We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain the formation of such self-organized motifs both on continuous domains or networked systems, where reactions occur in the nodes and the available links are used for species to diffuse. In many relevant applications, those links are not static, as very often assumed, but evolve in time and more importantly they adapt their weights to the states of the nodes. In this work, we make one step forward and we provide a general theory to prove the validity of Turing idea in the case of adaptive symmetric networks with positive weights. The conditions for the emergence of Turing instability rely on the spectral property of the Laplace matrix and the model parameters, thus strengthening the interplay between dynamics and network topology. A rich variety of patterns are presented by using two prototype models of nonlinear dynamical systems, the Brusselator and the FitzHugh-Nagumo model. Because many empirical networks adapt to changes in the system states, our results pave the way for a thorough understanding of self-organization in real-world systems.

In this paper, we present the separability criteria to identify non-$k$-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non-$k$-separability of Dicke class of states, anti W states and mixtures thereof and higher dimensional W class of states. We then investigate the performance of our criteria by considering $N$-qubit Dicke states with arbitrary excitations added with white noise and mixture of $N$-qudit W state with white noise. We also study the robustness of our criteria against white noise. Further, we demonstrate that our criteria are experimentally implementable by means of local observables such as Pauli matrices and generalized Gell-Mann matrices.

The intermetallic compound BaFe2Al9 exhibits unusual physical properties associated with a charge density wave (CDW) transition. Unlike conventional CDW materials, which typically display subtle structural distortions or lattice modulations, BaFe2Al9 undergoes a first-order phase transition in which lattice strain plays a crucial role in the formation of the CDW state. To further explore this unique behavior, we conducted high-pressure studies, examining the electrical transport, magnetic, and structural properties to gain deeper insight into the underlying CDW mechanism. At ambient pressure, electrical resistivity and magnetization measurements confirm the presence of a CDW transition. Upon applying pressure, the CDW transition temperature (TCDW) shifts to higher values, reaching approximately 300 K near 3.2 GPa, and the electrical resistivity increases, suggesting that pressure modulates the charge carrier concentration. Furthermore, the initially sharp first-order transition becomes more gradual, and analysis of the temperature derivative of resistivity indicates a crossover from first-order to second-order like behavior under pressure. High-pressure magnetization measurements are consistent with the electrical transport data, showing an enhancement of TCDW with increasing pressure. The residual resistivity increases with pressure, while the Fermi liquid coefficient A decreases above 2 GPa, pointing to a possible Fermi surface reconstruction. High-pressure synchrotron powder X-ray diffraction (XRD) measurements at room temperature reveal a lattice anomaly near 3.8 GPa, marked by a distinct trend change in macrostrain, further supporting the existence of a pressure induced structural response. These findings provide valuable insight into the nature of CDW formation in BaFe2Al9 and highlight the critical role of lattice strain and external pressure in tuning its electronic ground state.

Small Language Models (SLMs) have shown remarkable performance in general domain language understanding, reasoning and coding tasks, but their capabilities in the medical domain, particularly concerning radiology text, is less explored. In this study, we investigate the application of SLMs for general radiology knowledge specifically question answering related to understanding of symptoms, radiological appearances of findings, differential diagnosis, assessing prognosis, and suggesting treatments w.r.t diseases pertaining to different organ systems. Additionally, we explore the utility of SLMs in handling text-related tasks with respect to radiology reports within AI-driven radiology workflows. We fine-tune Phi-2, a SLM with 2.7 billion parameters using high-quality educational content from Radiopaedia, a collaborative online radiology resource. The resulting language model, RadPhi-2-Base, exhibits the ability to address general radiology queries across various systems (e.g., chest, cardiac). Furthermore, we investigate Phi-2 for instruction tuning, enabling it to perform specific tasks. By fine-tuning Phi-2 on both general domain tasks and radiology-specific tasks related to chest X-ray reports, we create Rad-Phi2. Our empirical results reveal that Rad-Phi2 Base and Rad-Phi2 perform comparably or even outperform larger models such as Mistral-7B-Instruct-v0.2 and GPT-4 providing concise and precise answers. In summary, our work demonstrates the feasibility and effectiveness of utilizing SLMs in radiology workflows both for knowledge related queries as well as for performing specific tasks related to radiology reports thereby opening up new avenues for enhancing the quality and efficiency of radiology practice.

