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Near-sensor convolution engines have many applications in Internet-of-Things. Pulsed unary processing has been recently proposed for high-performance and energy-efficient processing of data using simple digital logic. In this work, we propose a low-cost, high-performance, and energy-efficient near-sensor convolution engine based on pulsed unary processing. The proposed engine removes the necessity of using costly analog-to-digital converters. Synthesis results show that the proposed pulse-based design significantly improves the hardware cost and energy consumption compared to the conventional fixed-point binary and also to the stochastic computing-based designs.

Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions of the instance. The major known decidable cases of FQA derive from the following: the guarded fragment of first-order logic, which can express referential constraints (data in one place points to data in another) but cannot express number restrictions such as functional dependencies; and the guarded fragment with number restrictions but on a signature of arity only two. In this paper, we give the first decidability results for FQA that combine both referential constraints and number restrictions for arbitrary signatures: we show that, for unary inclusion dependencies and functional dependencies, the finiteness assumption of FQA can be lifted up to taking the finite implication closure of the dependencies. Our result relies on new techniques to construct finite universal models of such constraints, for any bound on the maximal query size., Comment: 70 pages. Extended journal version of arXiv:1505.04216. This article is the same as what will be published in ToCL, except for publisher-induced changes, minor changes, and reordering of the material (in the ToCL version some detailed proofs are moved from the article body to an appendix)

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures clustering structures among objects. An EM (expectation maximization) algorithm with MM (minorization maximization) steps is developed to perform parameter estimation while a cross validated likelihood approach is employed to perform model selection. The developed model is applied to three real-world data sets where interesting results are obtained., Comment: 27 pages, 6 figures

Robin Milner (1984) gave a sound proof system for bisimilarity of regular expressions interpreted as processes: Basic Process Algebra with unary Kleene star iteration, deadlock 0, successful termination 1, and a fixed-point rule. He asked whether this system is complete. Despite intensive research over the last 35 years, the problem is still open. This paper gives a partial positive answer to Milner's problem. We prove that the adaptation of Milner's system over the subclass of regular expressions that arises by dropping the constant 1, and by changing to binary Kleene star iteration is complete. The crucial tool we use is a graph structure property that guarantees expressibility of a process graph by a regular expression, and that is preserved when going over from a process graph to its bisimulation collapse.

Atom-like defects in solid-state hosts are promising candidates for the development of quantum information systems, but despite their importance, the host substrate/defect combinations currently under study have almost exclusively been found serendipitously. Here we systematically evaluate the suitability of host materials by applying a combined four-stage data mining and manual screening process to all entries in the Materials Project database, with literature-based experimental confirmation of band gap values. We identify 580 viable host substrates for quantum defect introduction and use in quantum information systems. While this constitutes a significant increase in the number of known and potentially viable material systems, it nonetheless represents a significant (99.54%) reduction from the total number of known inorganic phases, and the application of additional selection criteria for specific applications will reduce their number even further. The screening principles outlined may easily be applied to previously unrealized phases and other technologically important materials systems., Currently under consideration at npj Computational Materials

International audience; We study a variant of the Multi-Agent Path Finding (MAPF) problem in which the group of agents are required to stay connected with a supervising base station throughout the execution. In addition, we consider the problem of covering an area with the same connectivity constraint. We show that both problems are PSPACE-complete on directed and undirected topological graphs while checking the existence of a bounded plan is NP-complete when the bound is given in unary (and PSPACE-hard when the encoding is in binary). Moreover, we identify a realistic class of topo-logical graphs on which the decision problem falls in NLOGSPACE although the bounded versions remain NP-complete for unary encoding.

Recently proposed real number systems like Posits and Elias codes make use of tapered accuracy resulting from variable-length coding of exponents and significands. Several quite different interpretations of these number systems have been provided, though most often these rely on some combination of fixed- and variable-length codes for exponent and significand. We provide a new perspective on these number systems that unifies known representations while suggesting new ones. Our framework is based on multibit radix representations that encode the exponent in unary, the leading nonzero digit in a variablelength code, and the remaining digits in fixed-length binary code. We show how Posits, the various Elias codes, and ieee 754 like representations can be expressed in this framework. Moreover, we show that Posits and the Elias γ and δ codes represent the leading digit using the canonical Huffman code for a probability distribution given by Benford’s law, which governs the probability of leading digits. We further show that Posits correspond to the use of a fixed radix while Elias δ and ω codes are based on simple sequences of increasing radix. Our approach provides for an intuitive and uniform framework for representing numbers that reveals a visual mapping between codewords and the binary representation of real numbers obscured by prior frameworks. This new interpretation suggests a generalization of Posits and other number systems and provides simple rules for designing information-theoretically optimal codes.

