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 $X$.

Given a standard graded polynomial ring over a commutative Noetherian ring $A$, we prove that the cohomological dimension and the height of the ideals defining any of its Veronese subrings are equal. This result is due to Ogus when $A$ is a field of characteristic zero, and follows from a result of Peskine and Szpiro when $A$ is a field of positive characteristic; our result applies, for example, when $A$ is the ring of integers.

Recent studies of optimization methods and GNC of spacecraft near small bodies focusing on descent, landing, rendezvous, etc., with key safety constraints such as line-of-sight conic zones and soft landings have shown promising results; this paper considers descent missions to an asteroid surface with a constraint that consists of an onboard camera and asteroid surface markers while using a stochastic convex MPC law. An undermodeled asteroid gravity and spacecraft technology inspired measurement model is established to develop the constraint. Then a computationally light stochastic Linear Quadratic MPC strategy is presented to keep the spacecraft in satisfactory field of view of the surface markers while trajectory tracking, employing chance based constraints and up-to-date estimation uncertainty from navigation. The estimation uncertainty giving rise to the tightened constraints is particularly addressed. Results suggest robust tracking performance across a variety of trajectories.

In this paper, we characterize a mixed graph $F$ which contains $k$ edge and arc disjoint spanning mixed arborescences $F_{1}, ldots, F_{k}$, such that for each $v in V(F)$, the cardinality of ${i in [k]: v ext{ is the root of } F_{i}}$ lies in some prescribed interval. This generalizes both Nash-Williams and Tutte's theorem on spanning tree packing for undirected graphs and the previous characterization on digraphs which was given by Cai [in: Arc-disjoint arborescences of digraphs, J. Graph Theory 7(2) (1983), 235-240] and Frank [in: On disjoint trees and arborescences, Algebraic Methods in Graph Theory, Colloquia Mathematica Soc. J. Bolyai, Vol. 25 (North-Holland, Amsterdam) (1978), 159-169].

We study the non-relativity for two real analytic K"ahler manifolds and complex space forms of three types. The first one is a K"ahler manifold whose polarization of local K"ahler potential is a Nash function in a local coordinate. The second one is the Hartogs domain equpped with two canonical metrics whose polarizations of the K"ahler potentials are the diastatic functions.

The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the bi-axial Dirac operator. In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting, novel structures appear in the cases of negative even superdimensions. In these cases, the CK-extension depends on two initial functions on which two power series of differential operators act. These series are not only of Bessel type but they give rise to an additional structure in terms of Appell polynomials. This pattern also is present in the structure of the Pizzetti formula, which describes integration over the supersphere in terms of differential operators. We make this relation explicit by studying the decomposition of the generalized CK-extension into plane waves integrated over the supersphere. Moreover, these results are applied to obtain a decomposition of the Cauchy kernel in superspace into monogenic plane waves, which shall be useful for inverting the super Radon transform.

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions - Dirac delta, Gamma distribution, uniform and truncated normal distributions.

We prove that all non-degenerate relative equilibria of the planar Newtonian $n$--body problem can be continued to spaces of constant curvature $kappa$, positive or negative, for small enough values of this parameter. We also compute the extension of some classical relative equilibria to curved spaces using numerical continuation. In particular, we extend Lagrange's triangle configuration with different masses to both positive and negative curvature spaces.

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.

We investigate the Boundary Harnack Principle in H"older domains of exponent $alpha>0$ by the analytical method developed in our previous work "A short proof of Boundary Harnack Principle".

In this paper we study manifolds $M_{Sigma}$ with fibered singularities, more specifically, a relevant space $Riem^{psc}(X_{Sigma})$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space $Riem^{psc}(X_{Sigma})$ is homotopy invariant under certain surgeries on $M_{Sigma}$.

