cssi/SciSciGPT-SciSciNet huggingface dataset:
A general convergence result for the Ricci flow in higher dimensions

Let (M,g0) be a compact Riemannian manifold of dimension n≥4. We show that the normalized Ricci flow deforms g0 to a constant curvature metric, provided that (M,g0)×R has positive isotropic curvature. This condition is stronger than two-positive flag curvature but weaker than two-positive curvature operator
Three Dimensions of Knot Coloring

The 1926 paper of J. W. Alexander and G. B. Briggs suggests a simple combinato- rial invariant by coloring the crossings of a knot diagram. It is equivalent to the well-known Fox n-coloring of arcs and lesser-known Dehn n-coloring of regions. The equivalence of the three approaches to knot coloring is presented.
Subwavelength metal grating metamaterial for polarization-selective optical antireflection coating

A metamaterial structure consisting of a one-dimensional metal/air-gap subwavelength grating is investigated for optical antireflection for a germanium surface in the infrared regime. For incident light polarized perpendicularly to the metal grating lines, the metamaterial exhibits effective dielectric properties, and the Fabry–Perot-like resonance results in the elimination of the reflection and the enhancement of optical transmission. It is found that the subwavelength grating metamaterial antireflection structure does not require a deep-subwavelength grating period, which is advantageous for device fabrication. Optical transmittance as high as 93.4% with complete elimination of the reflection is shown in the midwave infrared range.
Bitcoin: A Natural Oligopoly

Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to capture miners' incentives to invest in equipment. In our model, n miners compete for a prize of fixed size. Each miner chooses an investment q_i, incurring cost c_i q_i, and then receives reward (q_i^alpha)/(sum_j q_j^alpha), for some alpha >= 1. When c_i = c_j for all i,j, and alpha = 1, there is a unique equilibrium where all miners invest equally. However, we prove that under seemingly mild deviations from this model, equilibrium outcomes become drastically more centralized. In particular, - When costs are asymmetric, if miner i chooses to invest, then miner j has market share at least 1-c_j/c_i. That is, if miner j has costs that are (e.g.) 20% lower than those of miner i, then miner j must control at least 20% of the total mining power. - In the presence of economies of scale (alpha > 1), every market participant has a market share of at least 1-1/(alpha), implying that the market features at most alpha/(alpha - 1) miners in total. We discuss the implications of our results for the future design of cryptocurrencies. In particular, our work further motivates the study of protocols that minimize "orphaned" blocks, proof-of-stake protocols, and incentive compatible protocols.
Towards tight(er) bounds for the Excluded Grid Theorem

Abstract We study the Excluded Grid Theorem, a fundamental structural result in graph theory, that was proved by Robertson and Seymour in their seminal work on graph minors. The theorem states that there is a function f : Z + → Z + , such that for every integer g > 0 , every graph of treewidth at least f ( g ) contains the ( g × g ) -grid as a minor. For every integer g > 0 , let f ( g ) be the smallest value for which the theorem holds. Establishing tight bounds on f ( g ) is an important graph-theoretic question. Robertson and Seymour showed that f ( g ) = Ω ( g 2 log ⁡ g ) must hold. For a long time, the best known upper bounds on f ( g ) were super-exponential in g. The first polynomial upper bound of f ( g ) = O ( g 98 poly log ⁡ g ) was proved by Chekuri and Chuzhoy. It was later improved to f ( g ) = O ( g 36 poly log ⁡ g ) , and then to f ( g ) = O ( g 19 poly log ⁡ g ) . In this paper we further improve this bound to f ( g ) = O ( g 9 poly log ⁡ g ) . We believe that our proof is significantly simpler than the proofs of the previous bounds. Moreover, while there are natural barriers that seem to prevent previous methods from yielding tight bounds for the theorem, it seems conceivable that the techniques proposed in this paper can lead to even tighter bounds on f ( g ) .
UAV assisted public safety communications with LTE-Advanced HetNets and FeICIC

