Datasets:

ttj

/

metadata_arxiv

like 0

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally we offer some speculations about the physical relevance of the localization transition in these models.

2104.14388

Quantum spins of mesoscopic size are a well-studied playground for engineering non-classical states. If the spin represents the collective state of an ensemble of qubits, its non-classical behavior is linked to entanglement between the qubits. In this work, we report on an experimental study of entanglement in dysprosium's electronic spin. Its ground state, of angular momentum $J=8$, can formally be viewed as a set of $2J$ qubits symmetric upon exchange. To access entanglement properties, we partition the spin by optically coupling it to an excited state $J'=J-1$, which removes a pair of qubits in a state defined by the light polarization. Starting with the well-known W and squeezed states, we extract the concurrence of qubit pairs, which quantifies their non-classical character. We also directly demonstrate entanglement between the 14- and 2-qubit subsystems via an increase in entropy upon partition. In a complementary set of experiments, we probe decoherence of a state prepared in the excited level $J'=J+1$ and interpret spontaneous emission as a loss of a qubit pair in a random state. This allows us to contrast the robustness of pairwise entanglement of the W state with the fragility of the coherence involved in a Schr\"odinger cat state. Our findings open up the possibility to engineer novel types of entangled atomic ensembles, in which entanglement occurs within each atom's electronic spin as well as between different atoms.

2104.14389

We provide a class of quantum evolution beyond Markovian semigroup. This class is governed by a hybrid Davies like generator such that dissipation is controlled by a suitable memory kernel and decoherence by standard GKLS generator. These two processes commute and both of them commute with the unitary evolution controlled by the systems Hamiltonian. The corresponding memory kernel gives rise to semi-Markov evolution of the diagonal elements of the density matrix. However, the corresponding evolution needs not be completely positive. The role of decoherence generator is to restore complete positivity. Hence, to pose the dynamical problem one needs two processes generated by classical semi-Markov memory kernel and purely quantum decoherence generator. This scheme is illustrated for a qubit evolution.

2104.14390

Atomic interference experiments can probe the gravitational redshift via the internal energy splitting of atoms and thus give direct access to test the universality of the coupling between matter-energy and gravity at different spacetime points. By including possible violations of the equivalence principle in a fully quantized treatment of all degrees of freedom, we characterize how the sensitivity to gravitational redshift violations arises in atomic clocks and atom interferometers, as well as their underlying limitations. Specifically, we show that: (i.) Contributions beyond linear order to trapping potentials lead to such a sensitivity of trapped atomic clocks. (ii.) While Bragg-type interferometers, even with a superposition of internal states, with state-independent, linear interaction potentials are at first insensitive to gravitational redshift tests, modified configurations, for example by relaunching the atoms, can mimic such tests tests under certain conditions. (iii.) Guided atom interferometers are comparable to atomic clocks. (iv.) Internal transitions lead to state-dependent interaction potentials through which light-pulse atom interferometers can become sensitive to gravitational redshift violations.

2104.14391

Intelligent task placement and management of tasks in large-scale fog platforms is challenging due to the highly volatile nature of modern workload applications and sensitive user requirements of low energy consumption and response time. Container orchestration platforms have emerged to alleviate this problem with prior art either using heuristics to quickly reach scheduling decisions or AI driven methods like reinforcement learning and evolutionary approaches to adapt to dynamic scenarios. The former often fail to quickly adapt in highly dynamic environments, whereas the latter have run-times that are slow enough to negatively impact response time. Therefore, there is a need for scheduling policies that are both reactive to work efficiently in volatile environments and have low scheduling overheads. To achieve this, we propose a Gradient Based Optimization Strategy using Back-propagation of gradients with respect to Input (GOBI). Further, we leverage the accuracy of predictive digital-twin models and simulation capabilities by developing a Coupled Simulation and Container Orchestration Framework (COSCO). Using this, we create a hybrid simulation driven decision approach, GOBI*, to optimize Quality of Service (QoS) parameters. Co-simulation and the back-propagation approaches allow these methods to adapt quickly in volatile environments. Experiments conducted using real-world data on fog applications using the GOBI and GOBI* methods, show a significant improvement in terms of energy consumption, response time, Service Level Objective and scheduling time by up to 15, 40, 4, and 82 percent respectively when compared to the state-of-the-art algorithms.

2104.14392

In a quantum-noise limited system, weak-value amplification using post-selection normally does not produce more sensitive measurements than standard methods for ideal detectors: the increased weak value is compensated by the reduced power due to the small post-selection probability. Here we experimentally demonstrate recycled weak-value measurements using a pulsed light source and optical switch to enable nearly deterministic weak-value amplification of a mirror tilt. Using photon counting detectors, we demonstrate a signal improvement by a factor of $4.4 \pm 0.2$ and a signal-to-noise ratio improvement of $2.10 \pm 0.06$, compared to a single-pass weak-value experiment, and also compared to a conventional direct measurement of the tilt. The signal-to-noise ratio improvement could reach around 6 for the parameters of this experiment, assuming lower loss elements.

2104.14393

We experimentally achieve wave mode conversion and rainbow trapping in an elastic waveguide loaded with an array of resonators. Rainbow trapping is a phenomenon that induces wave confinement as a result of a spatial variation of the wave velocity, here promoted by gently varying the length of consecutive resonators. By breaking the geometrical symmetry of the waveguide, we combine the wave speed reduction with a reflection mechanism that mode-converts flexural waves impinging on the array into torsional waves travelling along opposite directions. The framework presented herein may open new opportunities in the context of wave manipulation through the realization of novel structural components with concurrent wave conversion and energy trapping capabilities.

2104.14394

What does it mean today to study a problem from a computational point of view? We focus on parameterized complexity and on Column 16 "Graph Restrictions and Their Effect" of D. S. Johnson's Ongoing guide, where several puzzles were proposed in a summary table with 30 graph classes as rows and 11 problems as columns. Several of the 330 entries remain unclassified into Polynomial or NP-complete after 35 years. We provide a full dichotomy for the Steiner Tree column by proving that the problem is NP-complete when restricted to Undirected Path graphs. We revise Johnson's summary table according to the granularity provided by the parameterized complexity for NP-complete problems.

2104.14395

In robotics, accurate ground-truth position fostered the development of mapping and localization algorithms through the creation of cornerstone datasets. In outdoor environments and over long distances, total stations are the most accurate and precise measurement instruments for this purpose. Most total station-based systems in the literature are limited to three Degrees Of Freedoms (DOFs), due to the use of a single-prism tracking approach. In this paper, we present preliminary work on measuring a full pose of a vehicle, bringing the referencing system to six DOFs. Three total stations are used to track in real time three prisms attached to a target platform. We describe the structure of the referencing system and the protocol for acquiring the ground truth with this system. We evaluated its precision in a variety of different outdoor environments, ranging from open-sky to forest trails, and compare this system with another popular source of reference position, the Real Time Kinematics (RTK) positioning solution. Results show that our approach is the most precise, reaching an average positional error of 10 mm and 0.6 deg. This difference in performance was particularly stark in environments where Global Navigation Satellite System (GNSS) signals can be weaker due to overreaching vegetation.

2104.14396

In this paper, we study the feasibility of coupling the PN ranging with filtered high-order modulations, and investigate the simultaneous demodulation of a high-rate telemetry stream while tracking the PN ranging sequence. Accordingly, we design a receiver scheme that is able to perform a parallel cancellation, in closed-loop, of the ranging and the telemetry signal reciprocally. From our analysis, we find that the non-constant envelope property of the modulation causes an additional jitter on the PN ranging timing estimation that, on the other hand, can be limited by properly sizing the receiver loop bandwidth. Our study proves that the use of filtered high-order modulations combined with PN ranging outperforms the state-of-the-art in terms of spectral efficiency and achievable data rate, while having comparable ranging performance.

2104.14397

We study the MaxCut problem for graphs $G=(V,E)$. The problem is NP-hard, there are two main approximation algorithms with theoretical guarantees: (1) the Goemans \& Williamson algorithm uses semi-definite programming to provide a 0.878MaxCut approximation (which, if the Unique Games Conjecture is true, is the best that can be done in polynomial time) and (2) Trevisan proposed an algorithm using spectral graph theory from which a 0.614MaxCut approximation can be obtained. We discuss a new approach using a specific quadratic program and prove that its solution can be used to obtain at least a 0.502MaxCut approximation. The algorithm seems to perform well in practice.

2104.14404

A communicating system is $k$-synchronizable if all of the message sequence charts representing the executions can be divided into slices of $k$ sends followed by $k$ receptions. It was previously shown that, for a fixed given $k$, one could decide whether a communicating system is $k$-synchronizable. This result is interesting because the reachability problem can be solved for $k$-synchronizable systems. However, the decision procedure assumes that the bound $k$ is fixed. In this paper we improve this result and show that it is possible to decide if such a bound $k$ exists.

