Search

Remote epitaxy has garnered considerable attention as a promising method that facilitates the growth of thin films that replicate the crystallographic characteristics of a substrate by utilizing two-dimensional (2D) material interlayers like graphene. The resulting film can be exfoliated to form a freestanding membrane, and the substrate, if expensive, can be reused. However, atomically thin 2-D materials are susceptible to damage before and during film growth in the chamber, leading to a poor epitaxy. Oxide remote epitaxy using graphene, the most commonly available 2D material, is particularly challenging because the conventional conditions employed for the growth of epitaxial oxides also degrade graphene. In this study, we show for the first time that a direct correlation exists between the microstructure of graphene, its getting defective on exposure to the pulsed laser deposition plume, and the crystalline quality of the barium titanate film deposited on top. A controlled aperture method was used to reduce graphene damage. Even so, the degree of damage is more at the graphene grain boundaries than within the grains. Large grain-sized greater than 300 microns, graphene suffered less damage and yielded a film comparable to that grown directly on a strontium titanate substrate with a rocking curve half width of 0.6 degrees. Using large grain-sized bi-layer graphene, 4 mm x 5 mm oxide layers were successfully exfoliated and transferred onto SiOx-Si. These insights pave the way for the heterogeneous integration of functional oxides on foreign substrates, holding significant implications for commercializing perovskite oxides by integrating them with Si-CMOS and flexible electronics., Comment: 36 pages, 18 figures

Resistive Plate Chamber (RPC) is one of the most commonly used detectors in high energy physics experiments for triggering and tracking because of its good efficiency ($\textgreater$~90\%) and time resolution ($\sim$~1-2~ns). Generally, the bakelite which is one of the most commonly used materials used as electrode plates in RPC, sometimes suffer from surface roughness issues. If the surface is not smooth, the micro discharge probability and spurious pulses increase, which leads to the deterioration in the performance of the detector. We have developed a new method of linseed oil coating for the bakelite based detectors to avoid the surface roughness issue. The detector is characterised with Tetrafluoroethane based gas mixture. The detector is also tested with a high rate of gamma radiation environment in the lab for the radiation hardness test. The detailed measurement procedure and test results are presented in this article., Comment: 12 pages, 10 figures

Blazars, the peculiar class of active galactic nuclei (AGN), are known to show flux variations across the accessible electromagnetic spectrum. Though they have been studied extensively for their flux variability characteristics across wavelengths, information on their ultraviolet (UV) flux variations on time scales of hours is very limited. Here, we present the first UV flux variability study on intraday time scales of a sample of 10 blazars comprising 2 flat spectrum radio quasars (FSRQs) and 8 BL Lacertae objects (BL Lacs). These objects, spanning a redshift (z) range of 0.034 <= z <= 1.003, were observed in the far-UV (FUV: 1300 - 1800 \text{\AA}) and near-UV (NUV: 2000 - 3000 \text{\AA}) wavebands using the ultraviolet imaging telescope on board AstroSat. UV flux variations on time scales of hours were detected in 9 sources out of the observed 10 blazars. The spectral variability analysis showed a bluer-when-brighter trend with no difference in the UV spectral variability behavior between the studied sample of FSRQs and BL Lacs. The observed UV flux and spectral variability in our sample of both FSRQs and BL Lacs revealed that the observed UV emission in them is dominated by jet synchrotron process., Comment: 23 pages, 5 figures, 6 tables; accepted for publication in The Astrophysical Journal

The computationally cheap machine learning architecture of random feature maps can be viewed as a single-layer feedforward network in which the weights of the hidden layer are random but fixed and only the outer weights are learned via linear regression. The internal weights are typically chosen from a prescribed distribution. The choice of the internal weights significantly impacts the accuracy of random feature maps. We address here the task of how to best select the internal weights. In particular, we consider the forecasting problem whereby random feature maps are used to learn a one-step propagator map for a dynamical system. We provide a computationally cheap hit-and-run algorithm to select good internal weights which lead to good forecasting skill. We show that the number of good features is the main factor controlling the forecasting skill of random feature maps and acts as an effective feature dimension. Lastly, we compare random feature maps with single-layer feedforward neural networks in which the internal weights are now learned using gradient descent. We find that random feature maps have superior forecasting capabilities whilst having several orders of magnitude lower computational cost.

We demonstrate a micropatterned directional emitter ({\mu}DE) with an ultrabroadband, azimuthally selective and tailorable emittance across the thermal wavelengths and over wide angles. The {\mu}DE can enable a novel and passive seasonal thermoregulation of buildings by reducing summertime terrestrial radiative heat gain, and wintertime loss. We show several types of {\mu}DE, such as metallic and white variants, made using low-cost materials and scalable manufacturing techniques that are already in large-scale use. Furthermore, we show that its directional emittance can be geometrically tailored to sky-view factors in different urban scenarios. Outdoor experiments show that {\mu}DEs stay up to 1.53{\deg}C cooler than traditional building envelopes when exposed to direct sunlight on summer days and up to 0.46{\deg}C warmer during winter nights. Additionally, {\mu}DEs demonstrate significant cooling powers of up to 40 Wm-2 in warm conditions and heating powers of up to 30 Wm-2 in cool conditions, relative to typical building envelopes. Building energy models show that {\mu}DEs can achieve all-season energy savings similar to or higher than those of cool roofs. Collectively, our findings show {\mu}DEs as highly promising for thermoregulating buildings.

We consider the renormalization group equations within the Standard Model Effective Field Theory and compute two-loop contributions proportional to the top quark Yukawa coupling for the operator generating an effective Higgs-gluon coupling, focusing on the Yukawa-like operator. These two-loop running effects are relevant for processes where the effective Higgs-gluon coupling contributes at a lower loop order compared to the Standard Model contribution and where a dynamical scale choice is adopted. Such a situation arises, for instance, in the Higgs transverse momentum distribution and Higgs pair production. We investigate the phenomenological impact of our computations on these two processes and find that the two-loop contributions are significant and can lead to deviations of up to 20\% in the scenarios we consider.

