cssi/SciSciGPT-SciSciNet huggingface dataset:
Effective Quantization Approaches for Recurrent Neural Networks

Deep learning, Recurrent Neural Networks (RNN) in particular have shown superior accuracy in a large variety oftasks including machine translation, language understanding, and movie frames generation. However, these deep learning approaches are very expensive in terms of computation. In most cases, Graphic Processing Units (GPUs) are in used for large scale implementations. Meanwhile, energy efficient RNN approaches are proposed for deploying solutions on special purpose hardware including Field Programming Gate Arrays (FPGAs) and mobile platforms. In this paper, we propose an effective quantization approach for Recurrent Neural Networks (RNN) techniques including Long Short-Term Memory (LSTM), Gated Recurrent Units (GRU), and Convolutional Long Short Term Memory (ConvLSTM). We have implemented different quantization methods including Binary Connect $\{-1, 1\}$, Ternary Connect $\{-1, 0$, 1}, and Quaternary Connect $\{-1, -0.5, 0.5, 1\}$. These proposed approaches are evaluated on different datasets for sentiment analysis on IMDB and video frame predictions on the moving MNIST dataset. The experimental results are compared against the full precision versions of the LSTM, GRU, and ConvLSTM. They show promising results for both sentiment analysis and video frame prediction.
In the light of deep coalescence: revisiting trees within networks

Phylogenetic networks model reticulate evolutionary histories. The last two decades have seen an increased interest in establishing mathematical results and developing computational methods for inferring and analyzing these networks. A salient concept underlying a great majority of these developments has been the notion that a network displays a set of trees and those trees can be used to infer, analyze, and study the network. In this paper, we show that in the presence of coalescence effects, the set of displayed trees is not sufficient to capture the network. We formally define the set of parental trees of a network and make three contributions based on this definition. First, we extend the notion of anomaly zone to phylogenetic networks and report on anomaly results for different networks. Second, we demonstrate how coalescence events could negatively affect the ability to infer a species tree that could be augmented into the correct network. Third, we demonstrate how a phylogenetic network can be viewed as a mixture model that lends itself to a novel inference approach via gene tree clustering. Our results demonstrate the limitations of focusing on the set of trees displayed by a network when analyzing and inferring the network. Our findings can form the basis for achieving higher accuracy when inferring phylogenetic networks and open up new venues for research in this area, including new problem formulations based on the notion of a network’s parental trees.
Generating Random Networks Without Short Cycles

Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly underst...
Regularity properties of the Zakharov system on the half line

ABSTRACTIn this paper, we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results, and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial data. The gain in regularity coincides with the gain that was observed for the periodic Zakharov and the Zakharov on the real line. Uniqueness is proved in the class of smooth solutions. When the boundary value of the Schrodinger part of the solution is zero, uniqueness can be extended to the full range of local solutions. Under the same assumptions on the initial data, we also prove global-in-time existence and uniqueness of energy solutions. For more regular data, we prove that all higher Sobolev norms grow at most polynomially-in-time.
Compactness of Hankel Operators with Continuous Symbols

Let \(\Omega \) be a bounded convex Reinhardt domain in \(\mathbb {C}^2\) and \(\phi \in C({\overline{\Omega }})\). We show that the Hankel operator \(H_{\phi }\) is compact if and only if \(\phi \) is holomorphic along every non-trivial analytic disc in the boundary of \(\Omega \).
Generalized Blob Algebras and Alcove Geometry

A sequence of finite-dimensional quotients of affine Hecke algebras is studied. Each element of the sequence is constructed so as to have a weight space labelling scheme for Specht⁄standard modules. As in the weight space formalism of algebraic Lie theory, there is an action of an affine reflection group on this weight space that fixes the set of labelling weights. A linkage principle is proved in each case. Further, it is shown that the simplest non-trivial example may essentially be identified with the blob algebra (a physically motivated quasihereditary algebra whose representation theory is very well understood by Lie-theory-like methods). An extended role is hence proposed for Soergel's tilting algorithm, away from its algebraic Lie theory underpinning, in determining the simple content of standard modules for these algebras. This role is explicitly verified in the blob algebra case. A tensor space representation of the blob algebra is constructed, as a candidate for a full tilting module (subsequently proven to be so in a paper by Martin and Ryom-Hansen), further evidencing the extended utility of Lie-theoretic methods. Possible generalisations of this representation to other elements of the sequence are discussed.
Iterative methods for k-Hessian equations