Input transformation based defense strategies fall short in defending against strong adversarial attacks. Some successful defenses adopt approaches that either increase the randomness within the applied transformations, or make the defense computationally intensive, making it substantially more challenging for the attacker. However, it limits the applicability of such defenses as a pre-processing step, similar to computationally heavy approaches that use retraining and network modifications to achieve robustness to perturbations. In this work, we propose a defense strategy that applies random image corruptions to the input image alone, constructs a self-correlation based subspace followed by a projection operation to suppress the adversarial perturbation. Due to its simplicity, the proposed defense is computationally efficient as compared to the state-of-the-art, and yet can withstand huge perturbations. Further, we develop proximity relationships between the projection operator of a clean image and of its adversarially perturbed version, via bounds relating geodesic distance on the Grassmannian to matrix Frobenius norms. We empirically show that our strategy is complementary to other weak defenses like JPEG compression and can be seamlessly integrated with them to create a stronger defense. We present extensive experiments on the ImageNet dataset across four different models namely InceptionV3, ResNet50, VGG16 and MobileNet models with perturbation magnitude set to {epsilon} = 16. Unlike state-of-the-art approaches, even without any retraining, the proposed strategy achieves an absolute improvement of ~ 4.5% in defense accuracy on ImageNet.

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.

A standard approach to evaluating language models analyzes how models assign probabilities to valid versus invalid syntactic constructions (i.e. is a grammatical sentence more probable than an ungrammatical sentence). Our work uses ambiguous relative clause attachment to extend such evaluations to cases of multiple simultaneous valid interpretations, where stark grammaticality differences are absent. We compare model performance in English and Spanish to show that non-linguistic biases in RNN LMs advantageously overlap with syntactic structure in English but not Spanish. Thus, English models may appear to acquire human-like syntactic preferences, while models trained on Spanish fail to acquire comparable human-like preferences. We conclude by relating these results to broader concerns about the relationship between comprehension (i.e. typical language model use cases) and production (which generates the training data for language models), suggesting that necessary linguistic biases are not present in the training signal at all.

The connection between visual input and tactile sensing is critical for object manipulation tasks such as grasping and pushing. In this work, we introduce the challenging task of estimating a set of tactile physical properties from visual information. We aim to build a model that learns the complex mapping between visual information and tactile physical properties. We construct a first of its kind image-tactile dataset with over 400 multiview image sequences and the corresponding tactile properties. A total of fifteen tactile physical properties across categories including friction, compliance, adhesion, texture, and thermal conductance are measured and then estimated by our models. We develop a cross-modal framework comprised of an adversarial objective and a novel visuo-tactile joint classification loss. Additionally, we develop a neural architecture search framework capable of selecting optimal combinations of viewing angles for estimating a given physical property.

A k-proper edge-coloring of a graph G is called adjacent vertex-distinguishing if any two adjacent vertices are distinguished by the set of colors appearing in the edges incident to each vertex. The smallest value k for which G admits such coloring is denoted by $chi$'a (G). We prove that $chi$'a (G) = 2R + 1 for most circulant graphs Cn([[1, R]]).

A brain-computer interface (BCI) enables a user to communicate with a computer directly using brain signals. Electroencephalograms (EEGs) used in BCIs are weak, easily contaminated by interference and noise, non-stationary for the same subject, and varying across different subjects and sessions. Therefore, it is difficult to build a generic pattern recognition model in an EEG-based BCI system that is optimal for different subjects, during different sessions, for different devices and tasks. Usually, a calibration session is needed to collect some training data for a new subject, which is time consuming and user unfriendly. Transfer learning (TL), which utilizes data or knowledge from similar or relevant subjects/sessions/devices/tasks to facilitate learning for a new subject/session/device/task, is frequently used to reduce the amount of calibration effort. This paper reviews journal publications on TL approaches in EEG-based BCIs in the last few years, i.e., since 2016. Six paradigms and applications -- motor imagery, event-related potentials, steady-state visual evoked potentials, affective BCIs, regression problems, and adversarial attacks -- are considered. For each paradigm/application, we group the TL approaches into cross-subject/session, cross-device, and cross-task settings and review them separately. Observations and conclusions are made at the end of the paper, which may point to future research directions.

