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In this work, we present a new analysis for $f(R,T)$ gravity by exploring the energy momentum tensor. We demonstrate that $f(R,T)$ gravity with the form $f(R,T)=R+2 \kappa^2 \lambda T-2\Lambda$ is equivalent to Running Vacuum Energy (RVE), which interacts with the components of the cosmic fluid, namely dark matter and radiation. Interestingly, the form of such interaction is inferred from the non-conservation of the stress energy tensor in $f(R, T)$ gravity rather than being introduced in a phenomenological manner. Furthermore, the parameters that distinguish RVE from $\Lambda$CDM are fixed once the parameter of $f(R,T)$ gravity, $\lambda$, is known. To illustrate our setup, we perform a Markov Chain Monte Carlo analysis of three interaction scenarios using a combination of different data. we find that the parameters characterizing the RVE model are very small as expected. These results give an accuracy to this equivalence between $f(R,T)$ gravity under consideration and support the recent result obtained from a quantum field theory in curved space-time point of view which could open a new relationship between $f(R,T)$ gravity and quantum field theory. Finally, the interaction of the running vacuum increases the value of the current value of the Hubble rate by $3.5\%$ compared to the $\Lambda$CDM model, which may be a promising study for the Hubble tension., Comment: 8 figures, 18 pages

Multi-component liquid mixtures can be both complex and fascinating, with some systems being amenable to simple experimentation at home, giving valuable insight into fundamental aspects of bulk and interfacial phase behaviour. One particularly interesting mixture is the popular drink ouzo, which has charmed both the general public and scientists by virtue of its ability to display spontaneous emulsification when water is added. When these two clear (and potable) liquids are poured into each other, a single milky-coloured liquid is formed. In previous work [Archer et al., Soft Matter 20, 5889 (2024)], the equilibrium phase-diagram for the stable liquid phases of ouzo was captured via experiment and modelling. Here we consider the case when the two liquid phases also coexist with the vapour phase (i.e. along a line of triple points) and within our model uncover the complex bulk phase behaviour for this simple beverage. As a consequence, this leads to some interesting observations, that also apply more widely, about visualising phase diagrams in ternary systems of this type. We also examine the interfacial behaviour, connecting microscopic density functional theory results with macroscopic (Neumann) predictions for the shape of droplets at interfaces.

Contrastively-trained Vision-Language Models (VLMs) like CLIP have become the de facto approach for discriminative vision-language representation learning. However, these models have limited language understanding, often exhibiting a "bag of words" behavior. At the same time, Large Vision-Language Models (LVLMs), which combine vision encoders with LLMs, have been shown capable of detailed vision-language reasoning, yet their autoregressive nature renders them less suitable for discriminative tasks. In this work, we propose to combine "the best of both worlds": a new training approach for discriminative fine-tuning of LVLMs that results in strong discriminative and compositional capabilities. Essentially, our approach converts a generative LVLM into a discriminative one, unlocking its capability for powerful image-text discrimination combined with enhanced language understanding. Our contributions include: (1) A carefully designed training/optimization framework that utilizes image-text pairs of variable length and granularity for training the model with both contrastive and next-token prediction losses. This is accompanied by ablation studies that justify the necessity of our framework's components. (2) A parameter-efficient adaptation method using a combination of soft prompting and LoRA adapters. (3) Significant improvements over state-of-the-art CLIP-like models of similar size, including standard image-text retrieval benchmarks and notable gains in compositionality., Comment: Preprint. The first two authors contributed equally

We consider conformal prediction of multivariate data series, which consists of outputting prediction regions based on empirical quantiles of point-estimate errors. We actually consider hierarchical multivariate data series, for which some components are linear combinations of others. The intuition is that the hierarchical structure may be leveraged to improve the prediction regions in terms of their sizes for given coverage levels. We implement this intuition by including a projection step (also called reconciliation step) in the split conformal prediction [SCP] procedure and prove that the resulting prediction regions are indeed globally smaller than without the projection step. The associated strategies and their analyses rely on the literatures of both SCP and forecast reconciliation. We also illustrate the theoretical findings, both on artificial and on real data., Comment: 30 pages, 8 figures

