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In this paper, we discuss new efficient algorithms for nonnegative matrix factorization (NMF) with smoothness constraints imposed on nonnegative components or factors. Such constraints allow us to alleviate certain ambiguity problems, which facilitates better physical interpretation or meaning. In our approach, various basis functions are exploited to flexibly and efficiently represent the smooth nonnegative components. For noisy input data, the proposed algorithms are more robust than the existing smooth and sparse NMF algorithms. Moreover, we extend the proposed approach to the smooth nonnegative Tucker decomposition and smooth nonnegative canonical polyadic decomposition (also called smooth nonnegative tensor factorization). Finally, we conduct extensive experiments on synthetic and real-world multi-way array data to demonstrate the advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The coupled canonical polyadic decomposition (CPD) is an emerging tool for the joint analysis of multiple data sets in signal processing and statistics. Despite their importance, linear algebra based algorithms for coupled CPDs have not yet been developed. In this paper, we first explain how to obtain a coupled CPD from one of the individual CPDs. Next, we present an algorithm that directly takes the coupling between several CPDs into account. We extend the methods to single and coupled decompositions in multilinear rank-(Lr,n, Lr,n, 1) terms. Finally, numerical experiments demonstrate that linear algebra based algorithms can provide good results at a reasonable computational cost. [ABSTRACT FROM AUTHOR]

Looking at the operation of forming neat $$\alpha $$ -reducts as a functor, with $$\alpha $$ an infinite ordinal, we investigate when such a functor obtained by truncating $$\omega $$ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric algebras of infinite dimension, endowed with the merry go round identities, fails to have the amalgamation property answering a question of Németi's. We also study two variants of the so-called cylindric polyadic algebras introduced by Ferenczi (all are reducts of polyadic equality algebras, that are also varieties). We show that one is more cylindric than polyadic, and that the other is more polyadic than cylindric. Our classification is determined by results on neat embeddings and amalgamation expressed from the point of view of category theory, thereby witnessing, and, indeed, further emphasizing, the dichotomy between the cylindric and polyadic paradigms. For example, the first class does not have the unique neat embedding property, fails to have the amalgamation property and the neat reduct functor does not have a right adjoint, while the second class has the unique neat emdedding property, the superamalgamation property and the neat reduct functor is strongly invertible. Other results, like first order definability of the class of neat reducts and the class of completely representable algebras, confirming our classification along these lines are presented. [ABSTRACT FROM AUTHOR]

Let α be an ordinal and κ be a cardinal, both infinite, such that κ ≤ |α|. For τ ∈αα, letsup(τ) = {i ∈ α: τ(i) ≠ i}. LetGκ = {τ ∈αα: |sup(τ)| < κ}. We consider variants of polyadic equality algebras by taking cylindrifications on Γ ⊆ α, |Γ| < κ and substitutions restricted toGκ. Such algebras are also enriched with generalized diagonal elements. We show that for any varietyVcontaining the class of representable algebas and satisfying a finite schema of equations,Vfails to have the amalgamation property. In particular, many varieties of Halmos’ quasi-polyadic equality algebras and Lucas’ extended cylindric algebras (including that of the representable algebras) fail to have the amalgamation property. [ABSTRACT FROM AUTHOR]

Boolos has suggested a plural interpretation of second-order logic for two purposes: (i) to escape Quine's allegation that second-order logic is set theory in disguise, and (ii) to avoid the paradoxes arising if the second-order variables are given a set-theoretic interpretation in second-order set theory. Since the plural interpretation accounts only for monadic second-order logic, Rayo and Yablo suggest an new interpretation for polyadic second-order logic in a Boolosian spirit. The present paper argues that Rayo and Yablo's interpretation does not achieve the goal. [ABSTRACT FROM AUTHOR]

Coupled tensor decompositions are becoming increasingly important in signal processing and data analysis. However, the uniqueness properties of coupled tensor decompositions have not yet been studied. In this paper, we first provide new uniqueness conditions for one factor matrix of the coupled canonical polyadic decomposition (CPD) of third-order tensors. Then, we present necessary and sufficient overall uniqueness conditions for the coupled CPD of third-order tensors. The results demonstrate that improved uniqueness conditions can indeed be obtained by taking into account the coupling between several tensor decompositions. We extend the results to higher-order tensors and explain that the higher-order structure can further improve the uniqueness results. We discuss the special case of coupled matrix-tensor factorizations. We also present a new variant of the coupled CPD model called the coupled block term decomposition (BTD). On one hand, the coupled BTD can be seen as a variant of coupled CPD for the case where the common factor contains collinear columns. On the other hand, it can also be seen as an extension of the decomposition into multilinear rank-(Lr, Lr, 1) terms to coupled factorizations. [ABSTRACT FROM AUTHOR]