In our investigation, we pioneer the development of geometrically deformed strange stars within the framework of $f(\mathcal{T})$ gravity theory through gravitational decoupling via the complete geometric deformation (CGD) technique. The significant finding is the precise solution for deformed strange star (SS) models achieved through the vanishing complexity factor scenario. Further, we introduce the concept of space-time deformation caused by dark matter (DM) content in DM haloes, leading to perturbations in the metric potentials $g_{tt}$ and $g_{rr}$ components. Mathematically, this DM-induced deformation is achieved through the CGD method, where the decoupling parameter $\alpha$ governs the extent of DM influence. To validate our findings, we compare our model predictions with observational constraints, including GW190814 (with a mass range of $2.5-2.67 M_{\odot}$) and neutron stars (NSTRs) such as EXO 1785-248 [mass=$1.3_{-0.2}^{+0.2}~M_{\odot}$], 4U 1608-52 [mass=$1.74_{-0.14}^{+0.14}~M_{\odot}$], and PSR J0952-0607 [mass=$2.35_{-0.17}^{+0.17}~M_{\odot}$]. Our investigation delves into the stability of the model by considering causality conditions, Herrera's Cracking Method, the adiabatic index, and the Harrison-Zeldovich-Novikov criterion. We demonstrate that the developed model mimics a wide range of recently observed pulsars. To emphasize its compatibility, we highlight the predicted mass and radius in tabular form by varying both the parameters $\alpha$ and $\zeta_1$. Notably, our findings are consistent with the observation of gravitational waves from the first binary merger event. Furthermore, we compare our results with those obtained for a slow-rotating configuration. In addition to this, we discuss the moment of inertia using the Bejger-Haensel approach in this formulation., Comment: 22 pages, 10 figures. Comments are welcome

We investigate the nature of the linear-response tensors in planar Hall and planar thermal Hall setups, where we subject a Rarita-Schwinger-Weyl (RSW) semimetal to the combined influence of an electric field $\mathbf E $ (and/or temperature gradient $\nabla_{\mathbf r } T$) and a weak (i.e., non-quantizing) magnetic field $\mathbf B $. For computing the in-plane transport components, we have added an elastic deformation which gives rise to a chirality-dependent effective magnetic field $ \mathbf B^{\text{tot}} = \mathbf B + \chi \, \mathbf B_5 $, where $\chi $ is the chirality of an RSW node. We have included the effects of orbital magnetic moment (OMM), in conjunction with the Berry curvature (BC), both of which appear as a consequence of nontrivial topology of the bandstructure. Due to the presence of four bands, RSW semimetals provide a richer structure for obtaining the linear-response coefficients, compared to the Weyl semimetals. In particular, we have found that the OMM-contributed terms may oppose or add up to the BC-only parts, depending on which band we are considering. We have also considered the response arising from internode scatterings. Last, but not the least, we have determined the out-of-plane response comprising the intrinsic anomalous Hall and the Lorentz-force-contributed currents, whose nature corroborates the findings of some recent experimental results., Comment: 27 pages, 9 figures

A ring $S(X,\mathcal{A})$ of real valued $\mathcal{A}$-measurable functions defined over a measurable space $(X,\mathcal{A})$ is called a $\chi$-ring if for each $E\in \mathcal{A} $, the characteristic function $\chi_{E}\in S(X,\mathcal{A})$. The set $\mathcal{U}_X$ of all $\mathcal{A}$-ultrafilters on $X$ with the Stone topology $\tau$ is seen to be homeomorphic to an appropriate quotient space of the set $\mathcal{M}_X$ of all maximal ideals in $S(X,\mathcal{A})$ equipped with the hull-kernel topology $\tau_S$. It is realized that $(\mathcal{U}_X,\tau)$ is homeomorphic to $(\mathcal{M}_S,\tau_S)$ if and only if $S(X,\mathcal{A})$ is a Gelfand ring. It is further observed that $S(X,\mathcal{A})$ is a Von-Neumann regular ring if and only if each ideal in this ring is a $\mathcal{Z}_S$-ideal and $S(X,\mathcal{A})$ is Gelfand when and only when every maximal ideal in it is a $\mathcal{Z}_S$-ideal. A pair of topologies $u_\mu$-topology and $m_\mu$-topology, are introduced on the set $S(X,\mathcal{A})$ and a few properties are studied.

A graph is called claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph $K_{1, 3}$. The undirected power graph of a group $G$ has vertices the elements of $G$, with an edge between $g_1$ and $g_2$ if one of the two cyclic subgroups $\langle g_1\rangle, \langle g_2\rangle$ is contained in the other. It is denoted by $P(G)$. The reduced power graph, denoted by $P^*(G),$ is the subgraph of $P(G)$ induced by the non-identity elements. The main purpose of this paper is to explore the finite groups whose reduced power graph is claw-free. In particular we prove that if $P^*(G)$ is claw-free, then either $G$ is solvable or $G$ is an almost simple group. In the second case the socle of $G$ is isomorphic to $PSL(2,q)$ for suitable choices of $q$. Finally we prove that if $P^*(G)$ is claw-free, then the order of $G$ is divisible by at most 5 different primes.

Sampling is frequently used to collect data from large networks. In this article we provide valid asymptotic prediction intervals for subgraph counts and clustering coefficient of a population network when a network sampling scheme is used to observe the population. The theory is developed under a model based framework, where it is assumed that the population network is generated by a Stochastic Block Model (SBM). We study the effects of induced and ego-centric network formation, following the initial selection of nodes by Bernoulli sampling, and establish asymptotic normality of sample based subgraph count and clustering coefficient statistic under both network formation methods. The asymptotic results are developed under a joint design and model based approach, where the effect of sampling design is not ignored. In case of the sample based clustering coefficient statistic, we find that a bias correction is required in the ego-centric case, but there is no such bias in the induced case. We also extend the asymptotic normality results for estimated subgraph counts to a mildly sparse SBM framework, where edge probabilities decay to zero at a slow rate. In this sparse setting we find that the scaling and the maximum allowable decay rate for edge probabilities depend on the choice of the target subgraph. We obtain an expression for this maximum allowable decay rate and our results suggest that the rate becomes slower if the target subgraph has more edges in a certain sense. The simulation results suggest that the proposed prediction intervals have excellent coverage, even when the node selection probability is small and unknown SBM parameters are replaced by their estimates. Finally, the proposed methodology is applied to a real data set., Comment: 85 pages, 4 figures

