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 establish the functional convex order results for two scaled McKean-Vlasov processes $X=(X_{t})_{tin[0, T]}$ and $Y=(Y_{t})_{tin[0, T]}$ defined by

[egin{cases} dX_{t}=(alpha X_{t}+eta)dt+sigma(t, X_{t}, mu_{t})dB_{t}, quad X_{0}in L^{p}(mathbb{P}),\ dY_{t}=(alpha Y_{t},+eta)dt+ heta(t, Y_{t}, u_{t})dB_{t}, quad Y_{0}in L^{p}(mathbb{P}). end{cases}] If we make the convexity and monotony assumption (only) on $sigma$ and if $sigmaleq heta$ with respect to the partial matrix order, the convex order for the initial random variable $X_0 leq Y_0$ can be propagated to the whole path of process $X$ and $Y$. That is, if we consider a convex functional $F$ with polynomial growth defined on the path space, we have $mathbb{E}F(X)leqmathbb{E}F(Y)$; for a convex functional $G$ defined on the product space involving the path space and its marginal distribution space, we have $mathbb{E},Gig(X, (mu_t)_{tin[0, T]}ig)leq mathbb{E},Gig(Y, ( u_t)_{tin[0, T]}ig)$ under appropriate conditions. The symmetric setting is also valid, that is, if $ heta leq sigma$ and $Y_0 leq X_0$ with respect to the convex order, then $mathbb{E},F(Y) leq mathbb{E},F(X)$ and $mathbb{E},Gig(Y, ( u_t)_{tin[0, T]}ig)leq mathbb{E},G(X, (mu_t)_{tin[0, T]})$. The proof is based on several forward and backward dynamic programming and the convergence of the Euler scheme of the McKean-Vlasov equation.

We study SLE$_{kappa}$ theory with elements of Quasi-Sure Stochastic Analysis through Aggregation. Specifically, we show how the latter can be used to construct the SLE$_{kappa}$ traces quasi-surely (i.e. simultaneously for a family of probability measures with certain properties) for $kappa in mathcal{K}cap mathbb{R}_+ setminus ([0, epsilon) cup {8})$, for any $epsilon>0$ with $mathcal{K} subset mathbb{R}_{+}$ a nontrivial compact interval, i.e. for all $kappa$ that are not in a neighborhood of zero and are different from $8$. As a by-product of the analysis, we show in this language a version of the continuity in $kappa$ of the SLE$_{kappa}$ traces for all $kappa$ in compact intervals as above.

We investigate the evolution in time of the position of a fixed number inthe insertion tableau when the Robinson-Schensted-Knuth algorithm is applied to asequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministiccurve.

Let $G=(V,E)$ be a finite graph and $M_G$ be the centered Hardy-Littlewood maximal operator defined there. We found the optimal value $C_{G,p}$ such that the inequality $$Var_{p}(M_{G}f)le C_{G,p}Var_{p}(f)$$ holds for every every $f:V o mathbb{R},$ where $Var_p$ stands for the $p$-variation, when: (i)$G=K_n$ (complete graph) and $pin [frac{ln(4)}{ln(6)},infty)$ or $G=K_4$ and $pin (0,infty)$;(ii) $G=S_n$(star graph) and $1ge pge frac{1}{2}$; $pin (0,frac{1}{2})$ and $nge C(p)<infty$ or $G=S_3$ and $pin (1,infty).$ We also found the optimal value $L_{G,2}$ such that the inequality $$|M_{G}f|_2le L_{G,2}|f|_2$$ holds for every $f:V o mathbb{R}$, when: (i)$G=K_n$ and $nge 3$;(ii)$G=S_n$ and $nge 3.$

This is an expanded version of the talk given be the first author at the conference "Topology, Geometry, and Dynamics: Rokhlin - 100". The purpose of this talk was to explain our current results on classification of rational symplectic 4-manifolds equipped with an anti-symplectic involution. Detailed exposition will appear elsewhere.

Consider an infinite planar graph with uniform polynomial growth of degree d > 2. Many examples of such graphs exhibit similar geometric and spectral properties, and it has been conjectured that this is necessary. We present a family of counterexamples. In particular, we show that for every rational d > 2, there is a planar graph with uniform polynomial growth of degree d on which the random walk is transient, disproving a conjecture of Benjamini (2011).

By a well-known theorem of Benjamini and Schramm, such a graph cannot be a unimodular random graph. We also give examples of unimodular random planar graphs of uniform polynomial growth with unexpected properties. For instance, graphs of (almost sure) uniform polynomial growth of every rational degree d > 2 for which the speed exponent of the walk is larger than 1/d, and in which the complements of all balls are connected. This resolves negatively two questions of Benjamini and Papasoglou (2011).

