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We consider the stochastic Landau-Lifshitz-Gilbert equation in dimension 1. A control process is added to the effective field. We show the existence of a weak martingale solution for the resulting controlled equation. The proof uses the classical Faedo-Galerkin approximation, along with the Jakubowski version of the Skorohod Theorem. We then show pathwise uniqueness for the obtained solution, which is then coupled with the theory of Yamada and Watanabe to give the existence of a unique strong solution. We then show, using some semigroup techniques that the obtained solution satisfies the maximum regularity. We then show the existence of an optimal control. A main ingredient of the proof is using the compact embedding of a space into itself, albeit with the weak topology.

In this study, we theoretically investigate neuron-like spiking dynamics in an elliptic ferromagnet/heavy metal bilayer-based spin Hall nano oscillator (SHNO) in bias field-free condition, much suitable for practical realization of brain inspired computing schemes. We demonstrate regular periodic spiking with tunable frequency as well as the leaky-integrate-and-fire (LIF) behavior in a single SHNO by manipulating the pulse features of input current. The frequency of regular periodic spiking is tunable in a range of 0.5 GHz to 0.96 GHz (460 MHz bandwidth) through adjusting the magnitude of constant input dc current density. We further demonstrate the reconfigurability of spiking dynamics in response to a time varying input accomplished by continuously increasing the input current density as a linear function of time. Macrospin theory and micromagnetic simulation provide insights into the origin of bias field-free auto-oscillation and the spiking phenomena in our SHNO. In addition, we discuss how the shape anisotropy of the elliptic ferromagnet influence the bias field-free auto oscillation characteristics, including threshold current, frequency and transition from in-plane to out-of-plane precession. The SHNO operates below $10^{12} A/m^2$ input current density and exhibits a large auto-oscillation amplitude, ensuring high output power. We show that the threshold current density can be reduced by decreasing the ellipticity of the ferromagnet layer as well as enhancing the perpendicular magnetic anisotropy. These findings highlight the potential of bias field-free elliptic SHNO in designing power-efficient spiking neuron-based neuromorphic hardware.

Using a method of factorization and by introducing a generalized discrete Dirichlet's Laplacian matrix $(-\Delta_{\Lambda})$, we establish an extended improved discrete Hardy's inequality and Rellich inequality in one dimension. We prove that the discrete Copson inequality (E.T. Copson, \emph{Notes on a series of positive terms}, J. London Math. Soc., 2 (1927), 9-12.) in one-dimension admits an improvement. We also prove that the improved Copson's weights are optimal (in fact \emph{critical}). It is shown that improvement of the Knopp inequalities (Knopp in J. London Math. Soc. 3(1928), 205-211 and 5(1930), 13-21) lies on improvement of the Rellich inequalities. Further, an improvement of the generalized Hardy's inequality (Hardy in Messanger of Math. 54(1925), 150-156) in a special case is obtained., Comment: 23 pages

The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are adjacent if and only if either $u=v^m$ or $v=u^n$ for some positive integers $m$, $n$. Forbidden subgraph has a significant role in graph theory. In our previous work \cite{cmm}, we consider five important classes of forbidden subgraphs of power graph which include perfect graphs, cographs, chordal graphs, split graphs and threshold graphs. In this communication, we go even further in that way. This study, inspired by the articles \cite{celmmp,dong,ck}, examines additional $4$ significant forbidden classes, including chain graphs, diamond-free graphs, $\{P_{5}, \overline{P_{5}}\}$-free graphs and $\{P_{2}\cup P_{3}, \overline{P_{2}\cup P_{3}}\}$-free graph. The finite groups whose power graphs are chain graphs, diamond-free graphs, and $\{P_{2}\cup P_{3}, \overline{P_{2}\cup P_{3}}\}$-free graphs have been successfully identified in this work. In case of $\{P_{5}, \overline{P_{5}}\}$-free graphs, we completely determine all the nilpotent groups, direct product of two groups, finite simple groups whose power graph is $\{P_{5}, \overline{P_{5}}\}$-free., Comment: 20 pages

