Case-Marking in the Romance Languages

Case-marking is subject to several important developments in the passage from Latin to the Romance languages. With respect to synthetic marking, nouns and adjectives witness considerable simplification, leading (with some exceptions, i.e., the binary case systems) to the almost complete disappearance of inflectional case-marking, while pronouns continue to show consistent inflectional case-marking. In binary case systems, case distinctions are also marked in the inflection of determiners. Inflectional simplification is compensated for by the profusion of analytic and mixed case-marking strategies and by alternative strategies of encoding grammatical relations (see article on “Argument Marking in Romance” in this encyclopedia, forthcoming).

A Complete Description of the Dynamics of Legal Outer-totalistic Affine Continuous Cellular Automata

We present an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine Continuous Cellular Automata (ACCAs), with [0,1] as state set and local rules that are affine in each variable. We focus on legal outer-totalistic ACCAs, an interesting class of dynamical systems that show some properties that do not occur in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allow to lay bare the dynamics of each and every one of these cellular automata.

An Extension of the Gamma Test Statistics to Binary Variables and Some Applications

In this paper, we discuss the problem of estimating the minimum error reachable by a regression model given a dataset, prior to learning. More specifically, we extend the Gamma Test estimates of the variance of the noise from the continuous case to the binary case. We give some heuristics for further possible extensions of the theory in the continuous case with the [Formula: see text]-norm and conclude with some applications and simulations. From the point of view of machine learning, the result is relevant because it gives conditions under which there is no need to learn the model in order to predict the best possible performance.

Extended similarity indices: the benefits of comparing more than two objects simultaneously. Part 1: Theory and characteristics†

Quantification of the similarity of objects is a key concept in many areas of computational science. This includes cheminformatics, where molecular similarity is usually quantified based on binary fingerprints. While there is a wide selection of available molecular representations and similarity metrics, there were no previous efforts to extend the computational framework of similarity calculations to the simultaneous comparison of more than two objects (molecules) at the same time. The present study bridges this gap, by introducing a straightforward computational framework for comparing multiple objects at the same time and providing extended formulas for as many similarity metrics as possible. In the binary case (i.e. when comparing two molecules pairwise) these are naturally reduced to their well-known formulas. We provide a detailed analysis on the effects of various parameters on the similarity values calculated by the extended formulas. The extended similarity indices are entirely general and do not depend on the fingerprints used. Two types of variance analysis (ANOVA) help to understand the main features of the indices: (i) ANOVA of mean similarity indices; (ii) ANOVA of sum of ranking differences (SRD). Practical aspects and applications of the extended similarity indices are detailed in the accompanying paper: Miranda-Quintana et al. J Cheminform. 2021. 10.1186/s13321-021-00504-4. Python code for calculating the extended similarity metrics is freely available at: https://github.com/ramirandaq/MultipleComparisons.

An Analysis of the Inertia Weight Parameter for Binary Particle Swarm Optimization

In particle swarm optimization (PSO), the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This paper comprehensively investigates the effect of the inertia weight on the performance of binary PSO (BPSO), from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of BPSO, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for BPSO. This scheme allows the search process to start first with exploration and gradually move toward exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the BPSO with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This paper verifies the efficacy of increasing inertia weight in BPSO. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

An Analysis of the Inertia Weight Parameter for Binary Particle Swarm Optimization

In particle swarm optimization (PSO), the inertia weight is an important parameter for controlling its search capability. There have been intensive studies of the inertia weight in continuous optimization, but little attention has been paid to the binary case. This paper comprehensively investigates the effect of the inertia weight on the performance of binary PSO (BPSO), from both theoretical and empirical perspectives. A mathematical model is proposed to analyze the behavior of BPSO, based on which several lemmas and theorems on the effect of the inertia weight are derived. Our research findings suggest that in the binary case, a smaller inertia weight enhances the exploration capability while a larger inertia weight encourages exploitation. Consequently, this paper proposes a new adaptive inertia weight scheme for BPSO. This scheme allows the search process to start first with exploration and gradually move toward exploitation by linearly increasing the inertia weight. The experimental results on 0/1 knapsack problems show that the BPSO with the new increasing inertia weight scheme performs significantly better than that with the conventional decreasing and constant inertia weight schemes. This paper verifies the efficacy of increasing inertia weight in BPSO. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Analysis of linear complexity of generalized cyclotomic Q-ary sequences of pn period

The article presents the analysis of the linear complexity of periodic q-ary sequences when changing k of their terms per period. Sequences are formed on the basis of new generalized cyclotomy modulo equal to the degree of an odd prime. There has been obtained a recurrence relation and an estimate of the change in the linear complexity of these sequences, where q is a primitive root modulo equal to the period of the sequence. It can be inferred from the results that the linear complexity of these sequences does not sign ificantly decrease when k is less than half the period. The study summarizes the results for the binary case obtained earlier.

Polyadic Hopf Algebras and Quantum Groups

This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural conditions (“arity freedom principle”). In this way, generalized associative algebras, coassociative coalgebras, bialgebras and Hopf algebras are defined and investigated. They have many unusual features in comparison with the binary case. For instance, both the algebra and its underlying field can be zeroless and nonunital, the existence of the unit and counit is not obligatory, and the dimension of the algebra is not arbitrary, but “quantized”. The polyadic convolution product and bialgebra can be defined, and when the algebra and coalgebra have unequal arities, the polyadic version of the antipode, the querantipode, has different properties. As a possible application to quantum group theory, we introduce the polyadic version of braidings, almost co-commutativity, quasitriangularity and the equations for the R-matrix (which can be treated as a polyadic analog of the Yang-Baxter equation). We propose another concept of deformation which is governed not by the twist map, but by the medial map, where only the latter is unique in the polyadic case. We present the corresponding braidings, almost co-mediality and M-matrix, for which the compatibility equations are found.

A Framework for Detecting Vehicle Occupancy Based on the Occupant Labeling Method

High-occupancy vehicle (HOV) lanes or congestion toll discount policies are in place to encourage multipassenger vehicles. However, vehicle occupancy detection, essential for implementing such policies, is based on a labor-intensive manual method. To solve this problem, several studies and some companies have tried to develop an automated detection system. Due to the difficulties of the image treatment process, those systems had limitations. This study overcomes these limits and proposes an overall framework for an algorithm that effectively detects occupants in vehicles using photographic data. Particularly, we apply a new data labeling method that enables highly accurate occupant detection even with a small amount of data. The new labeling method directly labels the number of occupants instead of performing face or human labeling. The human labeling, used in existing research, and occupant labeling, this study suggested, are compared to verify the contribution of this labeling method. As a result, the presented model’s detection accuracy is 99% for the binary case (2 or 3 occupants or not) and 91% for the counting case (the exact number of occupants), which is higher than the previously studied models’ accuracy. Basically, this system is developed for the two-sided camera, left and right, but only a single side, right, can detect the occupancy. The single side image accuracy is 99% for the binary case and 87% for the counting case. These rates of detection are also better than existing labeling.

Bottleneck Problems: An Information and Estimation-Theoretic View

Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber’s Lemma), and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed “bottleneck problems”, by replacing mutual information in IB and PF with other notions of mutual information, namely f-information and Arimoto’s mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.