After the optimal parameters of additive quaternary codes of dimension k<=3 have been determined in [1], there was some activity to settle the next case of dimension k=3.5 [2,3]. Here we complete dimensions k=3.5 and k=4. We also solve the problem of the optimal parameters of additive quaternary codes of arbitrary dimension when assuming a sufficiently large minimum distance.
This paper proposes a novel image steganographic method based on discrete Rademacher functions combined with Least Significant Bit (LSB) embedding. Unlike conventional sequential LSB techniques, which modify pixel values in a deterministic scan order, the proposed approach introduces a mathematically structured selection mechanism that governs both spatial embedding locations and, in the case of color images, channel selection. The performance of the proposed method is evaluated using standard benchmark images, including grayscale and color versions of the Lena, Tank, and Pepper datasets at a resolution of 512 × 512 pixels. The quality of stego-images is measured using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), ensuring both pixel-level accuracy and perceptual similarity assessment. Experimental results demonstrate that the proposed method maintains PSNR values above conventional acceptability thresholds and SSIM values close to unity across various embedding rates. Comparative analysis with classical sequential LSB embedding confirms that the proposed approach achieves comparable or improved imperceptibility, particularly in color images due to distributed channel embedding. The results indicate that Rademacher-based LSB steganography offers a favorable trade-off between embedding capacity, visual quality, and security.
This article presents a methodology for the analysis and classification of communication protocols and data stream management systems used in machine-to-machine (M2M) environments. The focus is placed on non-functional characteristics such as latency, reliability, scalability, security, and message ordering, and their relevance in protocol selection across different functional domains. A comparative evaluation of established protocols - including MQTT, HTTP/1.1-3, Kafka, Pulsar, RabbitMQ, AMQP, and CoAP - is conducted based on objective criteria and existing literature. Building on this foundation, hybrid architectures are proposed that combine multiple technologies according to the criticality and technical requirements of specific scenarios. The paper offers structured recommendations for communication strategies in M2M contexts, with empirical validation planned as the subject of future work.
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$ is denoted by $m(k,q)$. Here we determine $m(7,2)$, $m(8,2)$, and $m(9,2)$, as well as full classifications of all codes attaining $m(k,2)$ for $k\le 7$ and those attaining $m(9,2)$. We give improved upper bounds for $m(k,2)$ for all $10\le k\le 17$. It turns out that in many cases the attaining extremal codes have the property that the weights of all codewords are divisible by some constant $\Delta>1$. So, here we study the minimum lengths of minimal codes where we additionally assume that the weights of the codewords are divisible by $\Delta$. As a byproduct we also give a few binary linear codes improving the best known lower bound for the minimum distance.
Consider a compact M ⊂ℝ^d and l > 0. A maximal distance minimizer problem is to find a connected compact set Σ of the length (one-dimensional Hausdorff measure $̋) at mostlthat minimizes max_y ∈ M dist (y, Σ), wherediststands for the Euclidean distance. We give a survey on the results on the maximal distance minimizers and related problems.
We will consider all policies of the agent and will prove that one of them is the best performing policy. While that policy is not computable, computable policies do exist in its proximity. We will define AI as a computable policy which is sufficiently proximal to the best performing policy. Before we can define the agent's best performing policy, we need a language for description of the world. We will also use this language to develop a program which satisfies the AI definition. The program will first understand the world by describing it in the selected language. The program will then use the description in order to predict the future and select the best possible move. While this program is extremely inefficient and practically unusable, it can be improved by refining both the language for description of the world and the algorithm used to predict the future. This can yield a program which is both efficient and consistent with the AI definition.
This research paper presents a linear programming model for network flow optimization, addressing the challenge of freshwater management in Bangalore. The model highlights the practicality of linear programming in real-world scenarios. Specifically, the efficient allocation and distribution of freshwater resources from various sources, including reservoirs, rivers, and groundwater, to meet the growing demands of domestic, industrial, and agricultural sectors, while adhering to sustainable practices.