Solid-state devices made from correlated oxides such as perovskite nickelates are promising for neuromorphic computing by mimicking biological synaptic function. However, comprehending dopant action at the nanoscale poses a formidable challenge to understanding the elementary mechanisms involved. Here, we perform operando infrared nanoimaging of hydrogen-doped correlated perovskite, neodymium nickel oxide (H-NdNiO3) devices and reveal how an applied field perturbs dopant distribution at the nanoscale. This perturbation leads to stripe phases of varying conductivity perpendicular to the applied field, which define the macroscale electrical characteristics of the devices. Hyperspectral nano-FTIR imaging in conjunction with density functional theory calculations unveil a real-space map of multiple vibrational states of H-NNO associated with OH stretching modes and their dependence on the dopant concentration. Moreover, the localization of excess charges induces an out-of-plane lattice expansion in NNO which was confirmed by in-situ - x-ray diffraction and creates a strain that acts as a barrier against further diffusion. Our results and the techniques presented here hold great potential to the rapidly growing field of memristors and neuromorphic devices wherein nanoscale ion motion is fundamentally responsible for function., Comment: 30 pages, 5 figures in the main text and 5 figures in the Supplementary Material

Glycolaldehyde (CH$_{2}$OHCHO) is the simplest monosaccharide sugar in the interstellar medium, and it is directly involved in the origin of life via the 'RNA world' hypothesis. We present the first detection of glycolaldehyde (CH$_{2}$OHCHO) towards the hot molecular core G358.93-0.03 MM1 using the Atacama Large Millimeter/Submillimeter Array (ALMA). The calculated column density of CH$_{2}$OHCHO towards G358.93-0.03 MM1 is (1.52$\pm$0.9)$\times$10$^{16}$ cm$^{-2}$ with an excitation temperature of 300$\pm$68.5 K. The derived fractional abundance of CH$_{2}$OHCHO with respect to H$_{2}$ is (4.90$\pm$2.92)$\times$10$^{-9}$, which is consistent with that estimated by existing two-phase warm-up chemical models. We discuss the possible formation pathways of CH$_{2}$OHCHO within the context of hot molecular cores and hot corinos and find that CH$_{2}$OHCHO is likely formed via the reactions of radical HCO and radical CH$_{2}$OH on the grain surface of G358.93-0.03 MM1., Comment: 12 pages, 4 figures, published in Monthly Notices of the Royal Astronomical Society (MNRAS)

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of $f(\bar{R}, \bar{T})$ gravity, specifically in K-essence theory. In this study, the Dirac-Born-Infeld type non-standard Lagrangian is used to calculate the emergent metric $\bar{G}_{\mu\nu}$, which is not conformally equivalent to the conventional gravitational metric. We use the function $f(\bar{R}, \bar{T})$ to reflect the additive nature of the emergent Ricci scalar ($\bar{R}$) and the trace of the emergent energy-momentum tensor ($\bar{T}$). Our study demonstrates that certain choices of $f(\bar{R}, \bar{T})$ may result in the existence of a naked singularity caused by gravitational collapse. The alternative $f(\bar{R}, \bar{T})$ values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. Furthermore, for a given quantity of kinetic part of the K-essence scalar field, mass is completely changed into energy, meaning that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena., Comment: 21 pages, 8 figures, 2 tables, Accepted from Chinese Journal of Physics

Let $G$ be a group. The intersection subgroup graph of $G$ (introduced by Anderson et al. \cite{anderson}) is the simple graph $\Gamma_{S}(G)$ whose vertices are those non-trivial subgroups say $H$ of $G$ with $H\cap K=\{e\}$ for some non-trivial subgroup $K$ of $G$; two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K=\{e\}$, where $e$ is the identity element of $G$. In this communication, we explore the groups whose intersection subgroup graph belongs to several significant graph classes including cluster graphs, perfect graphs, cographs, chordal graphs, bipartite graphs, triangle-free and claw-fee graphs. We categorize each nilpotent group $G$ so that $\Gamma_S(G)$ belongs to the above classes. We entirely classify the simple group of Lie type whose intersection subgroup graph is a cograph. Moreover, we deduce that $\Gamma_{S}(G)$ is neither a cograph nor a chordal graph if $G$ is a torsion-free nilpotent group.

In the realm of computer systems, efficient utilisation of the CPU (Central Processing Unit) has always been a paramount concern. Researchers and engineers have long sought ways to optimise process execution on the CPU, leading to the emergence of CPU scheduling as a field of study. This research proposes a novel algorithm for batch processing that operates on a preemptive model, dynamically assigning priorities based on a robust ratio, employing a dynamic time slice, and utilising periodic sorting technique to achieve fairness. By engineering this responsive and fair model, the proposed algorithm strikes a delicate balance between efficiency and fairness, providing an optimised solution for batch scheduling while ensuring system responsiveness.