Establishing a reliable communication infrastructure at an emergency site is a crucial task for mission-critical and real-time public safety communications (PSC). To this end, use of unmanned aerial vehicles (UAVs) has recently received extensive interest for PSC to establish reliable connectivity in a heterogeneous network (HetNet) environment. These UAVs can be deployed as unmanned aerial base stations (UABSs) as part of the HetNet infrastructure. In this article, we explore the role of agile UABSs in LTE-Advanced HetNets by applying 3GPP Release-11 further-enhanced inter-cell interference coordination (Fe-ICIC) and cell range expansion (CRE) techniques. Through simulations, we compare the system-wide 5th percentile spectral efficiency (SE) when UABSs are deployed in a hexagonal grid and when their locations are optimized using a genetic algorithm, while also jointly optimizing the CRE and the FeICIC parameters. Our simulation results show that at optimized UABS locations, the 3GPP Release-11 FeICIC with reduced power subframes can provide considerably better 5th percentile SE than the 3GPP Release-10 with almost blank subframes.
Pattern decomposition with complex combinatorial constraints: application to materials discovery

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.
Weakly Cohen–Macaulay posets and a class of finite-dimensional graded quadratic algebras

Abstract To a finite ranked poset Γ we associate a finite-dimensional graded quadratic algebra R Γ . Assuming Γ satisfies a combinatorial condition known as uniform, R Γ is related to a well-known algebra, the splitting algebra A Γ . First introduced by Gelfand, Retakh, Serconek, and Wilson, splitting algebras originated from the problem of factoring non-commuting polynomials. Given a finite ranked poset Γ, we ask: Is R Γ Koszul? The Koszulity of R Γ is related to a combinatorial topology property of Γ called Cohen–Macaulay. Kloefkorn and Shelton proved that if Γ is a finite ranked cyclic poset, then Γ is Cohen–Macaulay if and only if Γ is uniform and R Γ is Koszul. We define a new generalization of Cohen–Macaulay, weakly Cohen–Macaulay. This new class includes non-uniform posets and posets with disconnected open subintervals. Using a spectral sequence associated to Γ and the notion of a noncommutative Koszul filtration for R Γ , we prove: if Γ is a finite ranked cyclic poset, then Γ is weakly Cohen–Macaulay if and only if R Γ is Koszul. In addition, we prove that Γ is Cohen–Macaulay if and only if Γ is uniform and weakly Cohen–Macaulay.
Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others’ ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time.
A weighted renormalized curvature for manifolds with density

We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient $v_3$ in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are stable with respect to the associated $\mathcal{W}$-functional.
Are the incompressible 3d Navier–Stokes equations locally ill-posed in the natural energy space?

Abstract An important open problem in the theory of the Navier–Stokes equations is the uniqueness of the Leray–Hopf weak solutions with L 2 initial data. In this paper we give sufficient conditions for non-uniqueness in terms of spectral properties of a natural linear operator associated to scale-invariant solutions recently constructed in [8] . If the spectral conditions are satisfied, non-uniqueness and ill-posedness can appear for quite benign compactly supported data, just at the borderline of applicability of the classical perturbation theory. The verification of the spectral conditions seems to be approachable by numerical simulations which involve only smooth functions.
Adams filtration and generalized Hurewicz maps for infinite loopspaces

We study the Hurewicz map $$\begin{aligned} h_*: \pi _*(X) \rightarrow R_*(\Omega ^{\infty }X) \end{aligned}$$ where $$\Omega ^{\infty }X$$ is the 0th space of a spectrum X, and $$R_*$$ is the generalized homology theory associated to a connective commutative S-algebra R. We prove that the decreasing filtration of the domain associated to an R-based Adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative S-algebra $$\Sigma ^{\infty }(\Omega ^{\infty }X)_+$$ . The proof of our main theorem makes much use of composition properties of this filtration and its interaction with Topological Andre–Quillen homology. An application is a Connectivity Theorem: localize away from $$(p-1)!$$ and suppose X is $$(c-1)$$ -connected with $$c>0$$ . If $$\alpha \in \pi _*(X)$$ has Adams filtration s and $$|\alpha | < cp^s$$ , then $$h_*(\alpha )=0 \in R_*(\Omega ^{\infty }X)$$ . When specialized to mod p homology, this implies a Finiteness Theorem: if $$H^*(X;{{\mathbb {Z}}}/p)$$ is finitely presented as a module over the Steenrod algebra, then the image of the Hurewicz map in $$H_*(\Omega ^{\infty }X;{{\mathbb {Z}}}/p)$$ is finite. We illustrate these theorems with calculations of the mod 2 Hurewicz image of BO, its connected covers, and $$\Omega ^{\infty }tmf$$ , and the mod p Hurewicz image of all the spaces in the BP and $$BP\langle n \rangle $$ spectra. En route, we get new proofs of theorems of Milnor and Wilson. In the special case when X is the suspension spectrum of a space Z and $$R = H{{\mathbb {Z}}}/2$$ , we recover results announced by Lannes and Zarati in the 1980s, relating the Adams filtration of $$\pi _*^S(Z)$$ to Dyer-Lashof length in $$H_*(QZ;{{\mathbb {Z}}}/2)$$ , and generalize them to all primes p. For any X, we also get parallel results for the Hurewicz map for Morava E-theory, where $$\pi _*(X)$$ is now given the Adams–Novikov filtration.
Capturing the Drunk Robber on a Graph

