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We introduce multi-split continuous functions between topological spaces, a weaker form of continuity that generalizes split continuity while being stable under compositions. We will define the associated star multifunction and pre-multi-split multifunctions. Moreover, we will prove that multi-split continuity naturally emerges as the continuity property of selections of finite usco maps, relating their study to set-valued analysis. Finally, we introduce split homeomorphisms and split homeomorphic spaces, showing that for compact, regular Hausdorff spaces, split homeomorphisms characterize deformations with cuts and subsequent re-glues., Comment: 26 pages, 0 figures

Eye-tracking technology has gained significant attention in recent years due to its wide range of applications in human-computer interaction, virtual and augmented reality, and wearable health. Traditional RGB camera-based eye-tracking systems often struggle with poor temporal resolution and computational constraints, limiting their effectiveness in capturing rapid eye movements. To address these limitations, we propose EyeTrAES, a novel approach using neuromorphic event cameras for high-fidelity tracking of natural pupillary movement that shows significant kinematic variance. One of EyeTrAES's highlights is the use of a novel adaptive windowing/slicing algorithm that ensures just the right amount of descriptive asynchronous event data accumulation within an event frame, across a wide range of eye movement patterns. EyeTrAES then applies lightweight image processing functions over accumulated event frames from just a single eye to perform pupil segmentation and tracking. We show that these methods boost pupil tracking fidelity by 6+%, achieving IoU~=92%, while incurring at least 3x lower latency than competing pure event-based eye tracking alternatives [38]. We additionally demonstrate that the microscopic pupillary motion captured by EyeTrAES exhibits distinctive variations across individuals and can thus serve as a biometric fingerprint. For robust user authentication, we train a lightweight per-user Random Forest classifier using a novel feature vector of short-term pupillary kinematics, comprising a sliding window of pupil (location, velocity, acceleration) triples. Experimental studies with two different datasets demonstrate that the EyeTrAES-based authentication technique can simultaneously achieve high authentication accuracy (~=0.82) and low processing latency (~=12ms), and significantly outperform multiple state-of-the-art competitive baselines., Comment: 32 pages,15 figures

Test time adaptation (TTA) equips deep learning models to handle unseen test data that deviates from the training distribution, even when source data is inaccessible. While traditional TTA methods often rely on entropy as a confidence metric, its effectiveness can be limited, particularly in biased scenarios. Extending existing approaches like the Pseudo Label Probability Difference (PLPD), we introduce ETAGE, a refined TTA method that integrates entropy minimization with gradient norms and PLPD, to enhance sample selection and adaptation. Our method prioritizes samples that are less likely to cause instability by combining high entropy with high gradient norms out of adaptation, thus avoiding the overfitting to noise often observed in previous methods. Extensive experiments on CIFAR-10-C and CIFAR-100-C datasets demonstrate that our approach outperforms existing TTA techniques, particularly in challenging and biased scenarios, leading to more robust and consistent model performance across diverse test scenarios. The codebase for ETAGE is available on https://github.com/afsharshamsi/ETAGE.

Human activity recognition (HAR) is essential in healthcare, elder care, security, and human-computer interaction. The use of precise sensor data to identify activities passively and continuously makes HAR accessible and ubiquitous. Specifically, millimeter wave (mmWave) radar is promising for passive and continuous HAR due to its ability to penetrate non-metallic materials and provide high-resolution wireless sensing. Although mmWave sensors are effective at capturing macro-scale activities, like exercising, they fail to capture micro-scale activities, such as typing. In this paper, we introduce mmDoppler, a novel dataset that utilizes off-the-shelf (COTS) mmWave radar in order to capture both macro and micro-scale human movements using a machine-learning driven signal processing pipeline. The dataset includes seven subjects performing 19 distinct activities and employs adaptive doppler resolution to enhance activity recognition. By adjusting the radar's doppler resolution based on the activity type, our system captures subtle movements more precisely. mmDoppler includes range-doppler heatmaps, offering detailed motion dynamics, with data collected in a controlled environment with single as well as multiple subjects performing activities simultaneously. The dataset aims to bridge the gap in HAR systems by providing a more comprehensive and detailed resource for improving the robustness and accuracy of mmWave radar activity recognition., Comment: 16 pages. arXiv admin note: text overlap with arXiv:2309.11957