On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation for k=n. We analyze for smooth non degenerate solutions a 9-point finite difference scheme. We prove that the discrete scheme has a locally unique solution with a quadratic convergence rate. In addition we propose new iterative methods which are numerically shown to work for non smooth solutions. A connection of the latter with a popular Gauss-Seidel method for the Monge-Ampere equation is established and new Gauss-Seidel type iterative methods for 2-Hessian equations are introduced.
Injected and Delivered: Fabricating Implicit Control over Actuation Systems by Spoofing Inertial Sensors

Inertial sensors provide crucial feedback for control systems to determine motional status and make timely, automated decisions. Prior efforts tried to control the output of inertial sensors with acoustic signals. However, their approaches did not consider sample rate drifts in analog-to-digital converters as well as many other realistic factors. As a result, few attacks demonstrated effective control over inertial sensors embedded in real systems. This work studies the out-of-band signal injection methods to deliver adversarial control to embedded MEMS inertial sensors and evaluates consequent vulnerabilities exposed in control systems relying on them. Acoustic signals injected into inertial sensors are out-of-band analog signals. Consequently, slight sample rate drifts could be amplified and cause deviations in the frequency of digital signals. Such deviations result in fluctuating sensor output; nevertheless, we characterize two methods to control the output: digital amplitude adjusting and phase pacing. Based on our analysis, we devise non-invasive attacks to manipulate the sensor output as well as the derived inertial information to deceive control systems. We test 25 devices equipped with MEMS inertial sensors and find that 17 of them could be implicitly controlled by our attacks. Furthermore, we investigate the generalizability of our methods and show the possibility to manipulate the digital output through signals with relatively low frequencies in the sensing channel.
Combinatorial Interpretations of Binomial Coefficient Analogues Related to Lucas Sequences

Let s and t be variables. Define polynomials {n} in s, t by {0} = 0, {1} = 1, and {n} = s {n− 1}+t {n− 2} for n ≥ 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial coefficients by {n k } = {n}! {k}! {n− k}! where {n}! = {1} {2} · · · {n}. It is easy to see that { n k } is a polynomial in s and t. The purpose of this note is to give two combinatorial interpretations for this polynomial in terms of statistics on integer partitions inside a k × (n− k) rectangle. When s = t = 1 we obtain combinatorial interpretations of the fibonomial coefficients which are simpler than any that have previously appeared in the literature. Work partially done while a Program Officer at NSF. The views expressed are not necessarily those of the NSF. Partially supported by NSA grant H98230-08-1-0072 INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY x (200x), #Axx 2
Logarithmic Local Energy Decay for Scalar Waves on a General Class of Asymptotically Flat Spacetimes

This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $$d+1$$ , $$d\ge 3$$ , the local energy of solutions to the scalar wave equation $$\square _{g}{\uppsi }=0$$ decays at least with an inverse logarithmic rate. This class of Lorentzian manifolds includes (non-extremal) black hole spacetimes with no restriction on the nature of the trapped set. Spacetimes in this class are moreover allowed to have a small ergoregion, but are required to satisfy an energy boundedness statement. Without making further assumptions, this logarithmic decay rate is shown to be sharp. Our results can be viewed as a generalisation of a result of Burq, dealing with the case of the wave equation on flat space outside compact obstacles, and results of Rodnianski–Tao for asymptotically conic product Lorentzian manifolds. The proof will bridge ideas from Rodnianski and Tao (see [58]) with techniques developed in the black hole setting by Dafermos and Rodnianski (see [21, 22]). As a soft corollary of our results, we will infer an asymptotic completeness statement for the wave equation on the spacetimes considered in the case where no ergoregion is present.
A scalable end-to-end Gaussian process adapter for irregularly sampled time series classification

We present a general framework for classification of sparse and irregularly-sampled time series. The properties of such time series can result in substantial uncertainty about the values of the underlying temporal processes, while making the data difficult to deal with using standard classification methods that assume fixed-dimensional feature spaces. To address these challenges, we propose an uncertainty-aware classification framework based on a special computational layer we refer to as the Gaussian process adapter that can connect irregularly sampled time series data to any black-box classifier learnable using gradient descent. We show how to scale up the required computations based on combining the structured kernel interpolation framework and the Lanczos approximation method, and how to discriminatively train the Gaussian process adapter in combination with a number of classifiers end-to-end using backpropagation.
Singularity formation of the Yang–Mills Flow

