Search

Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by \'Ciri\'c et al. (2012) as fuzzy relations between the sets of states of the automata. However, they act as a crisp relationship between the automata. In particular, if there exists a (forward) bisimulation between two fuzzy automata, then the fuzzy languages recognized by them are crisply equal. Approximate simulations and bisimulations introduced by Stanimirovi\'c et al. (2020) aim at fuzzifying this phenomenon. However, they are defined only for fuzzy automata over a complete Heyting algebra and do not give the exact relationship between states of the automata. In this article, we introduce and study fuzzy simulations and bisimulations between fuzzy automata over a complete residuated lattice. These notions are novel and have good properties. They are defined for fuzzy automata over any complete residuated lattice. We prove that the fuzzy language recognized by a fuzzy automaton is fuzzily preserved by fuzzy simulations and fuzzily invariant under fuzzy bisimulations. We also prove that the notions of fuzzy simulation and bisimulation have the Hennessy-Milner properties, which are a logical characterization of the greatest fuzzy simulation or bisimulation between two fuzzy automata. In addition, we provide results showing that our notions of fuzzy simulation and bisimulation are more general and refined than the notions of simulation and bisimulation introduced by \'Ciri\'c et al. and the notions of approximate simulation and bisimulation introduced by Stanimirovi\'c et al.

Quipper is a functional programming language for quantum computing. Proto-Quipper is a family of languages aiming to provide a formal foundation for Quipper. In this paper, we extend Proto-Quipper-M with a construct called dynamic lifting , which is present in Quipper. By virtue of being a circuit description language, Proto-Quipper has two separate runtimes: circuit generation time and circuit execution time. Values that are known at circuit generation time are called parameters , and values that are known at circuit execution time are called states . Dynamic lifting is an operation that enables a state, such as the result of a measurement, to be lifted to a parameter, where it can influence the generation of the next portion of the circuit. As a result, dynamic lifting enables Proto-Quipper programs to interleave classical and quantum computation. We describe the syntax of a language we call Proto-Quipper-Dyn. Its type system uses a system of modalities to keep track of the use of dynamic lifting. We also provide an operational semantics, as well as an abstract categorical semantics for dynamic lifting based on enriched category theory. We prove that both the type system and the operational semantics are sound with respect to our categorical semantics. Finally, we give some examples of Proto-Quipper-Dyn programs that make essential use of dynamic lifting.

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of the six possible combinations of the preceding), those laws of random times are precisely characterized that are rendered no bigger [rendered no smaller; left invariant] by all possible restart laws (within the classes (i), (ii), (iii), as the case may be). Partial results in the same vein for reset with branching are obtained. In particular it is found that deterministic and arbitrary stochastic restart lead to the same characterizations, but this equivalence fails to persist for exponential (constant-rate) reset.

Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum devices such as those available at the IBM Q Experience. Quantum circuit reversibility is ensured by minimal complements, extended recursively. Measurements are postponed to the end of such recursive computations, termed "quantamorphisms", thus maximising the quantum effect. Quantamorphisms are classical catamorphisms which, extended to ensure quantum reversibility, implement quantum cycles (vulg. for-loops) and quantum folds on lists. By Kleisli correspondence, quantamorphisms can be written as monadic functional programs with quantum parameters. This enables the use of Haskell, a monadic functional programming language, to perform the experimental work. Such calculated quantum programs prepared in Haskell are pushed through Quipper to the Qiskit interface to IBM Q quantum devices. The generated quantum circuits - often quite large - exhibit the predicted behaviour. However, running them on real quantum devices incurs into a significant amount of errors. As quantum devices are constantly evolving, an increase in reliability is likely in the near future, allowing for our programs to run more accurately., 18 pages

Semantic network is a network of concepts connected by semantic relations. It contains two forms of binary semantic network and multiplex semantic network. The associated fact prediction is a link prediction task that aims to infer the implicitly connected facts by mining the high-level representation of the network. Previous methods for associated fact prediction put much emphasis on the topological feature of network but not utilize the information of semantic expression. This paper proposes a Semantic Network Encoder (SemNE), which learns a feature mapping function from the binary semantic networks and can be applied to the multiplex semantic networks in a pre-training manner. SemNE is a two-stage framework that contains an embedding encoder and a prediction decoder. It jointly models the semantic information and network topology to enrich the network representation. A word self-organization method based on the factual boundary is proposed to unify the topological feature and the semantic feature representations. Experimental results on binary semantic networks show that SemNE achieves the state-of-the-art results in associated fact prediction and experimental results on multiplex semantic networks show that SemNE is scalable and can effectively improve the performance of existing models.