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.

The paper proposes a polynomial formula for solution quadratic congruences in $mathbb{Z}_p$. This formula gives the correct answer for quadratic residue and zeroes for quadratic nonresidue. The general form of the formula for $p=3 ; m{mod},4$, $p=5 ; m{mod},8$ and for $p=9 ; m{mod},16$ are suggested.

We equip the type A diagrammatic Hecke category with a special derivation, so that after specialization to characteristic p it becomes a p-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. We conjecture that the $p$-dg Grothendieck group is isomorphic to the Iwahori-Hecke algebra, equipping it with a basis which may differ from both the Kazhdan-Lusztig basis and the p-canonical basis. More precise conjectures will be found in the sequel.

Here are some other results contained in this paper. We provide an incomplete proof of the classification of all degree +2 derivations on the diagrammatic Hecke category, and a complete proof of the classification of those derivations for which the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. In particular, our special derivation is unique up to duality and equivalence. We prove that no such derivation exists in simply-laced types outside of finite and affine type A. We also examine a particular Bott-Samelson bimodule in type A_7, which is indecomposable in characteristic 2 but decomposable in all other characteristics. We prove that this Bott-Samelson bimodule admits no nontrivial fantastic filtrations in any characteristic, which is the analogue in the p-dg setting of being indecomposable.

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.

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.

For an odd prime $p$, we determined the Brown-Peterson cohomology of $BPU_n$ in dimensions $-(2p-2)leq ileq 2p+2$, where $BPU_n$ is the classifying space of the projective unitary group $PU_n$. We construct a family of $p$-torsion classes $eta_{p,k}in BP^{2p^{k+1}+2}(BPU_n)$ for $p|n$ and $kgeq 0$ and identify their images under the Thom map with well understood cohomology classes in $H^*(BPU_n;mathbb{Z}_{(p)})$.

We prove that there are no irreducible representations of $B_n$ of dimension $n+1$ for $ngeq 10.$

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".

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.

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 $M_{Sigma}$.

Let $H$ be an infinite dimensional, reflexive, separable Hilbert space and $NA(H)$ the class of all norm-attainble operators on $H.$ In this note, we study an implicit scheme for a canonical representation of nonexpansive contractions in norm-attainable classes.

We introduce natural deformation classes of generalized K"ahler structures using the Courant symmetry group. We show that these yield natural extensions of the notions of K"ahler class and K"ahler cone to generalized K"ahler geometry. Lastly we show that the generalized K"ahler-Ricci flow preserves this generalized K"ahler cone, and the underlying real Poisson tensor.

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.

The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement structures allows the existence of general asymptotic regional gradient observer and we give a sufficient condition for such asymptotic regional gradient observer in general case. We also show that, there exists a dynamical system for the considered system is not general asymptotic gradient observer in the usual sense, but it may be general asymptotic regional gradient observer. Then, for this purpose we present various results related to different types of sensor structures, domains and boundary conditions in two dimensional distributed diffusion systems

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

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.

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.

We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.

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.

Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and necessary. In this paper, we present the third version of Automata Tutor, a tool for helping teachers and students in large courses on automata and formal languages. The second version of Automata Tutor supported automatic grading and feedback for finite-automata constructions and has already been used by thousands of users in dozens of countries. This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models - e.g., from regular expressions to nondeterministic finite automata. Moreover, for several problems, this new version also enables teachers and students to automatically generate new problem instances. We also present the results of a survey run on a class of 950 students, which shows very positive results about the usability and usefulness of the tool.

Large-scale pretrained language models are the major driving force behind recent improvements in performance on the Winograd Schema Challenge, a widely employed test of common sense reasoning ability. We show, however, with a new diagnostic dataset, that these models are sensitive to linguistic perturbations of the Winograd examples that minimally affect human understanding. Our results highlight interesting differences between humans and language models: language models are more sensitive to number or gender alternations and synonym replacements than humans, and humans are more stable and consistent in their predictions, maintain a much higher absolute performance, and perform better on non-associative instances than associative ones. Overall, humans are correct more often than out-of-the-box models, and the models are sometimes right for the wrong reasons. Finally, we show that fine-tuning on a large, task-specific dataset can offer a solution to these issues.

