In cite{CC} the authors, investigating a model of population dynamics, find the following result. Let $Omegasubset mathbb{R}^N$, $Ngeq 1$, be a bounded smooth domain. The weighted eigenvalue problem $-Delta u =lambda m u $ in $Omega$ under homogeneous Dirichlet boundary conditions, where $lambda in mathbb{R}$ and $min L^infty(Omega)$, is considered. The authors prove the existence of minimizers $check m$ of the principal positive eigenvalue $lambda_1(m)$ when $m$ varies in a class $mathcal{M}$ of functions where average, maximum, and minimum values are given. A similar result is obtained in cite{CCP} when $m$ is in the class $mathcal{G}(m_0)$ of rearrangements of a fixed $m_0in L^infty(Omega)$. In our work we establish that, if $Omega$ is Steiner symmetric, then every minimizer in cite{CC,CCP} inherits the same kind of symmetry.

We present a systematic derivation of the abelianity conditions for the $q$-deformed $W$-algebras constructed from the elliptic quantum algebra $mathcal{A}_{q,p}(widehat{gl}(N)_{c})$. We identify two sets of conditions on a given critical surface yielding abelianity lines in the moduli space ($p, q, c$). Each line is identified as an intersection of a countable number of critical surfaces obeying diophantine consistency conditions. The corresponding Poisson brackets structures are then computed for which some universal features are described.

Let $Gamma$ be a discrete group acting properly discontinuously and isometrically on the three-dimensional anti-de Sitter space $mathrm{AdS}^{3}$, and $square$ the Laplacian which is a second-order hyperbolic differential operator. We study linear independence of a family of generalized Poincar'{e} series introduced by Kassel-Kobayashi [Adv. Math. 2016], which are defined by the $Gamma$-average of certain eigenfunctions on $mathrm{AdS}^{3}$. We prove that the multiplicities of $L^{2}$-eigenvalues of the hyperbolic Laplacian $square$ on $Gammaackslashmathrm{AdS}^{3}$ are unbounded when $Gamma$ is finitely generated. Moreover, we prove that the multiplicities of extit{stable $L^{2}$-eigenvalues} for compact anti-de Sitter $3$-manifolds are unbounded.

Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to $p$-Laplace double obstacle problems involving the Schr"odinger term: $-Delta_p u + mathbb{V}|u|^{p-2}u$ with bound constraints $psi_1 le u le psi_2$ in non-smooth domains. This problem has its own interest in mathematics, engineering, physics and other branches of science. Our approach makes a novel connection between the study of Calder'on-Zygmund theory for nonlinear Schr"odinger type equations and variational inequalities for double obstacle problems.

In this paper we construct an equivariant embedding of the affine space $mathbb{A}^n$ with the translation group action into a complete non-projective algebraic variety $X$ for all $n geq 3$. The theory of toric varieties is used as the main tool for this construction. In the case of $n = 3$ we describe the orbit structure on the variety $X$.

In information theory, the so-called log-sum inequality is fundamental and a kind of generalization of the non-nagativity for the relative entropy. In this paper, we show the generalized log-sum inequality for two functions defined for scalars. We also give a new result for commutative matrices. In addition, we demonstrate further results for general non-commutative positive semi-definite matrices.

In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming from weight sequences. These sequences are required to satisfy certain (standard) growth and regularity properties which are frequently arising and used in the theory of ultradifferentiable and ultraholomorphic function classes (where also the associated weight function plays a prominent role). Thanks to this additional information we are able to see which growth behavior the so-called "Lusky-numbers", arising in the representations of the solid hulls and cores, have to satisfy resp. if such numbers can exist.

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs, because of three challenges: (1) difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based in sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first open-source linear algebra-based graph framework on GPU targeting high-performance computing. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.

Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.

Differential machine learning (ML) extends supervised learning, with models trained on examples of not only inputs and labels, but also differentials of labels to inputs.

Differential ML is applicable in all situations where high quality first order derivatives wrt training inputs are available. In the context of financial Derivatives risk management, pathwise differentials are efficiently computed with automatic adjoint differentiation (AAD). Differential ML, combined with AAD, provides extremely effective pricing and risk approximations. We can produce fast pricing analytics in models too complex for closed form solutions, extract the risk factors of complex transactions and trading books, and effectively compute risk management metrics like reports across a large number of scenarios, backtesting and simulation of hedge strategies, or capital regulations.

