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The celebrated canonical Ramsey theorem of Erd\H{o}s and Rado implies that for $2\leq k\in \mathbb{N}$, any colouring of the edges of $K_n$ with $n$ sufficiently large gives a copy of $C_{2k}$ which has one of three canonical colour patterns: monochromatic, rainbow or lexicographic. In this paper we show that if $p=\omega(n^{-1+1/(2k-1)}\log n)$, then ${\mathbf{G}}(n,p)$ will asymptotically almost surely also have the property that any colouring of its edges induces canonical copies of $C_{2k}$. This determines the threshold for the canonical Ramsey property with respect to even cycles, up to a $\log$ factor., Comment: 24 pages + 4 pages of appendix, 1 figure

In this paper, the Quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman functions, general expressions for the renormalized dispersion of the physical momentum are derived. Distinct expressions are found for the dispersion associated with each component of the particle physical momentum, indicating that the global properties of homogeneity and isotropy of space are lost, as a consequence of the introduced boundary conditions. Divergences also arise and are related to the compact nature of Einstein universe and the introduced boundary conditions., Comment: 19 pages, 2 Figures

The UNESCO (2022) points out that the gap between the existing awareness of a person or a community, and the actual habits of everyday life, is attributed to: low levels of understanding the environmental issues at stake; low levels of knowledge regarding energy and climate issues; and lack of attention to social, emotional or behavioral learning. In this context, as environmental and energetic concerns grow rapidly in our daily lives, RAISE - Raising environmental knowledge & awareness, an ERAMUS+ project with partners from three countries (Greece, Portugal, and Italy), was born. The project's first and main objective is to increase the environmental knowledge and awareness (EK&A) of schoolchildren. To achieve this goal, a survey was first carried out to ascertain the students' knowledge and, based on these results, scenarios and educational material were drawn up to build a pedagogical tool - a 3D Virtual World Learning Environment (3D VWLE). This paper presents the desktop research results and the main features of the game that are intended to match the identified educational needs. The 3D VWLE puts students in situations where they can acquire transferable skills. The project demonstrated that the simulation effect of 3D VWLE on skills provides an excellent online learning environment for students to work on and improve their abilities. In other words, virtual worlds open the door to a new way of learning and teaching.

In this paper we consider a massive self-interacting scalar quantum field in a Lorentz-violation scenario based on a Horava-Lifshitz model. Specifically, we investigate the vacuum energy density and its loop correction, up to first order in the self-interaction coupling constant, and also the topological mass generation. These quantities are also analyzed in the case where the field is massless. The scalar vacuum state is perturbed by the presence of two large parallel plates, placed at a distance L from each other, due to the imposition of Dirichlet boundary condition on the two plates. To perform this study, the effective potential approach in quantum field theory is applied., Comment: 14 pages, 3 Figures. arXiv admin note: text overlap with arXiv:2405.14656

Major Depressive Disorder and anxiety disorders affect millions globally, contributing significantly to the burden of mental health issues. Early screening is crucial for effective intervention, as timely identification of mental health issues can significantly improve treatment outcomes. Artificial intelligence (AI) can be valuable for improving the screening of mental disorders, enabling early intervention and better treatment outcomes. AI-driven screening can leverage the analysis of multiple data sources, including facial features in digital images. However, existing methods often rely on controlled environments or specialized equipment, limiting their broad applicability. This study explores the potential of AI models for ubiquitous depression-anxiety screening given face-centric selfies. The investigation focuses on high-risk pregnant patients, a population that is particularly vulnerable to mental health issues. To cope with limited training data resulting from our clinical setup, pre-trained models were utilized in two different approaches: fine-tuning convolutional neural networks (CNNs) originally designed for facial expression recognition and employing vision-language models (VLMs) for zero-shot analysis of facial expressions. Experimental results indicate that the proposed VLM-based method significantly outperforms CNNs, achieving an accuracy of 77.6% and an F1-score of 56.0%. Although there is significant room for improvement, the results suggest that VLMs can be a promising approach for mental health screening, especially in scenarios with limited data.