In this work, we investigate for an analytical solution under modified gravity theory, specifically the $f(R,T)$ gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$, respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe., Comment: 15 pages, 27 figures

Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal (HM) under the ferromagnetic resonance (FMR) condition, we report an enhancement in effective damping in $\beta$- W/Py bilayers by systematically varying resistivity ($\rho_{W}$) of $\beta$-W films. Different resistivity ranging from 100 $\mu\Omega$-cm to 1400 $\mu\Omega$-cm with a thickness of 8 nm can be achieved by varying the argon pressure ($P_{Ar}$) during the growth by the method of sputtering. The coefficient of effective damping $\alpha_{eff}$ is observed to increase from 0.010 to 0.025 with $\rho_{W}$, which can be modulated by $P_{Ar}$. We observe a modest dependence of $\alpha_{eff}$ on the sputtering power ($p_{S}$) while keeping the $P_{Ar}$ constant. $\alpha_{eff}$ dependence on both $P_{Ar}$ and $p_{S}$ suggests that there exists a strong correlation between $\alpha_{eff}$ and $\rho_{W}$. It is thus possible to utilize $\rho_{W}$ as a tuning parameter to regulate the $\alpha_{eff}$, which can be advantageous for faster magnetization dynamics switching. The thickness dependence study of Py in the aforementioned bilayers manifests a higher spin mixing conductance ($g^{\uparrow\downarrow}_{eff}$) which suggests a strong spin pumping from Py into the $\beta$-W layer. The effective spin current ($J_{S(eff)}$) is also evaluated by considering the spin-back flow in this process. Intrinsic spin mixing conductance ($g^{\uparrow\downarrow}_{W}$) and spin diffusion length ($\lambda_{SD}$) of $\beta$-W are additionally investigated using thickness variations in $\beta$-W. Furthermore, the low-temperature study in $\beta$-W/Py reveals an intriguing temperature dependence in $\alpha_{eff}$ which is quite different from $\alpha_{b}$ of single Py layer and the enhancement in $\alpha_{eff}$ at low temperature can be attributed to the spin-induced pumping from Py layer into $\beta$-W.

In contemporary self-supervised contrastive algorithms like SimCLR, MoCo, etc., the task of balancing attraction between two semantically similar samples and repulsion between two samples of different classes is primarily affected by the presence of hard negative samples. While the InfoNCE loss has been shown to impose penalties based on hardness, the temperature hyper-parameter is the key to regulating the penalties and the trade-off between uniformity and tolerance. In this work, we focus our attention on improving the performance of InfoNCE loss in self-supervised learning by proposing a novel cosine similarity dependent temperature scaling function to effectively optimize the distribution of the samples in the feature space. We also provide mathematical analyses to support the construction of such a dynamically scaled temperature function. Experimental evidence shows that the proposed framework outperforms the contrastive loss-based SSL algorithms.

Black hole driven outflows in galaxies hosting active galactic nuclei (AGN) may interact with their interstellar medium (ISM) affecting star formation. Such feedback processes, reminiscent of those seen in massive galaxies, have been reported recently in some dwarf galaxies. However, such studies have usually been on kiloparsec and larger scales and our knowledge on the smallest spatial scales to which these feedback processes can operate is unclear. Here we demonstrate radio jet$-$ISM interaction on the scale of an asymmetric triple radio structure of $\sim$ 10 parsec size in NGC 4395. This triple radio structure is seen in the 15 GHz continuum image and the two asymmetric jet-like structures are situated on either side of the radio core that coincides with the optical {\it Gaia} position. The high resolution radio image and the extended [OIII]$\lambda$5007 emission, indicative of an outflow, are spatially coincident and are consistent with the interpretation of a low power radio jet interacting with the ISM. Modelling of the spectral lines using {\tt MAPPINGS}, and estimation of temperature using optical integral field spectroscopic data suggest shock ionization of the gas. The continuum emission at 237 GHz, though weak, was found to spatially coincide with the AGN. However, the CO(2$-$1) line emission was found to be displaced by around 20 parsec northward of the AGN core. The spatial coincidence of molecular H$_2$$\lambda$2.4085 along the jet direction, the morphology of ionised [OIII]$\lambda$5007 and displacement of the CO(2$-$1) emission argues for conditions less favourable for star formation in the central $\sim$ 10 parsec region., Comment: 20 pages, 18 figures, accepted for the publication of The Astrophysical Journal