We characterize the optimal solution to the linear programming relaxation of the standard formulation for the minimum satisfiability problem. We give a O ( n m 2 ) combinatorial algorithm to solve the fractional version of the minimum satisfiability problem optimally where n ( m ) is the number of variables (clauses). As a by-product, we obtain a 2 ( 1 − 1 ∕ 2 k ) approximation algorithm for the minimum satisfiability problem where k is the maximum number of literals in any clause.

Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting their reusability. In other PPLs, models are not readily composable. Using Haskell as the host language, we present an embedded domain specific language based on algebraic effects, where probabilistic models are modular, first-class, and reusable for both simulation and inference. We also demonstrate how simulation and inference can be expressed naturally as composable program transformations using algebraic effect handlers.

Many problem domains, including program synthesis and rewrite-based optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—version-space algebras, finite tree automata, or e-graphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduce equality-constrained tree automata (ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a type-driven program synthesizer for Haskell. Hectare significantly outperforms a state-of-the-art synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller.

Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by uninterpreted events, while admitting a rich equational theory of equivalence. But monads are not the only way to structure effectful computation, why should we limit ourselves? In this paper, inspired by applicative functors, selective functors, and other structures, we define a collection of data structures and theories, which we call program adverbs, that capture a variety of computational patterns. Program adverbs are themselves composable, allowing them to be used to specify the semantics of languages with multiple computation patterns. We use program adverbs as the basis for a new class of semantic embeddings called Tl\"on embeddings. Compared with embeddings based on free monads, Tl\"on embeddings allow more flexibility in computational modeling of effects, while retaining more information about the program's syntactic structure., Comment: Accepted by ICFP 2022. 32 pages. Extended version

Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized by optimization techniques and, increasingly, by machine-learning methods. We study this approach from a programming-language perspective. We define two small languages that support decision-making abstractions: one with choices and rewards, and the other additionally with probabilities. We give both operational and denotational semantics. In the case of the second language we consider three denotational semantics, with varying degrees of correlation between possible program values and expected rewards. The operational semantics combine the usual semantics of standard constructs with optimization over spaces of possible execution strategies. The denotational semantics, which are compositional, rely on the selection monad, to handle choice, augmented with an auxiliary monad to handle other effects, such as rewards or probability. We establish adequacy theorems that the two semantics coincide in all cases. We also prove full abstraction at base types, with varying notions of observation in the probabilistic case corresponding to the various degrees of correlation. We present axioms for choice combined with rewards and probability, establishing completeness at base types for the case of rewards without probability.

We propose an IR for quantum computing that directly exposes quantum and classical data dependencies for the purpose of optimization. The Quantum Intermediate Representation for Optimization (QIRO) consists of two dialects, one input dialect and one that is specifically tailored to enable quantum-classical co-optimization. While the first employs a perhaps more intuitive memory-semantics (quantum operations act on qubits via side-effects), the latter uses value-semantics (operations consume and produce states) to integrate quantum dataflow in the IR’s Static Single Assignment (SSA) graph. Crucially, this allows for a host of optimizations that leverage dataflow analysis. We discuss how to map existing quantum programming languages to the input dialect and how to lower the resulting IR to the optimization dialect. We present a prototype implementation based on MLIR that includes several quantum-specific optimization passes. Our benchmarks show that significant improvements in resource requirements are possible even through static optimization. In contrast to circuit optimization at run time, this is achieved while incurring only a small constant overhead in compilation time, making this a compelling approach for quantum program optimization at application scale.

