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Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP2 for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach. [ABSTRACT FROM AUTHOR]

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Tamura proved that for any semigroup word U( x, y), if every group satisfying an identity of the form yx ~ xU( x, y) y is abelian, then so is every semigroup that satisfies that identity. Because a group has an identity element and the cancellation property, it is easier to show that a group is abelian than that a semigroup is. If we know that it is, then there must be a sequence of substitutions using xU( x, y) y ~ yx that transforms xy to yx. We examine such sequences and propose finding them as a challenge to proof by computer. Also, every model of y ~ xU( x, y) x is a group. This raises a similar challenge, which we explore in the special case y ~ x y x. In addition, we determine the free model with two generators of some of these identities. In particular, we find that the free model for y ~ x yx has order 32 and is the product of D (the symmetries of a square), C, and C, and point out relations between such identities and Burnside's Problem concerning models of x ~ y. We also examine several identities not related to groups. [ABSTRACT FROM AUTHOR]

We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure. [ABSTRACT FROM AUTHOR]

An improved circulating current control method by applying a digital plug-in repetitive controller is discussed for harmonic elimination of a carrier-phase-shift pulse-width-modulation (CPS-PWM)-based modular multilevel converter (MMC) in this paper. The performance of the controller is analyzed in detail based on an improved circulating current control model with the consideration of the submodule voltage disturbance. It is shown that the proposed control method has the merits of simplicity, versatility, and better performance of circulating harmonic current elimination than the traditional proportional integral controller. The stability analysis of the proposed method are also discussed in the paper as well as the design principles. Finally, the experimental results including the steady-state performance and the transient response are given, which validates the feasibility and excellent performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The extensive use of pulse width modulation control technology in smart grid will lead to prominent enlargement of high-frequency harmonics. The effects of the distributed capacitances of transmission line and transformer that are neglected previously will be very obvious. The performance of the traditional harmonic eliminating method for wideband harmonic is limited, which will lead to huge challenge to the analysis, evaluation, and elimination of harmonics as well as series and parallel resonance problem. In this paper, to accurately describe the influence of wideband harmonic on smart grid, the multiterminal analysis model of harmonic degradation in smart grid is established, especially the distributed capacitances of the transmission line and the transformer are considered. Then, a novel topology of hybrid active power filter (HAPF) for resonance damping and multitype harmonic eliminating is proposed. The resonance damping model of the new topology is established; analysis results indicate that the proposed HAPF has a good harmonic resonance damping characteristic. Both simulation and experimental results have validated the validity of the theoretical analysis in this paper. [ABSTRACT FROM AUTHOR]

A new type of partially global consistency derived from (2, k)-consistency called bounded (2, k)- consistency (B2C-consistency) is presented in this paper. It is designed for application in propositional satisfiability (SAT) as a building block for a preprocessing tool. Together with the new B2C-consistency a special mechanism for selecting regions of the input SAT instance with difficult constraint setup was also proposed. This mechanism is used to select suitable difficult sub-problems whose simplification through consistency can lead to a significant reduction in the effort needed to solve the instance. A new prototype preprocessing tool preprocessSIGMA which is based on the proposed techniques was implemented. As a proof of new concepts a competitive experimental evaluation on a set of relatively difficult SAT instances was conducted. It showed that our prototype preprocessor is competitive with respect to the existent preprocessing tools LiVer, NiVer, HyPre, blocked clause elimination (BCE), and Shatter with saucy 3.0. [ABSTRACT FROM AUTHOR]

Statistical engineering as proposed by Hoerl and Snee (2010a) aims to develop a discipline devoted to better understanding how to use statistical tools to support project goals. Existing examples abound but more work is needed. We discuss the use of statistical engineering to improve problem solving—that is, reducing variation in processes—and note that this requires a series of empirical investigations where we should use information gained to help plan subsequent investigations. The systematic use of prior/existing information, especially baseline information, in problem solving is illustrated using a crossbar dimension case study. The baseline results are used to help plan and analyze all subsequent investigations both when looking for a dominant cause of the variation and when assessing a possible solution. The effective use of prior statistical information and the consequences of its use in the variation reduction context are not commonly taught and thus opportunities for more efficient problem solving are lost. [ABSTRACT FROM AUTHOR]

