Road potholes pose significant safety hazards and maintenance challenges, particularly on India's diverse and under-maintained road networks. This paper presents iWatchRoadv2, a fully automated end-to-end platform for real-time pothole detection, GPS-based geotagging, and dynamic road health visualization using OpenStreetMap (OSM). We curated a self-annotated dataset of over 7,000 dashcam frames capturing diverse Indian road conditions, weather patterns, and lighting scenarios, which we used to fine-tune the Ultralytics YOLO model for accurate pothole detection. The system synchronizes OCR-extracted video timestamps with external GPS logs to precisely geolocate each detected pothole, enriching detections with comprehensive metadata, including road segment attribution and contractor information managed through an optimized backend database. iWatchRoadv2 introduces intelligent governance features that enable authorities to link road segments with contract metadata through a secure login interface. The system automatically sends alerts to contractors and officials when road health deteriorates, supporting automated accountability and warranty enforcement. The intuitive web interface delivers actionable analytics to stakeholders and the public, facilitating evidence-driven repair planning, budget allocation, and quality assessment. Our cost-effective and scalable solution streamlines frame processing and storage while supporting seamless public engagement for urban and rural deployments. By automating the complete pothole monitoring lifecycle, from detection to repair verification, iWatchRoadv2 enables data-driven smart city management, transparent governance, and sustainable improvements in road infrastructure maintenance. The platform and live demonstration are accessible at this https URL.

In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential in the dimension, resulting in inefficient algorithms for practical use. While recent results achieve efficient algorithms for product distributions with significantly smaller sample complexity, no efficient algorithm is expected when the marginals are not independent. We initialize the study of conditional sampling in the multidimensional setting. We propose a subcube conditional sampling model where the tester can condition on an (adaptively) chosen subcube of the domain. Due to its simplicity, this model is potentially implementable in many practical applications, particularly when the distribution is a joint distribution over $\Sigma^n$ for some set $\Sigma$. We present algorithms for various fundamental properties of distributions in the subcube-conditioning model and prove that the sample complexity is polynomial in the dimension $n$ (and not exponential as in the traditional model). We present an algorithm for testing identity to a known distribution using $\tilde{\mathcal{O}}(n^2)$-subcube-conditional samples, an algorithm for testing identity between two unknown distributions using $\tilde{\mathcal{O}}(n^5)$-subcube-conditional samples and an algorithm for testing identity to a product distribution using $tilde{\mathcal{O}}(n^5)$-subcube-conditional samples. The central concept of our technique involves an elegant chain rule which can be proved using basic techniques of probability theory yet powerful enough to avoid the curse of dimensionality.

We study the \emph{order-finding problem} for Read-once Oblivious Algebraic Branching Programs (ROABPs). Given a polynomial $f$ and a parameter $w$, the goal is to find an order $\sigma$ in which $f$ has an ROABP of \emph{width} $w$. We show that this problem is NP-hard in the worst case, even when the input is a constant degree polynomial that is given in its dense representation. We provide a reduction from CutWidth to prove these results. Owing to the exactness of our reduction, all the known results for the hardness of approximation of Cutwidth also transfer directly to the order-finding problem. Additionally, we also show that any constant-approximation algorithm for the order-finding problem would imply a polynomial time approximation scheme (PTAS) for it. On the algorithmic front, we design algorithms that solve the order-finding problem for generic ROABPs in polynomial time, when the width $w$ is polynomial in the individual degree $d$ of the polynomial $f$. That is, our algorithm is efficient for most/random ROABPs, and requires more time only on a lower-dimensional subspace (or subvariety) of ROABPs. Even when the individual degree is constant, our algorithm runs in time $n^{O(\log w)}$ for most/random ROABPs. This stands in strong contrast to the case of (Boolean) ROBPs, where only heuristic order-finding algorithms are known.

Pure spin current based research is mostly focused on ferromagnet (FM)/heavy metal (HM) system. Because of the high spin orbit coupling (SOC) these HMs exhibit short spin diffusion length and therefore possess challenges for device application. Low SOC (elements of light weight) and large spin diffusion length make the organic semiconductors (OSCs) suitable for future spintronic applications. From theoretical model it is explained that, due to $\pi$ - $\sigma$ hybridization the curvature of the C$_{60}$ molecules may increase the SOC strength. Here, we have investigated spin pumping and inverse spin hall effect (ISHE) in CoFeB/C$_{60}$ bilayer system using coplanar wave guide based ferromagnetic resonance (CPW-FMR) set-up. We have performed angle dependent ISHE measurement to disentangle the spin rectification effects for example anisotropic magnetoresistance, anomalous Hall effect etc. Further, effective spin mixing conductance (g$_{eff}^{\uparrow\downarrow}$) and spin Hall angle ($\theta_{SH}$) for C$_{60}$ have been reported here. The evaluated value for $\theta_{SH}$ is 0.055.