In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. In some cases, strong equivalence of programs in the input language of the grounder gringo can be established by deriving rules of each program from rules of the other. The possibility of such proofs has been demonstrated for a subset of that language that includes comparisons, arithmetic operations, and simple choice rules, but not aggregates. This method is extended here to a class of programs in which some uses of the #count aggregate are allowed. This paper is under consideration for acceptance in TPLP., Paper presented at the 38th International Conference on Logic Programming (ICLP 2022), 16 pages

In this study we analyzed turbulent heat fluxes over a seasonal ice cover on a boreal lake located in southern Finland. Eddy covariance (EC) flux measurements of sensible (H) and latent heat (LE) from four ice-on seasons between 2014 and 2019 are compared to three different bulk transfer models: one with a constant transfer coefficient and two with stability-adjusted transfer coefficients: the Lake Heat Flux Analyzer and SEA-ICE. All three models correlate well with the EC results in general while typically underestimating the magnitude and the standard deviation of the flux in comparison to the EC observations. Differences between the models are small, with the constant transfer coefficient model performing slightly better than the stability-adjusted models. Small difference in temperature and humidity between surface and air results in low correlation between models and EC. During melting periods (surface temperature T0>0 ∘C), the model performance for LE decreases when compared to the freezing periods (T0 ∘C), while the opposite is true for H. At low wind speed, EC shows relatively high fluxes (±20 W m−2) for H and LE due to non-local effects that the bulk models are not able to reproduce. The complex topography of the lake surroundings creates local violations of the Monin–Obukhov similarity theory, which helps explain this counterintuitive result. Finally, the uncertainty in the estimation of the surface temperature and humidity affects the bulk heat fluxes, especially when the differences between surface and air values are small.

Wraparound channels in Torus Network-on-Chip (NoC) help in reducing overall hop counts traversed by traffic. However, the cyclic paths created by wraparound channel make Torus NoC deadlock prone. Turn model and Channel Dependency Graph (CDG) are two classical approaches used for detecting and avoiding deadlock in NoC. In this work, we propose an Arc model for avoiding deadlock in Torus NoC. Arc model is an extension to Turn model and is useful for deadlock avoidance in Torus. Directional Dependency Graph (DDG) is also presented in this work by combining both Turn model and CDG for detecting deadlock in Torus NoC. DDG is a simpler approach for identifying deadlock scenarios, formulating deadlock avoidance and showing deadlock freedom while using Arc model along with a set of Turns.

The lattice-valued intuitionistic fuzzy set was introduced by Gerstenkorn and Tepavcevi as a generalization of both the fuzzy set and the L -fuzzy set by incorporating membership functions, nonmembership functions from a nonempty set X to any lattice L , and lattice homomorphism from L to the interval 0,1 . In this article, lattice-valued intuitionistic fuzzy subgroup type-3 (LIFSG-3) is introduced. Lattice-valued intuitionistic fuzzy type-3 normal subgroups, cosets, and quotient groups are defined, and their group theocratic properties are compared with the concepts in classical group theory. LIFSG-3 homomorphism is established and examined in relation to group homomorphism. The research findings are supported by provided examples in each section.

Families of 1- and 2-periodic knots and weavings that have isogonal (vertex-transitive) piecewise-linear embeddings are described. In these structures there is just one thread, or multiple threads with parallel or collinear axes. The principal structures are a large family of 1-periodic knots and related multi-thread infinite links, knitting patterns and chain-link weaving. The relevance to synthetic chemistry is described in terms of targets for designed synthesis such as mechanically interlocked polymers.

Symmetric monoidal theories (SMTs) generalise algebraic theories in a way that make them suitable to express resource-sensitive systems, in which variables cannot be copied or discarded at will. In SMTs, traditional tree-like terms are replaced by string diagrams, topological entities that can be intuitively thought of as diagrams of wires and boxes. Recently, string diagrams have become increasingly popular as a graphical syntax to reason about computational models across diverse fields, including programming language semantics, circuit theory, quantum mechanics, linguistics, and control theory. In applications, it is often convenient to implement the equations appearing in SMTs as rewriting rules. This poses the challenge of extending the traditional theory of term rewriting, which has been developed for algebraic theories, to string diagrams. In this paper, we develop a mathematical theory of string diagram rewriting for SMTs. Our approach exploits the correspondence between string diagram rewriting and double pushout (DPO) rewriting of certain graphs, introduced in the first paper of this series. Such a correspondence is only sound when the SMT includes a Frobenius algebra structure. In the present work, we show how an analogous correspondence may be established for arbitrary SMTs, once an appropriate notion of DPO rewriting (which we call convex) is identified. As proof of concept, we use our approach to show termination of two SMTs of interest: Frobenius semi-algebras and bialgebras.

