To optimize the reasoning and problem-solving capabilities of Large Language Models (LLMs), we propose a novel cloud-edge collaborative architecture that enables a structured, multi-agent prompting framework. This framework comprises three specialized components: GuideLLM, a lightweight model deployed at the edge to provide methodological guidance; SolverLLM, a more powerful model hosted in the cloud responsible for generating code solutions; and JudgeLLM, an automated evaluator for assessing solution correctness and quality. To evaluate and demonstrate the effectiveness of this architecture in realistic settings, we introduce RefactorCoderQA, a comprehensive benchmark designed to evaluate and enhance the performance of Large Language Models (LLMs) across multi-domain coding tasks. Motivated by the limitations of existing benchmarks, RefactorCoderQA systematically covers various technical domains, including Software Engineering, Data Science, Machine Learning, and Natural Language Processing, using authentic coding challenges from Stack Overflow. Extensive experiments reveal that our fine-tuned model, RefactorCoder-MoE, achieves state-of-the-art performance, significantly outperforming leading open-source and commercial baselines with an overall accuracy of 76.84%. Human evaluations further validate the interpretability, accuracy, and practical relevance of the generated solutions. In addition, we evaluate system-level metrics, such as throughput and latency, to gain deeper insights into the performance characteristics and trade-offs of the proposed architecture.

In the past few years, artificial intelligence (AI) techniques have been implemented in almost all verticals of human life. However, the results generated from the AI models often lag explainability. AI models often appear as a blackbox wherein developers are unable to explain or trace back the reasoning behind a specific decision. Explainable AI (XAI) is a rapid growing field of research which helps to extract information and also visualize the results generated with an optimum transparency. The present study provides and extensive review of the use of XAI in cybersecurity. Cybersecurity enables protection of systems, networks and programs from different types of attacks. The use of XAI has immense potential in predicting such attacks. The paper provides a brief overview on cybersecurity and the various forms of attack. Then the use of traditional AI techniques and its associated challenges are discussed which opens its doors towards use of XAI in various applications. The XAI implementations of various research projects and industry are also presented. Finally, the lessons learnt from these applications are highlighted which act as a guide for future scope of research.

We develop a procedure to analytically calculate higher-order contributions to the high-temperature real-time static potential in QCD. It is based on the introduction of a semi-hard external scale, which lies between the hard scale (the temperature) and the soft scale (the screening mass), and the method of integration by regions. We calculate the leading and next-to-leading corrections in the region where bound states transit from narrow resonances to wide ones. The calculation involves both loop diagrams calculated in the Hard Thermal Loop (HTL) effective theory and power corrections to the HTL Lagrangian calculated in QCD. We also calculate the thermal corrections to the heavy quarkonium spectrum, and estimate the dissociation temperatures. We compare our results with recent lattice data and discuss their usefulness to guide lattice inputs in inverse problems.

In this work, the authors describe efforts aimed at Indigenizing a second-year linear algebra course at a small liberal arts university in Manitoba, Canada. This is done through an assignment, part hands-on and part written work, that explores the connection between Indigenous beadwork and linear algebra. Our collaboration was perhaps unconventional: Sarah, the first author, is a mathematics professor; while Cathy, the second author, is an associate professor in art history. However, we both had similar goals of putting theory into practice and making positive changes to student learning outcomes in a culturally appropriate way. We situate our work in the context of the current scholarly literature, adding to the important ongoing dialogue on Indigenization of course content and reflecting on the process and outcomes. This transformation of the course curriculum represented an applied approach to immerse Indigenous knowledge and pedagogy into a mathematics classroom. We hope that it may serve as an example of how other educators, particularly in science, technology, engineering, and mathematics (STEM), can integrate Indigenous knowledge-centered pedagogy into their classroom.