This paper introduces new approaches for the analysis of frequent statement and dereference elimination for imperative and objectoriented distributed programs running on parallelmachines equipped with hierarchical memories.The paper uses languageswhose address spaces are globally partitioned. Distributed programs allow defining data layout and threads writing to and reading from other threadmemories. Three type systems (for imperative distributed programs) are the tools of the proposed techniques. Thefirst type systemdefines for every programpoint a set of calculated (ready) statements andmemory accesses.Thesecond type systemuses an enriched version of types of the first type system and determines which of the ready statements and memory accesses are used later in the program.Thethird type systemuses the information gather so far to eliminate unnecessary statement computations and memory accesses (the analysis of frequent statement and dereference elimination). Extensions to these type systems are also presented to cover object-oriented distributed programs. Two advantages of our work over related work are the following.The hierarchical style of concurrent parallel computers is similar to the memory model used in this paper. In our approach, each analysis result is assigned a type derivation (serves as a correctness proof). [ABSTRACT FROM AUTHOR]

Model structure selection is of crucial importance in radial basis function (RBF) neural networks. Existing model structure selection algorithms are essentially forward selection or backward elimination methods that may lead to sub-optimal models. This paper proposes an alternative selection procedure based on the kernelized least angle regression (LARS)–least absolute shrinkage and selection operator (LASSO) method. By formulating the RBF neural network as a linear-in-the-parameters model, we derive a l1-constrained objective function for training the network. The proposed algorithm makes it possible to dynamically drop a previously selected regressor term that is insignificant. Furthermore, inspired by the idea of LARS, the computing of output weights in our algorithm is greatly simplified. Since our proposed algorithm can simultaneously conduct model structure selection and parameter optimization, a network with better generalization performance is built. Computational experiments with artificial and real world data confirm the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A simple technique called the elimination method is proposed for calculation of the reflected and transmitted wave amplitudes in the case when two counterpropagating waves are incident on a multilayer structure with a step irregularity. The functioning of the method is exemplified by a structure consisting of ten media where the wave numbers are randomly distributed. The properties of the distribution of the reflected wave amplitude density that are due to the relationship between the structure's thickness and the minimum wavelength in it are revealed. It is shown that a disorder in the distribution of wave numbers in the interior of the structure reduces reflection, and a parameter quantitatively characterizing this reduction is proposed. [ABSTRACT FROM AUTHOR]

The Selective Harmonic Elimination Pulse Width Modulation technique (SHEPWM) is widely used for eliminating pre-selected lower order harmonics in multilevel inverters (MLI) output voltage with controlling the fundamental voltage component. The problem of roots solving of the set of transcendental nonlinear harmonic equations derived by Fourier analysis is addressed in many recent researches. The Newton Raphson (NR) method is limited used in case of multilevel inverter controlled by SHEPWM, due to the transcendental nature of the system set of equations and dependency of roots initial values. Modern optimization techniques such as Genetic Algorithm (GA) optimization are widely used in case of MLI controlled by SHEPWM. The main problem when using GA is how to find the switching angle patterns for a wide range of the modulation index (M). Which they eliminate pre-selected lower order harmonics and controlling the fundamental voltage component with minimum Total Harmonic Distortion (THD). In this paper a comprehensive study to obtain the required switching patterns which satisfy elimination pre-selected lower order harmonics at minimum THD from cascaded MLI output voltage controlled by SHEPWM was performed. The performance of cascaded multilevel inverter controlled by SHEPWM is compared based on calculating the required switching patterns using NR and GA methods. A significant improve in the obtained solution sets in a wide range of M in GA is achieved. In particular, it is shown that there are new solution sets which haven't been previously reported in literatures. Selected simulation and experimental results for 5, 7, 9 and 11 MLIs were reported to verify and to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