The article focuses on differential deep learning (DL), arguably the strongest application. Standard DL trains neural networks (NN) on punctual examples, whereas differential DL teaches them the shape of the target function, resulting in vastly improved performance, illustrated with a number of numerical examples, both idealized and real world. In the online appendices, we apply differential learning to other ML models, like classic regression or principal component analysis (PCA), with equally remarkable results.

This paper is meant to be read in conjunction with its companion GitHub repo https://github.com/differential-machine-learning, where we posted a TensorFlow implementation, tested on Google Colab, along with examples from the article and additional ones. We also posted appendices covering many practical implementation details not covered in the paper, mathematical proofs, application to ML models besides neural networks and extensions necessary for a reliable implementation in production.

Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independent sets or irredundant sets. Bounds on the number of sets of any such family of sets are interesting from a combinatorial point of view and have algorithmic applications. Many such bounds on different families of sets over different classes of graphs are already provided in the literature. In particular, Rote recently showed that the number of minimal dominating sets in trees of order $n$ is at most $95^{frac{n}{13}}$ and that this bound is asymptotically sharp up to a multiplicative constant. We build on his work to show that what he did for minimal dominating sets can be done for any family of sets definable by a monadic second order formula.

We first show that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the extit{growth rate of a bilinear system}. This mostly relies on well known links between monadic second order logic over trees and tree automata and basic tree automata manipulations. Then we show that this "growth rate" of a bilinear system can be approximated from above.We then use our implementation of this result to provide bounds on the number of independent dominating sets, total perfect dominating sets, induced matchings, maximal induced matchings, minimal perfect dominating sets, perfect codes and maximal irredundant sets on trees. We also solve a question from D. Y. Kang et al. regarding $r$-matchings and improve a bound from G'orska and Skupie'n on the number of maximal matchings on trees. Remark that this approach is easily generalizable to graphs of bounded tree width or clique width (or any similar class of graphs where tree automata are meaningful).

Lake ice, as part of the Essential Climate Variable (ECV) lakes, is an important indicator to monitor climate change and global warming. The spatio-temporal extent of lake ice cover, along with the timings of key phenological events such as freeze-up and break-up, provide important cues about the local and global climate. We present a lake ice monitoring system based on the automatic analysis of Sentinel-1 Synthetic Aperture Radar (SAR) data with a deep neural network. In previous studies that used optical satellite imagery for lake ice monitoring, frequent cloud cover was a main limiting factor, which we overcome thanks to the ability of microwave sensors to penetrate clouds and observe the lakes regardless of the weather and illumination conditions. We cast ice detection as a two class (frozen, non-frozen) semantic segmentation problem and solve it using a state-of-the-art deep convolutional network (CNN). We report results on two winters ( 2016 - 17 and 2017 - 18 ) and three alpine lakes in Switzerland. The proposed model reaches mean Intersection-over-Union (mIoU) scores >90% on average, and >84% even for the most difficult lake. Additionally, we perform cross-validation tests and show that our algorithm generalises well across unseen lakes and winters.

Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an obstacle's space: a polyhedron, such as a cuboid, or a nonlinear differentiable surface, such as an ellipsoid. The former approach relies on disjunctive programming, which has a relatively high computational cost that grows exponentially with the number of obstacles. The latter approach needs to be linearized locally to find a tractable evaluation of the chance constraints, which dramatically reduces the remaining free space and leads to over-conservative trajectories or even unfeasibility. In this work, we present a hybrid approach that eludes the pitfalls of both strategies while maintaining the original safety guarantees. The key idea consists in obtaining a safe differentiable approximation for the disjunctive chance constraints bounding the obstacles. The resulting nonlinear optimization problem is free of chance constraint linearization and disjunctive programming, and therefore, it can be efficiently solved to meet fast real-time requirements with multiple obstacles. We validate our approach through mathematical proof, simulation and real experiments with an aerial robot using nonlinear model predictive control to avoid pedestrians.