Neurological disorders that affect speech production, such as Alzheimer's Disease (AD), significantly impact the lives of both patients and caregivers, whether through social, psycho-emotional effects or other aspects not yet fully understood. Recent advancements in Large Language Model (LLM) architectures have developed many tools to identify representative features of neurological disorders through spontaneous speech. However, LLMs typically lack interpretability, meaning they do not provide clear and specific reasons for their decisions. Therefore, there is a need for methods capable of identifying the representative features of neurological disorders in speech and explaining clearly why these features are relevant. This paper presents an explainable LLM method, named SLIME (Statistical and Linguistic Insights for Model Explanation), capable of identifying lexical components representative of AD and indicating which components are most important for the LLM's decision. In developing this method, we used an English-language dataset consisting of transcriptions from the Cookie Theft picture description task. The LLM Bidirectional Encoder Representations from Transformers (BERT) classified the textual descriptions as either AD or control groups. To identify representative lexical features and determine which are most relevant to the model's decision, we used a pipeline involving Integrated Gradients (IG), Linguistic Inquiry and Word Count (LIWC), and statistical analysis. Our method demonstrates that BERT leverages lexical components that reflect a reduction in social references in AD and identifies which further improve the LLM's accuracy. Thus, we provide an explainability tool that enhances confidence in applying LLMs to neurological clinical contexts, particularly in the study of neurodegeneration., Comment: 27 pages, 6 figures, authors Marina Ribeiro and B\'arbara Malcorra have equal contribution, C\'esar Renn\'o-Costa is the corresponding author

We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the $SU(1,1)$ and $SU(2)$ groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its Hamiltonian in terms of the boson generators of the $SU(1,1)$ and $SU(2)$ groups. We use the one boson and two boson realizations of the $su(1,1)$ Lie algebra, and the one boson realization of the $su(2)$ Lie algebra to apply three tilting transformations to diagonalize the original Hamiltonian. These transformations let us to obtain the exact solutions of the isotropic and the anisotropic cases, from which the particular expected results are obtained for the cases where the coupling is neglected., Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:2409.08179

We study the Hamiltonian of two isotropic oscillators with weak coupling from an algebraic approach. We write the Hamiltonian of this problem in terms of the boson generators of the $SU(1,1)$ and $SU(2)$ groups. This allows us to apply two tilting transformations based on both group similarity transformations to obtain its energy spectrum and eigenfunctions. Then, we obtain the Mandel $Q-$parameter of the photon numbers $n_a$ and $n_b$. It is important to note that in our procedure we consider the case of weak coupling., Comment: 11 pages

In this paper, we investigate the vacuum bosonic current density induced by a carrying-magnetic-flux cosmic string in a $(D+1)$-de Sitter spacetime considering the presence of two flat boundaries perpendicular to it. In this setup, the Robin boundary conditions are imposed on the scalar charged quantum field on the boundaries. The particular cases of Dirichlet and Neumann boundary conditions are studied separately. Due to the coupling of the quantum scalar field with the classical gauge field, corresponding to a magnetic flux running along the string's core, a nonzero vacuum expectation value for the current density operator along the azimuthal direction is induced. The two boundaries divide the space in three regions with different properties of the vacuum states. In this way, our main objective is to calculate the induced currents in these three regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Because the vacuum bosonic current in dS space has been investigated before, in this paper we consider only the contributions induced by the boundaries. We show that for each region the azimuthal current densities are odd functions of the magnetic flux along the string. To probe the correctness of our results, we take the particular cases and analyze some asymptotic limits of the parameters of the model. Also some graphs are presented exhibiting the behavior of the current with relevant physical parameter of the system., Comment: 18 pages, 2 figures

The Euclid mission will measure cosmological parameters with unprecedented precision. To distinguish between cosmological models, it is essential to generate realistic mock observables from cosmological simulations that were run in both the standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) paradigm and in many non-standard models beyond $\Lambda$CDM. We present the scientific results from a suite of cosmological N-body simulations using non-standard models including dynamical dark energy, k-essence, interacting dark energy, modified gravity, massive neutrinos, and primordial non-Gaussianities. We investigate how these models affect the large-scale-structure formation and evolution in addition to providing synthetic observables that can be used to test and constrain these models with Euclid data. We developed a custom pipeline based on the Rockstar halo finder and the nbodykit large-scale structure toolkit to analyse the particle output of non-standard simulations and generate mock observables such as halo and void catalogues, mass density fields, and power spectra in a consistent way. We compare these observables with those from the standard $\Lambda$CDM model and quantify the deviations. We find that non-standard cosmological models can leave significant imprints on the synthetic observables that we have generated. Our results demonstrate that non-standard cosmological N-body simulations provide valuable insights into the physics of dark energy and dark matter, which is essential to maximising the scientific return of Euclid., Comment: 22 pages, 7 figures

