We study the time-averaged flux in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flux is given by a variational formulation involving paths of the density and flux. We give sufficient conditions under which the large deviations of a given time averaged flux is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5.

In 1978, Dwight Duffus---editor-in-chief of the journal "Order" from 2010 to 2018 and chair of the Mathematics Department at Emory University from 1991 to 2005---wrote that "it is not obvious that $P$ is connected and $P^P$ isomorphic to $Q^Q$ implies that $Q$ is connected," where $P$ and $Q$ are finite non-empty posets. We show that, indeed, under these hypotheses $Q$ is connected and $Pcong Q$.

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.

We study a two-stage reneging queue with Poisson arrivals, exponential services, and two levels of exponential reneging behaviors, extending the popular Erlang A model that assumes a constant reneging rate. We derive approximate analytical formulas representing performance measures for the two-stage queue following the Markov chain decomposition approach. Our formulas not only give accurate results spanning the heavy-traffic to the light-traffic regimes, but also provide insight into capacity decisions.

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.

In this note, we establish a local maximum principle along Ricci flow under scaling invariant curvature condition. This unifies the known preservation of nonnegativity results along Ricci flow with unbounded curvature. By combining with the Dirichlet heat kernel estimates, we also give a more direct proof of Hochard's localized version of a maximum principle given by R. Bamler, E. Cabezas-Rivas, and B. Wilking on the lower bound of curvature conditions.

In recent years, a large class of nuclear $C^ast$-algebras have been classified, modulo an assumption on the Universal Coefficient Theorem (UCT). We think this assumption is redundant and propose a strategy for proving it. Indeed, following the original proof of the classification theorem, we propose bridging the gap between reduction theorems and examples. While many such bridges are possible, various approximate ideal structures appear quite promising.

In this paper, we give new constructions of strongly regular Cayley graphs on abelian groups as generalizations of a series of known constructions: the construction of covering extended building sets in finite fields by Xia (1992), the product construction of Menon-Hadamard difference sets by Turyn (1984), and the construction of Paley type partial difference sets by Polhill (2010). Then, we obtain new large families of strongly regular Cayley graphs of Latin square type or negative Latin square type.

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.

We study the two-parameter quadratic sieve for a general test function. We prove, under some very general assumptions, that the function considered by Barban and Vehov [BV68] and Graham [Gra78] for this problem is optimal up to the second-order term. We determine that second-order term explicitly.

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.

Robots operating in household environments must find objects on shelves, under tables, and in cupboards. Previous work often formulate the object search problem as a POMDP (Partially Observable Markov Decision Process), yet constrain the search space in 2D. We propose a new approach that enables the robot to efficiently search for objects in 3D, taking occlusions into account. We model the problem as an object-oriented POMDP, where the robot receives a volumetric observation from a viewing frustum and must produce a policy to efficiently search for objects. To address the challenge of large state and observation spaces, we first propose a per-voxel observation model which drastically reduces the observation size necessary for planning. Then, we present a novel octree-based belief representation which captures beliefs at different resolutions and supports efficient exact belief update. Finally, we design an online multi-resolution planning algorithm that leverages the resolution layers in the octree structure as levels of abstractions to the original POMDP problem. Our evaluation in a simulated 3D domain shows that, as the problem scales, our approach significantly outperforms baselines without resolution hierarchy by 25%-35% in cumulative reward. We demonstrate the practicality of our approach on a torso-actuated mobile robot searching for objects in areas of a cluttered lab environment where objects appear on surfaces at different heights.

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.

In this work, we investigate multi-task learning as a way of pre-training models for classification tasks in digital pathology. It is motivated by the fact that many small and medium-size datasets have been released by the community over the years whereas there is no large scale dataset similar to ImageNet in the domain. We first assemble and transform many digital pathology datasets into a pool of 22 classification tasks and almost 900k images. Then, we propose a simple architecture and training scheme for creating a transferable model and a robust evaluation and selection protocol in order to evaluate our method. Depending on the target task, we show that our models used as feature extractors either improve significantly over ImageNet pre-trained models or provide comparable performance. Fine-tuning improves performance over feature extraction and is able to recover the lack of specificity of ImageNet features, as both pre-training sources yield comparable performance.

Large transformer-based language models have been shown to be very effective in many classification tasks. However, their computational complexity prevents their use in applications requiring the classification of a large set of candidates. While previous works have investigated approaches to reduce model size, relatively little attention has been paid to techniques to improve batch throughput during inference. In this paper, we introduce the Cascade Transformer, a simple yet effective technique to adapt transformer-based models into a cascade of rankers. Each ranker is used to prune a subset of candidates in a batch, thus dramatically increasing throughput at inference time. Partial encodings from the transformer model are shared among rerankers, providing further speed-up. When compared to a state-of-the-art transformer model, our approach reduces computation by 37% with almost no impact on accuracy, as measured on two English Question Answering datasets.

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.

Temporal event segmentation of a long video into coherent events requires a high level understanding of activities' temporal features. The event segmentation problem has been tackled by researchers in an offline training scheme, either by providing full, or weak, supervision through manually annotated labels or by self-supervised epoch based training. In this work, we present a continual learning perceptual prediction framework (influenced by cognitive psychology) capable of temporal event segmentation through understanding of the underlying representation of objects within individual frames. Our framework also outputs attention maps which effectively localize and track events-causing objects in each frame. The model is tested on a wildlife monitoring dataset in a continual training manner resulting in $80\%$ recall rate at $20\%$ false positive rate for frame level segmentation. Activity level testing has yielded $80\%$ activity recall rate for one false activity detection every 50 minutes.

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.

The quantum Fourier transform brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction and division operations are presented. The proposed arithmetic operations can perform non-modular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two's complement, absolute value and comparison operations are also presented by using the proposed QFT based addition and subtraction operations.

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)).