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We present a novel computational framework for simulating suspensions of rigid spherical Janus particles in Stokes flow. We show that long-range Janus particle interactions for a wide array of applications may be resolved using fast, spectrally accurate boundary integral methods tailored to polydisperse suspensions of spherical particles. These are incorporated into our rigid body Stokes platform. Our approach features the use of spherical harmonic expansions for spectrally accurate integral operator evaluation, complementarity-based collision resolution, and optimal O(n) scaling with the number of particles when accelerated via fast summation techniques. We demonstrate the flexibility of our platform through three key examples of Janus particle systems prominent in biomedical applications: amphiphilic, bipolar electric and phoretic particles. We formulate Janus particle interactions in boundary integral form and showcase characteristic self-assembly and complex collective behavior for each particle type.

2104.14068

Self-interacting dark matter (SIDM) models offer one way to reconcile inconsistencies between observations and predictions from collisionless cold dark matter (CDM) models on dwarf-galaxy scales. In order to incorporate the effects of both baryonic and SIDM interactions, we study a suite of cosmological-baryonic simulations of Milky-Way (MW)-mass galaxies from the Feedback in Realistic Environments (FIRE-2) project where we vary the SIDM self-interaction cross-section $\sigma/m$. We compare the shape of the main dark matter (DM) halo at redshift $z=0$ predicted by SIDM simulations (at $\sigma/m=0.1$, $1$, and $10$ cm$^2$ g$^{-1}$) with CDM simulations using the same initial conditions. In the presence of baryonic feedback effects, we find that SIDM models do not produce the large differences in the inner structure of MW-mass galaxies predicted by SIDM-only models. However, we do find that the radius where the shape of the total mass distribution begins to differ from that of the stellar mass distribution is dependent on $\sigma/m$. This transition could potentially be used to set limits on the SIDM cross-section in the MW.

2104.14069

Absolute Concentration Robustness (ACR) was introduced by Shinar and Feinberg as a way to define species concentration robustness in mass action dynamical systems. The idea was to devise a mathematical condition that will ensure robustness in the function of the biological system being modeled. The robustness of function rests on what we refer to as empirical robustness -- the concentration of a variable remains unvarying, when measured in the long run, across arbitrary initial conditions. While there is a positive correlation between ACR and empirical robustness, ACR is neither necessary nor sufficient for empirical robustness, a fact that can be noticed even in simple biochemical systems. To develop a stronger connection with empirical robustness, we define dynamic ACR, a property related to dynamics, rather than only to equilibrium behavior, and one that guarantees convergence to a robust value. We distinguish between wide basin and narrow basin versions of dynamic ACR, related to the size of the set of initial values that do not result in convergence to the robust value. We give numerous examples which help distinguish the various flavors of ACR as well as clearly illustrate and circumscribe the conditions that appear in the definitions. We discuss general dynamical systems with ACR properties as well as parametrized families of dynamical systems related to reaction networks. We discuss connections between ACR and complex balance, two notions central to the theory of reaction networks. We give precise conditions for presence and absence of dynamic ACR in complex balanced systems, which in turn yields a large body of reaction networks with dynamic ACR.

2104.14070

Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using higher-order tail dependence of copulas, we prove that a rapidly varying multivariate density implies rapid variation of the joint distribution tails. As a corollary, rapid variation of skew-elliptical distributions is established under the assumption that the underlying density generators belong to the max-domain of attraction of the Gumbel distribution.

2104.14071

A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Leveraging geometric information provided by the Implicit Function Theorem, the proposed algorithm effectively reduces the input dimension to the theoretical lower bound with minor accuracy loss, providing a one-dimensional representation of the function which can be used for regression and sensitivity analysis. Experiments and applications are presented which compare this modified NLL with the original NLL and the Active Subspaces (AS) method. While accommodating sparse input data, the proposed algorithm is shown to train quickly and provide a much more accurate and informative reduction than either AS or the original NLL on two example functions with high-dimensional domains, as well as two state-dependent quantities depending on the solutions to parametric differential equations.

2104.14072

With populations ageing, the number of people with dementia worldwide is expected to triple to 152 million by 2050. Seventy percent of cases are due to Alzheimer's disease (AD) pathology and there is a 10-20 year 'pre-clinical' period before significant cognitive decline occurs. We urgently need, cost effective, objective methods to detect AD, and other dementias, at an early stage. Risk factor modification could prevent 40% of cases and drug trials would have greater chances of success if participants are recruited at an earlier stage. Currently, detection of dementia is largely by pen and paper cognitive tests but these are time consuming and insensitive to pre-clinical phases. Specialist brain scans and body fluid biomarkers can detect the earliest stages of dementia but are too invasive or expensive for widespread use. With the advancement of technology, Artificial Intelligence (AI) shows promising results in assisting with detection of early-stage dementia. Existing AI-aided methods and potential future research directions are reviewed and discussed.

2104.14073

Bandit algorithms are increasingly used in real world sequential decision making problems, from online advertising to mobile health. As a result, there are more datasets collected using bandit algorithms and with that an increased desire to be able to use these datasets to answer scientific questions like: Did one type of ad increase the click-through rate more or lead to more purchases? In which contexts is a mobile health intervention effective? However, it has been shown that classical statistical approaches, like those based on the ordinary least squares estimator, fail to provide reliable confidence intervals when used with bandit data. Recently methods have been developed to conduct statistical inference using simple models fit to data collected with multi-armed bandits. However there is a lack of general methods for conducting statistical inference using more complex models. In this work, we develop theory justifying the use of M-estimation (Van der Vaart, 2000), traditionally used with i.i.d data, to provide inferential methods for a large class of estimators -- including least squares and maximum likelihood estimators -- but now with data collected with (contextual) bandit algorithms. To do this we generalize the use of adaptive weights pioneered by Hadad et al. (2019) and Deshpande et al. (2018). Specifically, in settings in which the data is collected via a (contextual) bandit algorithm, we prove that certain adaptively weighted M-estimators are uniformly asymptotically normal and demonstrate empirically that we can use their asymptotic distribution to construct reliable confidence regions for a variety of inferential targets.

2104.14074

A swarm of cooperating UAVs communicating with a distant multiantenna ground station can leverage MIMO spatial multiplexing to scale the capacity. Due to the line-of-sight propagation between the swarm and the ground station, the MIMO channel is highly correlated, leading to limited multiplexing gains. In this paper, we optimize the UAV positions to attain the maximum MIMO capacity given by the single user bound. An infinite set of UAV placements that attains the capacity bound is first derived. Given an initial swarm placement, we formulate the problem of minimizing the distance traveled by the UAVs to reach a placement within the capacity maximizing set of positions. An offline centralized solution to the problem using block coordinate descent is developed assuming known initial positions of UAVs. We also propose an online distributed algorithm, where the UAVs iteratively adjust their positions to maximize the capacity. Our proposed approaches are shown to significantly increase the capacity at the expense of a bounded translation from the initial UAV placements. This capacity increase persists when using a massive MIMO ground station. Using numerical simulations, we show the robustness of our approaches in a Rician channel under UAV motion disturbances.

2104.14075

We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in $\mathbb{S}^2$. Both examples are constructed by applying previously proposed methods. The proof of their hardness uses significant computational resources. We also determine that no small "standard" example of a hard unknot diagram requires more than one extra crossing for Reidemeister moves in $\mathbb{S}^2$.

2104.14076

The BFV-BRST Hamiltonian quantization method is presented for the theories where the gauge parameters are restricted by differential equations. The general formalism is exemplified by the Maxwell-like theory of symmetric tensor field.

2104.14077

State disturbance by a quantum measurement is at the core of foundational quantum physics and constitutes a fundamental basis of secure quantum information processing. While quantifying an information-disturbance relation has been a long-standing problem, recently verified reversibility of a quantum measurement requires to refine such a conventional information trade-off toward a complete picture of information conservation in quantum measurement. Here we experimentally demonstrate complete trade-off relations among all information contents, i.e., information gain, disturbance and reversibility in quantum measurement. By exploring various quantum measurements applied on a photonic qutrit, we observe that the information of a quantum state is split into three distinct parts accounting for the extracted, disturbed, and reversible information. We verify that such different parts of information are in trade-off relations not only pairwise but also globally all-at-once, and find that the global trade-off relation is tighter than any of the pairwise relations. Finally, we realize optimal quantum measurements that inherently preserve quantum information without loss of information, which offer wider applications in measurement-based quantum information processing.

2104.14078

Autonomous vehicles should be able to predict the future states of its environment and respond appropriately. Specifically, predicting the behavior of surrounding human drivers is vital for such platforms to share the same road with humans. Behavior of each of the surrounding vehicles is governed by the motion of its neighbor vehicles. This paper focuses on predicting the behavior of the surrounding vehicles of an autonomous vehicle on highways. We are motivated by improving the prediction accuracy when a surrounding vehicle performs lane change and highway merging maneuvers. We propose a novel pooling strategy to capture the inter-dependencies between the neighbor vehicles. Depending solely on Euclidean trajectory representation, the existing pooling strategies do not model the context information of the maneuvers intended by a surrounding vehicle. In contrast, our pooling mechanism employs polar trajectory representation, vehicles orientation and radial velocity. This results in an implicitly maneuver-aware pooling operation. We incorporated the proposed pooling mechanism into a generative encoder-decoder model, and evaluated our method on the public NGSIM dataset. The results of maneuver-based trajectory predictions demonstrate the effectiveness of the proposed method compared with the state-of-the-art approaches. Our "Pooling Toolbox" code is available at https://github.com/m-hasan-n/pooling.

2104.14079

A number of gamma-ray bursts (GRBs) exhibit the late simultaneous bumps in their optical and Xray afterglows around the jet break. Its origin is unclear. Based on the following two facts, we suggest that this feature may sound a transition of circum-burst environment from a free-wind medium to a homogeneous medium. (I) The late bump followed by a steep decay is strongly reminiscent of the afterglows of GRB 170817A, which is attributed to an off-axis observed external-forward shock (eFS) propagating in an interstellar medium. (II) Observations seem to feature a long shallow decay before the late optical bump, which is different from the afterglow of GRB 170817A. In this paper, we study the emission of an eFS propagating in a free-to-shocked wind for on/off-axis observers, where the mass density in the shocked-wind is almost constant. The late simultaneous bumps/plateaux in the optical and X-ray afterglows are really found around the jet break for high-viewing-angle observers. Moreover, there is a long plateau or shallow decay before the late bump in the theoretical light-curves, which is formed during the eFS propagating in the free-wind. For low-viewing-angle observers, the above bumps appear only in the situation that the structured jet has a low characteristic angle and the deceleration radius of the on-axis jet flow is at around or beyond the free-wind boundary. As examples, the X-ray and optical afterglows of GRBs 120326A, 120404A, and 100814A are fitted. We find that an off-axis observed eFS in a free-to-shocked wind can well explain the afterglows in these bursts.