Event-related potential (ERP) speller can be utilized in device control and communication for locked-in or severely injured patients. However, problems such as inter-subject performance instability and ERP-illiteracy are still unresolved. Therefore, it is necessary to predict classification performance before performing an ERP speller in order to use it efficiently. In this study, we investigated the correlations with ERP speller performance using a resting-state before an ERP speller. In specific, we used spectral power and functional connectivity according to four brain regions and five frequency bands. As a result, the delta power in the frontal region and functional connectivity in the delta, alpha, gamma bands are significantly correlated with the ERP speller performance. Also, we predicted the ERP speller performance using EEG features in the resting-state. These findings may contribute to investigating the ERP-illiteracy and considering the appropriate alternatives for each user.

With the increase in use of Unmanned Aerial Vehicles (UAVs)/drones, it is important to detect and identify causes of failure in real time for proper recovery from a potential crash-like scenario or post incident forensics analysis. The cause of crash could be either a fault in the sensor/actuator system, a physical damage/attack, or a cyber attack on the drone's software. In this paper, we propose novel architectures based on deep Convolutional and Long Short-Term Memory Neural Networks (CNNs and LSTMs) to detect (via Autoencoder) and classify drone mis-operations based on sensor data. The proposed architectures are able to learn high-level features automatically from the raw sensor data and learn the spatial and temporal dynamics in the sensor data. We validate the proposed deep-learning architectures via simulations and experiments on a real drone. Empirical results show that our solution is able to detect with over 90% accuracy and classify various types of drone mis-operations (with about 99% accuracy (simulation data) and upto 88% accuracy (experimental data)).

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]]).

We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of these properties. We also investigate new computational tasks related to such combinations. Thus, we advance the state-of-the-art in fair division of mixed manna.

Device fingerprints like sensor pattern noise (SPN) are widely used for provenance analysis and image authentication. Over the past few years, the rapid advancement in digital photography has greatly reshaped the pipeline of image capturing process on consumer-level mobile devices. The flexibility of camera parameter settings and the emergence of multi-frame photography algorithms, especially high dynamic range (HDR) imaging, bring new challenges to device fingerprinting. The subsequent study on these topics requires a new purposefully built image dataset. In this paper, we present the Warwick Image Forensics Dataset, an image dataset of more than 58,600 images captured using 14 digital cameras with various exposure settings. Special attention to the exposure settings allows the images to be adopted by different multi-frame computational photography algorithms and for subsequent device fingerprinting. The dataset is released as an open-source, free for use for the digital forensic community.

Many efforts of research are devoted to semantic role labeling (SRL) which is crucial for natural language understanding. Supervised approaches have achieved impressing performances when large-scale corpora are available for resource-rich languages such as English. While for the low-resource languages with no annotated SRL dataset, it is still challenging to obtain competitive performances. Cross-lingual SRL is one promising way to address the problem, which has achieved great advances with the help of model transferring and annotation projection. In this paper, we propose a novel alternative based on corpus translation, constructing high-quality training datasets for the target languages from the source gold-standard SRL annotations. Experimental results on Universal Proposition Bank show that the translation-based method is highly effective, and the automatic pseudo datasets can improve the target-language SRL performances significantly.

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.

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.

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.

We propose a new method for realistic human motion transfer using a generative adversarial network (GAN), which generates a motion video of a target character imitating actions of a source character, while maintaining high authenticity of the generated results. We tackle the problem by decoupling and recombining the posture information and appearance information of both the source and target characters. The innovation of our approach lies in the use of the projection of a reconstructed 3D human model as the condition of GAN to better maintain the structural integrity of transfer results in different poses. We further introduce a detail enhancement net to enhance the details of transfer results by exploiting the details in real source frames. Extensive experiments show that our approach yields better results both qualitatively and quantitatively than the state-of-the-art methods.

This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern semantically enriched language-independent MathML formulae in 2020. Additionally, we describe our plans to improve the accessibility and discoverability of mathematical knowledge in Wikimedia projects further.

Deep neural networks have exhibited promising performance in image super-resolution (SR). Most SR models follow a hierarchical architecture that contains both the cell-level design of computational blocks and the network-level design of the positions of upsampling blocks. However, designing SR models heavily relies on human expertise and is very labor-intensive. More critically, these SR models often contain a huge number of parameters and may not meet the requirements of computation resources in real-world applications. To address the above issues, we propose a Hierarchical Neural Architecture Search (HNAS) method to automatically design promising architectures with different requirements of computation cost. To this end, we design a hierarchical SR search space and propose a hierarchical controller for architecture search. Such a hierarchical controller is able to simultaneously find promising cell-level blocks and network-level positions of upsampling layers. Moreover, to design compact architectures with promising performance, we build a joint reward by considering both the performance and computation cost to guide the search process. Extensive experiments on five benchmark datasets demonstrate the superiority of our method over existing methods.

