We show that the local equivalence class of the collapsed link Floer complex $cCFL^infty(L)$, together with many $Upsilon$-type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants $Upsilon_L(t)$ and $ u^+(L)$ when $L$ is a link and we prove that they give a lower bound for the slice genus $g_4(L)$. Furthermore, in the last section of the paper we study the homology group $HFL'(L)$ and its behaviour under unoriented cobordisms. We obtain that a normalized version of the $upsilon$-set, introduced by Ozsv'ath, Stipsicz and Szab'o, produces a lower bound for the 4-dimensional smooth crosscap number $gamma_4(L)$.

This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers' second moment estimates. In this paper we establish such results in a very general framework. Namely, given any subhomogeneous function (a notion to be defined) $f: mathbb{R}^n o mathbb{R}$, we derive a necessary and sufficient condition on the approximating function $psi$ for guaranteeing that a generic element $fcirc g$ in the $G$-orbit of $f$ is $psi$-approximable; that is, $|fcirc g(mathbf{v})| le psi(|mathbf{v}|)$ for infinitely many $mathbf{v} in mathbb{Z}^n$. We also deduce a sufficient condition in the case of uniform approximation. Here, $G$ can be any closed subgroup of $operatorname{ASL}_n(mathbb{R})$ satisfying certain axioms that allow for the use of Rogers-type estimates.

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node in the class of methods with optimal number of communication steps takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique we show that all proposed methods with stochastic oracle can be additionally parallelized at each node.

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these results is an extension of the Shintani theta lift to meromorphic modular forms of positive even weight.

Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)in G^{(k)}$ such that $w(g_1,...,g_k)=1$. Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit's conjecture, and prove that $N_w(g) ge |G|^{k-2}$, where $g$ is a $w$-value in $G$, for finite groups $G$ of odd order and nilpotency class 2. If $w$ is a word in two variables, we further show that $N_w(g) ge |G|$, where $g$ is a $w$-value in $G$ for finite groups $G$ of nilpotency class 2. In addition, for $p$ a prime, we show that finite $p$-groups $G$, with two distinct irreducible complex character degrees, satisfy the generalized Amit conjecture for words $w_k =[x_1,y_1]...[x_k,y_k]$ with $k$ a natural number; that is, for $g$ a $w_k$-value in $G$ we have $N_{w_k}(g) ge |G|^{2k-1}$.

Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.

Let $f colon X o X$ be a surjective endomorphism of a normal projective surface. When $operatorname{deg} f geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology).

Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables, are characterised by having only logarithmic singularities along all the boundaries of the positive geometry. However, physical observables have logarithmic singularities just for a subset of theories. Thus, it becomes crucial to understand whether a similar paradigm can underlie their structure in more general cases. In this paper we start a systematic investigation of a geometric-combinatorial characterisation of differential forms with non-logarithmic singularities, focusing on projective polytopes and related meromorphic forms with multiple poles. We introduce the notions of covariant forms and covariant pairings. Covariant forms have poles only along the boundaries of the given polytope; moreover, their leading Laurent coefficients along any of the boundaries are still covariant forms on the specific boundary. Whereas meromorphic forms in covariant pairing with a polytope are associated to a specific (signed) triangulation, in which poles on spurious boundaries do not cancel completely, but their order is lowered. These meromorphic forms can be fully characterised if the polytope they are associated to is viewed as the restriction of a higher dimensional one onto a hyperplane. The canonical form of the latter can be mapped into a covariant form or a form in covariant pairing via a covariant restriction. We show how the geometry of the higher dimensional polytope determines the structure of these differential forms. Finally, we discuss how these notions are related to Jeffrey-Kirwan residues and cosmological polytopes.

We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the correpsonding lambda-cosine transforms.

We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem.

In this paper, we derive a formula for the sums of powers of the first $n$ positive integers that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression. Moreover, as a by-product, we express the Bernoulli polynomials in terms of the hyperharmonic polynomials and the Stirling numbers of the second kind.

Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor. We consider the system $mathcal L (H)$ of all sets of lengths of $H$ and study when $mathcal L (H)$ contains or is contained in a system $mathcal L (H')$ of a Krull monoid $H'$ with finite class group $G'$, prime divisors in all classes and Davenport constant $mathsf D (G')=mathsf D (G)$. Among others, we show that if $G$ is either cyclic of order $m ge 7$ or an elementary $2$-group of rank $m-1 ge 6$, and $G'$ is any group which is non-isomorphic to $G$ but with Davenport constant $mathsf D (G')=mathsf D (G)$, then the systems $mathcal L (H)$ and $mathcal L (H')$ are incomparable.

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.

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.

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.

In this work we study the dynamical behavior Tonelli Lagrangian systems defined on the tangent bundle of the torus $mathbb{T}^2=mathbb{R}^2 / mathbb{Z}^2$. We prove that the Lagrangian flow restricted to a high energy level $ E_L^{-1}(c)$ (i.e $ c> c_0(L)$) has positive topological entropy if the flow satisfies the Kupka-Smale propriety in $ E_L^{-1}(c)$ (i.e, all closed orbit with energy $c$ are hyperbolic or elliptic and all heteroclinic intersections are transverse on $E_L^{-1}(c)$). The proof requires the use of well-known results in Aubry-Mather's Theory.

ErdH{o}s and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and R"odl asked whether there is some integer $qge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset has 3 triples with distinct colors, and $N$ is double exponential in $n$. We make the first nontrivial progress on this problem by providing a $q$-coloring with this property for all $qgeq 9$, where $N$ is exponential in $n^{2+cq}$ and $c>0$ is an absolute constant.

We present the correspondence between Lax integrable systems with spectral parameter on a Riemann surface, and Conformal Field Theories, in quite general set-up suggested earlier by the author. This correspondence turns out to give a prequantization of the integrable systems in question.

Quantum computing has evolved quickly in recent years and is showing significant benefits in a variety of fields. Malware analysis is one of those fields that could also take advantage of quantum computing. The combination of software used to locate the most frequent hashes and $n$-grams between benign and malicious software (KiloGram) and a quantum search algorithm could be beneficial, by loading the table of hashes and $n$-grams into a quantum computer, and thereby speeding up the process of mapping $n$-grams to their hashes. The first phase will be to use KiloGram to find the top-$k$ hashes and $n$-grams for a large malware corpus. From here, the resulting hash table is then loaded into a quantum machine. A quantum search algorithm is then used search among every permutation of the entangled key and value pairs to find the desired hash value. This prevents one from having to re-compute hashes for a set of $n$-grams, which can take on average $O(MN)$ time, whereas the quantum algorithm could take $O(sqrt{N})$ in the number of table lookups to find the desired hash values.

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.

Recent advances in deep learning have facilitated the design of speaker verification systems that directly input raw waveforms. For example, RawNet extracts speaker embeddings from raw waveforms, which simplifies the process pipeline and demonstrates competitive performance. In this study, we improve RawNet by scaling feature maps using various methods. The proposed mechanism utilizes a scale vector that adopts a sigmoid non-linear function. It refers to a vector with dimensionality equal to the number of filters in a given feature map. Using a scale vector, we propose to scale the feature map multiplicatively, additively, or both. In addition, we investigate replacing the first convolution layer with the sinc-convolution layer of SincNet. Experiments performed on the VoxCeleb1 evaluation dataset demonstrate the effectiveness of the proposed methods, and the best performing system reduces the equal error rate by half compared to the original RawNet. Expanded evaluation results obtained using the VoxCeleb1-E and VoxCeleb-H protocols marginally outperform existing state-of-the-art systems.

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.

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.

