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Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realised the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform $E$- and $B$-fields and a static dipole $B$-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand-Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytic Aristotelian Electrodynamics expectations., Comment: 22 pages, 21 figures, accepted by journal

In point-free topology, one abstracts the poset of open subsets of a topological space, by replacing it with a frame (a complete lattice, where meet distributes over arbitrary join). In this paper we propose a similar abstraction of the posets of connected subsets in various space-like structures. The analogue of a frame is called a chainmail, which is defined as a poset admitting joins of its mails, i.e., subsets having a lower bound. The main result of the paper is an equivalence between a subcategory of the category of complete join-semilattices and the category of chainmails., Comment: 11 pages, 4 figures

In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur \cite{A91} and Waldspurger \cite{WalFTLtordue}. We also prove a formula for the regular germs of quasi-characters associated to strongly cuspidal functions in terms of certain weighted orbital integrals. As a consequence of our trace formula and the formula for regular germs of quasi-characters, we prove a simple local trace formula of those models for strongly cuspidal test functions which implies a multiplicity formula for these models. We also present various applications of our trace formula and multiplicity formula, including a necessary condition for a discrete L-packet to contain a representation with a unitary Shalika model (resp. a Galois model for classical groups) in terms of the associated Langlands parameter, and we also compute the summation of the corresponding multiplicities for certain discrete L-packets., Comment: 137 pages, comments are welcome

We compute and explore numerically the finite system size correction to NLO $2\to2$ scattering in massive scalar $\phi^4$ theory. The derivation uses "denominator regularization" (instead of the usual dimensional regularization) on a spacetime with spatial directions compactified to a torus, with characteristic lengths not necessarily of equal size. We determine a useful analytic continuation of the generalized Epstein zeta function to isolate the usual UV divergence. Self-consistently, the renormalized finite system size correction reduces to zero as the system size goes to infinity and, further, satisfies the optical theorem. One of our checks of unitarity leads to a generalization of a number theoretic result from Hardy and Ramanujan. Precise numerical exploration of the finite system size correction to the amplitude and coupling when two spatial dimensions are finite requires the exploitation of the analytic structure of the finite system size result via a dispersion relation. We find that the finite system size scattering amplitude exhibits "geometric" bound states. Even away from these bound states, the finite system size correction to the effective coupling can be large., Comment: 34 pages, 24 figures

An important result of Bilu deals with the equidistribution of the Galois orbits of a sequence $(\alpha_n)_n$ in $\overline{\mathbb{Q}}^*$. Here, we prove a quantitative equidistribution theorem for a sequence of finite subsets in $\overline{\mathbb{Q}}^*$ which are not necessarily stable by Galois action. We follow a method of Mignotte., Comment: Here is the second version of the preprint "Bilu's equidistribution theorem over algebraic fields of infinite degree". The organization of this version is totally different because the main result of the first one partially follows from a recent preprint due to Doyle, Fili and Tobin, of which we were unaware

The Internet of Things (IoT) is a futuristic technology that promises to connect tons of devices via the internet. As more individuals connect to the internet, it is believed that communication will generate mountains of data. IoT is currently leveraging Wireless Sensor Networks (WSNs) to collect, monitor, and transmit data and sensitive data across wireless networks using sensor nodes. WSNs encounter a variety of threats posed by attackers, including unauthorized access and data security. Especially in the context of the Internet of Things, where small embedded devices with limited computational capabilities, such as sensor nodes, are expected to connect to a larger network. As a result, WSNs are vulnerable to a variety of attacks. Furthermore, implementing security is time-consuming and selective, as traditional security algorithms degrade network performance due to their computational complexity and inherent delays. This paper describes an encryption algorithm that combines the Secure IoT (SIT) algorithm with the Security Protocols for Sensor Networks (SPINS) security protocol to create the Lightweight Security Algorithm (LSA), which addresses data security concerns while reducing power consumption in WSNs without sacrificing performance.

Wireless Body Sensor Networks (WBSNs) is one of the greatest growing technology for sensing and performing various tasks. The information transmitted in the WBSNs is vulnerable to cyber-attacks, therefore security is very important. Denial of Service (DoS) attacks are considered one of the major threats against WBSNs security. In DoS attacks, an adversary targets to degrade and shut down the efficient use of the network and disrupt the services in the network causing them inaccessible to its intended users. If sensitive information of patients in WBSNs, such as the medical history is accessed by unauthorized users, the patient may suffer much more than the disease itself, it may result in loss of life. This paper proposes a User-Based authentication scheme to mitigate DoS attacks in WBSNs. A five-phase User-Based authentication DoS mitigation scheme for WBSNs is designed by integrating Elliptic Curve Cryptography (ECC) with Rivest Cipher 4 (RC4) to ensure a strong authentication process that will only allow authorized users to access nodes on WBSNs.