We prove several interpolation theorems for many-valued infinitary logic with quantifiers by studying expansions of MV-algebras in the spirit of polyadic and cylindric algebras. We prove for various reducts of polyadic MV-algebras of infinite dimensions that ifis the free algebra in the given signature,,is in the subalgebra ofgenerated by,is in the subalgebra ofgenerated byand, then there exists an interpolantin the subalgebra generated byandsuch that. We call this a varying interpolation property because the integerdepends on the inequality. We also address cases where this interpolation property fails, but other weaker (also varying) ones hold. One such interpolation theorem says that though an interpolantmay not be found as above, an interpolant can always be found if finitely many universal quantifiers are applied tomaking it smaller and the same number of existential quantifiers are applied tomaking it bigger. This number of quantifiers also varies; it depends on the inequality. Several amalgamation theorems for classes (mostly varieties) of polyadic MV-algebras are obtained. Completeness theorems, relative to Hilbert-style axiomatisations, for the corresponding infinitary many-valued predicate logics are derived using the methodology of algebraic logic. [ABSTRACT FROM PUBLISHER]

Answering a question posed by Hodkinson, we show that for infinite ordinals α, every atomic polyadic algebra of dimension α ( PA) is completely representable if and only if it is completely additive. We readily infer, noting that complete additivity of an operation in an atomic algebra is a first order definable property, that the class of completely representable PAs, is elementary. This is in sharp contrast to the cylindric algebra case. [ABSTRACT FROM AUTHOR]

Non-negative tensor factorization (NTF) has been successfully applied to analyze event-related potentials (ERPs), and shown superiority in terms of capturing multi-domain features. However, the time-frequency representation of ERPs by higher-order tensors are usually large-scale, which prevents the popularity of most tensor factorization algorithms. To overcome this issue, we introduce a non-negative canonical polyadic decomposition (NCPD) based on low-rank approximation (LRA) and hierarchical alternating least square (HALS) techniques. We applied NCPD (LRAHALS and benchmark HALS) and CPD to extract multi-domain features of a visual ERP. The features and components extracted by LRAHALS NCPD and HALS NCPD were very similar, but LRAHALS NCPD was 70 times faster than HALS NCPD. Moreover, the desired multi-domain feature of the ERP by NCPD showed a significant group difference (control versus depressed participants) and a difference in emotion processing (fearful versus happy faces). This was more satisfactory than that by CPD, which revealed only a group difference. [ABSTRACT FROM AUTHOR]

The main aim of this article is to establish a characterization of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraic simpleness), and group theory, GTS (group theoretical simpleness). We obtain necessary and sufficient conditions for a polyadic group to be UAS or GTS. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, various growth rates and oscillation conditions for entire functions of exponential type are given which ensure validity of the classical cardinal series. Among other applications, a theorem of Plancherel and Polya is extended to show that any function of exponential type which decays to 0 along the real axis is a convergent cardinal series. Examples of functions which show the limitations of this extension are also presented. [Copyright &y& Elsevier]