Abstract We study singularity structure of Yang–Mills flow in dimensions n ≥ 4 . First we obtain a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow, which leads to a stratification of the singular set. By a refined blowup analysis we obtain Yang–Mills connections or solitons as blowup limits at any point in the singular set.
Boundary-based MWE segmentation with text partitioning

This submission describes the development of a fine-grained, text-chunking algorithm for the task of comprehensive MWE segmentation. This task notably focuses on the identification of colloquial and idiomatic language. The submission also includes a thorough model evaluation in the context of two recent shared tasks, spanning 19 different languages and many text domains, including noisy, user-generated text. Evaluations exhibit the presented model as the best overall for purposes of MWE segmentation, and open-source software is released with the submission (although links are withheld for purposes of anonymity). Additionally, the authors acknowledge the existence of a pre-print document on arxiv.org, which should be avoided to maintain anonymity in review.
How Do Classifiers Induce Agents to Invest Effort Strategically

Algorithms are often used to produce decision-making rules that classify or evaluate individuals. When these individuals have incentives to be classified a certain way, they may behave strategically to influence their outcomes. We develop a model for how strategic agents can invest effort in order to change the outcomes they receive, and we give a tight characterization of when such agents can be incentivized to invest specified forms of effort into improving their outcomes as opposed to "gaming" the classifier. We show that whenever any "reasonable" mechanism can do so, a simple linear mechanism suffices.
Symmetric criticality for tight knots

We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the same symmetry. We use this to construct new examples of ropelength-critical configurations for knots and links which are different from the ropelength minima for these knot and link types.
Elementary Symmetric Polynomials for Optimal Experimental Design

We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture "partial volumes" and offer a graded interpolation between the widely used A-optimal and D-optimal design models, obtaining each of them as special cases. We analyze properties of our models, and derive both greedy and convex-relaxation algorithms for computing the associated designs. Our analysis establishes approximation guarantees on these algorithms, while our empirical results substantiate our claims and demonstrate a curious phenomenon concerning our greedy algorithm. Finally, as a byproduct, we obtain new results on the theory of elementary symmetric polynomials that may be of independent interest.
Learning Optical Flow via Dilated Networks and Occlusion Reasoning

Despite the significant progress that has been made on estimating optical flow recently, most estimation methods, including classical and deep learning approaches, still have difficulty with multi-scale estimation, real-time computation, and/or occlusion reasoning. In this paper, we introduce dilated convolution and occlusion reasoning into unsupervised optical flow estimation to address these issues. The dilated convolution allows our network to avoid upsampling via deconvolution and the resulting gridding artifacts. Dilated convolution also results in a smaller memory footprint which speeds up interference. The occlusion reasoning prevents our network from learning incorrect deformations due to occluded image regions during training. Our proposed method outperforms state-of-the-art unsupervised approaches on the KITTI benchmark. We also demonstrate its generalization capability by applying it to action recognition in video.
Polygonal Bicycle Paths and the Darboux Transformation

A Bicycle $(n,k)$-gon is an equilateral $n$-gon whose $k$ diagonals are of equal length. In this paper we consider periodic bicycle $(n,k)$-paths, which are a natural variation in which the polygon is replaced with a periodic polygonal path.
An improved LR-aided K-best algorithm for MIMO detection

Recently, lattice reduction (LR) technique has caught great attention for multi-input multi-output (MIMO) receiver because of its low complexity and high performance. However, when the number of antennas is large, LR-aided linear detectors and successive interference cancellation (SIC) detectors still exhibit considerable performance gap to the optimal maximum likelihood detector (MLD). To enhance the performance of the LR-aided detectors, the LR-aided K-best algorithm was developed at the cost of the extra complexity on the order O(N2tK + NtK2), where Nt is the number of transmit antennas and K is the number of candidates. In this paper, we develop an LR-aided K-best algorithm with lower complexity by exploiting a priority queue. With the aid of the priority queue, our analysis shows that the complexity of the LR-aided K-best algorithm can be further reduced to O(N2tK + NtKlog2(K)). The low complexity of the proposed LR-aided K-best algorithm allows us to perform the algorithm for large MIMO systems (e.g., 50×50 MIMO systems) with large candidate sizes. Simulations show that as the number of antennas increases, the error performance approaches that of AWGN channel.
Subexponential convergence for information aggregation on regular trees