The sesquioxide, Ce$_{2}$O$_{3}$, has been a material of intense interest in recent years due to reports of an anomalous giant magnetodielectric effect and emergent mixed crystal field-phonon (vibronic) excitations below a putative antiferromagnetic transition at T$_{N}$ = 6.2 K. The claim of long-range magnetic order in this material is based on heat capacity and temperature-dependent susceptibility measurements; however, multiple neutron diffraction studies have been unable to distinguish any magnetic Bragg peaks. In this article, we present the results of a comprehensive investigation of the low-temperature phase in symmetry-broken polycrystalline Ce$_{2}$O$_{3}$ using a combination of magnetic susceptibility, heat capacity, neutron diffraction, triple-axis and time-of-flight (TOF) inelastic neutron scattering (INS), and muon spin rotation ($\mu$SR). Our measurements and subsequent analysis confirm that the transition at T$_{N}$ can be associated with the ordering of moments on the Ce$^{3+}$ site. Both a spontaneous magnetic order observed with $\mu$SR and a dispersive spin-wave spectrum observed with inelastic neutron scattering suggest a model wherein planar dipoles order antiferromagnetically. Notable inconsistencies between $\mu$SR and neutron scattering data within the dipole picture provide strong evidence for the ordering of higher-order moments., Comment: 12 pages, 8 figures

We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$. Our theorems are based on a comparison of the Jacquet-Rallis trace formulas. A new point is the expression of some interesting spectral contributions in these formulas in terms of integrals of relative characters. As an application of our mains theorems, we prove the global Gan-Gross-Prasad and the Ichino-Ikeda conjecture for Bessel periods of unitary groups., Comment: In English

How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete spacetime in quantum gravity; inferring network geometry in network science; and manifold learning in data science. The key contribution of this paper is to introduce and validate a new estimator of discrete sectional curvature for random graphs with low metric-distortion. The latter are constructed via a specific graph sprinkling method on different manifolds with constant sectional curvature. We define a notion of metric distortion, which quantifies how well the graph metric approximates the metric of the underlying manifold. We show how graph sprinkling algorithms can be refined to produce hard annulus random geometric graphs with minimal metric distortion. We construct random geometric graphs for spheres, hyperbolic and euclidean planes; upon which we validate our curvature estimator. Numerical analysis reveals that the error of the estimated curvature diminishes as the mean metric distortion goes to zero, thus demonstrating convergence of the estimate. We also perform comparisons to other existing discrete curvature measures. Finally, we demonstrate two practical applications: (i) estimation of the earth's radius using geographical data; and (ii) sectional curvature distributions of self-similar fractals.

Previously an equation of state for the relativistic hydrodynamics encountered in heavy-ion collisions at the LHC and RHIC has been calculated using lattice gauge theory methods. This leads to a prediction of very low viscosity, due to the calculated trace anomaly. Finite system corrections to this trace anomaly could challenge this calculation, since the lattice calculation was done in an effectively infinite system. In order to verify this trace anomaly it is sensible to add phenomenologically relevant finite system corrections. We investigate massive $\phi^4$ theory with periodic boundary conditions on $n$ of the 3 spatial dimensions. $2\to2$ NLO scattering is then computed. Using a newly derived formula for an arbitrary dimensional sum of sinc functions, we show that the NLO finite size corrections preserve unitarity., Comment: Submission to SciPost

The encoder network of an autoencoder is an approximation of the nearest point projection onto the manifold spanned by the decoder. A concern with this approximation is that, while the output of the encoder is always unique, the projection can possibly have infinitely many values. This implies that the latent representations learned by the autoencoder can be misleading. Borrowing from geometric measure theory, we introduce the idea of using the reach of the manifold spanned by the decoder to determine if an optimal encoder exists for a given dataset and decoder. We develop a local generalization of this reach and propose a numerical estimator thereof. We demonstrate that this allows us to determine which observations can be expected to have a unique, and thereby trustworthy, latent representation. As our local reach estimator is differentiable, we investigate its usage as a regularizer and show that this leads to learned manifolds for which projections are more often unique than without regularization., Comment: 11 pages, 10 figures