2104.14408

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob's ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. In order to generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water towards the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional.

2104.14410

In this note we confirm the guess of Calegari, Garoufalidis and Zagier in Arxiv 1712.04887 that $R_\zeta=c_\zeta^2$, where $R_\zeta$ is their map on $K_3$ defined using the cyclic quantum dilogarithm and $c_\zeta$ is the Chern class map on $K_3$.

2104.14413

We present a search for continuous gravitational-wave emission due to r-modes in the pulsar PSR J0537-6910 using data from the LIGO-Virgo Collaboration observing run O3. PSR J0537-6910 is a young energetic X-ray pulsar and is the most frequent glitcher known. The inter-glitch braking index of the pulsar suggests that gravitational-wave emission due to r-mode oscillations may play an important role in the spin evolution of this pulsar. Theoretical models confirm this possibility and predict emission at a level that can be probed by ground-based detectors. In order to explore this scenario, we search for r-mode emission in the epochs between glitches by using a contemporaneous timing ephemeris obtained from NICER data. We do not detect any signals in the theoretically expected band of 86-97 Hz, and report upper limits on the amplitude of the gravitational waves. Our results improve on previous amplitude upper limits from r-modes in J0537-6910 by a factor of up to 3 and place stringent constraints on theoretical models for r-mode driven spin-down in PSR J0537-6910, especially for higher frequencies at which our results reach below the spin-down limit defined by energy conservation.

2104.14417

The paper discusses how robots enable occupant-safe continuous protection for students when schools reopen. Conventionally, fixed air filters are not used as a key pandemic prevention method for public indoor spaces because they are unable to trap the airborne pathogens in time in the entire room. However, by combining the mobility of a robot with air filtration, the efficacy of cleaning up the air around multiple people is largely increased. A disinfection co-robot prototype is thus developed to provide continuous and occupant-friendly protection to people gathering indoors, specifically for students in a classroom scenario. In a static classroom with students sitting in a grid pattern, the mobile robot is able to serve up to 14 students per cycle while reducing the worst-case pathogen dosage by 20%, and with higher robustness compared to a static filter. The extent of robot protection is optimized by tuning the passing distance and speed, such that a robot is able to serve more people given a threshold of worst-case dosage a person can receive.

2104.14418

We report on experimental results obtained from collisions of slow highly charged Ar9+ ions with a carbon monoxide dimer (CO)2 target. A COLTRIMS setup and a Coulomb explosion imaging approach are used to reconstruct the structure of the CO dimers. The three dimensional structure is deduced from the 2-body and 3-body dissociation channels from which both the intermolecular bond length and the relative orientation of the two molecules are determined. For the 3-body channels, the experimental data are interpreted with the help of a classical model in which the trajectories of the three emitted fragments are numerically integrated. We measured the equilibrium intermolecular distance to be Re = 4.2 A. The orientation of both CO molecules with respect to the dimer axis is found to be quasi-isotropic due to the large vibrational temperature of the gas jet.

2104.14419

Non-small cell lung cancer (NSCLC) is a serious disease and has a high recurrence rate after the surgery. Recently, many machine learning methods have been proposed for recurrence prediction. The methods using gene data have high prediction accuracy but require high cost. Although the radiomics signatures using only CT image are not expensive, its accuracy is relatively low. In this paper, we propose a genotype-guided radiomics method (GGR) for obtaining high prediction accuracy with low cost. We used a public radiogenomics dataset of NSCLC, which includes CT images and gene data. The proposed method is a two-step method, which consists of two models. The first model is a gene estimation model, which is used to estimate the gene expression from radiomics features and deep features extracted from computer tomography (CT) image. The second model is used to predict the recurrence using the estimated gene expression data. The proposed GGR method designed based on hybrid features which is combination of handcrafted-based and deep learning-based. The experiments demonstrated that the prediction accuracy can be improved significantly from 78.61% (existing radiomics method) and 79.14% (deep learning method) to 83.28% by the proposed GGR.

2104.14420

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational inference or stochastic-gradient Markov chain Monte Carlo (SGMCMC). To investigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures. We show that (1) BNNs can achieve significant performance gains over standard training and deep ensembles; (2) a single long HMC chain can provide a comparable representation of the posterior to multiple shorter chains; (3) in contrast to recent studies, we find posterior tempering is not needed for near-optimal performance, with little evidence for a "cold posterior" effect, which we show is largely an artifact of data augmentation; (4) BMA performance is robust to the choice of prior scale, and relatively similar for diagonal Gaussian, mixture of Gaussian, and logistic priors; (5) Bayesian neural networks show surprisingly poor generalization under domain shift; (6) while cheaper alternatives such as deep ensembles and SGMCMC methods can provide good generalization, they provide distinct predictive distributions from HMC. Notably, deep ensemble predictive distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.

2104.14421

The IPv6 over Low-powered Wireless Personal Area Network (6LoWPAN) protocol was introduced to allow the transmission of Internet Protocol version 6 (IPv6) packets using the smaller-size frames of the IEEE 802.15.4 standard, which is used in many Internet of Things (IoT) networks. The primary duty of the 6LoWPAN protocol is packet fragmentation and reassembly. However, the protocol standard currently does not include any security measures, not even authenticating the fragments immediate sender. This lack of immediate-sender authentication opens the door for adversaries to launch several attacks on the fragmentation process, such as the buffer-reservation attacks that lead to a Denial of Service (DoS) attack and resource exhaustion of the victim nodes. This paper proposes a security integration between 6LoWPAN and the Routing Protocol for Low Power and Lossy Networks (RPL) through the Chained Secure Mode (CSM) framework as a possible solution. Since the CSM framework provides a mean of immediate-sender trust, through the use of Network Coding (NC), and an integration interface for the other protocols (or mechanisms) to use this trust to build security decisions, 6LoWPAN can use this integration to build a chain-of-trust along the fragments routing path. A proof-of-concept implementation was done in Contiki Operating System (OS), and its security and performance were evaluated against an external adversary launching a buffer-reservation attack. The results from the evaluation showed significant mitigation of the attack with almost no increase in power consumption, which presents the great potential for such integration to secure the forwarding process at the 6LoWPAN Adaptation Layer

2104.14422

Multicollinearity produces an inflation in the variance of the Ordinary Least Squares estimators due to the correlation between two or more independent variables (including the constant term). A widely applied solution is to estimate with penalized estimators (such as the ridge estimator, the Liu estimator, etc.) which exchange the mean square error by the bias. Although the variance diminishes with these procedures, all seems to indicate that the inference is lost and also the goodness of fit. Alternatively, the raise regression (\cite{Garcia2011} and \cite{Salmeron2017}) allows the mitigation of the problems generated by multicollinearity but without losing the inference and keeping the coefficient of determination. This paper completely formalizes the raise estimator summarizing all the previous contributions: its mean square error, the variance inflation factor, the condition number, the adequate selection of the variable to be raised, the successive raising and the relation between the raise and the ridge estimator. As a novelty, it is also presented the estimation method, the relation between the raise and the residualization, it is analyzed the norm of the estimator and the behaviour of the individual and joint significance test and the behaviour of the mean square error and the coefficient of variation. The usefulness of the raise regression as alternative to mitigate the multicollinearity is illustrated with two empirical applications.

2104.14423

We present a novel method for finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

2104.14424

We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit (SQL). We find that the Energy Resolution Limit (ERL), pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.

2104.14425

Discovering novel high-level concepts is one of the most important steps needed for human-level AI. In inductive logic programming (ILP), discovering novel high-level concepts is known as predicate invention (PI). Although seen as crucial since the founding of ILP, PI is notoriously difficult and most ILP systems do not support it. In this paper, we introduce POPPI, an ILP system that formulates the PI problem as an answer set programming problem. Our experiments show that (i) PI can drastically improve learning performance when useful, (ii) PI is not too costly when unnecessary, and (iii) POPPI can substantially outperform existing ILP systems.

2104.14426

Network visualisation, drawn from attitudinal survey data, exposes the structure of opinion-based groups. We make use of these network projections to identify the groups reliably through community detection algorithms and to examine social-identity-based polarisation.Our goal is to present a method for revealing polarisation in attitudinal surveys. This method can be broken down into the following steps: data preparation, construction of similarity-based net-works, algorithmic identification of opinion-based groups, and identification of item importance for community structure. We examine the method's performance and possible scope through applying it to empirical data and to a broad range of synthetic data sets. The empirical data application points out possible conclusions (i.e. social-identity polarization), whereas the synthetic data sets marks out the method's boundaries. Next to an application example on political attitude survey, our results suggest that the method works for various surveys but is also moderated by the efficacy of the community detection algorithms. Concerning the identification of opinion-based groups, we provide a solid method to rank the item's influence on group formation and as a group identifier. We discuss how this network approach to identifying polarization can classify non-overlapping opinion-based groups even in the absence of extreme opinions.