To eliminate the signal trend terms, wavelet base functions are introduced for signal decomposition and reconstruction. The selection of wavelet bases may affect the result of eliminating signal trend. The concept of error index of signal trend elimination was proposed and the formula for calculating the index was presented. Using this formula, the error indexes of signal trend elimination of 34 types of wavelet bases were calculated. It was found that the wavelet bases of sym10 and other 5 types could be selected as preferred ones with less error indexes of signal trend elimination. Further, the sym10 and other two non-preferred wavelet bases were used to carry out the signal trend elimination of measured car body acceleration signal. The result shows that wavelet base of sym10 extracts the signal trend more precisely than other two non-preferred wavelet bases and the effectiveness of the presented formula for calculating the error index of signal trend elimination is validated [ABSTRACT FROM AUTHOR]

In this paper, we present a simple strategy for the elimination of the translational kinetic energy contamination of the total energy in pre-Born–Oppenheimer calculations carried out in laboratory-fixed Cartesian coordinates (LFCCs). The simple expressions for the coordinates and the operators are thus preserved throughout the calculations, while the mathematical form and the parametrisation of the basis functions are chosen so that the translational and rotational invariances are respected. The basis functions are constructed using explicitly correlated Gaussian functions (ECGs) and the global vector representation. First, we observe that it is not possible to parametrise the ECGs so that the system is at rest in LFCCs and at the same time the basis functions are square integrable with a non-vanishing (positive-definite) norm. Then, we work out a practical strategy to circumvent this problem by making use of the properties of the linear transformation between the LFCCs and translationally invariant and centre-of-mass Cartesian coordinates as well as the transformation properties of the corresponding basis function parameter matrices. By exploiting these formal mathematical relationships, we can identify and separate the translational contamination terms in the matrix representation of the kinetic energy operator in the LFCC formalism. We present numerical examples for the translational contamination and its elimination for the two lowest rotational energy levels of the singlet hydrogen molecule, corresponding to para- and ortho-H2, respectively, treated as four-particle quantum systems. [ABSTRACT FROM AUTHOR]

An efficient one-pot method for the regioselective bromination of allylic alcohol derivatives (two-step reaction sequence) followed by Sonogashira, Negishi, or Suzuki-Miyaura coupling reactions in the same reaction vessel (three-step reaction sequence) has been developed. The key reaction in these one-pot systems is the regioselective DBU-promoted trans HBr elimination of vicinal dibromides bearing an adjacent O-functional group. [ABSTRACT FROM AUTHOR]

The problem of resolution of singularities in positive characteristic can be reformulated as follows: fix a hypersurface $X$, embedded in a smooth scheme, with points of multiplicity at most $n$. Let an $n$-sequence of transformations of $X$ be a finite composition of monoidal transformations with centers included in the $n$-fold points of $X$, and of its successive strict transforms. The open problem (in positive characteristic) is to prove that there is an $n$-sequence such that the final strict transform of $X$ has no points of multiplicity $n$ (no $n$-fold points). In characteristic zero, such an $n$-sequence is defined in two steps. The first consists of the transformation of $X$ to a hypersurface with $n$-fold points in the so-called monomial case. The second step consists of the elimination of these $n$-fold points (in the monomial case), which is achieved by a simple combinatorial procedure for choices of centers. The invariants treated in this work allow us to present a notion of strong monomial case which parallels that of monomial case in characteristic zero: if a hypersurface is within the strong monomial case we prove that a resolution can be achieved in a combinatorial manner. [ABSTRACT FROM AUTHOR]