Event-related desynchronization and synchronization (ERD/S) and movement-related cortical potential (MRCP) play an important role in brain-computer interfaces (BCI) for lower limb rehabilitation, particularly in standing and sitting. However, little is known about the differences in the cortical activation between standing and sitting, especially how the brain's intention modulates the pre-movement sensorimotor rhythm as they do for switching movements. In this study, we aim to investigate the decoding of continuous EEG rhythms during action observation (AO), motor imagery (MI), and motor execution (ME) for standing and sitting. We developed a behavioral task in which participants were instructed to perform both AO and MI/ME in regard to the actions of sit-to-stand and stand-to-sit. Our results demonstrated that the ERD was prominent during AO, whereas ERS was typical during MI at the alpha band across the sensorimotor area. A combination of the filter bank common spatial pattern (FBCSP) and support vector machine (SVM) for classification was used for both offline and pseudo-online analyses. The offline analysis indicated the classification of AO and MI providing the highest mean accuracy at 82.73$pm$2.38\% in stand-to-sit transition. By applying the pseudo-online analysis, we demonstrated the higher performance of decoding neural intentions from the MI paradigm in comparison to the ME paradigm. These observations led us to the promising aspect of using our developed tasks based on the integration of both AO and MI to build future exoskeleton-based rehabilitation systems.

The global health threat from COVID-19 has been controlled in a number of instances by large-scale testing and contact tracing efforts. We created this document to suggest three functionalities on how we might best harness computing technologies to supporting the goals of public health organizations in minimizing morbidity and mortality associated with the spread of COVID-19, while protecting the civil liberties of individuals. In particular, this work advocates for a third-party free approach to assisted mobile contact tracing, because such an approach mitigates the security and privacy risks of requiring a trusted third party. We also explicitly consider the inferential risks involved in any contract tracing system, where any alert to a user could itself give rise to de-anonymizing information.

More generally, we hope to participate in bringing together colleagues in industry, academia, and civil society to discuss and converge on ideas around a critical issue rising with attempts to mitigate the COVID-19 pandemic.

Given a fixed graph $H$ that embeds in a surface $Sigma$, what is the maximum number of copies of $H$ in an $n$-vertex graph $G$ that embeds in $Sigma$? We show that the answer is $Theta(n^{f(H)})$, where $f(H)$ is a graph invariant called the `flap-number' of $H$, which is independent of $Sigma$. This simultaneously answers two open problems posed by Eppstein (1993). When $H$ is a complete graph we give more precise answers.

There are $n ge 2$ stacks, each filled with $d$ items, and one empty stack. Every stack has capacity $d > 0$. A robot arm, in one stack operation (step), may pop one item from the top of a non-empty stack and subsequently push it onto a stack not at capacity. In a {em labeled} problem, all $nd$ items are distinguishable and are initially randomly scattered in the $n$ stacks. The items must be rearranged using pop-and-pushs so that in the end, the $k^{ m th}$ stack holds items $(k-1)d +1, ldots, kd$, in that order, from the top to the bottom for all $1 le k le n$. In an {em unlabeled} problem, the $nd$ items are of $n$ types of $d$ each. The goal is to rearrange items so that items of type $k$ are located in the $k^{ m th}$ stack for all $1 le k le n$. In carrying out the rearrangement, a natural question is to find the least number of required pop-and-pushes.

Our main contributions are: (1) an algorithm for restoring the order of $n^2$ items stored in an $n imes n$ table using only $2n$ column and row permutations, and its generalization, and (2) an algorithm with a guaranteed upper bound of $O(nd)$ steps for solving both versions of the stack rearrangement problem when $d le lceil cn ceil$ for arbitrary fixed positive number $c$. In terms of the required number of steps, the labeled and unlabeled version have lower bounds $Omega(nd + nd{frac{log d}{log n}})$ and $Omega(nd)$, respectively.

