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Memory effect reflects a system's ability to encode, retain and retrieve information about its past. Such effects are essentially an out-of-equilibrium phenomenon providing insight into the complex structural and dynamical behavior of the system. Kovacs effect is one such memory effect that is traditionally associated with thermal history. Although studies on the Kovacs-like memory effect have been extended to mechanical perturbations such as compression-decompression, whether such effects can also be observed under volume-conserving perturbations like shear, remains unclear. Combining experiments, simulations and linear response theory we demonstrate Kovacs-like memory effect in a sheared colloidal glass. Moreover, we explore the influence of non-linear perturbations and establish a correlation between the deviation from linear response prediction and microscopic non-affine flows generated due to such large deformations in affecting the memory effect. Our study not only extends Kovacs-like memory effect in the domain of volume-conserving mechanical perturbations, it also highlights the importance of the nature of underlying microscopic flows in controlling the memory effect in amorphous matter., Comment: 9 pages, 5 figures

Accreting millisecond pulsars (AMSPs) are excellent laboratories to study reflection spectra and their features from an accretion disk truncated by a rapidly rotating magnetosphere near the neutron star surface. These systems also exhibit thermonuclear (type-I) bursts that can provide insights on the accretion physics and fuel composition. We explore spectral properties of the AMSP SRGA J144459.2-0604207 observed during the outburst that recently led to its discovery in February 2024. We aim to characterize the spectral shape of the persistent emission, both its continuum and discrete features, and to analyze type-I bursts properties. We employ XMM and NuSTAR overlapping observations taken during the most recent outburst from SRGA J1444. We perform spectral analysis of the persistent (i.e., non-bursting) emission employing a semi-phenomenological continuum model composed of a dominant thermal Comptonization plus two thermal contributions, and a physical reflection model. We also perform time-resolved spectral analysis of a type-I burst employing a blackbody model. We observe a broadened iron emission line, thus suggesting relativistic effects, supported by the physical model accounting for relativistically blurred reflection. The resulting accretion disk extends down to 6 gravitational radii, inclined at ~$53^{\circ}$, and only moderately ionized (log$\xi\simeq2.3$). We observe an absorption edge at ~9.7 keV that can be interpreted as an Fe XXVI edge blueshifted by an ultrafast ($\simeq0.04$c) outflow. Our broadband observations of type-I bursts do not find evidence of photospheric radius expansion. The burst recurrence time shows a dependence on the count rate with the steepest slope ever observed in these systems. We also observe a discrepancy of ~3 between the observed and expected burst recurrence time, which we discuss in the framework of fuel composition and high NS mass scenarios., Comment: 8 pages. Submitted to A&A

Research in software engineering is essential for improving development practices, leading to reliable and secure software. Leveraging the principles of quantum physics, quantum computing has emerged as a new computational paradigm that offers significant advantages over classical computing. As quantum computing progresses rapidly, its potential applications across various fields are becoming apparent. In software engineering, many tasks involve complex computations where quantum computers can greatly speed up the development process, leading to faster and more efficient solutions. With the growing use of quantum-based applications in different fields, quantum software engineering (QSE) has emerged as a discipline focused on designing, developing, and optimizing quantum software for diverse applications. This paper aims to review the role of quantum computing in software engineering research and the latest developments in QSE. To our knowledge, this is the first comprehensive review on this topic. We begin by introducing quantum computing, exploring its fundamental concepts, and discussing its potential applications in software engineering. We also examine various QSE techniques that expedite software development. Finally, we discuss the opportunities and challenges in quantum-driven software engineering and QSE. Our study reveals that quantum machine learning (QML) and quantum optimization have substantial potential to address classical software engineering tasks, though this area is still limited. Current QSE tools and techniques lack robustness and maturity, indicating a need for more focus. One of the main challenges is that quantum computing has yet to reach its full potential., Comment: Has been accepted for publication in Automated Software Engineering Journal, Springer, 2025

We analyze the impact of higher-twist three-particle $B_s$-meson light-cone distribution amplitudes (LCDAs) on the non-local form factors for the $B_s\to \phi \bar{\ell} \ell$ transition focusing on the 'charm-loop' contribution within the light-cone sum rule (LCSR) framework. To analytically continue these charm-loop contributions into the kinematically allowed region of the decay, we employ a hadronic dispersion relation that incorporates intermediate resonant states such as the $\phi$, $J/\Psi$ and $\psi(2S)$ mesons. Here, the LCSR predictions serve as inputs, supplemented by experimental data from two-body decays $B_s \to \phi$ $+$ resonance states. Our results indicate that the inclusion of twist-5 and twist-6 LCDAs enhances the non-local form factors$-$by approximately an order of magnitude$-$compared to previous estimates, due to partial disruption of cancellation among different twist contributions. This leads to a dilepton invariant mass-squared ($q^2-$)dependent correction to the Wilson coefficient $C_9$, which is higher than, but still consistent with the Standard Model prediction within uncertainties. Additionally, we update the local form factors to include contributions from higher-twist three-particle $B_s-$meson LCDAs. The phenomenological implications, particularly for the differential branching fraction and angular observables, are also discussed., Comment: 32 Pages, 4 Figures and 9 Tables

In this study, we establish certain Landau-type theorems for functions with logharmonic Laplacian of the form $F(z)=|z|^2L(z)+K(z)$, $|z|<1$, where $L$ is logharmonic and $K$ is harmonic, with $L$ and $K$ having bounded length distortion in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$. Furthermore, we examine the univalence of the mappings $D(F)$, where $D$ is a differential operator., Comment: 14 pages