We design an algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its orthogonal projection along a given direction. The resultant is fundamental in algebraic elimination, optimization, and geometric modeling. Our algorithm exactly computes vertex- and halfspace-representations of the polytope using an oracle producing resultant vertices in a given direction, thus avoiding walking on the polytope whose dimension is α - n - 1, where the input consists of α points in ℤn. Our approach is output-sensitive as it makes one oracle call per vertex and per facet. It extends to any polytope whose oracle-based definition is advantageous, such as the secondary and discriminant polytopes. Our publicly available implementation uses the experimental CGAL package triangulation. Our method computes 5-, 6- and 7- dimensional polytopes with 35K, 23K and 500 vertices, respectively, within 2hrs, and the Newton polytopes of many important surface equations encountered in geometric modeling in < 1sec, whereas the corresponding secondary polytopes are intractable. It is faster than tropical geometry software up to dimension 5 or 6. Hashing determinantal predicates accelerates execution up to 100 times. One variant computes inner and outer approximations with, respectively, 90% and 105% of the true volume, up to 25 times faster. [ABSTRACT FROM AUTHOR]

A numerical method for solving the Cauchy problem for all the six Painlevé equations is proposed. The difficulty of solving these equations is that the unknown functions can have movable (that is, dependent on the initial data) singular points of the pole type. Moreover, the Painlevé III-VI equations may have singularities at points where the solution takes certain finite values. The positions of all these singularities are not a priori known and are determined in the process of solving the equation. The proposed method is based on the transition to auxiliary systems of differential equations in neighborhoods of the indicated points. The equations in these systems and their solutions have no singularities at the corresponding point and its neighborhood. Such auxiliary equations are derived for all Painlevé equations and for all types of singularities. Efficient criteria for transition to auxiliary systems are formulated, and numerical results illustrating the potentials of the method are presented. [ABSTRACT FROM AUTHOR]

RFID technologies are gaining much attention as they are attractive solutions to many applications. Localization based on active RFID technologies provides a much needed added-value to further expand the application domain. LANDMARC was the first attempt using active RFID for indoor location sensing with satisfactory results. However, the LANDMARC approach suffers from two drawbacks. First, it does not work well in a closed area with severe radio signal multi-path effects. Second, to further improve the localization accuracy, more reference tags are required which is costly and may trigger the RF interference phenomenon. The proposed VIRE approach can overcome the above drawbacks without any additional cost. Based on the concept of virtual reference tags, a proximity map is maintained by each reader. An elimination algorithm is used to eliminate those unlikely locations to reduce the estimation error. Our experimental results show that the new method consistently enhances the precision of indoor localization from 17 to 73 percent over the LANDMARC approach at different tag locations in different environments. [ABSTRACT FROM AUTHOR]

The first part of this article shows that qualitative comparative analysis (QCA)—also in its most recent form as in Ragin (2008)—does not correctly analyze data generated by causal chains. The incorrect modeling of data originating from chains essentially stems from QCA’s reliance on Quine-McCluskey optimization to eliminate redundancies from sufficient and necessary conditions. Baumgartner (2009a, 2009b) has introduced a Boolean methodology, termed coincidence analysis (CNA), which is related to QCA, yet, contrary to the latter, does not eliminate redundancies by means of Quine-McCluskey optimization. The second part of the article applies CNA to chain-generated data. It turns out that CNA successfully detects causal chains in small-n data. [ABSTRACT FROM AUTHOR]

We present an advanced design methodology for pulse-width-modulated (PWM) DC-AC signal generation. Using design methods based on the Walsh transform, AC sinusoidal signals can be approximated by suitable PWM signals. For different AC amplitudes, the switching instants of the PWM signals can be efficiently computed by using appropriate systems of explicit linear equations. However, the equation systems provided by conventional implementations of this approach are typically only valid for a restricted interval of AC amplitudes and, in general, a supervised implementation of several equation systems is necessary to cover the full AC amplitude range. Additionally, obtaining suitable equation systems for designs with a large number of switching instants requires solving a complex optimization problem. In defining the constitutive pulses of a PWM signal, a suitable partition of the time interval is used as a reference system. In the new methodology, pulses are chosen to be symmetric with respect to the partition points, and the switching times are specified by means of switching ratios with respect to the endpoint subintervals. This approach leads to particularly simple Walsh series representations, introduces a remarkable computational simplification, and achieves excellent results in reducing the harmonic distortion. [ABSTRACT FROM AUTHOR]