TALYS calculations were performed to obtain the theoretical proton capture cross-sections on the p-nuclei. A short review on the status of related experimental studies was also conducted. Some basic properties such as Q-values, Coulomb barrier, Gamow peak, Gamow Window, and decay properties of the parent and daughter nuclei were studied. Various experimental parameters, e.g., beam energy, beam current, targets, and detectors, used in experimental investigations reported in the literature, were tabulated. The results of the TALYS calculations in the Gamow region were compared with the corresponding experimental values wherever available. This study is expected to facilitate the planning of future experiments., Comment: 13 pages, 4 figures

We introduce an efficient discretization of a novel fractional-order adaptive exponential (FrAdEx) integrate-and-fire model, which is used to study the fractional-order dynamics of neuronal activities. The discretization is based on extension of L1-type methods that can accurately handle the exponential growth and the spiking mechanism of the model. This new method is implicit and uses adaptive time stepping to robustly handle the stiff system that arises due to the exponential term. The implicit nonlinear system can be solved exactly, without the need for iterative methods, making the scheme efficient while maintaining accuracy. We present a complete error model for the numerical scheme that can be extended to other integrate-and-fire models with minor changes. To show the feasibility of our approach, the numerical method has been rigorously validated and used to investigate several different spiking oscillations of the model. We observed that the fractional-order model is capable of predicting biophysical activities, which are interpreted through phase diagrams describing the transition from one firing type to another. This simple model shows significant promise, as it has sufficient expressive dynamics to reproduce several features qualitatively from a biophysical dynamical perspective., Comment: 27 pages, 9 figures. v1: changed title, updated references

Molecular transport maintains cellular structures and functions. For example, lipid and protein diffusion sculpts the dynamic shapes and structures on the cell membrane that perform essential cellular functions, such as cell signaling. Temperature variations in thermal equilibrium rapidly change molecular transport properties. The coefficient of lipid self-diffusion increases exponentially with temperature in thermal equilibrium, for example. Hence, in the noisy cellular environment, where temperatures can fluctuate widely due to local heat generation, maintaining cellular homeostasis through molecular transport is hard in thermal equilibrium. In this paper, using both molecular and lattice-based modeling of membrane transport, we show that the presence of active transport originating from the cell's cytoskeleton can make the self-diffusion of the molecules on the membrane robust to temperature fluctuations. The resultant temperature-independence of self-diffusion keeps the precision of cellular signaling invariant over a broad range of ambient temperatures, allowing cells to make robust decisions. We have also found that the Kawasaki algorithm, the widely used model of lipid transport on lattices, predicts incorrect temperature dependence of lipid self-diffusion in equilibrium. We propose a new algorithm that correctly captures the equilibrium properties of lipid self-diffusion and reproduces experimental observations., Comment: The movie is available in the ancillary folder

Precise ego-motion measurement is crucial for various applications, including robotics, augmented reality, and autonomous navigation. In this poster, we propose mmPhase, an odometry framework based on single-chip millimetre-wave (mmWave) radar for robust ego-motion estimation in mobile platforms without requiring additional modalities like the visual, wheel, or inertial odometry. mmPhase leverages a phase-based velocity estimation approach to overcome the limitations of conventional doppler resolution. For real-world evaluations of mmPhase we have developed an ego-vehicle prototype. Compared to the state-of-the-art baselines, mmPhase shows superior performance in ego-velocity estimation.

This study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a novel linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for DC conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of Hydrogen at a temperature of 30,000K. As for the radial distribution functions, we reveal a transition of Hydrogen from gas-like to liquid-like behavior as its density exceeds $4 g/cm^3$. As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7eV, which may be an additional signature of a gas-liquid transition in Hydrogen at 30,000K.

