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In this work, we consider a static wormhole in Bopp-Podolsky electrodynamics and convert it into its rotating counterpart by reducing it into Morris-Thorne form. We further study the null geodesics and effective potential along with the shadows for inner and outer unstable orbits for specific choices of parameters. It is found that for some cases smooth shadow curves are formed and for a few cases, the shadows formed are cuspy. All parameters have a significant impact on the shadows except for the parameter $b$ when either $a$ or $Q$ are kept small. We also analyze the gravitational lensing in the strong regime, considering that the observer and the source are on opposite sides of the throat. For this situation, we explore in detail the behavior of the deflection angle, Einstein rings and lensing observables.

Large language models (LLMs) have become increasingly prevalent in our daily lives, leading to an expectation for LLMs to be trustworthy -- - both accurate and well-calibrated (the prediction confidence should align with its ground truth correctness likelihood). Nowadays, fine-tuning has become the most popular method for adapting a model to practical usage by significantly increasing accuracy on downstream tasks. Despite the great accuracy it achieves, we found fine-tuning is still far away from satisfactory trustworthiness due to "tuning-induced mis-calibration". In this paper, we delve deeply into why and how mis-calibration exists in fine-tuned models, and how distillation can alleviate the issue. Then we further propose a brand new method named Efficient Trustworthy Distillation (FIRST), which utilizes a small portion of teacher's knowledge to obtain a reliable language model in a cost-efficient way. Specifically, we identify the "concentrated knowledge" phenomenon during distillation, which can significantly reduce the computational burden. Then we apply a "trustworthy maximization" process to optimize the utilization of this small portion of concentrated knowledge before transferring it to the student. Experimental results demonstrate the effectiveness of our method, where better accuracy (+2.3%) and less mis-calibration (-10%) are achieved on average across both in-domain and out-of-domain scenarios, indicating better trustworthiness., Comment: EMNLP 2024

Modern applications are end-to-end encrypted to prevent data from being read or secretly modified. 5G tech nology provides ubiquitous access to these applications without compromising the application-specific performance and latency goals. In this paper, we empirically demonstrate that 5G radio communication becomes the side channel to precisely infer the user's applications in real-time. The key idea lies in observing the 5G physical and MAC layer interactions over time that reveal the application's behavior. The MAC layer receives the data from the application and requests the network to assign the radio resource blocks. The network assigns the radio resources as per application requirements, such as priority, Quality of Service (QoS) needs, amount of data to be transmitted, and buffer size. The adversary can passively observe the radio resources to fingerprint the applications. We empirically demonstrate this attack by considering four different categories of applications: online shopping, voice/video conferencing, video streaming, and Over-The-Top (OTT) media platforms. Finally, we have also demonstrated that an attacker can differentiate various types of applications in real-time within each category., Comment: 9 pages, 8 figures, 2 tables. This paper has been accepted for publication by the 21st IEEE International Conference on Mobile Ad-Hoc and Smart Systems (MASS 2024)

Aging and chronic conditions affect older adults' daily lives, making early detection of developing health issues crucial. Weakness, common in many conditions, alters physical movements and daily activities subtly. However, detecting such changes can be challenging due to their subtle and gradual nature. To address this, we employ a non-intrusive camera sensor to monitor individuals' daily sitting and relaxing activities for signs of weakness. We simulate weakness in healthy subjects by having them perform physical exercise and observing the behavioral changes in their daily activities before and after workouts. The proposed system captures fine-grained features related to body motion, inactivity, and environmental context in real-time while prioritizing privacy. A Bayesian Network is used to model the relationships between features, activities, and health conditions. We aim to identify specific features and activities that indicate such changes and determine the most suitable time scale for observing the change. Results show 0.97 accuracy in distinguishing simulated weakness at the daily level. Fine-grained behavioral features, including non-dominant upper body motion speed and scale, and inactivity distribution, along with a 300-second window, are found most effective. However, individual-specific models are recommended as no universal set of optimal features and activities was identified across all participants.