When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. This paper aims to investigate the effect of geometric approximation error by using a high-order mesh with negligible geometric approximation error, even for high order polynomial of order p. To achieve this goal, the high-order mesh generator from CAD geometry called NekMesh is adapted for surface mesh generation in comparison to traditional meshes with non-negligible geometric approximation error. Two types of numerical tests are considered. Firstly, the accuracy of differential operators is compared for various p on a curved element of the sphere. Secondly, by applying the method of moving frames, four different time-dependent PDEs on the sphere are numerically solved to investigate the impact of geometric approximation error on the accuracy and conservation properties of high-order numerical schemes for PDEs on the sphere.

Restless multi-armed bandits are a class of discrete-time stochastic control problems which involve sequential decision making with a finite set of actions (set of arms). This paper studies a class of constrained restless multi-armed bandits (CRMAB). The constraints are in the form of time varying set of actions (set of available arms). This variation can be either stochastic or semi-deterministic. Given a set of arms, a fixed number of them can be chosen to be played in each decision interval. The play of each arm yields a state dependent reward. The current states of arms are partially observable through binary feedback signals from arms that are played. The current availability of arms is fully observable. The objective is to maximize long term cumulative reward. The uncertainty about future availability of arms along with partial state information makes this objective challenging. Applications for CRMAB abound in the domain of cyber-physical systems. This optimization problem is analyzed using Whittle's index policy. To this end, a constrained restless single-armed bandit is studied. It is shown to admit a threshold-type optimal policy, and is also indexable. An algorithm to compute Whittle's index is presented. Further, upper bounds on the value function are derived in order to estimate the degree of sub-optimality of various solutions. The simulation study compares the performance of Whittle's index, modified Whittle's index and myopic policies.

We develop a supervised machine learning algorithm that is able to learn topological phases for finite condensed matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any supervised learning algorithm to learn topological phases through an eigenvector ensembling procedure. We combine our algorithm with decision trees and random forests to successfully recover topological phase diagrams of Su-Schrieffer-Heeger (SSH) models from bulk lattice data in real space and show how the Shannon information entropy of ensembles of lattice eigenvectors can be used to retrieve a signal detailing how topological information is distributed in the bulk. The discovery of Shannon information entropy signals associated with topological phase transitions from the analysis of data from several thousand SSH systems illustrates how model explainability in machine learning can advance the research of exotic quantum materials with properties that may power future technological applications such as qubit engineering for quantum computing.

Dense kernel matrices $Theta in mathbb{R}^{N imes N}$ obtained from point evaluations of a covariance function $G$ at locations ${ x_{i} }_{1 leq i leq N} subset mathbb{R}^{d}$ arise in statistics, machine learning, and numerical analysis. For covariance functions that are Green's functions of elliptic boundary value problems and homogeneously-distributed sampling points, we show how to identify a subset $S subset { 1 , dots , N }^2$, with $# S = O ( N log (N) log^{d} ( N /epsilon ) )$, such that the zero fill-in incomplete Cholesky factorisation of the sparse matrix $Theta_{ij} 1_{( i, j ) in S}$ is an $epsilon$-approximation of $Theta$. This factorisation can provably be obtained in complexity $O ( N log( N ) log^{d}( N /epsilon) )$ in space and $O ( N log^{2}( N ) log^{2d}( N /epsilon) )$ in time, improving upon the state of the art for general elliptic operators; we further present numerical evidence that $d$ can be taken to be the intrinsic dimension of the data set rather than that of the ambient space. The algorithm only needs to know the spatial configuration of the $x_{i}$ and does not require an analytic representation of $G$. Furthermore, this factorization straightforwardly provides an approximate sparse PCA with optimal rate of convergence in the operator norm. Hence, by using only subsampling and the incomplete Cholesky factorization, we obtain, at nearly linear complexity, the compression, inversion and approximate PCA of a large class of covariance matrices. By inverting the order of the Cholesky factorization we also obtain a solver for elliptic PDE with complexity $O ( N log^{d}( N /epsilon) )$ in space and $O ( N log^{2d}( N /epsilon) )$ in time, improving upon the state of the art for general elliptic operators.