In this paper, we study two generalizations of Vertex Cover and Edge Cover, namely Colorful Vertex Cover and Colorful Edge Cover. In the Colorful Vertex Cover problem, given an $n$-vertex edge-colored graph $G$ with colors from $\{1, \ldots, \omega\}$ and coverage requirements $r_1, r_2, \ldots, r_\omega$, the goal is to find a minimum-sized set of vertices that are incident on at least $r_i$ edges of color $i$, for each $1 \le i \le \omega$, i.e., we need to cover at least $r_i$ edges of color $i$. Colorful Edge Cover is similar to Colorful Vertex Cover, except here we are given a vertex-colored graph and the goal is to cover at least $r_i$ vertices of color $i$, for each $1 \le i \le \omega$, by a minimum-sized set of edges. These problems have several applications in fair covering and hitting of geometric set systems involving points and lines that are divided into multiple groups. Here, fairness ensures that the coverage (resp. hitting) requirement of every group is fully satisfied. We obtain a $(2+\epsilon)$-approximation for the Colorful Vertex Cover problem in time $n^{O(\omega/\epsilon)}$. Thus, for a constant number of colors, the problem admits a $(2+\epsilon)$-approximation in polynomial time. Next, for the Colorful Edge Cover problem, we design an $O(\omega n^3)$ time exact algorithm, via a chain of reductions to a matching problem. For all intermediate problems in this chain of reductions, we design polynomial-time algorithms, which might be of independent interest.

The purpose of this article is to present a pedagogical review of T-dualityin in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, $T^d$. The known results are reviewed to elucidate that equations of motion for the compact coordinates are $O(d,d)$ covariant, $d$ being the number of compact directions. Next, the vertex operators of excited massive levels are considered in a simple compactification scheme. It is shown that the vertex operators for each massive level can be cast in a T-duality invariant form in such a case. Subsequently, the duality properties of superstring is investigated in the NSR formulation for the massless backgrounds such as graviton and antisymmetric tensor. The worldsheet superfield formulation is found to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields are $O(d,d)$ covariant when the backgrounds are independent of superfields along compact directions. The vertex operators for excited levels are presented in the NS-NS sector and it is shown that they can be cast in T-duality invariant form for the case of Hassan-Sen compactification scheme. An illustrative example is presented to realize our proposal.

The independence polynomial of a graph $G$ is the generating polynomial corresponding to its independent sets of different sizes. More formally, if $a_k(G)$ denotes the number of independent sets of $G$ of size $k$ then $$I(G,z) \as \sum_{k}^{} (-1)^k a_k(G) z^k.$$ The study of evaluating $I(G,z)$ has several deep connections to problems in combinatorics, complexity theory and statistical physics. Consequently, the roots of the independence polynomial have been studied in detail. In particular, many works have provided regions in the complex plane that are devoid of any roots of the polynomial. One of the first such results showed a lower bound on the absolute value of the smallest root $\beta(G)$ of the polynomial. Furthermore, when $G$ is connected, Goldwurm and Santini established that $\beta(G)$ is a simple real root of $I(G,z)$ smaller than one. An alternative proof was given by Csikvári. Both proofs do not provide a gap from $\beta(G)$ to the smallest absolute value amongst all the other roots of $I(G,z)$. In this paper, we quantify this gap.

In CRYPTO 2018, Russell et al introduced the notion of crooked indifferentiability to analyze the security of a hash function when the underlying primitive is subverted. They showed that the $n$-bit to $n$-bit function implemented using enveloped XOR construction (\textsf{EXor}) with $3n+1$ many $n$-bit functions and $3n^2$-bit random initial vectors (iv) can be proven secure asymptotically in the crooked indifferentiability setting. -We identify several major issues and gaps in the proof by Russel et al, We show that their proof can achieve security only when the adversary is restricted to make queries related to a single message. - We formalize new technique to prove crooked indifferentiability without such restrictions. Our technique can handle function dependent subversion. We apply our technique to provide a revised proof for the \textsf{EXor} construction. - We analyze crooked indifferentiability of the classical sponge construction. We show, using a simple proof idea, the sponge construction is a crooked-indifferentiable hash function using only $n$-bit random iv. This is a quadratic improvement over the {\sf EXor} construction and solves the main open problem of Russel et al.