We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the categorical universal property of two, necessarily equivalent, algebraic presentations of free commutative monoids using 1-HITs. These presentations correspond to two different equational theories invariably including commutation axioms. In this setting, we prove important structural combinatorial properties of finite multisets. These properties are established in full generality without assuming decidable equality on the carrier set. As an application, we present a constructive formalisation of the relational model of classical linear logic and its differential structure. This leads to constructively establishing that free commutative monoids are conical refinement monoids. Thereon we obtain a characterisation of the equality type of finite multisets and a new presentation of the free commutative-monoid construction as a set-quotient of the list construction. These developments crucially rely on the commutation relation of creation/annihilation operators associated with the free commutative-monoid construction seen as a combinatorial Fock space., Comment: Appeared in MFPS'22

An F-system is a computational model that performs a folding operation on words of a given language, following directions coded on words of another given language. This paper considers the case in which both given languages are regular, and it shows that the class of languages generated by such F-systems is a proper subset of the class of linear context-free languages., Comment: Nine pages. This is the accepted version of a manuscript submitted for publication in Information Processing Letters

Knaster-Tarski’s theorem, characterising the greatest fix- point of a monotone function over a complete lattice as the largest post-fixpoint, naturally leads to the so-called coinduction proof principle for showing that some element is below the greatest fixpoint (e.g., for providing bisimilarity witnesses). The dual principle, used for showing that an element is above the least fixpoint, is related to inductive invariants. In this paper we provide proof rules which are similar in spirit but for showing that an element is above the greatest fixpoint or, dually, below the least fixpoint. The theory is developed for non-expansive monotone functions on suitable lattices of the form$$\mathbb {M}^Y$$MY, whereYis a finite set and$$\mathbb {M}$$Man MV-algebra, and it is based on the construction of (finitary) approximations of the original functions. We show that our theory applies to a wide range of examples, including termination probabilities, behavioural distances for probabilistic automata and bisimilarity. Moreover it allows us to determine original algorithms for solving simple stochastic games.

This chapter discusses systems of ordinary differential equations. It presents a review of matrix algebra and calculus. It defines the characteristic equation and characteristic polynomial and shows how to calculate characteristic polynomial and eigenvalues of matrices through examples. Mathematica can compute both the characteristic polynomial and eigenvalues directly with the commands CharacteristicPolynomial and Eigenvalues. The chapter illustrates the homogeneous system of first-order linear differential equations. It provides solution of homogeneous linear systems with constant coefficients through some examples. It also discusses some theorems and terminology used in establishing the fundamentals of solving systems of differential equations. To apply variation of parameters, one first calculates a fundamental matrix for the associated homogeneous equation. In many cases, Laplace transforms can be used to solve a system of linear differential equations. The chapter illustrates the techniques needed to accomplish this with Mathematica through examples. It further explains nonlinear systems, linearization, and equilibrium points.

The main objective of this article is to establish generalized fractional Hermite–Hadamard and related type integral inequalities forh-Godunova–Levin convexity andh-Godunova–Levin preinvexity with extended Wright generalized Bessel function acting as kernel. Moreover, Hermite–Hadamard-type and trapezoid-type inequalities for several known convexities including Godunova–Levin function, classical convex,s-Godunova–Levin function,P-function, ands-convex function are deduced as corollaries. These obtained results are analyzed in the form of generalization of fractional inequalities.

In this paper, we aim to develop formulas of spectral radius for an operator S in terms of generalized Aluthge transform, numerical radius, iterated generalized Aluthge transform, and asymptotic behavior of powers of S . These formulas generalize some of the formulas of spectral radius existing in literature. As an application, these formulas are used to obtain several characterizations of normaloid operators.

The notion of Δ -metric spaces has been proposed in this study as a generalization of b -metric spaces, extended b -metric spaces, and p -metric spaces. A number of topological characteristics of such spaces have been investigated in this paper. On such spaces, a noncompactness measure has been established, and some results in the framework of noncompactness measure have been achieved. We prove an analogous of the Banach contraction principle in such spaces based on this approach. In order to investigate the validity of the underlying space and our proven fixed-point theorems, supporting examples have been presented. Furthermore, the well-posedness of the fixed-point problem has been tested using our fixed-point result.

The ‘cosmological constant problem’ (CCP) has historically been understood as describing a conflict between cosmological observations in the framework of general relativity (GR) and theoret...