SUMMARY We study the least squares functional of the canonical polyadic tensor decomposition for third order tensors by eliminating one factor matrix, which leads to a reduced functional. An analysis of the reduced functional leads to several equivalent optimization problem, such as a Rayleigh quotient or a projection. These formulations are the basis of several new algorithms as follows: the Centroid Projection method for efficient computation of suboptimal solutions and fixed-point iteration methods for approximating the best rank-1 and the best rank- R decompositions under certain nondegeneracy conditions. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Non-negative tensor factorization (NTF) has been successfully used to extract significant characteristics from polyadic data, such as data in social networks. Because these polyadic data have multiple dimensions (e.g., the author, content, and timestamp of a blog post), NTF fits in naturally and extracts data characteristics jointly from different data dimensions. In the traditional NTF, all information comes from the observed data, and therefore, the end users have no control over the outcomes. However, in many applications very often, the end users have certain prior knowledge, such as the demographic information about individuals in a social network or a pre-constructed ontology on the contents and therefore prefer the data characteristics extracting by NTF being consistent with such prior knowledge. To allow users' prior knowledge to be naturally incorporated into NTF, in this paper, we present a general framework-FacetCube-that extends the standard NTF. The new framework allows the end users to control the factorization outputs at three different levels for each of the data dimensions. The proposed framework is intuitively appealing in that it has a close connection to the probabilistic generative models. In addition to introducing the framework, we provide an iterative algorithm for computing the optimal solution to the framework. We also develop an efficient implementation of the algorithm that consists of several techniques to make our framework scalable to large data sets. Extensive experimental studies on a paper citation data set and a blog data set demonstrate that our new framework is able to effectively incorporate users' prior knowledge, improves performance over the traditional NTF on the task of personalized recommendation, and is scalable to large data sets from real-life applications. [ABSTRACT FROM AUTHOR]

Abstract: We show that for finite , every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras, polyadic algebras, and polyadic equality algebras contains an infinite number of non-canonical formulas. We also show that the class of structures for each of these varieties is non-elementary. The proofs employ algebras derived from random graphs. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a framework to compute approximate CANDECOMP / PARAFAC (CP) decompositions. Such tensor decompositions are viable tools in a broad range of applications, creating the need for versatile tools to compute such decompositions with an adjustable complexity-accuracy trade-off. To this end, we propose a novel SEmi-algebraic framework that allows the computation of approximate C P decompositions via SImultaneous Matrix Diagonalizations (SECSI). In contrast to previous Simultaneous Matrix Diagonalization (SMD)-based approaches, we use the tensor structure to construct not only one but the full set of possible SMDs. Solving all SMDs, we obtain multiple estimates of the factor matrices and present strategies to choose the best estimate in a subsequent step. This SECSI framework retains the option to choose the number of SMDs to solve and to adopt various strategies for the selection of the final solution out of the multiple estimates. A best matching scheme based on an exhaustive search as well as heuristic selection schemes are devised to flexibly adapt to specific applications. Four example algorithms with different accuracy-complexity trade-off points are compared to state-of-the-art algorithms. We obtain more reliable estimates and a reduced computational complexity. [Copyright &y& Elsevier]

For a digraph ℍ, the Constraint Satisfaction Problem with template ℍ, or CSP(ℍ), is the problem of deciding whether a given input digraph 픾 admits a homomorphism to ℍ. The CSP dichotomy conjecture of Feder and Vardi states that for any digraph ℍ, CSP(ℍ) is either in P or NP-complete. Barto, Kozik, Maróti and Niven ( Proc. Amer. Math. Soc. 137 (2009) 2921-2934) confirmed the conjecture for a class of oriented trees called special triads. We generalize this result, establishing the dichotomy for a class of oriented trees which we call special polyads. We prove that every tractable special polyad has bounded width and provide the description of special polyads of width 1. We also construct a tractable special polyad which neither has width 1 nor admits any near-unanimity polymorphism. [ABSTRACT FROM AUTHOR]

Canonical polyadic (also known as Candecomp/Parafac) decomposition (CPD) of a higher-order tensor is decomposition into a minimal number of rank-1 tensors. In Part I, we gave an overview of existing results concerning uniqueness and presented new, relaxed, conditions that guarantee uniqueness of one factor matrix. In Part II we use these results for establishing overall CPD uniqueness in cases where none of the factor matrices has full column rank. We obtain uniqueness conditions involving Khatri-Rao products of compound matrices and Kruskal-type conditions. We consider both deterministic and generic uniqueness. We also discuss uniqueness of INDSCAL and other constrained polyadic decompositions. [ABSTRACT FROM AUTHOR]

Canonical polyadic decomposition (CPD) of a higher-order tensor is decomposition into a minimal number of rank-1 tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee uniqueness of one factor matrix. These conditions involve Khatri-Rao products of compound matrices. We make links with existing results involving ranks and k-ranks of factor matrices. We give a shorter proof, based on properties of second compound matrices, of existing results concerning overall CPD uniqueness in the case where one factor matrix has full column rank. We develop basic material involving mth compound matrices that will be instrumental in Part II for establishing overall CPD uniqueness in cases where none of the factor matrices has full column rank. [ABSTRACT FROM AUTHOR]