The standard training algorithm in neural machine translation (NMT) suffers from exposure bias, and alternative algorithms have been proposed to mitigate this. However, the practical impact of exposure bias is under debate. In this paper, we link exposure bias to another well-known problem in NMT, namely the tendency to generate hallucinations under domain shift. In experiments on three datasets with multiple test domains, we show that exposure bias is partially to blame for hallucinations, and that training with Minimum Risk Training, which avoids exposure bias, can mitigate this. Our analysis explains why exposure bias is more problematic under domain shift, and also links exposure bias to the beam search problem, i.e. performance deterioration with increasing beam size. Our results provide a new justification for methods that reduce exposure bias: even if they do not increase performance on in-domain test sets, they can increase model robustness to domain shift.

This paper is the first to consider online algorithms to schedule a proportionate flexible flow shop of batching machines (PFFB). The scheduling model is motivated by manufacturing processes of individualized medicaments, which are used in modern medicine to treat some serious illnesses. We provide two different online algorithms, proving also lower bounds for the offline problem to compute their competitive ratios. The first algorithm is an easy-to-implement, general local scheduling heuristic. It is 2-competitive for PFFBs with an arbitrary number of stages and for several natural scheduling objectives. We also show that for total/average flow time, no deterministic algorithm with better competitive ratio exists. For the special case with two stages and the makespan or total completion time objective, we describe an improved algorithm that achieves the best possible competitive ratio $varphi=frac{1+sqrt{5}}{2}$, the golden ratio. All our results also hold for proportionate (non-flexible) flow shops of batching machines (PFB) for which this is also the first paper to study online algorithms.

Lexicographic Depth First Search (LexDFS) is a special variant of a Depth First Search (DFS), which was introduced by Corneil and Krueger in 2008. While this search has been used in various applications, in contrast to other graph searches, no general linear time implementation is known to date. In 2014, K"ohler and Mouatadid achieved linear running time to compute some special LexDFS orders for cocomparability graphs. In this paper, we present a linear time implementation of LexDFS for chordal graphs. Our algorithm is able to find any LexDFS order for this graph class. To the best of our knowledge this is the first unrestricted linear time implementation of LexDFS on a non-trivial graph class. In the algorithm we use a search tree computed by Lexicographic Breadth First Search (LexBFS).

Sentence level quality estimation (QE) for machine translation (MT) attempts to predict the translation edit rate (TER) cost of post-editing work required to correct MT output. We describe our view on sentence-level QE as dictated by several practical setups encountered in the industry. We find consumers of MT output---whether human or algorithmic ones---to be primarily interested in a binary quality metric: is the translated sentence adequate as-is or does it need post-editing? Motivated by this we propose a quality classification (QC) view on sentence-level QE whereby we focus on maximizing recall at precision above a given threshold. We demonstrate that, while classical QE regression models fare poorly on this task, they can be re-purposed by replacing the output regression layer with a binary classification one, achieving 50-60\% recall at 90\% precision. For a high-quality MT system producing 75-80\% correct translations, this promises a significant reduction in post-editing work indeed.

The patterns in which the syntax of different languages converges and diverges are often used to inform work on cross-lingual transfer. Nevertheless, little empirical work has been done on quantifying the prevalence of different syntactic divergences across language pairs. We propose a framework for extracting divergence patterns for any language pair from a parallel corpus, building on Universal Dependencies. We show that our framework provides a detailed picture of cross-language divergences, generalizes previous approaches, and lends itself to full automation. We further present a novel dataset, a manually word-aligned subset of the Parallel UD corpus in five languages, and use it to perform a detailed corpus study. We demonstrate the usefulness of the resulting analysis by showing that it can help account for performance patterns of a cross-lingual parser.

In encoder-decoder neural models, multiple encoders are in general used to represent the contextual information in addition to the individual sentence. In this paper, we investigate multi-encoder approaches in documentlevel neural machine translation (NMT). Surprisingly, we find that the context encoder does not only encode the surrounding sentences but also behaves as a noise generator. This makes us rethink the real benefits of multi-encoder in context-aware translation - some of the improvements come from robust training. We compare several methods that introduce noise and/or well-tuned dropout setup into the training of these encoders. Experimental results show that noisy training plays an important role in multi-encoder-based NMT, especially when the training data is small. Also, we establish a new state-of-the-art on IWSLT Fr-En task by careful use of noise generation and dropout methods.