2104.14080

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase coordinate, or the cycle coordinate. First, we introduce the geometric averaging method for this category of systems, and also analyze the accuracy of its averaging approximation. Specifically, we delve into the details of the geometrically periodic system through the tunnel of considering the convergence between the system and its geometrically averaging approximation. Under different corresponding conditions, the approximation on infinite time intervals can achieve certain accuracies, such that one can use the stability result of either the original system or the averaging system to deduce the stability of the other. After that, we employ the graphical stability to investigate the "pattern stability" with respect to the phase-based system. Finally, by virtue of the contraction analysis on the Finsler manifold, the idea of accentuating the periodic pattern incremental stability and convergence is nurtured in the phase-based differential inclusion system, and comes to its preliminary fruition in application to biomimetic mechanic robot control problem.

2104.14081

Current anchor-free object detectors are quite simple and effective yet lack accurate label assignment methods, which limits their potential in competing with classic anchor-based models that are supported by well-designed assignment methods based on the Intersection-over-Union~(IoU) metric. In this paper, we present \textbf{Pseudo-Intersection-over-Union~(Pseudo-IoU)}: a simple metric that brings more standardized and accurate assignment rule into anchor-free object detection frameworks without any additional computational cost or extra parameters for training and testing, making it possible to further improve anchor-free object detection by utilizing training samples of good quality under effective assignment rules that have been previously applied in anchor-based methods. By incorporating Pseudo-IoU metric into an end-to-end single-stage anchor-free object detection framework, we observe consistent improvements in their performance on general object detection benchmarks such as PASCAL VOC and MSCOCO. Our method (single-model and single-scale) also achieves comparable performance to other recent state-of-the-art anchor-free methods without bells and whistles. Our code is based on mmdetection toolbox and will be made publicly available at https://github.com/SHI-Labs/Pseudo-IoU-for-Anchor-Free-Object-Detection.

2104.14082

In this paper we derive a combinatorial formula for mixed Eulerian numbers in type $A$ from Peterson Schubert calculus. We also provide a simple computation for mixed $\Phi$-Eulerian numbers in arbitrary Lie types.

2104.14083

We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable $L^2$ energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as $t\to \infty$ with respect to weak and strong norms.

2104.14084

This paper presents a novel method, termed Bridge to Answer, to infer correct answers for questions about a given video by leveraging adequate graph interactions of heterogeneous crossmodal graphs. To realize this, we learn question conditioned visual graphs by exploiting the relation between video and question to enable each visual node using question-to-visual interactions to encompass both visual and linguistic cues. In addition, we propose bridged visual-to-visual interactions to incorporate two complementary visual information on appearance and motion by placing the question graph as an intermediate bridge. This bridged architecture allows reliable message passing through compositional semantics of the question to generate an appropriate answer. As a result, our method can learn the question conditioned visual representations attributed to appearance and motion that show powerful capability for video question answering. Extensive experiments prove that the proposed method provides effective and superior performance than state-of-the-art methods on several benchmarks.

2104.14085

Influence competition finds its significance in many applications, such as marketing, politics and public events like COVID-19. Existing work tends to believe that the stronger influence will always win and dominate nearly the whole network, i.e., "winner takes all". However, this finding somewhat contradicts with our common sense that many competing products are actually coexistent, e.g., Android vs. iOS. This contradiction naturally raises the question: will the winner take all? To answer this question, we make a comprehensive study into influence competition by identifying two factors frequently overlooked by prior art: (1) the incomplete observation of real diffusion networks; (2) the existence of information overload and its impact on user behaviors. To this end, we attempt to recover possible diffusion links based on user similarities, which are extracted by embedding users into a latent space. Following this, we further derive the condition under which users will be overloaded, and formulate the competing processes where users' behaviors differ before and after information overload. By establishing the explicit expressions of competing dynamics, we disclose that information overload acts as the critical "boundary line", before which the "winner takes all" phenomenon will definitively occur, whereas after information overload the share of influences gradually stabilizes and is jointly affected by their initial spreading conditions, influence powers and the advent of overload. Numerous experiments are conducted to validate our theoretical results where favorable agreement is found. Our work sheds light on the intrinsic driving forces behind real-world dynamics, thus providing useful insights into effective information engineering.

2104.14086

Serverless computing has emerged as a new paradigm for running short-lived computations in the cloud. Due to its ability to handle IoT workloads, there has been considerable interest in running serverless functions at the edge. However, the constrained nature of the edge and the latency sensitive nature of workloads result in many challenges for serverless platforms. In this paper, we present LaSS, a platform that uses model-driven approaches for running latency-sensitive serverless computations on edge resources. LaSS uses principled queuing-based methods to determine an appropriate allocation for each hosted function and auto-scales the allocated resources in response to workload dynamics. LaSS uses a fair-share allocation approach to guarantee a minimum of allocated resources to each function in the presence of overload. In addition, it utilizes resource reclamation methods based on container deflation and termination to reassign resources from over-provisioned functions to under-provisioned ones. We implement a prototype of our approach on an OpenWhisk serverless edge cluster and conduct a detailed experimental evaluation. Our results show that LaSS can accurately predict the resources needed for serverless functions in the presence of highly dynamic workloads, and reprovision container capacity within hundreds of milliseconds while maintaining fair share allocation guarantees.

2104.14087

The sixth generation (6G) systems are generally recognized to be established on ubiquitous Artificial Intelligence (AI) and distributed ledger such as blockchain. However, the AI training demands tremendous computing resource, which is limited in most 6G devices. Meanwhile, miners in Proof-of-Work (PoW) based blockchains devote massive computing power to block mining, and are widely criticized for the waste of computation. To address this dilemma, we propose an Evolved-Proof-of-Work (E-PoW) consensus that can integrate the matrix computations, which are widely existed in AI training, into the process of brute-force searches in the block mining. Consequently, E-PoW can connect AI learning and block mining via the multiply used common computing resource. Experimental results show that E-PoW can salvage by up to 80 percent computing power from pure block mining for parallel AI training in 6G systems.

2104.14088

Intelligent agents powered by AI planning assist people in complex scenarios, such as managing teams of semi-autonomous vehicles. However, AI planning models may be incomplete, leading to plans that do not adequately meet the stated objectives, especially in unpredicted situations. Humans, who are apt at identifying and adapting to unusual situations, may be able to assist planning agents in these situations by encoding their knowledge into a planner at run-time. We investigate whether people can collaborate with agents by providing their knowledge to an agent using linear temporal logic (LTL) at run-time without changing the agent's domain model. We presented 24 participants with baseline plans for situations in which a planner had limitations, and asked the participants for workarounds for these limitations. We encoded these workarounds as LTL constraints. Results show that participants' constraints improved the expected return of the plans by 10% ($p < 0.05$) relative to baseline plans, demonstrating that human insight can be used in collaborative planning for resilience. However, participants used more declarative than control constraints over time, but declarative constraints produced plans less similar to the expectation of the participants, which could lead to potential trust issues.

2104.14089

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable recovery with respect to data perturbations. Hand-chosen analytic regularization can yield desirable theoretical guarantees, but such approaches have limited effectiveness recovering signals due to their inability to leverage large amounts of available data. To this end, this work fuses data-driven regularization and convex feasibility in a theoretically sound manner. This is accomplished using feasibility-based fixed point networks (F-FPNs). Each F-FPN defines a collection of nonexpansive operators, each of which is the composition of a projection-based operator and a data-driven regularization operator. Fixed point iteration is used to compute fixed points of these operators, and weights of the operators are tuned so that the fixed points closely represent available data. Numerical examples demonstrate performance increases by F-FPNs when compared to standard TV-based recovery methods for CT reconstruction and a comparable neural network based on algorithm unrolling.

2104.14090

Estimation of population size using incomplete lists (also called the capture-recapture problem) has a long history across many biological and social sciences. For example, human rights and other groups often construct partial and overlapping lists of victims of armed conflicts, with the hope of using this information to estimate the total number of victims. Earlier statistical methods for this setup either use potentially restrictive parametric assumptions, or else rely on typically suboptimal plug-in-type nonparametric estimators; however, both approaches can lead to substantial bias, the former via model misspecification and the latter via smoothing. Under an identifying assumption that two lists are conditionally independent given measured covariate information, we make several contributions. First we derive the nonparametric efficiency bound for estimating the capture probability, which indicates the best possible performance of any estimator, and sheds light on the statistical limits of capture-recapture methods. Then we present a new estimator, and study its finite-sample properties, showing that it has a double robustness property new to capture-recapture, and that it is near-optimal in a non-asymptotic sense, under relatively mild nonparametric conditions. Next, we give a method for constructing confidence intervals for total population size from generic capture probability estimators, and prove non-asymptotic near-validity. Finally, we study our methods in simulations, and apply them to estimate the number of killings and disappearances attributable to different groups in Peru during its internal armed conflict between 1980 and 2000.

2104.14091

In this paper, we recall hypergeometric functions $\mathscr{F}^{\rm Dw}_{a_1,\cdots,a_s}(t),$ $\mathscr{F}^{(\sigma)}_{a_1,\cdots,a_s}(t)$, $\widehat{\mathscr{F}}^{(\sigma)} _{a,\cdots,a}(t)$ and their transformation formulas. Then we prove that one of transformation formula implies another.

2104.14092

Proton-rich nuclei possess unique properties in the nuclear chart. Due to the presence of both continuum coupling and Coulomb interaction, phenomena such as halos, Thomas-Ehrman shift, and proton emissions can occur. Experimental data are difficult to be obtained therein, so that theoretical calculations are needed to understand nuclei at drip-lines and guide experimentalists for that matter. In particular, the $^{16}$Ne and $^{18}$Mg isotopes are supposed to be one-proton and/or two-proton emitting nuclei, but associated experimental data are either incomplete or even unavailable. Consequently, we performed Gamow shell model calculations of carbon isotones bearing $A=15\text{-}18$. Isospin-symmetry breaking occurring in carbon isotones and isotopes is also discussed. It is hereby shown that the mixed effects of continuum coupling and Coulomb interaction at drip-lines generate complex patterns in isospin multiplets. Added to that, it is possible to determine the one-proton and two-proton widths of $^{16}$Ne and $^{18}$Mg. Obtained decay patterns are in agreement with those obtained in previous experimental and theoretical works. Moreover, up to the knowledge of authors, this is the first theoretical calculation of binding energy and partial decay widths of $^{18}$Mg in a configuration interaction picture.