In Probabilistic Abductive Logic Programming we are given a probabilistic logic program, a set of abducible facts, and a set of constraints. Inference in probabilistic abductive logic programs aims to find a subset of the abducible facts that is compatible with the constraints and that maximizes the joint probability of the query and the constraints. In this paper, we extend the PITA reasoner with an algorithm to perform abduction on probabilistic abductive logic programs exploiting Binary Decision Diagrams. Tests on several synthetic datasets show the effectiveness of our approach.

Partially lossy queue monoids (plq monoids) model the behavior of queues that can non-deterministically forget specified parts of their content at any time. We call the subsets of this monoid partially lossy queue languages (plq languages). While many decision problems on recognizable plq languages are decidable, most of them are undecidable if the languages are rational. In particular, in this monoid the classes of rational and recognizable languages do not coincide. This is due to the fact that the class of recognizable plq languages is not closed under multiplication and iteration. However, we can generate the recognizable plq languages using special rational expressions consisting of the Boolean operations and restricted versions of multiplication and iteration. From these special rational expressions we can also obtain an MSO logic describing the recognizable plq languages. Moreover, we provide similar results for the class of aperiodic languages in the plq monoid.

In this paper, we study α-cosymplectic manifoldMadmitting∗-Ricci tensor. First, it is shown that a∗-Ricci semisymmetric manifoldMis∗-Ricci flat and aϕ-conformally flat manifoldMis anη-Einstein manifold. Furthermore, the∗-Weyl curvature tensorW∗onMhas been considered. Particularly, we show that a manifoldMwith vanishing∗-Weyl curvature tensor is a weakϕ-Einstein and a manifoldMfulfilling the conditionRE1,E2⋅W∗=0isη-Einstein manifold. Finally, we give a characterization for α-cosymplectic manifoldMadmitting∗-Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting∗-Ricci soliton and almost∗-Ricci soliton are drawn.

Based on the Navier–Stokes equation for compressible media, this work studies the acoustic properties of a human cochlear model, in which the scala vestibuli and scala tympani are filled with compressible perilymph. Since the sound waves propagate as a compression wave in perilymph, this model can precisely handle the wave–based phenomena. Time domain analysis showed that a sound wave (fast wave) first propagates in the scala vestibuli and scala tympani, and then, a traveling wave (slow wave) is generated by the sound wave with some delay. Detailed studies based on even and odd mode analysis indicate that an odd mode sound wave, that is, the difference in the sound pressures between the scala vestibuli and scala tympani, excites the Békésy’s traveling wave, while an even mode sound determines the input impedance of the cochlea.

This paper scrutinizes the consequences of radiation and heat consumption of MHD convective flow of nanofluid on a heated stretchy plate with injection/suction and convective heating/cooling conditions. The nanofluid encompasses with C u and A g nanoparticles. We enforce the suited transformation to remodel the governing mathematical models to ODE models. The HAM (homotopy analysis method) idea is applied to derive the series solutions. The divergence of fluid velocity, temperature, skin friction coefficient, local Nusselt number, entropy generation, and Bejan number on disparate governing parameters is exhibited via graphs and tables. It is seen that the fluid velocity in both directions is subsided when elevating the magnetic field and Forchheimer number. Also, the C u nanoparticles possess hefty speed compared to A g nanoparticles because the density of A g nanoparticles is high compared to that of C u nanoparticles. The fluid temperature upturns when enlarging the heat generation and radiation parameters. The skin friction coefficients and local Nusselt number are high in A g nanoparticles than in C u nanoparticles.

We calculate the centrality dependence for coherent photoproduction of very low- p T J / ψ at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies within the impact parameter-dependent saturated color dipole model. By using the large equivalent photon fluxes, we present the differential cross-section of very low- p T J / ψ produced by coherent photonuclear in peripheral heavy ion collisions. The numerical results demonstrate that our calculation agrees with J / ψ data in peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) energies.

A directed graph (digraph) D of order n satisfies directed cut condition D C C if there are at least S arcs from any set S ⊆ V D , S ≤ n / 2 to its complement S ¯ = V D / S . We show that a digraph D of even order n has at least 2 n − 3 arcs if D satisfies D C C .