How to generate testing scenario libraries for connected and automated vehicles (CAVs) is a major challenge faced by the industry. In previous studies, to evaluate maneuver challenge of a scenario, surrogate models (SMs) are often used without explicit knowledge of the CAV under test. However, performance dissimilarities between the SM and the CAV under test usually exist, and it can lead to the generation of suboptimal scenario libraries. In this paper, an adaptive testing scenario library generation (ATSLG) method is proposed to solve this problem. A customized testing scenario library for a specific CAV model is generated through an adaptive process. To compensate the performance dissimilarities and leverage each test of the CAV, Bayesian optimization techniques are applied with classification-based Gaussian Process Regression and a new-designed acquisition function. Comparing with a pre-determined library, a CAV can be tested and evaluated in a more efficient manner with the customized library. To validate the proposed method, a cut-in case study was performed and the results demonstrate that the proposed method can further accelerate the evaluation process by a few orders of magnitude.

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 decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in a game against its antagonistic environment. Depending on the specification, optimal strategies might be simple or quite complex, for example having to use (possibly infinite) memory. Hence, research strives to understand which settings allow for simple strategies.

In 2005, Gimbert and Zielonka provided a complete characterization of preference relations (a formal framework to model specifications and game objectives) that admit memoryless optimal strategies for both players. In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory -- finite or infinite -- is almost always required. Despite much effort, the exact frontiers of the class of preference relations that admit finite-memory optimal strategies still elude us.

In this work, we establish a complete characterization of preference relations that admit optimal strategies using arena-independent finite memory, generalizing the work of Gimbert and Zielonka to the finite-memory case. We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games. Finally, we pinpoint the boundaries of our results with regard to the literature: our work completely covers the case of arena-independent memory (e.g., multiple parity objectives, lower- and upper-bounded energy objectives), and paves the way to the arena-dependent case (e.g., multiple lower-bounded energy objectives).

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.

High-resolution remote sensing images (HRRSIs) contain substantial ground object information, such as texture, shape, and spatial location. Semantic segmentation, which is an important task for element extraction, has been widely used in processing mass HRRSIs. However, HRRSIs often exhibit large intraclass variance and small interclass variance due to the diversity and complexity of ground objects, thereby bringing great challenges to a semantic segmentation task. In this paper, we propose a new end-to-end semantic segmentation network, which integrates lightweight spatial and channel attention modules that can refine features adaptively. We compare our method with several classic methods on the ISPRS Vaihingen and Potsdam datasets. Experimental results show that our method can achieve better semantic segmentation results. The source codes are available at https://github.com/lehaifeng/SCAttNet.

Stabilizing multi-steered articulated vehicles in backward motion is a complex task for any human driver. Unless the vehicle is accurately steered, its structurally unstable joint-angle kinematics during reverse maneuvers can cause the vehicle segments to fold and enter a jack-knife state. In this work, a model predictive path-following controller is proposed enabling automatic low-speed steering control of multi-steered articulated vehicles, comprising a car-like tractor and an arbitrary number of trailers with passive or active steering. The proposed path-following controller is tailored to follow nominal paths that contains full state and control-input information, and is designed to satisfy various physical constraints on the vehicle states as well as saturations and rate limitations on the tractor's curvature and the trailer steering angles. The performance of the proposed model predictive path-following controller is evaluated in a set of simulations for a multi-steered 2-trailer with a car-like tractor where the last trailer has steerable wheels.

In learning-to-rank for information retrieval, a ranking model is automatically learned from the data and then utilized to rank the sets of retrieved documents. Therefore, an ideal ranking model would be a mapping from a document set to a permutation on the set, and should satisfy two critical requirements: (1)~it should have the ability to model cross-document interactions so as to capture local context information in a query; (2)~it should be permutation-invariant, which means that any permutation of the inputted documents would not change the output ranking. Previous studies on learning-to-rank either design uni-variate scoring functions that score each document separately, and thus failed to model the cross-document interactions; or construct multivariate scoring functions that score documents sequentially, which inevitably sacrifice the permutation invariance requirement. In this paper, we propose a neural learning-to-rank model called SetRank which directly learns a permutation-invariant ranking model defined on document sets of any size. SetRank employs a stack of (induced) multi-head self attention blocks as its key component for learning the embeddings for all of the retrieved documents jointly. The self-attention mechanism not only helps SetRank to capture the local context information from cross-document interactions, but also to learn permutation-equivariant representations for the inputted documents, which therefore achieving a permutation-invariant ranking model. Experimental results on three large scale benchmarks showed that the SetRank significantly outperformed the baselines include the traditional learning-to-rank models and state-of-the-art Neural IR models.