This paper considers the multi-group multicast beamforming optimization problem, for which the optimal solution has been unknown due to the non-convex and NP-hard nature of the problem. By utilizing the successive convex approximation numerical method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure for both the quality-of-service (QoS) problem and the max-min fair (MMF) problem. The optimal structure brings valuable insights into multicast beamforming: We show that the notion of uplink-downlink duality can be generalized to the multicast beamforming problem. The optimal multicast beamformer is a weighted MMSE filter based on a group-channel direction: a generalized version of the optimal downlink multi-user unicast beamformer. We also show that there is an inherent low-dimensional structure in the optimal multicast beamforming solution independent of the number of transmit antennas, leading to efficient numerical algorithm design, especially for systems with large antenna arrays. We propose efficient algorithms to compute the multicast beamformer based on the optimal beamforming structure. Through asymptotic analysis, we characterize the asymptotic behavior of the multicast beamformers as the number of antennas grows, and in turn, provide simple closed-form approximate multicast beamformers for both the QoS and MMF problems. This approximation offers practical multicast beamforming solutions with a near-optimal performance at very low computational complexity for large-scale antenna systems.

A recently introduced classifier, called SS3, has shown to be well suited to deal with early risk detection (ERD) problems on text streams. It obtained state-of-the-art performance on early depression and anorexia detection on Reddit in the CLEF's eRisk open tasks. SS3 was created to deal with ERD problems naturally since: it supports incremental training and classification over text streams, and it can visually explain its rationale. However, SS3 processes the input using a bag-of-word model lacking the ability to recognize important word sequences. This aspect could negatively affect the classification performance and also reduces the descriptiveness of visual explanations. In the standard document classification field, it is very common to use word n-grams to try to overcome some of these limitations. Unfortunately, when working with text streams, using n-grams is not trivial since the system must learn and recognize which n-grams are important "on the fly". This paper introduces t-SS3, an extension of SS3 that allows it to recognize useful patterns over text streams dynamically. We evaluated our model in the eRisk 2017 and 2018 tasks on early depression and anorexia detection. Experimental results suggest that t-SS3 is able to improve both current results and the richness of visual explanations.

For future Internet of Things (IoT)-based Big Data applications (e.g., smart cities/transportation), wireless data collection from ubiquitous massive smart sensors with limited spectrum bandwidth is very challenging. On the other hand, to interpret the meaning behind the collected data, it is also challenging for edge fusion centers running computing tasks over large data sets with limited computation capacity. To tackle these challenges, by exploiting the superposition property of a multiple-access channel and the functional decomposition properties, the recently proposed technique, over-the-air computation (AirComp), enables an effective joint data collection and computation from concurrent sensor transmissions. In this paper, we focus on a single-antenna AirComp system consisting of $K$ sensors and one receiver (i.e., the fusion center). We consider an optimization problem to minimize the computation mean-squared error (MSE) of the $K$ sensors' signals at the receiver by optimizing the transmitting-receiving (Tx-Rx) policy, under the peak power constraint of each sensor. Although the problem is not convex, we derive the computation-optimal policy in closed form. Also, we comprehensively investigate the ergodic performance of AirComp systems in terms of the average computation MSE and the average power consumption under Rayleigh fading channels with different Tx-Rx policies. For the computation-optimal policy, we prove that its average computation MSE has a decay rate of $O(1/sqrt{K})$, and our numerical results illustrate that the policy also has a vanishing average power consumption with the increasing $K$, which jointly show the computation effectiveness and the energy efficiency of the policy with a large number of sensors.

The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical mixing time. In this article, we deal with analog quantum algorithms for mixing. First, we provide an analog quantum algorithm that given a Markov chain, allows us to sample from its stationary distribution in a time that scales as the sum of the square root of the classical mixing time and the square root of the classical hitting time. Our algorithm makes use of the framework of interpolated quantum walks and relies on Hamiltonian evolution in conjunction with von Neumann measurements.

