Coding Problem Research Articles

Guessing Numbers and Extremal Graph Theory

For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the colors of the vertices in its neighborhood. This quantity is related to problems in network coding, circuit complexity and graph entropy. We study the guessing number of graphs as a graph property in the context of classic extremal questions, and its relationship to the forbidden subgraph property. We find the extremal number with respect to the property of having guessing number $\leq a$, for fixed $a$. Furthermore, we find an upper bound on the saturation number for this property, and a method to construct further saturated graphs that lie between these two extremes. We show that, for a fixed number of colors, bounding the guessing number is equivalent to forbidding a finite set of subgraphs.

Siberian Animal Style as a Conceptual Basis for the Conversion of Traditional Artistic Heritage into Cultural Industries

The process of acquiring the author’s style, its semantic distinctive features, and the creation of the author’s identity is a fundamental problem for artists. The paper is devoted to the analysis of the artist’s native culture code influence on the creative concept and artistic language. Artistic inversion is important ‒ the inverse representation of the cultural code in the artist’s work. We consider artistic, pictorial inversion as a form of the artistic conceptualization. It contributes to the successful understanding of the connotations and intentions of the artist’s work by his audience. An analysis of Namdakov’s work allowed us to conceptualize the representation problem of the cultural code in Far East peoples’ contemporary art and describe artistic strategies that represent the influence of such semantic aspects of the cultural code as the influence of the artistic worldview, the strategies elevation of original interpretation and transformation of the animal style, the influence of the academic background. We define the artistic paradigm of the style as a style-forming factor in contemporary creative industries of artists who emerged from traditional crafts communities. The phenomenon of ethnic artistic tradition has been widely studied in the art history literature (T. M. Stepanskaya, A. V. Edokova, L. I. Nekhlyadovich). We believe, however, that attention should be focused on the content of “cultural code of artistic paradigm”, because ethnic artists consciously transform national artistic images and techniques through integration of their heritage into contemporary artistic language, culture and art background. This is particularly relevant for artists who institutionalize their style into a recognizable contemporary art language strategy. The main research question addressed in this paper is the representation peculiarities of the Namdakov’s artistic strategy semantic forms. He creates innovative ways of shaping, applies illogical, provocative and asymmetrical compositional solutions, creates fresh artistic metaphors, overcomes visual and figurative traditions and transforms ethnic artistic traditions into the leading artistic world-class trends of contemporary art. It has been proved that the animalistic style acquired a new modern dimension with the development of the creative industry in the regions of South-East Asia: the north of modern China and the art workshops of D. Namdakov and Zhigzhit Bayaskhalanov in the Russian Federation. It was the original interpretation of the animalistic style that became a powerful source for the development of traditional folk craft culture and brought the Far East peoples’ modern art to a new level of development, contributed to the evolution of the artist’s creative potential and gave many artists hope for creative expression.

Some new symmetric Hadamard matrices

Introduction: It is conjectured that the symmetric Hadamard matrices of order 4v exist for all odd integers v>0. In recent years, their existence has been proven for many new orders by using a special method known as the propus construction. This construction uses difference families Xk (k=1, 2, 3, 4) over the cyclic group Zv (integers mod v) with parameters (v; k1, k2, k3, k4; λ) where X1 is symmetric, X2=X3, and k1+2k2+k4=v+λ. It is also conjectured that such difference families (known as propus families) exist for all parameter sets mentioned above excluding the case when all the ki are equal. This new conjecture has been verified for all odd v≤53. Purpose: To construct many new symmetric Hadamard matrices by using the propus construction and to provide further support for the above-mentioned conjecture. Results: The first examples of symmetric Hadamard matrices of orders 4v are presented for v=127 and v=191. The systematic computer search for symmetric Hadamard matrices based on the propus construction has been extended to cover the cases v=55, 57, 59, 61, 63. Practical relevance: Hadamard matrices are used extensively in the problems of error-free coding, and compression and masking of video information.