We show that the expected time for a smart "cop"' to catch a drunk "robber" on an $n$-vertex graph is at most $n + {\rm o}(n)$. More precisely, let $G$ be a simple, connected, undirected graph with distinguished points $u$ and $v$ among its $n$ vertices. A cop begins at $u$ and a robber at $v$; they move alternately from vertex to adjacent vertex. The robber moves randomly, according to a simple random walk on $G$; the cop sees all and moves as she wishes, with the object of "capturing" the robber — that is, occupying the same vertex—in least expected time. We show that the cop succeeds in expected time no more than $n {+} {\rm o}(n)$. Since there are graphs in which capture time is at least $n {-} o(n)$, this is roughly best possible. We note also that no function of the diameter can be a bound on capture time.
Recurrent Novae — A Review

In recent years, recurrent nova eruptions are often observed very intensely in wide range of wavelengths from radio to optical to X-rays. Here I present selected highlights from recent multi-wavelength observations. The enigma of T Pyx is at the heart of this paper. While our current understanding of CV and symbiotic star evolution can explain why certain subset of recurrent novae have high accretion rate, that of T Pyx must be greatly elevated compared to the evolutionary mean. At the same time, we have extensive data to be able to estimate how the nova envelope was ejected in T Pyx, and it turns to be a rather complex tale. One suspects that envelope ejection in recurrent and classical novae in general is more complicated than the textbook descriptions. At the end of the review, I will speculate that these two may be connected.
Sentiment Adaptive End-to-End Dialog Systems

End-to-end learning framework is useful for building dialog systems for its simplicity in training and efficiency in model updating. However, current end-to-end approaches only consider user semantic inputs in learning and under-utilize other user information. Therefore, we propose to include user sentiment obtained through multimodal information (acoustic, dialogic and textual), in the end-to-end learning framework to make systems more user-adaptive and effective. We incorporated user sentiment information in both supervised and reinforcement learning settings. In both settings, adding sentiment information reduced the dialog length and improved the task success rate on a bus information search task. This work is the first attempt to incorporate multimodal user information in the adaptive end-to-end dialog system training framework and attained state-of-the-art performance.
Extension of Convolutional Neural Network with General Image Processing Kernels

We applied pre-defined kernels also known as filters or masks developed for image processing to convolution neural network. Instead of letting neural networks find its own kernels, we used 41 different general-purpose kernels of blurring, edge detecting, sharpening, discrete cosine transformation, etc. for the first layer of the convolution neural networks. This architecture, thus named as general filter convolutional neural network (GFNN), can reduce training time by 30% with a better accuracy compared to the regular convolutional neural network (CNN). GFNN also can be trained to achieve 90% accuracy with only 500 samples. Furthermore, even though these kernels are not specialized for the MNIST dataset, we achieved 99.56% accuracy without ensemble nor any other special algorithms.
Arnold-Thom gradient conjecture for the arrival time

We prove conjectures of Rene Thom and Vladimir Arnold for C^2 solutions to the degenerate elliptic equation that is the level set equation for motion by mean curvature. We believe these results are the first instances of a general principle: Solutions of many degenerate equations behave as if they are analytic, even when they are not. If so, this would explain various conjectured phenomena.
Smoothness of Minkowski sum and generic rotations