There also exists a different notion for quantum mixing: the problem of sampling from the limiting distribution of quantum walks, defined in a time-averaged sense. In this scenario, the quantum mixing time is defined as the time required to sample from a distribution that is close to this limiting distribution. Recently we provided an upper bound on the quantum mixing time for Erd"os-Renyi random graphs [Phys. Rev. Lett. 124, 050501 (2020)]. Here, we also extend and expand upon our findings therein. Namely, we provide an intuitive understanding of the state-of-the-art random matrix theory tools used to derive our results. In particular, for our analysis we require information about macroscopic, mesoscopic and microscopic statistics of eigenvalues of random matrices which we highlight here. Furthermore, we provide numerical simulations that corroborate our analytical findings and extend this notion of mixing from simple graphs to any ergodic, reversible, Markov chain.

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.

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to quickly return matrix entries upon demand. Either way, the construction can become costly due to non-trivial material parameters entering the equations, multigrid codes requiring cascades of matrices that depend upon each other, or dynamic adaptive mesh refinement that necessitates the recomputation of matrix entries or the whole equation system throughout the solve. We propose that these constructions can be performed concurrently with the multigrid cycles. Initial geometric matrices and low accuracy integrations kickstart the multigrid, while improved assembly data is fed to the solver as and when it becomes available. The time to solution is improved as we eliminate an expensive preparation phase traditionally delaying the actual computation. We eliminate algorithmic latency. Furthermore, we desynchronise the assembly from the solution process. This anarchic increase of the concurrency level improves the scalability. Assembly routines are notoriously memory- and bandwidth-demanding. As we work with iteratively improving operator accuracies, we finally propose the use of a hierarchical, lossy compression scheme such that the memory footprint is brought down aggressively where the system matrix entries carry little information or are not yet available with high accuracy.

We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.

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.

We present results showing the capability of concrete-based information processing substrate in the signal classification task in accordance with in materio computing paradigm. As the Reservoir Computing is a suitable model for describing embedded in materio computation, we propose that this type of presented basic construction unit can be used as a source for "reservoir of states" necessary for simple tuning of the readout layer. In that perspective, buildings constructed from computing concrete could function as a highly parallel information processor for smart architecture. We present an electrical characterization of the set of samples with different additive concentrations followed by a dynamical analysis of selected specimens showing fingerprints of memfractive properties. Moreover, on the basis of obtained parameters, classification of the signal waveform shapes can be performed in scenarios explicitly tuned for a given device terminal.

For any finite Galois field extension $mathsf{K}/mathsf{F}$, with Galois group $G = mathrm{Gal}(mathsf{K}/mathsf{F})$, there exists an element $alpha in mathsf{K}$ whose orbit $Gcdotalpha$ forms an $mathsf{F}$-basis of $mathsf{K}$. Such an $alpha$ is called a normal element and $Gcdotalpha$ is a normal basis. We introduce a probabilistic algorithm for testing whether a given $alpha in mathsf{K}$ is normal, when $G$ is either a finite abelian or a metacyclic group. The algorithm is based on the fact that deciding whether $alpha$ is normal can be reduced to deciding whether $sum_{g in G} g(alpha)g in mathsf{K}[G]$ is invertible; it requires a slightly subquadratic number of operations. Once we know that $alpha$ is normal, we show how to perform conversions between the working basis of $mathsf{K}/mathsf{F}$ and the normal basis with the same asymptotic cost.

One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems via the averaging method. We propose four symbolic algorithms to implement the averaging method. The first algorithm is based on the change of polar coordinates that allows one to transform a considered differential system to the normal form of averaging. The second algorithm is used to derive the solutions of certain differential systems associated to the unperturbed term of the normal of averaging. The third algorithm exploits the partial Bell polynomials and allows one to compute the integral formula of the averaged functions at any order. The last algorithm is based on the aforementioned algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The implementation of our algorithms is discussed and evaluated using several examples. The experimental results have extended the existing relevant results for certain classes of differential systems.