In the landscape of next-generation cellular networks, a projected surge of over 12 billion subscriptions foreshadows a considerable upswing in the network's overall energy consumption. The proliferation of User Equipment (UE) drives this energy demand, urging 5G deployments to seek more energy-efficient methodologies. In this work, we propose SmartMME, as a pivotal solution aimed at optimizing Base Station (BS) energy usage. By harnessing and analyzing critical network states-such as UE connections, data traffic at individual UEs, and other pertinent metrics-our methodology intelligently orchestrates the BS's power states, making informed decisions on when to activate or deactivate the BS. This meticulous approach significantly curtails the network's overall energy consumption. In a bid to validate its efficiency, we seamlessly integrated our module into Network Simulator-3 (ns-3), conducting extensive testing to demonstrate its prowess in effectively managing and reducing net energy consumption. As advocates of collaborative progress, we've opted to open-source this module, inviting the engagement and feedback of the wider research community on GitHub.

As global challenges of population growth, climate change, and resource scarcity intensify, the agricultural landscape is at a critical juncture. Sustainable vertical farming emerges as a transformative solution to address these challenges by maximizing crop yields in controlled environments. This paradigm shift necessitates the integration of cutting-edge technologies, with Artificial Intelligence (AI) at the forefront. The paper provides a comprehensive exploration of the role of AI in sustainable vertical farming, investigating its potential, challenges, and opportunities. The review synthesizes the current state of AI applications, encompassing machine learning, computer vision, the Internet of Things (IoT), and robotics, in optimizing resource usage, automating tasks, and enhancing decision-making. It identifies gaps in research, emphasizing the need for optimized AI models, interdisciplinary collaboration, and the development of explainable AI in agriculture. The implications extend beyond efficiency gains, considering economic viability, reduced environmental impact, and increased food security. The paper concludes by offering insights for stakeholders and suggesting avenues for future research, aiming to guide the integration of AI technologies in sustainable vertical farming for a resilient and sustainable future in agriculture.

Motorcycle accidents are a prevalent problem in Texas, resulting in hundreds of injuries and deaths each year. Motorcycles provide the driver with little physical protection during accidents compared to cars and other vehicles, so when there is a collision involving a motorcycle, the motorcyclist is likely to be injured. While there are numerous reasons for motorcycle accidents, most are caused by negligence and could have been avoided. Because of the increasing popularity of motorcycles and scooter in Texas, coupled with an increase in the number of motorcycle accidents, the Texas Department of Transportation (TxDOT) has amped its efforts to improve motorcycle safety. From the data, it has been visible that teenage drivers are the most vulnerable to motorcycle accidents. In this report, we have tried to find out the probability of young driver and passenger motorcyclist's injury based on different conditions and to predict the rate of changing injury to this group in the upcoming years., Comment: 10 pages

Continuous detection of human activities and presence is essential for developing a pervasive interactive smart space. Existing literature lacks robust wireless sensing mechanisms capable of continuously monitoring multiple users' activities without prior knowledge of the environment. Developing such a mechanism requires simultaneous localization and tracking of multiple subjects. In addition, it requires identifying their activities at various scales, some being macro-scale activities like walking, squats, etc., while others are micro-scale activities like typing or sitting, etc. In this paper, we develop a holistic system called MARS using a single Commercial off the-shelf (COTS) Millimeter Wave (mmWave) radar, which employs an intelligent model to sense both macro and micro activities. In addition, it uses a dynamic spatial time sharing approach to sense different subjects simultaneously. A thorough evaluation of MARS shows that it can infer activities continuously with a weighted F1-Score of > 94% and an average response time of approx 2 sec, with 5 subjects and 19 different activities.

Recent inspection of liquid-like state in ultracold atomic gases due to the stabilization mechanism through the delicate balance between effective mean-field and beyond mean-field (BMF) interactions, has motivated us to study the modified/extended Gross-Pitaevskii (eGP) equation which includes the BMF contribution. In this article, we focus on variational analysis of solitonic regime with eGP equation while the soliton is subjected to an obstacle. This reveals different scattering scenarios of the soliton with explicit dependence of the BMF interaction. The results show the existence of tunneling, partial and complete trappings, in different parameter domains. These observations are further corroborated by the fast-Fourier transform method. In the later part we also extend our analysis to trapped systems. The controlled trapping in defect potential and its release can be potentially useful for quantum information storage., Comment: 11 pages, 27 figures; To be published in European Physical Journal Plus