Simplified Chinese to Traditional Chinese character conversion is a common preprocessing step in Chinese NLP. Despite this, current approaches have poor performance because they do not take into account that a simplified Chinese character can correspond to multiple traditional characters. Here, we propose a model that can disambiguate between mappings and convert between the two scripts. The model is based on subword segmentation, two language models, as well as a method for mapping between subword sequences. We further construct benchmark datasets for topic classification and script conversion. Our proposed method outperforms previous Chinese Character conversion approaches by 6 points in accuracy. These results are further confirmed in a downstream application, where 2kenize is used to convert pretraining dataset for topic classification. An error analysis reveals that our method's particular strengths are in dealing with code-mixing and named entities.

MineRL 2019 competition challenged participants to train sample-efficient agents to play Minecraft, by using a dataset of human gameplay and a limit number of steps the environment. We approached this task with behavioural cloning by predicting what actions human players would take, and reached fifth place in the final ranking. Despite being a simple algorithm, we observed the performance of such an approach can vary significantly, based on when the training is stopped. In this paper, we detail our submission to the competition, run further experiments to study how performance varied over training and study how different engineering decisions affected these results.

Neural machine translation (NMT) needs large parallel corpora for state-of-the-art translation quality. Low-resource NMT is typically addressed by transfer learning which leverages large monolingual or parallel corpora for pre-training. Monolingual pre-training approaches such as MASS (MAsked Sequence to Sequence) are extremely effective in boosting NMT quality for languages with small parallel corpora. However, they do not account for linguistic information obtained using syntactic analyzers which is known to be invaluable for several Natural Language Processing (NLP) tasks. To this end, we propose JASS, Japanese-specific Sequence to Sequence, as a novel pre-training alternative to MASS for NMT involving Japanese as the source or target language. JASS is joint BMASS (Bunsetsu MASS) and BRSS (Bunsetsu Reordering Sequence to Sequence) pre-training which focuses on Japanese linguistic units called bunsetsus. In our experiments on ASPEC Japanese--English and News Commentary Japanese--Russian translation we show that JASS can give results that are competitive with if not better than those given by MASS. Furthermore, we show for the first time that joint MASS and JASS pre-training gives results that significantly surpass the individual methods indicating their complementary nature. We will release our code, pre-trained models and bunsetsu annotated data as resources for researchers to use in their own NLP tasks.

Hypertension is a potentially unsafe health ailment, which can be indicated directly from the Blood pressure (BP). Hypertension always leads to other health complications. Continuous monitoring of BP is very important; however, cuff-based BP measurements are discrete and uncomfortable to the user. To address this need, a cuff-less, continuous and a non-invasive BP measurement system is proposed using Photoplethysmogram (PPG) signal and demographic features using machine learning (ML) algorithms. PPG signals were acquired from 219 subjects, which undergo pre-processing and feature extraction steps. Time, frequency and time-frequency domain features were extracted from the PPG and their derivative signals. Feature selection techniques were used to reduce the computational complexity and to decrease the chance of over-fitting the ML algorithms. The features were then used to train and evaluate ML algorithms. The best regression models were selected for Systolic BP (SBP) and Diastolic BP (DBP) estimation individually. Gaussian Process Regression (GPR) along with ReliefF feature selection algorithm outperforms other algorithms in estimating SBP and DBP with a root-mean-square error (RMSE) of 6.74 and 3.59 respectively. This ML model can be implemented in hardware systems to continuously monitor BP and avoid any critical health conditions due to sudden changes.

We study the problem of pricing under a Multinomial Logit model where we incorporate network effects over the consumer's decisions. We analyse both cases, when sellers compete or collaborate. In particular, we pay special attention to the overall expected revenue and how the behaviour of the no purchase option is affected under variations of a network effect parameter. Where for example we prove that the market share for the no purchase option, is decreasing in terms of the value of the network effect, meaning that stronger communication among costumers increases the expected amount of sales. We also analyse how the customer's utility is altered when network effects are incorporated into the market, comparing the cases where both competitive and monopolistic prices are displayed. We use tools from stochastic approximation algorithms to prove that the probability of purchasing the available products converges to a unique stationary distribution. We model that the sellers can use this stationary distribution to establish their strategies. Finding that under those settings, a pure Nash Equilibrium represents the pricing strategies in the case of competition, and an optimal (that maximises the total revenue) fixed price characterise the case of collaboration.