By considering the concept of Barrow's idea of a fractal black hole horizon in the extended-phase space thermodynamics formalism, we explore the thermodynamic processes, the phase transition, and the stability of black holes. We study the impact of quantum gravity on the area of the black hole due to the fractal parameter, delta. In this regard, we show that the thermodynamic behavior of black holes is influenced by the impact of quantum gravity. We found that at low entropy, the value of the fractal parameter does not significantly affect thermodynamic characteristics; however, for medium and large entropy, the influence becomes apparent. The Joule-Thomson coefficient is examined to further check the impact of quantum gravity in the extended-phase space thermodynamics approach. The observation reveals that the influence of the fractal parameter on Joule-Thomson expansion is evident. As the parameter value increases, the inversion pressure rises, leading to an expansion of the cooling region and a contraction of the heating region in the pressure-temperature (P-T) plane., Comment: 11 pages, 7 figures

This paper presents a detailed study of the thermodynamics of charged BTZ black holes using the conformal holographic extended thermodynamics formalism and Tsallis statistics. The cornerstone of our thermodynamic framework is the re-scaling of CFT by the conformal factor, which is considered a thermodynamic parameter. Here, the AdS radius is distinct from the CFT radius, allowing for independent variations of the central charge and volume. Our analysis revealed that the thermodynamic behavior of charged BTZ black holes in three dimensions is characterized by the stability and absence of phase transitions, contrasting with the behavior of four-dimensional black holes. The central charge of CFT notably influences the thermal evolution of these black holes, with a smaller central charge leading to faster thermal processes. Additionally, the temperature of large black holes is proportional to their entropy. By incorporating Tsallis statistics into our study, we found that the stability of black holes depends on the Tsallis parameter. Black holes are always stable when the Tsallis parameter is less than 2. However, if this parameter is greater than 2, a first-order phase transition occurs between small stable and large unstable. Overall, our findings contribute to a deeper understanding of the holographic thermodynamics of lower-dimensional black holes and the impact of non-extensive statistics on their physical properties., Comment: 12 pages, 4 figures

In this paper, we observationally test the \( f(Q) \) gravity model at both background and perturbation levels using Pantheon$^+$, Hubble measurements, and Redshift Space Distortion Data. We obtain the best-fit parameters by solving numerically the modified Friedmann equations for two distinct cosmological models of \( f(Q) \) gravity namely the Power law and Exponential models. This involves performing a Markov Chain Monte Carlo analysis for these specific forms of \( f(Q) \). To evaluate the statistical significance of the \( f(Q) \) gravity models, we use the Bayesian and corrected Akaike Information Criteria. Our results indicate that the Exponential model in \( f(Q) \) gravity is statistically favored over both the Power-law model and the \( \Lambda \)CDM model.

Accurate electricity demand forecasting is essential for several reasons, especially as the integration of renewable energy sources and the transition to a decentralized network paradigm introduce greater complexity and uncertainty. The proposed methodology leverages graph-based representations to effectively capture the spatial distribution and relational intricacies inherent in this decentralized network structure. This research work offers a novel approach that extends beyond the conventional Generalized Additive Model framework by considering models like Graph Convolutional Networks or Graph SAGE. These graph-based models enable the incorporation of various levels of interconnectedness and information sharing among nodes, where each node corresponds to the combined load (i.e. consumption) of a subset of consumers (e.g. the regions of a country). More specifically, we introduce a range of methods for inferring graphs tailored to consumption forecasting, along with a framework for evaluating the developed models in terms of both performance and explainability. We conduct experiments on electricity forecasting, in both a synthetic and a real framework considering the French mainland regions, and the performance and merits of our approach are discussed., Comment: 17 pages, ECML PKDD 2024 Workshop paper

In this study, we analyse constraints on the growth index of matter perturbations, $\gamma$, within the framework of $f(Q)$ gravity, using recent cosmological observations, at the background and the perturbation levels, including Pantheon$^{+}$, Cosmic Chronometer (CC), and Redshift Space Distortion (RSD) datasets. Our analysis focuses on quantifying the distortion parameter, which measures the deviation of the $f(Q)$ gravity model from the concordance $\Lambda$CDM cosmology at the background level. Specifically, we investigate two cases of the growth index parameter: a constant $\gamma$ and a time-varying $\gamma(z)$. We investigate various parametrizations of the growth index $\gamma$, expressed as $\gamma = \gamma_{0} +\gamma_{1} y(z)$, where the function $y(z)$ assumes different forms, including constant ($\Gamma_{0}$), Taylor expansion around $z = 0$ ($\Gamma_{1}$), Taylor expansion around the scale factor ($\Gamma_{2}$), and an exponential form ($\Gamma_{3}$). By employing the Akaike Information Criterion and Bayesian Information Criterion, we find that the combined Pantheon$^{+}$+ CC+ RSD datasets impose stringent constraints on the value of the growth index. For the $\Gamma_{0}$ model, our results indicate that within the concordance $\Lambda$CDM model, $\gamma$ is constrained to $0.545 \pm 0.096$, showing strong agreement with the theoretical expectation of $\gamma_{\Lambda} = \frac{6}{11}$. However, within the framework of $f(Q)$ gravity, we observe $\gamma = 0.571^{+0.095}_{-0.110}$, slightly exceeding the $\Lambda$CDM value by 4.66 $\%$. Furthermore, when considering a time-varying growth index, our analysis reveals that the range of $\gamma_{0}$ spans from $0.596$ to $0.62$ across the $\Gamma_{1-3}$ models., Comment: 15 pages, 6 figures