Abstract Can the Minkowski sum of two convex bodies be made smoother by rotating one of them? We construct two C ∞ strictly convex plane bodies such that after any generic rotation (in the Baire category sense) of one of the summands the Minkowski sum is not C 5 . On the other hand, if for one of the bodies the zero set of the Gaussian curvature has countable spherical image, we show that any generic rotation makes their Minkowski sum as smooth as the summands. We also improve and clarify some previous results on smoothness of the Minkowski sum.
Predicting stock market movements using network science: an information theoretic approach

A stock market is considered as one of the highly complex systems, which consists of many components whose prices move up and down without having a clear pattern. The complex nature of a stock market challenges us on making a reliable prediction of its future movements. In this paper, we aim at building a new method to forecast the future movements of Standard & Poor’s 500 Index (S&P 500) by constructing time-series complex networks of S&P 500 underlying companies by connecting them with links whose weights are given by the mutual information of 60-min price movements of the pairs of the companies with the consecutive 5340 min price records. We showed that the changes in the strength distributions of the networks provide an important information on the network’s future movements. We built several metrics using the strength distributions and network measurements such as centrality, and we combined the best two predictors by performing a linear combination. We found that the combined predictor and the changes in S&P 500 show a quadratic relationship, and it allows us to predict the amplitude of the one step future change in S&P 500. The result showed significant fluctuations in S&P 500 Index when the combined predictor was high. In terms of making the actual index predictions, we built ARIMA models with and without inclusion of network measurements, and compared the predictive power of them. We found that adding the network measurements into the ARIMA models improves the model accuracy. These findings are useful for financial market policy makers as an indicator based on which they can interfere with the markets before the markets make a drastic change, and for quantitative investors to improve their forecasting models.
Security analysis and enhancement of model compressed deep learning systems under adversarial attacks

Thanks to recent machine learning model innovation and computing hardware advancement, the state-of-the-art of Deep Neural Network (DNN) is presenting human-level performance for many complex intelligent tasks in real-world applications. However, it also introduces ever-increasing security concerns for those intelligent systems. For example, the emerging adversarial attacks indicate that even very small and often imperceptible adversarial input perturbations can easily mislead the cognitive function of deep learning systems (DLS). Existing DNN adversarial studies are narrowly performed on the ideal software-level DNN models with a focus on single uncertainty factor, i.e. input perturbations, however, the impact of DNN model reshaping on adversarial attacks, which is introduced by various hardware-favorable techniques such as hash-based weight compression during modern DNN hardware implementation, has never been discussed. In this work, we for the first time investigate the multi-factor adversarial attack problem in practical model optimized deep learning systems by jointly considering the DNN model-reshaping (e.g. HashNet based deep compression) and the input perturbations. We first augment adversarial example generating method dedicated to the compressed DNN models by incorporating the software-based approaches and mathematical modeled DNN reshaping. We then conduct a comprehensive robustness and vulnerability analysis of deep compressed DNN models under derived adversarial attacks. A defense technique named "gradient inhibition" is further developed to ease the generating of adversarial examples thus to effectively mitigate adversarial attacks towards both software and hardware-oriented DNNs. Simulation results show that "gradient inhibition" can decrease the average success rate of adversarial attacks from 87.99% to 4.77% (from 86.74% to 4.64%) on MNIST (CIFAR-10) benchmark with marginal accuracy degradation across various DNNs.
Recovering a Hidden Community in a Preferential Attachment Graph

A message passing algorithm is derived for recovering a dense subgraph within a graph generated by a variation of the Barabasi-Albert preferential attachment model. The estimator is assumed to know the order of attachment, of the vertices. The derivation of the algorithm is based on belief propagation under an independence assumption. Two precursors to the message passing algorithm are analyzed: the first is a degree thresholding (DT) algorithm and the second is an algorithm based on the arrival times of the children (C) of a given vertex, where the children of a given vertex are the vertices that attached to it. Algorithm C significantly outperforms DT, showing it is beneficial to know the arrival times of the children, beyond simply knowing the number of them. For fixed fraction of vertices in the community, fixed number of new edges per arriving vertex, and fixed affinity between vertices in the community, the probability of error for recovering the label of a vertex is found as a function of the time of attachment, for either algorithm DT or C, in the large graph limit. By averaging over the time of attachment, the limit in probability of the fraction of label errors made over all vertices is identified, for either of the algorithms DT or C. An extended version of this paper is at arXiv 1801.06818, which also includes message passing for two symmetric communities.
A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks.