Correlations and fluctuations between produced particles in an ultra-relativistic nuclear collision remain one of the successor to understand the basics of the particle production mechanism. More differential tools like Forward-Backward (FB) correlations between particles from two different phase-space further strengthened our cognizance. We have studied the strength of FB correlations in terms of charged particle multiplicity and summed transverse momentum for proton-proton ($pp$) and proton-lead ($pPb$) collisions at the centre-of-mass energies $\sqrt{s}$ = 13 TeV and $\sqrt{s_{\rm NN}}$ = 5.02 TeV respectively for the EPOS3 simulated events with hydrodynamical evolution of produced particles. Furthermore, the correlation strengths are separately obtained for the particles coming from the core and the corona. FB correlation strengths are examined as a function of psedorapidity gap ($\eta_{gap}$), psedorapidity window-width ($\delta\eta$), centre-of-mass energy ($\sqrt{s}$), minimum transverse momentum ($p_{Tmin}$) and different multiplicity classes following standard kinematical cuts used by the ALICE and the ATLAS experiments at the LHC for all three EPOS3 event samples. EPOS3 model shows a similar trend of FB multiplicity and momentum correlation strengths for both $pp$ \& $pPb$ systems, though the correlation strengths are found to be larger for $pPb$ system than $pp$ system. Moreover, $\delta\eta$-weighted average of FB correlation strengths as a function of different center-of-mass energies for $pp$ collisions delineates a tendency of saturation at very high energies., Comment: 10 Pages, 13 Figures, Accepted in Physical Review D

We address static and dynamical properties of one-dimensional (1D) quantum droplets (QDs) under the action of local potentials in the form of narrow wells and barriers. The QDs are governed by the 1D Gross-Pitaevskii equation including the mean-field cubic repulsive term and the beyond-mean-field attractive quadratic one. In the case of the well represented by the delta-functional potential, three exact stable solutions are found for localized states pinned to the well. The Thomas-Fermi approximation for the well and the adiabatic approximation for the collision of the QD with the barrier are developed too. Collisions of incident QDs with the wells and barriers are analyzed in detail by means of systematic simulations. Outcomes, such as fission of the moving QD into transmitted, reflected, and trapped fragments, are identified in relevant parameter planes. In particular, a counter-intuitive effect of partial or full rebound of the incident QD from the potential well is studied in detail and qualitatively explained., Comment: 13 pages, 32 figures; To be published in Communions in Nonlinear Science and Numerical Simulation

Adaptive Bitrate (ABR) Streaming over the cellular networks has been well studied in the literature; however, existing ABR algorithms primarily focus on improving the end-users' Quality of Experience (QoE) while ignoring the resource consumption aspect of the underlying device. Consequently, proactive attempts to download video data to maintain the user's QoE often impact the battery life of the underlying device unless the download attempts are synchronized with the network's channel condition. In this work, we develop EnDASH-5G -- a wrapper over the popular DASH-based ABR streaming algorithm, which establishes this synchronization by utilizing a network-aware video data download mechanism. EnDASH-5G utilizes a novel throughput prediction mechanism for 5G mmWave networks by upgrading the existing throughput prediction models with a transfer learning-based approach leveraging publicly available 5G datasets. It then exploits deep reinforcement learning to dynamically decide the playback buffer length and the video bitrate using the predicted throughput. This ensures that the data download attempts get synchronized with the underlying network condition, thus saving the device's battery power. From a thorough evaluation of EnDASH-5G, we observe that it achieves a near $30.5\%$ decrease in the maximum energy consumption than the state-of-the-art Pensieve ABR algorithm while performing almost at par in QoE., Comment: 14 pages, 11 figures, journal