We report an ultrahigh pyroelectric response in van der Waals bonded layers of two-dimensional (2D) tellurium (Te) nanosheets (thickness, d = 4 to 5 nm) at periodic on-off temperature oscillations. For the first time a large pyroelectric coefficient, Pc ~ 3 mC.m-2.K-1, is observed which is eightfold higher than the traditional state-of-the-art pyroelectrics (lead zirconate titanate, PZT). The first-principles calculations point out that the breakdown of centro-symmetry in the 1-3 Te-layers (P-3m1 space group) of a non-centrosymmetry (higher-order symmetry of C2 space group) on an angular twist in the Te-Te bonds of an exotic electronic state in 2D Te. The angular Te-Te twisting elicits a surface-enhanced Raman band at 101 cm-1 (absent in bulk Te). The stimulation of the Born effective charge, in-plane piezoelectricity and thermal expansion coefficient are shown to tailor the large pyroelectricity. Thus, 2D Te nanosheets present a new paradigm for the wide application of pyroelectric materials for developing thermal energy-based flexible electronics., Comment: Research Article

Anomaly detection in computational workflows is critical for ensuring system reliability and security. However, traditional rule-based methods struggle to detect novel anomalies. This paper leverages large language models (LLMs) for workflow anomaly detection by exploiting their ability to learn complex data patterns. Two approaches are investigated: 1) supervised fine-tuning (SFT), where pre-trained LLMs are fine-tuned on labeled data for sentence classification to identify anomalies, and 2) in-context learning (ICL) where prompts containing task descriptions and examples guide LLMs in few-shot anomaly detection without fine-tuning. The paper evaluates the performance, efficiency, generalization of SFT models, and explores zero-shot and few-shot ICL prompts and interpretability enhancement via chain-of-thought prompting. Experiments across multiple workflow datasets demonstrate the promising potential of LLMs for effective anomaly detection in complex executions., Comment: 12 pages, 14 figures, paper is accepted by SC'24, source code, see: https://github.com/PoSeiDon-Workflows/LLM_AD

Modular architectures are a promising approach to scale quantum devices to the point of fault tolerance and utility. Modularity is particularly appealing for superconducting qubits, as monolithically manufactured devices are limited in both system size and quality. Constructing complex quantum systems as networks of interchangeable modules can overcome this challenge through `Lego-like' assembly, reconfiguration, and expansion, in a spirit similar to modern classical computers. First prototypical superconducting quantum device networks have been demonstrated. Interfaces that simultaneously permit interchangeability and high-fidelity operations remain a crucial challenge, however. Here, we demonstrate a high-efficiency interconnect based on a detachable cable between superconducting qubit devices. We overcome the inevitable loss in a detachable connection through a fast pump scheme, enabling inter-module SWAP efficiencies at the 99%-level in less than 100 ns. We use this scheme to generate high-fidelity entanglement and operate a distributed logical dual-rail qubit. At the observed ~1% error rate, operations through the interconnect are at the threshold for fault-tolerance. These results introduce a modular architecture for scaling quantum processors with reconfigurable and expandable networks., Comment: 15 pages, 9 figures, 1 table

A key challenge in citation text generation is that the length of generated text often differs from the length of the target, lowering the quality of the generation. While prior works have investigated length-controlled generation, their effectiveness depends on knowing the appropriate generation length. In this work, we present an in-depth study of the limitations of predicting scientific citation text length and explore the use of heuristic estimates of desired length.

Extreme edge-AI systems, such as those in readout ASICs for radiation detection, must operate under stringent hardware constraints such as micron-level dimensions, sub-milliwatt power, and nanosecond-scale speed while providing clear accuracy advantages over traditional architectures. Finding ideal solutions means identifying optimal AI and ASIC design choices from a design space that has explosively expanded during the merger of these domains, creating non-trivial couplings which together act upon a small set of solutions as constraints tighten. It is impractical, if not impossible, to manually determine ideal choices among possibilities that easily exceed billions even in small-size problems. Existing methods to bridge this gap have leveraged theoretical understanding of hardware to f architecture search. However, the assumptions made in computing such theoretical metrics are too idealized to provide sufficient guidance during the difficult search for a practical implementation. Meanwhile, theoretical estimates for many other crucial metrics (like delay) do not even exist and are similarly variable, dependent on parameters of the process design kit (PDK). To address these challenges, we present a study that employs intelligent search using multi-objective Bayesian optimization, integrating both neural network search and ASIC synthesis in the loop. This approach provides reliable feedback on the collective impact of all cross-domain design choices. We showcase the effectiveness of our approach by finding several Pareto-optimal design choices for effective and efficient neural networks that perform real-time feature extraction from input pulses within the individual pixels of a readout ASIC., Comment: 18 pages, 17 figures

Eylee Jung \textit{et.al}\cite{jung2008} had conjectured that $P_{max}=\frac{1}{2}$ is a necessary and sufficient condition for the perfect two-party teleportation and consequently the Groverian measure of entanglement for the entanglement resource must be $\frac{1}{\sqrt{2}}$. It is also known that prototype $W$ state is not useful for standard teleportation. Agrawal and Pati\cite{pati2006} have successfully executed perfect (standard) teleportation with non-prototype $W$ state. Aligned with Pati's protocol\cite{pati2006} we have considered here $Star$ type tripartite states and have shown that perfect teleportation is suitable with such states. Moreover, we have taken the linear superposition of non-prototype $W$ state and its spin-flipped version and shown that it belongs to $Star$ class. Also, standard teleportation is possible with these states. It is observed that genuine tripartite entanglement is not necessary requirement for a state to be used as a channel for successful standard teleportation. We have also shown that these $Star$ class states are $P_{max}=\frac{1}{4}$ states and their Groverian entanglement is $\frac{\sqrt{3}}{2}$, thus concluding that Jung conjecture is not a necessary condition.

Let $k$ be a complete ultrametric valued field. Let u($k$) (resp. u_s($k$)) denote the u-invariant (resp. the strong u-invariant) of $k$. We give a description of this invariant for $k$ in terms of the u-invariant (resp. the strong u-invariant) of its residue field. Let $C$ be a curve over $k$ and $F$ = $k(C)$. We prove similar results for the u-invariant of $F$. For $l$ a prime away from the characteristic of the residue field of $k$, we obtain bounds for the Brauer-$l$-dimensions of $k$ and $F$.