Abstract Background A better characterization of the early growth dynamics of an epidemic is needed to dissect the important drivers of disease transmission, refine existing transmission models, and improve disease forecasts. Materials and methods We introduce a 2-parameter generalized-growth model to characterize the ascending phase of an outbreak and capture epidemic profiles ranging from sub-exponential to exponential growth. We test the model against empirical outbreak data representing a variety of viral pathogens in historic and contemporary populations, and provide simulations highlighting the importance of sub-exponential growth for forecasting purposes. Results We applied the generalized-growth model to 20 infectious disease outbreaks representing a range of transmission routes. We uncovered epidemic profiles ranging from very slow growth (p = 0.14 for the Ebola outbreak in Bomi, Liberia (2014)) to near exponential (p > 0.9 for the smallpox outbreak in Khulna (1972), and the 1918 pandemic influenza in San Francisco). The foot-and-mouth disease outbreak in Uruguay displayed a profile of slower growth while the growth pattern of the HIV/AIDS epidemic in Japan was approximately linear. The West African Ebola epidemic provided a unique opportunity to explore how growth profiles vary by geography; analysis of the largest district-level outbreaks revealed substantial growth variations (mean p = 0.59, range: 0.14–0.97). The districts of Margibi in Liberia and Bombali and Bo in Sierra Leone had near-exponential growth, while the districts of Bomi in Liberia and Kenema in Sierra Leone displayed near constant incidences. Conclusions Our findings reveal significant variation in epidemic growth patterns across different infectious disease outbreaks and highlights that sub-exponential growth is a common phenomenon, especially for pathogens that are not airborne. Sub-exponential growth profiles may result from heterogeneity in contact structures or risk groups, reactive behavior changes, or the early onset of interventions strategies, and consideration of “deceleration parameters” may be useful to refine existing mathematical transmission models and improve disease forecasts.
DeepCodec: Adaptive sensing and recovery via deep convolutional neural networks

We develop a novel computational sensing framework for sensing and recovering structured signals. When trained on a set of representative signals, our framework learns to take undersampled measurements and recover signals from these measurements using a deep convolutional neural network. In other words, it learns a transformation from the original signals to a near-optimal number of undersampled measurements and the inverse transformation from measurements to signals. This is in contrast to conventional compressive sensing (CS) systems that use random linear measurements and convex optimization or iterative algorithms for signal recovery.
Non-uniform feature sampling for decision tree ensembles

We study the effectiveness of non-uniform randomized feature selection in decision tree classification. We experimentally evaluate two feature selection methodologies, based on information extracted from the provided dataset: (i) leverage scores-based and (ii) norm-based feature selection. Experimental evaluation of the proposed feature selection techniques indicate that such approaches might be more effective compared to naive uniform feature selection and moreover having comparable performance to the random forest algorithm [3].
The Orlik-Terao algebra and 2-formality

The Orlik-Solomon algebra is the cohomology ring of the complement of a hyperplane arrangement $\A \subseteq \C^n$; it is the quotient of an exterior algebra $\Lambda(V)$ on $|\A|$ generators. In \cite{ot1}, Orlik and Terao introduced a commutative analog $Sym(V^*)/I$ of the Orlik-Solomon algebra to answer a question of Aomoto and showed the Hilbert series depends only on the intersection lattice $L(\A)$. In \cite{fr}, Falk and Randell define the property of 2-formality; in this note we study the relation between 2-formality and the Orlik-Terao algebra. Our main result is a necessary and sufficient condition for 2-formality in terms of the quadratic component $I_2$ of the Orlik-Terao ideal $I$. The key is that 2-formality is determined by the tangent space $T_p(V(I_2))$ at a generic point $p$.
On the normal cycles of subanalytic sets

We present a very short and complete proof of the existence of the normal cycle of a subanalytic set. The approach is a blend of Morse theory and geometric integration theory and relies heavily on techniques from o-minimal geometry.
Building Ethically Bounded AI