Human visual attention is a complex phenomenon. A computational modeling of this phenomenon must take into account where people look in order to evaluate which are the salient locations (spatial distribution of the fixations), when they look in those locations to understand the temporal development of the exploration (temporal order of the fixations), and how they move from one location to another with respect to the dynamics of the scene and the mechanics of the eyes (dynamics). State-of-the-art models focus on learning saliency maps from human data, a process that only takes into account the spatial component of the phenomenon and ignore its temporal and dynamical counterparts. In this work we focus on the evaluation methodology of models of human visual attention. We underline the limits of the current metrics for saliency prediction and scanpath similarity, and we introduce a statistical measure for the evaluation of the dynamics of the simulated eye movements. While deep learning models achieve astonishing performance in saliency prediction, our analysis shows their limitations in capturing the dynamics of the process. We find that unsupervised gravitational models, despite of their simplicity, outperform all competitors. Finally, exploiting a crowd-sourcing platform, we present a study aimed at evaluating how strongly the scanpaths generated with the unsupervised gravitational models appear plausible to naive and expert human observers.

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. To remedy this, we introduce higher-order interactions, where a link can connect more than two individuals, and study their evolutionary dynamics. We first consider a public goods game on a uniform hypergraph, showing that it corresponds to the replicator dynamics in the well-mixed limit, and providing an exact theoretical foundation to study cooperation in networked groups. We also extend the analysis to heterogeneous hypergraphs that describe interactions of groups of different sizes and characterize the evolution of cooperation in such cases. Finally, we apply our new formulation to study the nature of group dynamics in real systems, showing how to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work is a first step towards the implementation of new actions to boost cooperation in social groups.

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.

Several problems of artificial intelligence, such as predictive learning, formal concept analysis or inductive logic programming, can be viewed as a special case of half-space separation in abstract closure systems over finite ground sets. For the typical scenario that the closure system is given via a closure operator, we show that the half-space separation problem is NP-complete. As a first approach to overcome this negative result, we relax the problem to maximal closed set separation, give a greedy algorithm solving this problem with a linear number of closure operator calls, and show that this bound is sharp. For a second direction, we consider Kakutani closure systems and prove that they are algorithmically characterized by the greedy algorithm. As a first special case of the general problem setting, we consider Kakutani closure systems over graphs, generalize a fundamental characterization result based on the Pasch axiom to graph structured partitioning of finite sets, and give a sufficient condition for this kind of closures systems in terms of graph minors. For a second case, we then focus on closure systems over finite lattices, give an improved adaptation of the greedy algorithm for this special case, and present two applications concerning formal concept and subsumption lattices. We also report some experimental results to demonstrate the practical usefulness of our algorithm.

For safety-critical black-box optimization tasks, observations of the constraints and the objective are often noisy and available only for the feasible points. We propose an approach based on log barriers to find a local solution of a non-convex non-smooth black-box optimization problem $min f^0(x)$ subject to $f^i(x)leq 0,~ i = 1,ldots, m$, at the same time, guaranteeing constraint satisfaction while learning an optimal solution with high probability. Our proposed algorithm exploits noisy observations to iteratively improve on an initial safe point until convergence. We derive the convergence rate and prove safety of our algorithm. We demonstrate its performance in an application to an iterative control design problem.

Introduction of spectrum-sharing in 5G and subsequent generation networks demand base-station(s) with the capability to characterize the wideband spectrum spanned over licensed, shared and unlicensed non-contiguous frequency bands. Spectrum characterization involves the identification of vacant bands along with center frequency and parameters (energy, modulation, etc.) of occupied bands. Such characterization at Nyquist sampling is area and power-hungry due to the need for high-speed digitization. Though sub-Nyquist sampling (SNS) offers an excellent alternative when the spectrum is sparse, it suffers from poor performance at low signal to noise ratio (SNR) and demands careful design and integration of digital reconstruction, tunable channelizer and characterization algorithms. In this paper, we propose a novel deep-learning framework via a single unified pipeline to accomplish two tasks: 1)~Reconstruct the signal directly from sub-Nyquist samples, and 2)~Wideband spectrum characterization. The proposed approach eliminates the need for complex signal conditioning between reconstruction and characterization and does not need complex tunable channelizers. We extensively compare the performance of our framework for a wide range of modulation schemes, SNR and channel conditions. We show that the proposed framework outperforms existing SNS based approaches and characterization performance approaches to Nyquist sampling-based framework with an increase in SNR. Easy to design and integrate along with a single unified deep learning framework make the proposed architecture a good candidate for reconfigurable platforms.