The visible universe is filled with different types of plasma media in the form of stars, nebulas and other forms of excited gases. These matter fields have a high influence on the gravity and are likely to be present around the black holes due to the immense gravitational attraction. Since a plasma medium affects the speed of light, therefore we investigated the null geodesics and various optical features around the rotating black hole in Kalb-Ramond gravity immersed in plasma medium. Various plasma distributions are considered to develop a comparative study for their influence on unstable null circular orbits, shadows and evaporation rate of the black hole in the presence of a plasma medium. Moreover, the shadow results are also compared with Event Horizon Telescope data for M78* and Sgr A* in order to estimate the parametric bounds for which the rotating black hole in Kalb-Ramond gravity is considered either M87* or Sgr A* under the different values of plasma parameters. From this analysis, we also found the distribution of plasma that has a significant impact on the above mentioned features and is most likely to be present around M87* and Sgr A*., Comment: 30 pages, 14 figures

We study the optical properties of spacetime around a novel regular black hole (BH) in general relativity (GR) coupled to nonlinear electrodynamics (NED), which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric BH spacetime. Later, the rotating regular BH solution is obtained using the Newmann-Janis algorithm, and the event horizon properties of the BH are determined. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating BH. Also, we analyze the photon sphere around the novel BH and its shadow using celestial coordinates. We obtain that an increase of the BH spin and charge as well as NED field nonlinearity parameters causes an increase in the distortion parameter of the BH shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the BH charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive BHs Sgr A* and M87*. Finally, the emission rate of BH evaporation through Hawking radiation is also studied.

This article deals with the study of some properties of the static and rotating black holes in Kalb-Ramond gravity in four dimensional spacetime. First, we discuss the action of the corresponding theory and the static black hole metric. Then we investigate the light sphere for the static black hole by using the Hamiltonian formalism and the corresponding linear radius of the shadow, angular velocity and Lyapunov exponent. For the rotating black hole, we discuss the horizon structure. Moreover, we study the effective potential to discuss the structure of null sphere and unstable circular null orbits around the rotating black hole. The properties such as energy emission rate and distortion are calculated and analyzed by using the numerical data for the shadows calculated by appropriately chosen parametric values for two different angular locations of the observer off the equatorial plane. We also obtain the constraints on the black hole parameters by comparing the shadow sizes of the black hole in Kalb-Ramond gravity and the supermassive black holes M87* and Sgr A*. Finally, we investigate the effect of mass, energy, angular momentum and the black hole parameters on the center of mass energy of two colliding particles that are accelerated in the vicinity of the black hole., Comment: 29 pages, 15 figures

Software systems are increasingly relying on deep learning components, due to their remarkable capability of identifying complex data patterns and powering intelligent behaviour. A core enabler of this change in software development is the availability of easy-to-use deep learning libraries. Libraries like PyTorch and TensorFlow empower a large variety of intelligent systems, offering a multitude of algorithms and configuration options, applicable to numerous domains of systems. However, bugs in those popular deep learning libraries also may have dire consequences for the quality of systems they enable; thus, it is important to understand how bugs are identified and fixed in those libraries. Inspired by a study of Jia et al., which investigates the bug identification and fixing process at TensorFlow, we characterize bugs in the PyTorch library, a very popular deep learning framework. We investigate the causes and symptoms of bugs identified during PyTorch's development, and assess their locality within the project, and extract patterns of bug fixes. Our results highlight that PyTorch bugs are more like traditional software projects bugs, than related to deep learning characteristics. Finally, we also compare our results with the study on TensorFlow, highlighting similarities and differences across the bug identification and fixing process.

We consider a static black hole immersed in the Power-Yang-Mills field in four dimensional Einstein-Gauss-Bonnet gravity and investigate the effect of various parameters on the radius of the photon sphere. The modified form of the Newman-Janis algorithm is used for obtaining a rotating black hole solution in this gravity. Further, we try to explore the influence of the Yang-Mills magnetic charge $Q$ with power $q$, Gauss-Bonnet parameter $\alpha$ and spin $a$ on the horizon radius. The geodesic equations are constructed by incorporating the Hamilton-Jacobi formalism. The radial component of the geodesic equations gives the effective potential which is further used in deriving the mathematical structure for the shadows by using Bardeen's procedure for a fixed observer at infinity. The shadows are calculated and plotted in terms of two celestial coordinates for an equatorial observer. It is observed that all the parameters have a very significant effect on the shadow and related physical observables. {We also obtain the constraint values for the spin, magnetic charge and Gauss-Bonnet parameters, using the shadow size of supermassive black holes Sagittarius A$^*$ and M$87$* from the EHT observations for the cases of $q=0.6$ and $0.9$. It is shown that there are upper and lower bounds for the charge and spin of M$87$* at $q=0.6$, while only the upper bounds for charge and spin of Sagittarius A$^*$. Finally, we investigate the energy emission rate in the Hawking radiation around the $4D$ Einstein-Gauss-Bonnet black hole in the Power-Yang-Mills field.}