Iridates with the 5$d^4$ electronic configuration have attracted recent interest due to reports of magnetically-ordered ground states despite longstanding expectations that their strong spin-orbit coupling would generate a $J = 0$ electronic ground state for each Ir$^{5+}$ ion. The major focus of prior research has been on the double perovskite iridates Ba$_2$YIrO$_6$ and Sr$_2$YIrO$_6$, where the nature of the ground states (i.e. ordered vs non-magnetic) is still controversial. Here we present neutron powder diffraction, high energy resolution fluorescence detected x-ray absorption spectroscopy (HERFD-XAS), resonant inelastic x-ray scattering (RIXS), magnetic susceptibility, and muon spin relaxation data on the related double perovskite iridates Ba$_2$LuIrO$_6$, Sr$_2$LuIrO$_6$, Ba$_2$ScIrO$_6$, and Sr$_2$ScIrO$_6$ that enable us to gain a general understanding of the electronic and magnetic properties for this family of materials. Our HERFD-XAS and RIXS measurements establish $J = 0$ electronic ground states for the Ir$^{5+}$ ions in all cases, with similar values for Hund's coupling $J_{\rm H}$ and the spin-orbit coupling constant $\lambda_{\rm SOC}$. Our bulk susceptibility and muon spin relaxation data find no evidence for long-range magnetic order or spin freezing, but they do reveal weak magnetic signals that are consistent with extrinsic local moments. Our results indicate that the large $\lambda_{\rm SOC}$ is the key driving force behind the electronic and magnetic ground states realized in the 5$d^4$ double perovskite iridates, which agrees well with conventional wisdom., Comment: 13 pages, 7 figures, accepted for publication by PRM

We compute $2\rightarrow2$ scattering in massive $\phi^4$ theory on $\mathbb R^{1,m}\times T^n$ to NLO. We perform the calculations using "denominator regularization" instead of the usual dimensional regularization, which allows for asymmetric configurations of the $T^n$. We give a transparent derivation of and equation for the analytic continuation of the generalized Epstein zeta function. We show that the Optical Theorem is satisfied and generalize a conjecture by Hardy on square counting functions. We comment on the implications., Comment: 6 pages. Minor revisions to align the arXiv version with the published Phys.Rev.D Letter version

Automating quality inspection with computer vision techniques is often a very data-demanding task. Specifically, supervised deep learning requires a large amount of annotated images for training. In practice, collecting and annotating such data is not only costly and laborious, but also inefficient, given the fact that only a few instances may be available for certain defect classes. If working with video frames can increase the number of these instances, it has a major disadvantage: the resulting images will be highly correlated with one another. As a consequence, models trained under such constraints are expected to be very sensitive to input distribution changes, which may be caused in practice by changes in the acquisition system (cameras, lights), in the parts or in the defects aspect. In this work, we demonstrate the use of randomly generated synthetic training images can help tackle domain instability issues, making the trained models more robust to contextual changes. We detail both our synthetic data generation pipeline and our deep learning methodology for answering these questions., Comment: 15 pages, 7 figures

Let $\Gamma\subset \bar{\mathbb{Q}}^*$ be a finitely generated subgroup. Denote by $\Gamma_\mathrm{div}$ its division group. A recent conjecture due to R\'emond, related to the Zilber-Pink conjecture, predicts that the absolute logarithmic Weil height of an element of $\mathbb{Q}(\Gamma_\mathrm{div})^*\backslash \Gamma_{\mathrm{div}}$ is bounded from below by a positive constant depending only on $\Gamma$. In this paper, we propose a new way to tackle this problem., Comment: Theorem 1.2 has been added and the organization of this paper is largely different, although the proofs of theorems remain the same

AR Sco is a binary system that contains a white and red dwarf. The rotation rate of the white dwarf has been observed to slow down, analogous to rotation-powered radio pulsars; it has thus been dubbed a "white dwarf pulsar". We previously fit the traditional radio pulsar rotating vector model to the linearly polarised optical data from this source, constraining the system geometry as well as the white dwarf mass. Using a much more extensive dataset, we now explore the application of the same model to binary phase-resolved optical polarimetric data, thought to be the result of non-thermal synchrotron radiation, and derive the magnetic inclination angle $\alpha$ and the observer angle $\zeta$ at different orbital phases. We obtain a $\sim 10^{\circ}$ variation in $\alpha$ and $\sim 30^{\circ}$ variation in $\zeta$ over the orbital period. The variation patterns in these two parameters is robust, regardless of the binning and epoch of data used. We speculate that the observer is detecting radiation from an asymmetric emission region that is a stable structure over several orbital periods. The success of this simple model lastly implies that the pitch angles of the particles are small and the pulsed, non-thermal emission originates relatively close to the white dwarf surface., Comment: 13 pages, 14 figures, accepted by MNRAS