General Relativity (GR) remains the cornerstone of gravitational physics, providing remarkable success in describing a wide range of astrophysical and cosmological phenomena. However, several challenges underscore the urgent need to explore modified gravity theories. GR struggles to reconcile with quantum mechanics, fails to provide fundamental explanations for dark matter and dark energy, and faces limitations in describing extreme regimes such as black hole singularities and the very early universe. This review provides an organized perspective on modified gravity theories by classifying them based on the principles of GR they preserve or violate. Specifically, we consider three broad categories: (1) metric theories that uphold local Lorentz invariance (LLI) and gauge invariance, (2) theories that break gauge invariance, LLI, or parity, and (3) beyond-metric theories that violate the Einstein's equivalence principle (EEP). This classification highlights the underlying assumptions of GR that these theories challenge or extend, providing a framework for understanding their motivations and implications. The review also discusses the current and upcoming experimental and observational tests of GR, including those probing its foundational principles, such as LLI, gauge invariance, and EEP. For each class of modified theories, we examine their ability to address critical open questions in cosmology and black hole physics. These include their potential to explain the accelerated expansion of the current universe, the nature of dark matter, and deviations in black hole dynamics from GR predictions. This review aims to provide a structured understanding of modified gravity theories and their observational implications in the multimessenger era by focusing on the principles preserved or violated. [abridged], Comment: 62 pages, 7 figures, This is a pre-print of two chapters for the Encyclopedia of Astrophysics (edited by I. Mandel, section editor C. Howlett) to be published by Elsevier as a Reference Module

As the popularity of Internet of Things (IoT) platforms grows, users gain unprecedented control over their homes, health monitoring, and daily task automation. However, the testing of software for these platforms poses significant challenges due to their diverse composition, e.g., common smart home platforms are often composed of varied types of devices that use a diverse array of communication protocols, connections to mobile apps, cloud services, as well as integration among various platforms. This paper is the first to uncover both the practices and perceptions behind testing in IoT platforms, particularly open-source smart home platforms. Our study is composed of two key components. First, we mine and empirically analyze the code and integrations of two highly popular and well-maintained open-source IoT platforms, OpenHab and HomeAssitant. Our analysis involves the identification of functional and related test methods based on the focal method approach. We find that OpenHab has only 0.04 test ratio ($\approx 4K$ focal test methods from $\approx 76K$ functional methods) in Java files, while HomeAssitant exhibits higher test ratio of $0.42$, which reveals a significant dearth of testing. Second, to understand the developers' perspective on testing in IoT, and to explain our empirical observations, we survey 80 open-source developers actively engaged in IoT platform development. Our analysis of survey responses reveals a significant focus on automated (unit) testing, and a lack of manual testing, which supports our empirical observations, as well as testing challenges specific to IoT. Together, our empirical analysis and survey yield 10 key findings that uncover the current state of testing in IoT platforms, and reveal key perceptions and challenges. These findings provide valuable guidance to the research community in navigating the complexities of effectively testing IoT platforms., Comment: 10 pages, 4 figures

We revisit the problem of transmission of quasiparticles through a rectangular potential barrier for semimetals featuring quadratic-in-momentum band-crossings at a nodal point. Although this was considered in Annals of Physics 419 (2020) 168235, the solutions corresponding to evanescent waves were missed, leading to a partial fulfillment of the boundary conditions required to determine the piecewise-continuous wavefunctions. In this paper, our aim is to correct those shortcomings, recompute the transmission coefficients, and show the resulting behaviour of the conductivity and the Fano factor for some representative parameter values., Comment: corrects the solutions shown in arXiv:2004.06134 by incorporating the missing evanescent waves

We study the dynamics of Stirling's iterative root-finding method $St_f(z)$ for rational and polynomial functions. It is seen that the Scaling theorem is not satisfied by Stirling's iterative root-finding method. We prove that for a rational function $R(z)$ with simple zeroes, the zeroes are the superattracting fixed points of $St_{R}(z)$ and all the extraneous fixed points of $St_{R}(z)$ are rationally indifferent. For a polynomial $p(z)$ with simple zeroes, we show that the Julia set of $St_p(z)$ is connected. Also, the symmetry of the dynamical plane and free critical orbits of Stirling's iterative method for quadratic unicritical polynomials are discussed. The dynamics of this root-finding method applied to M\"{o}bius map is investigated here. We have shown that the possible number of Herman rings of this method for M\"{o}bius map is at most $2$., Comment: 17 pages

There has been significant interest in exploring topological disclination states, which effectively probe the band topology of the host material beyond the conventional bulk-edge correspondence. While most studies in this area have primarily focused on Hermitian systems, recent theoretical work predicts that non-Hermiticity can drive topological phase transitions and host topological disclination states associated with fractional charge. However, no experimental observations have been reported to date. Here, we report the first experimental observation of topological disclination states in electric circuits, induced solely by gain and loss. Through admittance matrix measurements and eigenstate analysis, we confirm their emergence and compute the corresponding fractional charge. Moreover, the disclination mode profile and localization effect can be directly visualized via monochromatic field excitation. Additionally, we demonstrate the emergence of degenerate zero-energy topological disclination states, devoid of fractional charge, in distinct non-Hermitian geometries. Our findings open the possibility of non-Hermiticity-induced fractional charges in two-dimensional non-Hermitian lattices, which may pave the way for advancements in active topological photonic devices., Comment: 16 pages, 4 figures