In this article, we demonstrate how a 3-point correlation function can capture the out-of-time-ordered features of a higher point correlation function, in the context of a conformal field theory (CFT) with a boundary, in two dimensions. Our general analyses of the analytic structures are independent of the details of the CFT and the operators, however, to demonstrate a Lyapunov growth we focus on the Virasoro identity block in large-c CFT's. Motivated by this, we also show that the phenomenon of pole-skipping is present in a 2-point correlation function in a two-dimensional CFT with a boundary. This pole-skipping is related, by an analytic continuation, to the maximal Lyapunov exponent for maximally chaotic systems. Our results hint that, the dynamical content of higher point correlation functions, in certain cases, may be encrypted within low-point correlation functions, and analytic properties thereof.

Considering ground state of a quantum spin model as the initial state of the quantum battery, we show that both ordered and disordered interaction strengths play a crucial role to increase the extraction of power from it. In particular, we demonstrate that exchange interactions in the xy-plane and in the z-direction, leading to the XYZ spin chain, along with local charging field in the x-direction substantially enhance the efficiency of the battery compared to the model without interactions. Moreover, such an advantage in power obtained due to interactions is almost independent of the system size. We find that the behavior of the power, although measured during dynamics, can faithfully mimic the equilibrium quantum phase transitions present in the model. We observe that with the proper tuning of system parameters, initial state prepared at finite temperature can generate higher power in the battery than that obtained with zero-temperature. Finally, we report that defects or impurities, instead of reducing the performance, can create larger amount of quenched averaged power in the battery in comparison with the situation when the initial state is produced from the spin chain without disorder, thereby showing the disorder-induced order in dynamics.

Understanding the basic physics related to archetypal lithium battery material (such as LiCo$_y$Mn$_{2-y}$O$_{4}$) is of considerable interest and is expected to aid designing of cathodes of high capacity. The relation between electrochemical performance, activated-transport parameters, thermal expansion, and cooperativity of electron-phonon-interaction distortions in LiCo$_y$Mn$_{2-y}$O$_{4}$ is investigated. The first order cooperative-normal-mode transition, detected through coefficient of thermal expansion, is found to disappear at a critical doping ($y \sim 0.16$); interestingly, for $y \gtrsim 0.16$ the resistivity does not change much with doping and the electrochemical capacity becomes constant over repeated cycling. The critical doping $y \sim 0.16$ results in breakdown of the network of cooperative/coherent normal-mode distortions; this leads to vanishing of the first-order transition, establishment of hopping channels with lower resistance, and enhancing lithiation and delithiation of the battery, thereby minimizing electrochemical capacity fading.

We present a method that generalises the standard mean field theory of correlated lattice bosons to include amplitude and phase fluctuations of the $U(1)$ field that induces onsite particle number mixing. This arises formally from an auxiliary field decomposition of the kinetic term in a Bose Hubbard model. We solve the resulting problem, initially, by using a classical approximation for the particle number mixing field and a Monte Carlo treatment of the resulting bosonic model. In two dimensions we obtain $T_c$ scales that dramatically improve on mean field theory and are within about 20% of full quantum Monte Carlo estimates. The `classical approximation' ground state, however, is still mean field, with an overestimate of the critical interaction, $U_c$, for the superfluid to Mott transition. By further including low order quantum fluctuations in the free energy functional we improve significantly on the $U_c$, and the overall thermal phase diagram. The classical approximation based method has a computational cost linear in system size. The methods readily generalise to multispecies bosons and the presence of traps.