A maverick top partner model, decaying to a dark photon was suggested. The dark photon decays to two overlapping electrons for dark photon masses of $\approx 100$ GeV, and results in a so-called lepton-jet. The event includes a top quark as well, which results in events with two boosted objects, one heavy and the other light. We propose a search strategy exploiting the unique signal topology. We show that for a set of kinematic selections, both in hadronic and leptonic decay channel of the SM top quark, almost all background can be eliminated, leaving enough signal events up to top partner mass of about 3 TeV for the search to be viable at the LHC., Comment: Prepared for submission to SciPost Physics (updated in response to referee report)

Magnetar hyperflares are the most plausible explanation for fast radio bursts (FRB) -- enigmatic powerful radio pulses with durations of several milliseconds and high brightness temperatures. The first observational evidence for this scenario was obtained in 2020 April when a FRB was detected from the direction of the Galactic magnetar and soft gamma-ray repeater SGR\,1935+2154. The FRB was preceded by two gamma-ray outburst alerts by the BAT instrument aboard the Swift satellite, which triggered follow-up observations by the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. has observed SGR\,1935+2154 for 2 hr on 2020 April 28. The observations are coincident with X-ray bursts from the magnetar detected by INTEGRAL and Fermi-GBM, thus providing the first very high energy (VHE) gamma-ray observations of a magnetar in a flaring state. High-quality data acquired during these follow-up observations allow us to perform a search for short-time transients. No significant signal at energies $E>0.6$~TeV is found and upper limits on the persistent and transient emission are derived. We here present the analysis of these observations and discuss the obtained results and prospects of the H.E.S.S. follow-up program for soft gamma-ray repeaters., Comment: Received 2021 June 13; accepted 2021 June 28; published 2021 September 29

For a connected reductive group $G$ over a non-archime\-dean local field $F$ of positive characteristic, Genestier and Lafforgue have attached a semisimple parameter $\CL^{ss}(\pi)$ to each irreducible representation $\pi$. Our first result shows that the Genestier-Lafforgue parameter of a tempered $\pi$ can be uniquely refined to a tempered L-parameter $\CL(\pi)$, thus giving the unique local Langlands correspondence which is compatible with the Genestier-Lafforgue construction. Our second result establishes ramification properties of $\CL^{ss}(\pi)$ for unramfied $G$ and supercuspidal $\pi$ constructed by induction from an open compact (modulo center) subgroup. If $L^{ss}(\pi)$ is pure in an appropriate sense, we show that $\CL^{ss}(\pi)$ is ramified (unless $G$ is a torus). If the inducing subgroup is sufficiently small in a precise sense, we show $\mathcal{L}^{ss}(\pi)$ is wildly ramified. The proofs are via global arguments, involving the construction of Poincar\'e series with strict control on ramification when the base curve is $\PP^1$ and a simple application of Deligne's Weil II., Comment: Appendix by Rapha\"el Beuzart-Plessis added to version 3. The result on tempered Weil-Deligne parameters has been extended to discrete series, using the results of the Appendix. The result on ramification of pure supercuspidal parameters is now stated for general unramified reductive groups