Interest in vibrational polaritonic chemistry, where ground-state chemical kinetics are modified via confined optical modes in a cavity, has surged in recent years. Although models have been developed to understand cavity-modified reactions, fully quantum mechanical simulations remain out of reach for the collective regime that involves many molecules, a critical aspect of the phenomenon. Mixed quantum-classical (MQC) simulations offer a scalable alternative, but their accuracy requires testing and potential improvements even in the single-molecule limit. In this work, we take this step by first introducing the mapping approach to surface hopping (MASH) to address the limitations of traditional MQC methods. Second, we incorporate a quantum treatment of the cavity mode, moving beyond the classical approximations often employed in previous studies. Results for a single-molecule model of vibrational polaritonic chemistry show that combining MASH with a quantum cavity mode yields the most accurate rates. However, this scheme may produce different long-time population dynamics at zero coupling depending on whether the cavity mode is quantized; a problem known as size-inconsistency in MASH. We address this problem proposing the $\epsilon$-MASH approach, which forbids hopping between states with negligible nonadiabatic couplings (NACs). Combining MASH with a quantum cavity mode thus provides a promising approach for scalable and accurate MQC simulations in the collective regime., Comment: 14 pages, 9 figures

The question of whether Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels has drawn attention since it was resolved positively for the binary erasure channel by Kudekar et al. in 2016. In 2021, Reeves and Pfister extended this to prove the bit-error probability vanishes on BMS channels when the code rate is less than capacity. In 2023, Abbe and Sandon improved this to show the block-error probability also goes to zero. These results analyze decoding functions using symmetry and the nested structure of RM codes. In this work, we focus on binary-input symmetric classical-quantum (BSCQ) channels and the Holevo capacity. For a BSCQ, we consider observables that estimate the channel input in the sense of minimizing the mean-squared error (MSE). Using the orthogonal decomposition of these observables under a weighted inner product, we establish a recursive relation for the minimum MSE estimate of a single bit in the RM code. Our results show that any set of $2^{o(\sqrt{\log N})}$ bits can be decoded with a high probability when the code rate is less than the Holevo capacity., Comment: Extended Version of ISIT 2025 Submission

In this paper, we have found that some certain Fermat-type shift and difference equations have the meromorphic solutions generated by Riccati type functions. Also we have solved the open problems posed by Liu and Yang (A note on meromorphic solutions of Fermat types equations, An. Stiint. Univ. Al. I. Cuza Lasi Mat. (N. S.), 62(2)(1), 317-325 (2016)). We have fortified the claims by some examples.

It is crucial to explore the sharp bounds of logarithmic coefficients and the Hankel determinant involving logarithmic coefficients as part of coefficient problems in various function classes. Our primary objective in this study is to determine the sharp bounds for logarithmic coefficients as well as logarithmic inverse coefficients of bounded analytic functions associated with a bean-shaped domain in the class $\mathcal{BT_\mathfrak{B}}$. For this class, we also establish the sharp bounds for the second Hankel determinant involving logarithmic coefficients as well as logarithmic inverse coefficients. In addition, we establish sharp bounds for the generalized Zalcman conjecture inequality and the moduli differences of logarithmic coefficients for the class $\mathcal{BT_\mathfrak{B}}$., Comment: 16 pages, 8 figures

The Cold Dark Matter (CDM) hypothesis accurately predicts large-scale structure formation and fits the Cosmic Microwave Background temperature fluctuations (CMB). However, observations of the inner regions of dark matter halos and dwarf galaxy satellites have consistently posed challenges to CDM. On the other hand, the Modified Newtonian Dynamics (MOND) hypothesis can explain galactic phenomena but fails to account for the complex shape of the CMB and matter power spectra. CDM and MOND are effective in nearly mutually exclusive regimes, prompting the question: Is there a physical mechanism where CDM and MOND share a common origin? Q-balls, which are localized, non-topological solitons, can be a bridge between the two hypotheses. Q-balls formed in the early Universe can mimic CDM at cosmological scales. Interestingly, Q-balls can exhibit MOND-like behavior in the late Universe at galactic scales, providing a unified framework. Specifically, we demonstrate that millicharged composite Q-balls formed from complex scalar fields, decoupled from the background radiation, can naturally arise during the radiation-dominated epoch. From the matter-radiation equality, we also obtain the mass of Q-balls to be $1~{eV}$, which are much smaller than the electron mass. Using the constraints from the invisible decay mode of ortho-positronium, we obtain $Q < 3.4 \times 10^{-5}$. We also establish an upper bound on the number density of Q-balls, which depends on the charge of the Q-ball and the small initial charge asymmetry. Furthermore, we demonstrate that the MOND naturally emerges at the galactic scale within the framework of our Q-ball model., Comment: 46 pages, 3 figures, version accepted in European Physical Journal C

Information removal or suppression in large language models (LLMs) is a desired functionality, useful in AI regulation, legal compliance, safety, and privacy. LLM unlearning methods aim to remove information on demand from LLMs. Current LLM unlearning methods struggle to balance the unlearning efficacy and utility due to the competing nature of these objectives. Keeping the unlearning process computationally feasible without assuming access to the model weights is an overlooked area. We present the first agentic LLM unlearning (ALU) method, a multi-agent, retrain-free, model-agnostic approach to LLM unlearning that achieves effective unlearning while preserving the utility. Our ALU framework unlearns by involving multiple LLM agents, each designed for a specific step in the unlearning process, without the need to update model weights for any of the agents in the framework. Users can easily request any set of unlearning instances in any sequence, and ALU seamlessly adapts in real time. This is facilitated without requiring any changes in the underlying LLM model. Through extensive experiments on established benchmarks (TOFU, WMDP, WPU) and jailbreaking techniques (many shot, target masking, other languages), we demonstrate that ALU consistently stands out as the most robust LLM unlearning framework among current state-of-the-art methods while incurring a low constant-time cost. We further highlight ALU's superior performance compared to existing methods when evaluated at scale. Specifically, ALU is assessed on up to 1000 unlearning targets, exceeding the evaluation scope of all previously proposed LLM unlearning methods.