A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of freedom, i.e. problems composed of or approximated by $d$-level particles (qudits). Recently, several methods for encoding these systems into a set of qubits have been introduced, where each encoding's efficiency was studied in terms of qubit and gate counts. Here, we build on previous results by including effects of hardware connectivity. To study the number of SWAP gates required to Trotterize commonly used quantum operators, we use both analytical arguments and automatic tools that optimize the schedule in multiple stages. We study the unary (or one-hot), Gray, standard binary, and block unary encodings, with three connectivities: linear array, ladder array, and square grid. Among other trends, we find that while the ladder array leads to substantial efficiencies over the linear array, the advantage of the square over the ladder array is less pronounced. These results are applicable in hardware co-design and in choosing efficient qudit encodings for a given set of near-term quantum hardware. Additionally, this work may be relevant to the scheduling of other quantum algorithms for which matrix exponentiation is a subroutine., Accepted to QCE20 (IEEE Quantum Week). Corrected erroneous circuits in Figure 3

General matrix multiplication (GEMM) is universal in various applications, such as signal processing, machine learning, and computer vision. Conventional GEMM hardware architectures based on binary computing exhibit low area and energy efficiency as they scale due to the spatial nature of number representation and computing. Unary computing, on the other hand, can be performed with extremely simple processing units, often just with a single logic gate. But currently there exist no efficient architectures for unary GEMM. In this paper, we present uGEMM, an area- and energy-efficient unary GEMM architecture enabled by novel arithmetic units. The proposed design relaxes previously-imposed constraints on input bit streams---low correlation and long stream length---and achieves superior area and energy efficiency over existing unary systems. Furthermore, uGEMM's output bit streams exhibit higher accuracy and faster convergence, enabling dynamic energy-accuracy scaling on resource-constrained systems.

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

In covering-based rough sets, many basic issues are related to minimal and maximal descriptions. For a covering approximation space with a large cardinal, it would be tedious and complicated to use set representations to solve the issues about minimal and maximal descriptions. Therefore it is necessary to study matrix representations by which calculations will become algorithmic and can be easily implemented by computers. In this paper, we use matrix approaches to investigate some issues about minimal and maximal descriptions in covering-based rough sets. Firstly, several new matrices and matrix operations are defined by which one can compute the minimal description and the approximation operator about the minimal description. Inspired by this result, a matrix method is presented to judge whether a covering is unary. Secondly, the maximal description and the approximation operator about the maximal description are also computed by these new matrices and matrix operations. Finally, based on the above results, we propose a matrix method to efficiently compute reductions of coverings. Moreover, we propose two types of reducts of covering information systems via minimal and maximal descriptions respectively, and we use matrix approaches to compute them. In a word, these results show an interesting view to investigate the combination between matrices and covering-based rough sets.

In this study, we formulate the concept of “mining maximal-size frequent subgraphs” in the challenging domain of visual data (images and videos). In general, visual knowledge can usually be modeled as attributed relational graphs (ARGs) with local attributes representing local parts and pairwise attributes describing the spatial relationship between parts. Thus, from a practical perspective, such mining of maximal-size subgraphs can be regarded as the discovery of common objects from visual data without given annotations of object bounding boxes. From a theoretical perspective, in this study, we propose a generic definition of common subgraphs among ARGs. Many previous studies can be roughly considered as special cases of the definition. In our definition, we consider 1) variations of unary/pairwise attributes among different ARGs, 2) linkage conditions of different nodes, and 3) the learning of similarity metrics for each node. The generality of our subgraph pattern proposes great challenges to the graph-mining algorithm. We propose an approximate but efficient solution to the mining problem. We conduct five experiments to evaluate our method with different kinds of visual data, including videos and RGB/RGB-D images. These experiments demonstrate the generality of the proposed method.

This paper studies operations on possibilistic belief structures, which are constructed by basic possibility assignments, or equivalently, maxitive belief structures, as a framework for modeling imprecise possibility distributions. Different from Dempster–Shafer structures, it is shown that there is no one-to-one correspondence between basic possibility assignments and their induced upper and lower possibilities. The operations on the set of basic possibility assignments might not induce the operations on their upper and lower possibilities. An operation on basic possibility assignments is called proper if it is also the operation on their upper and lower possibilities. We introduce set operations and point operations on basic possibility assignments. Set operations include intersection, union, complement, difference, projection, marginalization, cylindrical extension, vacuous extension and Cartesian product operations. Point operations include all binary and unary operations. We show that all point operations are proper. For set operations, it is shown that union, projection, marginalization, cylindrical extension, vacuous extension and Cartesian product operations are proper, while intersection, complement and difference operations are not proper. In addition, we study construction of compatible possibility distributions and show that the lower possibility of a basic possibility assignment can be represented by the infinimum of compatible possibility distributions. We also show that the local computation technique can be applied to the computation problem of possibilistic belief structures.