2104.14093

Information flow control type systems statically restrict the propagation of sensitive data to ensure end-to-end confidentiality. The property to be shown is noninterference, asserting that an attacker cannot infer any secrets from made observations. Session types delimit the kinds of observations that can be made along a communication channel by imposing a protocol of message exchange. These protocols govern the exchange along a single channel and leave unconstrained the propagation along adjacent channels. This paper contributes an information flow control type system for linear session types. The type system stands in close correspondence with intuitionistic linear logic. Intuitionistic linear logic typing ensures that process configurations form a tree such that client processes are parent nodes and provider processes child nodes. To control the propagation of secret messages, the type system is enriched with secrecy levels and arranges these levels to be aligned with the configuration tree. Two levels are associated with every process: the maximal secrecy denoting the process' security clearance and the running secrecy denoting the highest level of secret information obtained so far. The computational semantics naturally stratifies process configurations such that higher-secrecy processes are parents of lower-secrecy ones, an invariant enforced by typing. Noninterference is stated in terms of a logical relation that is indexed by the secrecy-level-enriched session types. The logical relation contributes a novel development of logical relations for session typed languages as it considers open configurations, allowing for more nuanced equivalence statement.

2104.14094

Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from traditional end-to-end settings, and explore a step-wise polynomial simplification task. Polynomials can be written in a simple normal form as a sum of monomials which are ordered in a lexicographic order. For a polynomial which is not necessarily in this normal form, a sequence of simplification steps is applied to reach the fully simplified (i.e., in the normal form) polynomial. We propose a synthetic Polynomial dataset generation algorithm that generates polynomials with unique proof steps. Through varying coefficient configurations, input representation, proof granularity, and extensive hyper-parameter tuning, we observe that Transformers consistently struggle with numeric multiplication. We explore two ways to mitigate this: Curriculum Learning and a Symbolic Calculator approach (where the numeric operations are offloaded to a calculator). Both approaches provide significant gains over the vanilla Transformers-based baseline.

2104.14095

Recently, inspired by quantum annealing, many solvers specialized for unconstrained binary quadratic programming problems have been developed. For further improvement and application of these solvers, it is important to clarify the differences in their performance for various types of problems. In this study, the performance of four quadratic unconstrained binary optimization problem solvers, namely D-Wave Hybrid Solver Service (HSS), Toshiba Simulated Bifurcation Machine (SBM), Fujitsu DigitalAnnealer (DA), and simulated annealing on a personal computer, was benchmarked. The problems used for benchmarking were instances of real problems in MQLib, instances of the SAT-UNSAT phase transition point of random not-all-equal 3-SAT(NAE 3-SAT), and the Ising spin glass Sherrington-Kirkpatrick (SK) model. Concerning MQLib instances, the HSS performance ranked first; for NAE 3-SAT, DA performance ranked first; and regarding the SK model, SBM performance ranked first. These results may help understand the strengths and weaknesses of these solvers.

2104.14096

Recent study predicts that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a $\mathbb{Z}_2$ invariant and the density distribution.

2104.14097

Boolean Skolem function synthesis concerns synthesizing outputs as Boolean functions of inputs such that a relational specification between inputs and outputs is satisfied. This problem, also known as Boolean functional synthesis, has several applications, including design of safe controllers for autonomous systems, certified QBF solving, cryptanalysis etc. Recently, complexity theoretic hardness results have been shown for the problem, although several algorithms proposed in the literature are known to work well in practice. This dichotomy between theoretical hardness and practical efficacy has motivated the research into normal forms or representations of input specifications that permit efficient synthesis, thus explaining perhaps the efficacy of these algorithms. In this paper we go one step beyond this and ask if there exists a normal form representation that can in fact precisely characterize "efficient" synthesis. We present a normal form called SAUNF that precisely characterizes tractable synthesis in the following sense: a specification is polynomial time synthesizable iff it can be compiled to SAUNF in polynomial time. Additionally, a specification admits a polynomial-sized functional solution iff there exists a semantically equivalent polynomial-sized SAUNF representation. SAUNF is exponentially more succinct than well-established normal forms like BDDs and DNNFs, used in the context of AI problems, and strictly subsumes other more recently proposed forms like SynNNF. It enjoys compositional properties that are similar to those of DNNF. Thus, SAUNF provides the right trade-off in knowledge representation for Boolean functional synthesis.

2104.14098

We study the "twisted" Poincar\'e duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex associated to the Poisson complex which, combining with the twisted Poincar\'e duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology, and a gravity algebra structure on the negative cyclic Poisson homology. This generalizes the previous results obtained by Xu et al for unimodular Poisson algebras. We also show that these two algebraic structures are preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras they are also preserved by Koszul duality.

2104.14099

Inspired by an interesting counterexample to the cosmic no-hair conjecture found in a supergravity-motivated model recently, we propose a multi-field extension, in which two scalar fields are allowed to non-minimally couple to two vector fields, respectively. This model is shown to admit an exact Bianchi type I power-law solution. Furthermore, stability analysis based on the dynamical system method is performed to show that this anisotropic solution is indeed stable and attractive if both scalar fields are canonical. Nevertheless, if one of the two scalar fields is phantom then the corresponding anisotropic power-law inflation turns unstable as expected.

2104.14100

We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee linear convergence. However, a major difficulty in choosing the sketch size in terms of the effective dimension lies in the fact that the latter is usually unknown in practice. Current sketching-based solvers for regularized least-squares fall short on addressing this issue. Our main contribution is to propose adaptive versions of standard sketching-based iterative solvers, namely, the iterative Hessian sketch and the preconditioned conjugate gradient method, that do not require a priori estimation of the effective dimension. We propose an adaptive mechanism to control the sketch size according to the progress made in each step of the iterative solver. If enough progress is not made, the sketch size increases to improve the convergence rate. We prove that the adaptive sketch size scales at most in terms of the effective dimension, and that our adaptive methods are guaranteed to converge linearly. Consequently, our adaptive methods improve the state-of-the-art complexity for solving dense, ill-conditioned least-squares problems. Importantly, we illustrate numerically on several synthetic and real datasets that our method is extremely efficient and is often significantly faster than standard least-squares solvers such as a direct factorization based solver, the conjugate gradient method and its preconditioned variants.

2104.14101

Recent advances in natural language processing and computer vision have led to AI models that interpret simple scenes at human levels. Yet, we do not have a complete understanding of how humans and AI models differ in their interpretation of more complex scenes. We created a dataset of complex scenes that contained human behaviors and social interactions. AI and humans had to describe the scenes with a sentence. We used a quantitative metric of similarity between scene descriptions of the AI/human and ground truth of five other human descriptions of each scene. Results show that the machine/human agreement scene descriptions are much lower than human/human agreement for our complex scenes. Using an experimental manipulation that occludes different spatial regions of the scenes, we assessed how machines and humans vary in utilizing regions of images to understand the scenes. Together, our results are a first step toward understanding how machines fall short of human visual reasoning with complex scenes depicting human behaviors.

2104.14102

This paper summarizes the progress in developing a rugged, low-cost, automated ground cone robot network capable of traffic delineation at lane-level precision. A holonomic omnidirectional base with a traffic delineator was developed to allow flexibility in initialization. RTK GPS was utilized to reduce minimum position error to 2 centimeters. Due to recent developments, the cost of the platform is now less than $1,600. To minimize the effects of GPS-denied environments, wheel encoders and an Extended Kalman Filter were implemented to maintain lane-level accuracy during operation and a maximum error of 1.97 meters through 50 meters with little to no GPS signal. Future work includes increasing the operational speed of the platforms, incorporating lanelet information for path planning, and cross-platform estimation.

2104.14103

Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate surface dynamics, based on a 2D anisotropic damped Kuramoto-Sivashinsky equation, with periodic boundary conditions. A finite-difference semi-implicit time splitting scheme is employed on the discretization of the governing equation. Simulations were conducted with realistic coefficients related to physical parameters (anisotropies, beam orientation, diffusion). The stability of the numerical scheme is analyzed with time step and grid spacing tests for the pattern evolution, and the Method of Manufactured Solutions has been used to verify the proposed scheme. Ripples and hexagonal patterns were obtained from a monomodal initial condition for certain values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The anisotropy effects on pattern formation were studied, varying the angle of incidence of the ion beam with respect to the irradiated surface. Analytical discussions are based on linear and weakly nonlinear analysis.

2104.14104

How to design silicon-based quantum wires with figure of merit ($ZT$) larger than three is under hot pursuit due to the advantage of low cost and the availability of matured fabrication technique. Quantum wires consisting of finite three dimensional quantum dot (QD) arrays coupled to electrodes are proposed to realize high efficient thermoelectric devices with optimized power factors. The transmission coefficient of 3D QD arrays can exhibit 3D, 2D, 1D and 0D topological distribution functions by tailoring the interdot coupling strengths. Such topological effects on the thermoelectric properties are revealed. The 1D topological distribution function shows the maximum power factor and the best $ZT$ value. We have demonstrated that 3D silicon QD array nanowires with diameters below $20~nm$ and length $250~nm$ show high potential to achieve $ZT\ge 3$ near room temperature.

2104.14105

This paper develops a distributed collaborative localization algorithm based on an extended kalman filter. This algorithm incorporates Ultra-Wideband (UWB) measurements for vehicle to vehicle ranging, and shows improvements in localization accuracy where GPS typically falls short. The algorithm was first tested in a newly created open-source simulation environment that emulates various numbers of vehicles and sensors while simultaneously testing multiple localization algorithms. Predicted error distributions for various algorithms are quickly producible using the Monte-Carlo method and optimization techniques within MatLab. The simulation results were validated experimentally in an outdoor, urban environment. Improvements of localization accuracy over a typical extended kalman filter ranged from 2.9% to 9.3% over 180 meter test runs. When GPS was denied, these improvements increased up to 83.3% over a standard kalman filter. In both simulation and experimentally, the DCL algorithm was shown to be a good approximation of a full state filter, while reducing required communication between vehicles. These results are promising in showing the efficacy of adding UWB ranging sensors to cars for collaborative and landmark localization, especially in GPS-denied environments. In the future, additional moving vehicles with additional tags will be tested in other challenging GPS denied environments.