The impurity incorporation in host high-spin orbit coupling materials like platinum has shown improved charge-to-spin conversion by modifying the up-spin and down-spin electron trajectories by bending or skewing them in opposite directions. This enables efficient generation, manipulation, and transport of spin currents. In this study, we irradiate the platinum with non-focus dense plasma to incorporate the oxygen ion species. We systematically analyze the spin Hall angle of the oxygen plasma irradiated Pt films using spin torque ferromagnetic resonance. Our results demonstrate a 2.4 times enhancement in the spin Hall effect after plasma treatment of Pt as compared to pristine Pt. This improvement is attributed to the introduction of disorder and defects in the Pt lattice, which enhances the spin-orbit coupling and leads to more efficient charge-to-spin conversion without breaking the spin-orbit torque symmetries. Our findings offer a new method of dense plasma-based modification of material for the development of advanced spintronic devices based on Pt and other heavy metals.

Free-space modulation of light is crucial for many applications, from light detection and ranging to virtual or augmented reality. Traditional means of modulating free-space light involves spatial light modulators based on liquid crystals and microelectromechanical systems, which are bulky, have large pixel areas (~10 micron x 10 micron), and require high driving voltage. Recent progress in meta-optics has shown promise to circumvent some of the limitations. By integrating active materials with sub-wavelength pixels in a meta-optic, the power consumption can be dramatically reduced while achieving a faster speed. However, these reconfiguration methods are volatile and hence require constant application of control signals, leading to phase jitter and crosstalk. Additionally, to control a large number of pixels, it is essential to implement a memory within each pixel to have a tractable number of control signals. Here, we develop a device with nonvolatile, electrically programmable, phase-only modulation of free-space infrared radiation in transmission using the low-loss phase-change material (PCM) Sb2Se3. By coupling an ultra-thin PCM layer to a high quality (Q)-factor (Q~406) diatomic metasurface, we demonstrate a phase-only modulation of ~0.25pi (~0.2pi) in simulation (experiment), ten times larger than a bare PCM layer of the same thickness. The device shows excellent endurance over 1,000 switching cycles. We then advance the device geometry, to enable independent control of 17 meta-molecules, achieving ten deterministic resonance levels with a 2pi phase shift. By independently controlling the phase delay of pixels, we further show tunable far-field beam shaping. Our work paves the way to realizing non-volatile transmissive phase-only spatial light modulators.

Spin Hall nano oscillators (SHNOs) have shown applications in unconventional computing schemes and broadband frequency generation in the presence of applied external magnetic field. However, under field-free conditions, the oscillation characteristics of SHNOs display a significant dependence on the effective field, which can be tuned by adjusting the constriction width, thereby presenting an intriguing area of study. Here we study the effect of nano constriction width on the magnetization dynamics in anisotropy assisted field free SHNOs. In uniaxial anisotropy-based field-free SHNOs, either the anisotropy field or the demagnetization field can dominate the magnetization dynamics depending on the constriction width. Our findings reveal distinct auto-oscillation characteristics in narrower constrictions with 20 nm and 30 nm constriction width compared to their wider counterpart with 100 nm width. The observed frequency shift variations with input current and constriction widths stem from the inherent nonlinearity of the system. The interplay between the B_demag and B_anis, coupled with changes in constriction width, yields rich dynamics and offers control over frequency tunability, auto oscillation amplitude, and threshold current. Notably, the spatial configuration of spin wave wells within the constriction undergoes transformations in response to changes in both constriction width and anisotropy. The findings highlight the significant influence of competing fields at the constriction on the field-free auto oscillations of SHNOs, with this impact intensifying as the constriction width is varied., Comment: 25 pages, 11 figures

Existential rules form an expressive Datalog-based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass Datalog and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $\mathcal{C}$ of existential rules, a new class called Dyadic-$\mathcal{C}$ enjoying the following properties: $(i)$ it is decidable; $(ii)$ it generalises Datalog; $(iii)$ it generalises $\mathcal{C}$; $(iv)$ it can effectively exploit any reasoner for query answering over $\mathcal{C}$; and $(v)$ its computational complexity does not exceed the highest between the one of $\mathcal{C}$ and the one of Datalog. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