Neural network (NN) computing contains a large number of multiply-and-accumulate (MAC) operations, which is the speed bottleneck in traditional von Neumann architecture. Resistive random access memory (ReRAM)-based crossbar is well suited for matrix-vector multiplication. Existing ReRAM-based NNs are mainly based on the binary coding for synaptic weights. However, the imperfect fabrication process combined with stochastic filament-based switching leads to resistance variations, which can significantly affect the weights in binary synapses and degrade the accuracy of NNs. Further, as multi-level cells (MLCs) are being developed for reducing hardware overhead, the NN accuracy deteriorates more due to the resistance variations in the binary coding. In this paper, a novel unary coding of synaptic weights is presented to overcome the resistance variations of MLCs and achieve reliable ReRAM-based neuromorphic computing. The priority mapping is also proposed in compliance with the unary coding to guarantee high accuracy by mapping those bits with lower resistance states to ReRAMs with smaller resistance variations. Our experimental results show that the proposed method provides less than 0.45% and 5.48% accuracy loss on LeNet (on MNIST dataset) and VGG16 (on CIFAR-10 dataset), respectively, with acceptable hardware cost.

The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse (Bakinova et al., “Formal languages over GF(2)”, LATA 2018), in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages recognized by an m-state and an n-state DFA is recognized by a DFA with 2 m n states, and this number of states is necessary in the worst case, as long as m and n are relatively prime. This operation is known to have an inverse, and the state complexity of the GF(2)-inverse operation over a unary alphabet is proved to be exactly 2 n − 1 + 1 , with the proof based on primitive polynomials over GF(2). For a generalization of the GF(2)-inverse, called the GF(2)-star, the state complexity in the unary case is exactly 2 n .

Union-free languages are described by regular expressions using only concatenation and Kleene-star. Every regular language can be given as a union of finitely many union-free languages. By the minimal number of union-free languages needed in such union-free decompositions of a regular language, its union-complexity is defined. In this paper, the union-complexity of the languages obtained by various operations is studied, e.g., having two languages with union-complexities n and m, respectively, what could be the union-complexity of their union/concatenation/shuffle. Particularly, it is shown that the Kleene-star of any regular language has union-complexity 1. In some cases, e.g., at union and concatenation, the resulting language has a bounded union-complexity. In some other cases, e.g., at complement, the resulted language can have arbitrarily large union-complexity. At (k-th) power of a language, the case of the unary alphabet and the general case (alphabet with at least two symbols) have different upper bounds. While, in case of shuffle, there is an unbounded growth in the general case, while for languages over the unary alphabet the growth is bounded. Tight upper bounds are shown for all of the above mentioned cases (whenever the growth is bounded). At intersection we also show an unbounded growth in the general case, especially, over a binary alphabet.

We consider finitary relations (also known as crosses) that are definable via finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite parameter set $\Gamma$. We prove that whenever $\Gamma$ contains at least one non-empty relation distinct from the full carrier set, there is a countably infinite number of polymorphism clones determined by relations that are disjunctively definable from $\Gamma$. Finally, we extend our result to finitely related polymorphism clones and countably infinite sets $\Gamma$., Comment: manuscript to be published in Theory of Computing Systems

Every Berman’s variety $$\mathbb {K}_p^q$$ which is the subvariety of Ockham algebras defined by the equation $${\sim ^{2p+q}}a = {\sim ^q}a$$ ($$p\ge 1$$ and $$q\ge 0$$) determines a finitary substitution invariant consequence relation $$\vdash _p^q$$. A sequent system $$\mathsf {S}_p^q$$ is introduced as an axiomatization of the consequence relation $$\vdash _p^q$$. The system $$\mathsf {S}_p^q$$ is characterized by a single finite frame $$\mathfrak {F}_p^q$$ under the frame semantics given for the formal language. By the duality between frames and algebras, $$\mathsf {S}_p^q$$ can be viewed as a $$4^{2p+q}$$-valued logic as it is characterized by a distributive lattice of $$4^{2p+q}$$ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system $$\mathsf {G}_p^q$$ is established for $$\vdash _p^q$$. The Craig interpolation property of $$\vdash _p^q$$ is shown proof-theoretically utilizing $$\mathsf {G}_p^q$$.