2104.14106

Convolution is one of the basic building blocks of CNN architectures. Despite its common use, standard convolution has two main shortcomings: Content-agnostic and Computation-heavy. Dynamic filters are content-adaptive, while further increasing the computational overhead. Depth-wise convolution is a lightweight variant, but it usually leads to a drop in CNN performance or requires a larger number of channels. In this work, we propose the Decoupled Dynamic Filter (DDF) that can simultaneously tackle both of these shortcomings. Inspired by recent advances in attention, DDF decouples a depth-wise dynamic filter into spatial and channel dynamic filters. This decomposition considerably reduces the number of parameters and limits computational costs to the same level as depth-wise convolution. Meanwhile, we observe a significant boost in performance when replacing standard convolution with DDF in classification networks. ResNet50 / 101 get improved by 1.9% and 1.3% on the top-1 accuracy, while their computational costs are reduced by nearly half. Experiments on the detection and joint upsampling networks also demonstrate the superior performance of the DDF upsampling variant (DDF-Up) in comparison with standard convolution and specialized content-adaptive layers.

2104.14107

Among the most promising terahertz (THz) radiation devices, gyrotrons can generate powerful THz-wave radiation in an open resonant structure. Unfortunately, such an oscillation using high-Q axial mode has been theoretically and experimentally demonstrated to suffer from strong ohmic losses. In this paper, a solution to such a challenging problem is to include a narrow belt of lossy section in the interaction circuit to stably constitute the traveling wave interaction (high-order-axial-mode, HOAM), and employ a down-tapered magnetic field to amplify the forward-wave component. A scheme based on the traveling-wave interaction concept is proposed to strengthen electron beam-wave interaction efficiency and simultaneously reduce the ohmic loss in a 1-THz third harmonic gyrotron, which is promising for further advancement of high-power continuous-wave operation.

2104.14108

Regional facial image synthesis conditioned on semantic mask has achieved great success using generative adversarial networks. However, the appearance of different regions may be inconsistent with each other when conducting regional image editing. In this paper, we focus on the problem of harmonized regional style transfer and manipulation for facial images. The proposed approach supports regional style transfer and manipulation at the same time. A multi-scale encoder and style mapping networks are proposed in our work. The encoder is responsible for extracting regional styles of real faces. Style mapping networks generate styles from random samples for all facial regions. As the key part of our work, we propose a multi-region style attention module to adapt the multiple regional style embeddings from a reference image to a target image for generating harmonious and plausible results. Furthermore, we propose a new metric "harmony score" and conduct experiments in a challenging setting: three widely used face datasets are involved and we test the model by transferring the regional facial appearance between datasets. Images in different datasets are usually quite different, which makes the inconsistency between target and reference regions more obvious. Results show that our model can generate reliable style transfer and multi-modal manipulation results compared with SOTAs. Furthermore, we show two face editing applications using the proposed approach.

2104.14109

What are the necessary and sufficient conditions for a proposition to be called a requirement? In Requirements Engineering research, a proposition is a requirement if and only if specific grammatical and/or communication conditions hold. I offer an alternative, that a proposition is a requirement if and only if specific contractual, economic, and engineering relationships hold. I introduce and define the concept of "Requirements Contract" which defines these conditions. I argue that seeing requirements as propositions governed by specific types of contracts leads to new and interesting questions for the field, and relates requirements engineering to such topics as economic incentives, interest alignment, principal agent problem, and decision-making with incomplete information.

2104.14110

We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding energies but also the corresponding wave functions. When the mass of impurity atom is vary large, there are at most three three-body bound states. We then study the effect of three-body zero-range interaction and unveil that it can induces one more three-body bound state at a certain region of coupling strength ratio under a fixed mass ratio.

2104.14111

The effective photon-quark-antiquark ($\gamma q \overline{q}$) vertex function is evaluated at finite temperature in presence of an arbitrary external magnetic field using the 2-flavour gauged Nambu--Jona-Lasinio (NJL) model in the mean field approximation. The lowest order diagram contributing to the magnetic form factor and the anomalous magnetic moment (AMM) of the quarks is calculated at finite temperature and external magnetic field using the imaginary time formalism of finite temperature field theory and the Schwinger proper time formalism. The Schwinger propagator including all the Landau levels with non-zero AMM of the dressed quarks is considered while calculating the loop diagram. Using sharp as well as smooth three momentum cutoff, we regularize the UV divergences arising from the vertex function and the parameters of our model are chosen to reproduce the well known phenomenological quantities at zero temperature and zero magnetic field, such as pion-decay constant ($f_\pi$), vacuum quark condensate, vacuum pion mass ($m_\pi$) as well as the magnetic moments of proton and neutron. We then study the temperature and magnetic field dependence of the AMM and constituent mass of the quark. We found that, the AMM as well as the constituent quark mass are large at the chiral symmetry broken phase in the low temperature region. Around the pseudo-chiral phase transition they decrease rapidly and at high temperatures both of them approach vanishingly small values in the symmetry restored phase.

2104.14112

The goal of this paper is to characterize Gaussian-Process optimization in the setting where the function domain is large relative to the number of admissible function evaluations, i.e., where it is impossible to find the global optimum. We provide upper bounds on the suboptimality (Bayesian simple regret) of the solution found by optimization strategies that are closely related to the widely used expected improvement (EI) and upper confidence bound (UCB) algorithms. These regret bounds illuminate the relationship between the number of evaluations, the domain size (i.e. cardinality of finite domains / Lipschitz constant of the covariance function in continuous domains), and the optimality of the retrieved function value. In particular, they show that even when the number of evaluations is far too small to find the global optimum, we can find nontrivial function values (e.g. values that achieve a certain ratio with the optimal value).

2104.14113

Academic administrators and funding agencies must predict the publication productivity of research groups and individuals to assess authors' abilities. However, such prediction remains an elusive task due to the randomness of individual research and the diversity of authors' productivity patterns. We applied two kinds of approaches to this prediction task: deep neural network learning and model-based approaches. We found that a neural network cannot give a good long-term prediction for groups, while the model-based approaches cannot provide short-term predictions for individuals. We proposed a model that integrates the advantages of both data-driven and model-based approaches, and the effectiveness of this method was validated by applying it to a high-quality dblp dataset, demonstrating that the proposed model outperforms the tested data-driven and model-based approaches.

2104.14114

Existing blind image quality assessment (BIQA) methods are mostly designed in a disposable way and cannot evolve with unseen distortions adaptively, which greatly limits the deployment and application of BIQA models in real-world scenarios. To address this problem, we propose a novel Lifelong blind Image Quality Assessment (LIQA) approach, targeting to achieve the lifelong learning of BIQA. Without accessing to previous training data, our proposed LIQA can not only learn new distortions, but also mitigate the catastrophic forgetting of seen distortions. Specifically, we adopt the Split-and-Merge distillation strategy to train a single-head network that makes task-agnostic predictions. In the split stage, we first employ a distortion-specific generator to obtain the pseudo features of each seen distortion. Then, we use an auxiliary multi-head regression network to generate the predicted quality of each seen distortion. In the merge stage, we replay the pseudo features paired with pseudo labels to distill the knowledge of multiple heads, which can build the final regressed single head. Experimental results demonstrate that the proposed LIQA method can handle the continuous shifts of different distortion types and even datasets. More importantly, our LIQA model can achieve stable performance even if the task sequence is long.

2104.14115

Since the outbreak of Coronavirus Disease 2019 (COVID-19), most of the impacted patients have been diagnosed with high fever, dry cough, and soar throat leading to severe pneumonia. Hence, to date, the diagnosis of COVID-19 from lung imaging is proved to be a major evidence for early diagnosis of the disease. Although nucleic acid detection using real-time reverse-transcriptase polymerase chain reaction (rRT-PCR) remains a gold standard for the detection of COVID-19, the proposed approach focuses on the automated diagnosis and prognosis of the disease from a non-contrast chest computed tomography (CT)scan for timely diagnosis and triage of the patient. The prognosis covers the quantification and assessment of the disease to help hospitals with the management and planning of crucial resources, such as medical staff, ventilators and intensive care units (ICUs) capacity. The approach utilises deep learning techniques for automated quantification of the severity of COVID-19 disease via measuring the area of multiple rounded ground-glass opacities (GGO) and consolidations in the periphery (CP) of the lungs and accumulating them to form a severity score. The severity of the disease can be correlated with the medicines prescribed during the triage to assess the effectiveness of the treatment. The proposed approach shows promising results where the classification model achieved 93% accuracy on hold-out data.

2104.14116

To achieve the low latency, high throughput, and energy efficiency benefits of Spiking Neural Networks (SNNs), reducing the memory and compute requirements when running on a neuromorphic hardware is an important step. Neuromorphic architecture allows massively parallel computation with variable and local bit-precisions. However, how different bit-precisions should be allocated to different layers or connections of the network is not trivial. In this work, we demonstrate how a layer-wise Hessian trace analysis can measure the sensitivity of the loss to any perturbation of the layer's weights, and this can be used to guide the allocation of a layer-specific bit-precision when quantizing an SNN. In addition, current gradient based methods of SNN training use a complex neuron model with multiple state variables, which is not ideal for compute and memory efficiency. To address this challenge, we present a simplified neuron model that reduces the number of state variables by 4-fold while still being compatible with gradient based training. We find that the impact on model accuracy when using a layer-wise bit-precision correlated well with that layer's Hessian trace. The accuracy of the optimal quantized network only dropped by 0.2%, yet the network size was reduced by 58%. This reduces memory usage and allows fixed-point arithmetic with simpler digital circuits to be used, increasing the overall throughput and energy efficiency.