Interaction languages such as MSC are often associated with formal semantics by means of translations into distinct behavioral formalisms such as automatas or Petri nets. In contrast to translational approaches we propose an operational approach. Its principle is to identify which elementary communication actions can be immediately executed, and then to compute, for every such action, a new interaction representing the possible continuations to its execution. We also define an algorithm for checking the validity of execution traces (i.e. whether or not they belong to an interaction's semantics). Algorithms for semantic computation and trace validity are analyzed by means of experiments.

Due to the exponential growth of biomedical literature, event and relation extraction are important tasks in biomedical text mining. Most work only focus on relation extraction, and detect a single entity pair mention on a short span of text, which is not ideal due to long sentences that appear in biomedical contexts. We propose an approach to both relation and event extraction, for simultaneously predicting relationships between all mention pairs in a text. We also perform an empirical study to discuss different network setups for this purpose. The best performing model includes a set of multi-head attentions and convolutions, an adaptation of the transformer architecture, which offers self-attention the ability to strengthen dependencies among related elements, and models the interaction between features extracted by multiple attention heads. Experiment results demonstrate that our approach outperforms the state of the art on a set of benchmark biomedical corpora including BioNLP 2009, 2011, 2013 and BioCreative 2017 shared tasks.

For real-time semantic video segmentation, most recent works utilised a dynamic framework with a key scheduler to make online key/non-key decisions. Some works used a fixed key scheduling policy, while others proposed adaptive key scheduling methods based on heuristic strategies, both of which may lead to suboptimal global performance. To overcome this limitation, we model the online key decision process in dynamic video segmentation as a deep reinforcement learning problem and learn an efficient and effective scheduling policy from expert information about decision history and from the process of maximising global return. Moreover, we study the application of dynamic video segmentation on face videos, a field that has not been investigated before. By evaluating on the 300VW dataset, we show that the performance of our reinforcement key scheduler outperforms that of various baselines in terms of both effective key selections and running speed. Further results on the Cityscapes dataset demonstrate that our proposed method can also generalise to other scenarios. To the best of our knowledge, this is the first work to use reinforcement learning for online key-frame decision in dynamic video segmentation, and also the first work on its application on face videos.

For $n$-vertex graphs with treewidth $k = O(n^{1/2-epsilon})$ and an arbitrary $epsilon>0$, we present a word-RAM algorithm to compute vertex separators using only $O(n)$ bits of working memory. As an application of our algorithm, we give an $O(1)$-approximation algorithm for tree decomposition. Our algorithm computes a tree decomposition in $c^k n (log log n) log^* n$ time using $O(n)$ bits for some constant $c > 0$.

We finally use the tree decomposition obtained by our algorithm to solve Vertex Cover, Independent Set, Dominating Set, MaxCut and $3$-Coloring by using $O(n)$ bits as long as the treewidth of the graph is smaller than $c' log n$ for some problem dependent constant $0 < c' < 1$.

Noisy Intermediate-Scale Quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of Quantum Supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the World. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.

Stockhusen and Tantau (IPEC 2013) defined the operators paraW and paraBeta for parameterised space complexity classes by allowing bounded nondeterminism with multiple read and read-once access, respectively. Using these operators, they obtained characterisations for the complexity of many parameterisations of natural problems on graphs.