The paper develops a robotic manipulation system to treat the pressing needs for handling a large number of test tubes in clinical examination and replace or reduce human labor. It presents the technical details of the system, which separates and arranges test tubes in racks with the help of 3D vision and artificial intelligence (AI) reasoning/planning. The developed system only requires a person to put a rack with mixed and non-arranged tubes in front of a robot. The robot autonomously performs recognition, reasoning, planning, manipulation, etc., and returns a rack with separated and arranged tubes. The system is simple-to-use, and there are no requests for expert knowledge in robotics. We expect such a system to play an important role in helping managing public health and hope similar systems could be extended to other clinical manipulation like handling mixers and pipettes in the future.

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints.In this setting, the paper proposes an online algorithm based on the alternating direction method of multipliers(ADMM), to track the optimal solution trajectory of the time-varying problem; in particular, the proposed algorithm consists of a primal proximal gradient descent step and an appropriately perturbed dual ascent step. The paper derives tracking results, asymptotic bounds, and linear convergence results. The proposed algorithm is then specialized to a multi-area power grid optimization problem, and our numerical results verify the desired properties.

Avikainen proved the estimate $mathbb{E}[|f(X)-f(widehat{X})|^{q}] leq C(p,q) mathbb{E}[|X-widehat{X}|^{p}]^{frac{1}{p+1}} $ for $p,q in [1,infty)$, one-dimensional random variables $X$ with the bounded density function and $widehat{X}$, and a function $f$ of bounded variation in $mathbb{R}$. In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in $mathbb{R}^{d}$, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces. The main idea of our arguments is to use Hardy-Littlewood maximal estimates and pointwise characterizations of these function spaces. We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method, and to estimates of the $L^{2}$-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.

Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly unrelated topic in pure and applied mathematics, is a class of stochastic point processes with probability distribution characterized by sub-determinants of a kernel matrix. Recent work has uncovered deep and fruitful connections between DPPs and RandNLA which lead to new guarantees and improved algorithms that are of interest to both areas. We provide an overview of this exciting new line of research, including brief introductions to RandNLA and DPPs, as well as applications of DPPs to classical linear algebra tasks such as least squares regression, low-rank approximation and the Nystr"om method. For example, random sampling with a DPP leads to new kinds of unbiased estimators for least squares, enabling more refined statistical and inferential understanding of these algorithms; a DPP is, in some sense, an optimal randomized algorithm for the Nystr"om method; and a RandNLA technique called leverage score sampling can be derived as the marginal distribution of a DPP. We also discuss recent algorithmic developments, illustrating that, while not quite as efficient as standard RandNLA techniques, DPP-based algorithms are only moderately more expensive.

Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a cylinder at the same Reynolds number. The linear terms of the governing equations are reduced by Galerkin projection onto a POD basis of the flow state, while the reduced nonlinear convection terms are obtained either by a Galerkin projection onto the same state basis, by a Galerkin projection onto a POD basis representing the nonlinearities or by applying the Discrete Empirical Interpolation Method (DEIM) to a POD basis of the nonlinearities. The quality of the reduced order models is assessed as to their stability, accuracy and robustness, and appropriate quantitative measures are introduced and compared. In particular, the properties of the reduced linear terms are compared to those of the full-scale terms, and the structure of the nonlinear quadratic terms is analyzed as to the conservation of kinetic energy. It is shown that all three reduction techniques provide excellent and similar results for the cases of the Kuramoto-Sivashinsky equation and the limit-cycle cylinder flow. For the case of the transient regime of flow past a cylinder, only the pure Galerkin techniques are successful, while the DEIM technique produces reduced-order models that diverge in finite time.

Unsupervised machine translation (MT) has recently achieved impressive results with monolingual corpora only. However, it is still challenging to associate source-target sentences in the latent space. As people speak different languages biologically share similar visual systems, the potential of achieving better alignment through visual content is promising yet under-explored in unsupervised multimodal MT (MMT). In this paper, we investigate how to utilize visual content for disambiguation and promoting latent space alignment in unsupervised MMT. Our model employs multimodal back-translation and features pseudo visual pivoting in which we learn a shared multilingual visual-semantic embedding space and incorporate visually-pivoted captioning as additional weak supervision. The experimental results on the widely used Multi30K dataset show that the proposed model significantly improves over the state-of-the-art methods and generalizes well when the images are not available at the testing time.