We have investigated the normal and superconducting states of the technologically important compound Nb$_3$Sn using $^{93}$Nb nuclear magnetic resonance. From spin-lattice relaxation we find strong suppression of the zero-temperature superconducting order parameter by magnetic field. We have identified an anomalously large electron-nuclear exchange interaction from spin-spin relaxation measurements, an order of magnitude beyond that of the dipole-dipole interaction, and thereby sensitive to vortex dynamics and vortex pinning.

Mental illness is a widespread and debilitating condition with substantial societal and personal costs. Traditional diagnostic and treatment approaches, such as self-reported questionnaires and psychotherapy sessions, often impose significant burdens on both patients and clinicians, limiting accessibility and efficiency. Recent advances in Artificial Intelligence (AI), particularly in Natural Language Processing and multimodal techniques, hold great potential for recognizing and addressing conditions such as depression, anxiety, bipolar disorder, schizophrenia, and post-traumatic stress disorder. However, privacy concerns, including the risk of sensitive data leakage from datasets and trained models, remain a critical barrier to deploying these AI systems in real-world clinical settings. These challenges are amplified in multimodal methods, where personal identifiers such as voice and facial data can be misused. This paper presents a critical and comprehensive study of the privacy challenges associated with developing and deploying AI models for mental health. We further prescribe potential solutions, including data anonymization, synthetic data generation, and privacy-preserving model training, to strengthen privacy safeguards in practical applications. Additionally, we discuss evaluation frameworks to assess the privacy-utility trade-offs in these approaches. By addressing these challenges, our work aims to advance the development of reliable, privacy-aware AI tools to support clinical decision-making and improve mental health outcomes., Comment: 18 pages, 2 figures

We develop an analytical microscopic theory to describe the polaron-polariton dispersion, formed by hybridizing excitons, photons, and phonons, and their coherent dynamics inside optical cavities. Starting from a microscopic light-matter Hamiltonian, we derive a simple analytical model by pursuing a non-perturbative treatment of the phonon and photon couplings to excitons. Within our theoretical framework, the phonons are treated as classical fields that are then quantized via the Floquet formalism. We show that, to a good approximation, the entire polaron-polariton system can be described using a band picture despite the phonons breaking translational symmetry. Our theory also sheds light on the long-lived coherent ballistic motion of exciton-polaritons with high excitonic character that propagate with group velocities lower than is expected from pure exciton-polariton bands, offering a microscopic explanation for these puzzling experimental observations.

Enterprise level data is often distributed across multiple sources and identifying the correct set-of data-sources with relevant information for a knowledge request is a fundamental challenge. In this work, we define the novel task of routing an end-user query to the appropriate data-source, where the data-sources are databases. We synthesize datasets by extending existing datasets designed for NL-to-SQL semantic parsing. We create baselines on these datasets by using open-source LLMs, using both pre-trained and task specific embeddings fine-tuned using the training data. With these baselines we demonstrate that open-source LLMs perform better than embedding based approach, but suffer from token length limitations. Embedding based approaches benefit from task specific fine-tuning, more so when there is availability of data in terms of database specific questions for training. We further find that the task becomes more difficult (i) with an increase in the number of data-sources, (ii) having data-sources closer in terms of their domains,(iii) having databases without external domain knowledge required to interpret its entities and (iv) with ambiguous and complex queries requiring more fine-grained understanding of the data-sources or logical reasoning for routing to an appropriate source. This calls for the need for developing more sophisticated solutions to better address the task., Comment: Accepted at 1st Workshop on GenAI and RAG Systems for Enterprise at CIKM 2024 Conference. 10 pages, 1 figure

Lamellar or smectic phases often have an intricate intralamellar structure that remains scarcely understood from a microscopic viewpoint. In this work, we use molecular dynamics simulations to study the effect of volume exclusion and electrostatic repulsion on the phase transitions of a flat membrane of soft spherocylinders. With increasing rod packing, we identify nematic and solid phases and find that the nematic-crystal phase transition happens at a uniform packing fraction ($\eta_c \approx 0.82$), independent of the spherocylinder aspect ratio. This value is considerably higher than the well-known critical freezing transition of a hard disk fluid ($\eta_c \approx 0.7$) to which one could naively map a system of near-parallel rods with co-planar mass centers. We attribute this difference to a non-vanishing residual orientational entropy per rod. Our findings are corroborated by a simple theory based on a simple microscopic density functional theory of freezing of a two-dimensional rod fluid. Introduction of electrostatic interactions between the rods reduces the lateral compressibility of the monolayer fluid but keeps the positional order unhindered, which in turn maintains the packing fraction at the nematic-crystal transition. The strength of the orientational fluctuations of the individual rods in our membranes exhibits a density scaling that differs from 3D bulk smectics. Our findings contribute to a qualitative understanding of liquid crystal phase stability in strong planar confinement and engage with recent experimental explorations involving nanorods on 2D substrates., Comment: 10 pages, 9 figures