We investigate the emergence of a non-Fermi liquid (NFL) at a putative quantum critical point signalling the onset of superradiance, in a set-up involving cavity quantum electrodynamics. Although the finiteness of the cavity, being bounded by reflecting mirrors, endows the cavity photons with an effective mass, they become massless at the continuous phase transition point. We consider the matter part coming from the fermions hopping on a honeycomb lattice near half-filling, featuring doped Dirac cones at two sets of inequivalent valleys. This choice is dictated by the presence of a fermion-boson interaction vertex which can give rise to Landau damping of the critical bosons, eventually leading to an NFL phase for the fermions. To set up the quantum effective action, we identify the hot spots of the generically anisotropic (trigonally-warped) Fermi surfaces, which are the set of points having parallel/antiparallel tangent vectors. The cavity photons act as charge density wave (CDW) order parameters, connecting pairs of hot spots belonging to the Fermi surface of a single valley. With these ingredients, we have set upon identifying NFL phases, using the tools of dimensional regularization and renormalization-group-flow equations. Our final results indicate that stable NFL phases exist in the low-energy limit, for the projections of the flows along the CDW coupling constant., Comment: sign of velocities at hot spots corrected; a different CDW variation of arXiv:2403.02322

The finite momentum superconducting pairing states (FMPs), where Cooper pairs carry non-zero momentum, are believed to give rise to exotic physical phenomena including the pseudogap phase of cuprate high-Tc superconductors and Majorana fermions in topological superconductivity. FMPs can emerge in intertwined electronic liquids with strong spin-spin interactions or be induced by lifting the spin degeneracy under magnetic field as originally proposed by Fulde-Ferrell and Larkin-Ovchinnikov. In quantum materials with strong Ising-type spin-orbit coupling, such as the 2D transition metal dichalcogenides (TMDs), the spin degree of freedom is frozen enabling novel orbital driven FMPs via magnetoelectric effect. While evidence of orbital driven FMPs has been revealed in bilayer TMDs, its realization in 3D bulk materials remains an unresolved challenge. Here we report experimental signatures of FMP in a locally noncentrosymmetric bulk superconductor 4Hb-TaS2. Using hard X-ray diffraction and angle-resolved photoemission spectroscopy, we reveal unusual 2D chiral charge density wave (CDW) and weak interlayer hopping in 4Hb-TaS2. Below the superconducting transition temperature, the upper critical field, Hc2, linearly increases via decreasing temperature, and well exceeds the Pauli limit, thus establishing the dominant orbital pair-breaking mechanism. Remarkably, we discover a field-induced superconductivity-to-superconductivity transition that breaks continuous rotational symmetry of the s-wave uniform pairing in the Bardeen-Cooper-Schrieffer theory down to the six-fold rotation symmetry. Combining with a Ginzburg-Landau free energy analysis that incorporates magnetoelectric effect, our observations provide strong evidence of orbital driven FMP in the 3D quantum heterostructure 4Hb-TaS2.

We study uniform $\epsilon-$BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of $\epsilon,$ many geometric properties like smoothness, norm attainment and extremality of operators are preserved under such approximations. We present examples of pairs of Banach spaces satisfying non-trivial norm preserving uniform $\epsilon-$BPB approximation property in the global sense. We also study these concepts in case of bounded linear operators between Hilbert spaces. Our approach in the present article leads to the improvement and generalization of some earlier results in this context.

General relativity and quantum field theory govern all fundamental physical processes, from nuclear and subatomic scales to the solar system, galactic, and cosmology. Both theories work remarkably well in their tested domains. However, there is minimal overlap between the two domains. Our work demonstrates that the non-overlapping of domains \emph{no longer} holds when non-perturbative effects are considered. We introduce a novel mechanism in which the gravitons acquire \emph{effective mass} due to the spontaneous symmetry breaking (SSB) of global or local symmetry of complex scalar field minimally coupled to gravity. In the flat space-time limit, we demonstrate that the resulting action for the graviton is identical to the extended Fierz-Pauli (FP) action, corresponding to the mass deformation parameter $\alpha = 1/2$. The extended FP action has 6 Degrees of freedom and no ghost. For local $U(1)$ SSB, we establish that the effective graviton mass is related to the mass of the gauge boson and the electric charge of the complex scalar field. Interestingly, our results indicate that the millicharged dark matter scalar fields, generating dark photons, can produce graviton mass of the same order as the Hubble constant $(H_0)$. Hence, we argue that the dark sector offers a natural explanation for the acceleration of the current Universe., Comment: The key results of the paper are in the first 10 pages. The detailed calculations and other technicalities are deferred to the five Appendices

In recent years, deep reinforcement learning (DRL) approaches have generated highly successful controllers for a myriad of complex domains. However, the opaque nature of these models limits their applicability in aerospace systems and safety-critical domains, in which a single mistake can have dire consequences. In this paper, we present novel advancements in both the training and verification of DRL controllers, which can help ensure their safe behavior. We showcase a design-for-verification approach utilizing k-induction and demonstrate its use in verifying liveness properties. In addition, we also give a brief overview of neural Lyapunov Barrier certificates and summarize their capabilities on a case study. Finally, we describe several other novel reachability-based approaches which, despite failing to provide guarantees of interest, could be effective for verification of other DRL systems, and could be of further interest to the community., Comment: 10 pages, 3 figures

We have studied the effect of nonmagnetic Ti substitution Eu2(Ir1-xTix)2O7 with the help of electrical transport and magnetic measurement. The minor structural modification enhances the orbital overlapping and favours its electrical transport properties with Ti doping though the tuning of SOC and U with site dilution opposes it. As a result, metal insulator transition (MIT) is disappeared and resistivity of the system throughout the temperature increases with Ti doping. The nature of the conduction mechanism at low temperature follows power law like variation. As the Ti4+ is nonmagnetic, the introduction of Ti at Ir site dilutes the magnetic interaction at Ir octahedral network, which in turn decreases the magnetic moment and magnetic frustration in the system though the magnetic irreversibility temperature is hardly affected by Ti.