To constrain models beyond $\Lambda$CDM, the development of the Euclid analysis pipeline requires simulations that capture the nonlinear phenomenology of such models. We present an overview of numerical methods and $N$-body simulation codes developed to study the nonlinear regime of structure formation in alternative dark energy and modified gravity theories. We review a variety of numerical techniques and approximations employed in cosmological $N$-body simulations to model the complex phenomenology of scenarios beyond $\Lambda$CDM. This includes discussions on solving nonlinear field equations, accounting for fifth forces, and implementing screening mechanisms. Furthermore, we conduct a code comparison exercise to assess the reliability and convergence of different simulation codes across a range of models. Our analysis demonstrates a high degree of agreement among the outputs of different simulation codes, providing confidence in current numerical methods for modelling cosmic structure formation beyond $\Lambda$CDM. We highlight recent advances made in simulating the nonlinear scales of structure formation, which are essential for leveraging the full scientific potential of the forthcoming observational data from the Euclid mission., Comment: 20 pages, 7 figures, 1 appendix; submitted on behalf of the Euclid Collaboration

In this work, we constrain the values of the parameters of the Generalized Tolman-Oppenheimer-Volkoff (GTOV) equation through Bayesian inference. We use the mass and radius data from the Neutron Star Interior Composition Explorer (NICER) for PSR J0740+6620 and PSR J0030+0451, as well as the mass, radius, and dimensionless tidal deformability from the gravitational wave (GW) events GW190814 and GW170817. We use two distinct parameterizations of the extended non-linear Walecka model (eNLW) with and without hyperons. The GTOV employed for the study contains additional free parameters with different physical motivations. Two possible scenarios are considered in our analysis: conservative and speculative. In the first case, we take into account the most reliable neutron star (NS) data from NICER and the GW170817 event. In the second case, we consider the possibility that the compact object with a mass of $2.54 M_{\odot}$ in the GW190814 event is an NS. Our findings show significant improvements in the physical quantities analyzed, leading to better agreement with the observational data compared to the results obtained using the TOV equation.

We investigate anisotropic equation of state parameterization of dark energy within the framework of an axisymmetric (planar) Bianchi-I universe. In addition to constraining the equation of state for anisotropic dark energy and other standard cosmological model parameters, we also constrain any underlying anisotropic axis using the latest Pantheon+ Type Ia Supernovae data set augmented by SH0ES Cepheid distance calibrators. The mean anisotropic dark energy equation of state and corresponding difference in the equation of states in and normal to the plane of our axisymmetric Bianchi-I space-time are found to be $\bar{w}=-0.90^{+0.16}_{-0.12}$ and $\delta_w=-0.140^{+0.11}_{-0.082}$ respectively. We also find an axis of anisotropy in this planar Bianchi-I model with anisotropic dark energy to be $\approx(279^{\circ} ,12^{\circ})$ in galactic coordinates. Our analysis of different cosmological models suggests that while a Bianchi-I universe with anisotropic dark energy (the $w_b$CDM model) shows some preference over other anisotropic models, it is still less likely than the standard $\Lambda$CDM model or a model with a constant dark energy equation of state ($w$CDM). Overall, the $\Lambda$CDM model remains the most probable model based on the Akaike Information Criterion., Comment: 12 pages, 6 figures, 2 tables; Comments are welcome

From the proliferative mechanisms generating neurons from progenitor cells to neuron migration and synaptic connection formation, several vicissitudes culminate in the mature brain. Both component loss and gain remain ubiquitous during brain development. For example, rodent brains lose over half of their initial neurons and synapses during healthy development. The role of deleterious steps in network ontogeny remains unclear, yet it is unlikely these costly processes are random. Like neurogenesis and synaptogenesis, synaptic pruning and neuron death likely evolved to support complex, efficient computations. In order to incorporate both component loss and gain in describing neuronal networks, we propose an algorithm where a directed network evolves through the selective deletion of less-connected nodes (neurons) and edges (synapses). Resulting in networks that display scale-invariant degree distributions, provided the network is predominantly feed-forward. Scale-invariance offers several advantages in biological networks: scalability, resistance to random deletions, and strong connectivity with parsimonious wiring. Whilst our algorithm is not intended to be a realistic model of neuronal network formation, our results suggest selective deletion is an adaptive mechanism contributing to more stable and efficient networks. This process aligns with observed decreasing pruning rates in animal studies, resulting in higher synapse preservation. Our overall findings have broader implications for network science. Scale-invariance in degree distributions was demonstrated in growing preferential attachment networks and observed empirically. Our preferential detachment algorithm offers an alternative mechanism for generating such networks, suggesting that both mechanisms may be part of a broader class of algorithms resulting in scale-free networks.