Detecting dangerous driving has been of critical interest for the past few years. However, a practical yet minimally intrusive solution remains challenging as existing technologies heavily rely on visual features or physical proximity. With this motivation, we explore the feasibility of purely using mmWave radars to detect dangerous driving behaviors. We first study characteristics of dangerous driving and find some unique patterns of range-doppler caused by 9 typical dangerous driving actions. We then develop a novel Fused-CNN model to detect dangerous driving instances from regular driving and classify 9 different dangerous driving actions. Through extensive experiments with 5 volunteer drivers in real driving environments, we observe that our system can distinguish dangerous driving actions with an average accuracy of > 95%. We also compare our models with existing state-of-the-art baselines to establish their significance., Comment: 11 pages, 13 figures, conference

Pervasive applications over large-scale, distributed embedded devices and the Internet of Things (IoT) demand precise coordination with the network; for example, several such applications, like collaborative video streaming and live analysis, augmented reality, etc., need continuous monitoring of network throughput and adapt the application behavior accordingly. Although the idea of network throughput prediction is not new and quite dated, in this paper, we show that the existing approaches fail to correctly infer the throughput when the network operator or the device change, and thus, not generic enough for Internet-scale applications. We propose \ourmethod, a novel approach that allows collaborative training across different client hardware by capturing throughput variations based on devices' sensitivity towards the corresponding network configurations. Rigorous evaluations show that \ourmethod{} outperforms various standard baseline algorithms with more than $80\%$ R2-score over different datasets. We also analyze the performance of \ourmethod{} over a network-aware streaming media application and demonstrate its efficacy for various application scenarios., Comment: 12 pages, 10 figures, Accepted in International Conference on Embedded Wireless Systems and Networks (EWSN 2023)

Spatially resolved transcriptomics (SRT) has evolved rapidly through various technologies, enabling scientists to investigate both morphological contexts and gene expression profiling at single-cell resolution in parallel. SRT data are complex and multi-modal, comprising gene expression matrices, spatial information, and often high-resolution histology images. Because of this complexity and multi-modality, sophisticated computational algorithms are required to accurately analyze SRT data. Most efforts in this domain have been made to utilize conventional machine learning and statistical approaches, exhibiting sub-optimal results due to the complicated nature of SRT datasets. To address these shortcomings, researchers have recently employed deep learning algorithms including various state-of-the-art methods mainly in spatial clustering, spatially variable gene identification, and alignment. While great progress has been made in developing deep learning-based models for SRT data analysis, further improvement is still needed to create more biologically aware models that consider aspects such as phylogeny-aware clustering or the analysis of small histology image patches. Additionally, strategies for batch effect removal, normalization, and handling overdispersion and zero inflation patterns of gene expression are still needed in the analysis of SRT data using deep learning methods. In this paper, we provide a comprehensive overview of these deep learning methods, including their strengths and limitations. We also highlight new frontiers, current challenges, limitations, and open questions in this field. Also, we provide a comprehensive list of all available SRT databases that can be used as an extensive resource for future studies.

In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of the coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of the propagating pulses. The symmetric or asymmetric nature of the traveling pulses is characterized and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of the pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions and show how system parameters and the coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves., Comment: 17 pages, 7 figures

We apply a complex network-based method of visibility graph to explore the degree of complexity and fractal nature in the multiparticle production process at the LHC energy regime. For the investigation, we have used proton-proton (pp) collision events at $\sqrt{s}$ = 7 and 13 TeV and proton-nucleus (p-A) collision events at $\sqrt{s_{\rm NN}}$ = 5.02 TeV, generated using a hybrid Monte-Carlo model, EPOS3 with hydrodynamical evolution. Particle production in high energy collisions becomes gradually harder with the increase of the produced particle's transverse momentum. We have presented for the first time a detailed analysis of the change of fractal behaviour as the process becomes gradually harder than the soft ones for the above mentioned colliding systems. The study reveals that the degree of complexity depends on the hardness of the particle production process. System size dependency, as well as energy dependency of fractal nature, are also exhibited by the present analysis., Comment: 16 pages, 5 figures, Proceedings of the DAE Symp. on Nucl. Phys. 65 (2021)

In this article, we discuss the dynamics of the 3-dimensional FitzHugh-Rinzel (FHR) model and a class of non-homogeneous FitzHugh-Nagumo (Nh-FHN) Reaction-Diffusion systems. The Nh-FHN models can be used to generate relevant wave propagation phenomena in Neuroscience context. This gives raise locally to complex dynamics such as canards, Mixed Mode Oscillations, Hopf-Bifurcations some of which can be observed in the FHR model.