2104.14117

Despite the impressive progress achieved in robust grasp detection, robots are not skilled in sophisticated grasping tasks (e.g. search and grasp a specific object in clutter). Such tasks involve not only grasping, but comprehensive perception of the visual world (e.g. the relationship between objects). Recently, the advanced deep learning techniques provide a promising way for understanding the high-level visual concepts. It encourages robotic researchers to explore solutions for such hard and complicated fields. However, deep learning usually means data-hungry. The lack of data severely limits the performance of deep-learning-based algorithms. In this paper, we present a new dataset named \regrad to sustain the modeling of relationships among objects and grasps. We collect the annotations of object poses, segmentations, grasps, and relationships in each image for comprehensive perception of grasping. Our dataset is collected in both forms of 2D images and 3D point clouds. Moreover, since all the data are generated automatically, users are free to import their own object models for the generation of as many data as they want. We have released our dataset and codes. A video that demonstrates the process of data generation is also available.

2104.14118

In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning strategies that partition the feasible region using solutions that has already been simulated as well as prior knowledge of the problem of interesting. We integrate the proposed strategies with the Empirical Stochastic Branch-and-Bound framework proposed by Xu and Nelson (2013). This combination leads to a general-purpose discrete simulation-based optimization algorithm that is both globally convergent and has good small sample (finite-time) performance. The proposed general-purpose discrete simulation-based optimization algorithm is validated on a synthetic discrete simulation-based optimization problem and is then used to address a real-world car-sharing fleet assignment problem. Experiment results show that the proposed strategy can increase the algorithm efficiency significantly.

2104.14119

$J/\psi$ production in p-p ultra-peripheral collisions through the elastic and inelastic photoproduction processes, where the virtual photons emitted from the projectile interact with the target, are studied. The comparisions between the exact treatment results and the ones of equivalent photon approximation are expressed as $Q^{2}$ (virtuality of photon), $z$ and $p_{T}$ distributions, and the total cross sections are also estimated. The method developed by Martin and Ryskin is employed to avoid double counting when the different production mechanism are considered simultaneously. The numerical results indicate that, the equivalent photon approximation can be only applied to the coherent or elastic electromagnetic process, the improper choice of $Q^{2}_{\mathrm{max}}$ and $y_{\mathrm{max}}$ will cause obvious errors. And the exact treatment is needed to deal accurately with the $J/\psi$ photoproduction.

2104.14120

One of the difficulties of conversion rate (CVR) prediction is that the conversions can delay and take place long after the clicks. The delayed feedback poses a challenge: fresh data are beneficial to continuous training but may not have complete label information at the time they are ingested into the training pipeline. To balance model freshness and label certainty, previous methods set a short waiting window or even do not wait for the conversion signal. If conversion happens outside the waiting window, this sample will be duplicated and ingested into the training pipeline with a positive label. However, these methods have some issues. First, they assume the observed feature distribution remains the same as the actual distribution. But this assumption does not hold due to the ingestion of duplicated samples. Second, the certainty of the conversion action only comes from the positives. But the positives are scarce as conversions are sparse in commercial systems. These issues induce bias during the modeling of delayed feedback. In this paper, we propose DElayed FEedback modeling with Real negatives (DEFER) method to address these issues. The proposed method ingests real negative samples into the training pipeline. The ingestion of real negatives ensures the observed feature distribution is equivalent to the actual distribution, thus reducing the bias. The ingestion of real negatives also brings more certainty information of the conversion. To correct the distribution shift, DEFER employs importance sampling to weigh the loss function. Experimental results on industrial datasets validate the superiority of DEFER. DEFER have been deployed in the display advertising system of Alibaba, obtaining over 6.0% improvement on CVR in several scenarios. The code and data in this paper are now open-sourced {https://github.com/gusuperstar/defer.git}.

2104.14121

This study investigates the structure of Arf rings. From the perspective of ring extensions, a decomposition of integrally closed ideals is given. Using this, we present a kind of their prime ideal decomposition in Arf rings, and determine their structure in the case where both R and the integral closure of R are local rings.

2104.14122

We describe a method to select the nodes in Graph datasets for training so that the model trained on the points selected will be be better than the ones if we select other points for the purpose of training. This is a very important aspect as the process of labelling the points is often a costly affair. The usual Active Learning methods are good but the penalty involved with these methods is that, we need to re-train the model after selecting the nodes in each iteration of Active Learning cycle. We come up with a method which use the concept of Graph Centrality to select the nodes for labeling and training initially and the training is needed to perform only once. We have tested this idea on three graph datasets - Cora, Citeseer and Pubmed- and the results are really encouraging.

2104.14123

"Lightweight convolutional neural networks" is an important research topic in the field of embedded vision. To implement image recognition tasks on a resource-limited hardware platform, it is necessary to reduce the memory size and the computational cost. The contribution of this paper is stated as follows. First, we propose an algorithm to process a specific network architecture (Condensation-Net) without increasing the maximum memory storage for feature maps. The architecture for virtual feature maps saves 26.5% of memory bandwidth by calculating the results of cross-channel pooling before storing the feature map into the memory. Second, we show that cross-channel pooling can improve the accuracy of object detection tasks, such as face detection, because it increases the number of filter weights. Compared with Tiny-YOLOv2, the improvement of accuracy is 2.0% for quantized networks and 1.5% for full-precision networks when the false-positive rate is 0.1. Last but not the least, the analysis results show that the overhead to support the cross-channel pooling with the proposed hardware architecture is negligible small. The extra memory cost to support Condensation-Net is 0.2% of the total size, and the extra gate count is only 1.0% of the total size.

2104.14124

In order to handle modern convolutional neural networks (CNNs) efficiently, a hardware architecture of CNN inference accelerator is proposed to handle depthwise convolutions and regular convolutions, which are both essential building blocks for embedded-computer-vision algorithms. Different from related works, the proposed architecture can support filter kernels with different sizes with high flexibility since it does not require extra costs for intra-kernel parallelism, and it can generate convolution results faster than the architecture of the related works. The experimental results show the importance of supporting depthwise convolutions and dilated convolutions with the proposed hardware architecture. In addition to depthwise convolutions with large-kernels, a new structure called DDC layer, which includes the combination of depthwise convolutions and dilated convolutions, is also analyzed in this paper. For face detection, the computational costs decrease by 30%, and the model size decreases by 20% when the DDC layers are applied to the network. For image classification, the accuracy is increased by 1% by simply replacing $3 \times 3$ filters with $5 \times 5$ filters in depthwise convolutions.

2104.14125

The field of view (FOV) of convolutional neural networks is highly related to the accuracy of inference. Dilated convolutions are known as an effective solution to the problems which require large FOVs. However, for general-purpose hardware or dedicated hardware, it usually takes extra time to handle dilated convolutions compared with standard convolutions. In this paper, we propose a network module, Cascaded and Separable Structure of Dilated (CASSOD) Convolution, and a special hardware system to handle the CASSOD networks efficiently. A CASSOD-Net includes multiple cascaded $2 \times 2$ dilated filters, which can be used to replace the traditional $3 \times 3$ dilated filters without decreasing the accuracy of inference. Two example applications, face detection and image segmentation, are tested with dilated convolutions and the proposed CASSOD modules. The new network for face detection achieves higher accuracy than the previous work with only 47% of filter weights in the dilated convolution layers of the context module. Moreover, the proposed hardware system can accelerate the computations of dilated convolutions, and it is 2.78 times faster than traditional hardware systems when the filter size is $3 \times 3$.

2104.14126

It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM structure and to distinguish different topological phases from transport behaviors remains unknown. We show that, due to the presence of combined time-reversal and fractional translation symmetry, the recently proposed second-order nonlinear Hall effect can be used to characterize different topological phases with various AFM configurations. Guided by the symmetry analysis, we obtain the expressions of the Berry curvature dipole for different AFM configurations. Based on the effective model, we explicitly calculate the Berry curvature dipole, which is found to be vanishingly small for the triple-point semimetal phase, and large in the Weyl semimetal phase. Our results not only put forward an effective method for the identification of magnetic orders and topological phases in AFM half-Heusler materials, but also suggest these materials as a versatile platform for engineering the non-linear Hall effect.

2104.14127

Timoshenko's theory for bending vibrations of a beam has been extensively studied since its development nearly one hundred years ago. Unfortunately there are not many analytical results. The results above the critical frequency inclusive haeve been tested only recently. Here an analytical expression for the solutions of the Timoshenko equation for free-free boundary conditions, below the critical frequency, is obtained. The analytical results are compared with recent experimental results reported of aluminum and brass beams The agreement is excellent, with an error of less than 3%, for the aluminum beam and of 5.5% for the brass beam. Some exact results are also given for frequencies above the critical frequency.

2104.14128

The increasing size of neural network models has been critical for improvements in their accuracy, but device memory is not growing at the same rate. This creates fundamental challenges for training neural networks within limited memory environments. In this work, we propose ActNN, a memory-efficient training framework that stores randomly quantized activations for back propagation. We prove the convergence of ActNN for general network architectures, and we characterize the impact of quantization on the convergence via an exact expression for the gradient variance. Using our theory, we propose novel mixed-precision quantization strategies that exploit the activation's heterogeneity across feature dimensions, samples, and layers. These techniques can be readily applied to existing dynamic graph frameworks, such as PyTorch, simply by substituting the layers. We evaluate ActNN on mainstream computer vision models for classification, detection, and segmentation tasks. On all these tasks, ActNN compresses the activation to 2 bits on average, with negligible accuracy loss. ActNN reduces the memory footprint of the activation by 12x, and it enables training with a 6.6x to 14x larger batch size.

2104.14129

Recent years, analysis dictionary learning (ADL) and its applications for classification have been well developed, due to its flexible projective ability and low classification complexity. With the learned analysis dictionary, test samples can be transformed into a sparse subspace for classification efficiently. However, the underling locality of sample data has rarely been explored in analysis dictionary to enhance the discriminative capability of the classifier. In this paper, we propose a novel locality constrained analysis dictionary learning model with a synthesis K-SVD algorithm (SK-LADL). It considers the intrinsic geometric properties by imposing graph regularization to uncover the geometric structure for the image data. Through the learned analysis dictionary, we transform the image to a new and compact space where the manifold assumption can be further guaranteed. thus, the local geometrical structure of images can be preserved in sparse representation coefficients. Moreover, the SK-LADL model is iteratively solved by the synthesis K-SVD and gradient technique. Experimental results on image classification validate the performance superiority of our SK-LADL model.