Smart meters enable remote and automatic electricity, water and gas consumption reading and are being widely deployed in developed countries. Nonetheless, there is still a huge number of non-smart meters in operation. Image-based Automatic Meter Reading (AMR) focuses on dealing with this type of meter readings. We estimate that the Energy Company of Paran'a (Copel), in Brazil, performs more than 850,000 readings of dial meters per month. Those meters are the focus of this work. Our main contributions are: (i) a public real-world dial meter dataset (shared upon request) called UFPR-ADMR; (ii) a deep learning-based recognition baseline on the proposed dataset; and (iii) a detailed error analysis of the main issues present in AMR for dial meters. To the best of our knowledge, this is the first work to introduce deep learning approaches to multi-dial meter reading, and perform experiments on unconstrained images. We achieved a 100.0% F1-score on the dial detection stage with both Faster R-CNN and YOLO, while the recognition rates reached 93.6% for dials and 75.25% for meters using Faster R-CNN (ResNext-101).

The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory technologies, a set of sequences which generalize sequences in the de Bruijn graph are defined. These sequences can be also defined and viewed as constrained sequences. Hence, they will be called constrained de Bruijn sequences and a set of such sequences will be called a constrained de Bruijn code. Several properties and alternative definitions for such codes are examined and they are analyzed as generalized sequences in the de Bruijn graph (and its generalization) and as constrained sequences. Various enumeration techniques are used to compute the total number of sequences for any given set of parameters. A construction method of such codes from the theory of shift-register sequences is proposed. Finally, we show how these constrained de Bruijn sequences and codes can be applied in constructions of codes for correcting synchronization errors in the $ell$-symbol read channel and in the racetrack memory channel. For this purpose, these codes are superior in their size on previously known codes.

Narrowband internet-of-things (NB-IoT) is a competitive 5G technology for massive machine-type communication scenarios, but meanwhile introduces narrowband interference (NBI) to existing broadband transmission such as the long term evolution (LTE) systems in enhanced mobile broadband (eMBB) scenarios. In order to facilitate the harmonic and fair coexistence in wireless heterogeneous networks, it is important to eliminate NB-IoT interference to LTE systems. In this paper, a novel sparse machine learning based framework and a sparse combinatorial optimization problem is formulated for accurate NBI recovery, which can be efficiently solved using the proposed iterative sparse learning algorithm called sparse cross-entropy minimization (SCEM). To further improve the recovery accuracy and convergence rate, regularization is introduced to the loss function in the enhanced algorithm called regularized SCEM. Moreover, exploiting the spatial correlation of NBI, the framework is extended to multiple-input multiple-output systems. Simulation results demonstrate that the proposed methods are effective in eliminating NB-IoT interference to LTE systems, and significantly outperform the state-of-the-art methods.

In this paper, we present a novel method for line artefacts quantification in lung ultrasound (LUS) images of COVID-19 patients. We formulate this as a non-convex regularisation problem involving a sparsity-enforcing, Cauchy-based penalty function, and the inverse Radon transform. We employ a simple local maxima detection technique in the Radon transform domain, associated with known clinical definitions of line artefacts. Despite being non-convex, the proposed method has guaranteed convergence via a proximal splitting algorithm and accurately identifies both horizontal and vertical line artefacts in LUS images. In order to reduce the number of false and missed detection, our method includes a two-stage validation mechanism, which is performed in both Radon and image domains. We evaluate the performance of the proposed method in comparison to the current state-of-the-art B-line identification method and show a considerable performance gain with 87% correctly detected B-lines in LUS images of nine COVID-19 patients. In addition, owing to its fast convergence, which takes around 12 seconds for a given frame, our proposed method is readily applicable for processing LUS image sequences.