2104.14427

We take the opportunity offered by Schirmacher, Bryk, Ruocco et al. to explain more in depth the details of our theoretical model (Phys. Rev. Lett. 112, 145501 (2019)) and its improved and extended version (Phys. Rev. Research 2, 013267, (2020)). We unequivocally show the presence of a boson peak (BP) anomaly in solids due to anharmonic diffusive damping (of the Akhiezer type) and anharmonic corrections to the low-energy plane wave $\omega=v\,k$ dispersion relation. Finally, we emphasize the need of going beyond the old-fashion "harmonic disorder" BP picture which is clearly unable to explain the recent experimental observations of BP in perfectly ordered crystals. For the sake of openness and transparency, we provide a Mathematica file downloadable by all interested readers who wish to check our calculations.

2104.14428

Randomized Numerical Linear Algebra (RandNLA) is a powerful class of methods, widely used in High Performance Computing (HPC). RandNLA provides approximate solutions to linear algebra functions applied to large signals, at reduced computational costs. However, the randomization step for dimensionality reduction may itself become the computational bottleneck on traditional hardware. Leveraging near constant-time linear random projections delivered by LightOn Optical Processing Units we show that randomization can be significantly accelerated, at negligible precision loss, in a wide range of important RandNLA algorithms, such as RandSVD or trace estimators.

2104.14429

Recently, people tried to use a few anomalies for video anomaly detection (VAD) instead of only normal data during the training process. A side effect of data imbalance occurs when a few abnormal data face a vast number of normal data. The latest VAD works use triplet loss or data re-sampling strategy to lessen this problem. However, there is still no elaborately designed structure for discriminative VAD with a few anomalies. In this paper, we propose a DiscRiminative-gEnerative duAl Memory (DREAM) anomaly detection model to take advantage of a few anomalies and solve data imbalance. We use two shallow discriminators to tighten the normal feature distribution boundary along with a generator for the next frame prediction. Further, we propose a dual memory module to obtain a sparse feature representation in both normality and abnormality space. As a result, DREAM not only solves the data imbalance problem but also learn a reasonable feature space. Further theoretical analysis shows that our DREAM also works for the unknown anomalies. Comparing with the previous methods on UCSD Ped1, UCSD Ped2, CUHK Avenue, and ShanghaiTech, our model outperforms all the baselines with no extra parameters. The ablation study demonstrates the effectiveness of our dual memory module and discriminative-generative network.

2104.14430

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. In particular, the upper bound of order $\mathsf{A} \log^2(\mathsf{A})$ and lower bound of order $\sqrt{\mathsf{A}}$ are established where $\mathsf{A}$ is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to $ - \log P_{Y^\star}(0)$ where $P_{Y^\star}$ is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established.

2104.14431

Hydrodynamic flow of charge carriers in graphene is an energy flow unlike the usual mass flow in conventional fluids. In neutral graphene, the energy flow is decoupled from the electric current, making it diffcult to observe the hydrodynamic effects and measure the viscosity of the electronic fluid by means of electric current measurements. Nevertheless one can observe nonuniform current densities by confining the charge flow to a narrow channel, where the current can exhibit the well known ballistic-diffusive crossover. The standard diffusive behavior with the uniform current density across the channel is achieved under the assumptions of specular scattering on the channel boundaries. This flow can also be made nonuniform by applying weak magnetic fields. In this case, the curvature of the current density profile is determined by the quasiparticle recombination processes dominated by the disorder-assisted electron-phonon scattering - the so-called supercollisions.

2104.14432

In this note, we present deterministic algorithms for the Hidden Subgroup Problem. The algorithm for abelian groups achieves the same asymptotic query complexity as the optimal randomized algorithm. The algorithm for non-abelian groups comes within a polylogarithmic factor of the optimal randomized query complexity.

2104.14436

Imagine, you enter a grocery store to buy food. How many peopledo you overlap with in this store? How much time do you overlap witheach person in the store? In this paper, we answer these questions bystudying the overlap times between customers in the infinite serverqueue. We compute in closed form the steady state distribution ofthe overlap time between a pair of customers and the distribution ofthe number of customers that an arriving customer will overlap with.Finally, we define a residual process that counts the number of over-lapping customers that overlap in the queue for at least{\delta}time unitsand compute its mean, variance, and distribution in the exponentialservice setting

2104.14437

Strong field processes in the non-relativistic regime are insensitive to the electron spin, i.e. the observables appear to be independent of this electron property. This does not have to be the case for several active electrons where Pauli principle may affect the their dynamics. We exemplify this statement studying model atoms with three active electrons interacting with strong pulsed radiation, using an ab-initio time-dependent Schr\"odinger equation on a grid. In our restricted dimensionality model we are able, for the first time, to analyse momenta correlations of the three outgoing electrons using Dalitz plots. We show that significant differences are obtained between model Neon and Nitrogen atoms. These differences are traced back to the different symmetries of the electronic wavefunctions, and directly related to the different initial state spin components.

2104.14438

Machine learning potentials have emerged as a powerful tool to extend the time and length scales of first principles-quality simulations. Still, most machine learning potentials cannot distinguish different electronic spin orientations and thus are not applicable to materials in different magnetic states. Here, we propose spin-dependent atom-centered symmetry functions as a new type of descriptor taking the atomic spin degrees of freedom into account. When used as input for a high-dimensional neural network potential (HDNNP), accurate potential energy surfaces of multicomponent systems describing multiple magnetic states can be constructed. We demonstrate the performance of these magnetic HDNNPs for the case of manganese oxide, MnO. We show that the method predicts the magnetically distorted rhombohedral structure in excellent agreement with density functional theory and experiment. Its efficiency allows to determine the N\'{e}el temperature considering structural fluctuations, entropic effects, and defects. The method is general and is expected to be useful also for other types of systems like oligonuclear transition metal complexes.

2104.14439

By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the virial expansion, together with resummation techniques, to calculate the compressibility and spin susceptibility.

2104.14440

Inconsistencies regarding the nature of globular cluster multiple population radial distributions is a matter for concern given their role in testing or validating cluster dynamical evolution modeling. In this study, we present a re-analysis of eight globular cluster radial distributions using publicly available ground-based ugriz and UBVRI photometry; correcting for a systematic error identified in the literature. We detail the need for including and considering not only K-S probabilities but critical K-S statistic values as well when drawing conclusions from radial distributions, as well as the impact of sample incompleteness. Revised cumulative radial distributions are presented, and the literature of each cluster reviewed to provide a fuller picture of our results. We find that many multiple populations are not as segregated as once thought, and that there is a pressing need for better understanding of the spatial distributions of multiple populations in globular clusters.

2104.14441

Starting from $\mathbb{C}^*$-actions on complex projective varieties, we construct and investigate birational maps among the corresponding extremal fixed point components. We study the case in which such birational maps are locally described by toric flips, either of Atiyah type or so called non-equalized. We relate this notion of toric flip with the property of the action being non-equalized. Moreover, we find explicit examples of rational homogeneous varieties admitting a $\mathbb{C}^*$-action whose weighted blow-up at the extremal fixed point components gives a birational map among two projective varieties that is locally a toric non-equalized flip.

2104.14442

We present an effective field theory describing the relevant interactions of the Standard Model with an electrically neutral particle that can account for the dark matter in the Universe. The possible mediators of these interactions are assumed to be heavy. The dark matter candidates that we consider have spin 0, 1/2 or 1, belong to an electroweak multiplet with arbitrary isospin and hypercharge and their stability at cosmological scales is guaranteed by imposing a $\mathbb{Z}_2$ symmetry. We present the most general framework for describing the interaction of the dark matter with standard particles, and construct a general non-redundant basis of the gauge-invariant operators up to dimension six. The basis includes multiplets with non-vanishing hypercharge, which can also be viable DM candidates. We give two examples illustrating the phenomenological use of such a general effective framework. First, we consider the case of a scalar singlet, provide convenient semi-analytical expressions for the relevant dark matter observables, use present experimental data to set constraints on the Wilson coefficients of the operators, and show how the interplay of different operators can open new allowed windows in the parameter space of the model. Then we study the case of a lepton isodoublet, which involves co-annihilation processes, and we discuss the impact of the operators on the particle mass splitting and direct detection cross sections. These examples highlight the importance of the contribution of the various non-renormalizable operators, which can even dominate over the gauge interactions in certain cases.

2104.14443

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural Networks. By enforcing cyclic coordinates with appropriate loss functions, we find that we can achieve improved accuracy on simple classical dynamics tasks. By fitting analytic formulae to the latent variables in our network we recover that our networks are utilizing conserved quantities such as (angular) momentum.

2104.14444

We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. To showcase an application of Trakthenbrot's theorem, we continue our reduction chain with a many-one reduction from FSAT to separation logic. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.