A canonical (propositional) Gentzen-type system is a system in which every rule has the subformula property, it introduces exactly one occurrence of a connective, and it imposes no restrictions on the contexts of its applications. A larger class of Gentzen-type systems which is also extensively in use is that of quasi-canonical systems. In such systems a special role is given to a unary connective $$\lnot $$ of the language (usually, but not necessarily, interpreted as negation). Accordingly, each application of a logical rule in such systems introduces either a formula of the form $$\diamond (\psi _1,\ldots ,\psi _n)$$ , or of the form $$\lnot \diamond (\psi _1,\ldots ,\psi _n)$$ , and all the active formulas of its premises belong to the set $$\{\psi _1,\ldots ,\psi _n,\lnot \psi _1,\ldots ,\lnot \psi _n\}$$ . In this paper we investigate the whole class of quasi-canonical systems. We provide a constructive coherence criterion for such systems, and show that a quasi-canonical system is coherent iff it is analytic iff it has a characteristic non-deterministic matrix (Nmatrix) which is based on some subset of the set of the four truth-values which are used in the famous Dunn–Belnap four-valued (deterministic) matrix for information processing. In addition, we determine when a quasi-canonical system admits (strong) cut-elimination.

Recurrent neural networks (RNNs) are now widely used on sequence generation tasks due to their ability to learn long-range dependencies and to generate sequences of arbitrary length. However, their left-to-right generation procedure only allows a limited control from a potential user which makes them unsuitable for interactive and creative usages such as interactive music generation. This article introduces a novel architecture called anticipation-RNN which possesses the assets of the RNN-based generative models while allowing to enforce user-defined unary constraints. We demonstrate its efficiency on the task of generating melodies satisfying unary constraints in the style of the soprano parts of the J.S. Bach chorale harmonizations. Sampling using the anticipation-RNN is of the same order of complexity than sampling from the traditional RNN model. This fast and interactive generation of musical sequences opens ways to devise real-time systems that could be used for creative purposes.

Hypergraph matching utilizes high order constraints rather than unary or pairwise ones, which aims to establish a more reliable correspondence between two sets of image features. Although many hypergraph matching methods have been put forward over the past decade, it remains a challenging problem to be solved due to its combinatorial nature. Most of these methods are based on tensor marginalization, where tensor entries representing joint probabilities of the assignment are fixed during the iterations meanwhile the individual assignment probabilities evolving. This will cause some incomplete information which may hurt the matching performance. Addressing this issue, we propose a novel hypergraph matching algorithm based on tensor refining, accompanied with an alternative adjustment method to accelerate the convergence. We make a comparison between the proposed approach and several outstanding matching algorithms on three commonly used benchmarks. The experimental results validate the superiority of our method on both matching accuracy and robustness against noise and deformation.

Martensitic phase transformations in palladium-titanium high-temperature shape-memory alloys (HTSMA) are studied using molecular dynamics simulations. On the basis of the second nearest-neighbor modified embedded-atom method formalism, an interatomic potential for the binary palladium-titanium system is determined by improving the unary descriptions of pure palladium. The developed interatomic potential accurately reproduces physical properties at the equiatomic composition and the resultant temperature- and stress-induced phase transformations between B2 austenite and B19 martensite structures. Subsequent large-scale molecular dynamics simulations demonstrate that the developed potential can be successfully utilized to investigate atomic details of phase transformations in nanocrystalline palladium-titanium alloys.

Purpose Typical feature-matching algorithms use only unary constraints on appearances to build correspondences where little structure information is used. Ignoring structure information makes them sensitive to various environmental perturbations. The purpose of this paper is to propose a novel graph-based method that aims to improve matching accuracy by fully exploiting the structure information. Design/methodology/approach Instead of viewing a frame as a simple collection of keypoints, the proposed approach organizes a frame as a graph by treating each keypoint as a vertex, where structure information is integrated in edges between vertices. Subsequently, the matching process of finding keypoint correspondence is formulated in a graph matching manner. Findings The authors compare it with several state-of-the-art visual simultaneous localization and mapping algorithms on three datasets. Experimental results reveal that the ORB-G algorithm provides more accurate and robust trajectories in general. Originality/value Instead of viewing a frame as a simple collection of keypoints, the proposed approach organizes a frame as a graph by treating each keypoint as a vertex, where structure information is integrated in edges between vertices. Subsequently, the matching process of finding keypoint correspondence is formulated in a graph matching manner.

The multi-covering rough sets (MCRSs) are a popular aspect of rough sets. It is easy to see that classical rough sets, covering rough sets (CRSs) and multi-granulation rough sets (MGRSs) are all the special cases of the MCRSs. Recently, the algebraic theory of these rough set models mentioned above have been researched in detail. However, the algebraic theory of MCRSs has not been studied until now. It is necessary for researchers to explore the algebraic theory of MCRSs. In this paper, we focus on the operation and algebraic theories of two types of MCRS models. First, the properties of the two types of multi-covering set approximations are discussed. Especially, the properties of multi-covering approximation operators based on the unary coverings are deeply researched. Second, the operation properties with respect to intersection and union of MCRSs are researched. Meanwhile, to compute the intersection and union of MCRSs, several algorithms are constructed. Finally, on the basis of the operation properties of MCRSs, many meaningful algebraic properties of MCRSs are deeply studied.