Perpetual exploration is a fundamental problem in the domain of mobile agents, where an agent needs to visit each node infinitely often. This issue has received lot of attention, mainly for ring topologies, presence of black holes adds more complexity. A black hole can destroy any incoming agent without any observable trace. In \cite{BampasImprovedPeriodicDataRetrieval,KralovivcPeriodicDataRetrievalFirst}, the authors considered this problem in the context of \textit{ Periodic data retrieval}. They introduced a variant of black hole called gray hole (where the adversary chooses whether to destroy an agent or let it pass) among others and showed that 4 asynchronous and co-located agents are essential to solve this problem (hence perpetual exploration) in presence of such a gray hole if each node of the ring has a whiteboard. This paper investigates the exploration of a ring in presence of a ``byzantine black hole''. In addition to the capabilities of a gray hole, in this variant, the adversary chooses whether to erase any previously stored information on that node. Previously, one particular initial scenario (i.e., agents are co-located) and one particular communication model (i.e., whiteboard) are investigated. Now, there can be other initial scenarios where all agents may not be co-located. Also, there are many weaker models of communications (i.e., Face-to-Face, Pebble) where this problem is yet to be investigated. The agents are synchronous. The main results focus on minimizing the agent number while ensuring that perpetual exploration is achieved even in presence of such a node under various communication models and starting positions. Further, we achieved a better upper and lower bound result (i.e., 3 agents) for this problem (where the malicious node is a generalized version of a gray hole), by trading-off scheduler capability, for co-located and in presence of a whiteboard.

Biological microswimmers, like euglena, deform their body shape to swim through tight confinements having length scales comparable to the microswimmer length scale. Recently, it was shown that self-propelling active droplets can also squeeze through tight microconfinements by elongating their shape. However, the evolution of the hydrodynamic signature, or the velocity field, generated by the active droplet, as it deforms its shape to swim through increasingly tight microconfinements, has remained scarcely studied. Using high-resolution fluorescence microscopy and $\mu$-Particle Image Velocimetry (PIV) analysis, we show here that as the swimming active droplet deforms from a spherical shape to a `stadium'-like shape, and eventually to an elongated `capsule'-like shape in increasingly tighter microchannels, its hydrodynamic signature changes from a `pusher'-like velocity field to a `puller'-like velocity field, and finally to an asymmetric velocity field. We characterize such alterations in the active droplet dynamics using the distributions of the local velocity magnitude, axial and transverse components of the local flow velocity, vorticity, and the filled micelle concentration. Finally, we use finite-element based numerical simulations to explain the aforementioned evolution of the velocity field stemming from the underlying physico-chemical hydrodynamics in the presence of a thin lubrication film between the swimming active droplet and the tight microconfinement walls. The present work provides a comprehensive understanding of the chemo-hydrodynamic characteristics of active droplets navigating extreme confined spaces, which can be beneficial for many autonomous cargo-delivery applications.

Let $\nu=(n_1,\ldots, n_s), s\ge 2,$ be a sequence of positive integers and let $n=\sum_{1\le j\le s}n_j$. Let $\mathbb CG(\nu)=U(n)/(U(n_1)\times \cdots\times U(n_s))$ be the complex flag manifold. Denote by $P(m,\nu)=P(\mathbb S^m,\mathbb CG(\nu))$ the generalized Dold manifold $\mathbb S^m\times \mathbb CG(\nu)/\langle \theta\rangle $ where $\theta=\alpha\times \sigma$ with $\alpha:\mathbb S^m\to \mathbb S^m$ being the antipodal map and $\sigma:\mathbb CG(\nu)\to \mathbb CG(\nu)$, the complex conjugation. The manifold $P(m,\nu)$ has the structure of a smooth $\mathbb CG(\nu)$-bundle over the real projective space $\mathbb RP^m.$ We determine the additive structure of $H^*(P(m,\nu);R)$ when $R=\mathbb Z$ and its ring structure when $R$ is a commutative ring in which $2$ is invertible. As an application, we determine the additive structure of $K(P(m,\nu))$ almost completely and also obtain partial results on its ring structure. The results for the singular homology are obtained for generalized Dold spaces $P(S,X)=S\times X/\langle \theta\rangle$, where $\theta=\alpha\times \sigma$, $\alpha:S\to S$ is a fixed point free involution and $\sigma:X\to X$ is an involution with $\mathrm{Fix}(\sigma)\ne \emptyset,$ for a much wider class of spaces $S$ and $X$.

The intermediate scattering function is interpreted as a correlation function of thermal wave packets of the scattering centers perturbed by the scattering particles at different times. A proof of concept is given at the example of ballistic moving centers. The ensuing numerical method is then illustrated at the example of CO adsorbed on Cu(100)., Comment: 8 pages, 2 figures

We investigate dark matter (DM)-electron scattering in a minimal $U(1)_X$ extension of the Standard Model (SM), where the DM can appear as a Majorana fermion, a complex singlet scalar or a Dirac fermion. To study bounds on the $U(1)_X$ gauge coupling $(g_X)$ and new gauge boson mass $(M_{Z^\prime})$, from DM-electron scattering, we consider several direct search experiments like CDMS, DAMIC, SENSEI, PandaX-II, DarkSide-50 and XENON1T-S2 for different $U(1)_X$ charges. In this set-up we consider DM production via freeze-in both in radiation dominated and modified cosmological background to project sensitivities on $g_X-M_{Z^\prime}$ plane satisfying observed relic abundance. DM-electron scattering could provide comparable, or even stronger bounds than those obtained from the electron/ muon $(g-2)$, low energy scattering and intensity frontier experiments within 0.01 GeV $\lesssim M_{Z^\prime} \lesssim$ 0.1 GeV. Constrains from freeze-in could provide stronger sensitivities for $M_{Z^\prime}\gtrsim \mathcal{O}(1)$ GeV, however, these limits are comparable to those obtained from LHCb, LEP experiments for $\mathcal{O}(10)$ GeV $\lesssim M_{Z^\prime} \lesssim 150$ GeV. In future, electron-muon scattering (MUonE), proton (FASER, DUNE) and electron/positron (ILC) beam dump experiments could probe these parameters., Comment: 22 pages, 6 figures