2104.14445

We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve et al. (J. Fluid Mech. 848, 508-544, 2018). Using a normal mode streamwise and temporal expansion for flows in ducts with various aspect ratios $B$ and non-trivial transverse velocity profiles, we calculate two-dimensional (2D) dispersion relations with associated eigenfunctions varying in the 'crosswise' direction, in which the density varies, and the spanwise direction, both normal to the duct walls and to the flow direction. We also compare these 2D dispersion relations to the so-called one-dimensional (1D) dispersion relation obtained for spanwise invariant perturbations, for different aspect ratios $B$ and bulk Richardson numbers $Ri_b$. In this limited parameter space, the presence of lateral walls has a stabilizing effect. Furthermore, accounting for spanwise-varying perturbations results in a plethora of unstable modes, the number of which increases as the aspect ratio is increased. These modes present an odd-even regularity in their spatial structures, which is rationalized by comparison to the so-called one-dimensional oblique (1D-O) dispersion relation obtained for oblique waves. Finally, we show that in most cases, the most unstable 2D mode is the one that oscillates the least in the spanwise direction, as a consequence of viscous damping. However, in a limited region of the parameter space and in the absence of stratification, we show that a secondary mode with a more complex `twisted' structure dominated by crosswise vorticity becomes more unstable than the least oscillating Kelvin-Helmholtz mode associated with spanwise vorticity.

2104.14446

A parallel implementation of a compatible discretization scheme for steady-state Stokes problems is presented in this work. The scheme uses generalized moving least squares to generate differential operators and apply boundary conditions. This meshless scheme allows a high-order convergence for both the velocity and pressure, while also incorporates finite-difference-like sparse discretization. Additionally, the method is inherently scalable: the stencil generation process requires local inversion of matrices amenable to GPU acceleration, and the divergence-free treatment of velocity replaces the traditional saddle point structure of the global system with elliptic diagonal blocks amenable to algebraic multigrid. The implementation in this work uses a variety of Trilinos packages to exploit this local and global parallelism, and benchmarks demonstrating high-order convergence and weak scalability are provided.

2104.14447

We prove that for every $n \ge 2$, there exists a pseudoconvex domain $\Omega \subset \mathbb{C}^n$ such that $\mathfrak{c}^0(\Omega) \subsetneq \mathfrak{c}^1(\Omega)$, where $\mathfrak{c}^k(\Omega)$ denotes the core of $\Omega$ with respect to $\mathcal{C}^k$-smooth plurisubharmonic functions on $\Omega$. Moreover, we show that there exists a bounded continuous plurisubharmonic function on $\Omega$ that is not the pointwise limit of a sequence of $\mathcal{C}^1$-smooth bounded plurisubharmonic functions on $\Omega$.

2104.14448

Signed network embedding is an approach to learn low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining frameworks. Due to the distinct properties and significant added value of negative links, existing signed network embedding methods usually design dedicated methods based on social theories such as balance theory and status theory. However, existing signed network embedding methods ignore the characteristics of multiple facets of each node and mix them up in one single representation, which limits the ability to capture the fine-grained attentions between node pairs. In this paper, we propose MUSE, a MUlti-faceted attention-based Signed network Embedding framework to tackle this problem. Specifically, a joint intra- and inter-facet attention mechanism is introduced to aggregate fine-grained information from neighbor nodes. Moreover, balance theory is also utilized to guide information aggregation from multi-order balanced and unbalanced neighbors. Experimental results on four real-world signed network datasets demonstrate the effectiveness of our proposed framework.

2104.14449

In the first part of the paper, we study the discontinuous Galerkin (DG) and $C^0$ interior penalty ($C^0$-IP) finite element approximation of the periodic strong solution to the fully nonlinear second-order Hamilton--Jacobi--Bellman--Isaacs (HJBI) equation with coefficients satisfying the Cordes condition. We prove well-posedness and perform abstract a posteriori and a priori analyses which apply to a wide family of numerical schemes. These periodic problems arise as the corrector problems in the homogenization of HJBI equations. The second part of the paper focuses on the numerical approximation to the effective Hamiltonian of ergodic HJBI operators via DG/$C^0$-IP finite element approximations to approximate corrector problems. Finally, we provide numerical experiments demonstrating the performance of the numerical schemes.

2104.14450

We determine exactly the short-distance effective potential between two "guest" charges immersed in a two-dimensional two-component charge-asymmetric plasma composed of positively ($q_1 = +1$) and negatively ($q_2 = -1/2$) charged point particles. The result is valid over the whole regime of stability, where the Coulombic coupling (dimensionless inverse temperature) $\beta <4$. At high Coulombic coupling $\beta>2$, this model features like-charge attraction. Also, there cannot be repulsion between opposite-charges at short-distances, at variance with large-distance interactions.

2104.14451

The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques depends on the value of the regularization parameter balancing data fidelity and regularity of the solution. Here we consider the Total Generalized Variation regularization introduced in [SIAM J. Imag. Sci, 3(3), 492-526, 2010], which has demonstrated its ability of preserving sharp features as well as smooth transition variations, and introduce an automatic strategy for defining the value of the regularization parameter. We solve the corresponding optimization problem by using a 3-block version of ADMM. Preliminary numerical experiments support the proposed approach.

2104.14452

X-ray and gamma-ray emissions observed in lightning and long sparks are usually connected with the bremsstrahlung of high-energy runaway electrons. Here, an alternative physical mechanism for producing X-ray and gamma-ray emissions caused by the polarization current and associated electromagnetic field moving with relativistic velocity along a curved discharge channel has been proposed. It is pointed out that lightning and spark discharges should also produce a coherent radio-frequency radiation. The influence of the conductivity and the radius of the lightning channel on the propagation velocity of electromagnetic waves, taking into account the absorption, have been investigated. The existence of fast electromagnetic surface waves propagating along the lightning discharge channel at a speed close to the speed of light in vacuum is shown. The possibility of the production of microwave, X-ray and gamma-ray emissions by a polarization current pulse moving along a curved path via synchrotron radiation mechanism during the lightning leader steps formation and the very beginning of the return stroke stage is pointed out. The existence of long tails in the power spectrum is shown, which explains observations of photon energies in the range of 10-100 MeV in the TGF, as well as measured power spectrum of laboratory spark discharge.

2104.14454

Selenium is a crucial earth-abundant and non-toxic semiconductor with a wide range of applications across the semiconductor industries. Selenium has drawn attention from scientific communities for its wide range of applicability: from photovoltaics to imaging devices. Its usage as a photosensitive material largely involves the synthesis of the amorphous phase (a-Se) via various experimental techniques. However, the ground state crystalline phase of this material, known as the trigonal selenium (\textit{t}-Se), is not extensively studied for its optimum electronic and optical properties. In this work, we present density functional theory (DFT) based systematic studies on the ultra-thin $(10\overline{1}0)$ surface slabs of \textit{t}-Se. We report the surface energies, work function, electronic and optical properties as a function of number of layers for $(10\overline{1}0)$ surface slabs to access its suitability for applications as a photosensitive material.

2104.14455

This chapter addresses the question of how to efficiently solve many-objective optimization problems in a computationally demanding black-box simulation context. We shall motivate the question by applications in machine learning and engineering, and discuss specific harsh challenges in using classical Pareto approaches when the number of objectives is four or more. Then, we review solutions combining approaches from Bayesian optimization, e.g., with Gaussian processes, and concepts from game theory like Nash equilibria, Kalai-Smorodinsky solutions and detail extensions like Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding algorithms and provide some illustrating results.

2104.14456

There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, here we present stellar wind models for the active planet-hosting M dwarf AU Mic. Our models incorporate the large-scale photospheric magnetic field map of the star, reconstructed using the Zeeman-Doppler Imaging method. We use our models to assess if planet-induced radio emission could be generated in the corona of AU Mic, through a mechanism analogous to the sub-Alfv\'enic Jupiter-Io interaction. In the case that AU Mic has a mass-loss rate of 27 times that of the Sun, we find that both planets b and c in the system can induce radio emission from 10 MHz to 3 GHz in the corona of the host star for the majority of their orbits, with peak flux densities of 10 mJy. Our predicted emission bears a striking similarity to that recently reported from GJ 1151 by Vedantham et al. (2020), which is indicative of being induced by a planet. Detection of such radio emission would allow us to place an upper limit on the mass-loss rate of the star.

2104.14457

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form restrictions or an additive time trend, and we are invariant to the scaling of the dependent variable. Under our conditions, the time trend can be identified using a control group, as in the binary difference-in-differences literature. In our scenario, however, this control group is defined by the data. We then identify average and quantile treatment effect parameters. We develop corresponding nonparametric estimators and study their asymptotic properties. Finally, we apply our results to the effect of disposable income on consumption.

2104.14458

In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional $s$-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students -- both theorists and experimentalists -- seeking to familiarize themselves with some of the basic concepts in the field.