Despite recent successes, LVLMs or Large Vision Language Models are prone to hallucinating details like objects and their properties or relations, limiting their real-world deployment. To address this and improve their robustness, we present CLIP-DPO, a preference optimization method that leverages contrastively pre-trained Vision-Language (VL) embedding models, such as CLIP, for DPO-based optimization of LVLMs. Unlike prior works tackling LVLM hallucinations, our method does not rely on paid-for APIs, and does not require additional training data or the deployment of other external LVLMs. Instead, starting from the initial pool of supervised fine-tuning data, we generate a diverse set of predictions, which are ranked based on their CLIP image-text similarities, and then filtered using a robust rule-based approach to obtain a set of positive and negative pairs for DPO-based training. We applied CLIP-DPO fine-tuning to the MobileVLM-v2 family of models and to LlaVA-1.5, in all cases observing significant improvements in terms of hallucination reduction over baseline models. We also observe better performance for zero-shot classification, suggesting improved grounding capabilities, and verify that the original performance on standard LVLM benchmarks is overall preserved., Comment: Accepted at ECCV 2024

In this paper, we present an analytical solution for the interacting generalized holographic dark energy model, assuming a linear interaction rate between dark energy and dark matter. We determine the equation of state parameter, the generalized holographic Ricci dark energy density, the matter density, and the deceleration parameter. By analyzing the behavior of these cosmological parameters, we demonstrate that our model aligns with recent observations and reproduces the late-time accelerated expansion of the Universe. To compare our model with the $\Lambda$CDM model, we use various diagnostic tools including statefinder, $Om(z)$-diagnostic, statefinder hierarchy, growth rate analysis, and $\omega_H$-$\omega'_H$ plane. We also analyze the stability of the model by examining the speed of sound. These methods show that the dynamics of the Universe remain very close to that of the standard cosmological model.

Extended teleparallel gravity, characterized by $F(Q)$ function where $Q$ is the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable from the $\Lambda$CDM model at present time and exhibits a special event in the future, within $F(Q)$ gravity. To constrain the free parameters of the model, we perform a Markov Chain Monte Carlo (MCMC) analysis, using the last data from Pantheon$^{+}$ and the latest measurements of the H(z) parameter combined. On the basis of this analysis, we have find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime as in the case of general relativity. Furthermore, this behaviour affects the future expansion of the Universe as it becomes decelerating at $1\sigma$ confidence level for $z<-0.5$ and showing a bounce at $z_{\text{B}}\approx -0.835$. Finally, we have support our conclusion with a cosmographic analysis., Comment: 15 pages, 9 figures

In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev setting. The proofs of these properties are mainly based on a basic technique of convolution, joined with a cutoff, with some care needed in order not to exceed the original support.