Vision-based object tracking is an essential precursor to performing autonomous aerial navigation in order to avoid obstacles. Biologically inspired neuromorphic event cameras are emerging as a powerful alternative to frame-based cameras, due to their ability to asynchronously detect varying intensities (even in poor lighting conditions), high dynamic range, and robustness to motion blur. Spiking neural networks (SNNs) have gained traction for processing events asynchronously in an energy-efficient manner. On the other hand, physics-based artificial intelligence (AI) has gained prominence recently, as they enable embedding system knowledge via physical modeling inside traditional analog neural networks (ANNs). In this letter, we present an event-based physics-guided neuromorphic planner (EV-Planner) to perform obstacle avoidance using neuromorphic event cameras and physics-based AI. We consider the task of autonomous drone navigation where the mission is to detect moving gates and fly through them while avoiding a collision. We use event cameras to perform object detection using a shallow spiking neural network in an unsupervised fashion. Utilizing the physical equations of the brushless DC motors present in the drone rotors, we train a lightweight energy-aware physics-guided neural network (PgNN) with depth inputs. This predicts the optimal flight time responsible for generating near-minimum energy paths. We spawn the drone in the Gazebo simulator and implement a sensor-fused vision-to-planning neuro-symbolic framework using Robot Operating System (ROS). Simulation results for safe collision-free flight trajectories are presented with performance analysis, ablation study and potential future research directions, Comment: accepted for publication at IEEE Robotics and Automation Letters

Shot noise at a conductance plateau in a quantum point contact (QPC) can be explained by considering equilibrations at the quantum Hall edges. The indication from recent experiments is that the charge equilibration length is much shorter than the thermal equilibration length. We discuss how this discovery gives rise to different thermal equilibration regimes in the presence of full charge equilibration. In this work, we classify these distinct regimes via dc current-current correlations \emph{(electrical shot noise)} at distinct QPC conductance plateaus for the edges of integer, particle-like, and hole-like filling fractions in a two dimensional electron gas., Comment: 8 pages, 3 figures, 2 tables

The $\nu = 2/3$ filling is the simplest paradigmatic example of a fractional quantum Hall state, which contains counter-propagating edge modes. These modes can be either in the unequilibrated regime or equilibrated to different extents, on top of a possible edge reconstruction. In the unequilibrated regime, two distinct renormalization group fixed points have been previously proposed, namely Kane-Fischer-Polchinski and Wang-Meir-Gefen. In the equilibration regime, different degree of thermal equilibration may occur, while charge is fully equilibrated. Here, we show that this rich variety of models can give rise to three possible conductance plateaus at $e^2/2h$ (recently observed in experiments), $5e^2/9h$ (predicted here), and $e^2/3h$ (observed earlier in experiments) in a quantum point contact geometry. We identify different mechanisms for \emph{electrical shot noise} generation at these plateaus, which provides an experimentally accessible venue for distinguishing among the distinct models., Comment: 10 pages, 6 figures. Submitted to the special issue of Low Temperature Physics, dedicated to the memory of Sergei Gredeskul. This article comprises an extension of our recent work arXiv:2307.05173 (2023)

Two-terminal conductance quantization in the context of quantum Hall (QH) physics is intimately related to current carried by a discrete number of edge modes. Upon pinching off of a QH bar, one may reach regimes in which some modes which are fully transmitted (while the others are fully reflected), giving rise to quantized conductance plateaus. Here we study an alternative protocol for quantized values of the conductance, which relies on inter-mode equilibration. Concretely this is the result of considering different inequalities between charge equilibration and thermal equilibration lengths on one hand and geometrical lengths on the other hand, and accounting for the possibility of edge reconstruction. Taking the 2/3 state as a prototypical example, we obtain a host of scenarios leading to conductance plateaus at $e^2/3h$ (observed previously), $e^2/2h$ (recently observed), and $5e^2/9h$ (our prediction). Our approach facilitates distinguishing among various scenarios based on dc current auto- and cross-correlation (shot noise)., Comment: 6 pages, 3 figures, 1 table

Individuals socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognized, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behavior relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the Covid-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination attitudes. We find that generally privileged groups of the population have higher number of contact and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioral differences. Finally, we apply our model to analyze the fourth wave of Covid-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies., Comment: 33 pages, 22 figures

We prove that the volume preserving fractional mean curvature flow starting from a convex set does not develop singularities along the flow. By the recent result of Cesaroni-Novaga \cite{CN} this then implies that the flow converges to a ball exponentially fast. In the proof we show that the apriori estimates due to Cinti-Sinestrari-Valdinoci \cite{CSV2} imply the $C^{1+\alpha}$-regularity of the flow and then provide a regularity argument which improves this into $C^{2+\alpha}$-regularity of the flow. The regularity step from $C^{1+\alpha}$ into $C^{2+\alpha}$ does not rely on convexity and can probably be adopted to more general setting.