In order to study the investment portfolio problem, this paper propose a class of stochastic programming model with rough feasible region, where randomness and roughness coexist. Based on the covering rough set, the concept of the discrete degree covering is defined to divide the rough feasible region. Furthermore, the discrete degree covering stochastic rough programming model (DDC-SRP) is constructed depending on a synthesis effect function that considers discrete degree and the expectation and variance for random objective function. Properties of the DDC-SRP model are discussed. In addition, the convexity of the DDC-SRP model is obtained in some certain conditions. Considering the random rough simulation, a genetic algorithm is introduced. Finally, a numerical example is given to show the validity of the DDC-SRP model.

The role of Fuzzy topology in logic programming and algorithm has been recognized and applied on various programs to and more accurate result. In particular, topological methods are employed in order to obtain fixed point semantics for logic programs. In this paper, we prove some fixed point theorems in fuzzy metric spaces. As an application, some consequence theorems are given in support of our result.

In this paper, we define λ-approximate simulations and bisimulations for fuzzy automata over complete Heyting algebras. The value λ presents the degree of language similarity or equality between observed fuzzy automata. Algorithms for computing the greatest λ-approximate simulations and bisimulations are given. We show that λ-approximate simulations and bisimulations on a fuzzy automaton can be effectively used for factorization of fuzzy automata. We present the algorithm that splits the interval of the degrees of language similarity or equality into subintervals with same minimal corresponding factor fuzzy automata.

The new outcomes of the present paper are q -analogues ( q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.

The two main results of this paper concern the regularity of the invariant foliation of a C0-integrable symplectic twist diffeomorphisms of the 2-dimensional annulus, namely that $\bullet$ the generating function of such a foliation is C1 ; $\bullet$ the foliation is H{\"o}lder with exponent 1/2. We also characterize foliations by graphs that are straightenable via a symplectic homeomorphism and prove that every symplectic homeomorphism that leaves invariant all the leaves of a straightenable foliation has Arnol'd-Liouville coordinates, in which the Dynamics restricted to the leaves is conjugated to a rotation. We deduce that every Lipschitz integrable symplectic twist diffeomorphisms of the 2-dimensional annulus has Arnol'd-Liouville coordinates and then provide examples of 'strange' Lipschitz foliations in smooth curves that cannot be straightened by a symplectic homeomorphism and cannot be invariant by a symplectic twist diffeomorphism.This article is a part of another preprint of the authors, entitled On the transversal dependence of weak K.A.M. solutions for symplectic twist maps, after rewriting ant adding of the H{\"o}lder part., Comment: arXiv admin note: substantial text overlap with arXiv:1809.02372

The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter λ . The parameter λ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter λ . Moreover, the efficiency and reliability of this technique are verified by the numerical examples.

Imprecision is inherent in any decidable (sound) approximation of undecidable program properties. In abstract interpretation this corresponds to the release of false alarms, e.g., when it is used for program analysis and program verification. As all alarming systems, a program analysis tool is credible when few false alarms are reported. As a consequence, we have to live together with false alarms, but also we need methods to control them. As for all approximation methods, also for abstract interpretation we need to estimate the accumulated imprecision during program analysis. In this paper we introduce a theory for estimating the error propagation in abstract interpretation, and hence in program analysis. We enrich abstract domains with a weakening of a metric distance. This enriched structure keeps coherence between the standard partial order relating approximated objects by their relative precision and the effective error made in this approximation. An abstract interpretation is precise when it is complete. We introduce the notion of partial completeness as a weakening of precision. In partial completeness the abstract interpreter may produce a bounded number of false alarms. We prove the key recursive properties of the class of programs for which an abstract interpreter is partially complete with a given bound of imprecision. Then, we introduce a proof system for estimating an upper bound of the error accumulated by the abstract interpreter during program analysis. Our framework is general enough to be instantiated to most known metrics for abstract domains.