The launches of NASA Kepler and TESS missions have significantly enhanced the interest in the exoplanet field during the last 15 years, providing a vast amount of public data that is being exploited by the community thanks to the continuous development of new analysis tools. However, using these tools is not straightforward, and users must dive into different codes, input-output formats, and methodologies, hindering an efficient and robust exploration of the available data. We present the SHERLOCK pipeline, an end-to-end public software that allows the users to easily explore observations from space-based missions such as TESS or Kepler to recover known planets and candidates issued by the official pipelines and search for new planetary candidates that remained unnoticed. The pipeline incorporates all the steps to search for transit-like features, vet potential candidates, provide statistical validation, conduct a Bayesian fitting, and compute observational windows from ground-based observatories. Its performance is tested against a catalog of known and confirmed planets from the TESS mission, trying to recover the official TESS Objects of Interest (TOIs), explore the existence of companions that have been missed, and release them as new planetary candidates. SHERLOCK demonstrated an excellent performance, recovering 98% of the TOIs and confirmed planets in our test sample and finding new candidates. Specifically, we release four new planetary candidates around the systems WASP-16 (with P$\sim$10.46 d and R$\sim$2.20 $R_\oplus$), HAT-P-27 (with P$\sim$1.20 d and R$\sim$4.33 $R_\oplus$), HAT-P-26 (with P$\sim$6.59 d and R$\sim$1.97 $R_\oplus$), and TOI-2411 (with P$\sim$18.75 d and R$\sim$2.88 $R_\oplus$)., Comment: 23 pages, 14 figures, 4 tables, This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society Published by Oxford University Press on behalf of the Royal Astronomical Society

This paper presents the development and comparative evaluation of three voice command pipelines for controlling a Tello drone, using speech recognition and deep learning techniques. The aim is to enhance human-machine interaction by enabling intuitive voice control of drone actions. The pipelines developed include: (1) a traditional Speech-to-Text (STT) followed by a Large Language Model (LLM) approach, (2) a direct voice-to-function mapping model, and (3) a Siamese neural network-based system. Each pipeline was evaluated based on inference time, accuracy, efficiency, and flexibility. Detailed methodologies, dataset preparation, and evaluation metrics are provided, offering a comprehensive analysis of each pipeline's strengths and applicability across different scenarios.

Assuming the availability of a reliable aircraft trajectory planner, this paper presents a probabilistic methodology to detect conflicts between aircraft, in the cruise phase of the flight, in the presence of wind prediction uncertainties quantified by ensemble weather forecasts, which are regarded as realizations of correlated random processes and employed to derive the eastward and northward components of the wind velocity. First, the Karhunen-Lo`eve expansion is used to obtain a series expansion of the wind components in terms of a set of uncorrelated random variables and deterministic coefficients. Then, the uncertainty induced by these uncorrelated random variables in the outputs of the aircraft trajectory planner is quantified by means of the arbitrary polynomial chaos technique. Finally, the probability density function of the great circle distance between each pair of aircraft is derived from the polynomial expansions using a Gaussian kernel density estimator and employed to estimate the probability of conflict. The arbitrary polynomial chaos technique allows the effects of uncertainties in complex nonlinear dynamical system, such as those underlying aircraft trajectory planners, to be quantified with high computational efficiency, only requiring the existence of a finite number of statistical moments of the random variables of the Karhunen-Lo`eve expansion, while avoiding any assumption on their probability distributions. In order to demonstrate the effectiveness of the proposed conflict detection method, numerical experiments are conducted through an optimal control based aircraft trajectory planner for a given wind forecast represented by an ensemble prediction system.