Kernel methods are highly flexible and powerful tools for capturing complex, nonlinear relationships in data. In this paper, we propose a substantial extension of existing network-based regression models by integrating kernel methods with graph-theoretic constraints. Our approach builds upon the foundational work of Li et al. [1], who incorporated network cohesion into generalized linear models (GLMs). We extend their framework by introducing a kernelized regression model that allows for the modeling of nonlinear interactions while leveraging network data. This kernelized framework relaxes the linearity constraints of GLMs, making the model more versatile and capable of capturing complex patterns in high-dimensional spaces. We demonstrate the effectiveness of our approach using simulated and real-world datasets, such as the Teenage Friends and Lifestyle Study. Results show that our kernelized network regression model not only outperforms traditional linear and generalized linear models in predictive accuracy but also scales efficiently to larger datasets. Our work represents a significant advancement in the modeling of network-linked data, providing a robust, scalable, and interpretable framework that extends the application of kernel methods beyond their traditional constraints. Future directions include exploring more complex graph structures, such as weighted and directed graphs, and developing optimized algorithms for even larger datasets.
A q-ary linear code is an [n,k,d]q code, which is a linear code of length n, dimension k and minimum weight d over Fq, the field of order q. A fundamental problem in coding theory is to find nq(k,d), the minimum length n for which an [n,k,d]q code exists for given k,d and q. We introduce a new notion "e-locally 2-weight (mod q)" for linear codes over Fq and we give a necessary condition for the property. As an application, we prove the non-existence of some [n,4,d]9 codes with d ≡ −1 (mod 9), which determines n9(4,d) for some d.
Accurate recognition of handwritten mathematical expressions has proven difficult due to their two-dimensional structure. Various machine-learning techniques have previously been employed to transcribe handwritten math, including approaches based on convolutional neural networks (CNNs) and larger encoder/decoder-based models. In this work, we explore a CNN-based method for transcribing handwritten math expressions into the typesetting language known as LaTeX. This approach utilizes machine learning not only for classifying individual characters but also for extracting individual characters from handwritten inputs and determining what forms of two-dimensionality exist within the expression. This approach achieves significant reliability when recognizing common mathematical expressions.
This paper explores the Minimum Weighted Independent Dominating Set Problem and proposes novel approaches to tackle it. Namely, two integer linear programming formulations and a fast greedy heuristic as an alternative approach are proposed. Extensive computational experiments are conducted to evaluate the performance of these approaches on the established set of benchmark instances for the problem. The obtained results demonstrate that the introduced integer linear programming models are able to achieve optimal solutions on all instances with 100 nodes and significantly outperform existing exact methods on numerous other instances. Additionally, the greedy heuristic exhibits superior performance compared to competing greedy heuristics, particularly on random graphs. These findings suggest promising directions for future research, including the integration of these methods into hybrid algorithms or metaheuristic frameworks.
In this paper, we propose the bivariate distribution of the Katz distribution [1] constructed by the trivariate reduction method, method developed in [6] and used in [5] to give an equivalent definition of the bivariate Poisson distribution [7, 8]. The constructed distribution includes, in particular, the bivariate Poisson distribution [5] and has interesting properties. For the estimation of the parameters, we used two methods: the method of moments and the maximum likelihood method using the EM algorithm. An application to concrete data has been made in order to carry out a comparative study between bivariate Poisson and Katz distributions, and we discuss the likelihood-ratio test, which assesses the goodness of fit of two competing statistical models.
We will reduce the task of creating AI to the task of finding an appropriate language for description of the world. This will not be a programing language because programing languages describe only computable functions, while our language will describe a somewhat broader class of functions. Another specificity of this language will be that the description will consist of separate modules. This will enable us look for the description of the world automatically such that we discover it module after module. Our approach to the creation of this new language will be to start with a particular world and write the description of that particular world. The point is that the language which can describe this particular world will be appropriate for describing any world. This is the first part of the paper. In this part we will define the basic theoretical concepts which will we will need when creating the language we are looking for.
Activation functions are used in Artificial Neural Networks to provide non-linearity to the system. Several different activation functions in use are very well known by almost any AI practitioner however this is not the case for polynomial activation functions. Increasing attention to these valuable mathematical functions can encourage more research and help to fill the gap. During this work, Chebyshev and Hermite orthogonal polynomials were used as activation functions. Calculations were conducted on 3 different datasets with different hyperparameters. According to the results, calculations done by Chebyshev activation functions take less time, but Chebyshev can be more fragile depending on the solved problem. On the other hand, Hermite shows a more robust and generalized behavior, it is less dependent on the problem type, and it improves by necessary adjustments.