The more AI agents are deployed in scenarios with possibly unexpected situations, the more they need to be flexible, adaptive, and creative in achieving the goal we have given them. Thus, a certain level of freedom to choose the best path to the goal is inherent in making AI robust and flexible enough. At the same time, however, the pervasive deployment of AI in our life, whether AI is autonomous or collaborating with humans, raises several ethical challenges. AI agents should be aware and follow appropriate ethical principles and should thus exhibit properties such as fairness or other virtues. These ethical principles should define the boundaries of AI’s freedom and creativity. However, it is still a challenge to understand how to specify and reason with ethical boundaries in AI agents and how to combine them appropriately with subjective preferences and goal specifications. Some initial attempts employ either a data-driven examplebased approach for both, or a symbolic rule-based approach for both. We envision a modular approach where any AI technique can be used for any of these essential ingredients in decision making or decision support systems, paired with a contextual approach to define their combination and relative weight. In a world where neither humans nor AI systems work in isolation, but are tightly interconnected, e.g., the Internet of Things, we also envision a compositional approach to building ethically bounded AI, where the ethical properties of each component can be fruitfully exploited to derive those of the overall system. In this paper we define and motivate the notion of ethically-bounded AI, we describe two concrete examples, and we outline some outstanding challenges.
Deterministic Preparation of Dicke States

The Dicke state Open image in new window is an equal-weight superposition of all n-qubit states with Hamming Weight k (i.e. all strings of length n with exactly k ones over a binary alphabet). Dicke states are an important class of entangled quantum states that among other things serve as starting states for combinatorial optimization quantum algorithms.
Interaction-aware Multi-agent Tracking and Probabilistic Behavior Prediction via Adversarial Learning

In order to enable high-quality decision making and motion planning of intelligent systems such as robotics and autonomous vehicles, accurate probabilistic predictions for surrounding interactive objects is a crucial prerequisite. Although many research studies have been devoted to making predictions on a single entity, it remains an open challenge to forecast future behaviors for multiple interactive agents simultaneously. In this work, we take advantage of the Generative Adversarial Network (GAN) due to its capability of distribution learning and propose a generic multi-agent probabilistic prediction and tracking framework which takes the interactions among multiple entities into account, in which all the entities are treated as a whole. However, since GAN is very hard to train, we make an empirical research and present the relationship between training performance and hyperparameter values with a numerical case study. The results imply that the proposed model can capture both the mean, variance and multi-modalities of the groundtruth distribution. Moreover, we apply the proposed approach to a real-world task of vehicle behavior prediction to demonstrate its effectiveness and accuracy. The results illustrate that the proposed model trained by adversarial learning can achieve a better prediction performance than other state-of-the-art models trained by traditional supervised learning which maximizes the data likelihood. The well-trained model can also be utilized as an implicit proposal distribution for particle filtered based Bayesian state estimation.
A Direct tilde{O}(1/epsilon) Iteration Parallel Algorithm for Optimal Transport

Optimal transportation, or computing the Wasserstein or ``earth mover's'' distance between two $n$-dimensional distributions, is a fundamental primitive which arises in many learning and statistical settings. We give an algorithm which solves the problem to additive $\epsilon$ accuracy with $\tilde{O}(1/\epsilon)$ parallel depth and $\tilde{O}\left(n^2/\epsilon\right)$ work. \cite{BlanchetJKS18, Quanrud19} obtained this runtime through reductions to positive linear programming and matrix scaling. However, these reduction-based algorithms use subroutines which may be impractical due to requiring solvers for second-order iterations (matrix scaling) or non-parallelizability (positive LP). Our methods match the previous-best work bounds by \cite{BlanchetJKS18, Quanrud19} while either improving parallelization or removing the need for linear system solves, and improve upon the previous best first-order methods running in time $\tilde{O}(\min(n^2 / \epsilon^2, n^{2.5} / \epsilon))$ \cite{DvurechenskyGK18, LinHJ19}. We obtain our results by a primal-dual extragradient method, motivated by recent theoretical improvements to maximum flow \cite{Sherman17}.
Universal Meshes for the Simulation of Brittle Fracture and Moving Boundary Problems

