing multidimensional distribution induced from data by a number of so-called prime disjunctions upper bounding its surface. Each prime disjunction represents a wide multidimensional interval of impossible combinations of attribute values. This original formalism generalises the conventional boolean approach in two directions: (i) finite-valued attributes (instead of only 0 and 1), and (ii) continuous-valued semantics instead of (true and false). In addition, we describe an efficient algorithm, which carries out the generalised dual transformation from possibilistic disjunctive normal form (DNF) representing data into conjunctive normal form (CNF) representing knowledge and thus generates all the most interesting prime disjunctions. Once obtained they can be used to build different forms of rules or for other purposes (prediction, clustering etc.).

Normal forms for fuzzy logic functions and their approximation ability

Translation among CNFs, characteristic models and ordered binary decision diagrams

Fuzzy set theories allow us to represent our knowledge under various interpretations and axiomatic foundations from linguistic to computational representations. There are at least four levels of knowledge representation: (i) linguistic, (ii) meta-linguistic, (iii) propositional, and (iv) computational. There are three transformations, which depend on the particular interpretations put on a knowledge representation schema. There are various choices, corresponding to one's interpretation of: (a) type of set representation, (fuzzy or crisp), (b) type of propositional connectives and normal forms, and (c) type of computational connectives, i.e., weak or strong t-norms and co-norms. In the light of these selections, fuzzy disjunctive and conjunctive normal forms (FDNF, FCNF) are derived from fuzzy truth tables. It is shown that classical expressions such as excluded middle etc., when fuzzified, ought to be reinterpreted with a type II, second order, semantic uncertainty. The classical expressions should not be interpreted as to whether they are valid or not. One can only state that the well-known tautologies of classical logic are valid to many degrees specified by an interval defined by their FDNF and FCNF. FDNF and FCNF boundaries identify the nonspecificity measure associated with type II, second order, semantic uncertainty. Thus, those researchers who are not familiar or who are not concerned with type II semantic uncertainty work with a myopic understanding of fuzzy set and logic theories. >

Feature terms are a common denominator of basic data-structures in knowledge representation and computational linguistics. The adaptation of the usual unification algorithms for first order terms is not straightforward, because feature terms may contain logical disjunction. Expansion into disjunctive normal form would reduce the problem more or less to unification of first order terms. But for reasons of efficiency, rewriting into disjunctive normal form should not be compulsory. In this paper, a sequent calculus is defined which gives a clear formal basis for proof optimizations: inference steps which require more than one subproof, i.e. which lead towards a “disjunctive normal form”, are only performed when they are no longer unavoidable. It is shown that the calculus is sound and complete with respect to the so-called feature structure interpretations of feature terms.

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.