The earliest phase of an ultrarelativistic heavy ion collision can be described as a highly populated system of gluons called glasma. The system's dynamics is governed by the classical Yang-Mills equation. Solutions can be found at early times using a proper time expansion. Since the expansion parameter is the time, this method is necessarily limited to the study of early time dynamics. In addition compute time and memory limitations restrict practical calculations to no more than eighth order in the expansion. The result is that the method produces reliable results only for very early times. In this paper we explore several different methods to increase the maximum time that can be reached. We find that, depending slightly on the quantity being calculated, the latest time for which reliable results are obtained can be extended approximately 1.5 times (from $\sim0.05$~fm/$c$ using previous methods to about $0.08$~fm/$c$).

[Abridged] We present a new deep 21-cm survey of the Andromeda galaxy, based on high resolution observations performed with the Synthesis Telescope and the 26-m antenna at DRAO. The HI distribution and kinematics of the disc are analyzed and basic dynamical properties are given. The rotation curve is measured out to 38 kpc, showing a nuclear peak, a dip around 4 kpc, two distinct flat parts and an increase in the outermost regions. Except for the innermost regions, the axisymmetry of the gas rotation is very good. A very strong warp of the HI disc is evidenced. The central regions appear less inclined than the average disc inclination, while the outer regions appear more inclined. Mass distribution models by LCDM NFW, Einasto or pseudo-isothermal dark matter halos with baryonic components are presented. They fail to reproduce the exact shape of the rotation curve. No significant differences are measured between the various shapes of halo. The dynamical mass of M31 enclosed within a radius of 38 kpc is (4.7 +/- 0.5) x 10^11 Msol. The dark matter component is almost 4 times more massive than the baryonic mass inside this radius. A total mass of 1.0 x 10^12 Msol is derived inside the virial radius. New HI structures are discovered in the datacube, like the detection of up to five HI components per spectrum, which is very rarely seen in other galaxies. The most remarkable new HI structures are thin HI spurs and an external arm in the disc outskirts. A relationship between these spurs and outer stellar clumps is evidenced. The external arm is 32 kpc long, lies on the far side of the galaxy and has no obvious counterpart on the other side of the galaxy. Its kinematics clearly differs from the outer adjacent disc. Both these HI perturbations could result from tidal interactions with galaxy companions.

Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equations that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest ($n$=2) level. In this paper we show how to obtain renormalized results from an $n$-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms.

Recent literature highlights a significant cross-impact between transfer learning and cybersecurity. Many studies have been conducted on using transfer learning to enhance security, leading to various applications in different cybersecurity tasks. However, previous research is focused on specific areas of cybersecurity. This paper presents a comprehensive survey of transfer learning applications in cybersecurity by covering a wide range of domains, identifying current trends, and shedding light on under-explored areas. The survey highlights the significance of transfer learning in addressing critical issues in cybersecurity, such as improving detection accuracy, reducing training time, handling data imbalance, and enhancing privacy preservation. Additional insights are provided on the common problems solved using transfer learning, such as the lack of labeled data, different data distributions, and privacy concerns. The paper identifies future research directions and challenges that require community attention, including the need for privacy-preserving models, automatic tools for knowledge transfer, metrics for measuring domain relatedness, and enhanced privacy preservation mechanisms. The insights and roadmap presented in this paper will guide researchers in further advancing transfer learning in cybersecurity, fostering the development of robust and efficient cybersecurity systems to counter emerging threats and protect sensitive information. To the best of our knowledge, this paper is the first of its kind to present a comprehensive taxonomy of all areas of cybersecurity that benefited from transfer learning and propose a detailed future roadmap to shape the possible research direction in this area.

We define and study the notion of a locally bounded enriched category over a (locally bounded) symmetric monoidal closed category, generalizing the locally bounded ordinary categories of Freyd and Kelly. In addition to proving several general results for constructing examples of locally bounded enriched categories and locally bounded closed categories, we demonstrate that locally bounded enriched categories admit fully enriched analogues of many of the convenient results enjoyed by locally bounded ordinary categories. In particular, we prove full enrichments of Freyd and Kelly's reflectivity and local boundedness results for orthogonal subcategories and categories of models for sketches and theories. We also provide characterization results for locally bounded enriched categories in terms of enriched presheaf categories, and we show that locally bounded enriched categories admit useful adjoint functor theorems and a representability theorem. We also define and study the notion of $\alpha$-bounded-small weighted limit enriched in a locally $\alpha$-bounded closed category, which parallels Kelly's notion of $\alpha$-small weighted limit enriched in a locally $\alpha$-presentable closed category, and we show that enriched categories of models of $\alpha$-bounded-small weighted limit theories are locally $\alpha$-bounded.