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP (which is built in the $$ \{\vee ,\wedge ,\lnot \} $$ -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete analogue of LP, strong Kleene logic $$ \mathbf K_3 $$ . In this paper, we generalize these results for the negative fragments of LP and $$ \mathbf K_3 $$ , respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or $$ \mathbf K_3 $$ , but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of $$ \mathbf K_3 $$ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic $$ \mathbf G_3 $$ and its dual $$ \mathbf DG_3 $$ (which have different interpretations of negation than $$ \mathbf K_3 $$ and LP).

In this paper, we investigate the safety of unary inflationary fixed point operators (IFPoperators). The safety is a computability in finitely many steps. IFP-operators exactly correspond to recursive SQL-queries hence this problem has a value for database theory. The problem appears from the fact that if recursive queries contain universe functions and relations, then its execution can fall into an infinite loop. Moreover, universal computational devices (Turing machines et al.) can be modelled by such queries. Hence the problem of the finite computability for such queries is undecidable. In our previous works we established some properties of a universe which imply the finite computability of all IFP-operators in the universe. Here, we investigate a connection between an arity of IFP-operators and their safety. We prove that some results for general IFP-operators don’t hold for unary ones. We construct a universe where all unary unnesed IFP-operators are safe. But in this universe there exist unsafe nested unary IFP-operators and unsafe unnested binary IFP-operators. This differs from general IFP-operators because in general case the safety of all unnesed IFP-operators implies the safety of all IFP-operators. Also there exist elementary equivalent universes where some unary unnesed IFPoperators become unsafe. For general IFP-operators it is also impossible.

In connection to developing the third generation of Calphad databases a new thermodynamic description is presented for unary carbon. Models used in this work have more physical basis and are valid down to 0 K. The anisotropy in graphite, caused by weak Van der Waals inter-plane forces makes it impossible to fit the heat capacity data by a single Einstein temperature for modelling the harmonic vibration of the atoms. By using multiple Einstein temperatures this problem is solved and a good agreement with the experimental data at both low and other temperatures is achieved. Diamond is modeled using multiple Einstein temperatures due to its specific heat capacities at very low temperatures too, and the two-state model is used for modelling the liquid phase.

We investigate the following problem: given a sample of classified strings, find a first-order sentence of minimal quantifier rank that is consistent with the sample. We represent strings as successor string structures, that is, finite structures with unary predicates to denote symbols in an alphabet, and a successor relation. We use results of the Ehrenfeucht-Fra\"iss\'e game over successor string structures in order to design an algorithm to find such sentence. We use conditions characterizing the winning strategies for the Spoiler on successor strings structures in order to define formulas which distinguish two strings. Our algorithm returns a boolean combination of such formulas., Comment: In Proceedings GandALF 2018, arXiv:1809.02416

Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, and other questions of recent interest. Unary patterns with permutations have been previously analysed only for lengths up to 3. Consider a pattern p = π i 1 ( x ) … π i r ( x ) , with r ≥ 4 , x a word variable over an alphabet Σ and π i j function variables, to be replaced by morphic or antimorphic permutations of Σ. If | Σ | ≥ 3 , we show the existence of an infinite word avoiding all pattern instances having | x | ≥ 2 . If | Σ | = 3 and all π i j are powers of a single morphic or antimorphic π, the length restriction is removed. For the case when π is morphic, the length dependency can be removed also for | Σ | = 4 , but not for | Σ | = 5 , as the pattern x π 2 ( x ) π 56 ( x ) π 33 ( x ) becomes unavoidable. Thus, in general, the restriction on x cannot be removed, even for powers of morphic permutations. Moreover, we show that for every positive integer n there exists N and a pattern π i 1 ( x ) … π i n ( x ) which is unavoidable over all alphabets Σ with at least N letters and π morphic or antimorphic permutation.

Commutativity is an important property in two-step information merging procedure. It is shown that the result obtained from the procedure should not depend on the order in which signal steps are performed. In the case of a bisymmetric aggregation operator with the neutral element, Saminger et al. have provided a full characterization of commutative n-ary operator by means of unary distributive functions. Further, characterizations of these unary distributive functions can be viewed as resolving a kind of the Cauchy-like equations f ( x ⊕ y ) = f ( x ) ⊕ f ( y ) , where f : [ 0 , 1 ] → [ 0 , 1 ] is a monotone function, ⊕ is a bisymmetric aggregation operator with the neutral element. In this paper, we are still devoted to investigating and fully characterizing the Cauchy-like equation f ( U ( x , y ) ) = U ( f ( x ) , f ( y ) ) , where f : [ 0 , 1 ] → [ 0 , 1 ] is an unknown function but not necessarily monotone, U is a uninorm continuous in ( 0 , 1 ) 2 . These results show the key technology is how to find a transformation from this equation into several known cases. Moreover, this equation has completely different and non-monotone solutions in comparison with the obtained results.