Multivariate polynomials are usually discussed in the framework of algebraic geometry. Solving problems in algebraic geometry usually involves the use of a Gröbner basis. This article shows that linear algebra without any Gröbner basis computation suffices to solve basic problems from algebraic geometry by describing three operations: multiplication, division, and elimination. This linear algebra framework will also allow us to give a geometric interpretation. Multivariate division will involve oblique projections, and a link between elimination and principal angles between subspaces (CS decomposition) is revealed. The main computational tool in this approach is the QR decomposition. [ABSTRACT FROM AUTHOR]

SUMMARY The most efficient way to parallelize computation is to build and evaluate the task graph constrained only by the data dependencies between the tasks. Both Intel's C++ Concurrent Collections (CnC) and Threading Building Blocks (TBB) libraries allow such task-based parallel programming. CnC also adapts the macro data flow model by providing only single-assignment data objects in its global data space. Although CnC makes parallel programming easier, by specifying data flow dependencies only through single-assignment data objects, its macro data flow model incurs overhead. Intel's C++ CnC library is implemented on top of its C++ TBB library. We can measure the overhead of CnC by comparing its performance with that of TBB. In this paper, we analyze all three types of data dependencies in the tiled in-place Gauss-Jordan elimination algorithm for the first time. We implement the task-based parallel tiled Gauss-Jordan algorithm in TBB using the data dependencies analyzed and compare its performance with that of the CnC implementation. We find that the overhead of CnC over TBB is only 12 %- 15 % of the TBB time, and CnC can deliver as much as 87 %- 89 % of the TBB performance for Gauss-Jordan elimination, using the optimal tile size. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof-theoretic (rather than set-theoretic) notion of definition (Hallnäs, 1991 [18], Eriksson, 1991 [11], Schroeder-Heister, 1993 [38], McDowell and Miller, 2000 [22]). Definitions are akin to logic programs, where the left and right rules for defined atoms allow one to view theories as “closed” or defining fixed points. The use of definitions and free equality makes it possible to reason intensionally about syntax. We add in a consistent way rules for pre- and post-fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give a direct cut-elimination procedure in the presence of general inductive and co-inductive definitions via the parametric reducibility technique. [Copyright &y& Elsevier]

Lean manufacturing is a manufacturing system aimed at waste elimination thereby streamlining the process. Leanness is the performance measure of lean manufacturing. The measurement of leanness necessitates fuzzy logic, due of the existence of impreciseness and vagueness. The calculation of leanness using fuzzy logic manually is a time consuming and highly repetitive job. To overcome this, fuzzy logic-based inference method has been attempted in this research study. A conceptual model consisting of three levels namely enabler, criterion, and attributes has been developed. Then the linguistic variables are assigned and the membership functions are defined. Leanness level has been computed using IF-THEN rules based interface method. This is followed by gap analysis to identify the weaker criteria. Then suitable proposals have been derived to overcome these obstacles towards leanness improvement of the organization. [ABSTRACT FROM AUTHOR]

We characterize epistemic consequences of truthful communication among rational agents in a game-theoretic setting. To this end we introduce normal-form games equipped with an interaction structure, which specifies which groups of players can communicate their preferences with each other. We then focus on a specific form of interaction, namely a distributed form of iterated elimination of strictly dominated strategies (IESDS), driven by communication among the agents. We study the outcome of IESDS after some (possibly all) messages about players' preferences have been sent. The main result of the paper, Theorem 4, provides an epistemic justification of this form of IESDS. [ABSTRACT FROM AUTHOR]