Critical current density (Jc), thermal activation energy (U0), and upper critical field (Hc2) of La1-xSmxO0.5F0.5BiS2 (x = 0.2, 0.8) superconductors are investigated from magnetic field dependent \r{ho}(T) studies. The estimated upper critical field (Hc2) has low values of 1.04 T for x = 0.2 and 1.41 T for x = 0.8. These values are lower than Sm free LaO0.5F0.5BiS2 superconductor (1.9 T). The critical current density (Jc) is estimated to be 1.35*105 A/cm2 and 5.07 *105 A/cm2 (2 K) for x = 0.2 and 0.8 respectively, using the Bean's model. The thermal activation energy (U0/kB) is 61 K for x = 0.2 and 140 K for x =0.8 as calculated from Arrhenius plots at low magnetic field (1 T) and indicates a strong flux pinning potential which might be co-existing with applied magnetic field.

In this study, we explore the dynamics of breathers and positons in a nonlinear electrical transmission line modeled by the modified Naguchi circuit, governed by the Kundu-Eckhaus equation. Utilizing the reductive perturbation method and a specific transformation, we analyze the influence of different time-dependent linear potentials on these nonlinear wave structures. The analysis is conducted for three representative cases: (i) a constant potential, which modifies the orientation and amplitude of breathers and positons, (ii) a periodically modulated potential, which transforms them into crescent-shaped structures with unique spatial characteristics, and (iii) an exponentially varying potential, which induces asymmetric crescent-shaped waveforms. Additionally, we show that linear potentials significantly influence breather and positon dynamics in the modified electrical transmission line by altering their position and positon amplitude-constant potentials maintain peaks at the origin, periodic potentials shift breathers forward and positons backward, while exponential potentials move breathers backward and positons forward. Our findings highlight the critical role of external modulation in shaping wave propagation, localizing waves, and altering their amplitude, demonstrating its potential for controlling wave dynamics in nonlinear transmission lines. Unlike previous studies that focused on rogue waves, this work provides new insights into the evolution of breathers and positons under external perturbations. The results may have significant implications for applications in electrical transmission networks.

Following the concept of $\mathcal{PT}$-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multi-stability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratio between the input and output intensities leading to an efficient way of controlling light with light.

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.

In recent times, bound soliton states have often been referred to as soliton molecules in the nonlinear optics literature. The striking analogies between photonic bound states and matter molecular structures in chemistry and physics have intensified studies on optical soliton molecules in both conservative and dissipative systems. In this paper, we demonstrate the existence of vector soliton molecules and their related isomer structures in a conservative optical fiber system by considering the integrable Manakov equation. We show their existence by applying the velocity resonance condition and appropriate choice of temporal separations to the degenerate $N=(\bar{N}+\bar{M})$-soliton solution. Then, we classify the obtained molecular states as either dissociated or synthesized molecular states based on the temporal locations of the constituent solitons. Furthermore, we analyze the collision properties of vector soliton molecules in the present conservative system. The collision scenarios reveal that the soliton molecules undergo intriguing energy-sharing collisions through energy redistribution among the modes. To characterize these collisions, we have carried out an appropriate asymptotic analysis and found that elastic collisions arise as a special case of energy-sharing collisions under specific choices of polarization constants. Finally, we numerically verify the robustness of vector soliton molecules. We believe that the results presented in this paper show potential for soliton molecule-based applications such as optical computation and multi-level encoding for communications.

In this paper we report the occurrence of sliding bifurcations admitted by the memristive Murali-Lakshmanan-Chua circuit \cite{icha13} and the memristive driven Chua oscillator \citep{icha11}. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their non-linear element. The three segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three sub-regions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as \textit{Filippov} systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the sub-regions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.

We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix elements can be reformulated by the expectation values of these non-Hermitian operators and vice versa. We consider the condition of pure states and pure product states and rewrite them in terms of expectation values and density matrix elements respectively. We utilize expectation values of these operators to present the condition for separability of ${C}^d \otimes {C}^d$ bipartite states. With the help of our separability criterion we detect entanglement in certain classes of higher dimensional bipartite states.

Adaptive network is a powerful presentation to describe different real-world phenomena. However, current models often neglect higher-order interactions (beyond pairwise interactions) and diverse adaptation types (cooperative and competitive) commonly observed in systems like the human brain and social networks. This work addresses this gap by incorporating these factors into a model that explores their impact on collective properties like synchronization. Through simplified network representations, we investigate how the simultaneous presence of cooperative and competitive adaptations influences phase transitions. Our findings reveal a transition from first-order to second-order synchronization as the strength of higher-order interactions increases under competitive adaptation. We also demonstrate the possibility of synchronization even without pairwise interactions, provided there is strong enough higher-order coupling. When only competitive adaptations are present, the system exhibits second-order-like phase transitions and clustering. Conversely, with a combination of cooperative and competitive adaptations, the system undergoes a first-order-like phase transition, characterized by a sharp transition to the synchronized state without reverting to an incoherent state during backward transitions. The specific nature of these second-order-like transitions varies depending on the coupling strengths and mean degrees. With our model, we can control not only when the system synchronizes but also the way the system goes to synchronization.