Assistive technology for visually impaired individuals is extremely useful to make them independent of another human being in performing day-to-day chores and instill confidence in them. One of the important aspects of assistive technology is outdoor navigation for visually impaired people. While there exist several techniques for outdoor navigation in the literature, they are mainly limited to obstacle detection. However, navigating a visually impaired person through the sidewalk (while the person is walking outside) is important too. Moreover, the assistive technology should ensure low-energy operation to extend the battery life of the device. Therefore, in this work, we propose an end-to-end technology deployed on an edge device to assist visually impaired people. Specifically, we propose a novel pruning technique for transformer algorithm which detects sidewalk. The pruning technique ensures low latency of execution and low energy consumption when the pruned transformer algorithm is deployed on the edge device. Extensive experimental evaluation shows that our proposed technology provides up to 32.49% improvement in accuracy and 1.4 hours of extension in battery life with respect to a baseline technique., Comment: Accepted for publication in ISLPED'24

We study superconductor-barrier-superconductor (S-B-S) Josephson junctions constructed out of two-dimensional and three-dimensional triple-point semimetals, which feature a threefold degeneracy at a single nodal point. We assume a weak and homogeneous s-wave pairing in each superconducting region, and a potential difference is applied across a piece of normal-state semimetal to create the barrier region. We apply the BdG formalism to compute the wavefunctions of the subgap Andreev bound states (ABSs), considering the thin-barrier limit, in a piecewise-continuous manner. The appropriate boundary conditions at the S-B and B-S junctions allow us to compute the discrete energy eigenvalues $\pm |\varepsilon| $ of the ABSs. We get two distinct solutions for $|\varepsilon| $. This result is different from the S-B-S set-ups in graphene and Weyl semimetals (each featuring twofold-degenerate nodal points), where one obtains only one solution for $|\varepsilon| $. Although the three bands of the triple-point fermions comprise a nondispersive flat band, the multifold nature of the bandstructure is responsible for this difference. We also illustrate the behaviour of the Josephson current flowing across the S-B-S junction, contributed by the two pairs of ABSs., Comment: 13 pages, 3 figures; Follow-up paper of arxiv:2312.16164

This article undertakes an exploration of simple modules of 3-cyclic quantum Weyl algebra at roots of unity. Under the roots of unity assumption, the algebra becomes a Polynomial Identity algebra and the vector space dimension of the simple modules is bounded above by its PI degree. The article systematically classifies all potential simple modules and computes the algebra's center., Comment: 23 pages. Comments are welcomed

In 2009, T. Banica and R. Speicher introduced the orthogonal easy quantum group which can be completely determined using the combinatorics of set partitions. Later, P. Tarrago and M. Weber extended this formulation to another special class of compact matrix quantum groups, known as unitary easy quantum groups, which are quantum subgroups of the free unitary quantum group ($U_n^+$) containing $S_n$. On the other hand, the quantum symmetry of graph $C^{*}$-algebras has been explored by several mathematicians within different categories in the past few years. In this article, we establish that there are exactly three families of unitary easy quantum groups that can be achieved as the quantum symmetry of graph $C^*$-algebra $C^*(\Gamma)$ associated with a finite, connected, directed graph $\Gamma$ in the category introduced by Joardar and Mandal. Moreover, we demonstrate that there does not exist any graph $C^*$-algebra associated with a finite, connected, directed graph $\Gamma$ having $A_{U^t}(F^{\Gamma})$ as the quantum automorphism group of $C^*(\Gamma)$ for non-scalar matrix $F^{\Gamma}$., Comment: The title of the article and the proof of Theorem 3.8 have been modified, A few stylistic changes have been made. Comments are welcome

The integration of pretrained language models (PLMs) like BERT and GPT has revolutionized NLP, particularly for English, but it has also created linguistic imbalances. This paper strategically identifies the need for linguistic equity by examining several knowledge editing techniques in multilingual contexts. We evaluate the performance of models such as Mistral, TowerInstruct, OpenHathi, Tamil-Llama, and Kan-Llama across languages including English, German, French, Italian, Spanish, Hindi, Tamil, and Kannada. Our research identifies significant discrepancies in normal and merged models concerning cross-lingual consistency. We employ strategies like 'each language for itself' (ELFI) and 'each language for others' (ELFO) to stress-test these models. Our findings demonstrate the potential for LLMs to overcome linguistic barriers, laying the groundwork for future research in achieving linguistic inclusivity in AI technologies., Comment: Under review

Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be formulated both in the Jordan and Einstein frame, which are related by a Weyl transformation with a field transformation, known together as a frame transformation. These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory. However, this is no longer true from the quantum field theoretical perspective. In the present article, we show that the Ward identities derived in the above two frames are not connected through the frame transformation. This shows that the quantum field theories formulated in these two frames are not equivalent to each other. Moreover, this inequivalence is also shown by comparing the effective actions derived in these two frames., Comment: 14 pages, Accepted in Communications in Theoretical Physics

The study of nonclassical properties of two-mode quantum states is particularly useful in quantum information theory because of the possibilities of obtaining entanglement and other two-mode quantum correlations in these states. Here we have investigated the possibilities of the existence of nonclassicality in a two-mode New generalized binomial state (TMNGBS). Specifically two-mode antibunching, Quadrature squeezing, sum \& difference squeezing, and various entanglement criteria e.g Shchukin-Vogel entanglement criterion, the uncertainty relation of SU(1,1) Algebra and EPR entanglement criterion are explored in two mode particular example of quantum state named as New generalized binomial state. Earlier we studied nonclassicality in single-mode NGBS, here we are extending our study toward the two-mode version of a quantum state. Here we provide the general expressions of moments for a two-mode quantum state (Fock basis) and explore the quantification in a particular example NGBS. It is found that antibunching, squeezing, and SV entanglement are possible with different limits of depending parameters but the entanglement criteria (EPR, SU (1,1) algebra and Cauchy - Schwarz inequality based)for NGBS are not possible. This study opens up the possibility of exploring the two-mode nonclassicality in other states too., Comment: 9 pages and 11 Figures