Spectroscopic ellipsometry is a powerful method with high surface sensitivity that can be used to monitor the growth of even sub-monolayer film. However, the analysis of ultrathin films is complicated by the correlation of the dielectric constant and the thickness. This problem is usually resolved by fixing one or the other value, limiting the information that can be extracted. Here, we propose a method to determine unambiguously the refractive index, extinction coefficient and thickness of a film when a transparent range is available in the energy range investigated. We decompose the analysis in three steps. First, the thickness of the film is determined from the transparent range of the film. Then, knowing the thickness of the layer, an initial estimation of the refractive index and extinction coefficient is made based on a first-order Taylor expansion of the ellipsometric ratio. Finally, using this estimation, a numerical regression is done to ensure the convergence of the fit towards the solution. A theoretical example of the method is given for two different thicknesses of TiO2 films. Finally, the method is applied to the experimental data measured during the atomic layer deposition of a thin film of Hf0.5Zr0.5O2 grown on Si. The thickness, refractive index and extinction coefficient are retrieved with a high precision in the energy range of 3.5 - 6.5 eV. A detailed analysis is presented on the accuracy of the retrieved values and their dependency on random and systematic errors for different energy ranges.

In this article, we considered the strong field approximation of nonlinear electrodynamics black hole and constructed its rotating counterpart by applying the modified Newman-Janis algorithm. The corresponding metric function in the strong field limit of the static black hole is identified in order to study the radius of photon sphere. However, the metric function for the rotating counterpart in the strong field limit is considered in order to study the horizon radius w.r.t spin parameter. We considered the Hamilton-Jacobi method to derive the geodesic equations for photon and constructed an orthonormal tetrad for deriving the equations for celestial coordinates in the observer's sky. Shadows, distortions and energy emission rates are investigated and the results are compared for different values of nonlinear electrodynamics parameter, charge and spin. It is found that the presence of the nonlinear electrodynamics parameter affects the shape and size of the shadows and thus the distortion in the case of rotation. It is also found that the nonlinearity of electrodynamics diminishes the flatness in the shadow due to the effect of spin and other parameters., Comment: 18 pages, 7 figures, Accepted for Publication in European Physical Journal C

Learning object-centric scene representations is essential for attaining structural understanding and abstraction of complex scenes. Yet, as current approaches for unsupervised object-centric representation learning are built upon either a stationary observer assumption or a static scene assumption, they often: i) suffer single-view spatial ambiguities, or ii) infer incorrectly or inaccurately object representations from dynamic scenes. To address this, we propose Dynamics-aware Multi-Object Network (DyMON), a method that broadens the scope of multi-view object-centric representation learning to dynamic scenes. We train DyMON on multi-view-dynamic-scene data and show that DyMON learns -- without supervision -- to factorize the entangled effects of observer motions and scene object dynamics from a sequence of observations, and constructs scene object spatial representations suitable for rendering at arbitrary times (querying across time) and from arbitrary viewpoints (querying across space). We also show that the factorized scene representations (w.r.t. objects) support querying about a single object by space and time independently., Comment: Accepted at NeurIPS 2021

Anti-malware engines are the first line of defense against malicious software. While widely used, feature engineering-based anti-malware engines are vulnerable to unseen (zero-day) attacks. Recently, deep learning-based static anti-malware detectors have achieved success in identifying unseen attacks without requiring feature engineering and dynamic analysis. However, these detectors are susceptible to malware variants with slight perturbations, known as adversarial examples. Generating effective adversarial examples is useful to reveal the vulnerabilities of such systems. Current methods for launching such attacks require accessing either the specifications of the targeted anti-malware model, the confidence score of the anti-malware response, or dynamic malware analysis, which are either unrealistic or expensive. We propose MalRNN, a novel deep learning-based approach to automatically generate evasive malware variants without any of these restrictions. Our approach features an adversarial example generation process, which learns a language model via a generative sequence-to-sequence recurrent neural network to augment malware binaries. MalRNN effectively evades three recent deep learning-based malware detectors and outperforms current benchmark methods. Findings from applying our MalRNN on a real dataset with eight malware categories are discussed., Comment: Accepted in 35th AAAI Conference on Artificial Intelligence, Workshop on Robust, Secure, and Efficient Machine Learning (RSEML)