We establish Bernstein-type inequalities for the quantum algebras $K_{n,\Gamma}^{P,Q}(\mathbb{K})$ introduced by K. L. Horton that include the graded quantum Weyl algebra, the quantum symplectic space, the quantum Euclidean space, and quantum Heisenberg algebra etc., obtaining new results and as well as simplified proofs of previously known results. The Krull and global dimensions of certain further localizations of $K_{n,\Gamma}^{P,Q}(\mathbb{K})$ are computed., Comment: 19 pages

Modern cosmological research still thoroughly debates the discrepancy between local probes and the Cosmic Microwave Background observations in the Hubble constant ($H_0$) measurements, ranging from $4\sigma$ to $6\sigma$. In the current study we examine this tension using the Supernovae Ia (SNe Ia) data from the Pantheon, PantheonPlus, Joint Lightcurve Analysis (JLA), and Dark Energy Survey (DES) catalogs together with their combination called Master Sample containing 3789 SNe Ia, and dividing all of them into redshift-ordered bins. Two main binning techniques are presented: the equipopulation and the equispace in the $\log\, z$. We perform a Markov-Chain Monte Carlo analysis (MCMC) for each bin to determine the $H_0$ value, estimating it within the standard flat $\Lambda$CDM and the $w_{0}w_{a}$CDM models. These $H_0$ values are then fitted with the following phenomenological function: $\mathcal{H}_0(z) = \tilde{H}_0 / (1 + z)^\alpha$, where $\tilde{H}_0$ is a free parameter representing $\mathcal{H}_0(z)$ fitted at $z=0$, and $\alpha$ is the evolutionary parameter. Our results indicate a decreasing trend characterized by $\alpha \sim 0.01$ whose consistency with zero range from $1.00 \sigma$ at 3 bins in the Pantheon sample with the $w_{0}w_{a}$CDM model to $\geq 6 \sigma$ at 12 bins with the JLA and DES samples within the $\Lambda$CDM model. Such a trend in the SNe Ia catalogs could be due to evolution with redshift for the SNe Ia astrophysical variables or unveiled selection biases. Alternatively, intrinsic physics, possibly the $f(R)$ theory of gravity, could be responsible for this trend., Comment: 45 pages, 8 figures, 7 tables. Submitted to JHEAP. Comments are welcome

Motivated by the famous Blanco-Koldobsky-Turn\v{s}ek characterization of isometries, we study the \textit{approximate preservation of Birkhoff-James orthogonality by a linear operator between Banach spaces}. In particular, we investigate various geometric and analytic properties related to such preservation on finite-dimensional polyhedral Banach spaces. As an application of the results obtained here, we present refinements of the Blanco-Koldobsky-Turn\v{s}ek characterization of isometries on certain Banach spaces.

In this paper, we present an analysis of the equation $\ddot{x} - (1/2x) \dot{x}^2 + 2 \omega^2 x - 1/8x = 0$, where $\omega > 0$ and $x = x(t)$ is a real-valued variable. We first discuss the appearance of this equation from a position-dependent-mass scenario in which the mass profile goes inversely with $x$, admitting a singularity at $x = 0$. The associated potential is also singular at $x = 0$, splitting the real axis into two halves, i.e., $x > 0$ and $x < 0$. The dynamics is exactly solvable for both the branches and so for definiteness, we stick to the $x > 0$ branch. Performing a canonical quantization in the position representation and upon employing the ordering strategy of the kinetic-energy operator due to von Roos, we show that the problem is isospectral with the isotonic oscillator. Thus, the quantum spectrum consists of an infinite number of equispaced levels which is in line with the expectation that classical systems that support isochronous oscillations are associated in their quantized versions with equally-spaced spectra. The spacing between energy levels is found to be insensitive to the specific choices of the ambiguity parameters that are employed for ordering the kinetic-energy operator \`a la von Roos., Comment: v1: Comments are welcome

Electron glasses offer a convenient laboratory platform to study glassy dynamics. Traditionally, the interplay between long-range Coulomb interactions and disorder is deemed instrumental in stabilizing the electron glass phase. Existing experimental studies on electron glass have focused on doped semiconductors, strongly correlated systems, granular systems, etc., all of which are far from the well-delocalized limit. In this work, we expand the study of electron glasses to a well-known quantum paraelectric SrTiO$_3$ (STO) and unveil a new scenario: how naturally occurring ferroelastic twin walls of STO could result in glassy electrons, even in a metallic state. We show that the emergent two-dimensional electron gas at the $\gamma$-Al$_2$O$_3$/STO interface exhibits long-lasting temporal relaxations in resistance and memory effects at low temperatures, which are hallmarks of glassiness. We also demonstrate that the glass-like relaxations could be further tuned by application of an electric field. This implies that the observed glassy dynamics is connected with the development of polarity near the structural twin walls of STO and the complex interactions among them, arising from the coupling between ferroelastic and ferroelectric orders. The observation of this glassy metal phase not only extends the concept of electron glasses to metallic systems with multiple order parameters but also contributes to the growing understanding of the fascinating and diverse physical phenomena that emerge near the quantum critical point., Comment: 20 pages, 5 figures

We use an infinite $k$-ary tree with a self-loop at the root as our underlying graph. We consider a chip-firing process starting with $N$ chips at the root. We describe the stable configurations. We calculate the number of fires for each vertex and the total number of fires. We study a sequence of the number of root fires for a given $k$ as a function of $N$ and study its properties. We do the same for the total number of fires., Comment: 22 pages, 1 figure

We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting features explore the nonlinear, non-saturated regions of the activation function. We introduce skip connections and construct a deep variant of random feature maps by combining several units. To mitigate the curse of dimensionality, we introduce localization where we learn local maps, employing conditional independence. Our modified random feature maps provide excellent forecasting skill for both single trajectory forecasts as well as long-time estimates of statistical properties, for a range of chaotic dynamical systems with dimensions up to 512. In contrast to other methods such as reservoir computers which require extensive hyperparameter tuning, we effectively need to tune only a single hyperparameter, and are able to achieve state-of-the-art forecast skill with much smaller networks.