Higher order tensor inversion is possible for even order. This is due to the fact that a tensor group endowed with the contracted product is isomorphic to the general linear group of degree n. With these isomorphic group structures, we derive a tensor SVD which we have shown to be equivalent to well-known canonical polyadic decomposition and multilinear SVD provided that some constraints are satisfied. Moreover, within this group structure framework, multilinear systems are derived and solved for problems of high-dimensional PDEs and large discrete quantum models. We also address multilinear systems which do not fit the framework in the least-squares sense. These are cases when there is an odd number of modes or when each mode has distinct dimension. Numerically we solve multilinear systems using iterative techniques, namely, biconjugate gradient and Jacobi methods. [ABSTRACT FROM AUTHOR]

Non-negative Canonical Polyadic decomposition (NCPD) and non-negative Tucker decomposition (NTD) were compared for extracting the. multi-domain feature of visual mismatch negativity (vMMN), a small event-related potential (ERP), for the cognitive research. Since signal-to-noise ratio in vMMN is low, NTD outperformed NCPD. Moreover, we proposed an approach to select the multi-domain feature of an ERP among all extracted features and discussed determination of numbers of extracted components in NCPD and NTD regarding the ERP context. [ABSTRACT FROM AUTHOR]

The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in linguistic theory and offer new empirical predictions for sentence processing with embedded quantifiers. [ABSTRACT FROM AUTHOR]

The vibrational nonlinear dynamics of HOBr in the bending and O-Br stretching coordinates with anharmonicity and Fermi 2:1 coupling are studied with dynamical potentials in this article. The result shows that the H-O stretching vibration mode has significantly different effects on the coupling between the O-Br stretching mode and the H-O-Br bending mode under different Polyad numbers. The dynamical potentials and the corresponding phase space trajectories are obtained when the Polyad number is 27, for instance, and the fixed points in the dynamical potentials of HOBr are shown to govern the various quantal environments in which the vibrational states lie. Furthermore, it is also found that the quantal environments could be identified by the numerical values of action integrals, which is consistent with former research. [ABSTRACT FROM AUTHOR]

We prove three interpolation theorems for typless logics with equality. Typless logics, introduced by Henkin and Tarski, are algebraizable extensions of first-order logic allowing infinitary predicate symbols. Δα (α an infinite ordinal) denotes the language of a typless logic with α many variables. As a sample, we shall prove:THEOREM 1Let Δα be a language (possibly uncountable). Let ψ, ø, be formulas such that Then there exist m<α, i&varepsilon;m α and ŋ a formula containing only atomic formulas occurring in ψ and ø, in short such that Fmr denotes the set of all formulas in a language. Now assuming, that everything is countable, we show that there exists two unary connectives, such that if Fm denotes the formulas in this expanded language, thenTHEOREM 2 That is, in the countable case, we can add finitely many connectives to code the quantified variables in Theorem 1. Our last interpolation theorem addresses certain (natural) expansions of Fmr. We also give counterexamples showing that the scope of our results is the best possible. Our treatmet is algebraic via reducts of polyadic equality algebras. (2000 Mathematics Subject Classification. Primary 03G15. Secondary 03C05, 03C40.) [ABSTRACT FROM PUBLISHER]

Vaught's Conjecture states that if Σ is a complete first order theory in a countable language such that Σ has uncountably many pairwise non-isomorphic countably infinite models, then Σ has 2ℵ0 many pairwise non-isomorphic countably infinite models. Continuing investigations initiated in Sági (2011, submitted for publication), we apply methods of algebraic logic to study some variants of Vaught's conjecture. More concretely, let S ⊆ ωω be a σ-compact monoid. We prove, among other things, that if a complete first order theory Σ has at least ℵ1 many countable models that cannot be elementarily embedded into each other by elements of S, then, in fact, Σ has continuum many such models. We also study-related questions in the context of equality free logics and obtain similar results. Our proofs are based on the representation theory of cylindric and quasi-polyadic algebras (for details see Henkin, Monk and Tarski (cylindric Algebras Part 1 and Part 2)) and topological properties of the Stone spaces of these algebras. [ABSTRACT FROM PUBLISHER]