Recently, the Edge Computing paradigm has gained significant popularity both in industry and academia. Researchers now increasingly target to improve performance and reduce energy consumption of such devices. Some recent efforts focus on using emerging RRAM technologies for improving energy efficiency, thanks to their no leakage property and high integration density. As the complexity and dynamism of applications supported by such devices escalate, it has become difficult to maintain ideal performance by static RRAM controllers. Machine Learning provides a promising solution for this, and hence, this work focuses on extending such controllers to allow dynamic parameter updates. In this work we propose an Adaptive RRAM Variability-Aware Controller, AVAC, which periodically updates Wait Buffer and batch sizes using on-the-fly learning models and gradient ascent. AVAC allows Edge devices to adapt to different applications and their stages, to improve computation performance and reduce energy consumption. Simulations demonstrate that the proposed model can provide up to 29% increase in performance and 19% decrease in energy, compared to static controllers, using traces of real-life healthcare applications on a Raspberry-Pi based Edge deployment.

An approach is given for solving large linear systems that combines Krylov methods with use of two different grid levels. Eigenvectors are computed on the coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type methods are first used on both the coarse and fine grids. Then another approach is given that has a restarted BiCGStab (or IDR) method on the fine grid. While BiCGStab is generally considered to be a non-restarted method, it works well in this context with deflating and restarting. Tests show this new approach can be very efficient for difficult linear equations problems.

The increasing ubiquity of low-cost wireless sensors in smart homes and buildings has enabled users to easily deploy systems to remotely monitor and control their environments. However, this raises privacy concerns for third-party occupants, such as a hotel room guest who may be unaware of deployed clandestine sensors. Previous methods focused on specific modalities such as detecting cameras but do not provide a generalizable and comprehensive method to capture arbitrary sensors which may be "spying" on a user. In this work, we seek to determine whether one can walk in a room and detect any wireless sensor monitoring an individual. As such, we propose SnoopDog, a framework to not only detect wireless sensors that are actively monitoring a user, but also classify and localize each device. SnoopDog works by establishing causality between patterns in observable wireless traffic and a trusted sensor in the same space, e.g., an inertial measurement unit (IMU) that captures a user's movement. Once causality is established, SnoopDog performs packet inspection to inform the user about the monitoring device. Finally, SnoopDog localizes the clandestine device in a 2D plane using a novel trial-based localization technique. We evaluated SnoopDog across several devices and various modalities and were able to detect causality 96.6% percent of the time, classify suspicious devices with 100% accuracy, and localize devices to a sufficiently reduced sub-space.

Retired Soccer Star Briana Scurry describes how the computerized baseline test works and how it is used for athletes who have sustained a concussion.

As a small or midsize business (SMB), your company website is often the first touchpoint for potential clients — and you want it to make a great first impression. The secret to hitting home with your audience is to have a sophisticated and lively website design that’s aesthetically pleasing and provides great user experience (UX). […]

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Did you know that over 70% of people will research a company on the web before deciding to buy or visit, yet 46% of small businesses in the U.S. don’t have a website? If you don’t have a site, people can’t research your company and determine if you’re a good fit for their needs. If […]

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Coronavirus Family Tree The University of Washington Virology lab, which is testing samples for coronavirus, tweeted last night.…

Agencies, local authorities and national governments do not agree on who should be quarantined or what that should actually look like. Here’s what we do know. By Maya Miller, Caroline Chen and Joshua Kaplan ProPublica People who have been exposed to the coronavirus are being given incomplete or misleading information about whether they should quarantine themselves, exposing major gaps in the public health response to the pandemic and illuminating disagreement among officials about how useful the tactic even is at this point in the disease’s spread.…

You shouldn't find yourself rewatching some sitcom for the thousandth time or sitting through a vacuous Hollywood blockbuster just because you're stoned and stuck inside during the age of social distancing.…

[IMAGE-1] I honestly don't know how people like Bryan Stevenson keep up the fight. Just Mercy is the true origin story of a literal social justice warrior, a Harvard-educated lawyer who, in the late 1980s, launched the Equal Justice Initiative in Montgomery, Alabama, to take on the neediest, most desperate cases.…

PROPHET OF DOOM…

Pardon the interruption for a little fanboy boosterism, but one of my favorite all-time bands surprise-dropped a brand new album on Bandcamp today, and damned if I'm not going to tell you to go listen to it. The band is X, pioneering Los Angeles legends who helped establish the West Coast punk scene in the late '70s and early '80s with a sound that was rooted in American rock's roots.…