In the proof-theoretic semantics approach to meaning, harmony, requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony, requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony: imposes the existence of certain transformations of derivations, known as reduction and expansion. We propose a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen's (and Pawitz') remark, that E-rules can be 'read off' I-rules. [ABSTRACT FROM AUTHOR]

Let T be a first-order theory. A correspondence is established between internal covers of models of T and definable groupoids within T . We also consider amalgamations of independent diagrams of algebraically closed substructures, and find strong relation between covers, uniqueness for 3-amalgamation, existence of 4-amalgamation, imaginaries of Tσ, and definable groupoids. As a corollary, we describe the imaginary elements of families of finite-dimensional vector spaces over pseudo-finite fields. [ABSTRACT FROM AUTHOR]

In this paper we inject four Hilbert functions in the determination of the defining equations of the Rees algebra of almost complete intersections of finite co-length. Because three of the corresponding modules are Artinian, some of these relationships are very effective, with the novel approach opening up tracks to the determination of the equations and also to processes of going from homologically defined sets of equations to higher degrees ones. While not specifically directed towards the extraction of elimination equations, it will show how some of these arise naturally. [ABSTRACT FROM AUTHOR]

Valentini (1983) has presented a proof of cut-elimination for provability logic GL for a sequent calculus using sequents built from sets as opposed to multisets, thus avoiding an explicit contraction rule. From a formal point of view, it is more syntactic and satisfying to explicitly identify the applications of the contraction rule that are ‘hidden’ in proofs of cut-elimination for such sequent calculi. There is often an underlying assumption that the move to a proof of cut-elimination for sequents built from multisets is straightforward. Recently, however, it has been claimed that Valentini’s arguments to eliminate cut do not terminate when applied to a multiset formulation of the calculus with an explicit rule of contraction. The claim has led to much confusion and various authors have sought new proofs of cut-elimination for GL in a multiset setting.Here we refute this claim by placing Valentini’s arguments in a formal setting and proving cut-elimination for sequents built from multisets. The use of sequents built from multisets enables us to accurately account for the interplay between the weakening and contraction rules. Furthermore, Valentini’s original proof relies on a novel induction parameter called “width” which is computed ‘globally’. It is difficult to verify the correctness of his induction argument based on “width.” In our formulation however, verification of the induction argument is straightforward. Finally, the multiset setting also introduces a new complication in the case of contractions above cut when the cut-formula is boxed. We deal with this using a new transformation based on Valentini’s original arguments.Finally, we discuss the possibility of adapting this cut-elimination procedure to other logics axiomatizable by formulae of a syntactically similar form to the GL axiom. [ABSTRACT FROM AUTHOR]

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic. [ABSTRACT FROM AUTHOR]

In this paper, we describe a code transformation technique that, given a code for a vector function F, produces a code suitable for computing collections of Jacobian-vector products F′(x)x˙ or Jacobian-transpose-vector products F′(x)T y¯. Exploitation of scarcity – a measure of the degrees of freedom in the Jacobian matrix – requires solving a combinatorial optimization problem that is believed to be hard. Our heuristics transform the computational graph for F, producing, in the form of a transformed graph G′, a representation of the Jacobian F′(x) that is both concise and suitable for evaluating large collections of the Jacobian-vector products or the Jacobian-transpose-vector products. Our heuristics are randomized and compare favourably in all cases with the best known heuristics. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal non-homogeneous version of a type theory, in which we show the embedding of the modal operators into standard group knowledge operators. [Copyright &y& Elsevier]

Abstract: State-of-the-art software packages for solving large-scale linear systems are predominantly founded on Gaussian elimination techniques (e.g. LU-decomposition). This paper presents an efficient framework for solving large-scale linear systems by means of a novel utilization of Cramerʼs rule. While the latter is often perceived to be impractical when considered for large systems, it is shown that the algorithm proposed retains an complexity with pragmatic forward and backward stability properties. Empirical results are provided to substantiate the stated accuracy and computational complexity claims. [Copyright &y& Elsevier]