Universal meshes have recently appeared in the literature as a computationally efficient and robust paradigm for the generation of conforming simplicial meshes for domains with evolving boundaries. The main idea behind a universal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adjusting a few elements of the background mesh. In this manuscript we present the application of universal meshes to the simulation of brittle fracturing. To this extent, we provide a high level description of a crack propagation algorithm and showcase its capabilities. Alongside universal meshes for the simulation of brittle fracture, we provide other examples for which universal meshes prove to be a powerful tool, namely fluid flow past moving obstacles. Lastly, we conclude the manuscript with some remarks on the current state of universal meshes and future directions.
Training Classifiers For Feedback Control

One approach for feedback control using high dimensional and rich sensor measurements is to classify the measurement into one out of a finite set of situations, each situation corresponding to a (known) control action. This approach computes a control action without estimating the state. Such classifiers are typically learned from a finite amount of data using supervised machine learning algorithms. We model the closed-loop system resulting from control with feedback from classifier outputs as a piece-wise affine differential inclusion. We show how to train a linear classifier based on performance measures related to learning from data and the local stability properties of the resulting closed-loop system. The training method is based on the projected gradient descent algorithm. We demonstrate the advantage of training classifiers using control-theoretic properties on a case study involving navigation using range-based sensors.
The Omega spectrum for Pengelley’s $BoP$

We compute the homology of the spaces in the Omega spectrum for $BoP$. There is no torsion in $H_*(\underline{BoP}_{\; i})$ for $i \ge 2$, and things are only slightly more complicated for $i 6$. This completes the computation of all $H_*(\underline{MSU}_{\;*})$.
Blinded prediction of protein-ligand binding affinity using Amber thermodynamic integration for the 2018 D3R grand challenge 4.

In the framework of the 2018 Drug Design Data Resource grand challenge 4, blinded predictions on relative binding free energy were performed for a set of 39 ligands of the Cathepsin S protein. We leveraged the GPU-accelerated thermodynamic integration of Amber 18 to advance our computational prediction. When our entry was compared to experimental results, a good correlation was observed (Kendall’s τ: 0.62, Spearman’s ρ: 0.80 and Pearson’s R: 0.82). We designed a parallelized transformation map that placed ligands into several groups based on common alchemical substructures; TI transformations were carried out for each ligand to the relevant substructure, and between substructures. Our calculations were all conducted using the linear potential scaling scheme in Amber TI because we believe the softcore potential/dual-topology approach as implemented in current Amber TI is highly fault-prone for some transformations. The issue is illustrated by using two examples in which typical preparation for the dual-topology approach of Amber TI fails. Overall, the high accuracy of our prediction is a result of recent advances in force fields (ff14SB and GAFF), as well as rapid calculation of ensemble averages enabled by the GPU implementation of Amber. The success shown here in a blinded prediction strongly suggests that alchemical free energy calculation in Amber is a promising tool for future commercial drug design.
Conditional Hardness of Earth Mover Distance.

The Earth Mover Distance (EMD) between two sets of points $A, B \subseteq \mathbb{R}^d$ with $|A| = |B|$ is the minimum total Euclidean distance of any perfect matching between $A$ and $B$. One of its generalizations is asymmetric EMD, which is the minimum total Euclidean distance of any matching of size $|A|$ between sets of points $A,B \subseteq \mathbb{R}^d$ with $|A| \leq |B|$. The problems of computing EMD and asymmetric EMD are well-studied and have many applications in computer science, some of which also ask for the EMD-optimal matching itself. Unfortunately, all known algorithms require at least quadratic time to compute EMD exactly. Approximation algorithms with nearly linear time complexity in $n$ are known (even for finding approximately optimal matchings), but suffer from exponential dependence on the dimension. In this paper we show that significant improvements in exact and approximate algorithms for EMD would contradict conjectures in fine-grained complexity. In particular, we prove the following results: (1) Under the Orthogonal Vectors Conjecture, there is some $c>0$ such that EMD in $\Omega(c^{\log^* n})$ dimensions cannot be computed in truly subquadratic time. (2) Under the Hitting Set Conjecture, for every $\delta>0$, no truly subquadratic time algorithm can find a $(1 + 1/n^\delta)$-approximate EMD matching in $\omega(\log n)$ dimensions. (3) Under the Hitting Set Conjecture, for every $\eta = 1/\omega(\log n)$, no truly subquadratic time algorithm can find a $(1 + \eta)$-approximate asymmetric EMD matching in $\omega(\log n)$ dimensions.
Direct current stimulation boosts hebbian plasticity in vitro.