Rotational Freudenthal duality (RFD) relates two extremal Kerr-Newman (KN) black holes (BHs) with different angular momenta and electric-magnetic charges, but with the same Bekenstein-Hawking entropy. Through the Kerr/CFT correspondence (and its KN extension), a four-dimensional, asymptotically flat extremal KN BH is endowed with a dual thermal, two-dimensional conformal field theory (CFT) such that the Cardy entropy of the CFT is the same as the Bekenstein-Hawking entropy of the KN BH itself. Using this connection, we study the effect of the RFD on the thermal CFT dual to the KN extremal BH. We find that the RFD maps two different thermal, two-dimensional CFTs with different temperatures and central charges, but with the same asymptotic density of states, thereby matching the Cardy entropy. In an appendix, we discuss the action of the RFD on doubly-extremal rotating BHs, finding a spurious branch in the non-rotating limit, and determining that for this class of BH solutions the image of the RFD necessarily over-rotates., Comment: 13+11 pages, comments welcome

It is commonly held that quantum states with energy $E = 0$ would belong to the continuum. However, several situations have been reported when a zero-energy state becomes bound subject to certain restrictions on the coupling constants defining the potential. In the present work, we present another evidence of the existence of regular zero-energy normalizable solutions for a system of QES potentials that correspond to rationally extended many-body truncated Calogero-Sutherland model. Our procedure is based upon the potential group approach with an underlying so$(2, 1)$ structure that utilizes the three cases guided by it on profitably carrying out a point canonical transformation. We deal with each case separately by suitably restricting the coupling parameters., Comment: 12 Pages, 4 Figs

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. Here, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann's dream of engineering synthetic living systems that adapt to the environment., Comment: 6 pages, 3 figures

We describe a new exact lattice bosonization of matrix quantum mechanics (equivalently of non-relativistic fermions) that is valid for arbitrary rank N of the matrix, based on an exact operator bosonization introduced earlier in [1]. The trace identities are automatically incorporated in this formalism. The finite number N of fermions is reflected in the finite number N of bosonic oscillators, or equivalently to the finite number N of lattice points. The fermion Hamiltonian is exactly mappable to a bosonic Hamiltonian. At large N, the latter becomes local and corresponds to the lattice version of a relativistic boson Hamiltonian, with a lattice spacing of order 1/N. The finite lattice spacing leads to a finite entanglement entropy (EE) of the bosonic theory, which reproduces the finite EE of the fermionic theory. Such a description is not available in the standard bosonization in terms of fermion density fluctuations on the Fermi surface, which does not have a built-in short distance cut-off (see, however, [2]). The bosonic lattice is equipped with a geometry determined by the matrix potential or equivalently by the shape of the Fermi surface. Our bosonization also works in the double scaled c=1 model, where the bosonic EE again turns out to be finite, with the short distance cut-off turning as g_s l_s, and reproduces the matrix result. Once again, such a short distance cut-off cannot appear in the conventional dual of c=1 in terms of the 2D string ``tachyon'', where the expected short distance scale is l_s. This indicates our bosonization as a possibly different dual description to the c=1 matrix model appropriate for ``local physics'' like quantum entanglement, by contrast with the conventional duality to the eigenvalue density which works well for asymptotic observables like S-matrices. We briefly discuss possible relation of our bosonization to D0 branes., Comment: 25 pages + appendices, 9 figures (v1)

The emergence of high-entropy oxides has spurred significant research interest in recent times. These compounds exhibit exotic functional properties that often transcend simple linear combinations of their constituent elements. Herein, we present a new series of Cr-based low, medium, and high entropy spinel oxides with composition NiCr2O4, [Ni0.5Mn0.5]Cr2O4, [Ni0.33Mn0.33Co0.33]Cr2O4, [Ni0.25Mn0.25Co0.25Cu0.25]Cr2O4, [Ni0.2Mn0.2Co0.2Cu0.2Zn0.2]Cr2O4, and [Ni0.2Mg0.2Co0.2Cu0.2Zn0.2]Cr2O4. We conducted detailed structural (X-ray and Neutron diffraction), microstructural, Raman spectroscopy, magnetic, and X-ray absorption spectroscopy measurements on these materials. Our study reveals that the incorporation of multiple cations at the A-site of the structure (AB2O4) significantly modulates the magnetic properties. These compounds exhibit transitions from complex ferrimagnetic ([Ni0.2Mn0.2Co0.2Cu0.2Zn0.2]Cr2O4) to antiferromagnetic ([Ni0.2Mg0.2Co0.2Cu0.2Zn0.2]Cr2O4) states, with remarkable coercivity variations, demonstrating the ability to tailor magnetic responses through compositional design.

Visual Question Answering (VQA) is an important task in multimodal AI, and it is often used to test the ability of vision-language models to understand and reason on knowledge present in both visual and textual data. However, most of the current VQA models use datasets that are primarily focused on English and a few major world languages, with images that are typically Western-centric. While recent efforts have tried to increase the number of languages covered on VQA datasets, they still lack diversity in low-resource languages. More importantly, although these datasets often extend their linguistic range via translation or some other approaches, they usually keep images the same, resulting in narrow cultural representation. To address these limitations, we construct CVQA, a new Culturally-diverse multilingual Visual Question Answering benchmark, designed to cover a rich set of languages and cultures, where we engage native speakers and cultural experts in the data collection process. As a result, CVQA includes culturally-driven images and questions from across 28 countries on four continents, covering 26 languages with 11 scripts, providing a total of 9k questions. We then benchmark several Multimodal Large Language Models (MLLMs) on CVQA, and show that the dataset is challenging for the current state-of-the-art models. This benchmark can serve as a probing evaluation suite for assessing the cultural capability and bias of multimodal models and hopefully encourage more research efforts toward increasing cultural awareness and linguistic diversity in this field.