The enigma surrounding the existence of black holes has recently been substantiated through the groundbreaking work of experimental physicists \cite{genzel2024}. Exploring quantum systems under the gravitational influence of black holes has emerged as a pivotal area of research. Among the frontier works in quantum information processing is the utilization of quantum states as quantum channels. A fundamental quantum information protocol is teleportation, in which two parties, Alice and Bob, share entangled states. In this protocol, the sender, Alice, who holds an unknown qubit, utilizes local operations and classical communication (LOCC) to recreate the qubit at the recipient's (Bob's) end. Notably, during the execution of this protocol, Alice loses the unknown qubit on her side. The teleportation protocol, originally proposed by Bennett et al. \cite{bennett1993}, has been extensively studied with various states and under different physical setups. Researchers have explored both modifications to the protocol itself and the viability of various quantum states as teleportation channels. In this paper, we investigate whether bipartite mixed states derived from two inequivalent classes of tripartite pure states, subjected to the gravitational influence of two different black hole models, can still serve as efficient quantum channels for teleportation. We emphasize the teleportation fidelity of these states, a critical factor for determining their efficacy as quantum channels. Specifically, the fidelity must exceed the classical limit of $\frac{2}{3}$ to be considered effective \cite{pop1994}. We conjecture that, even under the gravitational influence of black holes, the quantum characteristics of the given states are preserved, enabling them to function effectively as quantum channels for teleportation., Comment: 16 pages, 10 figures

Restless multi-armed bandits (RMABs) have been highly successful in optimizing sequential resource allocation across many domains. However, in many practical settings with highly scarce resources, where each agent can only receive at most one resource, such as healthcare intervention programs, the standard RMAB framework falls short. To tackle such scenarios, we introduce Finite-Horizon Single-Pull RMABs (SPRMABs), a novel variant in which each arm can only be pulled once. This single-pull constraint introduces additional complexity, rendering many existing RMAB solutions suboptimal or ineffective. %To address this, we propose using dummy states to duplicate the system, ensuring that once an arm is activated, it transitions exclusively within the dummy states. To address this shortcoming, we propose using \textit{dummy states} that expand the system and enforce the one-pull constraint. We then design a lightweight index policy for this expanded system. For the first time, we demonstrate that our index policy achieves a sub-linearly decaying average optimality gap of $\tilde{\mathcal{O}}\left(\frac{1}{\rho^{1/2}}\right)$ for a finite number of arms, where $\rho$ is the scaling factor for each arm cluster. Extensive simulations validate the proposed method, showing robust performance across various domains compared to existing benchmarks., Comment: 17 Pages, 8 figures. Accepted by AAMAS 2025

We analytically investigate the dynamic behavior of an an-isotropic active Brownian particle under various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to an-isotropic diffusion at short times, whereas rotational diffusion causes the transport to become isotropic at longer times. We have considered three different resetting protocols: (a) complete resetting, when both position and orientation are reset to their initial states, (b) only position is reset to its initial state, (c) only orientation is reset to its initial state. We reveal that orientation resetting sustains asymmetry even at late times. When both the spatial position and orientation are subject to resetting, a complex position probability distribution forms in the steady state. All the analytical findings are thoroughly validated by corresponding simulation results., Comment: 21 pages, 13 figures

Purpose: Quantum computing promises to transform problem-solving across various domains with rapid and practical solutions. Within Software Evolution and Maintenance, Quantum Machine Learning (QML) remains mostly an underexplored domain, particularly in addressing challenges such as detecting buggy software commits from code repositories. Methods: In this study, we investigate the practical application of Quantum Support Vector Classifiers (QSVC) for detecting buggy software commits across 14 open-source software projects with diverse dataset sizes encompassing 30,924 data instances. We compare the QML algorithm PQSVC (Pegasos QSVC) and QSVC against the classical Support Vector Classifier (SVC). Our technique addresses large datasets in QSVC algorithms by dividing them into smaller subsets. We propose and evaluate an aggregation method to combine predictions from these models to detect the entire test dataset. We also introduce an incremental testing methodology to overcome the difficulties of quantum feature mapping during the testing approach. Results: The study shows the effectiveness of QSVC and PQSVC in detecting buggy software commits. The aggregation technique successfully combines predictions from smaller data subsets, enhancing the overall detection accuracy for the entire test dataset. The incremental testing methodology effectively manages the challenges associated with quantum feature mapping during the testing process. Conclusion: We contribute to the advancement of QML algorithms in defect prediction, unveiling the potential for further research in this domain. The specific scenario of the Short-Term Activity Frame (STAF) highlights the early detection of buggy software commits during the initial developmental phases of software systems, particularly when dataset sizes remain insufficient to train machine learning models., Comment: Accepted for publication in the Springer Journal: Quantum Machine Intelligence (https://link.springer.com/journal/42484)