2104.14130

Event perception tasks such as recognizing and localizing actions in streaming videos are essential for tackling visual understanding tasks. Progress has primarily been driven by the use of large-scale, annotated training data in a supervised manner. In this work, we tackle the problem of learning \textit{actor-centered} representations through the notion of continual hierarchical predictive learning to localize actions in streaming videos without any training annotations. Inspired by cognitive theories of event perception, we propose a novel, self-supervised framework driven by the notion of hierarchical predictive learning to construct actor-centered features by attention-based contextualization. Extensive experiments on three benchmark datasets show that the approach can learn robust representations for localizing actions using only one epoch of training, i.e., we train the model continually in streaming fashion - one frame at a time, with a single pass through training videos. We show that the proposed approach outperforms unsupervised and weakly supervised baselines while offering competitive performance to fully supervised approaches. Finally, we show that the proposed model can generalize to out-of-domain data without significant loss in performance without any finetuning for both the recognition and localization tasks.

2104.14131

Neural Architecture Search (NAS) is a popular method for automatically designing optimized architectures for high-performance deep learning. In this approach, it is common to use bilevel optimization where one optimizes the model weights over the training data (lower-level problem) and various hyperparameters such as the configuration of the architecture over the validation data (upper-level problem). This paper explores the statistical aspects of such problems with train-validation splits. In practice, the lower-level problem is often overparameterized and can easily achieve zero loss. Thus, a-priori it seems impossible to distinguish the right hyperparameters based on training loss alone which motivates a better understanding of the role of train-validation split. To this aim this work establishes the following results. (1) We show that refined properties of the validation loss such as risk and hyper-gradients are indicative of those of the true test loss. This reveals that the upper-level problem helps select the most generalizable model and prevent overfitting with a near-minimal validation sample size. Importantly, this is established for continuous spaces -- which are highly relevant for popular differentiable search schemes. (2) We establish generalization bounds for NAS problems with an emphasis on an activation search problem. When optimized with gradient-descent, we show that the train-validation procedure returns the best (model, architecture) pair even if all architectures can perfectly fit the training data to achieve zero error. (3) Finally, we highlight rigorous connections between NAS, multiple kernel learning, and low-rank matrix learning. The latter leads to novel algorithmic insights where the solution of the upper problem can be accurately learned via efficient spectral methods to achieve near-minimal risk.

2104.14132

Recently, much progress in natural language processing has been driven by deep contextualized representations pretrained on large corpora. Typically, the fine-tuning on these pretrained models for a specific downstream task is based on single-view learning, which is however inadequate as a sentence can be interpreted differently from different perspectives. Therefore, in this work, we propose a text-to-text multi-view learning framework by incorporating an additional view -- the text generation view -- into a typical single-view passage ranking model. Empirically, the proposed approach is of help to the ranking performance compared to its single-view counterpart. Ablation studies are also reported in the paper.

2104.14133

Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.

2104.14134

Weakly supervised temporal action localization aims to detect and localize actions in untrimmed videos with only video-level labels during training. However, without frame-level annotations, it is challenging to achieve localization completeness and relieve background interference. In this paper, we present an Action Unit Memory Network (AUMN) for weakly supervised temporal action localization, which can mitigate the above two challenges by learning an action unit memory bank. In the proposed AUMN, two attention modules are designed to update the memory bank adaptively and learn action units specific classifiers. Furthermore, three effective mechanisms (diversity, homogeneity and sparsity) are designed to guide the updating of the memory network. To the best of our knowledge, this is the first work to explicitly model the action units with a memory network. Extensive experimental results on two standard benchmarks (THUMOS14 and ActivityNet) demonstrate that our AUMN performs favorably against state-of-the-art methods. Specifically, the average mAP of IoU thresholds from 0.1 to 0.5 on the THUMOS14 dataset is significantly improved from 47.0% to 52.1%.

2104.14135

In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. We first prove the local well-posedness of the two phase flow problem with surface tension, then demonstrate that as surface tension tends to zero, the solution of the two phase flow problem with surface tension converges to the solution of the two phase flow problem without surface tension.

2104.14136

We study bilinear rough singular integral operators $\mathcal{L}_{\Omega}$ associated with a function $\Omega$ on the sphere $\mathbb{S}^{2n-1}$. In the recent work of Grafakos, He, and Slav\'ikov\'a (Math. Ann. 376: 431-455, 2020), they showed that $\mathcal{L}_{\Omega}$ is bounded from $L^2\times L^2$ to $L^1$, provided that $\Omega\in L^q(\mathbb{S}^{2n-1})$ for $4/3<q\le \infty$ with mean value zero. We generalize their result to the boundedness for all Banach points. We actually prove $L^{p_1}\times L^{p_2}\to L^p$ estimates for $\mathcal{L}_{\Omega}$ under the assumption $$\Omega\in L^q(\mathbb{S}^{2n-1}) \quad \text{ for }~\max{\Big(\;\frac{4}{3}\;,\; \frac{p}{2p-1} \;\Big)<q\le \infty}$$ where $1<p_1,p_2<\infty$ with $1/p=1/p_1+1/p_2$. Our result improves that of Grafakos, He, and Honz\'ik (Adv. Math. 326: 54-78, 2018), in which the more restrictive condition $\Omega\in L^{\infty}(\mathbb{S}^{2n-1})$ is required for the $L^{p_1}\times L^{p_2}\to L^p$ boundedness.

2104.14137

In this paper we consider reinforcement learning tasks with progressive rewards; that is, tasks where the rewards tend to increase in magnitude over time. We hypothesise that this property may be problematic for value-based deep reinforcement learning agents, particularly if the agent must first succeed in relatively unrewarding regions of the task in order to reach more rewarding regions. To address this issue, we propose Spectral DQN, which decomposes the reward into frequencies such that the high frequencies only activate when large rewards are found. This allows the training loss to be balanced so that it gives more even weighting across small and large reward regions. In two domains with extreme reward progressivity, where standard value-based methods struggle significantly, Spectral DQN is able to make much farther progress. Moreover, when evaluated on a set of six standard Atari games that do not overtly favour the approach, Spectral DQN remains more than competitive: While it underperforms one of the benchmarks in a single game, it comfortably surpasses the benchmarks in three games. These results demonstrate that the approach is not overfit to its target problem, and suggest that Spectral DQN may have advantages beyond addressing reward progressivity.

2104.14138

Baryon number is an accidental symmetry in the standard model, while Peccei-Quinn symmetry is hypothetical symmetry which is introduced to solve the strong CP problem. We study the possible connections between Peccei-Quinn symmetry and baryon number symmetry. In this framework, an axion is identified as the Nambu-Goldstone boson of baryon number violation. As a result, characteristic baryon number violating processes are predicted. We developed the general method to determine the baryon number and lepton number of new scalar in the axion model.

2104.14139

One of the fundamental properties of an intermediate polar is the dynamical nature of the accretion flow as it encounters the white dwarf's magnetosphere. Many works have presumed a dichotomy between disk-fed accretion, in which the WD accretes from a Keplerian disk, and stream-fed accretion, in which the matter stream from the donor star directly impacts the WD's magnetosphere without forming a disk. However, there is also a third, poorly understood regime in which the accretion flow consists of a torus of diamagnetic blobs that encircles the WD. This mode of accretion is expected to exist at mass-transfer rates below those observed during disk-fed accretion, but above those observed during pure stream-fed accretion. We invoke the diamagnetic-blob regime to explain the exceptional TESS light curve of the intermediate polar TX Col, which transitioned into and out of states of enhanced accretion during Cycles 1 and 3. Power-spectral analysis reveals that the accretion was principally stream-fed. However, when the mass-transfer rate spiked, large-amplitude quasi-periodic oscillations (QPOs) abruptly appeared and dominated the light curve for weeks. The QPOs have two striking properties: they appear in a stream-fed geometry at elevated accretion rates, and they occur preferentially within a well-defined range of frequencies (~10-25 cycles per day). We propose that during episodes of enhanced accretion, a torus of diamagnetic blobs forms near the binary's circularization radius and that the QPOs are beats between the white dwarf's spin frequency and unstable blob orbits within the WD's magnetosphere. We discuss how such a torus could be a critical step in producing an accretion disk in a formerly diskless system.

2104.14140

In this paper we analyze $(-1)$- curves in the blown up projective space $\mathbb{P}^r$ in general points. The notion of $(-1)$-curves was analyzed in the early days of mirror symmetry by Kontsevich with the motivation of counting curves on a Calabi-Yau. In dimension two, Nagata studied planar $(-1)$-curves in order to construct counterexample to Hilbert's 14th problem. In this paper, we first analyze the Coxeter systems and the Weyl group action on curves, to identify infinitely many $(-1)$-curves on the blown-up $\mathbb{P}^r$ when the number of points is at least $r+5$. We introduce a bilinear form on a space of curves, that extends the intersection product in dimension $2$, and a unique symmetric Weyl-invariant class (that we will refer to as the anticanonical curve class). For Mori Dream Spaces we prove that $(-1)$-curves can be defined arithmetically by the linear and quadratic invariants determined by the bilinear form, while the set of $(0)$- and $(1)$-Weyl lines determine the cone of effective divisors in blown-up $\mathbb{P}^r$ with $r+3$ points.

2104.14141

Topological photonics and its topological edge state which can suppress scattering and immune defects set off a research boom. Recently, the quantum valley Hall effect (QVHE) with large valley Chern number and its multimode topological transmission have been realized, which greatly improve the mode density of the topological waveguide and its coupling efficiency with other photonic devices. The multifrequency QVHE and its topological transmission have been realized to increase the transmission capacity of topological waveguide, but multifrequency and multimode QVHE have not been realized simultaneously. In this Letter, the valley photonic crystal (VPC) is constructed with the Stampfli-triangle photonic crystal (STPC), and its degeneracies in the low-frequency and high-frequency bands are broken simultaneously to realize the multifrequency and multimode QVHE. The multifrequency and multimode topological transmission is realized through the U-shaped waveguide constructed with two VPCs with opposite valley Chern numbers. According to the bulk-edge correspondence principle, the Chern number is equal to the number of topological edge states or topological waveguide modes. Therefore, we can determine the valley Chern number of the VPC by the number of topological edge states or topological waveguide modes, further determine the realization of large valley Chern number. These results provide new ideas for high-efficiency and high-capacity optical transmission and communication devices and their integration, and broaden the application range of topological edge states.

2104.14142

In this paper, starting with an arbitrary graph $G$, we give a construction of a graph $[G]$ with Cohen-Macaulay binomial edge ideal. We have extended this construction for clutters also. We also discuss unmixed and Cohen-Macaulay properties of binomial edge ideals of subgraphs.