This is the second part of the paper. In this part we will use the world of the chess game in order to create the language we are looking for. We will show how a complex world can be described in a simple and understandable way. Before describing the movement of chess pieces, we will need to extend the concept of algorithm. The new concept describes the algorithm as a sequence of actions performed in an arbitrary world. In the meaning of the new concept, a cooking recipe is also an algorithm. If we look at a world in which there is an infinite tape and a head which travels over the tape, then the algorithm of that world will be a Turing machine. This means that the new concept of algorithm is a generalization of the old one. Computer programs are algorithms both in the new concept and in the old one, however, there are many other sequences of actions which extend the concept.
Malicious attacks are one of the main threats facing today's most used Android and Windows operating systems, as well as the Internet of Things (IoT) and web environments. Markov models and hidden Markov models have been used successfully over the past few decades to identify a variety of malicious activity, including as viruses, worms, Trojan horses, rootkits, ransomware, and phishing assaults. But they have their limits. One of their main limitations is that they are unable to detect subtle changes in malicious behaviour. This paper presents Markov models and hidden Markov models as a tool for detecting malicious attacks and briefly reviews different studies from the past five years that use these models as a detection tool. This review, based on publications drawn from three databases, outlines the continuing interest of security researchers in these models. Most of the chosen research papers show that these models are applied to create systems that have a detection accuracy of malicious attacks above 94%. This study can be helpful to beginners who are interested in starting their research in the field of detecting malicious attacks.
Over the recent past a lot of work has been done around the topic of gamifying online learning. There are a number of useful papers discussing either the benefits of the process or the details of how to carry it out but there seem to be few dealing with both. In this paper the authors present the results of a lengthy research process which has culminated in the implementation and the delivery of a fully gamified Moodle-based course. The questions the researchers have addressed in their work attempt to determine the kind of influence gamification can have on the process of learning. In the experiment they have conducted, the gamified version of a key university course is delivered to a test group of 65 students, whereas a control group of 125 students takes the regular non-gamified version of the same course. The presentation of their work starts with an introduction to the key concepts and a review of some of the work done already, followed by a discussion of the complete set of gamification tools currently available in Moodle. The gamification of the UX Design course is then described in detail. Finally, the authors discuss the results of the experiment they have conducted and draw some conclusions that link the use of gamification to increased student motivation and engagement in the course, a lower level of attrition, and a significantly improved student success rate.
An efficient scheduler (algorithm) as a part of batch processing, implemented in a real warehouse management system is considered. The goal is not completion time but rather the fairness of the schedule expressed as a minimal overload of working places (machines, workers, etc.) used. As a combinatorial optimization problem, the objective is to find the permutation of the rows of a n x k boolean matrix B that minimizes the sum of the scalar products of each two consecutive rows. For the above-mentioned warehouse, the size n of a batch is in thousands and the number of working places is up to ten. The problem is modeled as many visits traveling salesman problem over the vertices of k dimensional unit hypercube with distances equal to the scalar products of the coordinate vectors of the vertices. The case n= 2^k is proven NP-hard and for the needs of the practice, where n >> k a heuristic greedy algorithm with a good, experimentally proven precision is proposed.
CWE is a community-supported database of known weaknesses. It is under permanent update and development. MITRE Corporation hosts this database. It consists of several viewpoints structured at several abstract levels. CWE database is the base of CWE ontology. It redefines weaknesses in terms of the Semantic Web. This ontology is a part of ontology ecosystem developed to capture cybersecurity knowledge on known vulnerabilities, weaknesses, and attacks patterns. CWE ontology classifies CVE/NVD vulnerabilities. It is useful for research and investigation on new vulnerabilities and weaknesses using reasoners. In addition, CWE is useful for cybersecurity incident forensic investigations, software acquisition and development.
A vector space partition P of the projective space PG(v-1,q) is a set of subspaces in PG(v-1,q) which partitions the set of points. We say that a vector space partition P has type (v-1)^{m_{v-1}} ... 2^{m_2}1^{m_1} if precisely m_i of its elements have dimension i, where 1 <= i <= v-1. Here we determine all possible types of vector space partitions in PG(7,2).