2104.14459

Plasma accelerators driven by intense laser or particle beams provide gigavolt-per-meter accelerating fields, promising to drastically shrink particle accelerators for high-energy physics and photon science. Applications such as linear colliders and free-electron lasers (FELs) require high energy and energy efficiency, but also high stability and beam quality. The latter includes low energy spread, which can be achieved by precise beam loading of the plasma wakefield using longitudinally shaped bunches, resulting in efficient and uniform acceleration. However, the plasma wavelength, which sets the scale for the region of very large accelerating fields to be 100 {\mu}m or smaller, requires bunches to be synchronized and shaped with extreme temporal precision, typically on the femtosecond scale. Here, a self-correction mechanism is introduced, greatly reducing the susceptibility to jitter. Using multiple accelerating stages, each with a small bunch compression between them, almost any initial bunch, regardless of current profile or injection phase, will self-correct into the current profile that flattens the wakefield, damping the relative energy spread and any energy offsets. As a consequence, staging can be used not only to reach high energies, but also to produce the exquisite beam quality and stability required for a variety of applications.

2104.14460

Recently, it has been proposed that fruitful synergies may exist between Deep Learning (DL) and Case Based Reasoning (CBR); that there are insights to be gained by applying CBR ideas to problems in DL (what could be called DeepCBR). In this paper, we report on a program of research that applies CBR solutions to the problem of Explainable AI (XAI) in the DL. We describe a series of twin-systems pairings of opaque DL models with transparent CBR models that allow the latter to explain the former using factual, counterfactual and semi-factual explanation strategies. This twinning shows that functional abstractions of DL (e.g., feature weights, feature importance and decision boundaries) can be used to drive these explanatory solutions. We also raise the prospect that this research also applies to the problem of Data Augmentation in DL, underscoring the fecundity of these DeepCBR ideas.

2104.14461

We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased (SIRD) compartmental model of epidemiology, which is achieved by replacing compartmental populations by their densities. Building on our recent work (Computational Mechanics, 66, 1177, 2020), we replace our earlier use of global polynomial basis functions with those having local support, as epitomized in the finite element method, for the spatial representation of the SIRD parameters. The time dependence is treated by inferring constant parameters over time intervals that coincide with the time step in semi-discrete numerical implementations. In combination, this amounts to a scheme of field inversion of the SIRD parameters over each time step. Applied to data over ten months of 2020 for the pandemic in the US state of Michigan and to all of Mexico, our system inference via field inversion infers spatio-temporally varying PDE SIRD parameters that replicate the progression of the pandemic with high accuracy. It also produces accurate predictions, when compared against data, for a three week period into 2021. Of note is the insight that is suggested on the spatio-temporal variation of infection, recovery and death rates, as well as patterns of the population's mobility revealed by diffusivities of the compartments.

2104.14462

In this paper we define and explore the analytic spread $\ell(\mathcal I)$ of a filtration in a local ring. We show that, especially for divisorial and symbolic filtrations, some basic properties of the analytic spread of an ideal extend to filtrations, even when the filtration is non Noetherian. We also illustrate some significant differences between the analytic spread of a filtration and the analytic spread of an ideal with examples. In the case of an ideal $I$, we have the classical bounds $\mbox{ht}(I)\le\ell(I)\le \dim R$. The upper bound $\ell(\mathcal I)\le \dim R$ is true for filtrations $\mathcal I$, but the lower bound is not true for all filtrations. We show that for the filtration $\mathcal I$ of symbolic powers of a height two prime ideal $\mathfrak p$ in a regular local ring of dimension three (a space curve singularity), so that $\mbox{ht}(\mathcal I) =2$ and $\dim R=3$, we have that $0\le \ell(\mathcal I)\le 2$ and all values of 0,1 and 2 can occur. In the cases of analytic spread 0 and 1 the symbolic algebra is necessarily non-Noetherian. The symbolic algebra is non-Noetherian if and only if $\ell(\mathfrak p^{(n)})=3$ for all symbolic powers of $\mathfrak p$ and if and only if $\ell(\mathcal I_a)=3$ for all truncations $\mathcal I_a$ of $\mathcal I$.

2104.14463

We investigate the electronic structure of tungsten ditelluride (WTe$_2$) flakes with different thicknesses in magneto-transport studies. The temperature-dependent resistance and magnetoresistance (MR) measurements both confirm the breaking of carrier balance induced by thickness reduction, which suppresses the `turn-on' behavior and large positive MR. The Shubnikov-de-Haas oscillation studies further confirm the thickness-dependent change of electronic structure of WTe$_2$ and reveal a possible temperature-sensitive electronic structure change. Finally, we report the thickness-dependent anisotropy of Fermi surface, which reveals that multi-layer WTe$_2$ is an electronic 3D material and the anisotropy decreases as thickness decreases.

2104.14464

In this work, we propose a Cross-view Contrastive Learning framework for unsupervised 3D skeleton-based action Representation (CrosSCLR), by leveraging multi-view complementary supervision signal. CrosSCLR consists of both single-view contrastive learning (SkeletonCLR) and cross-view consistent knowledge mining (CVC-KM) modules, integrated in a collaborative learning manner. It is noted that CVC-KM works in such a way that high-confidence positive/negative samples and their distributions are exchanged among views according to their embedding similarity, ensuring cross-view consistency in terms of contrastive context, i.e., similar distributions. Extensive experiments show that CrosSCLR achieves remarkable action recognition results on NTU-60 and NTU-120 datasets under unsupervised settings, with observed higher-quality action representations. Our code is available at https://github.com/LinguoLi/CrosSCLR.

2104.14466

Articulatory-to-acoustic (forward) mapping is a technique to predict speech using various articulatory acquisition techniques as input (e.g. ultrasound tongue imaging, MRI, lip video). The advantage of lip video is that it is easily available and affordable: most modern smartphones have a front camera. There are already a few solutions for lip-to-speech synthesis, but they mostly concentrate on offline training and inference. In this paper, we propose a system built from a backend for deep neural network training and inference and a fronted as a form of a mobile application. Our initial evaluation shows that the scenario is feasible: a top-5 classification accuracy of 74% is combined with feedback from the mobile application user, making sure that the speaking impaired might be able to communicate with this solution.

2104.14467

In this paper, we address the speech denoising problem, where white Gaussian additive noise is to be removed from a given speech signal. Our approach is based on a redundant, analysis-sparse representation of the original speech signal. We pick an eigenvector of the Zauner unitary matrix and -- under certain assumptions on the ambient dimension -- we use it as window vector to generate a spark deficient Gabor frame. The analysis operator associated with such a frame, is a (highly) redundant Gabor transform, which we use as a sparsifying transform in denoising procedure. We conduct computational experiments on real-world speech data, solving the analysis basis pursuit denoising problem, with four different choices of analysis operators, including our Gabor analysis operator. The results show that our proposed redundant Gabor transform outperforms -- in all cases -- Gabor transforms generated by state-of-the-art window vectors of time-frequency analysis.

2104.14468

Hybrid Morphology Radio Sources (HyMoRS) are a very rare and newly discovered subclass of radio galaxies that have mixed FR morphology i.e., these galaxies have FR-I structure on one side of the core and FR-II structure on the other side of the core. We systematically searched for HyMoRS using VLA Faint Images of the Radio Sky at Twenty-cm (FIRST) survey at 1400 MHz and identified forty-five confirmed HyMoRS and five candidates HyMoRS. Our finding significantly increased the known sample size of HyMoRS. HyMoRS may play an essential role in understanding the interaction of jets with the interstellar medium and a very debated topic of the FR dichotomy. We identified optical/IR counterparts for thirty-nine sources in our catalogue. In our sample of sources, five sources had Quasar-like behavior. We had estimated the spectral index and radio luminosity of HyMoR sources in our catalogue, when possible. We found that the source J1336+2329 ($\log L=26.93$ W Hz$^{-1}$sr$^{-1}$) was the most luminous and the source J1204+3801, a Quasar, was the farthest HyMoRS (with redshift $z$=1.28) in our sample. With the help of a large sample size of the newly discovered sources, various statistical properties were studied.

2104.14469

Boosted by the simultaneous translation shared task at IWSLT 2020, promising end-to-end online speech translation approaches were recently proposed. They consist in incrementally encoding a speech input (in a source language) and decoding the corresponding text (in a target language) with the best possible trade-off between latency and translation quality. This paper investigates two key aspects of end-to-end simultaneous speech translation: (a) how to encode efficiently the continuous speech flow, and (b) how to segment the speech flow in order to alternate optimally between reading (R: encoding input) and writing (W: decoding output) operations. We extend our previously proposed end-to-end online decoding strategy and show that while replacing BLSTM by ULSTM encoding degrades performance in offline mode, it actually improves both efficiency and performance in online mode. We also measure the impact of different methods to segment the speech signal (using fixed interval boundaries, oracle word boundaries or randomly set boundaries) and show that our best end-to-end online decoding strategy is surprisingly the one that alternates R/W operations on fixed size blocks on our English-German speech translation setup.