This paper develops the novel convergence analysis of a generic class of descent methods in nonsmooth and nonconvex optimization under several versions of the Kurdyka-\L ojasiewicz (KL) property. Along other results, we prove the finite termination of generic algorithms under the KL property with lower exponents. Specifications are given to convergence rates of some particular algorithms including inexact reduced gradient methods and the boosted algorithm in DC programming. It revealed, e.g., that the lower exponent KL property in the DC framework is incompatible with the gradient Lipschitz continuity for the plus function around a local minimizer. On the other hand, we show that the above inconsistency observation may fail if the Lipschitz continuity is replaced by merely the gradient continuity., Comment: 12 pages

Turnover consists of moving into and out of professional employees in the company in a given period. Such a phenomenon significantly impacts the software industry since it generates knowledge loss, delays in the schedule, and increased costs in the final project. Despite the efforts made by researchers and professionals to minimize the turnover, more studies are needed to understand the motivation that drives Software Engineers to leave their jobs and the main strategies CEOs adopt to retain these professionals in software development companies. In this paper, we contribute a mixed methods study involving semi-structured interviews with Software Engineers and CEOs to obtain a wider opinion of these professionals about turnover and a subsequent validation survey with additional software engineers to check and review the insights from interviews. In studying such aspects, we identified 19 different reasons for software engineers' turnover and 18 more efficient strategies used in the software development industry to reduce it. Our findings provide several implications for industry and academia, which can drive future research.

This paper introduces a novel reconfigurable and power-efficient FPGA (Field-Programmable Gate Array) implementation of an operator splitting algorithm for Non-Terrestial Network's (NTN) relay satellites model predictive orientation control (MPC). Our approach ensures system stability and introduces an innovative reconfigurable bit-width FPGA-based optimization solver. To demonstrate its efficacy, we employ a real FPGA-In-the-Loop hardware setup to control simulated satellite dynamics. Furthermore, we conduct an in-depth comparative analysis, examining various fixed-point configurations to evaluate the combined system's closed-loop performance and power efficiency, providing a holistic understanding of the proposed implementation's advantages.

In this paper the vacuum energy density and generation of topological mass are investigated for a system of a real and complex scalar fields interacting with each other. In addition to that, it is also included the quartic self-interaction for each one of the fields. The condition imposed on the real field is the periodic condition, while the complex field obey a quasi-periodic condition. The system is placed in a scenario where the CPT-even aether-type Lorentz symmetry violation takes place. We allow that the Lorentz violation affects the fields with different intensities. The vacuum energy density, its loop correction, and the topological mass are evaluated analytically. It is also discussed the possibility of different vacuum states and their corresponding stability requirements, which depends on the conditions imposed on the fields, the interaction coupling constants and also the Lorentz violation parameters. The formalism used here to perform this investigation is the effective potential one, which is written as a loop expansion via path integral in quantum field theory., Comment: 18 pages, 6 figures, version accepted for publication in IJMPD. arXiv admin note: text overlap with arXiv:2302.14540

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Cosmic rays (CRs) interact with turbulent magnetic fields in the intestellar medium, generating nonthermal emission. After many decades of studies, the theoretical understanding of their diffusion in the ISM continues to pose a challenge. This study numerically explores a recent prediction termed "mirror diffusion" and its synergy with traditional diffusion mechanism based on gyroresonant scattering. Our study combines 3D MHD simulations of star-forming regions with test particle simulations to analyze CR diffusion. We demonstrate the significance of mirror diffusion in CR diffusion parallel to the magnetic field, when the mirroring condition is satisfied. Our results support the theoretical expectation that the resulting particle propagation arising from mirror diffusion in combination with much faster diffusion induced by gyroresonant scattering resembles a Levy-flight-like propagation. Our study highlights the necessity to reevaluate the diffusion coefficients traditionally adopeted in the ISM based on gyroresonant scattering alone. For instance, our simulations imply a diffusion coefficient $\sim10^{27}cm^2/s$ for particles with a few hundred TeV within regions spanning a few parsecs around the source. This estimate is in agreement with gamma-ray observations, which shows the relevance of our results for understanding of diffuse gamma-ray emission in star-forming regions.