The first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional fractional parabolic partial differential equations. [ABSTRACT FROM AUTHOR]

Abstract: The dichromatic polynomial can be characterized as the most general C-invariant, i.e., a graph polynomial satisfying a linear recurrence with respect to edge deletion and edge contraction. Similarly, the universal edge elimination polynomial introduced in [Ilya Averbouch, Benny Godlin, and Johann A. Makowsky. An extension of the bivariate chromatic polynomial. Eur. J. Comb, 31(1):1–17, 2010] can be characterized as the most general EE-invariant, i.e., a graph polynomial satisfying a linear recurrence with respect to edge deletion, edge contraction and edge extraction. In this paper we examine substitution instances of and show that among these the dichromatic polynomial plays a distinctive rôle. [Copyright &y& Elsevier]

We analyze a class of matrices generalizing strictly diagonally dominant matrices and included in the important class of H-matrices. Adequate pivoting strategies and the corresponding Schur complements are studied. A new class of matrices with all their principal minors positive is presented. [ABSTRACT FROM AUTHOR]

An optimal stopping problem of Markov chain with infinite horizon is considered. For the case of finite number m of states, Sonin proposed an algorithm, which allows to find the value function and the stopping set in not more than steps. The algorithm is based on a modification of Markov chain on each step, related with the elimination of the states which certainly belong to the continuation set. To solve the problem with arbitrary state space and to have a possibility of generalization to the continuous time, one needs to modify the procedure. We propose a procedure which is based on a sequential modification of the pay-off function for the same chain in such a way, that the value function is the same for both problems and the modified pay-off function is greater than the initial one on some set and is equal to it on the complement. We show the efficiency of this procedure. [ABSTRACT FROM AUTHOR]

There is a well-known connection between the three problems related to the optimal stopping of Markov chains and the equality of three corresponding indices: the classical Gittins index (GI) in the ratio maximization problem, the Kathehakis–Veinott index in a restart problem and Whittle index in a family of retirement problems. In Sonin [Statist. Probab. Lett. 78 (12,1) (2008), pp. 1526–1533], these three problems and these three indices were generalized in such a way that it became possible to use the state elimination algorithm [Sonin, Math. Meth of Oper. Res. (1999), pp. 111–123] to calculate this common generalized GI α. The main goal of this note is to demonstrate that the equality of these (generalized) indices is a special case of a more general relation between three simple abstract optimization problems. [ABSTRACT FROM AUTHOR]

We study a system, called NEL, which is the mixed commutative/noncommutative linear logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented with the noncommutative self-dual connective seq. In this article, we show a basic compositionality property of NEL, which we call decomposition. This result leads to a cut-elimination theorem, which is proved in the next article of this series. To control the induction measure for the theorem, we rely on a novel technique that extracts from NEL proofs the structure of exponentials, into what we call !-?-Flow-Graphs. [ABSTRACT FROM AUTHOR]

We consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over $\mathbb{F}_{2}$ generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. Although in most such applications any cycle basis can be used, a low weight cycle basis often translates to better performance and/or numerical stability. Despite the fact that the problem can be solved exactly in polynomial time, we design approximation algorithms since the performance of the exact algorithms may be too expensive for some practical applications. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k≥1, we give (2 k−1)-approximation algorithms with expected running time O( kmn+ mn) and deterministic running time O( n), respectively. Here ω is the best exponent of matrix multiplication. It is presently known that ω<2.376. Both algorithms are o( m) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the Θ( m) bound. We also present a 2-approximation algorithm with expected running time $O(m^{\omega}\sqrt{n\log n})$ , a linear time 2-approximation algorithm for planar graphs and an O( n) time 2.42-approximation algorithm for the complete Euclidean graph in the plane. [ABSTRACT FROM AUTHOR]

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the 'connectedness' of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an 'auxiliary logic' (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., 'red'. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. [ABSTRACT FROM AUTHOR]