Cosmological $N$-body simulations show that Milky Way-sized galaxies harbor a population of unmerged dark matter subhalos. These subhalos could shine in gamma-rays and be eventually detected in gamma-ray surveys as unidentified sources. We performed a thorough selection among unidentified Fermi-LAT Objects (UFOs) to identify them as possible TeV-scale dark matter subhalo candidates. We search for very-high-energy (E $\gtrsim$ 100 GeV) gamma-ray emissions using H.E.S.S. observations towards four selected UFOs. Since no significant very-high-energy gamma-ray emission is detected in any dataset of the four observed UFOs nor in the combined UFO dataset, strong constraints are derived on the product of the velocity-weighted annihilation cross section $\langle \sigma v \rangle$ by the $J$-factor for the dark matter models. The 95% C.L. observed upper limits derived from combined H.E.S.S. observations reach $\langle \sigma v \rangle J$ values of 3.7$\times$10$^{-5}$ and 8.1$\times$10$^{-6}$ GeV$^2$cm$^{-2}$s$^{-1}$ in the $W^+W^-$ and $\tau^+\tau^-$ channels, respectively, for a 1 TeV dark matter mass. Focusing on thermal WIMPs, the H.E.S.S. constraints restrict the $J$-factors to lie in the range 6.1$\times$10$^{19}$ - 2.0$\times$10$^{21}$ GeV$^2$cm$^{-5}$, and the masses to lie between 0.2 and 6 TeV in the $W^+W^-$ channel. For the $\tau^+\tau^-$ channel, the $J$-factors lie in the range 7.0$\times$10$^{19}$ - 7.1$\times$10$^{20}$ GeV$^2$cm$^{-5}$ and the masses lie between 0.2 and 0.5 TeV. Assuming model-dependent predictions from cosmological N-body simulations on the $J$-factor distribution for Milky Way-sized galaxies, the dark matter models with masses greater than 0.3 TeV for the UFO emissions can be ruled out at high confidence level., Comment: 11 pages, 7 figures, matches accepted version in The Astrophysical Journal

The effect of silica-promotion on the reduction of iron oxides in hydrogen was investigated using in situ X-ray diffraction and aberration-corrected transmission electron microscopy to understand the mechanism of reduction and the identity of the iron(II) silicate phase that has historically been designated as the cause of the iron-silica interaction in such materials. In the absence of a silica promoter the reduction of hematite to {\alpha}-Fe proceeds via magnetite. Silica promoted amorphous iron oxide is reduced to {\alpha}-Fe via stable magnetite and w\"ustite phases. During reduction of silica-promoted iron oxide, Fe0 diffuses out of the amorphous silica-promoted iron oxide matrix upon reduction from Fe2+ and coexists with an amorphous Fe-O-Si matrix. Certain portions of w\"ustite remain difficult to reduce to {\alpha}-Fe owing to the formation of a protective silica-containing layer covering the remaining iron oxide regions. Given sufficient energy, this amorphous Fe-O-Si material forms ordered, crystalline fayalite., Comment: 8 figures

Sc3Mn3Al7Si5 is a rare example of a correlated metal in which the Mn moments form a kagome lattice. The absence of magnetic ordering to the lowest temperatures suggests that geometrical frustration of magnetic interactions may lead to strong magnetic fluctuations. We have performed inelastic neutron scattering measurements on Sc3Mn3Al7Si5, finding that phonon scattering dominates for energies from ~20 - 50 meV. These results are in good agreement with ab initio calculations of the phonon dispersions and densities of states, and as well reproduce the measured specific heat. A weak magnetic signal was detected at energies less than ~10 meV, present only at the lowest temperatures. The magnetic signal is broad and quasielastic, as expected for metallic paramagnets.

Let $E$ be an elliptic curve defined over a number field $K$ and let $v$ be a finite place of $K$. Write $K^{tv}$ the maximal extension of $K$ in which $v$ is totally split and $L$ the field generated over $K^{tv}$ by all torsion points of $E$. Under some conditions, we will show that the absolute logarithmic Weil height (resp. N\'eron-Tate height) of any element of $L^*$ (resp. $E(L)$) is either $0$ or bounded from below by a positive constant depending only on $E, K$ and $v$. This lower bound will be explicit in the toric case when $K=\mathbb{Q}$., Comment: Theorem 1.6 has been improved. As a very special case, we provide, for every D\in\N and every elliptic curve E defined over Q(\sqrt{D}), an explicit lower bound of the Weil height for points lying in Q(\sqrt{D}, E_\tors)^*\backslash \mu_\infty

Pyrochlore lattices, which are found in two important classes of materials -- the $A_2B_2X_7$ pyrochlore family and the $AB_2X_4$ spinel family -- are the quintessential 3-dimensional frustrated lattice architecture. While historically oxides ($X =$~O) have played the starring role in this field, the past decade has seen materials synthesis breakthroughs that have lead to the emergence of fluoride ($X =$~F) and chalcogenide ($X =$~S, Se) pyrochlore lattice materials. In this Research Update, we summarize recent progress in understanding the magnetically frustrated ground states in three families of non-oxide pyrochlore lattice materials: (i) $3d$-transition metal fluoride pyrochlores, (ii) rare earth chalcogenide spinels, and (iii) chromium chalcogenide spinels with a breathing pyrochlore lattice. We highlight how the change of anion can modify the single ion spin anisotropy due to crystal electric field effects, stabilize the incorporation of new magnetic elements, and dramatically alter the exchange pathways and thereby lead to new magnetic ground states. We also consider a range of future directions -- materials with the potential to define the next decade of research in frustrated magnetism., Comment: 12 pages, 6 figures, 2 tables