Canonical polyadic decomposition (CPD) of a higher-order tensor is an important tool in mathematical engineering. In many applications at least one of the matrix factors is constrained to be columnwise orthonormal. We first derive a relaxed condition that guarantees uniqueness of the CPD under this constraint. Second, we give a simple proof of the existence of the optimal low-rank approximation of a tensor in the case that a factor matrix is columnwise orthonormal. Third, we derive numerical algorithms for the computation of the constrained CPD. In particular, orthogonality-constrained versions of the CPD methods based on simultaneous matrix diagonalization and alternating least squares are presented. Numerical experiments are reported. [ABSTRACT FROM AUTHOR]

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor () and one by Dowty (). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that the positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. [ABSTRACT FROM AUTHOR]

Abstract: We combine two of the existing approaches to the study of concurrency by means of multiset rewriting: multiset rewriting with existential quantification (MSR) and constrained multiset rewriting. We obtain ν-MSR, where we rewrite multisets of atomic formulae, in which terms can only be pure names, where some names can be restricted. We consider the subclass of depth-bounded ν-MSR, for which the interdependence of names is bounded. We prove that they are strictly Well Structured Transition Systems, so that coverability, termination and boundedness are all decidable for depth-bounded ν-MSR. This allows us to obtain new verification results for several formalisms with name binding that can be encoded within ν-MSR, namely polyadic ν-PN (Petri nets with tuples of names as tokens), the π-calculus, MSR or Mobile Ambients. [Copyright &y& Elsevier]

In this paper we introduce the polyadic tense $$\theta$$-valued $$\L$$ukasiewicz-Moisil algebras (=polyadic tense $$\hbox{LM}_{\theta}$$-algebras), as a common generalization of polyadic tense Boolean algebras and polyadic $$\hbox{LM}_{\theta}$$-algebras. Our main result is a representation theorem for polyadic tense $$\hbox{LM}_{\theta}$$-algebras. [ABSTRACT FROM AUTHOR]

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group (G, f) = der θ, b (G, ·), we obtain a complete description of automorphisms and representations of (G, f) in terms of automorphisms and representations of the binary group (G, ·). [ABSTRACT FROM PUBLISHER]

A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the authors discus various reports within the issue on topics including probability interpretation, polyadic inductive logic, and the nature of probabilities from deterministic processes.

A version of the classical representation theorem for Boolean algebras states that the fields of sets form a variety and that a possible axiomatization is the system of Boolean axioms. An important case for fields of sets occurs when the unit V is a subset of an ?-power ?U. Beyond the usual set operations union, intersection, and complement, new operations are needed to describe such a field of sets, e.g., the ith cylindrification Ci, the constant ijth diagonal Dij , the elementary substitution [i / j] and the transposition [i, j] for all i, j < ? restricted to the unit V . Here it is proven that such generalized fields of sets being closed under the above operations form a variety; further, a first order finite scheme axiomatization of this variety is presented. In the proof a crucial role is played by the existence of the operator transposition. The foregoing axiomatization is close to that of finitary polyadic equality algebras (or quasi-polyadic equality algebras). [ABSTRACT FROM AUTHOR]

Abstract: Computing the minimal polyadic decomposition (also often referred to as canonical decomposition or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the enhanced line search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors. [Copyright &y& Elsevier]

Using games, as introduced by Hirsch and Hodkinson in algebraic logic, we give a recursive axiomatization of the class of representable quasi-polyadic equality algebras of any dimension α. Following Sain and Thompson in modifying Andréka's methods of splitting, to adapt the quasi-polyadic equality case, we show that if Σ is a set of equations axiomatizing for and , k′ < ω are natural numbers, then Σ contains infinitely equations in which − occurs, one of + or · occurs, a diagonal or a permutation with index l occurs, more than k cylindrifications and more than k′ variables occur. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim [ABSTRACT FROM AUTHOR]

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study the phenomenon that instruction sequences are split into fragments which somehow produce a joint behaviour. In order to bring this phenomenon better into the picture, we formalize a simple mechanism by which several instruction sequence fragments can produce a joint behaviour. We also show that, even in the case of this simple mechanism, it is a non-trivial matter to explain by means of a translation into a single instruction sequence what takes place on execution of a collection of instruction sequence fragments. [ABSTRACT FROM AUTHOR]