In this article, we study the counting versions of such operators and introduce variants based on tail-nondeterminism, paraW[1] and paraBetaTail, in the setting of parameterised logarithmic space. We examine closure properties of the new classes under the central reductions and arithmetic operations. We also identify a wide range of natural complete problems for our classes in the areas of walk counting in digraphs, first-order model-checking and graph-homomorphisms. In doing so, we also see that the closure of #paraBetaTail-L under parameterised logspace parsimonious reductions coincides with #paraBeta-L. We show that the complexity of a parameterised variant of the determinant function is #paraBetaTail-L-hard and can be written as the difference of two functions in #paraBetaTail-L for (0,1)-matrices. Finally, we characterise the new complexity classes in terms of branching programs.

The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, which is a central component to computing and analyzing the angular power spectrum of the massive CMB data sets. The method uses a novel combination of a non-uniform fast Fourier transform, the double Fourier sphere method, and Slevinsky's fast spherical harmonic transform (Slevinsky, 2019). For a HEALPix grid with $N$ pixels (points), the computational complexity of the method is $mathcal{O}(Nlog^2 N)$, with an initial set-up cost of $mathcal{O}(N^{3/2}log N)$. This compares favorably with $mathcal{O}(N^{3/2})$ runtime complexity of the current methods available in the HEALPix software when multiple maps need to be analyzed at the same time. Using numerical experiments, we demonstrate that the new method also appears to provide better accuracy over the entire angular power spectrum of synthetic data when compared to the current methods, with a convergence rate at least two times higher.

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.

We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $mathcal{NP}$-complete in the case where each side of the bipartitioning must contain a linear fraction of the nonzeros.

We present an improved exact branch-and-bound algorithm which finds the minimum communication volume for a given matrix and maximum allowed imbalance. The algorithm is based on a maximum-flow bound and a packing bound, which extend previous matching and packing bounds.

We implemented the algorithm in a new program called MP (Matrix Partitioner), which solved 839 matrices from the SuiteSparse collection to optimality, each within 24 hours of CPU-time. Furthermore, MP solved the difficult problem of the matrix cage6 in about 3 days. The new program is on average more than ten times faster than the previous program MondriaanOpt.

Benchmark results using the set of 839 optimally solved matrices show that combining the medium-grain/iterative refinement methods of the Mondriaan package with the hypergraph bipartitioner of the PaToH package produces sparse matrix bipartitionings on average within 10% of the optimal solution.

Compromised accounts on social networks are regular user accounts that have been taken over by an entity with malicious intent. Since the adversary exploits the already established trust of a compromised account, it is crucial to detect these accounts to limit the damage they can cause. We propose a novel general framework for discovering compromised accounts by semantic analysis of text messages coming out from an account. Our framework is built on the observation that normal users will use language that is measurably different from the language that an adversary would use when the account is compromised. We use our framework to develop specific algorithms that use the difference of language models of users and adversaries as features in a supervised learning setup. Evaluation results show that the proposed framework is effective for discovering compromised accounts on social networks and a KL-divergence-based language model feature works best.

This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional problems. We propose an efficient space-time multigrid method based on the waveform relaxation technique, which accounts for the nonlocal character of the fractional differential operator. To maintain an optimal complexity, which can be obtained for the case of uniform grids, we approximate the coefficient matrix corresponding to the temporal discretization by its hierarchical matrix (${cal H}$-matrix) representation. In particular, the proposed method has a computational cost of ${cal O}(k N M log(M))$, where $M$ is the number of time steps, $N$ is the number of spatial grid points, and $k$ is a parameter which controls the accuracy of the ${cal H}$-matrix approximation. The efficiency and the good convergence of the algorithm, which can be theoretically justified by a semi-algebraic mode analysis, are demonstrated through numerical experiments in both one- and two-dimensional spaces.