This paper focuses on the representation of place of articulation features in consonants and vowels, on the basis of interaction between consonant and vowel place. New data from Sichuan Chinese are examined, which show at least four types of consonant–vowel interaction: labial attraction, two types of coronal attraction and velar attraction. Since consonants and vowels show patterns of interaction at all places of articulation, we argue that consonant and vowel place should be described using the same representational elements. We propose that the relevant generalizations reflect the historical development (not synchronic alternation), and show that an account using standard Dependency Phonology unary features can capture these facts.

The chemical potential of a component in a system is customarily defined as the Gibbs energy of transferring of one mole of this component from a unary reservoir to the system at constant temperatu...

Inclusion dependencies form one of the most fundamental classes of integrity constraints. Their importance in classical data management is reinforced by modern applications like data profiling, data cleaning, entity resolution, and schema matching. Their discovery in an unknown dataset is at the core of any data-analysis effort. Therefore, several research approaches have focused on their efficient discovery in a given, static dataset. However, none of these approaches are appropriate for application on dynamic datasets. In these cases, discovery techniques should be able to efficiently update the inclusion dependencies after an update in the dataset, without reprocessing the entire dataset. We present the first approach for incrementally updating the unary inclusion dependencies. In particular, our approach is based on the concept of attribute clustering, from which the unary inclusion dependencies are efficiently derivable. We incrementally update the clusters after each update of the dataset. An update of the clusters does not need access to the dataset because of special data structures designed to efficiently support the updating process. We performed an exhaustive analysis of our approach by applying it to large datasets with several hundred attributes and more than 116.2 million tuples. The results showed that the incremental discovery significantly reduces the runtime needed by the static discovery. This reduction in the runtime is up to 99.9996% for both the insertion and the deletion.

Let K n be the class of finite structures of the form ( A , f 1 A , . . . , f n A ) where each f i A is a unary function on A. Let CK n be a class of finite structures of the form ( A , f 1 A , . . . , f n A , ≤ A ) with the property that ( A , f 1 A , . . . , f n A ) ∈ K n and ≤ A is a linear ordering on A. We give an example of the Ramsey class CK n which satisfies the ordering property with respect to K n .

Encoding radix-2 data in radix-3 has the potential to allow faster computation with reduced power dissipation, reduced chip area and reduced interconnect overhead. Use of ternary encoding has the potential to minimize hot-spot generation and bring down fabrication costs due to reduced complexity. Efficient binary-to-ternary conversion is needed to attain these benefits in today's binary-dominated digital world. This paper presents a novel strategy to convert from a 2-valued binary input to a 3-valued ternary output. The proposed converter operates in 4 steps: (I) Synchronous complementary input generation, (II) Binary to unary conversion, (III) Unary to ternary interfacing, and (IV) Ternary output generation. A design using double pass-transistor logic delay equalized through coarse and fine-tuning is presented. Ternary values are encoded using 0, 0.9 and 1.8 V to represent ternary digit (trit) values of 0, 1 and 2. The proposed converter design has been validated using T-Spice transient-response simulation on TSMC 0.18 µm SPDM CMOS technology at 25 °C on Tanner EDA V.13. The worst-case response of the proposed design was identified using corner analysis with typical, slow and fast PVT variation.

Sorting is a common task in a wide range of applications from signal and image processing to switching systems. For applications that require high performance, sorting is often performed in hardware with application-specified integrated circuits or field-programmable gate arrays. Hardware cost and power consumption are the dominant concerns. The usual approach is to wire up a network of compare-and-swap units in a configuration called the Batcher (or bitonic) network. Such networks can readily be pipelined. This paper proposes a novel area-efficient and power-efficient approach to sorting networks, based on “unary processing.” In unary processing, numbers are encoded uniformly by a sequence of one value (say 1) followed by a sequence of the other value (say 0) in a stream of 0’s and 1’s with the value defined by the fraction of 1’s in the stream. Synthesis results of complete sorting networks show up to 92% area and power saving compared to the conventional binary implementations. However, the latency increases. To mitigate the increased latency, this paper uses a novel time-encoding of data. The approach is validated with two implementations of an important application of sorting: median filtering. The result is a low cost, energy-efficient implementation of median filtering with only a slight accuracy loss, compared to conventional implementations.