On Universal D-Semifaithful Coding for Memoryless Sources With Infinite Alphabets

The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worse-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on $\infty$-alphabets. An important implication of these results is that universal D-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on $\infty$-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the well-known impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal D-semifaithful coding for a family of distributions $\Lambda$. This reduces to finding a collection of quantizations of the product space at different block-lengths -- reflecting the fixed distortion restriction -- that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to $\Lambda$, and the second is a vanishing information radius (I-radius) condition for $\Lambda$ reminiscent of the condition known for lossless universal source coding.

Crowdsmelling: A preliminary study on using collective knowledge in code smells detection

Code smells are seen as major source of technical debt and, as such, should be detected and removed. However, researchers argue that the subjectiveness of the code smells detection process is a major hindrance to mitigate the problem of smells-infected code. We proposed the crowdsmelling approach based on supervised machine learning techniques, where the wisdom of the crowd (of software developers) is used to collectively calibrate code smells detection algorithms, thereby lessening the subjectivity issue. This paper presents the results of a validation experiment for the crowdsmelling approach. In the context of three consecutive years of a Software Engineering course, a total "crowd" of around a hundred teams, with an average of three members each, classified the presence of 3 code smells (Long Method, God Class, and Feature Envy) in Java source code. These classifications were the basis of the oracles used for training six machine learning algorithms. Over one hundred models were generated and evaluated to determine which machine learning algorithms had the best performance in detecting each of the aforementioned code smells. Good performances were obtained for God Class detection (ROC=0.896 for Naive Bayes) and Long Method detection (ROC=0.870 for AdaBoostM1), but much lower for Feature Envy (ROC=0.570 for Random Forrest). Obtained results suggest that crowdsmelling is a feasible approach for the detection of code smells, but further validation experiments are required to cover more code smells and to increase external validity.

Theoretical-Conceptual, Legal and Social Problems of the Albanian Criminal Code: Some Useful Observations in view of its Reform

The problems of the Albanian criminal code are many and of different nature. In this short article, only some of the main issues will be highlighted, by underlying the most critical issues, while - for obvious reasons of space - individual institutes will not be explored in detail. We will try to carry out a general examination to understand what are the gaps, problems and possible solutions in view of a reform. In this regard, in fact, some elements will be highlighted that are believed to be of help to the ministerial commission that will be invested in the preparation of the new text.
 Received: 8 December 2021 / Accepted: 31 January 2022 / Published: 5 March 2022

Odin and Shadow Cretan matrices accompanying primes and their powers

Introduction: Cretan matrices – orthogonal matrices, consisting of the elements 1 and –b (real number), are an ideal object for the visual application of finite-dimensional mathematics. These matrices include, in particular, the Hadamard matrices and, with the expansion of the number of elements, the conference matrices. The most convenient research apparatus is to use field theory and multiplicative Galois groups, which is especially important for new types of Cretan matrices. Purpose: To study the symmetries of the Cretan matrices and to investigate two new types of matrices of odd and even orders, distinguished by symmetries, respectively, which differ significantly from the previously known Mersenne, Euler and Fermat matrices. Results: Formulas for levels are given and symmetries of new Cretan matrices: Odin bicycles (with a border) of orders 4t – 1 and 4t – 3 and shadow matrices of orders 4t – 2 and 4t – 4 are described. For odd character sizes equal to prime numbers and powers of primes, the existence of matrix symmetries of special types, doubly symmetric, consisting of skew-symmetric (with respect to the signs of elements) and symmetric cyclic blocks, is proved. It is shown that the previously distinguished Cretan matrices are their special case: Mersenne matrices of orders 4t – 1 and Euler matrices of orders 4t – 2 existing in the absence of symmetry for all selected orders without exception. Practical relevance: Оrthogonal sequences and methods of their effective finding by the theory of finite fields and groups are of direct practical importance for the problems of noise-immune coding, compression and masking of video information.

An Equivalent Expression for the Wyner-Ziv Source Coding Problem

We consider the coding problem for lossy source coding with side information at the decoder, which is known as the Wyner-Ziv source coding problem. The goal of the coding problem is to find the minimum rate such that the probability of exceeding a given distortion threshold is less than the desired level. We give an equivalent expression of the minimum rate by using the chromatic number and a notion of covering of a set. This allows us to analyze the coding problem in terms of graph coloring and covering.