2104.14470

The transformation method is a powerful tool for providing the constitutive parameters of the transformed material in the new coordinates. In transformation elasticity, a general curvilinear change of coordinates transforms conventional Hooke's law into a different constitutive law in which the transformed material is not only anisotropic but also polar and chiral and no known elastic solid satisfies. However, this state-of-the-art description provides no insight as to what the underlying microstructure of this transformed material could be, the design of which is a major challenge in this field. The study aims to theoretically justify the fundamental need for the polar material by critically revisiting the discrete transformation method. The key idea is to let transformation gradient operate not only on the elastic properties but on the underlying architectures of the mechanical lattice. As an outstanding application, we leverage the proposed design paradigm to physically construct a polar lattice metamaterial for the observation of elastic carpet cloaking. Numerical simulations are then implemented to show excellent cloaking performance under different static and dynamic mechanical loads. The approach presented herein could promote and accelerate new designs of lattice topologies for transformation elasticity in particular and is able to be extended for realizing other emerging elastic properties and unlocking peculiar functions including statics and dynamics in general.

2104.14471

In previous work, we study the Gan-Gross-Prasad problem for unipotent representations of finite classical groups. In this paper, we deduce the Gan-Gross-Prasad problem for arbitrary representations from the unipotent representations by Lusztig correspondence.

2104.14473

Given a set P of n points in the plane, a unit-disk graph G_{r}(P) with respect to a radius r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at most r. The length of any path in G_r(P) is the number of edges of the path. Given a value \lambda>0 and two points s and t of P, we consider the following reverse shortest path problem: finding the smallest r such that the shortest path length between s and t in G_r(P) is at most \lambda. It was known previously that the problem can be solved in O(n^{4/3} \log^3 n) time. In this paper, we present an algorithm of O(\lfloor \lambda \rfloor \cdot n \log n) time and another algorithm of O(n^{5/4} \log^2 n) time.

2104.14476

Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions in different topics and therefore n-dimensional models are best suited to deal with these cases. While there have been many efforts to develop analytical models for one dimensional opinion models, less attention has been paid to multidimensional ones. In this work, we develop an analytical approach for multidimensional models of continuous opinions where dimensions can be correlated or uncorrelated. We show that for any generic reciprocal interactions between agents, the mean value of initial opinion distribution is conserved. Moreover, for positive social influence interaction mechanisms, the variance of opinion distributions decreases with time and the system converges to a delta distributed function. In particular, we calculate the convergence time when agents get closer in a discrete quantity after interacting, showing a clear difference between correlated and uncorrelated cases.

2104.14477

Human evaluation of modern high-quality machine translation systems is a difficult problem, and there is increasing evidence that inadequate evaluation procedures can lead to erroneous conclusions. While there has been considerable research on human evaluation, the field still lacks a commonly-accepted standard procedure. As a step toward this goal, we propose an evaluation methodology grounded in explicit error analysis, based on the Multidimensional Quality Metrics (MQM) framework. We carry out the largest MQM research study to date, scoring the outputs of top systems from the WMT 2020 shared task in two language pairs using annotations provided by professional translators with access to full document context. We analyze the resulting data extensively, finding among other results a substantially different ranking of evaluated systems from the one established by the WMT crowd workers, exhibiting a clear preference for human over machine output. Surprisingly, we also find that automatic metrics based on pre-trained embeddings can outperform human crowd workers. We make our corpus publicly available for further research.

2104.14478

This paper describes my personal appreciation of some of Tini Veltman's great research achievements and how my own research career has followed the pathways he opened. Among the topics where he has been the most influential have been the pursuit and study of the Higgs boson and the calculation of radiative corrections that enabled the masses of the top quark and the Higgs boson to be predicted ahead of their discoveries. The search for physics beyond the Standard Model may require a complementary approach, such as the search for non-renormalizable interactions via the Standard Model Effective Field Theory.

2104.14479

In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined, and introduce the concept of a two parameter BBGKY hierarchy to handle the non-symmetric interaction of these gases. As a corollary of the derivation, we prove Boltzmann's propagation of chaos assumption for the case of a mixtures of gases.

2104.14480

We use an up to date compilation of Tully-Fisher data to search for transitions in the evolution of the Tully-Fisher relation. Using a recently published data compilation, we find hints at $\approx 3\sigma$ level for a transition at a critical distance $D_c \simeq 17 Mpc$. The zero point (intercept) amplitude of the transition is $\Delta \log A_B \simeq 0.2 \pm 0.06$ while the slope remains practically unchanged. If the transition is interpreted as due to a gravitational strength transition, it would imply a shift of the effective gravitational constant to lower values for distances larger than $D_c\simeq 17 Mpc$ by $\frac{\Delta G}{G}=-0.1 \pm 0.03$. Such a shift is of the anticipated sign and magnitude but at somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions ($\frac{\Delta G}{G}\simeq -0.1$ at transition redshift $z_t\lesssim 0.01$ ($D_c\lesssim 40 Mpc$)).

2104.14481

In addition to its suite of narrow dense rings, Uranus is surrounded by an extremely complex system of dusty rings that were most clearly seen by the Voyager spacecraft after it flew past the planet. A new analysis of the highest resolution images of these dusty rings reveals that a number of them are less than 20 km wide. The extreme narrowness of these rings, along with the fact that most of them do not appear to fall close to known satellite resonances, should provide new insights into the forces responsible for sculpting the Uranian ring system.

2104.14482

Multi-state survival analysis considers several potential events of interest along a disease pathway. Such analyses are crucial to model complex patient trajectories and are increasingly being used in epidemiological and health economic settings. Multi-state models often make the Markov assumption, whereby an individual's future trajectory is dependent only upon their present state, not their past. In reality, there may be transitional dependence upon either previous events and/or more than one timescale, for example time since entry to the current or previous state(s). The aim of this study was to develop an illness-death Weibull model allowing for multiple timescales to impact the future risk of death. Following this, we evaluated the performance of the multiple timescale model against a Markov illness-death model in a set of plausible simulation scenarios when the Markov assumption was violated. Guided by a study in breast cancer, data were simulated from Weibull baseline distributions, with hazard functions dependent on single and multiple timescales. Markov and non-Markov models were fitted to account for/ignore the underlying data structure. Ignoring the presence of multiple timescales led to bias in underlying transition rates between states and associated covariate effects, while transition probabilities and lengths of stay were fairly robustly estimated. Further work may be needed to evaluate different estimands or more complex multi-state models. Software implementations in Stata are also described for simulating and estimating multiple timescale multi-state models.

2104.14483

We formalize the notion of vector semi-inner products and introduce a class of vector seminorms which are built from these maps. The classical Pythagorean theorem and parallelogram law are then generalized to vector seminorms that have a geometric mean closed vector lattice for codomain. In the special case that this codomain is a square root closed, semiprime $f$-algebra, we provide a sharpening of the triangle inequality as well as a condition for equality.

2104.14484

The $\{0,\frac{1}{2}\}$-closure of a rational polyhedron $\{ x \colon Ax \le b \}$ is obtained by adding all Gomory-Chv\'atal cuts that can be derived from the linear system $Ax \le b$ using multipliers in $\{0,\frac{1}{2}\}$. We show that deciding whether the $\{0,\frac{1}{2}\}$-closure coincides with the integer hull is strongly NP-hard. A direct consequence of our proof is that, testing whether the linear description of the $\{0,\frac{1}{2}\}$-closure derived from $Ax \le b$ is totally dual integral, is strongly NP-hard.

2104.14486

We present high-pressure electrical transport measurements on the newly discovered V-based superconductors $A$V$_3$Sb$_5$ ($A$ = Rb and K), which have an ideal Kagome lattice of vanadium. Two superconducting domes under pressure are observed in both compounds, as previously observed in their sister compound CsV$_3$Sb$_5$. For RbV$_3$Sb$_5$, the $T_c$ increases from 0.93 K at ambient pressure to the maximum of 4.15 K at 0.38 GPa in the first dome. The second superconducting dome has the highest $T_c$ of 1.57 K at 28.8 GPa. KV$_3$Sb$_5$ displays a similar double-dome phase diagram, however, its two maximum $T_c$s are lower, and the $T_c$ drops faster in the second dome than RbV$_3$Sb$_5$. An integrated temperature-pressure phase diagram of $A$V$_3$Sb$_5$ ($A$ = Cs, Rb and K) is constructed, showing that the ionic radius of the intercalated alkali-metal atoms has a significant effect. Our work demonstrates that double-dome superconductivity under pressure is a common feature of these V-based Kagome metals.

2104.14487

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial algebra. We also give a hopefully palatable proof of a theorem of V.T. Markov stating that the Gelfand-Kirillov dimension of any affine representable algebra is an integer.

2104.14488

We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the extrinsic Dirac operator and a generalized MIT Bag Dirac operator. This extends some results previously known for the Euclidean spaces to the case of general spin geometry.

