The main aim of this paper is to detect dynamical properties of the Gy"orgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, the analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques. Namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, and approximate entropy. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. Moreover, the three-stage system of nested subintervals of flow rates, for which in every level the 0-1 test for chaos and approximate entropy was computed, is showing the same pattern. The study leads to an open problem whether the set of flow rate parameters has Cantor like structure.

In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of this is to study the soliton solutions of the coupled Fokas-Lenells(FL) equations for any positive integer $N$, which have more complex linear relationship than the analogues reported before. We first analyze the spectral analysis of the Lax pair associated with a $(N+1) imes (N+1)$ matrix spectral problem for the $N$-component FL equations. Then, a kind of RH problem is successfully formulated. By introducing the special conditions of irregularity and reflectionless case, the $N$-soliton solution formula of the equations are derived through solving the corresponding RH problem. Furthermore, take $N=2,3$ and $4$ for examples, the localized structures and dynamic propagation behavior of their soliton solutions and their interactions are discussed by some graphical analysis.

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.

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

Let $(K, u)$ be a valued field, the notions of emph{augmented valuation}, of emph{limit augmented valuation} and of emph{admissible family} of valuations enable to give a description of any valuation $mu$ of $K [x]$ extending $ u$. In the case where the field $K$ is algebraically closed, this description is particularly simple and we can reduce it to the notions of emph{minimal pair} and emph{pseudo-convergent family}. Let $(K, u )$ be a henselian valued field and $ar u$ the unique extension of $ u$ to the algebraic closure $ar K$ of $K$ and let $mu$ be a valuation of $ K [x]$ extending $ u$, we study the extensions $armu$ from $mu$ to $ar K [x]$ and we give a description of the valuations $armu_i$ of $ar K [x]$ which are the extensions of the valuations $mu_i$ belonging to the admissible family associated with $mu$.

In this paper, we give an alternate definition of the well-known Parry measure on an aperiodic subshift of finite type using correlation between the forbidden words. We use the concept of the local escape rate to obtain this definition. We also compute Perron eigenvectors corresponding to the Perron root of the associated adjacency matrix.

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.

Let $E$ be the self-similar set generated by the {it iterated function system} {[ f_0(x)=frac{x}{eta},quad f_1(x)=frac{x+1}{eta}, quad f_{eta+1}=frac{x+eta+1}{eta} ]}with $etage 3$. {Then} $E$ is a self-similar set with complete {overlaps}, i.e., $f_{0}circ f_{eta+1}=f_{1}circ f_1$, but $E$ is not totally self-similar.

We investigate all its generating iterated function systems, give the spectrum of $E$, and determine the Hausdorff dimension and Hausdorff measure of $E$ and of the sets which contain all points in $E$ having finite or infinite different triadic codings.

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

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

Let $Nge 2$ and $ hoin(0,1/N^2]$. The homogenous Cantor set $E$ is the self-similar set generated by the iterated function system

[

left{f_i(x)= ho x+frac{i(1- ho)}{N-1}: i=0,1,ldots, N-1 ight}.

]

Let $s=dim_H E$ be the Hausdorff dimension of $E$, and let $mu=mathcal H^s|_E$ be the $s$-dimensional Hausdorff measure restricted to $E$. In this paper we describe, for each $xin E$, the pointwise lower $s$-density $Theta_*^s(mu,x)$ and upper $s$-density $Theta^{*s}(mu, x)$ of $mu$ at $x$. This extends some early results of Feng et al. (2000). Furthermore, we determine two critical values $a_c$ and $b_c$ for the sets

[

E_*(a)=left{xin E: Theta_*^s(mu, x)ge a ight}quad extrm{and}quad E^*(b)=left{xin E: Theta^{*s}(mu, x)le b ight}

] respectively, such that $dim_H E_*(a)>0$ if and only if $a<a_c$, and that $dim_H E^*(b)>0$ if and only if $b>b_c$. We emphasize that both values $a_c$ and $b_c$ are related to the Thue-Morse type sequences, and our strategy to find them relies on ideas from open dynamics and techniques from combinatorics on words.

The problem of minimizing an entropy functional subject to linear constraints is a useful example of partially finite convex programming. In the 1990s, Borwein and Lewis provided broad and easy-to-verify conditions that guarantee strong duality for such problems. Their approach is to construct a function in the quasi-relative interior of the relevant infinite-dimensional set, which assures the existence of a point in the core of the relevant finite-dimensional set. We revisit this problem, and provide an alternative proof by directly appealing to the definition of the core, rather than by relying on any properties of the quasi-relative interior. Our approach admits a minor relaxation of the linear independence requirements in Borwein and Lewis' framework, which allows us to work with certain piecewise-defined moment functions precluded by their conditions. We provide such a computed example that illustrates how this relaxation may be used to tame observed Gibbs phenomenon when the underlying data is discontinuous. The relaxation illustrates the understanding we may gain by tackling partially-finite problems from both the finite-dimensional and infinite-dimensional sides. The comparison of these two approaches is informative, as both proofs are constructive.

The congruence subgroup problem for a finitely generated group $Gamma$ and $Gleq Aut(Gamma)$ asks whether the map $hat{G} o Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(G,Gamma ight)$? Here $hat{X}$ denotes the profinite completion of $X$. In the case $G=Aut(Gamma)$ we denote $Cleft(Gamma ight)=Cleft(Aut(Gamma),Gamma ight)$.

Let $Gamma$ be a finitely generated group, $ar{Gamma}=Gamma/[Gamma,Gamma]$, and $Gamma^{*}=ar{Gamma}/tor(ar{Gamma})congmathbb{Z}^{(d)}$. Denote $Aut^{*}(Gamma)= extrm{Im}(Aut(Gamma) o Aut(Gamma^{*}))leq GL_{d}(mathbb{Z})$. In this paper we show that when $Gamma$ is nilpotent, there is a canonical isomorphism $Cleft(Gamma ight)simeq C(Aut^{*}(Gamma),Gamma^{*})$. In other words, $Cleft(Gamma ight)$ is completely determined by the solution to the classical congruence subgroup problem for the arithmetic group $Aut^{*}(Gamma)$.

In particular, in the case where $Gamma=Psi_{n,c}$ is a finitely generated free nilpotent group of class $c$ on $n$ elements, we get that $C(Psi_{n,c})=C(mathbb{Z}^{(n)})={e}$ whenever $ngeq3$, and $C(Psi_{2,c})=C(mathbb{Z}^{(2)})=hat{F}_{omega}$ = the free profinite group on countable number of generators.

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].

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 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.

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 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.

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.

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 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.

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.

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.

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.

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)).

Image analysis in the field of digital pathology has recently gained increased popularity. The use of high-quality whole slide scanners enables the fast acquisition of large amounts of image data, showing extensive context and microscopic detail at the same time. Simultaneously, novel machine learning algorithms have boosted the performance of image analysis approaches. In this paper, we focus on a particularly powerful class of architectures, called Generative Adversarial Networks (GANs), applied to histological image data. Besides improving performance, GANs also enable application scenarios in this field, which were previously intractable. However, GANs could exhibit a potential for introducing bias. Hereby, we summarize the recent state-of-the-art developments in a generalizing notation, present the main applications of GANs and give an outlook of some chosen promising approaches and their possible future applications. In addition, we identify currently unavailable methods with potential for future applications.

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.