We consider the decentralized binary hypothesis testing problem on trees of bounded degree and increasing depth. For a regular tree of depth t and branching factor k ≥ 2, we assume that the leaves have access to independent and identically distributed noisy observations of the ‘state of the world’ s. Starting with the leaves, each node makes a decision in a finite alphabet M, that it sends to its parent in the tree. Finally, the root decides between the two possible states of the world based on the information it receives. We prove that the error probability vanishes only subexponentially in the number of available observations, under quite general hypotheses. More precisely, in the case of binary messages, decay is subexponential for any decision rule. For general (finite) message alphabet M, decay is subexponential for ‘node-oblivious’ decision rules, that satisfy a mild irreducibility condition. In the latter case, we propose a family of decision rules with close-to-optimal asymptotic behavior.
Robust 6D Object Pose Estimation with Stochastic Congruent Sets.

Object pose estimation is frequently achieved by first segmenting an RGB image and then, given depth data, registering the corresponding point cloud segment against the object's 3D model. Despite the progress due to CNNs, semantic segmentation output can be noisy, especially when the CNN is only trained on synthetic data. This causes registration methods to fail in estimating a good object pose. This work proposes a novel stochastic optimization process that treats the segmentation output of CNNs as a confidence probability. The algorithm, called Stochastic Congruent Sets (StoCS), samples pointsets on the point cloud according to the soft segmentation distribution and so as to agree with the object's known geometry. The pointsets are then matched to congruent sets on the 3D object model to generate pose estimates. StoCS is shown to be robust on an APC dataset, despite the fact the CNN is trained only on synthetic data. In the YCB dataset, StoCS outperforms a recent network for 6D pose estimation and alternative pointset matching techniques.
RED: Reinforced Encoder-Decoder Networks for Action Anticipation

Action anticipation aims to detect an action before it happens. Many real world applications in robotics and surveillance are related to this predictive capability. Current methods address this problem by first anticipating visual representations of future frames and then categorizing the anticipated representations to actions. However, anticipation is based on a single past frame's representation, which ignores the history trend. Besides, it can only anticipate a fixed future time. We propose a Reinforced Encoder-Decoder (RED) network for action anticipation. RED takes multiple history representations as input and learns to anticipate a sequence of future representations. One salient aspect of RED is that a reinforcement module is adopted to provide sequence-level supervision; the reward function is designed to encourage the system to make correct predictions as early as possible. We test RED on TVSeries, THUMOS-14 and TV-Human-Interaction datasets for action anticipation and achieve state-of-the-art performance on all datasets.
Compressive neural representation of sparse, high-dimensional probabilities

This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions rather than to the usual sparse signals. The compressive measurements correspond to expected values of nonlinear functions of the probabilistically distributed variables. When these expected values are estimated by sampling, the quality of the compressed representation is limited only by the quality of sampling. Since the compression preserves the geometric structure of the space of sparse probability distributions, probabilistic computation can be performed in the compressed domain. Interestingly, functions satisfying the requirements of compressive sensing can be implemented as simple perceptrons. If we use perceptrons as a simple model of feedforward computation by neurons, these results show that the mean activity of a relatively small number of neurons can accurately represent a high-dimensional joint distribution implicitly, even without accounting for any noise correlations. This comprises a novel hypothesis for how neurons could encode probabilities in the brain.
Clicks and cliques: exploring the soul of the community

In this paper we analyze 26 communities across the United States with the objective to understand what attaches people to their community and how this attachment differs among communities. How different are attached people from unattached? What attaches people to their community? How different are the communities? What are key drivers behind emotional attachment? To address these questions, graphical, supervised and unsupervised learning tools were used and information from the Census Bureau and the Knight Foundation were combined. Using the same pre-processed variables as Knight (Soul of the community, Technical report, 2010) most likely will drive the results towards the same conclusions than the Knight foundation, so this paper does not use those variables.
Extending Precolorings to Distinguish Group Actions