Spherical plasma lens models are known to suffer from a severe over-pressure problem, with some observations requiring lenses with central pressures up to millions of times in excess of the ambient ISM. There are two ways that lens models can solve the over-pressure problem: a confinement mechanism exists to counter the internal pressure of the lens, or the lens has a unique geometry, such that the projected column-density appears large to an observer. This occurs with highly asymmetric models, such as edge-on sheets or filaments, with potentially low volume-density. In the first part of this work we investigate the ability of non-magnetized plasma filaments to mimic the magnification of sources seen behind spherical lenses and we extend a theorem from gravitational lens studies regarding this model degeneracy. We find that for plasma lenses, the theorem produces unphysical charge density distributions. In the second part of the work, we consider the plasma lens over-pressure problem. Using magnetohydrodynamics, we develop a non self-gravitating model filament confined by a helical magnetic field. We use toy models in the force-free limit to illustrate novel lensing properties. Generally, magnetized filaments may act as lenses in any orientation with respect to the observer, with the most high density events produced from filaments with axes near the line of sight. We focus on filaments that are perpendicular to the line of sight that show the toroidal magnetic field component may be observed via the lens rotation measure.

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI re-summed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the 4-loop 4PI effective action for a scalar theory with cubic and quartic interactions in the presence of spontaneous symmetry breaking. We obtain a set of integral equations that determine the re-summed 2-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.

In recent years, social media has become a ubiquitous and integral part of social networking. One of the major attentions made by social researchers is the tendency of like-minded people to interact with one another in social groups, a concept which is known as Homophily. The study of homophily can provide eminent insights into the flow of information and behaviors within a society and this has been extremely useful in analyzing the formations of online communities. In this paper, we review and survey the effect of homophily in social networks and summarize the state of art methods that has been proposed in the past years to identify and measure the effect of homophily in multiple types of social networks and we conclude with a critical discussion of open challenges and directions for future research.

Associated to a graph $G$ is a set $\mathcal{S}(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be chosen. If $G$ has $n$ vertices, then the multiplicities of the eigenvalues of any matrix in $\mathcal{S}(G)$ partition $n$; this is called a multiplicity partition. We study graphs for which a multiplicity partition with only two integers is possible. The graphs $G$ for which there is a matrix in $\mathcal{S}(G)$ with partitions $[n-2,2]$ have been characterized. We find families of graphs $G$ for which there is a matrix in $\mathcal{S}(G)$ with multiplicity partition $[n-k,k]$ for $k\geq 2$. We focus on generalizations of the complete multipartite graphs. We provide some methods to construct families of graphs with given multiplicity partitions starting from smaller such graphs. We also give constructions for graphs with matrix in $\mathcal{S}(G)$ with multiplicity partition $[n-k,k]$ to show the complexities of characterizing these graphs.

For quantum communications, the use of Earth-orbiting satellites to extend distances has gained significant attention in recent years, exemplified in particular by the launch of the Micius satellite in 2016. The performance of applied protocols such as quantum key distribution (QKD) depends significantly upon the transmission efficiency through the turbulent atmosphere, which is especially challenging for ground-to-satellite uplink scenarios. Adaptive optics (AO) techniques have been used in astronomical, communication, and other applications to reduce the detrimental effects of turbulence for many years, but their applicability to quantum protocols, and their requirements specifically in the uplink scenario, are not well established. Here, we model the effect of the atmosphere on link efficiency between an Earth station and a satellite using an optical uplink, and how AO can help recover from loss due to turbulence. Examining both low-Earth-orbit and geostationary uplink scenarios, we find that a modest link transmissivity improvement of about 3dB can be obtained in the case of a co-aligned downward beacon, while the link can be dramatically improved, up to 7dB, using an offset beacon, such as a laser guide star. AO coupled with a laser guide star would thus deliver a significant increase in the secret key generation rate of the QKD ground-to-space uplink system, especially as reductions of channel loss have favourably nonlinear key-rate response within this high-loss regime.