Objective The Arden Syntax for Medical Logic Systems is a standard for encoding and sharing medical knowledge in the form of Medical Logic Modules. To improve accessibility for clinicians, the originators of the standard deliberately designed Arden Syntax expressions to resemble natural language, and parentheses around operands are not generally required. For certain patterns of nested expressions, however, the use of parentheses is mandatory, otherwise they are not accepted by an Arden Syntax environment. In this study, we refer to such patterns as anomalies. The purpose of this paper is to investigate the extent and the circumstances of such anomalies, and to outline a solution based on an alternative grammar encoding approach. Methods To analyze the distribution of anomalies in nested expressions, we developed two custom-made complementary utilities. The first utility, termed parser, checks a single expression pattern against the specification-compliant grammar for syntactic correctness. The second utility, termed composer, automatically creates an extensive amount of expression patterns by permuting and nesting operators without the use of parentheses, and stores these together with the expected syntactic correctness. By means of these utilities we conducted a comprehensive analysis of anomalies by comparing the expected correctness with the actual correctness. Any detected anomalies are stored into a set of files, grouped by the respective top-level operator, for a subsequent analysis. Results The composer utility nested 165 unary, binary, or ternary operators of Arden Syntax version 2.8 to a depth of two, resulting in a set of 76,533 expression patterns, of which 18,978 (24.8%) have been identified as anomalies. An automated assessment of their practical relevance for medical knowledge encoding is infeasible. Manual screening of selected samples indicated that only a small proportion of the detected anomalies would be relevant. The cause of the anomalies lies in the encoding of the grammar. A change of the basic encoding approach with some additional customizations eliminates the anomalies. A working expression parser is included in the supplementary material. Conclusion Arden Syntax expressions are affected by anomalies. Since only a small proportion of them have practical relevance and they cannot cause false calculations or clinical decisions, their practical impact is likely limited. However, they may be potential points of confusion for knowledge engineers. An alternative expression grammar, based on a different encoding approach, would not only eliminate the anomalies, but could considerably facilitate both maintenance and further development of the standard.

Recently, Hillert and Selleby proposed a simple method for expression of the lattice stability or Gibbs energy of formation that does not violate the third law of thermodynamics. This method describes the derivation of the Gibbs energy function from high temperatures down to 0 K by interpolation, instead of extrapolation from room temperature to 0 K. In the present work, their original method is discussed in terms of determination of the characteristic parameter values. Keeping the essential interpolation character of their method, a generalized approach is presented for expressing the lattice stability through parameter optimizations. This approach retains the zero point entropy of substances and is in line with the development of the third generation CALPHAD databases. Using the Al unary system as a case study, the lattice stabilities of the hcp and bcc phases are investigated. The respective Einstein temperatures are also evaluated. At high temperatures, the present descriptions reproduce the lattice stabilities suggested by SGTE for the existing second generation of databases, with a reasonable accuracy. More importantly, information from ab initio calculations (total energy at 0 K) is also used for this optimization and the present method results in a physically sounder description of thermodynamic properties at lower temperatures down to 0 K. The present approach provides a simple and flexible way to estimate the lattice stabilities, with potential applicability for the Gibbs energy of formation of stoichiometric compounds and the excess energy of solution phases, in accordance with the third law of thermodynamics.

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kuhr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halas (Arch Math Log 48:243–255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation.

Left restriction semigroups are the unary semigroups that abstractly characterize semigroups of partial maps on a set, where the unary operation associates to a map the identity element on its domain. This paper is the sequel to two recent papers by the author, melding the results of the first, on membership in the variety $\mathbf{B}$ of left restriction semigroups generated by Brandt semigroups and monoids, with the connection established in the second between subvarieties of the variety $\mathbf{B}_{R}$ of two-sided restriction semigroups similarly generated and varieties of categories, in the sense of Tilson. We show that the respective lattices ${\mathcal{L}}(\mathbf{B})$ and ${\mathcal{L}}(\mathbf{B}_{R})$ of subvarieties are almost isomorphic, in a very specific sense. With the exception of the members of the interval $[\mathbf{D},\mathbf{D}\vee \mathbf{M}]$, every subvariety of $\mathbf{B}$ is induced from a member of $\mathbf{B}_{R}$ and vice versa. Here $\mathbf{D}$ is generated by the three-element left restriction semigroup $D$ and $\mathbf{M}$ is the variety of monoids. The analogues hold for pseudovarieties.

This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed to solve the problem to optimality for small instances. Tight lower bounds and a 4-approximation algorithm are developed. A constraint programming-based method is also proposed. Numerical results demonstrate that the proposed algorithms can obtain high quality solutions and have a competitive performance. Sensitivity analysis indicates that the performance of the proposed algorithms is also robust on different problem structures.