Assistive shared-control robots have the potential to transform the lives of millions of people afflicted with severe motor impairments. The usefulness of shared-control robots typically relies on the underlying autonomy's ability to infer the user's needs and intentions, and the ability to do so unambiguously is often a limiting factor for providing appropriate assistance confidently and accurately. The contributions of this paper are four-fold. First, we introduce the idea of intent disambiguation via control mode selection, and present a mathematical formalism for the same. Second, we develop a control mode selection algorithm which selects the control mode in which the user-initiated motion helps the autonomy to maximally disambiguate user intent. Third, we present a pilot study with eight subjects to evaluate the efficacy of the disambiguation algorithm. Our results suggest that the disambiguation system (a) helps to significantly reduce task effort, as measured by number of button presses, and (b) is of greater utility for more limited control interfaces and more complex tasks. We also observe that (c) subjects demonstrated a wide range of disambiguation request behaviors, with the common thread of concentrating requests early in the execution. As our last contribution, we introduce a novel field-theoretic approach to intent inference inspired by dynamic field theory that works in tandem with the disambiguation scheme.

In the era of Internet of Things (IoT), Malware has been proliferating exponentially over the past decade. Traditional anti-virus software are ineffective against modern complex Malware. In order to address this challenge, researchers have proposed Hardware-assisted Malware Detection (HMD) using Hardware Performance Counters (HPCs). The HPCs are used to train a set of Machine learning (ML) classifiers, which in turn, are used to distinguish benign programs from Malware. Recently, adversarial attacks have been designed by introducing perturbations in the HPC traces using an adversarial sample predictor to misclassify a program for specific HPCs. These attacks are designed with the basic assumption that the attacker is aware of the HPCs being used to detect Malware. Since modern processors consist of hundreds of HPCs, restricting to only a few of them for Malware detection aids the attacker. In this paper, we propose a Moving target defense (MTD) for this adversarial attack by designing multiple ML classifiers trained on different sets of HPCs. The MTD randomly selects a classifier; thus, confusing the attacker about the HPCs or the number of classifiers applied. We have developed an analytical model which proves that the probability of an attacker to guess the perfect HPC-classifier combination for MTD is extremely low (in the range of $10^{-1864}$ for a system with 20 HPCs). Our experimental results prove that the proposed defense is able to improve the classification accuracy of HPC traces that have been modified through an adversarial sample generator by up to 31.5%, for a near perfect (99.4%) restoration of the original accuracy.

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.

There exist two notions of equivalence of behavior between states of a Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The first one can be considered as an appropriate generalization to continuous spaces of Larsen and Skou's probabilistic bisimilarity, while the second one is characterized by a natural logic. C. Zhou expressed state bisimilarity as the greatest fixed point of an operator $mathcal{O}$, and thus introduced an ordinal measure of the discrepancy between it and event bisimilarity. We call this ordinal the "Zhou ordinal" of $mathbb{S}$, $mathfrak{Z}(mathbb{S})$. When $mathfrak{Z}(mathbb{S})=0$, $mathbb{S}$ satisfies the Hennessy-Milner property. The second author proved the existence of an LMP $mathbb{S}$ with $mathfrak{Z}(mathbb{S}) geq 1$ and Zhou showed that there are LMPs having an infinite Zhou ordinal. In this paper we show that there are LMPs $mathbb{S}$ over separable metrizable spaces having arbitrary large countable $mathfrak{Z}(mathbb{S})$ and that it is consistent with the axioms of $mathit{ZFC}$ that there is such a process with an uncountable Zhou ordinal.

In response to the coronavirus disease (COVID-19) outbreak, there is an ever-increasing number of national governments that are rolling out contact-tracing Apps to aid the containment of the virus. The first hugely contentious issue facing the Apps is the deployment framework, i.e. centralised or decentralised. Based on this, the debate branches out to the corresponding technologies that underpin these architectures, i.e. GPS, QR codes, and Bluetooth. This work conducts a pioneering review of the above scenarios and contributes a geolocation mapping of the current deployment. The vulnerabilities and the directions of research are identified, with a special focus on the Bluetooth-based decentralised scheme.