Glaucoma is a chronic eye disease characterized by optic neuropathy, leading to irreversible vision loss. It progresses gradually, often remaining undiagnosed until advanced stages. Early detection is crucial to monitor atrophy and develop treatment strategies to prevent further vision impairment. Data-centric methods have enabled computer-aided algorithms for precise glaucoma diagnosis. In this study, we use deep learning models to identify complex disease traits and progression criteria, detecting subtle changes indicative of glaucoma. We explore the structure-function relationship in glaucoma progression and predict functional impairment from structural eye deterioration. We analyze statistical and machine learning methods, including deep learning techniques with optical coherence tomography (OCT) scans for accurate progression prediction. Addressing challenges like age variability, data imbalances, and noisy labels, we develop novel semi-supervised time-series algorithms: 1. Weakly-Supervised Time-Series Learning: We create a CNN-LSTM model to encode spatiotemporal features from OCT scans. This approach uses age-related progression and positive-unlabeled data to establish robust pseudo-progression criteria, bypassing gold-standard labels. 2. Semi-Supervised Time-Series Learning: Using labels from Guided Progression Analysis (GPA) in a contrastive learning scheme, the CNN-LSTM architecture learns from potentially mislabeled data to improve prediction accuracy. Our methods outperform conventional and state-of-the-art techniques., Comment: Dissertation

In the digital world, memes present a unique challenge for content moderation due to their potential to spread harmful content. Although detection methods have improved, proactive solutions such as intervention are still limited, with current research focusing mostly on text-based content, neglecting the widespread influence of multimodal content like memes. Addressing this gap, we present \textit{MemeGuard}, a comprehensive framework leveraging Large Language Models (LLMs) and Visual Language Models (VLMs) for meme intervention. \textit{MemeGuard} harnesses a specially fine-tuned VLM, \textit{VLMeme}, for meme interpretation, and a multimodal knowledge selection and ranking mechanism (\textit{MKS}) for distilling relevant knowledge. This knowledge is then employed by a general-purpose LLM to generate contextually appropriate interventions. Another key contribution of this work is the \textit{\textbf{I}ntervening} \textit{\textbf{C}yberbullying in \textbf{M}ultimodal \textbf{M}emes (ICMM)} dataset, a high-quality, labeled dataset featuring toxic memes and their corresponding human-annotated interventions. We leverage \textit{ICMM} to test \textit{MemeGuard}, demonstrating its proficiency in generating relevant and effective responses to toxic memes.

The quantum-classical hybrid Variational Quantum Eigensolver (VQE) algorithm is recognized to be the method of choice to obtain ground state energies of quantum many-body systems in the noisy intermediate scale quantum (NISQ) era. This study not only extends the VQE algorithm to the relativistic regime, but also calculates a property other than energy, namely the molecular permanent electric dipole moment (PDM). We carry out 18-qubit quantum simulations to obtain ground state energies as well as PDMs of single-valence diatomic molecules, ranging from the light BeH to the heavy radioactive RaH molecule. We investigate the correlation trends in these systems as well as access the precision in our results. Furthermore, we measure the PDM of the moderately heavy SrH and SrF molecules on the optimized unitary coupled cluster state, using the state-of-the-art IonQ Aria-I quantum computer in an active space of 6 qubits. The associated quantum circuits for these computations were extensively optimized in view of limitations imposed by NISQ hardware. To that end, we employ an array of techniques, including the use of point group symmetries, integrating ZX-Calculus into our pipeline-based circuit optimization, and energy sort VQE procedure. Through these methods, we compress our 6-qubit quantum circuit from 280 two-qubit gates to 37 two-qubit gates (with a marginal trade-off of 0.33 and 0.31 percent in the PDM for SrH and SrF in their respective 6-spin orbital active spaces). We anticipate that our proof-of-concept demonstration lays the groundwork for future quantum hardware calculations involving heavy atoms and molecules.

We show that a non-Hermitian lattice with a disclination can host topological disclination states that are induced by on-site gain and loss. The disclination states are inherently non-Hermitian as they do not exist in the limit of zero gain/loss. They arise from charge fractionalization in the non-Hermitian lattice, which we establish using non-Hermitian Wilson loops calculated with biorthogonal products. The model can be realized using an array of optical resonators, with the emergence of the topological disclination states manifesting as an abrupt shift in emission intensity and frequency upon tuning the gain/loss level., Comment: 7 pages and 4 figures

Classical machine learning, extensively utilized across diverse domains, faces limitations in speed, efficiency, parallelism, and processing of complex datasets. In contrast, quantum machine learning algorithms offer significant advantages, including exponentially faster computations, enhanced data handling capabilities, inherent parallelism, and improved optimization for complex problems. In this study, we used the entanglement-enhanced quantum kernel in quantum support vector machine to train complex respiratory data sets. Compared to classical algorithms, our findings reveal that QSVM performs better with 45% higher accuracy for complex respiratory data sets while maintaining comparable performance with linear datasets in contrast to their classical counterparts executed on a 2-qubit system. Through our study, we investigate the efficacy of the QSVM-Kernel algorithm in harnessing the enhanced dimensionality of the quantum Hilbert space for effectively training complex datasets.

We consider the problem of recovering the ground truth ordering (ranking, top-$k$, or others) over a large number of alternatives. The wisdom of crowd is a heuristic approach based on Condorcet's Jury theorem to address this problem through collective opinions. This approach fails to recover the ground truth when the majority of the crowd is misinformed. The surprisingly popular (SP) algorithm cite{prelec2017solution} is an alternative approach that is able to recover the ground truth even when experts are in minority. The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives. However, when the number of alternatives, $m$, is large, eliciting the prediction report or even the vote over $m$ alternatives might be too costly. In this paper, we design a scalable alternative of the SP algorithm which only requires eliciting partial preferences from the voters, and propose new variants of the SP algorithm. In particular, we propose two versions -- Aggregated-SP and Partial-SP -- that ask voters to report vote and prediction on a subset of size $k$ ($\ll m$) in terms of top alternative, partial rank, or an approval set. Through a large-scale crowdsourcing experiment on MTurk, we show that both of our approaches outperform conventional preference aggregation algorithms for the recovery of ground truth rankings, when measured in terms of Kendall-Tau distance and Spearman's $\rho$. We further analyze the collected data and demonstrate that voters' behavior in the experiment, including the minority of the experts, and the SP phenomenon, can be correctly simulated by a concentric mixtures of Mallows model. Finally, we provide theoretical bounds on the sample complexity of SP algorithms with partial rankings to demonstrate the theoretical guarantees of the proposed methods.

In this paper we propose necessary upper bounds for second, third and fourth smallest prime divisors of friend of 10 based on the number of distinct prime divisors of it., Comment: 9 pages