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter can be used to forecast the future reproduction number and together with the forecast on the number of infected and dead individuals, our approach can be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This can help reduce the impact of the spread around the world and improve the wellbeing of people., Comment: 16 pages, 6 figures, 1 table

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a $2$-dimensional lattice having three cyclically-competing species. The spatio-temporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of diffusion. It reveals that the joint effect of death rate and diffusion (migration) leads to new coexistence and extinction scenarios., Comment: 7 pages, 5 figures

We report a droplet to a soliton crossover by tuning the external confinement potential in a dilute Bose-Eienstein condensate by numerically solving the modified Gross-Pitaevskii equation. The testimony of such a crossover is presented via studying the fractional density of the condensate which smoothly migrates from being a flat-head curve at weak confinement to a bright soliton at strong confinement. Such a transition occurs across a region of the potential whose strength varies over an order of magnitude and thus should be fit to be termed as a crossover. We supplement our studies via exploring the size of the bound pairs and the ramifications of the particle density therein. Eventually, all of these aid us in arriving at a phase diagram in a space defined by the trap strength and the particle number that shows the formation of two phases consisting of droplets and solitons, along with a regime of coexistence of these two., Comment: 7 Pages, 9 Figures; To appear in Physics Letters A

Forward-backward (FB) multiplicity and momentum correlations of produced particles between symmetrically located pseudorapidity ($\eta$) intervals have been studied using the $p$QCD inspired EPOS3 model with and without hydrodynamical evolution of particles in proton-proton ($pp$) collisions at the center-of-mass energy, $\sqrt{s}=13$ TeV. The pseudorapidity-gap ($\eta_{gap}$) dependence of FB correlation strength is compared with our previously published results at $\sqrt{s}=$ 0.9, 2.76 and 7 TeV. The study reveals that the general trends of FB correlation strength at $\sqrt{s}=13$ TeV are similar to our previous observations at lower center-of-mass energies. We also find that the $\delta\eta$-weightage average of FB correlation strength as a function of different center-of-mass energies ($\sqrt{s}=$ 0.9, 2.76, 7 and 13 TeV) tends to saturate at very high energy., Comment: 4 pages, 2 figures, ISMD-2021 Conference Proceedings

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform, patterns that emerge due to instability in an extended homogeneous 2D spatial domain, using the excitable Izhikevich neuron model. We examine diffusive instability and perform bifurcation and fixed-point analyses to characterize the patterns and their stability. Then, we derive analytically the amplitude equations that establish the activities of reaction-diffusion structures. We report on the emergence of diverse spatial structures including hexagonal and mixed-type patterns by providing a systematic mathematical approach, including variations in correlated oscillations, pattern variations and amplitude fluctuations. Our work shows that the emergence of spatiotemporal behavior, commonly found in excitable systems, has the potential to contribute significantly to the study of diffusively-coupled biophysical systems at large., Comment: 12 pages, 4 figures

We present analytical solution, which is periodic in nature, for a driven cubic-quartic nonlinear Schr\"odinger equation (DCQNLSE) placed in a bi-chromatic optical lattice. The solution indicates the creation of density wave. Since, beyond mean-field contribution in quasi one dimensional and one-dimensional geometry differs on the even exponents of the nonlinearity thus we extend our analysis towards quadratic-cubic-quartic and quadratic-cubic nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study indicates the existence of stripe phase along with considerable phase coherence. These findings allow us to comment on the possible emergence of supersolid phase in a condensate., Comment: 10 pages, 8 figures; To appear in Journal of Physics B: Atomic, Molecular and Optical Physics

Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in detail. Precisely, we are interested in investigating the possibility of droplet formation in a quasi-one-dimensional geometry. The recent observations have concluded that the droplets are stabilized by the competition between effective mean-field and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\"odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and verified them numerically. Based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self-bound droplet formations., Comment: To appear in Annalen der Physik