We continue our investigations of the nature of the linear-response tensors in planar-Hall and planar-thermal Hall configurations, involving three-dimensional nodal-point semimetals, by considering here nodes hosting pseudospin-1 quasiparticles. Such systems exemplify multifold semimetals, as they have three bands crossing at a nodal point. We derive the explicit expressions of the electric, thermoelectric, and thermal coefficients, when the nodes are subjected to the combined influence of an electric field (and/or temperature gradient) and a weak (i.e., nonquantizing) magnetic field. In order to have a complete description, we consider the effects of the Berry curvature and the orbital magnetic moment on an equal footing, both of which originate from the underlying topological features of the bandstructure. Going beyond our previous works, we determine the out-of-plane response comprising the intrinsic anomalous-Hall and the Lorentz-force-contributed currents, and chalk out the effects of internode-scatterings as well. Our theoretical explorations shed light on the mechanisms of transport in multifold semetals, which are being investigated in contemporary experiments., Comment: follow-up paper of arXiv:2405.14844 and arXiv:2408.01422; formulae from arXiv:2411.18434 used

We study the local preservation of Birkhoff-James orthogonality by linear operators between normed linear spaces, at a point and in a particular direction. We obtain a complete characterization of the same, which allows us to present refinements of the local preservation of orthogonality explored earlier. We also study the directional preservation of orthogonality with respect to certain special subspaces of the domain space, and apply the results towards identifying the isometries on a polyhedral normed linear space. In particular, we obtain refinements of the Blanco-Koldobsky-Turn\v{s}ek Theorem for polyhedral normed linear spaces, including $ \ell_{\infty}^{n}, \ell_{1}^{n}. $

Let $\mathcal{H}$ be the class of harmonic functions $f=h+\overline{g}$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, where $h$ and $g$ are analytic in $\mathbb{D}$ with the normalization $h(0)=g(0)=h'(0)-1=0$. Let $\mathcal{P}_{\mathcal{H}}^0(\alpha,M)$ denote the subclass of $\mathcal{H}$ in $\mathbb{D}$ satisfying $\text{Re}\left((1-\alpha)h'(z)+\alpha zh''(z)\right)>-M+\left|(1-\alpha)g'(z)+\alpha zg''(z)\right|$ with $g'(0)=0$, $M>0$ and $\alpha\in(0,1]$. In this paper, we investigate some fundamental properties of functions belonging to the class $\mathcal{P}_{\mathcal{H}}^0(\alpha,M)$, including coefficient bounds, growth estimates, convexity, starlikeness, convex combinations, and convolution., Comment: 15 Pages

The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex variables. These results represent some refinements and generalizations of the earlier findings, especially the results due to Xu {\it et al.} (J. Math. Anal. Appl. 483(2) (2020)). We provide some examples to support the results., Comment: 24 Pages

Altermagnetism, a new collinear magnetic state, has gained significant attention in the last few years, and the underlying mechanisms driving this quantum phase are still evolving. Going beyond the group theoretical analyses, which focus on providing a binary description of the presence or absence of the altermagnetic state, in this work, we explore the role of crystal chemical bonding. As the latter successfully integrates the crystal and orbital symmetries and is tunable, it provides a quantitative and realistic mechanism to explain the formation of altermagnetism. From the first principles calculations and tight-binding models within the framework of the linear combination of atomic orbitals on NiS, we establish a set of selection rules for the formation of altermagnetism in the NiAs prototype compounds (e.g. CrSb, MnTe, etc.). Broadly, if single orbitals from Ni and S sites are involved in the bonding, the second neighbor interaction between the nonmagnetic atoms is a must to modulate the intra-sublattice interactions differently for the opposite spin sublattices so that the antiferromagnetic sublattice band degeneracy is lifted and momentum-dependent altermagnetic spin split (ASS) appears. However, when multiple orbitals are involved from the Ni and S sites in the chemical bonding, altermagnetism is naturally present. Together they amplify the ASS. Further, we propose twelve antinodal regions in the NiAs type hexagonal crystals, where ASS split is maximum. Specific to NiS, ASS increases with correlation, and for the edge valence and conduction bands it can go beyond 1eV. The present study opens up new pathways to design chemical bonding driven selection rules in addition to the existing crystal symmetry criteria to tailor tunable altermagnetism., Comment: 13 pages, 11 figures, and 6 tables

The collider phenomenology of leptoquarks (LQs) and right-handed neutrinos (RHNs) has been studied extensively in the literature. Because of the gauge singlet nature, the production of RHNs at the LHC is typically suppressed by the tiny light-heavy neutrino mixing angles. In this study, we explore a promising scenario where the presence of an LQ mediator significantly enhances RHN production. We focus on first-generation scalar and vector LQs interacting with the first-generation RHN. The prospects are better for the first-generation scenario than the other generations because of the enhanced parton distribution functions (PDFs) of first-generation quarks. The enhanced PDFs boost the production cross sections of LQs, particularly their single and indirect productions. Incorporating all production modes of LQs that result in a pair of RHNs, we estimate the discovery prospects by analysing the monoelectron and dielectron channels arising from the decay of the RHN pair. We find that the indirect production of LQs is crucial in determining the discovery reach at the HL-LHC for the first-generation scenario., Comment: 11 pages, 5 figures, 5 tables. Updated references