2104.14143

A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the existing works on identification can be categorized as special cases of these two phenomena. Several effective criteria for determining the identifiability and the corresponding identification algorithms are proposed. Three important results are derived: (1) If a BN is observable, it is uniquely identifiable; (2) If a BCN is O1-observable, it is uniquely identifiable, where O1-observability is the most general form of the existing observability terms; (3) A BN or BCN may be identifiable, but not observable. In addition, remarks present some challenging future research and contain a preliminary attempt about how to identify unobservable systems.

2104.14144

Primary mechanism governed the emerge of near-room-temperature superconductivity in superhydrides is widely accepted to be the electron-phonon interaction. If so, the temperature dependent resistance, R(T), in these materials should be obey the Bloch-Gr\"uneisen equation, where the power-law exponent, p, should be equal to exact integer value of p=5. From other hand, there is a well-established theoretical result that the pure electron-magnon interaction should be manifested by p=3, and p=2 is the value for pure electron-electron interaction. Here we analysed the temperature dependent resistance, R(T), for high-entropy alloy (ScZrNb)0.65[RhPd]0.35 and highly-compressed boron and superhydrides H3S, LaHx, PrH9 and BaH12. In result, we showed that high-entropy alloy (ScZrNb)0.65[RhPd]0.35 exhibited pure electron-phonon mediated superconductor with p = 4.9. Unexpectedly we revealed that all studied superhydrides exhibit 1.8 < p < 3.2. This implies that it is unlikely that the electron-phonon interaction is the primary mechanism for the Cooper pairs formation in highly-compressed superhydrides and alternative pairing mechanisms, for instance, the electron-magnon, the electron-polaron, the electron-electron or other, should be considered as the origin for the emerge of near-room-temperature superconductivity in these compounds.

2104.14145

The question whether a partition $\mathcal{P}$ and a hierarchy $\mathcal{H}$ or a tree-like split system $\mathfrak{S}$ are compatible naturally arises in a wide range of classification problems. In the setting of phylogenetic trees, one asks whether the sets of $\mathcal{P}$ coincide with leaf sets of connected components obtained by deleting some edges from the tree $T$ that represents $\mathcal{H}$ or $\mathfrak{S}$, respectively. More generally, we ask whether a refinement $T^*$ of $T$ exists such that $T^*$ and $\mathcal{P}$ are compatible. We report several characterizations for (refinements of) hierarchies and split systems that are compatible with (sets of) partitions. In addition, we provide a linear-time algorithm to check whether refinements of trees and a given partition are compatible. The latter problem becomes NP-complete but fixed-parameter tractable if a set of partitions is considered instead of a single partition. We finally explore the close relationship of the concept of compatibility and so-called Fitch maps.

2104.14146

Many quantum materials of interest, ex., bilayer graphene, possess a number of closely spaced but not fully degenerate bands near the Fermi level, where the coupling to the far detuned remote bands can induce Berry curvatures of the non-Abelian character in this active multiple-band manifold for transport effects. Under finite electric fields, non-adiabatic interband transition processes are expected to play significant roles in the associated Hall conduction. Here through an exemplified study on the valley Hall conduction in AB-stacked bilayer graphene, we show that the contribution arising from non-adiabatic transitions around the bands near the Fermi energy to the Hall current is not only quantitatively about an order-of-magnitude larger than the contribution due to adiabatic inter-manifold transition with the non-Abelian Berry curvatures. Due to the trigonal warping, the former also displays an anisotropic response to the orientation of the applied electric field that is qualitatively distinct from that of the latter. We further show that these anisotropic responses also reveal the essential differences between the diagonal and off-diagonal elements of the non-Abelian Berry curvature matrix in terms of their contributions to the Hall currents. We provide a physically intuitive understanding of the origin of distinct anisotropic features from different Hall current contributions, in terms of band occupations and interband coherence. This then points to the generalization beyond the specific example of bilayer graphenes.

2104.14147

A line-of-sight towards the Galactic Center (GC) offers the largest number of potentially habitable systems of any direction in the sky. The Breakthrough Listen program is undertaking the most sensitive and deepest targeted SETI surveys towards the GC. Here, we outline our observing strategies with Robert C. Byrd Green Bank Telescope (GBT) and Parkes telescope to conduct 600 hours of deep observations across 0.7--93 GHz. We report preliminary results from our survey for ETI beacons across 1--8 GHz with 7.0 and 11.2 hours of observations with Parkes and GBT, respectively. With our narrowband drifting signal search, we were able to place meaningful constraints on ETI transmitters across 1--4 GHz and 3.9--8 GHz with EIRP limits of $\geq$4$\times$10$^{18}$ W among 60 million stars and $\geq$5$\times$10$^{17}$ W among half a million stars, respectively. For the first time, we were able to constrain the existence of artificially dispersed transient signals across 3.9--8 GHz with EIRP $\geq$1$\times$10$^{14}$ W/Hz with a repetition period $\leq$4.3 hours. We also searched our 11.2 hours of deep observations of the GC and its surrounding region for Fast Radio Burst-like magnetars with the DM up to 5000 pc cm$^{-3}$ with maximum pulse widths up to 90 ms at 6 GHz. We detected several hundred transient bursts from SGR J1745$-$2900, but did not detect any new transient burst with the peak luminosity limit across our observed band of $\geq$10$^{31}$ erg s$^{-1}$ and burst-rate of $\geq$0.23 burst-hr$^{-1}$. These limits are comparable to bright transient emission seen from other Galactic radio-loud magnetars, constraining their presence at the GC.

2104.14148

In the paper we study algebraic property of the monoid $\mathbf{I}\mathbb{N}_{\infty}^{\textbf{g}[j]}$ of cofinite partial isometries of the set of positive integers $\mathbb{N}$ with the bounded finite noise $j$. We extend the Eberhart and Selden results for the closure of the bicyclic monoid onto $\mathbf{I}\mathbb{N}_{\infty}^{\textbf{g}[j]}$ for any positive integer $j$. In particular we show that for any positive integer $j$ every Hausdorff shift-continuous topology $\tau$ on $\mathbf{I}\mathbb{N}_{\infty}^{\textbf{g}[j]}$ is discrete and if $\mathbf{I}\mathbb{N}_{\infty}^{\textbf{\emph{g}}[j]}$ is a proper dense subsemigroup of a Hausdorff semitopological semigroup $S$, then $S\setminus \mathbf{I}\mathbb{N}_{\infty}^{\textbf{\emph{g}}[j]}$ is a closed ideal of $S$, and moreover if $S$ is a topological inverse semigroup then $S\setminus \mathbf{I}\mathbb{N}_{\infty}^{\textbf{\emph{g}}[j]}$ is a topological group. Also we describe the algebraic and topological structure of the closure of the monoid $\mathbf{I}\mathbb{N}_{\infty}^{\textbf{\emph{g}}[j]}$ in a locally compact topological inverse semigroup.

2104.14149

Extracting patterns and useful information from Natural Language datasets is a challenging task, especially when dealing with data written in a language different from English, like Italian. Machine and Deep Learning, together with Natural Language Processing (NLP) techniques have widely spread and improved lately, providing a plethora of useful methods to address both Supervised and Unsupervised problems on textual information. We propose RECKONition, a NLP-based system for Industrial Accidents at Work Prevention. RECKONition, which is meant to provide Natural Language Understanding, Clustering and Inference, is the result of a joint partnership with the Italian National Institute for Insurance against Accidents at Work (INAIL). The obtained results showed the ability to process textual data written in Italian describing industrial accidents dynamics and consequences.

2104.14150

The main goal of this paper is to determine the asymptotic behavior of the number $X_n$ of cut-vertices in random planar maps with $n$ edges. It is shown that $X_n/n \to c$ in probability (for some explicit $c>0$). For so-called subcritical classes of planar maps (like outerplanar maps) we obtain a central limit theorem, too. Interestingly the combinatorics behind this seemingly simple problem is quite involved.

2104.14151

We study the ground state properties of the doped Hubbard model with strong interactions on honeycomb lattice by the Density Matrix Renormalization Group (DMRG) method. At half-filling, due to the absence of minus sign problem, it is now well established by large-scale Quantum Monte Carlo calculations that a Dirac semi-metal to anti-ferromagnetic Mott insulator transition occurs with the increase of the interaction strength $U$ for the Hubbard model on honeycomb lattice. However, an understanding of the fate of the anti-ferromagnetic Mott insulator when holes are doped into the system is still lacking. In this work, by calculating the local spin and charge density for width-4 cylinders with DMRG, we discover a half-filled stripe order in the doped Hubbard model on honeycomb lattice. We also perform complementary large-scale mean-field calculations with renormalized interaction strength. We observe half-filled stripe order and find stripe states with filling close to one half are nearly degenerate in energy.

2104.14152

In this article we present a novel discrete-time design approach which reduces the deteriorating effects of sampling on stability and performance in digitally controlled nonlinear mechanical systems. The method is motivated by recent results for linear systems, where feedback imposes closed-loop behavior that exactly represents the symplectic discretization of a desired target system. In the nonlinear case, both the second order accurate representation of the sampling process and the definition of the target dynamics stem from the application of the implicit midpoint rule. The implicit nature of the resulting state feedback requires the numerical solution of an in general nonlinear system of algebraic equations in every sampling interval. For an implementation with pure position feedback, the velocities/momenta have to be approximated in the sampling instants, which gives a clear interpretation of our approach in terms of the St\"ormer-Verlet integration scheme on a staggered grid. We present discrete-time versions of impedance or energy shaping plus damping injection control as well as computed torque tracking control. Both the Hamiltonian and the Lagrangian perspective are adopted. Besides a linear example to introduce the concept, the simulations with a planar two link robot model illustrate the performance and stability gain compared to the discrete implementations of continuous-time control laws. A short analysis of computation times shows the real-time capability of our method.