Chords are not pure sets of tones or notes. They are mainly characterized by their matrices. A chord matrix is the pattern of all the lengths of intervals given without further context. Chords are well-structured invariants. They show their inner logical form. This opens up the possibility to develop a molecular logic of chords. Chords are our primitive, but, nevertheless, already interrelated expressions. The logical space of internal harmony is our well-known chromatic scale represented by an infinite line of integers. Internal harmony is nothing more than the pure interrelatedness of two or more chords. We consider three cases: (a) chords inferentially related to subchords, (b) pairs of chords in the space of major–minor tonality and (c) arbitrary chords as arguments of unary chord operators in relation to their outputs. One interesting result is that chord negation transforms any pure major chord into its pure minor chord and vice versa. Another one is the fact that the negation of chords with symmetric matrices does not change anything. A molecular logic of chords is mainly characterized by combining general rules for chord operators with the inner logical form of their arguments.

This article presents an axiom system for an arithmetic of the even and the odd, one that is stronger than those discussed in Pambuccian (2016) and Menn & Pambuccian (2016). It consists of universal sentences in a language extending the usual one with 0, 1, +, ·, $[{ \cdot \over 2}]$, and two unary operation symbols.

Tchebycheff decomposition represents one of the most widely used decomposition approaches that can convert a multiobjective optimization problem into a set of scalar optimization subproblems. Nevertheless, the geometric properties of the subproblem objective functions in Tchebycheff decomposition have not been explicitly studied. This paper proposes a Tchebycheff decomposition with ${l_{p}}$ -norm constraint on direction vectors in which the subproblem objective functions are endowed with clear geometric property. Especially, the Tchebycheff decomposition with ${l_{2}}$ -norm constraint on direction vectors is taken as an example to illustrate its advantage. A new unary ${R_{2}}$ indicator is also introduced to approximate the hyper-volume metric and justify the efficiency of the proposed Tchebycheff decomposition. A resultant Tchebycheff decomposition-based multiobjective evolutionary algorithm (MOEA) with ${l_{2}}$ -norm constraint and a new population update strategy is proposed to solve multiobjective optimization problems. The experimental results on both benchmark and real-world multiobjective optimization problems show that the proposed algorithm is capable of obtaining high quality solutions compared with other state-of-the-art MOEAs.

Different types of subregular expressions are studied. Each type is obtained by either omitting one of the regular operations or replacing it by complementation or intersection. For uniformity and in order to allow non-trivial languages to be expressed, the set of literals is a finite set of words instead of letters. The power and limitations as well as relations with each other are considered, which is often done in terms of unary languages. Characterizations of some of the language families are obtained. A finite hierarchy is shown that reveals that the operation complementation is generally stronger than intersection. Furthermore, we investigate the closures of language families described by regular expressions with omitted operation under that operation. While it is known that in case of union this closure captures all regular languages, for the cases of concatenation and star incomparability results are obtained with the corresponding language families where the operation is replaced by complementation.

It is known that poly-time constant-space quantum Turing machines (QTMs) and logarithmic-space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (A.C. Cem Say and A. Yakaryılmaz, Magic coins are useful for small-space quantum machines. Quant. Inf. Comput. 17 (2017) 1027–1043). In this paper, we investigate more restricted cases for both models to recognize uncountably many languages with bounded error. We show that double logarithmic space is enough for PTMs on unary languages in sweeping reading mode or logarithmic space for one-way head. On unary languages, for quantum models, we obtain middle logarithmic space for counter machines. For binary languages, arbitrary small non-constant space is enough for PTMs even using only counter as memory. For counter machines, when restricted to polynomial time, we can obtain the same result for linear space. For constant-space QTMs, we obtain the result for a restricted sweeping head, known as restarting realtime.

Extending qualitative CSPs with the ability of restricting selected variables to finite sets of possible values has been proposed as an interesting research direction with important applications, c ...

Spatiotemporal data represent the real-world objects that move in geographic space over time. The enormous numbers of mobile sensors and location tracking devices continuously produce massive amounts of such data. This leads to the need for scalable spatiotemporal data management systems. Such systems shall be capable of representing spatiotemporal data in persistent storage and in memory. They shall also provide a range of query processing operators that may scale out in a cloud setting. Currently, very few researches have been conducted to meet this requirement. This paper proposes a Hadoop extension with a spatiotemporal algebra. The algebra consists of moving object types added as Hadoop native types, and operators on top of them. The Hadoop file system has been extended to support parameter passing for files that contain spatiotemporal data, and for operators that can be unary or binary. Both the types and operators are accessible for the MapReduce jobs. Such an extension allows users to write Hadoop programs that can perform spatiotemporal analysis. Certain queries may call more than one operator for different jobs and keep these operators running in parallel. This paper describes the design and implementation of this algebra, and evaluates it using a benchmark that is specific to moving object databases.