We introduce the leptoquark (LQ) toolkit, TooLQit, which includes leading-order FeynRules models for all types of LQs and a Python-based calculator, named CaLQ, to test if a set of parameter points are allowed by the LHC dilepton searches. The models include electroweak gauge interactions of the LQs and follow a set of intuitive notations. Currently, CaLQ can calculate the LHC limits on LQ ($S_1$ and $U_1$) couplings (one or more simultaneously) for any mass between $1$ and $5$ TeV using a $\chi^2$ method. In this manual for TooLQit, we describe the FeynRules models and discuss the techniques used in CaLQ. We outline the workflow to check parameter spaces of LQ models with an example. We show some illustrative scans for one- and multi-coupling scenarios for the $U_1$ vector LQ. The TooLQit code is available at https://github.com/rsrchtsm/TooLQit, Comment: 19 pages, 9 figures, and 2 tables. Code available at https://github.com/rsrchtsm/TooLQit

We test the standardizability of a homogeneous sample of 41 lower-redshift ($0.00415\leq z \leq 0.474$) active galactic nuclei (AGNs) reverberation-mapped (RM) using the broad H$\alpha$ and H$\beta$ emission lines. We find that these sources can be standardized using four radius$-$luminosity ($R-L$) relations incorporating H$\alpha$ and H$\beta$ time delays and monochromatic and broad H$\alpha$ luminosities. Although the $R-L$ relation parameters are well constrained and independent of the six cosmological models considered, the resulting cosmological constraints are weak. The measured $R-L$ relations exhibit slightly steeper slopes than predicted by a simple photoionization model and steeper than those from previous higher-redshift H$\beta$ analyses based on larger datasets. These differences likely reflect the absence of high-accreting sources in our smaller, lower-redshift sample, which primarily comprises lower-accreting AGNs. The inferred cosmological parameters are consistent within 2$\sigma$ (or better) with those from better-established cosmological probes. This contrasts with our earlier findings using a larger, heterogeneous sample of 118 H$\beta$ AGNs, which yielded cosmological constraints differing by $\gtrsim 2\sigma$ from better-established cosmological probes. Our analysis demonstrates that sample homogeneity$-$specifically, the use of a consistent time-lag determination method$-$is crucial for developing RM AGNs as a cosmological probe., Comment: 34 pages, 18 figures, 9 tables, submitted to PRD

Quantum computation based on superconducting circuits utilizes superconducting qubits with Josephson tunnel junctions. Engineering high-coherence qubits requires materials optimization. In this work, we present two superconducting thin film systems, grown on silicon (Si), and one obtained from the other via annealing. Cobalt (Co) thin films grown on Si were found to be superconducting [EPL 131 (2020) 47001]. These films also happen to be a self-organised hybrid superconductor/ferromagnet/superconductor (S/F/S) structure. The S/F/S hybrids are important for superconducting $\pi$-qubits [PRL 95 (2005) 097001] and in quantum information processing. Here we present our results on the superconductivity of a hybrid Co film followed by the superconductivity of a CoSi$_2$ film, which was prepared by annealing the Co film. CoSi$_2$, with its $1/f$ noise about three orders of magnitude smaller compared to the most commonly used superconductor aluminium (Al), is a promising material for high-coherence qubits. The hybrid Co film revealed superconducting transition temperature $T_c$ = 5 K and anisotropy in the upper critical field between the in-plane and out-of-plane directions. The anisotropy was of the order of ratio of lateral dimensions to thickness of the superconducting Co grains, suggesting a quasi-2D nature of superconductivity. On the other hand, CoSi$_2$ film showed a $T_c$ of 900 mK. In the resistivity vs. temperature curve, we observe a peak near $T_c$. Magnetic field scan as a function of $T$ shows a monotonic increase in intensity of this peak with temperature. The origin of the peak has been explained in terms of parallel resistive model for the particular measurement configuration. Although our CoSi$_2$ film contains grain boundaries, we observed a perpendicular critical field of 15 mT and a critical current density of 3.8x10$^7$ A/m$^2$, comparable with epitaxial CoSi$_2$ films., Comment: 15 pages, 7 figures, 2 tables

In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those of Haldar and Ahamed (Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in $\mathbb{C}^2$, Anal. Math. Phys., 12 (2022)). In addition, the results improve the previous results from the situation with two complex variables to the situation with several complex variables. To support our results, we have included several examples., Comment: Pages-24, Latex-V1

The objective of this study is to ascertain the existence and forms of the finite order meromorphic and entire functions of several complex variables satisfying some certain Fermat-type partial differential-difference equations by considering the more general forms of the PDDEs in an open problem on $\mathbb{C}^2$ due to Xu and Wang (Notes on the existence of entire solutions for several partial differential-difference equations, Bull. Iran. Math. Soc., 47, 1477-1489 (2020)). We provide examples to illustrate the results., Comment: 17 Pages, Latex-V1

We present a numerical study to determine nucleation rates for magnetisation reversal within the Ising model (lattice gas model) in the low-temperature regime, a domain less explored in previous research. To achieve this, we implemented the N-Fold way algorithm, a well-established method for low-temperature simulations, alongside a novel, highly efficient cluster identification algorithm. Our method can access nucleation rates up to 50 orders of magnitude lower than previously reported results. We examine three cases: homogeneous pure system, system with static impurities, and system with mobile impurities, where impurities are defined as sites with zero interactions with neighbouring spins (spin value of impurities is set to 0). Classical nucleation theory holds across the entire temperature range studied in the paper, for both the homogeneous system and the static impurity case. However, in the case of mobile impurities, the umbrella sampling technique seems ineffective at low mobility values. These findings provide valuable insights into nucleation phenomena at low temperatures, contributing to theoretical and experimental understanding., Comment: 9 figures