Large-scale complex network data poses significant challenges for the analytic ideas and tools to monitor and analyze complex networks. As classical structure descriptors, average path length ( $L$ ), global and local network efficiency ( $E_{glob}$ and $E_{loc}$ ), general and loop clustering coefficient ( $C_{3}$ and $D$ ), play significant roles in complex network analysis. In this paper, we make use of resistive distance instead of the shortest path distance to suggest resistive distance descriptors, i.e., $L_{r}$ , $\Omega _{glob}$ and $\Omega _{loc}$ , $\Omega _{3}$ and $D_{r}$ . We investigate all the resistive descriptors on classical WS, BA and ER models and find some interesting phenomenons. On one hand, $L_{r}$ and $\Omega _{3}$ (resp., $\Omega _{glob}$ and $\Omega _{loc}$ ) can be used to characterize the features of small-word networks. On the other hand, $L_{r}$ , $\Omega _{3}$ , and $\Omega _{glob}$ can be utilized to measure network invulnerability. To access the effectiveness of the resistive distance descriptors, we conduct extensive numerical simulations on synthetic and real networks. In comparison with the baselines, the proposed metrics show competitive performance on classical network models and are more efficient for networks with small and medium size.

An ultra-low specific on-resistance 4H-SiC power laterally diffused metal oxide semiconductor (LDMOS) device is proposed for 1200V-class applications. In the proposed SiC LDMOS device, a double-trench gate is introduced to reduce the channel region resistance. And a p-type variation lateral doping (VLD) region is also employed in the drift region, which not only optimizes the surface electric field and improves the breakdown voltage, but also increases the doping concentration of the N-drift region, resulting in a low drift region resistance. So that, the proposed device achieves an ultra-low specific on-resistance ( ${R} _{\mathrm{ on,sp}}$ ). Numerical Simulation results show that the ${R} _{\mathrm{ on,sp}}$ of the proposed SiC LDMOS is 3.5 $\text{m}\boldsymbol{\Omega }\cdot {\mathrm{ cm}}^{2}$ with a breakdown voltage of ~1460V, which is reduced by more than 46% compared with the conventional field-plate SiC LDMOS with a ${R} _{\mathrm{ on,sp}}$ of 6.6 $\text{m}\boldsymbol{\Omega }\cdot {\mathrm{ cm}}^{2}$ and a breakdown voltage of ~1210V. The transconductance of the proposed device is improved greatly. And the trade-off relationship between the ${R} _{\mathrm{ on,sp}}$ and the breakdown voltage is also significantly improved compared with those of the conventional device and the previous literature.

A $(m,n)$ sonar sequence is an $m\times n$ array with exactly one dot in each column and where all lines connecting two dots in the array are distinct as vectors. These arrays are known to have many applications such as sonar and radar detection and these are studied as a particular case of Golomb rectangles or two-dimensional Sidon sets. The main open problem for sonar sequences is: for fixed $m$ , find the largest $n$ for which there is an $(m,n)$ sonar sequence, these sequences are called the best sonar sequences. The extended sonar sequences are generalizations of sonar sequences where each column has at most one dot, the motivation to study these arrays are the best results obtained when applied to radar and sonar detection. In this paper, we give the best sonar sequences with $m\leq 100$ obtained from an exhaustive computational search based on the Caicedo, Ruiz and Trujillo constructions and we present new constructions of extended sonar sequences that use Sidon sets.

In this paper, our aim is to obtain the $ K_2 $ analogues of both the Herbrand-Ribet theorem and the Vandiver's conjecture.

In this paper, we consider the performance of exclusive-OR (XOR) rule in detecting the presence or absence of a deterministic signal in bivariate Gaussian noise. Signals, when present at the two sensors, are assumed unequal, whereas the noise components have identical marginal distribution but are correlated. The sensors send their one-bit quantized data to a fusion center, which then employs the XOR rule to arrive at the final decision. Here we prove that, in the limit as the correlation coefficient $r$ approaches 1, the optimum fusion rule for both parallel and tandem topologies is XOR with identical, alternating partitions (XORAP) of the observations at the sensors. We further quantify the asymptotic decrease of the Bayes error of XORAP towards zero as a constant multiplied by $\sqrt {1-r}$ , as $r$ approaches 1. When compared to the asymptotic Bayes error of CLRT, which decreases to zero exponentially fast, as a function of $1/(1-r)$ , the Bayes error of XORAP decreases to zero much slower.