On Smooth Rényi Entropies: A Novel Information Measure, One-Shot Coding Theorems, and Asymptotic Expansions

This study considers the unconditional smooth Rényi entropy proposed by Renner and Wolf [ASIACRYPT, 2005], the smooth conditional Rényi entropy proposed by Kuzuoka [IEEE Trans. Inf. Th., 66(3), 1674–1690, 2020], and a novel quantity which we term the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">conditional smooth</i> -⋆ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">entropy.</i> The latter two quantities can be specialized to the first in the absence of side-information. We explore the operational roles of these smooth Rényi entropies by establishing one-shot coding theorems for several information-theoretic problems, including Campbell’s source coding problem, the Arıkan–Massey guessing problem, and the Bunte–Lapidoth task encoding problem. We consider these problems in cases where the errors are non-vanishing and for each problem, we consider two error formalisms: the average and maximum error criteria, where the averaging and maximization are taken with respect to the side-information. Using the one-shot coding theorems, we conclude that Kuzuoka’s smooth conditional Rényi entropy and the conditional smooth-⋆ entropy are the solutions to the problems involving the average and maximum error criteria, respectively. Furthermore, we examine asymptotic expansions of these entropies when the underlying source with its side-information is stationary and memoryless. Applying our asymptotic expansions to the one-shot coding theorems, we derive various fundamental limits for these problems. We show that, under non-degenerate settings, the first-order fundamental limits differ under the average and maximum error criteria. This is in contrast to a different but related setting considered by the present authors [IEEE Trans. Inf. Th., 66(12), 7565–7587, 2020], for variable-length conditional source coding allowing errors, in which the first-order terms are identical but the second-order terms are different under these error criteria.

Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump

AbstractWe investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability.

Model-driven deep unrolling: Towards interpretable deep learning against noise attacks for intelligent fault diagnosis

Intelligent fault diagnosis (IFD) has experienced tremendous progress owing to a great deal to deep learning (DL)-based methods over the decades. However, the “black box” nature of DL-based methods still seriously hinders wide applications in industry, especially in aero-engine IFD, and how to interpret the learned features is still a challenging problem. Furthermore, IFD based on vibration signals is often affected by the heavy noise, leading to a big drop in accuracy. To address these two problems, we develop a model-driven deep unrolling method to achieve ante-hoc interpretability, whose core is to unroll a corresponding optimization algorithm of a predefined model into a neural network, which is naturally interpretable and robust to noise attacks. Motivated by the recent multi-layer sparse coding (ML-SC) model, we herein propose to solve a general sparse coding (GSC) problem across different layers and deduce the corresponding layered GSC (LGSC) algorithm. Based on the ideology of deep unrolling, the proposed algorithm is unfolded into LGSC-Net, whose relationship with the convolutional neural network (CNN) is also discussed in depth. The effectiveness of the proposed model is verified by an aero-engine bevel gear fault experiment and a helical gear fault experiment with three kinds of adversarial noise attacks. The interpretability is also discussed from the perspective of the core of model-driven deep unrolling and its inductive reconstruction property.

Spatial Linear Coding in Joint Radar and Multicast Communication Systems

Introduction. This paper presents optimization methods for the amplitude-phase distribution in a transmitting antenna array in a system with a common signal for multicast data transmission and radar sensing in a given sector of space. Two approaches are considered for the choice of an objective function for the optimization problem. The first approach involves minimizing the transmitted power for a given quality of user service and radar surveillance. The second approach involves optimizing the quality of service for the worst radar and communication channel under a given power budget. The value that determines the quality of service is the signal-to-noise ratio, for both communication and radar.Aim. Тo solve the optimization problem of spatial linear coding of signals in a joint multicast radar and communication system, which shares a common signal.Materials and methods. Optimization of spatial linear coding in a joint radio radar and communication system was carried out by the methods of statistical theory and optimization theory using the numerical solution of optimization problems. The performance characteristics of the system were analyzed by Monte Carlo simulation. Statistical simulation was performed in the MATLAB environment using standard tools, as well as the CVX package for the numerical solution of convex optimization problems.Results. Optimization problems were formulated based on the criteria of the minimum radiated power and the maximum signal-to-noise ratio in the worst channel. A limitation on the radiated power of individual antenna channels was used for both cases. Optimization problems were approximately reduced to convex problems with semidefinite constraints, which could be solved using the wellknown interior point algorithm with polynomial complexity. The performed statistical simulation produced optimal performance characteristics of a joint system, including the total power versus the threshold signal-to-noise ratio and the signal-to-noise ratio for the worst channel versus the power budget.Conclusion. The proposed numerical optimization methods for spatial linear coding in a transmitting antenna array can be recommended when designing joint radar communication systems.