Identification of a person from fingerprints of good quality has been used by commercial applications and law enforcement agencies for many years, however identification of a person from latent fingerprints is very difficult and challenging. A latent fingerprint is a fingerprint left on a surface by deposits of oils and/or perspiration from the finger. It is not usually visible to the naked eye but may be detected with special techniques such as dusting with fine powder and then lifting the pattern of powder with transparent tape. We have evaluated the quality of machine learning techniques that has been implemented in automatic fingerprint identification. In this paper, we use fingerprints of low quality from database DB1 of Fingerprint Verification Competition (FVC 2002) to conduct our experiments. Fingerprints are processed to find its core point using Poincare index and carry out enhancement using Diffusion coherence filter whose performance is known to be good in the high curvature regions of fingerprints. Grey-level Co-Occurrence Matrix (GLCM) based seven statistical descriptors with four different inter pixel distances are then extracted as features and put forward to train and test REPTree, RandomTree, J48, Decision Stump and Random Forest Machine Learning techniques for personal identification. Experiments are conducted on 80 instances and 28 attributes. Our experiments proved that Random Forests and J48 give good results for latent fingerprints as compared to other machine learning techniques and can help improve the identification accuracy.

Software Defined Networking (SDN) has brought significant advancements in network management and programmability. However, this evolution has also heightened vulnerability to Advanced Persistent Threats (APTs), sophisticated and stealthy cyberattacks that traditional detection methods often fail to counter, especially in the face of zero-day exploits. A prevalent issue is the inadequacy of existing strategies to detect novel threats while addressing data privacy concerns in collaborative learning scenarios. This paper presents P3GNN (privacy-preserving provenance graph-based graph neural network model), a novel model that synergizes Federated Learning (FL) with Graph Convolutional Networks (GCN) for effective APT detection in SDN environments. P3GNN utilizes unsupervised learning to analyze operational patterns within provenance graphs, identifying deviations indicative of security breaches. Its core feature is the integration of FL with homomorphic encryption, which fortifies data confidentiality and gradient integrity during collaborative learning. This approach addresses the critical challenge of data privacy in shared learning contexts. Key innovations of P3GNN include its ability to detect anomalies at the node level within provenance graphs, offering a detailed view of attack trajectories and enhancing security analysis. Furthermore, the models unsupervised learning capability enables it to identify zero-day attacks by learning standard operational patterns. Empirical evaluation using the DARPA TCE3 dataset demonstrates P3GNNs exceptional performance, achieving an accuracy of 0.93 and a low false positive rate of 0.06.

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.

We present the most sensitive and detailed view of the neutral hydrogen (HI) emission associated with the Small Magellanic Cloud (SMC), through the combination of data from the Australian Square Kilometre Array Pathfinder (ASKAP) and Parkes (Murriyang), as part of the Galactic Australian Square Kilometre Array Pathfinder (GASKAP) pilot survey. These GASKAP-HI pilot observations, for the first time, reveal HI in the SMC on similar physical scales as other important tracers of the interstellar medium, such as molecular gas and dust. The resultant image cube possesses an rms noise level of 1.1 K (1.6 mJy/beam) per 0.98 km s$^{-1}$ spectral channel with an angular resolution of 30$''$ ($\sim$10 pc). We discuss the calibration scheme and the custom imaging pipeline that utilizes a joint deconvolution approach, efficiently distributed across a computing cluster, to accurately recover the emission extending across the entire $\sim$25 deg$^2$ field-of-view. We provide an overview of the data products and characterize several aspects including the noise properties as a function of angular resolution and the represented spatial scales by deriving the global transfer function over the full spectral range. A preliminary spatial power spectrum analysis on individual spectral channels reveals that the power-law nature of the density distribution extends down to scales of 10 pc. We highlight the scientific potential of these data by comparing the properties of an outflowing high velocity cloud with previous ASKAP+Parkes HI test observations.