In this paper, we present a Model-Free Stochastic Inverse Optimal Control (IOC) algorithm for the discrete-time infinite-horizon stochastic linear quadratic regulator (LQR). Our proposed algorithm exploits the richness of the available system trajectories to recover the control gain $K$ and cost function parameters $(Q,R)$ in a low (space, sample, and computational) complexity manner. By leveraging insights on the stochastic LQR, we guarantee well-posedness of the Model-Free Stochastic IOC LQR via satisfaction of the Certainty Equivalence optimality conditions. The exact solution of the control gain $K$ is recovered via a deterministic, low complexity Least Squares approach. Using $K$ , we solve a completely model-free non-iterative SemiDefinite Programming (SDP) problem to obtain a unique (up to a scalar ambiguity) $(Q,R)$ , in which optimality and feasibility are jointly ensured. Via derivation of the sample complexity bounds, we show that the non-asymptotic performance of the Model-Free Stochastic IOC LQR can be characterized by the signal-to-noise (SNR) ratio of the finite set of system state and input signals. We present a model-based version of the algorithm for the special case where $(A,B)$ is available, and we, further, provide the extension to the Stochastic Model-Free IOC linear quadratic tracking (LQT) case.

Let $G$ be an additive group of order $v$ . A $k$ -element subset $D$ of $G$ is called a $(v, k, \lambda, t)$ -almost difference set if the expressions $g-h$ , for $g$ and $h$ in $D$ , represent $t$ of the non-identity elements in $G$ exactly $\lambda $ times and every other non-identity element $\lambda + 1$ times. Almost difference sets are highly sought after as they can be used to produce functions with optimal nonlinearity, cyclic codes, and sequences with three-level autocorrelation. A set of positive integers $A$ is called a Golomb ruler if the difference between two distinct elements of $A$ are different. In this paper, we use Singer type Golomb rulers to construct new families of almost difference sets. Additionally, we constructed 2-adesigns from these almost difference sets.

Sea ice concentration algorithms using brightness temperatures ($T_{B}$) from satellite microwave radiometers are used to compute sea ice concentration ($c_{\text{ice}}$), sea ice extent, and generate sea ice climate data records. Therefore, it is important to minimize the sensitivity of $c_{\text{ice}}$ estimates to geophysical noise caused by snow/sea ice thermal microwave emission signature variations, and presence of WV and clouds in the atmosphere and/or near-surface winds. In this study, we investigate the effect of geophysical noise leading to systematic $c_{\text{ice}}$ biases and affecting $c_{\text{ice}}$ standard deviations (STD) using simulated top of the atmosphere $T_{B}$s over open water and 100% sea ice. We consider three case studies for the Arctic and the Antarctic and eight different $c_{\text{ice}}$ algorithms, representing different families of algorithms based on the selection of channels and methodologies. Our simulations show that, over open water and low $c_{\text{ice}}$, algorithms using gradients between V-polarized 19-GHz and 37-GHz $T_{B}$s show the lowest sensitivity to the geophysical noise, while the algorithms exclusively using near-90-GHz channels have by far the highest sensitivity. Over sea ice, the atmosphere plays a much smaller role than over open water, and the $c_{\text{ice}}$ STD for all algorithms is smaller than over open water. The hybrid and low-frequency (6 GHz) algorithms have the lowest sensitivity to noise over sea ice, while the polarization type of algorithms has the highest noise levels.

$(\alpha,\beta)$ -Pythagorean fuzzy set is a very efficient way of dealing with uncertainty. In this article, we have introduced the notions of $(\alpha,\beta)$ - Pythagorean fuzzy subring and $(\alpha,\beta)$ - Pythagorean fuzzy ideal of a ring. Further, we have briefly described various results related to it. Also, we have discussed the level subring of an $(\alpha,\beta)$ - Pythagorean fuzzy subring. Moreover, we have studied the direct product and ring homomorphism of $(\alpha,\beta)$ - Pythagorean fuzzy subrings.

In this paper, a class of Clifford-valued neutral-type recurrent neural networks with $D$ operator is explored. By using non-decomposition method and the Banach fixed point theorem, we obtain several sufficient conditions for the existence of anti-periodic solutions for Clifford-valued neutral-type recurrent neural networks with $D$ operator. By using the proof by contradiction and inequality techniques, we obtain the global exponential synchronization of anti-periodic solutions for Clifford-valued neutral-type recurrent neural networks with $D$ operator. Finally, we give one example to illustrate the feasibility and effectiveness of main results.

In this paper, we define the operational and denotational semantics of a special class of parallel quantum programs, namely disjoint parallel quantum programs. Based on them, a proof system for reasoning about disjoint parallel quantum programs is developed, which is (relatively) complete even when entanglement between different processes appears in the preconditions and postconditions.