We study the $(a:b)$ Maker-Breaker subgraph game played on the edges of the complete graph $K_n$ on $n$ vertices, $n,a,b \in \mathbb{N}$ where the goal of Maker is to build a copy of a specific fixed subgraph $H$. In our work this is a spanning graph with minimum degree $k=k(n)$, a connected spanning subgraph or a Hamiltonian subgraph. In the $(a:b)$ game in each round Maker chooses $a$ unclaimed edges of $K_n$ and Breaker chooses $b$ unclaimed edges. Maker wins, if he succeeds to build a copy of the subgraph under consideration, otherwise Breaker wins. For the $k$-minimum-degree, we present a winning strategy for Maker leading to a bound that generalizes a bound of Gebauer and Szab{\'o} for the $(1:b)$ case. Moreover, we give an explicit strategy for Breaker for $b >(1+o(1)) \frac{an}{a+\ln(n)}$ in case of $a=o\left(\sqrt{\frac{n}{\ln(n)}}\right)$ and $k=o(\ln(n))$. Note that this bound is the same as the Maker bound presented by Hefetz et al. (2012) for the $(a:b)$ connectivity game, which implies that the asymptotic optimal bias for this game is $\frac{an}{a+\ln(n)}$. This resolves the open problem stated by these authors. We also study the $(a:b)$ Hamiltonicity game in which Maker's goal is to create a Hamiltonian subgraph. For the $(1:b)$ variant Krivelevich proved that $\left(1+o(1) \right)\frac{n}{\ln n}$ is the exact threshold bias. Controlling Breaker's vertex degree in the $(a:b)$ Maker-Breaker minimum degree game enables us to the asymptotic optimal generalized threshold bias for the $(a:b)$-game, both for $a=o\left(\sqrt{\frac{n}{\ln n}} \right)$ and $a=\Omega\left(\sqrt{\frac{n}{\ln n}} \right)$.

Despite noise and caption quality having been acknowledged as important factors impacting vision-language contrastive pre-training, in this paper, we show that the full potential of improving the training process by addressing such issues is yet to be realized. Specifically, we firstly study and analyze two issues affecting training: incorrect assignment of negative pairs, and low caption quality and diversity. Then, we devise effective solutions for addressing both problems, which essentially require training with multiple true positive pairs. Finally, we propose training with sigmoid loss to address such a requirement. We show very large gains over the current state-of-the-art for both image recognition ($\sim +6\%$ on average over 11 datasets) and image retrieval ($\sim +19\%$ on Flickr30k and $\sim +15\%$ on MSCOCO)., Comment: Accepted at CVPR 2024

Ouzo is a well-known drink in Mediterranean countries, with ingredients water, alcohol and trans-anethole oil. The oil is insoluble in water, but completely soluble in alcohol, so when water is added to the spirit, the available alcohol is depleted and the mixture exhibits spontaneous emulsification. This process is commonly known as the louche or Ouzo effect. Although the phase boundaries of this archetypal ternary mixture are well known, the properties of coexisting phases have not previously been studied. Here, we present a detailed experimental investigation into the phase behaviour, including tie-lines connecting coexisting phases, determination of the critical point (also called the plait point in ternary systems) and measurements of the surface tension and density for varying alcohol concentrations. Additionally, we present a theory for the thermodynamics and phase diagram of the system. With suitable selection of the interaction parameters, the theory captures nearly all features of the experimental work. This simple model can be used to determine both bulk and non-uniform (e.g. interfacial) properties, paving the way for a wide range of future applications of the model to ternary mixtures in general. We show how our accurate equilibrium phase diagram can be used to provide improved understanding of non-equilibrium phenomena., Comment: 15 pages, 9 figures

In this paper, we study the post-inflationary era called reheating stage. For this purpose, we consider a model in which the inflaton is non-minimally coupled to the curvature within the hybrid metric-Palatini approach. Furthermore, to investigate the consistency of our results with the observational data, we relate reheating parameters to those of inflation model. By taking into consideration the Higgs potential $V(\phi)=\lambda/4 \phi^4$; we derive the necessary quantities needed to obtain the reheating duration and the reheating temperature. Moreover, we plot reheating e-folds and temperature as a function of the spectral index, respectively. We consider three cases depending on the coupling constant $\xi$. In addition, we use some specific values of the effective equation of state $\omega$, which is presumed to remain relatively constant within the range of $-\frac{1}{3} \leq \omega < \frac{1}{3}$. We find that for $\xi=10^{-4.1}$ our results are in agreement with the recent Planck data as the reheating instant is corresponding to the central value of the spectral index and to a maximum temperature required by the scale of baryogenesis models., Comment: 10 pages, 7 figures

In this paper, we examine the acceleration of the Universe's expansion in $F(R,T)$ gravity, where $R$ denotes the Ricci scalar and $T$ the trace of energy-momentum tensor. Indeed, the unknown nature of the source controlling this acceleration in general relativity leads scientists to investigate its properties by means of some alternative theories to general relativity. Our study is restricted to the particular case where $F(R,T)=R+2\kappa^2 \lambda T$ , with $\lambda$ being a constant. We use a Bayesian analysis of current observational datasets, including the type Ia supernovae constitution compilation and $H(z)$ measurements, to constrain free parameters of the model. To parametrize dark energy, we consider two well known equations of state. We find the best fit values for each model by running a Markov chain Monte Carlo technic. The best fit parameters are used to compare both models to $\Lambda$CDM by means of the Akaike information criterion and the Bayesian information criterion. We show that the Universe underwent recently a transition from a deceleration to an acceleration for both models. Furthermore, the data shows a phantom nature of the equation of state for both models., Comment: 13 pages, 5 figures

In this paper, we introduce a new fractional Musielak-Sobolev space $Ws,{\Phi}x,y({\Omega})$ where ${\Omega}$ is an open subset in RN and we show some density properties of smooth and compactly supported functions in this space.