We present a new system, EEV, for verifying binarized neural networks (BNNs). We formulate BNN verification as a Boolean satisfiability problem (SAT) with reified cardinality constraints of the form $y = (x_1 + cdots + x_n le b)$, where $x_i$ and $y$ are Boolean variables possibly with negation and $b$ is an integer constant. We also identify two properties, specifically balanced weight sparsity and lower cardinality bounds, that reduce the verification complexity of BNNs. EEV contains both a SAT solver enhanced to handle reified cardinality constraints natively and novel training strategies designed to reduce verification complexity by delivering networks with improved sparsity properties and cardinality bounds. We demonstrate the effectiveness of EEV by presenting the first exact verification results for $ell_{infty}$-bounded adversarial robustness of nontrivial convolutional BNNs on the MNIST and CIFAR10 datasets. Our results also show that, depending on the dataset and network architecture, our techniques verify BNNs between a factor of ten to ten thousand times faster than the best previous exact verification techniques for either binarized or real-valued networks.

Passive optical networks (PON) can play a vital role in data centres and access fog solutions by providing scalable, cost and energy efficient architectures. This paper proposes a Mixed Integer Linear Programming (MILP) model to optimize the placement of virtual machines (VMs) over an energy efficient WDM-TDM AWGR PON based data centre architecture. In this optimization, the use of VMs and their requirements affect the optimum number of servers utilized in the data centre when minimizing the power consumption and enabling more efficient utilization of servers is considered. Two power consumption minimization objectives were examined for up to 20 VMs with different computing and networking requirements. The results indicate that considering the minimization of the processing and networking power consumption in the allocation of VMs in the WDM-TDM AWGR PON can reduce the networking power consumption by up to 70% compared to the minimization of the processing power consumption.

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly logical foundations while ITPs are meant for formalizing existing proofs rather than problem solving. We aim to create a simple human-friendly logical system for mathematical problem solving. We picked the case study of Euclidean geometry as it can be easily visualized, has simple logic, and yet potentially offers many high-school problems of various difficulty levels. To make the environment user friendly, we abandoned strict logic required by ITPs, allowing to infer topological facts from pictures. We present our system for Euclidean geometry, together with a graphical application GeoLogic, similar to GeoGebra, which allows users to interactively study and prove properties about the geometrical setup.

We consider the problem of efficiently simulating population protocols. In the population model, we are given a distributed system of $n$ agents modeled as identical finite-state machines. In each time step, a pair of agents is selected uniformly at random to interact. In an interaction, agents update their states according to a common transition function. We empirically and analytically analyze two classes of simulators for this model.

First, we consider sequential simulators executing one interaction after the other. Key to the performance of these simulators is the data structure storing the agents' states. For our analysis, we consider plain arrays, binary search trees, and a novel Dynamic Alias Table data structure.

Secondly, we consider batch processing to efficiently update the states of multiple independent agents in one step. For many protocols considered in literature, our simulator requires amortized sub-constant time per interaction and is fast in practice: given a fixed time budget, the implementation of our batched simulator is able to simulate population protocols several orders of magnitude larger compared to the sequential competitors, and can carry out $2^{50}$ interactions among the same number of agents in less than 400s.

We present a novel numerical scheme to approximate the solution map $smapsto u(s) := mathcal{L}^{-s}f$ to partial differential equations involving fractional elliptic operators. Reinterpreting $mathcal{L}^{-s}$ as interpolation operator allows us to derive an integral representation of $u(s)$ which includes solutions to parametrized reaction-diffusion problems. We propose a reduced basis strategy on top of a finite element method to approximate its integrand. Unlike prior works, we deduce the choice of snapshots for the reduced basis procedure analytically. Avoiding further discretization, the integral is interpreted in a spectral setting to evaluate the surrogate directly. Its computation boils down to a matrix approximation $L$ of the operator whose inverse is projected to a low-dimensional space, where explicit diagonalization is feasible. The universal character of the underlying $s$-independent reduced space allows the approximation of $(u(s))_{sin(0,1)}$ in its entirety. We prove exponential convergence rates and confirm the analysis with a variety of numerical examples.

Further improvements are proposed in the second part of this investigation to avoid inversion of $L$. Instead, we directly project the matrix to the reduced space, where its negative fractional power is evaluated. A numerical comparison with the predecessor highlights its competitive performance.