Spontaneous phase separation, or demixing, is important in biological phenomena such as cell sorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While differential-diffusivity-induced phase separation occurs in mixtures with a packing fraction up to $0.7$ [Weber et al. Phys Rev Lett 2016], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between $0.7$ and $1.0$ the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram. We also find that a confluent Voronoi model for tissues does not phase separate, consistent with the highest-density particle-based simulations., Comment: 4 pages, plus 4 page supplemental materials

The measurement problem dates back to the dawn of quantum mechanics. Here, we measure a quantum dot electron spin qubit through off-resonant coupling with thousands of redundant nuclear spin ancillae. We show that the link from quantum to classical can be made without any "wavefunction collapse", in agreement with the Quantum Darwinism concept. Large ancilla redundancy allows for single-shot readout with high fidelity $\approx99.85\%$. Repeated measurements enable heralded initialization of the qubit and probing of the equilibrium electron spin dynamics. Quantum jumps are observed and attributed to burst-like fluctuations in a thermally populated phonon bath.

Contact matrices have become a key ingredient of modern epidemic models. They account for the stratification of contacts for the age of individuals and, in some cases, the context of their interactions. However, age and context are not the only factors shaping contact structures and affecting the spreading of infectious diseases. Socio-economic status (SES) variables such as wealth, ethnicity, and education play a major role as well. Here, we introduce generalized contact matrices capable of stratifying contacts across any number of dimensions including any SES variable. We derive an analytical expression for the basic reproductive number of an infectious disease unfolding on a population characterized by such generalized contact matrices. Our results, on both synthetic and real data, show that disregarding higher levels of stratification might lead to the under-estimation of the reproductive number and to a mis-estimation of the global epidemic dynamics. Furthermore, including generalized contact matrices allows for more expressive epidemic models able to capture heterogeneities in behaviours such as different levels of adoption of non-pharmaceutical interventions across different groups. Overall, our work contributes to the literature attempting to bring socio-economic, as well as other dimensions, to the forefront of epidemic modeling. Tackling this issue is crucial for developing more precise descriptions of epidemics, and thus to design better strategies to contain them.

We include strong parity-violating contributions to inclusive deep inelastic scattering (DIS) of longitudinally polarized leptons off an unpolarized target. At variance with standard results, we obtain nonvanishing parity-violating structure functions in the case of pure photon exchange. The addition of these strong parity-violating contributions improves the description of existing experimental data on DIS parity-violating asymmetries. We find the size of these contributions small but exhibiting a deviation from zero of about 1.5 $\sigma$. The associated $p$-value is 0.063, indicating that the probability of making an error by rejecting the hypothesis of no parity-violating contributions is 6.3\%, which is small but not negligible. Further improvement on the limit of the strong parity-violation can be expected from the future SoLID program at Jefferson Lab., Comment: Revised version, 10 pages, 3 figures, RevTeX style; accepted for publication in Phys. Lett. B

In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a functional for certain value of the mass. We give a positive answer in dimension two while in higher dimension the situation is different. In fact, for small value of mass the ball centered at the origin is a local minimizer while for large values the ball is a maximizer among convex sets with uniform bound on the curvature.

We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. Our main contributions are as follows: -We establish the local well-posedness in Orlicz spaces. -By considering small initial data in suitable Lebesgue spaces, we derive the existence of global weak-mild solutions. -We provide precise decay estimates for large time, revealing that the decay rate depends on the behavior of the nonlinearity near the origin. -Furthermore, we demonstrate that when considering certain non-negative initial data within the appropriate Orlicz space, the existence of local non-negative classical solutions is no longer guaranteed. In summary, our work addresses the local and global behavior of solutions, decay estimates, and the impact of nonlinearity on the existence of classical solutions, offering some insights into the dynamics of the considered heat equation with a fractional harmonic oscillator and exponential nonlinearity., Comment: Corrected typos and improved exposition