An accurate load forecast is always important for the power industry and energy players as it enables stakeholders to make critical decisions. In addition, its importance is further increased with growing uncertainties in the generation sector due to the high penetration of renewable energy and the introduction of demand side management strategies. An incremental improvement in grid-level demand forecast of anomalous days can potentially save millions of dollars. However, due to an increasing penetration of renewable energy resources and their dependency on several meteorological and exogenous variables, accurate load forecasting of anomalous days has now become very challenging. To improve the prediction accuracy of the load forecasting, an ensemble forecast framework (ENFF) is proposed with a systematic combination of three multiple predictors, namely Elman neural network (ELM), feedforward neural network (FNN) and radial basis function (RBF) neural network. These predictors are trained using global particle swarm optimization (GPSO) to improve their prediction capability in the ENFF. The outputs of individual predictors are combined using a trim aggregation technique by removing forecasting anomalies. Real recorded data of New England ISO grid is used for training and testing of the ENFF for anomalous days. The forecast results of the proposed ENFF indicate a significant improvement in prediction accuracy in comparison to autoregressive integrated moving average (ARIMA) and back-propagation neural networks (BPNN) based benchmark models.

The uncertainty associated with solar photo-voltaic (PV) power output is a big challenge to design, manage and implement effective demand response and management strategies. Therefore, an accurate PV power output forecast is an utmost importance to allow seamless integration and a higher level of penetration. In this research, a neural network ensemble (NNE) scheme is proposed, which is based on particle swarm optimization (PSO) trained feedforward neural network (FNN). Five different FFN structures with varying network complexities are used to achieve the diverse and accurate forecast results. These results are combined using trim aggregation after removing the upper and lower forecast error extremes. Correlated variables namely wavelet transformed historical power output of PV, solar irradiance, wind speed, temperature and humidity are applied as inputs to the multivariate NNE. Clearness index is used to classify days into clear, cloudy and partial cloudy days. Test case studies are designed to predict the solar output for these days selected from all seasons. The performance of the proposed framework is analyzed by applying training data set of different resolution, length and quality from seven solar PV sites of the University of Queensland, Australia. The forecast results demonstrate that the proposed framework improves the forecast accuracy significantly in comparison with individual and benchmark models.

The problem of providing massive connectivity in Internet-of-Things (IoT) with a limited number of available resources motivates the non-orthogonal multiple access (NOMA) solutions. In this article, we provide a comprehensive review of the signature-based NOMA (S-NOMA) schemes as potential candidates for IoT. The signature in S-NOMA represents the way the data stream of an active device is spread over available resources in a non-orthogonal manner. It can be designed based on device-specific codebook structures, delay patterns, spreading sequences, interleaving patterns, and scrambling sequences. Additionally, we present the detection algorithms employed to decode each device's data from non-orthogonally superimposed signals at the receiver. The bit error rate of different S-NOMA schemes is simulated in impulsive noise environments, which can be important in machine-type communications. Simulation results show that the performance of the S-NOMA schemes degrades under such conditions. Finally, research challenges in S-NOMA oriented IoT are presented.

Mobile Internet is becoming the norm. With more personalized mobile devices in hand, many services choose to offer alternative, usually more convenient, approaches to authenticating and delivering the content between mobile users and service providers. One main option is to use SMS (i.e., short messaging service). Such carrier-grade text service has been widely used to assist versatile mobile services, including social networking, banking, to name a few. Though the text service can be spoofed via certain Internet text service providers which cooperated with carriers, such attacks haven well studied and defended by industry due to the efforts of research community. However, as cellular network technology advances to the latest IP-based 4G LTE, we find that these mobile services are somehow exposed to new threats raised by this change, particularly on 4G LTE Text service (via brand-new distributed Mobile-Initiated Spoofed SMS attack which is not available in legacy 2G/3G systems). The reason is that messaging service over LTE shifts from the circuit-switched (CS) design to the packet-switched (PS) paradigm as 4G LTE supports PS only. Due to this change, 4G LTE Text Service becomes open to access. However, its shields to messaging integrity and user authentication are not in place. As a consequence, such weaknesses can be exploited to launch attacks (e.g., hijack Facebook accounts) against a targeted individual, a large scale of mobile users and even service providers, from mobile devices. Current defenses for Internet-Initiated Spoofed SMS attacks cannot defend the unprecedented attack. Our study shows that 53 of 64 mobile services over 27 industries are vulnerable to at least one threat. We validate these proof-of-concept attacks in one major US carrier which supports more than 100 million users. We finally propose quick fixes and discuss security insights and lessons we have learnt., Comment: 16 pages, 13 figures