Abstract Given a group Γ acting on a set X , a k -coloring ϕ : X → { 1 , … , k } of X is distinguishing with respect to Γ if the only γ ∈ Γ that fixes ϕ is the identity action. The distinguishing number of the action Γ , denoted D Γ ( X ) , is then the smallest positive integer k such that there is a distinguishing k -coloring of X with respect to Γ . This notion has been studied in a number of settings, but by far the largest body of work has been concerned with finding the distinguishing number of the action of the automorphism group of a graph G upon its vertex set, which is referred to as the distinguishing number of G . The distinguishing number of a group action is a measure of how difficult it is to “break” all of the permutations arising from that action. In this paper, we aim to further differentiate the resilience of group actions with the same distinguishing number. In particular, we introduce a precoloring extension framework to address this issue. A set S ⊆ X is a fixing set for Γ if for every non-identity element γ ∈ Γ there is an element s ∈ S such that γ ( s ) ≠ s . The distinguishing extension number ext D ( X , Γ ; k ) is the minimum number m such that for all fixing sets W ⊆ X with | W | ≥ m , every k -coloring c : X ∖ W → [ k ] can be extended to a k -coloring that distinguishes X . In this paper, we prove that ext D ( R , Aut ( R ) ; 2 ) = 4 , where Aut ( R ) is comprised of compositions of translations and reflections. We also consider the distinguishing extension number of the circle and (finite) cycles, obtaining several exact results and bounds.
A Computationally Surveyable Proof of the Group Properties of an Elliptic Curve.

We present an elementary proof of the group properties of the elliptic curve known as "Curve25519", as a component of a comprehensive proof of correctness of a hardware implementation of the associated Diffie-Hellman key agreement algorithm. The entire proof has been formalized and mechanically verified with ACL2, and is computationally surveyable in the sense that all steps that require mechanical support are presented in such a way that they may readily reproduced in any suitable programming language.
Satirical News Detection and Analysis using Attention Mechanism and Linguistic Features

Satirical news is considered to be entertainment, but it is potentially deceptive and harmful. Despite the embedded genre in the article, not everyone can recognize the satirical cues and therefore believe the news as true news. We observe that satirical cues are often reflected in certain paragraphs rather than the whole document. Existing works only consider document-level features to detect the satire, which could be limited. We consider paragraph-level linguistic features to unveil the satire by incorporating neural network and attention mechanism. We investigate the difference between paragraph-level features and document-level features, and analyze them on a large satirical news dataset. The evaluation shows that the proposed model detects satirical news effectively and reveals what features are important at which level.
Long time behavior of solutions to the 3D Hall-magneto-hydrodynamics system with one diffusion

Abstract This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space R 3 . We establish that, in the inviscid resistive case, the energy ‖ b ( t ) ‖ 2 2 vanishes and ‖ u ( t ) ‖ 2 2 converges to a constant as time tends to infinity provided the velocity is bounded in W 1 − α , 3 α ( R 3 ) ; in the viscous non-resistive case, the energy ‖ u ( t ) ‖ 2 2 vanishes and ‖ b ( t ) ‖ 2 2 converges to a constant provided the magnetic field is bounded in W 1 − β , ∞ ( R 3 ) . In summary, one single diffusion, being as weak as ( − Δ ) α b or ( − Δ ) β u with small enough α , β , is sufficient to prevent asymptotic energy oscillations for certain smooth solutions to the system.
Principal ideals in mod-$$\ell $$ Milnor K-theory

Fix a symbol \(\underline{a}\) in the mod-\(\ell \) Milnor K-theory of a field k, and a norm variety X for \(\underline{a}\). We show that the ideal generated by \(\underline{a}\) is the kernel of the K-theory map induced by \(k\subset k(X)\) and give generators for the annihilator of the ideal. When \(\ell =2\), this was done by Orlov, Vishik and Voevodsky.
A Practical Method for Solving Contextual Bandit Problems Using Decision Trees

Many efficient algorithms with strong theoretical guarantees have been proposed for the contextual multi-armed bandit problem. However, applying these algorithms in practice can be difficult because they require domain expertise to build appropriate features and to tune their parameters. We propose a new method for the contextual bandit problem that is simple, practical, and can be applied with little or no domain expertise. Our algorithm relies on decision trees to model the context-reward relationship. Decision trees are non-parametric, interpretable, and work well without hand-crafted features. To guide the exploration-exploitation trade-off, we use a bootstrapping approach which abstracts Thompson sampling to non-Bayesian settings. We also discuss several computational heuristics and demonstrate the performance of our method on several datasets.
Quantitative Representation Stability Over Linear Groups

We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher syzygies of VIC- and SI-modules, which can be thought of as a weaker version of a regularity theorem of Church-Ellenberg in the context of FI-modules. We apply these techniques to the rational homology of congruence subgroups of mapping class groups and congruence subgroups of automorphism groups of free groups. This partially resolves a question raised by Church and Putman-Sam. We also prove new homological stability results for mapping class groups and automorphism groups of free groups with twisted coefficients.
On Brendle’s Estimate for the Inscribed Radius Under Mean Curvature Flow

In a recent paper, Brendle proved that the inscribed radius of closed embedded mean convex hypersurfaces moving by mean curvature flow is at least 1/((1+\delta)H) at all points with H > C(\delta,M_0). In this note, we give a shorter proof of Brendle's estimate, and of a more general result for alpha-Andrews flows, based on our recent estimates from Haslhofer-Kleiner.
EDGEWORTH CORRECTION FOR THE LARGEST EIGENVALUE IN A SPIKED PCA MODEL.