Towards a taxonomy of code review smells

Code review is a crucial step of the software development life cycle in order to detect possible problems in source code before merging the changeset to the codebase. Although there is no consensus on a formally defined life cycle of the code review process, many companies and open source software (OSS) communities converge on common rules and best practices. In spite of minor differences in different platforms, the primary purpose of all these rules and practices leads to a faster and more effective code review process. Non-conformance of developers to this process does not only reduce the advantages of the code review but can also introduce waste in later stages of the software development.

Characteristics of the legal institution of co-ownership in Korea

The present article examines the legal institution of co-ownership in the Civil Code of the Republic of Korea (hereinafter — CC RK), with the center of focus being on joint and collective ownership. Unfortunately the Civil Code was prepared rather hastily in the aftermath of more than three decades of colonial rule under the Japanese Empire and the Korean War of 1950–1953. As a result the CC RK has no lack of legislative errors and shortcomings. One of the more serious of these is the conflict of norms on joint ownership. Similar, if not almost identical, provisions on joint ownership exist in Part II (Real Rights) and Part III (Claims) of the CC RK. It is necessary to resolve this conflict of norms by repealing the problematic provision, i. e. Article 704 (Partnership-ownership of Partnership Property), as well as amending provision, i. e. paragraph 2 Article 271 (Partnership-ownership of Property), so as to have the latter conform better to the whole structure of the Civil Code in general. The norms on collective ownership pose no less of a problem for the application of the Civil Code. Although the legal concept of collective ownership was born and developed in German jurisprudence, the institution never made it into the German Civil Code. It was at the opposite side of the globe in Korea that collective ownership was recognized and stipulated in the Civil Code. However such legislation cannot be deemed rational. The concept of collective ownership does not reflect the characteristics of the Korean society and the various transactions that are conducted therein, and therefore lacks practicality and applicability. The sole reason for including norms of collective ownership in the first place was to regulate the particular co-ownership form of unregistered incorporations. It would have been more desirable to include the relevant provisions not in Part II (Real Rights) but Chapter III (Juristic Persons) of Part I (General Provisions), and recognize the grounds for the provisions on juristic persons to apply to unregistered incorporations, unless registration is deemed essential for the application of such norms. Aside from legislative recommendations for addressing the current problems of the Civil Code, the author of the present paper provides a critique of the legal thinking and doctrines on various aspects of co-ownership in Korea.

Multi-label Multi-task Deep Learning for Behavioral Coding.

We propose a methodology for estimating human behaviors in psychotherapy sessions using mutli-label and multi-task learning paradigms. We discuss the problem of behavioral coding in which data of human interactions is the annotated with labels to describe relevant human behaviors of interest. We describe two related, yet distinct, corpora consisting of therapist client interactions in psychotherapy sessions. We experimentally compare the proposed learning approaches for estimating behaviors of interest in these datasets. Specifically, we compare single and multiple label learning approaches, single and multiple task learning approaches, and evaluate the performance of these approaches when incorporating turn context. We demonstrate the prediction performance gains which can be achieved by using the proposed paradigms and discuss the insights these models provide into these complex interactions.

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the conditional mean in the case of finite-variance input signals and additive Gaussian noise. The main result is a new lower bound in terms of the differential entropies of the input signal and the noisy observation. The main results are also extended to the vector Gaussian channel and to the natural exponential family. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. Two applications of the lower bound in the remote-source coding and CEO problem are discussed.

