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Community detection has been a subject of extensive research due to its broad applications across social media, computer science, biology, and complex systems. Modularity stands out as a predominant metric guiding community detection, with numerous algorithms aimed at maximizing modularity. However, modularity encounters a resolution limit problem when identifying small community structures. To tackle this challenge, this paper presents a novel approach by defining community structure information from the perspective of encoding edge information. This pioneering definition lays the foundation for the proposed fast community detection algorithm CSIM, boasting an average time complexity of only O (n log n) . Experimental results showcase that communities identified via the CSIM algorithm across various graph data types closely resemble ground truth community structures compared to those revealed via modularity-based algorithms. Furthermore, CSIM not only boasts lower time complexity than greedy algorithms optimizing community structure information but also achieves superior optimization results. Notably, in cyclic network graphs, CSIM surpasses modularity-based algorithms in effectively addressing the resolution limit problem. [ABSTRACT FROM AUTHOR]

In this article, we study some new properties of twin primes and algorithms for their generation. We find the necessary conditions to generate a pair of twins. These conditions seem to indicate that the conjecture is true, namely, there are infinitely many twin primes. Furthermore, we developed some algorithms that are very useful from a computer science point of view, which can be applied in cryptography and data encryption. [ABSTRACT FROM AUTHOR]

A new algorithm is presented for detecting the local weak reflection symmetries in raster images. It uses contours extracted from the segmented image. A convex hull is constructed on the contours, and so-called anchor points are placed on it. The bundles of symmetry line candidates are placed in these points. Each line splits the plane into two open half-planes and arranges the contours into three sets: the first contains the contours pierced by the considered line, while the second and the third include the contours located in one or the other half-plane. The contours are then checked for the reflection symmetry. This means looking for self-symmetries in the first set, and symmetric pairs with one contour in the second set and one contour in the third set. The line which is evaluated as the best symmetry line is selected. After that, the symmetric contours are removed from sets two and three. The remaining contours are then checked again for symmetry. A multi-branch tree representing the hierarchy of the detected local symmetries is the result of the algorithm. [ABSTRACT FROM AUTHOR]

Designing automatic optimizing compilers is an advanced engineering process requiring a great deal of expertise, programming, testing, and experimentation. Maintaining the approach and adapting it to evolving libraries and environments is a time-consuming effort. In recent years, OpenAI has presented the GPT model, which is designed for many fields like computer science, image processing, linguistics, and medicine. It also supports automatic programming and translation between programming languages, as well as human languages. This article will verify the usability of the commonly known LLM model, GPT, for the non-trivial NPDP Nussinov's parallel algorithm code within the OpenMP standard to create a parallel equivalent of CUDA for NVIDIA graphics cards. The goal of this approach is to avoid creating any post-processing scripts and writing any lines of target code. To validate the output code, we compare the resulting arrays with the ones calculated by the optimized code for the CPU generated employing the polyhedral compilers. Finally, the code will be checked for scalability and performance. We will concentrate on assessing the capabilities of GPT, highlighting common challenges that can be refined during future learning processes. This will enhance code generation for various platforms by leveraging the outcomes from polyhedral optimizers. [ABSTRACT FROM AUTHOR]