The manipulation of mesoscale domain wall phenomena has emerged as a powerful strategy for designing ferroelectric responses in functional devices, but its full potential has not yet been realized in the field of magnetism. We show that mechanically strained samples of Mn$_3$O$_4$ and MnV$_2$O$_4$ exhibit a stripe-like patterning of the bulk magnetization below known magnetostructural transitions, similar to the structural domains reported in ferroelectric materials. Building off our previous magnetic force microscopy data, we use small angle neutron scattering to show that these patterns extend to the bulk, and demonstrate an ability to manipulate the domain walls via applied magnetic field and mechanical stress. We then connect these domains back to the anomalously large magnetoelastic and magnetodielectric response functions reported in these materials, directly correlating local and macroscopic measurements on the same crystals., Comment: 19 pages, 13 figures

Multi-agent reinforcement learning has recently shown great promise as an approach to networked system control. Arguably, one of the most difficult and important tasks for which large scale networked system control is applicable is common-pool resource management. Crucial common-pool resources include arable land, fresh water, wetlands, wildlife, fish stock, forests and the atmosphere, of which proper management is related to some of society's greatest challenges such as food security, inequality and climate change. Here we take inspiration from a recent research program investigating the game-theoretic incentives of humans in social dilemma situations such as the well-known tragedy of the commons. However, instead of focusing on biologically evolved human-like agents, our concern is rather to better understand the learning and operating behaviour of engineered networked systems comprising general-purpose reinforcement learning agents, subject only to nonbiological constraints such as memory, computation and communication bandwidth. Harnessing tools from empirical game-theoretic analysis, we analyse the differences in resulting solution concepts that stem from employing different information structures in the design of networked multi-agent systems. These information structures pertain to the type of information shared between agents as well as the employed communication protocol and network topology. Our analysis contributes new insights into the consequences associated with certain design choices and provides an additional dimension of comparison between systems beyond efficiency, robustness, scalability and mean control performance., Comment: 17 pages, 16 Figures, to appear in Advances of Neural Information Processing Systems (NeurIPS) conference, 2020

Heavy transition metal magnets with $J_{\rm eff}$ $=$ 1/2 electronic ground states have attracted recent interest due to their penchant for hosting new classes of quantum spin liquids and superconductors. Unfortunately, model systems with ideal $J_{\rm eff}$ $=$ 1/2 states are scarce due to the importance of non-cubic local distortions in most candidate materials. In this work, we identify a family of iridium halide systems [i.e. K$_2$IrCl$_6$, K$_2$IrBr$_6$, (NH$_4$)$_2$IrCl$_6$, and Na$_2$IrCl$_6 \cdotp $ 6(H$_2$O)] with Ir$^{4+}$ electronic ground states in extremely close proximity to the ideal $J_{\rm eff}$ $=$ 1/2 limit, despite a variation in the low-temperature global crystal structures. We also find ordered magnetic ground states for the three anhydrous systems, with single crystal neutron diffraction on K$_2$IrBr$_6$ revealing Type-I antiferromagnetism. This spin configuration is consistent with expectations for significant Kitaev exchange in a face-centered-cubic magnet., Comment: 14 pages, 9 figures

This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case. The second is a formula for the multiplicities of generic representations in the $p$-adic case that extends previous work of Feigon-Lapid-Offen. Both results are stated in terms of Arthur-Clozel's quadratic local base-change and the proofs are based on local analogs of two relative trace formulas previously studied by Jacquet and Ye and known as (relative) Kuznetsov trace formulas.