Covariance-Free Sparse Bayesian Learning

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new method for accelerating SBL inference -- named covariance-free expectation maximization (CoFEM) -- that avoids explicit computation of the covariance matrix. CoFEM solves multiple linear systems to obtain unbiased estimates of the posterior statistics needed by SBL. This is accomplished by exploiting innovations from numerical linear algebra such as preconditioned conjugate gradient and a little-known diagonal estimation rule. For a large class of compressed sensing matrices, we provide theoretical justifications for why our method scales well in high-dimensional settings. Through simulations, we show that CoFEM can be up to thousands of times faster than existing baselines without sacrificing coding accuracy. Through applications to calcium imaging deconvolution and multi-contrast MRI reconstruction, we show that CoFEM enables SBL to tractably tackle high-dimensional sparse coding problems of practical interest.

Coupling a Borehole Thermal Model and MT3DMS to Simulate Dynamic Ground Source Heat Pump Efficiency.

We present a novel integrated two-region model that couples simulation of local heat transfer processes in borehole heat exchangers (BHEs) with field-scale heat transport simulation using MT3DMS to fulfill the dynamic simulation of the borehole geothermal systems. This includes the prediction of subsurface thermal perturbation induced by BHEs, derivation of the U-pipe circulating fluid temperature profile within boreholes, and the evaluation of the ground source heat pump efficiency based on available time series of building heat load. In our approach, MT3DMS is the simulator for the two-dimensional field-scale heat transport, while new Python modules are developed to analytically solve the thermal transfer process within boreholes and interface iteratively with MT3DMS. A Python package for scripting MODFLOW-based code named Flopy is used to establish the MT3DMS numerical model. The proposed model is validated against analytical solutions and we demonstrate the application to more complex test problems with field-scale heterogeneity and pumping. Instructions are provided to access the source code and example problems which are available online.

ABOUT NON-LINGUISTIC CODES OF COMMUNICATION

The article analyzes the views on the concept of a code in linguistics, the problem of cultural code, the semantics of the code, the equivalence of the concept of a code and the concept of a cipher, as well as the non-identity between them. Among the various functions of language, a special role belongs to the cultural function, this function is performed by the language with the help of vocabulary, texts, and the language becomes the archive of culture, its «memory». And the cultural code is a set of signs, symbols. It conveys important cultural information by collecting all verbal and non-verbal communication. There is a great need for non-verbal thinking or non-linguistic codes to translate information from one form to another. Non-verbal means of communication are auxiliary means performed by communicators, which are used in parallel with words in communication or are located near them. Their functions are different and their application is not always the same. And this diversity is associated with the intentions of the communicators. There are several ways to distinguish non-verbal means from other means, from various psychological actions. These include: make sense in communication, have a role in achieving a certain goal in communication, understandability for the linguistic community, etc. These features indicate the relevance of studying paralinguistics. Examples of non-verbal elements were selected from fiction.

Factors Driving the Transition of Alzheimer’s Disease Patients to Institutional Long-term Care

Progression of Alzheimer’s disease (AD) may ultimately lead to costly institutional long term care (ILTC) so its avoidance is often a goal of care management. We studied predictors of AD patients transitioning to ILTC in the Veterans Affairs healthcare system (VA). We identified 30,017 Veterans at least 50 years old, with ≥2 ICD-9/10-CM diagnosis codes for AD on separate days, with first AD code in 2013-2018, at least 2 years of prior continuous VA service use, and no prior ILTC. Patients who subsequently transitioned to ILTC (cases) were matched to other AD patients with the same time since first AD code but no ILTC (controls) (median of 13 months; mean age of 80.2 years). The 8,261 matched sets were split randomly to a training sample, where logistic and random forest regressions were used to develop models, and a validation sample, where final models were evaluated. Predictors of ILTC initiation included measures of (1) poor health, such as high morbidity counts (Elixhauser score of 15+, odds ratio=1.31) and weight loss (1.29), (2) heavy service use, such as hospitalization (2.25) and home health care (1.54), and (3) dementia symptoms, such as a diagnosis code for dementia not-otherwise-specified recorded well before the AD code (1.93), functional/mobility difficulties (1.35), and lifestyle or psychosocial problems (1.53). The full model C statistic was 0.78. Transition to ILTC in AD patients is driven by many factors, including comorbidities, need for acute care, nonspecific symptoms of dementias, and functional challenges. Targeted interventions may delay transitions to ILTC.