2104.14153

Stellar atmospheric parameters (effective temperature, luminosity classifications, and metallicity) estimates for some 24 million stars (including over 19 million dwarfs and 5 million giants) are determined from the stellar colors of SMSS DR2 and Gaia EDR3, based on training datasets with available spectroscopic measurements from previous high/medium/low-resolution spectroscopic surveys. The number of stars with photometric-metallicity estimates is 4--5 times larger than that collected by the current largest spectroscopic survey to date -- LAMOST -- over the course of the past decade. External checks indicate that the precision of the photometric-metallicity estimates are quite high, comparable to or slightly better than that derived from spectroscopy, with typical values around 0.05--0.10 dex for [Fe/H] $> -1.0$, 0.10--0.20 dex for $-2.0 <$ [Fe/H]$ \le -1.0$ and 0.20--0.25dex for [Fe/H] $\le -2.0$, and include estimates for stars as metal-poor as [Fe/H] $\sim -3.5$, substantially lower than previous photometric techniques. Photometric-metallicity estimates are obtained for an unprecedented number of metal-poor stars, including a total of over three million metal-poor (MP; [Fe/H] $\le -1.0$) stars, over half a million very metal-poor (VMP; [Fe/H] $\le -2.0)$ stars, and over 25,000 extremely metal-poor (EMP; [Fe/H] $\le -3.0$) stars. From either parallax measurements from Gaia EDR3 or metallicity-dependent color-absolute magnitude fiducials, distances are determined for over 20 million stars in our sample. For the over 18 million sample stars with accurate absolute magnitude estimates from Gaia parallaxes, stellar ages are estimated by comparing with theoretical isochrones. Astrometric information is provided for the stars in our catalog, along with radial velocities for ~10% of our sample stars, taken from completed or ongoing large-scale spectroscopic surveys.

2104.14154

The architecture of a coarse-grained reconfigurable array (CGRA) processing element (PE) has a significant effect on the performance and energy efficiency of an application running on the CGRA. This paper presents an automated approach for generating specialized PE architectures for an application or an application domain. Frequent subgraphs mined from a set of applications are merged to form a PE architecture specialized to that application domain. For the image processing and machine learning domains, we generate specialized PEs that are up to 10.5x more energy efficient and consume 9.1x less area than a baseline PE.

2104.14155

Highly automated driving functions currently often rely on a-priori knowledge from maps for planning and prediction in complex scenarios like cities. This makes map-relative localization an essential skill. In this paper, we address the problem of localization with automotive-grade radars, using a real-time graph-based SLAM approach. The system uses landmarks and odometry information as an abstraction layer. This way, besides radars, all kind of different sensor modalities including cameras and lidars can contribute. A single, semantic landmark map is used and maintained for all sensors. We implemented our approach using C++ and thoroughly tested it on data obtained with our test vehicles, comprising cars and trucks. Test scenarios include inner cities and industrial areas like container terminals. The experiments presented in this paper suggest that the approach is able to provide a precise and stable pose in structured environments, using radar data alone. The fusion of additional sensor information from cameras or lidars further boost performance, providing reliable semantic information needed for automated mapping.

2104.14156

Electromagnetically induced transparency (EIT) cooling has established itself as one of the most widely used cooling schemes for trapped ions during the past twenty years. Compared to its alternatives, EIT cooling possesses important advantages such as a tunable effective linewidth, a very low steady state phonon occupation, and applicability for multiple ions. However, existing analytic expression for the steady state phonon occupation of EIT cooling is limited to the zeroth order of the Lamb-Dicke parameter. Here we extend such calculations and present the explicit expression to the second order of the Lamb-Dicke parameter. We discuss several implications of our refined formula and are able to resolve certain mysteries in existing results.

2104.14157

The regular (Bardeen)-AdS (BAdS) black hole (BH) in the extended phase space is taken as an example for investigating the BH phase transition grade from both macroscopic and microscopic points of view. The equation of state and thermodynamic quantities of this BH are obtained. It is found that the BAdS BH phase space in the extended phase space should be a second-order phase transition near the critical point by verifying the Ehrenfest's equation, and the possibility of its first-order phase transition can be ruled out by the entropy continuity and the heat capacity mutation. The critical exponents from the microscopic structure are analytically and numerically presented with the Landau continuous phase transition theory by introducing a microscopic order-parameter.

2104.14158

Autonomous vehicles face tremendous challenges while interacting with human drivers in different kinds of scenarios. Developing control methods with safety guarantees while performing interactions with uncertainty is an ongoing research goal. In this paper, we present a real-time safe control framework using bi-level optimization with Control Barrier Function (CBF) that enables an autonomous ego vehicle to interact with human-driven cars in ramp merging scenarios with a consistent safety guarantee. In order to explicitly address motion uncertainty, we propose a novel extension of control barrier functions to a probabilistic setting with provable chance-constrained safety and analyze the feasibility of our control design. The formulated bi-level optimization framework entails first choosing the ego vehicle's optimal driving style in terms of safety and primary objective, and then minimally modifying a nominal controller in the context of quadratic programming subject to the probabilistic safety constraints. This allows for adaptation to different driving strategies with a formally provable feasibility guarantee for the ego vehicle's safe controller. Experimental results are provided to demonstrate the effectiveness of our proposed approach.

2104.14159

We study the ground state of the doped Hubbard model on the honeycomb lattice in the small doping and strongly interacting region. The nature of the ground state by doping holes into the anti-ferromagnetic Mott insulating states on the honeycomb lattice remains a long-standing unsolved issue, even though tremendous efforts have been spent to investigate this challenging problem. An accurate determination of the ground state in this system is crucial to understand the interplay between the topology of Fermi surface and strong correlation effect. In this work, we employ two complementary, state-of-the-art, many-body computational methods -- constrained path (CP) auxiliary-field quantum Monte Carlo (AFQMC) with self-consistent constraint and density matrix renormalization group (DMRG) methods. Systematic and detailed cross-validations are performed between these two methods for narrow systems where DMRG can produce reliable results. AFQMC are then utilized to study wider systems to investigate the thermodynamic limit properties. The ground state is found to be a half-filled stripe state in the small doping and strongly interacting region. The pairing correlation shows $d$-wave symmetry locally, but decays exponentially with the distance between two pairs.

2104.14160

In this paper, channel estimation techniques and phase shift design for intelligent reflecting surface (IRS)-empowered single-user multiple-input multiple-output (SU-MIMO) systems are proposed. Among four channel estimation techniques developed in the paper, the two novel ones, single-path approximated channel (SPAC) and selective emphasis on rank-one matrices (SEROM), have low training overhead to enable practical IRS-empowered SU-MIMO systems. SPAC is mainly based on parameter estimation by approximating IRS-related channels as dominant single-path channels. SEROM exploits IRS phase shifts as well as training signals for channel estimation and easily adjusts its training overhead. A closed-form solution for IRS phase shift design is also developed to maximize spectral efficiency where the solution only requires basic linear operations. Numerical results show that SPAC and SEROM combined with the proposed IRS phase shift design achieve high spectral efficiency even with low training overhead compared to existing methods.

2104.14161

We describe a transformation rule for Bergman kernels under a proper holomorphic mapping which is factored by automorphisms $G$, where the group $G$ is a finite pseudoreflection group or conjugate to a finite pseudoreflection group. Explicit formulae for Bergman kernels of several domains have been deduced to demonstrate the adequacy of the described transformation rule.

2104.14162

Line-graph (LG) lattices are known for having topological flat bands (FBs) from the destructive interference of Bloch wavefunctions encoded in lattice symmetry. Here, we develop an atomic/molecular orbital design principle for the existence of FBs in non-LG lattices. Using a generic tight-binding model, we demonstrate that the underlying wavefunction symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We show such orbital-designed topological FBs in three common 2D non-LG, square, trigonal, and hexagonal lattices, where the chosen orbitals faithfully reproduce the corresponding localized FB plaquette states of checkerboard, Kagome, and diatomic-Kagome lattices, respectively. Fundamentally our theory enriches the FB physics; practically the proposed orbital design principle is expected to significantly expand the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory.

2104.14163

The hidden $\mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) has recently been revealed via a systematic construction of the underlying symmetry operator. Based on the AQRM result, we propose an ansatz for the general form of the symmetry operators for AQRM-related models. Applying this ansatz we obtain the symmetry operator for three models: the anisotropic AQRM, the asymmetric Rabi-Stark model (ARSM) and the anisotropic ARSM.

2104.14164

The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization, $\boldsymbol{M}(\boldsymbol{x})$, based on a perturbative approach. We identify the magnetic textures that contribute to the Hall conductivity up to third order in magnetization and second order in spatial differentiation. We treat magnetization as a perturbation to calculate the Hall conductivity for each magnetic texture based on the linear response theory. Furthermore, we estimate the skyrmion-induced Hall conductivity and confirm that it depends on the shape of skyrmions, such as Bloch-type or N\'eel-type skyrmions. The results of this study can be applied not only to conventional skyrmion systems but also to more general magnetic structures.

2104.14165

The Cauchy problem for the Hardy-H\'enon parabolic equation is studied in the critical and subcritical regime in weighted Lebesgue spaces on the Euclidean space $\mathbb{R}^d$. Well-posedness for singular initial data and existence of non-radial forward self-similar solution of the problem are previously shown only for the Hardy and Fujita cases ($\gamma\le 0$) in earlier works. The weighted spaces enable us to treat the potential $|x|^{\gamma}$ as an increase or decrease of the weight, thereby we can prove well-posedness to the problem for all $\gamma$ with $-\min\{2,d\}<\gamma$ including the H\'enon case ($\gamma>0$). As a byproduct of the well-posedness, the self-similar solutions to the problem are also constructed for all $\gamma$ without restrictions. A non-existence result of local solution for supercritical data is also shown. Therefore our critical exponent $s_c$ turns out to be optimal in regards to the solvability.

2104.14166

Topological flat band (TFB) has been proposed theoretically in various lattice models, to exhibit a rich spectrum of intriguing physical behaviors. However, the experimental demonstration of flat band (FB) properties has been severely hindered by the lack of materials realization. Here, by screening materials from a first-principles materials database, we identify a group of 2D materials with TFBs near the Fermi level, covering most of the known line-graph and generalized line-graph FB lattice models. These include the Kagome sublattice of O in TiO2 yielding a spin-unpolarized TFB, and that of V in ferromagnetic V3F8 yielding a spin-polarized TFB. Monolayer Nb3TeCl7 and its counterparts from element substitution are found to be breathing-Kagome-lattice crystals. The family of monolayer III2VI3 compounds exhibit a TFB representing the coloring-triangle lattice model. ReF3, MnF3 and MnBr3 are all predicted to be diatomic-Kagome-lattice crystals, with TFB transitions induced by atomic substitution. Finally, HgF2, CdF2 and ZnF2 are discovered to host dual TFBs in the diamond-octagon lattice. Our findings pave the way to further experimental exploration of eluding FB materials and properties.

2104.14167