In this paper, we examine the restricted phase space (RPS) thermodynamics for charged AdS black holes by considering the impact of quantum gravity on the event horizon area. The primary aim of this work is to elucidate the influence of quantum gravitational effects on thermodynamic behaviors, critical phenomena, phase transitions, and the stability of black holes. We observe that charged AdS black holes exhibit thermodynamic behavior similar to that of Van der Waals fluids when influenced by quantum gravity. Furthermore, we introduce a novel black hole thermodynamic phenomenon, which we term ``resistance of phase transitions". Our study uncovers a violation of the homogeneity property of the Smarr relation in RPS thermodynamics due to the effects of quantum gravity., Comment: 11 pages, 4 figures

In this paper, we study the thermodynamic behavior of charged AdS black holes in a conformal holographic extended thermodynamic. Our setup is constructed using a new dictionary that relates AdS black hole quantities to the corresponding dual conformal field theory (CFT) one, with the conformal factor being treated as a variable thermodynamic. In this thermodynamic study, we investigate the critical phenomena of charged AdS black holes and their relationship to the central charge value, \(C\). Additionally, we examine the phase transitions and black hole stability using the free energy and the heat capacity, respectively. Furthermore, by examining the chemical potential, we establish criteria that differentiate between quantum and classical black hole behaviors. Our setup highlights one of the key findings, namely traditional black hole thermodynamics acts as a boundary between quantum and classical regimes., Comment: 11 pages, 4 figures

To ensure the proper functioning of the current and future electrical grid, it is necessary for Transmission System Operators (TSOs) to verify that energy providers comply with the grid code and specifications provided by TSOs. A lot of energy production are conntected to the grid through a power electronic inverter. Grid Forming (GFM) and Grid Following (GFL) are the two types of operating modes used to control power electronic converters. The choice of control mode by TSOs to avoid impacting the stability of the grid is crucial, as is the commitment to these choices by energy suppliers. This article proposes a comparison between commonplace machine learning algorithms for converter control mode classification: GFL or GFM. The classification is based on frequency-domain admittance obtained by external measurement methods. Most algorithms are able to classify accurately when the control structure belongs to the training data, but they fail to classify modified control structures with the exception of the random forest algorithm.

Recently, the scalar-tensor representation of $f (R,T)$ gravity was used to explore gravitationally induced particle production/annihilation. Using the framework of irreversible thermodynamics of open systems in the presence of matter creation/annihilation, the physical and cosmological consequences of this setup were investigated in detail. In this paper, we test observationally the scalar-tensor representation of $f(R,T)$ gravity in the context of the aforementioned framework, using the Hubble and Pantheon+ measurements. The best fit parameters are obtained by solving numerically the modified Friedmann equations of two distinct cosmological models in scalar tensor $f(R, T)$ gravity, corresponding to two different choices of the potential, and by performing a Markov Chain Monte Carlo analysis. The best parameters are used to compute the cosmographic parameters, i.e., the deceleration, the jerk and the snap parameters. Using the output resulting from the Markov Chain Monte Carlo analysis, the cosmological evolution of the creation pressure and of the matter creation rates are presented for both models. To figure out the statistical significance of the studied scalar-tensor $f(R,T)$ gravity, the Bayesian and the corrected Akaike information criteria are used. The latter indicates that the first considered model in scalar tensor $f(R,T)$ gravity is statistically better than $\Lambda$CDM, i.e., it is more favored by observations. Besides, a continuous particle creation process is present in Model 1. On the other hand, for large redshifts, in Model 2 the particle creation rate may become negative, thus indicating the presence of particle annihilation processes. However, both models lead to an accelerating expansion of the Universe at late times, with a deceleration parameter equivalent to that of the $\Lambda$CDM model., Comment: 17 pages, 14 figures; accepted for publication in MNRAS