We study improved approximations to the distribution of the largest eigenvalue l^ of the sample covariance matrix of n zero-mean Gaussian observations in dimension p + 1. We assume that one population principal component has variance l > 1 and the remaining 'noise' components have common variance 1. In the high-dimensional limit p/n → γ > 0, we study Edgeworth corrections to the limiting Gaussian distribution of l^ in the supercritical case l​> 1 +γ . The skewness correction involves a quadratic polynomial, as in classical settings, but the coefficients reflect the high-dimensional structure. The methods involve Edgeworth expansions for sums of independent non-identically distributed variates obtained by conditioning on the sample noise eigenvalues, and the limiting bulk properties and fluctuations of these noise eigenvalues.
Root-theoretic Young diagrams and Schubert calculus: Planarity and the adjoint varieties

Abstract We study root-theoretic Young diagrams to investigate the existence of a Lie-type uniform and nonnegative combinatorial rule for Schubert calculus. We provide formulas for (co)adjoint varieties of classical Lie type. This is a simplest case after the (co)minuscule family (where a rule has been proved by H. Thomas and the second author using work of R. Proctor). Our results build on earlier Pieri-type rules of P. Pragacz–J. Ratajski and of A. Buch–A. Kresch–H. Tamvakis. Specifically, our formula for OG ( 2 , 2 n ) is the first complete rule for a case where diagrams are non-planar. Yet the formulas possess both uniform and non-uniform features. Using these classical type rules, as well as results of P.-E. Chaput–N. Perrin in the exceptional types, we suggest a connection between polytopality of the set of nonzero Schubert structure constants and planarity of the diagrams. This is an addition to work of A. Klyachko and A. Knutson–T. Tao on the Grassmannian and of K. Purbhoo–F. Sottile on cominuscule varieties, where the diagrams are always planar.
Recovery of the Interface Velocity for the Incompressible Flow in Enhanced Velocity Mixed Finite Element Method

The velocity, coupling term in the flow and transport problems, is important in the accurate numerical simulation or in the posteriori error analysis for adaptive mesh refinement. We consider Enhanced Velocity Mixed Finite Element Method (EVMFEM) for the incompressible Darcy flow. In this paper, our aim is to study the improvement of velocity at interface to achieve the better approximation of velocity between subdomains. We propose the reconstruction of velocity at interface by using the post-processed pressure. Numerical results at the interface show improvement on convergence rate.
Attitude estimation with feedback particle filter

This paper presents theory, application, and comparisons of the feedback particle filter (FPF) algorithm for the problem of attitude estimation. The paper builds upon our recent work on the exact FPF solution of the continuous-time nonlinear filtering problem on matrix Lie groups. In this paper, the details of the FPF algorithm are presented for the problem of attitude estimation - a nonlinear filtering problem on SO(3). Quaternions are employed for computational purposes. The algorithm requires a numerical solution of the filter gain function, and two methods are applied for this purpose. Comparisons are also provided between the FPF and some popular algorithms for attitude estimation, including the multiplicative EKF, the unscented quaternion estimator, the invariant EKF, and the invariant ensemble Kalman filter. Simulation results are presented that help illustrate the comparisons.
A Diagrammatic Categorification of a Clifford Algebra

We give a graphical calculus for a categorification of a Clifford algebra and its Fock space representation via differential graded categories. The categorical action is motivated by the gluing action between the contact categories of infinite strips.
THE COLUMN GROUP AND ITS LINK INVARIANTS

The column group is a subgroup of the symmetric group on the elements of a finite birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples which show that the enhanced invariant is stronger than the unenhanced invariant.
Concentration Phenomena of a Semilinear Elliptic Equation with Large Advection in an Ecological Model

Abstract We consider a reaction–diffusion–advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In particular, a conjecture of Cantrell, Cosner and Lou on concentration phenomena is resolved under mild conditions. Applications to a related parabolic competition system are also discussed.
Prolegomena to a non-equilibrium quantum statistical mechanics