In this paper, we will analyse the cosmological models in Einstein-aether gravity, which is a modified theory of gravity in which a time-like vector field breaks the Lorentz symmetry. We will use this formalism to analyse different cosmological models with different behavior of the scale factor. In this analysis, we will use a certain functional dependence of the dark energy on the Hubble parameter. It will be demonstrated that the aether vector field has a non-trivial effect on these cosmological models. We will also perform the \emph{Om} diagnostic in Einstein-aether gravity. Thus, we will fit parameters of the cosmological models using recent observational data., Comment: 47 pages, 9 figures, 5 tables,Major Rvised version

In this paper, we investigate the mathematical modeling for the cosmological attractors propagated in mimetic gravity upon which an interacting dark energy-dark matter is supposed to be existed. The average value of the interaction of these percentages, namely $\Gamma_i$ say, may be used to investigate generally the modeling of an attractor; the actual value could only be determined by data in any particular case. We have seen, for example, that it was led to investigate the subject of initially invariant submanifolds.

This paper is devoted to investigate cylindrical solutions in mimetic gravity. The explicit forms of the metric of this theory, namely mimetic-Kasner (say) have been obtained. In this study we have noticed that the Kasner's family of exact solutions needs to be reconsidered under this type of modified gravity. A no-go theorem is proposed for the exact solutions in the presence of a cosmological constant., Comment: 8 pages, Title changed,references added, final version accepted in the" European Physical Journal C"

A metric is proposed to explore the noncommutative form of the Anti-de Sitter space due to quantum effects. It has been proved that the non commutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu-Takayanagi (RT) algorithm is then applied to compute the entanglement entropy in dual $CFT_2$. This calculation can be exploited to compute UV-IR cutoff dependent central charge of the certain noncommutative $CFT_2$. This non commutative computation of the entanglement entropy can be interpreted in the form of the surface/state correspondence. We have shown that non commutativity increases the dimension of the effective Hilbert space of the dual CFT., Comment: 6 pages, Version accepted for publication in "Modern Physics Letters A"

The aim of the present letter is to find the holographic entanglement entropy (HEE) in 2D holographic superconductors (HSC). Indeed, it is possible to compute the exact form of this entropy due to an advantage of approximate solutions inside normal and superconducting phases with backreactions. By making the UV and IR limits applied to the integrals, an approximate expression for HEE is obtained. In case the software cannot calculate minimal surface integrals analytically, it offers the possibility to proceed with a numerical evaluation of the corresponding terms. We'll understand how the area formula incorporates the structure of the domain wall approximation. We see that HEE changes linearly with belt angle. It's due to the extensivity of this type of entropy and the emergent of an entropic force. We find that the wider belt angle corresponds to a larger holographic surface. Another remarkable observation is that no "confinement/deconfinement" phase transition point exists in our $2D$ dual field theory. Furthermore we observe that the slope of the HEE with respect to the temperature freedom(s) in low temperature system. A first order phase transition is detected near the critical point., Comment: Accepted for publication in Physics Letters B

Non-local $f(R)$ gravity was proposed as a powerfull alternative to general relativity (GR) . This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolent(UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar-tensor frame comprising two auxiliary scalar fields, used to reduce complex action. However this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region of spacetime had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to non-local $f(R)$. The Tolman-Oppenheimer-Volkoff (TOV) equations would be a set of first order differential equations from which we can deduce all mathematical (physical) truths and derive all dynamical objects. This set of dynamical equations govern pressure $p$, density $\rho$, mass $m$ and auxiliary fields $\{\psi,\xi\}$. The full conditional solutions are evaluated and inverted numerically to obtain exact forms of the compact stars Her X-1, SAX J 1808.4-3658 and 4U 1820-30 for non-local Starobinsky model of $f(\Box^{-1}R)=\Box^{-1}R+\alpha \Big(\Box^{-1}R\Big)^2$. The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state $\frac{P}{P_c}= a (1- e^{-b\frac{\rho}{\rho_c}})$ for star which is informative in so far as it excludes an alternative non local approach to compact star formation. This model is most suited for astrophysical observation., Comment: Accepted in "International Journal of Modern Physics A",20 pages, 10 figures, 2 tables