2104.14489

We present theoretical transmission spectra of a strongly driven, damped, flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime. Such a qubit-oscillator system, described within a dissipative Rabi model, constitutes the building block of superconducting circuit QED platforms. The addition of a strong drive allows one to characterize the system properties and study novel phenomena, leading to a better understanding and control of the qubit-oscillator system. In this work, the calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the influence of the quantized resonator and of the strong microwave drive. We find distinctive features of the entangled driven qubit-resonator spectrum, namely resonant features and avoided crossings, modified by the presence of the dissipative environment. The magnitude, positions, and broadening of these features are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, the driving amplitude, and the interaction with the heat bath. This work establishes the theoretical basis for future experiments in the driven ultrastrong coupling regime and their impact to develop novel quantum technologies with superconducting circuits.

2104.14490

We compute explicitly the Khovanov polynomials (using the computer program from katlas.org) for the two simplest families of the satellite knots, which are the twisted Whitehead doubles and the two-strand cables. We find that a quantum group decomposition for the HOMFLY polynomial of a satellite knot can be extended to the Khovanov polynomial, whose quantum group properties are not manifest. Namely, the Khovanov polynomial of a twisted Whitehead double or two-strand cable (the two simplest satellite families) can be presented as a naively deformed linear combination of the pattern and companion invariants. For a given companion, the satellite polynomial "smoothly" depends on the pattern but for the "jump" at one critical point defined by the s-invariant of the companion knot. A similar phenomenon is known for the knot Floer homology and tau-invariant for the same kind of satellites.

2104.14491

The COVID-19 pandemic has spurred a large amount of observational studies reporting linkages between the risk of developing severe COVID-19 or dying from it, and sex and gender. By reviewing a large body of related literature and conducting a fine grained analysis based on sex-disaggregated data of 61 countries spanning 5 continents, we discover several confounding factors that could possibly explain the supposed male vulnerability to COVID-19. We thus highlight the challenge of making causal claims based on available data, given the lack of statistical significance and potential existence of biases. Informed by our findings on potential variables acting as confounders, we contribute a broad overview on the issues bias, explainability and fairness entail in data-driven analyses. Thus, we outline a set of discriminatory policy consequences that could, based on such results, lead to unintended discrimination. To raise awareness on the dimensionality of such foreseen impacts, we have compiled an encyclopedia-like reference guide, the Bias Catalog for Pandemics (BCP), to provide definitions and emphasize realistic examples of bias in general, and within the COVID-19 pandemic context. These are categorized within a division of bias families and a 2-level priority scale, together with preventive steps. In addition, we facilitate the Bias Priority Recommendations on how to best use and apply this catalog, and provide guidelines in order to address real world research questions. The objective is to anticipate and avoid disparate impact and discrimination, by considering causality, explainability, bias and techniques to mitigate the latter. With these, we hope to 1) contribute to designing and conducting fair and equitable data-driven studies and research; and 2) interpret and draw meaningful and actionable conclusions from these.

2104.14492

We propose a new way to compute the genus zero Gopakumar-Vafa invariants for two families of non-toric non-compact Calabi-Yau threefolds that admit simple flops: Reid's Pagodas, and Laufer's examples. We exploit the duality between M-theory on these threefolds, and IIA string theory with D6-branes and O6-planes. From this perspective, the GV invariants are detected as five-dimensional open string zero modes. We propose a definition for genus zero GV invariants for threefolds that do not admit small crepant resolutions. We find that in most cases, non-geometric T-brane data is required in order to fully specify the invariants.

2104.14493

We present a detailed analysis of the temperature dependence of the thermal conductivity of a ferroelectric PbTiO3 thin film deposited in a composition-spread geometry enabling a continuous range of compositions from ~25% titanium-deficient to ~20% titanium-rich to be studied. By fitting the experimental results to the Debye model we deconvolve and quantify the two main phonon scattering sources in the system: ferroelectric domain walls (DWs) and point defects. Our results prove that ferroelectric DWs are the main agent limiting the thermal conductivity in this system, not only in the stoichiometric region of the thin film ([Pb]/[Ti]~1), but also when the concentration of cation point defects is significant (up to ~15%). Hence, DWs in ferroelectric materials are a source of phonon scattering at least as effective as point defects. Our results demonstrate the viability and effectiveness of using reconfigurable DWs to control the thermal conductivity in solid-state devices.

2104.14494

We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More specifically, we define a new notion of being asymptotically $\psi$-weakly contractive with modulus, and present a series of abstract convergence theorems which both generalise and unify known results from the literature. Rates of convergence are formulated in terms of our modulus of contractivity, in conjunction with other moduli and functions which form quantitative analogues of additional assumptions that are required in each case. Our approach makes use of ideas from proof theory, in particular our emphasis on abstraction and on formulating our main results in a quantitative manner. As such, the paper can be seen as a contribution to the proof mining program.

2104.14495

We study the possibility of low scale leptogenesis along with dark matter (DM) in the presence of primordial black holes (PBH). For a common setup to study both leptogenesis and DM we consider the minimal scotogenic model which also explains light neutrino mass at radiative level. While PBH in the mass range of $0.1-10^5$ g can, in principle, affect leptogenesis, the required initial PBH fraction usually leads to overproduction of DM whose thermal freeze-out occurs before PBH evaporation. PBH can lead to non-thermal source of leptogenesis as well as dilution of thermally generated lepton asymmetry via entropy injection, with the latter being dominant. The parameter space of scotogenic model which leads to overproduction of baryon or lepton asymmetry in standard cosmology can be made consistent in the presence of PBH with appropriate initial mass and energy fraction. On the other hand, for such PBH parameters, the DM is constrained to be in light mass regime where its freeze-out occurs after PBH evaporation.

2104.14496

We present a non perturbative and formally exact approach for charge transport in interacting nanojunctions based on a real time path integral formulation of the reduced system dynamics. An expansion of the influence functional in terms of the number of tunneling transitions, and integration of the Grassmann variables between the tunneling times, allows us to obtain a still exact generalized master equation (GME) for the populations of the reduced density matrix (RDM) in the occupation number representation, as well as a formally exact expression for the current. By borrowing the nomenclature of the famous spin-boson problem, we characterize the two-state dynamics of such degrees of freedom on the forward and backward branches in terms of single four-state paths with alternating blips and sojourns. This allows a diagrammatic representation of the GME kernel and its parametrization in terms of sequences of blips and sojourns. We apply our formalism to the exactly solvable resonant level model (RLM) and to the the single impurity Anderson model (SIAM), the latter being a prototype system for studying strong correlations. For both systems, we demonstrate a hierarchical diagrammatic structure of the exact GME kernel. While the hierarchy closes at the second-tier level for the RLM, this is not the case for the interacting SIAM. Upon inspection of the GME, known results from various perturbative and nonperturbative approximation schemes to quantum transport in the SIAM are recovered. Finally, a noncrossing approximation for the hierarchical kernel is developed, which enables us to systematically decrease temperature at each next level of the approximation. Analytical results for a simplified fourth-tier scheme are presented.

2104.14497

Understanding how electrolyte solutions behave out of thermal equilibrium is a long-standing endeavor in many areas of chemistry and biology. Although mean-field theories are widely used to model the dynamics of electrolytes, it is also important to characterize the effects of fluctuations in these systems. In a previous work, we showed that the dynamics of the ions in a strong electrolyte that is driven by an external electric field can generate long-ranged correlations manifestly different from the equilibrium screened correlations; in the nonequilibrium steady state, these correlations give rise to a novel long-range fluctuation-induced force (FIF). Here, we extend these results by considering the dynamics of the strong electrolyte after it is quenched from thermal equilibrium upon the application of a constant electric field. We show that the asymptotic long-distance limit of both charge and density correlations is generally diffusive in time. These correlations give rise to long-ranged FIFs acting on the neutral confining plates with long-time regimes that are governed by power-law temporal decays toward the steady-state value of the force amplitude. These findings show that nonequilibrium fluctuations have nontrivial implications on the dynamics of objects immersed in a driven electrolyte, and they could be useful for exploring new ways of controlling long-distance forces in charged solutions.

2104.14498

We address an inherent difficulty in welfare-theoretic fair machine learning, proposing an equivalently-axiomatically justified alternative, and studying the resulting computational and statistical learning questions. Welfare metrics quantify overall wellbeing across a population of one or more groups, and welfare-based objectives and constraints have recently been proposed to incentivize fair machine learning methods to produce satisfactory solutions that consider the diverse needs of multiple groups. Unfortunately, many machine-learning problems are more naturally cast as loss minimization, rather than utility maximization tasks, which complicates direct application of welfare-centric methods to fair-ML tasks. In this work, we define a complementary measure, termed malfare, measuring overall societal harm (rather than wellbeing), with axiomatic justification via the standard axioms of cardinal welfare. We then cast fair machine learning as a direct malfare minimization problem, where a group's malfare is their risk (expected loss). Surprisingly, the axioms of cardinal welfare (malfare) dictate that this is not equivalent to simply defining utility as negative loss. Building upon these concepts, we define fair-PAC learning, where a fair PAC-learner is an algorithm that learns an $\varepsilon$-$\delta$ malfare-optimal model with bounded sample complexity, for any data distribution, and for any malfare concept. We show broad conditions under which, with appropriate modifications, many standard PAC-learners may be converted to fair-PAC learners. This places fair-PAC learning on firm theoretical ground, as it yields statistical, and in some cases computational, efficiency guarantees for many well-studied machine-learning models, and is also practically relevant, as it democratizes fair ML by providing concrete training algorithms and rigorous generalization guarantees for these models.