The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral

The acquisition of different data modalities can enhance our knowledge and understanding of various diseases, paving the way for a more personalized healthcare. Thus, medicine is progressively moving towards the generation of massive amounts of multi-modal data (\emph{e.g,} molecular, radiology, and histopathology). While this may seem like an ideal environment to capitalize data-centric machine learning approaches, most methods still focus on exploring a single or a pair of modalities due to a variety of reasons: i) lack of ready to use curated datasets; ii) difficulty in identifying the best multi-modal fusion strategy; and iii) missing modalities across patients. In this paper we introduce a real world multi-modal dataset called MMIST-CCRCC that comprises 2 radiology modalities (CT and MRI), histopathology, genomics, and clinical data from 618 patients with clear cell renal cell carcinoma (ccRCC). We provide single and multi-modal (early and late fusion) benchmarks in the task of 12-month survival prediction in the challenging scenario of one or more missing modalities for each patient, with missing rates that range from 26$\%$ for genomics data to more than 90$\%$ for MRI. We show that even with such severe missing rates the fusion of modalities leads to improvements in the survival forecasting. Additionally, incorporating a strategy to generate the latent representations of the missing modalities given the available ones further improves the performance, highlighting a potential complementarity across modalities. Our dataset and code are available here: https://multi-modal-ist.github.io/datasets/ccRCC, Comment: Accepted in DCA in MI Workshop@CVPR2024

A new degravitation mechanism within the framework of scalar tensor gravity is proposed. The mechanism eliminates all constant contributions from the potential to the Friedmann equation, leaving only the kinematic and the dynamic terms of the potential to drive cosmic acceleration. We explore a scenario involving a density-triggered phase transition in the late-time universe, and argue that the resulting effective energy density and equation of state parameter can explain late-time cosmology when extrapolated to a region of the parameter space., Comment: 5 pages, 2 figures

We study the Barrow cosmological model, which proposes that quantum gravity effects create a complex, fractal structure for the universe's apparent horizon. We leverage the thermodynamics - gravity conjecture. By applying the Clausius relation to the apparent horizon of the Friedmann - Lema\^itre - Robertson - Walker universe within this framework, we derive modified field equations where the Barrow entropy is linked to the horizon. We assess the Barrow cosmology against current observations - cosmic microwave background , supernovae , and baryon acoustic oscillations data - and include projections for future Laser Interferometer Space Antenna (LISA) standard sirens (SS). Our numerical results suggest a modest improvement in the Hubble tension for Barrow cosmology with phantom dark energy behavior, compared to the standard cosmological model. Furthermore, incorporating simulated LISA SS data alongside existing observational constraints tightens the limitations on cosmological parameters, particularly the deformation exponent., Comment: 26 pages, 5 figures

The investigation of non-vacuum cosmological backgrounds containing black holes is greatly enhanced by the Kiselev solution. This solution plays a crucial role in understanding the properties of the background and its relationship with the features of the black hole. Consequently, the gravitational memory effects at large distances from the black hole offer a valuable means of obtaining information about the surrounding field parameter N and parameters related to the hair of the hairy Kiselev Black hole. This paper investigates the gravitational memory effects in the context of the Kiselev solution through two distinct approaches. At first, the gravitational memory effect at null infinity is explored by utilizing the Bondi-Sachs formalism by introducing a gravitational wave (GW) pulse to the solution. The resulting Bondi mass is then analyzed to gain further insight. Therefore, the Kiselev solution is being examined to determine the variations in Bondi mass caused by the pulse of GWs. The study of changes in Bondi mass is motivated by the fact that it is dynamic and time-dependent, and it measures mass on an asymptotically null slice or the densities of energy on celestial spheres. In the second approach, the investigation of displacement and velocity memory effects is undertaken in relation to the deviation of two neighboring geodesics and the deviation of their derivative influenced by surrounding field parameter N and the hair of hairy Kiselev black hole. This analysis is conducted within the context of a gravitational wave pulse present in the background of a hairy Kiselev black hole surrounded by a field parameter N., Comment: 18 pages, 30 figures

This work investigates the thermal Casimir effect associated with a massive spinor field defined on a four-dimensional flat space with a circularly compactified spatial dimension whose periodicity is oriented along a vector in $xy$-plane. We employ the generalized zeta function method to establish a finite definition for the vacuum free energy density. This definition conveniently separates into the zero-temperature Casimir energy density and additional terms accounting for temperature corrections. The structure of existing divergences is analyzed from the asymptotic behavior of the spinor heat kernel function and removed in the renormalization by subtracting scheme. The only non-null heat coefficient is the one associated with the Euclidean divergence. We also address the need for a finite renormalization to treat the ambiguity in the zeta function regularization prescription \text{associated} with this Euclidean heat kernel coefficient and ensure that the renormalization procedure is unique. The high- and low-temperature asymptotic limits are also explored. In particular, we explicitly show that free energy density lacks a classical limit at high temperatures, and the entropy density agrees with the Nernst heat theorem at low temperatures.