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.
Integrating ultra-fast charging stations within the power grids of smart cities: a review

Plug-in electric vehicles (PEVs) have become a key factor driving towards smart cities, which allow for higher energy efficiency and lower environmental impact across urban sectors. Industry vision for future PEV includes the ability to recharge a vehicle at a speed comparable to traditional gas refuelling, i.e. <3 min. per vehicle. Such a technology, referred to as ultra-fast charging (UFC), has drawn much interest from research and industry. However, UFC poses unprecedented challenges to existing electricity supply infrastructure due to its large power density, impulsive, and stochastic load characteristics. Planning the locations and electric capacities of UFC stations is critical to preventing detrimental impacts. In particular, efforts must be made of mitigate grid asset depreciation, grid instabilities, and deteriorated power quality. The authors first review planning methods for conventional charging stations. Next, they discuss outlooks for UFC planning solutions by drawing an analogy with renewable energy (RE) source planning. This analogy is based on the similar power density and stochastic characteristics of RE and UFC. While this study mainly focuses on UFC planning from the power grid perspective, other urban aspects, including traffic flow and end-user behaviour, are examined for feasible UFC integration within smart cities.
Compare and Contrast: Learning Prominent Visual Differences

Relative attribute models can compare images in terms of all detected properties or attributes, exhaustively predicting which image is fancier, more natural, and so on without any regard to ordering. However, when humans compare images, certain differences will naturally stick out and come to mind first. These most noticeable differences, or prominent differences, are likely to be described first. In addition, many differences, although present, may not be mentioned at all. In this work, we introduce and model prominent differences, a rich new functionality for comparing images. We collect instance-level annotations of most noticeable differences, and build a model trained on relative attribute features that predicts prominent differences for unseen pairs. We test our model on the challenging UT-Zap50K shoes and LFW10 faces datasets, and outperform an array of baseline methods. We then demonstrate how our prominence model improves two vision tasks, image search and description generation, enabling more natural communication between people and vision systems.
Affine reductions for LPs and SDPs

We define a reduction mechanism for LP and SDP formulations that degrades approximation factors in a controlled fashion. Our reduction mechanism is a minor restriction of classical hardness reductions requiring an additional independence assumption and it allows for reusing many hardness reductions that have been used to show inapproximability in the context of PCP theorems. As a consequence we establish strong linear programming inapproximability (for LPs with a polynomial number of constraints) for many problems. In particular we obtain a $$\frac{3}{2}-\varepsilon $$ inapproximability for answering an open question in Chan et al. (Proceedings of FOCS, pp. 350–359, 2013, https://doi.org/10.1109/FOCS.2013.45 ) and prove an inapproximability factor of $$\frac{1}{2}+\varepsilon $$ for bounded degree . In the case of SDPs, we obtain inapproximability results for these problems relative to the SDP-inapproximability of $${\textsf {MaxCUT}}_{}$$ . Moreover, using our reduction framework we are able to reproduce various results for CSPs from Chan et al. (Proceedings of FOCS, pp. 350–359, 2013, https://doi.org/10.1109/FOCS.2013.45 ) via simple reductions from Max- $$2$$ -XOR.
T-count and Qubit Optimized Quantum Circuit Design of the Non-Restoring Square Root Algorithm

Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant, but the T gate is very costly to implement. As a result, reducing T-count has become an important optimization goal. Further, quantum circuits with many qubits are difficult to realize, making designs that save qubits and produce no garbage outputs desirable. In this work, we present a T-count optimized quantum square root circuit with only 2 ṡ n + 1 qubits and no garbage output. To make a fair comparison against existing work, the Bennett’s garbage removal scheme is used to remove garbage output from existing works. We determined that our proposed design achieves an average T-count savings of 43.44%, 98.95%, 41.06%, and 20.28% as well as qubit savings of 85.46%, 95.16%, 90.59%, and 86.77% compared to existing works.
Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.
A singular local minimizer for the volume- constrained minimal surface problem in a nonconvex domain

It has recently been established byWang and Xia [WX] that local minimizers of perimeter within a ball subject to a volume constraint must be spherical caps or planes through the origin. This verifies a conjecture of the authors and is in contrast to the situation of area minimizing surfaces with prescribed boundary where singularities can be present in high dimensions. This result lends support to the more general conjecture that volume-constrained minimizers in arbitrary convex sets may enjoy better regularity properties than their boundary-prescribed cousins. Here, we show the importance of the convexity condition by exhibiting a simple example, given by the Simons cone, of a singular volume-constrained locally area-minimizing surface within a nonconvex domain that is arbitrarily close to the unit ball.
A microservice architecture for online mobile app optimization