We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in both parameters. This yields two natural questions: 1) Does there exist an initial counter value that makes the language universal? 2) Does there exist a sufficiently high ceiling so that the bounded language is universal? Despite the fact that unparameterized universality is Ackermann-complete and that these problems seem to reduce to checking basic structural properties of the underlying automaton, we show that in fact both problems are undecidable. We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.

Rescue vessels are the main actors in maritime safety and rescue operations. At the same time, aerial drones bring a significant advantage into this scenario. This paper presents the research directions of the AutoSOS project, where we work in the development of an autonomous multi-robot search and rescue assistance platform capable of sensor fusion and object detection in embedded devices using novel lightweight AI models. The platform is meant to perform reconnaissance missions for initial assessment of the environment using novel adaptive deep learning algorithms that efficiently use the available sensors and computational resources on drones and rescue vessel. When drones find potential objects, they will send their sensor data to the vessel to verity the findings with increased accuracy. The actual rescue and treatment operation are left as the responsibility of the rescue personnel. The drones will autonomously reconfigure their spatial distribution to enable multi-hop communication, when a direct connection between a drone transmitting information and the vessel is unavailable.

With the rapidly worldwide spread of Coronavirus disease (COVID-19), it is of great importance to conduct early diagnosis of COVID-19 and predict the time that patients might convert to the severe stage, for designing effective treatment plan and reducing the clinicians' workloads. In this study, we propose a joint classification and regression method to determine whether the patient would develop severe symptoms in the later time, and if yes, predict the possible conversion time that the patient would spend to convert to the severe stage. To do this, the proposed method takes into account 1) the weight for each sample to reduce the outliers' influence and explore the problem of imbalance classification, and 2) the weight for each feature via a sparsity regularization term to remove the redundant features of high-dimensional data and learn the shared information across the classification task and the regression task. To our knowledge, this study is the first work to predict the disease progression and the conversion time, which could help clinicians to deal with the potential severe cases in time or even save the patients' lives. Experimental analysis was conducted on a real data set from two hospitals with 422 chest computed tomography (CT) scans, where 52 cases were converted to severe on average 5.64 days and 34 cases were severe at admission. Results show that our method achieves the best classification (e.g., 85.91% of accuracy) and regression (e.g., 0.462 of the correlation coefficient) performance, compared to all comparison methods. Moreover, our proposed method yields 76.97% of accuracy for predicting the severe cases, 0.524 of the correlation coefficient, and 0.55 days difference for the converted time.

Most studies on speaker verification systems focus on long-duration utterances, which are composed of sufficient phonetic information. However, the performances of these systems are known to degrade when short-duration utterances are inputted due to the lack of phonetic information as compared to the long utterances. In this paper, we propose a method that compensates for the performance degradation of speaker verification for short utterances, referred to as "crop aggregating". The proposed method adopts an ensemble-based design to improve the stability and accuracy of speaker verification systems. The proposed method segments an input utterance into several short utterances and then aggregates the segment embeddings extracted from the segmented inputs to compose a speaker embedding. Then, this method simultaneously trains the segment embeddings and the aggregated speaker embedding. In addition, we also modified the teacher-student learning method for the proposed method. Experimental results on different input duration using the VoxCeleb1 test set demonstrate that the proposed technique improves speaker verification performance by about 45.37% relatively compared to the baseline system with 1-second test utterance condition.

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given distance is not exceed. We provide a mathematical programming framework for the problem and different resolution strategies. First, we propose a Mixed Integer Non Linear Programming formulation, and derive properties of the problem that allow us to project the continuous variables out avoiding the nonlinear constraints, resulting in an equivalent pure integer programming formulation. Since the number of constraints in the integer programming formulation is large and the constraints are, in general, difficult to handle, we propose two branch-&-cut approaches that avoid the complete enumeration of the constraints resulting in more efficient procedures. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.