In this paper we study decidability of several extensions of P/T nets with name creation and/or replication. In particular, we study how to restrict the models of RN systems (P/T nets extended with replication, for which reachability is undecidable) and ν-RN systems (RN extended with name creation, which are Turing-complete, so that coverability is undecidable), in order to obtain decidability of reachability and coverability, respectively. We prove that if we forbid synchronizations between the different components in a RN system, then reachability is still decidable. Similarly, if we forbid name communication between the different components in a ν-RN system, or restrict communication so that it is allowed only for a given finite set of names, we obtain decidability of coverability. Finally, we consider a polyadic version of ν-PN (P/T nets extended with name creation), that we call pν-PN, in which tokens are tuples of names. We prove that pν-PN are Turing complete, and discuss how the results obtained for ν-RN systems can be translated to them. [ABSTRACT FROM AUTHOR]

We show that the representability of cylindric algebras by relativized set algebras depends on the scope of the operation transposition which can be defined on the algebra. The existence of 'partial transposition' assures this kind of representability of the cylindric algebra (while the existence of transposition assures polyadic representation). Further we characterize those cylindric algebras in which the operator transposition can be introduced (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In [10], Sayed Ahmed recently has shown that there exists an infinite dimensional non-representable quasi-polyadic equality algebra (QPEAω, for short) with a representable cylindric reduct. In this paper we continue related investigations and show that if G⊆ωω is a semigroup containing at least one constant function, then a wide class of representable cylindric algebras occur as the cylindric reduct of some non-representable G-PEAω. More concretely, we prove that if A is an ω-dimensional cylindric set algebra with an infinite base set, then there exists a non-representable G-PEAω whose cylindric reduct is representable and contains an isomorphic copy of A. [ABSTRACT FROM PUBLISHER]

In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12]. [ABSTRACT FROM PUBLISHER]

We show that the bounded fragment of first–order logic and the hybrid language with 'downarrow' and 'at' operators are equally expressive even with polyadic modalities, but that their 'positive' fragments are equally expressive only for unary modalities. [ABSTRACT FROM AUTHOR]

Abstract: We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a measure of separation between radiating sources called coherence, one could always guarantee the existence and uniqueness of a best rank-r approximation of the tensor representing the signal. We also deduce a computationally feasible variant of Kruskal''s uniqueness condition, where the coherence appears as a proxy for k-rank. Problems of sparsest recovery with an infinite continuous dictionary, lowest-rank tensor representation, and blind source separation are treated in a uniform fashion. The decomposition of the measurement tensor leads to simultaneous localization and extraction of radiating sources, in an entirely deterministic manner. [Copyright &y& Elsevier]

In this article we define polyadic BL-algebras as algebraic structures for BL-predicate calculus (BL∀). We prove a representation theorem, which is the algebraic counterpart of the completeness theorem for BL∀, and we obtain as a particular case a representation theorem for polyadic Pavelka algebras. [ABSTRACT FROM AUTHOR]

We show that for infinite ordinals α the class of polyadic algebras of dimension α has the super amalgamation property (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The article discusses the ways to make change for a U.S. dollar. It mentions several methods including the Brute force approach which tallies the solutions to the equation and the Pòlya's recurrence formula method which yields an algorithm for generating ways to make change for a dollar. In addition, a generating function is best understood if it is expressed in a rational function.

We show that there exists an atomic polyadic equality algebra of dimension n that is elementary equivalent to a completely representable algebra, but its diagonal free reduct (obtained by deleting diagonals and substitutions) is not completely representable. [ABSTRACT FROM PUBLISHER]

We consider algebras with a single n-ary operation and a certain type of associativity. We prove that (up to isomorphism) there are exactly 5 of these associative mono-n-ary algebras with 2 elements for even n ≥ 2 and 6 for odd n ≥ 3. These algebras are described explicitly. It is shown that a similar result is impossible for algebras with at least 4 elements. An application concerning the assignment of a control bit to a string is given. [ABSTRACT FROM AUTHOR]

A class of many-sorted polyadic set algebras is introduced. These generalise structure and model in a way that is relevant in regards to the Entscheidungsproblem and to automated reasoning. A downward Löwenheim-Skolem property is shown in that each satisfiable finite conjunction of purely relational first-order prenex sentences has a finite generalised model. This property does, together with a construction related to doubling the size of a finite structure, provide several strict generalisations of the strategy of finite model search for disproving. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]