A large number of techniques for analyzing and optimizing mobile apps have emerged in the past decade. However, those techniques' components are notoriously difficult to extract and reuse outside their original tools. This paper introduces MAOMAO, a microservice-based reference architecture for reusing and integrating such components. MAOMAO's twin goals are (1) adoption of available app optimization techniques in practice and (2) improved construction and evaluation of new techniques. The paper uses several existing app optimization techniques to illustrate both the motivation behind MAOMAO and its potential to fundamentally alter the landscape in this area.
Mixed-Granularity Human-Swarm Interaction

We present an augmented reality human-swarm interface that combines two modalities of interaction: environment-oriented and robot-oriented. The environment-oriented modality allows the user to modify the environment (either virtual or physical) to indicate a goal to attain for the robot swarm. The robot-oriented modality makes it possible to select individual robots to reassign them to other tasks to increase performance or remedy failures. Previous research has concluded that environment-oriented interaction might prove more difficult to grasp for untrained users. In this paper, we report a user study which indicates that, at least in collective transport, environment-oriented interaction is more effective than purely robot-oriented interaction, and that the two combined achieve remarkable efficacy.
Educational System Building in a Changing Educational Sector: Environment, Organization, and the Technical Core:

The institutional environment of U.S. school systems has changed considerably over a quarter century as standards and test-based accountability became central ideas in policy texts and discourses a...
DHHC5 Mediates β-Adrenergic Signaling in Cardiomyocytes by Targeting Gα Proteins

S-palmitoylation is a reversible posttranslational modification that plays an important role in regulating protein localization, trafficking, and stability. Recent studies have shown that some proteins undergo extremely rapid palmitoylation/depalmitoylation cycles after cellular stimulation supporting a direct signaling role for this posttranslational modification. Here, we investigated whether β-adrenergic stimulation of cardiomyocytes led to stimulus-dependent palmitoylation of downstream signaling proteins. We found that β-adrenergic stimulation led to rapidly increased Gαs and Gαi palmitoylation. The kinetics of palmitoylation was temporally consistent with the downstream production of cAMP and contractile responses. We identified the plasma membrane-localized palmitoyl acyltransferase DHHC5 as an important mediator of the stimulus-dependent palmitoylation in cardiomyocytes. Knockdown of DHHC5 showed that this enzyme is necessary for palmitoylation of Gαs, Gαi, and functional responses downstream of β-adrenergic stimulation. A palmitoylation assay with purified components revealed that Gαs and Gαi are direct substrates of DHHC5. Finally, we provided evidence that the C-terminal tail of DHHC5 can be palmitoylated in response to stimulation and such modification is important for its dynamic localization and function in the plasma membrane. Our results reveal that DHHC5 is a central regulator of signaling downstream of β-adrenergic receptors in cardiomyocytes.
Taking Stock of the Benefit Corporation

Almost a decade ago, the “benefit corporation” made its first appearance on American soil. Its supporters proclaimed that this would usher in a new era of corporate social responsibility. Its detractors complained, among other things, that the Benefit Corporation would facilitate managerial abuses that corporate law had worked so hard to curb. After nearly ten years of experience with the benefit corporation, who was the more accurate prognosticator? Moreover, has the benefit corporation given rise to developments, whether beneficial or negative, that were not expected or foreseen? This article traces the history of the benefit corporation, with a focus on the promise that its early supporters identified with it. It also examines the criticisms that this new form of business organization provoked. The article concludes that, contrary to the predictions of both camps, the benefit corporation has not, apparently, resulted in much change at all. In its final section, the article explores the reasons why the benefit corporation has had, thus far at least, such minimal impact on the course of American business and corporate law. The conclusion reached is that, for good or for ill, benefit corporation statutes do not materially change the rules of corporate governance. Rather, they simply explicitly permit benefit corporations to conduct themselves according to standards of conduct that traditional corporate law statutes already implicitly permit. Although the promoters of benefit corporation legislation have argued that even this minor change would have an impact on businesses, insofar as it would effectuate a normative shift in corporate decision making, contemporary market forces appear to have had the same result on a far broader scale. Lastly, this article considers some of the unexpected repercussions of the benefit corporation, whether manifested or growing in potential. An Appendix is appended to the article, comparing the benefit corporation statutes of every state.