2104.14504

Difference schemes are considered for dynamical systems $ \dot x = f (x) $ with a quadratic right-hand side, which have $t$-symmetry and are reversible. Reversibility is interpreted in the sense that the Cremona transformation is performed at each step in the calculations using a difference scheme. The inheritance of periodicity and the Painlev\'e property by the approximate solution is investigated. In the computer algebra system Sage, such values are found for the step $ \Delta t $, for which the approximate solution is a sequence of points with the period $ n \in \mathbb N $. Examples are given and hypotheses about the structure of the sets of initial data generating sequences with the period $ n $ are formulated.

2104.14507

For every tuple $d_1,\dots, d_l\geq 2,$ let $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}$ denote the tensor product of $\mathbb{R}^{d_i},$ $i=1,\dots,l.$ Let us denote by $\mathcal{B}(d)$ the hyperspace of centrally symmetric convex bodies in $\mathbb{R}^d,$ $d=d_1\cdots d_l,$ endowed with the Hausdorff distance, and by $\mathcal{B}_\otimes(d_1,\dots,d_l)$ the subset of $\mathcal{B}(d)$ consisting of the convex bodies that are closed unit balls of reasonable crossnorms on $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}.$ It is known that $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is a closed, contractible and locally compact subset of $\mathcal{B}(d).$ The hyperspace $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is called the space of tensorial bodies. In this work we determine the homeomorphism type of $\mathcal{B}_\otimes(d_1,\dots,d_l).$ We show that even if $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is not convex with respect to the Minkowski sum, it is an Absolute Retract homeomorphic to $\mathcal{Q}\times\mathbb{R}^p,$ where $\mathcal{Q}$ is the Hilbert cube and $p=\frac{d_1(d_1+1)+\cdots+d_l(d_l+1)}{2}.$ Among other results, the relation between the Banach-Mazur compactum and the Banach-Mazur type compactum associated to $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is examined.

2104.14509

In an edge modification problem, we are asked to modify at most $k$ edges to a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A great amount of efforts have been devoted to understanding the kernelization complexity of these problems. We revisit several well-studied edge modification problems, and develop improved kernels for them: \begin{itemize} \item a $2 k$-vertex kernel for the cluster edge deletion problem, \item a $3 k^2$-vertex kernel for the trivially perfect completion problem, \item a $5 k^{1.5}$-vertex kernel for the split completion problem and the split edge deletion problem, and \item a $5 k^{1.5}$-vertex kernel for the pseudo-split completion problem and the pseudo-split edge deletion problem. \end{itemize} Moreover, our kernels for split completion and pseudo-split completion have only $O(k^{2.5})$ edges. Our results also include a $2 k$-vertex kernel for the strong triadic closure problem, which is related to cluster edge deletion.

2104.14510

In event-based sensing, many sensors independently and asynchronously emit events when there is a change in their input. Event-based sensing can present significant improvements in power efficiency when compared to traditional sampling, because (1) the output is a stream of events where the important information lies in the timing of the events, and (2) the sensor can easily be controlled to output information only when interesting activity occurs at the input. Moreover, event-based sampling can often provide better resolution than standard uniform sampling. Not only does this occur because individual event-based sensors have higher temporal resolution, it also occurs because the asynchrony of events allows for less redundant and more informative encoding. We would like to explain how such curious results come about. To do so, we use ideal time encoding machines as a proxy for event-based sensors. We explore time encoding of signals with low rank structure, and apply the resulting theory to video. We then see how the asynchronous firing times of the time encoding machines allow for better reconstruction than in the standard sampling case, if we have a high spatial density of time encoding machines that fire less frequently.

2104.14511

The AGM postulates by Alchourr\'{o}n, G\"{a}rdenfors, and Makinson continue to represent a cornerstone in research related to belief change. We generalize the approach of Katsuno and Mendelzon (KM) for characterizing AGM base revision from propositional logic to the setting of (multiple) base revision in arbitrary monotonic logics. Our core result is a representation theorem using the assignment of total - yet not transitive - "preference" relations to belief bases. We also provide a characterization of all logics for which our result can be strengthened to preorder assignments (as in KM's original work).

2104.14512

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}$Si and $^{250}$Cf are presented and discussed.

2104.14513

We present a spinning black hole solution in $d$ dimensions with a maximal number of rotation parameters in the context of the Eistein-Maxwell-Dilaton theory. An interesting feature of such a solution is that it accommodates Lifshitz black holes when the rotation parameters are set to zero. We verify the rotating nature of the black hole solution by performing the quasi-local analysis of conserved charges and defining the corresponding angular momenta. In addition, we perform the thermodynamical analysis of the black hole configuration, show that the first law of thermodynamics is completely consistent, and obtain a Smarr-like formula. We further study the thermodynamic stability of the constructed solution from a local viewpoint, by computing the associated specific heats, and a global perspective, by using the so-called new thermodynamic geometry. We finally make some comments related to a pathology found in the causal structure of the obtained rotating black hole spacetime.

2104.14514

The DES-CMASS sample (DMASS) is designed to optimally combine the weak lensing measurements from the Dark Energy Survey (DES) and redshift-space distortions (RSD) probed by the CMASS galaxy sample from the Baryonic Oscillation Spectroscopic Survey (BOSS). In this paper, we demonstrate the feasibility of adopting DMASS as the equivalent of BOSS CMASS for a joint analysis of DES and BOSS in the framework of modified gravity. We utilize the angular clustering of the DMASS galaxies, cosmic shear of the DES METACALIBRATION sources, and cross-correlation of the two as data vectors. By jointly fitting the combination of the data with the RSD measurements from the BOSS CMASS sample and Planck data, we obtain the constraints on modified gravity parameters $\mu_0 = -0.37^{+0.47}_{-0.45}$ and $\Sigma_0 = 0.078^{+0.078}_{-0.082}$. We do not detect any significant deviation from General Relativity. Our constraints of modified gravity measured with DMASS are tighter than those with the DES Year 1 redMaGiC galaxy sample with the same external data sets by $29\%$ for $\mu_0$ and $21\%$ for $\Sigma_0$, and comparable to the published results of the DES Year 1 modified gravity analysis despite this work using fewer external data sets. This improvement is mainly because the galaxy bias parameter is shared and more tightly constrained by both CMASS and DMASS, effectively breaking the degeneracy between the galaxy bias and other cosmological parameters. Such an approach to optimally combine photometric and spectroscopic surveys using a photometric sample equivalent to a spectroscopic sample can be applied to combining future surveys having a limited overlap such as DESI and LSST.

2104.14515

We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy method, one can find explicit constructions and counterexamples to several open conjectures in extremal combinatorics and graph theory. Amongst the conjectures we refute are a question of Brualdi and Cao about maximizing permanents of pattern avoiding matrices, and several problems related to the adjacency and distance eigenvalues of graphs.

2104.14516

New computing technologies inspired by the brain promise fundamentally different ways to process information with extreme energy efficiency and the ability to handle the avalanche of unstructured and noisy data that we are generating at an ever-increasing rate. To realise this promise requires a brave and coordinated plan to bring together disparate research communities and to provide them with the funding, focus and support needed. We have done this in the past with digital technologies; we are in the process of doing it with quantum technologies; can we now do it for brain-inspired computing?

2104.14517

Generalizing our recent joint paper with Vasily Pestun, we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices polynomial in the spectral parameter, parametrized by the divisors on the projective line with coefficients being dominant integral coweights of associated Lie algebras. To this end, we provide the RTT realization of the antidominantly shifted extended Drinfeld Yangians of $\mathfrak{so}_{2r}, \mathfrak{sp}_{2r}, \mathfrak{so}_{2r+1}$, and their coproduct homomorphisms.

2104.14518

We introduce an automata model for describing interesting classes of differential privacy mechanisms/algorithms that include known mechanisms from the literature. These automata can model algorithms whose inputs can be an unbounded sequence of real-valued query answers. We consider the problem of checking whether there exists a constant $d$ such that the algorithm described by these automata are $d\epsilon$-differentially private for all positive values of the privacy budget parameter $\epsilon$. We show that this problem can be decided in time linear in the automaton's size by identifying a necessary and sufficient condition on the underlying graph of the automaton. This paper's results are the first decidability results known for algorithms with an unbounded number of query answers taking values from the set of reals.

2104.14519