In this paper we present new versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time, yielding both stationary and non-stationary solutions. New versions of programs were developed using CUDA toolkit and can make use of Nvidia GPU devices. The algorithm used is the same split-step semi-implicit Crank-Nicolson method as in the previous version (R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)), which is here implemented as a series of CUDA kernels that compute the solution on the GPU. In addition, the Fast Fourier Transform (FFT) library used in the previous version is replaced by cuFFT library, which works on CUDA-enabled GPUs. We present speedup test results obtained using new versions of programs and demonstrate an average speedup of 12 to 25, depending on the program and input size.

We propose a nonlinear one-dimensional FitzHugh--Nagumo neuronal model with an asymmetric potential driven by both a high-frequency and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay on vibrational resonance and delay-induced resonance phenomena. The response amplitude at the low-frequency is explored to characterize the vibrational resonance and delay-induced resonance. By this effort, we realize that for smaller values of the amplitude of the state-dependent time-delay velocity component, vibrational resonance and multi-resonance occur in the neuronal model. For large values of the high-frequency excitation amplitude, vibrational resonance appears with one peak. We observe a decrease in the response when the amplitude of the state-dependent time-delay velocity component increases. Also, we analyze how the state-dependent time-delay position and velocity components can give birth to delay-induced resonance for separate and together. The main results of this work are that the state-dependent time-delay velocity component can play a major role in both phenomena. In fact the parameter of the delay can control the triggering of the two resonances.

In this paper we report the control and synchronization of chaos in a Memristive Murali-Lakshmanan-Chua circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques, the concept of adaptive synchronization and observer based approaches have been used to effect synchronization of chaos. Both of these techniques are based on state space representation theory which is well known in the field of control engineering. As in our earlier works on this circuit, we have derived the Poincar\'{e} Discontinuity Mapping (PDM) and Zero Time Discontinuity Mapping (ZDM) corrections, both of which are essential for realizing the true dynamics of non-smooth systems. Further we have constructed the observer and controller based canonical forms of the state space representations, have set up the Luenberger observer, derived the controller gain vector to implement state feedback control and calculated the gain matrices for switch feed back and finally performed parameter estimation for effecting observer based adaptive synchronization. Our results obtained by numerical simulation include time plots, phase portraits, estimation of the parameters and convergence of errors graphs and phase plots showing complete synchronization.

We perform a detailed analysis of the behaviour of a non-autonomous prey-predator model where age based growth with age discriminatory harvesting in prey and predator's reliance upon alternative food in the absence of that particular prey are considered. We begin by deriving certain sufficient conditions for permanence and positive invariance and then proceed to construct a Lyapunov function to derive some constraints for global attractivity. With the help of continuation theorem we arrive at the best fit criterion to prove the occurrence of a positive periodic solution. Moreover, using Arzela-Ascoli theorem we formulate a proof for a unique positive solution to be almost periodic and we carry out numerical simulation to verify the analytical findings. With the aid of graphs and tables we show the nature of the prey-predator system in response to the alternative food and delays.

In this paper, we examine the binary linear codes with respect to Hamming metric from incidence matrix of a unit graph $G(\mathbb{Z}_{n})$ with vertex set is $\mathbb{Z}_{n}$ and two distinct vertices $x$ and $y$ being adjacent if and only if $x+y$ is unit. The main parameters of the codes are given.

We consider a general multicomponent (2+1)-dimensional long-wave--short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlev\'e analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

We investigate the effect of the spin-orbit (SO) and Rabi couplings on the localization of the spin-1/2 condensate trapped in a one-dimensional random potential. Our studies reveal that the spin-dependent couplings create distinct localization regimes, resulting in various relations between localization and spin-related properties. First, we examine the localization in the linear condensate and find that the SO coupling can lead to a transition of the localized state from the "basin-like" to the "void" region of the potential. For a weak random potential upon an increase in the SO coupling, we find a re-entrant transition from a broad to narrow localized state and back at a higher SO coupling. Further, we analyze the competing role of inter-species and intra-species interactions on the localization of the condensate. We find the appearance of spin-dependent localization as the interactions increase beyond threshold values for a sufficiently strong disorder. Our findings on controlling spin-dependent localization may be useful for future ultracold atomic experiments and corresponding spin-related quantum technologies.