We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings.

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Sigma$ and a stochastic memoryless map $Psi$. After that, we extend the result to the class of large scale systems in which: $Sigma$ consists of many sub-systems; and $Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.

In this technical report we give an elementary introduction to Quantum Computing for non-physicists. In this introduction we describe in detail some of the foundational Quantum Algorithms including: the Deutsch-Jozsa Algorithm, Shor's Algorithm, Grocer Search, and Quantum Counting Algorithm and briefly the Harrow-Lloyd Algorithm. Additionally we give an introduction to Solomonoff Induction, a theoretically optimal method for prediction. We then attempt to use Quantum computing to find better algorithms for the approximation of Solomonoff Induction. This is done by using techniques from other Quantum computing algorithms to achieve a speedup in computing the speed prior, which is an approximation of Solomonoff's prior, a key part of Solomonoff Induction. The major limiting factors are that the probabilities being computed are often so small that without a sufficient (often large) amount of trials, the error may be larger than the result. If a substantial speedup in the computation of an approximation of Solomonoff Induction can be achieved through quantum computing, then this can be applied to the field of intelligent agents as a key part of an approximation of the agent AIXI.

Different state-of-the-art methods of the detection of schizophrenia symptoms based on the estimation of text coherence have been analyzed. The analysis of a text at the level of phrases has been suggested. The method based on the graph of the consistency of phrases has been proposed to evaluate the semantic coherence and the cohesion of a text. The semantic coherence, cohesion, and other linguistic features (lexical diversity, lexical density) have been taken into account to form feature vectors for the training of a model-classifier. The training of the classifier has been performed on the set of English-language interviews. According to the retrieved results, the impact of each feature on the output of the model has been analyzed. The results obtained can indicate that the proposed method based on the graph of the consistency of phrases may be used in the different tasks of the detection of mental illness.

Graphic design is everywhere — it’s used in traditional marketing efforts like billboards and fliers, and more importantly, it’s used in nearly every single digital marketing initiative from web design to social media marketing. If you’re a business that’s working with a digital marketing agency for any number of marketing campaigns (especially web design), it’s […]

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Are you looking for a content management system (CMS) that will help you create the digital content you need? With so many options on the market, it’s challenging to know which one is the best CMS software for your business. On this page, we’ll take a look at the six best CMS’s for website development […]

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By Evan H. DeLucia Courtesy of EOS Critics of biofuels like ethanol argue they are an unsustainable use of land. But with careful management, next-generation grass-based biofuels can net climate savings and improve their ecosystems. As the world seeks strategies … Continue reading →

As Android and iOS continue to dominate the mobile market, businesses need to develop applications that meet the diverse requirements of each operating system. Launching native mobile applications for Apple App Store and Google Play Store is going to be a long and expensive process. Not every business has adequate time and funds for developing native mobile applications. That is why cross-platform app frameworks have been rising to popularity.

Choosing cross-platform mobile app development services enables organizations to add their presence to both Android and iOS markets. Xamarin, recently acquired by Microsoft, is one of the best frameworks for cross-platform mobile app development. Rich features, agility, and cost-effectiveness make it an ideal choice for building cross-platform apps.

The Cannabis Issue As we look ahead to sunnier days, few things are as satisfying as a scoop of nice, cold ice cream.…

Once upon a time, Clint Eastwood, a notoriously outspoken conservative in supposedly liberal Hollywood, had no problem at all with cops who employed their own unconventional extra-legal brand of law enforcement (see: Dirty Harry). Today, in Richard Jewell, he really doesn't like the FBI.…

Uncut Gems is one of those "his own worst enemy" capers. You know, the kind of movie where you sit there for two hours watching some doofus constantly trip over his own laces — usually figuratively, sometimes literally — on the way to a personal epiphany about how all his bad choices and lack of useful self-awareness have led him to whatever unpleasant place they lead him to.…