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called $*$-generic, to the Jacquet-Rallis trace formula for linear groups. We offer two different computations of these contributions: one, based on truncation, is expressed in terms of regularized Rankin-Selberg periods of Eisenstein series and Flicker-Rallis intertwining periods. The other, built upon Zeta integrals, is expressed in terms of functionals on the Whittaker model. A direct proof of the equality between the two expressions is also given. Finally several useful auxiliary results about the spectral expansion of the Jacquet-Rallis trace formula are provided., Comment: In English

We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: $D$, which determines the range of the coefficients of the on-site potentials, and $W$, which defines the strength of the nearest-neighbor interactions. We fix $W=4$ and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. $D\rightarrow 0$. We show that the probability density distribution of the normal modes' frequencies takes a `U'-shaped profile as $D$ decreases. Furthermore, we use two quantities for estimating the modes' spatial extent, the so-called localization volume $V$ (which is related to the mode's second moment) and the mode's participation number $P$. We show that both quantities scale as $\propto D^{-2}$ when $D$ approaches zero and we numerically verify a proportionality relation between them as $V/P \approx 2.6$., Comment: 6 pages, 7 figures

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its refinement Ichino--Ikeda conjecture for $\mathrm{U}(n)\times\mathrm{U}(n+1)$ in the stable case., Comment: minor revision; 48 pages; to appear in Annals of Mathematics

Let $E$ be an elliptic curve defined over a number field $K$ without complex multiplication. If $\Gamma \subset E(\overline{K})$ is a subgroup of finite rank, a very special case of a conjecture of R\'emond predicts that points of small height in $E(K(\Gamma))$ lie in the division group of $\Gamma$. Using an equidistribution argument, we will show that this conjecture is true for groups of rank arbitrarily large., Comment: Amoroso pointed out that [14, Lemma 5.8] was false (a counterexample has been provided). Hence, the previous version has been modified in order to make it independent of this lemma. Consequently, the descent argument presented in Section 3 (and used in Section 4) is different. Moreover, the main theorem suffered a slight degradation. Final version

We apply the standard radio pulsar rotating vector model to the white dwarf pulsar AR Sco's optical polarization position angle swings folded at the white dwarf's spin period as obtained by Buckley et al. (2017). Owing to the long duty cycle of spin pulsations with a good signal-to-noise ratio over the entire spin phase, in contrast to neutron star radio pulsars, we find well-constrained values for the magnetic obliquity $\alpha$ and observer viewing direction $\zeta$ with respect to the spin axis. We find $\cos\alpha=0.060^{+0.050}_{-0.053}$ and $\cos\zeta=0.49^{+0.09}_{-0.08}$, implying an orthogonal rotator with an observer angle $\zeta={60.4^\circ}^{+5.3^\circ}_{-6.0^\circ}$. This orthogonal nature of the rotator is consistent with the optical light curve consisting of two pulses per spin period, separated by $180^\circ$ in phase. Under the assumption that $\zeta \approx i$, where $i$ is the orbital inclination, and a Roche-lobe-filling companion M star, we obtain $m_{\rm WD} = 1.00^{+0.16}_{-0.10} M_\odot$ for the white dwarf mass. These polarization modeling results suggest the that non-thermal emission arises from a dipolar white dwarf magnetosphere and close to the star, with synchrotron radiation (if non-zero pitch angles can be maintained) being the plausible loss mechanism, marking AR Sco as an exceptional system for future theoretical and observational study., Comment: 11 pages, 7 figures, accepted by ApJ

Marsh et al. detected radio and optical pulsations from the binary system AR Scorpii (AR Sco). This system, with an orbital period of 3.56 h, is composed of a cool, low-mass star and a white dwarf with a spin period of 1.95 min. Optical observations by Buckley et al. showed that the polarimetric emission from the white dwarf is strongly linearly polarised ( up to $\sim40\%$) with periodically changing intensities. This periodic non-thermal emission is thought to be powered by the highly magnetised ($ 5 \times 10^{8} $ G) white dwarf that is spinning down. The morphology of the polarisation signal, namely the position angle plotted against the phase angle, is similar to that seen in many radio pulsars. In this paper, we demonstrate that we can fit the traditional pulsar rotating vector model to the optical position angle. We used a Markov-chain-Monte-Carlo technique to find the best fit for the model yielding a magnetic inclination angle of $\alpha = (86.6^{+3.0}_{-2.8})^{\circ}$ and an observer angle of $\zeta = (60.5^{+5.3}_{-6.1})^{\circ}$. This modelling supports the scenario that the synchrotron emission originates above the polar caps of the white dwarf pulsar and that the latter is an orthogonal rotator., Comment: 6 pages, 2 figures, HEASA 2018 proceedings of science