A quick review on the analytical aspects of holographic superconductors (HSC) with Weyl corrections has been presented. Mainly we focus on matching method and variations approaches. Different types of such HSC have been investigated, s-wave, p-wave and St\'{u}ckelberg ones. We also review the fundamental construction of a p-wave type , in which the non-Abelian gauge field is coupled to the Weyl tensor. The results are compared from numerics to analytical results., Comment: Accepted for publication in International Journal of Geometric Methods in Modern Physics, Title changed, references added, comments included

In past years, triggered by their successful realizations in electromagnetics, invisible cloaks have experienced rapid development and have been widely pursued in many different fields, though so far only for a single physical system. In this letter we made an unprecedented experimental attempt to show a multidisciplinary framework designed on the basis of two different physical equations. The proposed structure has the exceptional capability to simultaneously control two different physical phenomena according to the predetermined evolution scenarios. As a proof of concept, we implemented an electric-thermal bifunctional device that can guide both electric current and heat flux "across" a strong 'scatter' (air cavity) and restore their original diffusion directions as if nothing exists along the paths, thus rending dual cloaking effects for objects placed inside the cavity. This bifunctional cloaking performance is also numerically verified for a point-source nonuniform excitation. Our results and the fabrication technique presented here will help broaden the current research scope for multiple disciplines and may pave a prominent way to manipulate multiple flows and create new functional devices, e.g., for on-chip applications., Comment: 4 figures

We analytically study the critical phase of a mixed system of the U(2) gauge fields and global symmetry on the boundary using gauge/gravity. A variational minimization problem has been formulated. The numerical results pertinently show that there exists a minimum chemical potential in which both scalar (s-wave) and vector (p-wave) condensates exist in a mixture, as well as in the distinct s- and p-phases. This result is obtained by breaking the symmetry into U(1) symmetry and rotational symmetry. While the analytical solutions of condensates and charge densities are achieved in both cases: the balanced and unbalanced holographic superconductors. This is the first an- alytical study of the coexistence of two modes of the superconductivity with different order parameters. The realistic model consists of two different phases of the superfluidity in Helium., Comment: version accepted in "International Journal of Geometric Methods in Modern Physics"; 19 pages

In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether Gauge Symmetries (NGS). Motivated by this mathematical tool, in this article, we discuss the generalized Noether symmetry of Quintom model of dark energy, which is a two component fluid model of quintessence and phantom fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated, Comment: 23 Pages, 4 Figures, Published in "Astrophysics and Space Science"

The holographic model for a two-dimensional superconductor has been investigated by considering the three-dimensional gravity in the bulk. To find the critical temperature, we used the Sturm-Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary. We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously., Comment: Published in "Int J Theor Phys"

We have developed the recent investigations on the second-order phase transition in the holographic superconductor using the probe limit for a nonlinear Maxwell field strength coupled to a massless scalar field. By analytic methods, based on the variational Sturm- Liouville minimization technique, we study the effects of the space-time dimension and the non-linearity parameter on the critical temperature and the scalar condensation of the dual operators on the boundary. Further, as a motivated result, we analytically deduce the DC conductivity in the low and zero temperatures regime. Especially in the zero temperature limit and in two dimensional toy model, we thoroughly compute the conductivity analytically. Our work clarifies more features of the holographic superconductors both in different space dimensions and on the effect of the non-linearity in Maxwell's strength field., Comment: Journal of Gravity, Volume 2013, Article ID 782512

In this work we study the analytical properties of a 2+1 dimensional magnetically charged holographic superconductor in $AdS_4$. We obtain the critical chemical potential $\mu_c$ analytically, using the Sturm-Liouville variational approach. Also, the obtained analytic result can be used to back up the numerical computations in the holographic superconductor in the probe limit.

In this work, we have considered variable G in flat FRW universe filled with the mixture of dark energy, dark matter and radiation. If there is no interaction between the three fluids, the deceleration parameter and statefinder parameters have been calculated in terms of dimensionless density parameters which can be fixed by observational data. Also the interaction between three fluids has been analyzed due to constant $G$. The statefinder parameters also calculated in two cases: pressure is constant and pressure is variable., Comment: 5 pages, Accepted for publication in "Astrophysics and Space Science"

In this paper, we reconstruct cosmological models in the framework of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. We show that the dust fluid reproduces $\Lambda $CDM, phantom-non-phantom era and the phantom cosmology. Further, we reconstruct different cosmological models including, Chaplygin gas, scalar field with some specific forms of $f(R,T)$. Our numerical simulation for Hubble parameter shows good agreement with the BAO observational data for low redshifts $z<2$., Comment: 12 pages, 2 figures