We report the temperature and magnetic field dependence of resistivity ($\rho$) for single-crystalline EuTi$_{1-x}$Nb$_{x}$O$_3$ ($x$=0.10$-$0.20), an itinerant ferromagnetic system with very low Curie temperature ($T_C$). The detailed analysis reveals that the charge conduction in EuTi$_{1-x}$Nb$_{x}$O$_3$ is extremely sensitive to Nb concentration and dominated by several scattering mechanisms. Well below the $T_C$, where the spontaneous magnetization follows the Bloch's $T^{3/2}$ law, $\rho$ exhibits $T^2$ dependence with a large coefficient $\sim$10$^{-8}$ $\Omega$ cm K$^{-2}$ due to the electron-magnon scattering. Remarkably, all the studied samples exhibit a unique resistivity minimum at $T$$=$$T_{\rm min}$ below which $\rho$ shows logarithmic increment with $T$ (for $T_{\rm C}$<$T$<$T_{\rm min}$) due to the Kondo scattering of Nb 4$d^1$ itinerant electrons by the localized 4$f$ moments of Eu$^{2+}$ ions which suppresses strongly with applied magnetic field. In the paramagnetic state, $T^{2}$ and $T^{3/2}$ dependence of the resistivity have been observed, suggesting an unusual crossover from a Fermi-liquid to a non-Fermi-liquid behavior with increasing $T$. The observed temperature and magnetic field dependence of resistivity has been analysed using different theoretical models.

We study the infrared (IR) structure of $SU(N) \times U(1)$ (QCD $\times$ QED) gauge theory with $n_f$ quarks and $n_l$ leptons within the framework of perturbation theory. In particular, we unravel the IR structure of the form factors and inclusive real emission cross sections that contribute to inclusive production of color neutral states, such as a pair of leptons or single W/Z in Drell-Yan processes and a Higgs boson in bottom quark annihilation, in Large Hadron Collider (LHC) in the threshold limit. Explicit computation of the relevant form factors to third order and the use of Sudakov's $K+G$ equation in $SU(N)\times U(1)$ gauge theory demonstrate the universality of the cusp anomalous dimensions ($A_I , I = q, b$). The abelianization rules that relate $A_I$ of $SU(N)$ with those from $U(1)$ and $SU(N)\times U(1)$ can be used to predict the soft distribution that results from the soft gluon emission subprocesses in the threshold limit. Using the latter and the third order form factors, we can obtain the collinear anomalous dimensions ($B_I$ ) and the renormalisation constant $Z_b$ to third order in perturbation theory. The form factors, the process independent soft distribution functions can be used to predict fixed and resummed inclusive cross sections to third order in couplings and in leading logarithmic approximation respectively.

One of the outstanding problems in Iron pnictide research is the unambiguous detection of its pairing symmetry. The most probable candidates are the two-band s$++$ and sign reversed s$\pm$ wave pairing. In this work, the Andreev conductance and shot noise are used as a probe for the pairing symmetry of Iron pnictide superconductors. Clear differences emerge in both the zero bias differential conductance and the shot noise in the tunneling limit for the two cases enabling an effective distinction between the two.

We report dynamical quantum phase transition portrait in the alternating field transverse XY spin chain with Dzyaloshinskii-Moriya interaction by investigating singularities in the Loschmidt echo and the corresponding rate function after a sudden quench of system parameters. Unlike the Ising model, the analysis of Loschmidt echo yields non-uniformly spaced transition times in this model. Comparative study between the equilibrium and the dynamical quantum phase transitions in this case reveals that there are quenches where one occurs without the other, and the regimes where they co-exist. However, such transitions happen only when quenching is performed across at least a single gapless or critical line. Contrary to equilibrium phase transitions, bipartite entanglement measures do not turn out to be useful for the detection, while multipartite entanglement emerges as a good identifier of this transition when the quench is done from a disordered phase of this model.

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing

A ferromagnetic Josephson junction with a spin-flipper (magnetic impurity) sandwiched in-between acts as a phase battery that can store quantized amounts of superconducting phase difference $\Phi_0$ in the ground state of the junction. Moreover, for such $\Phi_0$-Josephson junction anomalous Josephson current appears at zero phase difference. We study the properties of this quantum spin-flip scattering induced anomalous Josephson current, especially its tun-ability via misorientation angle between two Ferromagnets.

We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of sub-unit norm, where the estimator is the commutator of the observable and its incoherent or classical part. The relation provides a direct method of obtaining an estimate of the quantum coherence of an arbitrary quantum state, without resorting to quantum state tomography or the existing witness operators.

We first show a counter intuitive result that in the ring of real valued continuous functions on $[0,1]$ non maximal prime ideals exist. This is a standard proof and a well known result. Interestingly, a non maximal prime ideal in this ring is actually contained inside a unique maximal ideal. We arrive at this result merely by looking at the zero set of ideals in this ring and by making simple geometrical observations. We end by leaving the reader with an interesting open problem that logically follows from this article.