The symmetry of local moments plays a defining role in the nature of exotic grounds states stabilized in frustrated magnetic materials. We present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). These compounds form in the spinel structure, with the rare earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed modes in the INS spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground state wavefunctions in the local electron picture. In this way, we experimentally confirm MgTm$_2$Se$_4$ has a non-magnetic ground state, and MgYb$_2$Se$_4$ has effective $S=\frac{1}{2}$ spins with $g_\parallel = 5.188(79)$ and $g_\perp = 0.923(85)~\mu_B$. The spectrum of MgHo$_2$Se$_4$ indicates a ground state doublet containing Ising spins with $g_\parallel = 2.72(46)$, though low-lying CEF levels are also seen at thermally accessible energies $\delta_E = 0.591(36)$, 0.945(30) and 2.88(7)~meV, which can complicate interpretation. These results are used to comment on measured magnetization data of all compounds, and are compared to published results on the material MgEr$_2$Se$_4$., Comment: 13 pages, 7 figures

We study digital images of r-regular objects where a pixel is black if it is completely inside the object, white if it is completely inside the complement of the object, and grey otherwise. We call such images trinary. We discuss possible configurations of pixels in trinary images of r-regular objects at certain resolutions and propose a method for reconstructing objects from such images. We show that the reconstructed object is close to the original object in Hausdorff norm, and that there is a homeomorphism of the plane taking the reconstructed set to the original.

Quantum magnets with significant bond-directional Ising interactions, so-called Kitaev materials, have attracted tremendous attention recently in the search for exotic spin liquid states. Here we present a comprehensive set of measurements that enables us to investigate the crystal structures, Ir$^{4+}$ single ion properties, and magnetic ground states of the double perovskite iridates La$_2B$IrO$_6$ ($B$ $=$ Mg, Zn) and $A_2$CeIrO$_6$ ($A$ $=$ Ba, Sr) with a large nearest neighbor distance $>$ 5 Angstroms between Ir$^{4+}$ ions. Our neutron powder diffraction data on Ba$_2$CeIrO$_6$ can be refined in the cubic space group Fm$\bar{3}$m, while the other three systems are characterized by weak monoclinic structural distortions. Despite the variance in the non-cubic crystal field experienced by the Ir$^{4+}$ ions in these materials, X-ray absorption spectroscopy and resonant inelastic x-ray scattering are consistent with $J_{\rm eff}$ $=$ 1/2 moments in all cases. Furthermore, neutron scattering and resonant magnetic x-ray scattering show that these systems host A-type antiferromagnetic order. These electronic and magnetic ground states are consistent with expectations for face-centered-cubic magnets with significant antiferromagnetic Kitaev exchange, which indicates that spacing magnetic ions far apart may be a promising design principle for uncovering additional Kitaev materials., Comment: 12 pages, 7 figures

Recently, R\'emond stated a very general conjecture on lower bounds of a normalized height on either an abelian variety or a power of the multiplicative group. In this note, we extend a particular case of this conjecture to split semi-abelian varieties of the form $\mathbb{G}_m^n \times A$. This allows us to connect many results already existing in the litterature. Finally, we give new examples for which this conjecture holds., Comment: Final version. in French language. Published in Bull. Lond. Math. Soc. NB: this version is slightly different from the one published http://doi.org/10.1112/blms.12693

We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on a previous result of W. Zhang on the compatibility of smooth transfer with a (partial) Fourier transform., Comment: Streamlined proof avoiding to use the existence of smooth transfer and local relative trace formulas

We establish an explicit Plancherel decomposition for $\mathrm{GL}_n(F)\backslash \mathrm{GL}_n(E)$ where $E/F$ is a quadratic extension of local fields of characteristic zero by making use of a local functional equation for Asai $\gamma$-factors. We also give two applications of this Plancherel formula: first to the global Ichino-Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by W. Zhang and secondly to the Hiraga-Ichino-Ikeda conjecture on formal degrees in the case of unitary groups.

In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places and prove the equality between Rankin-Selberg's and Langlands-Shahidi's $\epsilon$-factors at every place. Our proofs work uniformly for any characteristic zero local field and use as only input the global functional equation and a globalization result for a dense subset of tempered representations that we infer from work of Finis-Lapid-M\"uller. These results are used in another paper by the author to establish an explicit Plancherel decomposition for $\mathrm{GL}_n(F)\backslash \mathrm{GL}_n(E)$, $E/F$ a quadratic extension of local fields, with applications to the Ichino-Ikeda and formal degree conjecture for unitary groups.