Abstract Background There is evidence that transcranial direct current stimulation (tDCS) can improve learning performance. Arguably, this effect is related to long term potentiation (LTP), but the precise biophysical mechanisms remain unknown. Hypothesis We propose that direct current stimulation (DCS) causes small changes in postsynaptic membrane potential during ongoing endogenous synaptic activity. The altered voltage dynamics in the postsynaptic neuron then modify synaptic strength via the machinery of endogenous voltage-dependent Hebbian plasticity. This hypothesis predicts that DCS should exhibit Hebbian properties, namely pathway specificity and associativity. Methods We studied the effects of DCS applied during the induction of LTP in the CA1 region of rat hippocampal slices and using a biophysical computational model. Results DCS enhanced LTP, but only at synapses that were undergoing plasticity, confirming that DCS respects Hebbian pathway specificity. When different synaptic pathways cooperated to produce LTP, DCS enhanced this cooperation, boosting Hebbian associativity. Further slice experiments and computer simulations support a model where polarization of postsynaptic pyramidal neurons drives these plasticity effects through endogenous Hebbian mechanisms. The model is able to reconcile several experimental results by capturing the complex interaction between the induced electric field, neuron morphology, and endogenous neural activity. Conclusions These results suggest that tDCS can enhance associative learning. We propose that clinical tDCS should be applied during tasks that induce Hebbian plasticity to harness this phenomenon, and that the effects should be task specific through their interaction with endogenous plasticity mechanisms. Models that incorporate brain state and plasticity mechanisms may help to improve prediction of tDCS outcomes.
Improving Usability, Efficiency, and Safety of UAV Path Planning through a Virtual Reality Interface

As the capability and complexity of UAVs continue to increase, specifying the complex 3D flight paths necessary for instructing gets more complicated. Immersive interfaces, such as those afforded by virtual reality (VR), have several unique traits which may improve the user’s ability to perceive and specify 3D information. These traits include stereoscopic depth cues which induce a sense of physical space as well as six degrees of freedom (DoF) natural head-pose and gesture interactions. This work introduces an open-source platform for 3D aerial path planning in VR and compares it to existing UAV piloting interfaces. Our study has found statistically significant improvements in safety over a manual control interface and in efficiency over a 2D touchscreen interface. The results illustrate that immersive interfaces provide a viable alternative to touchscreen interfaces for UAV path planning.
Sparse mean-reverting portfolios via penalized likelihood optimization

An optimization approach is proposed to construct sparse portfolios with mean-reverting price behaviors. Our objectives are threefold: (i) design a multi-asset long-short portfolio that best fits an Ornstein–Uhlenbeck process in terms of maximum likelihood, (ii) select portfolios with desirable characteristics of high mean reversion through penalization, and (iii) select a parsimonious portfolio using l0-regularization, i.e. find a small subset of a larger universe of assets that can be used for long and short positions. We present the full problem formulation, and develop a provably convergent algorithm for the nonsmooth, nonconvex objective based on partial minimization and projection. We demonstrate model functionalities on simulated and empirical price data, and include comparison with a pairs trading algorithm.
Quantum sampling and entropic uncertainty

In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation based on smooth min- entropy, the binary Shannon entropy of an observed outcome, and the probability of failure of a classical sampling strategy. We then show two applications of our new relation. First, we use it to develop a simple proof of a version of the Maassen and Uffink uncertainty relation. Second, we show how it may be applied to quantum random number generation.
Effects of Lattice O Atom Coordination and Pore Confinement on Selectivity Limitations for Ethane Oxidative Dehydrogenation Catalyzed by Vanadium-Oxo Species

M1-phase MoVTeNb mixed oxides contain V-oxo species isolated by dispersion in the Mo-oxo framework and one-dimensional heptagonal micropores that tightly enclose C2H6 molecules. These oxides cataly...
Testing for Multiple-Horizon Predictability: Direct Regression Based versus Implication Based

Research in finance and macroeconomics has routinely employed multiple horizons to test asset return predictability. In a simple predictive regression model, we find the popular scaled test can have zero power when the predictor is not sufficiently persistent. A new test based on implication of the short-run model is suggested and is shown to be uniformly more powerful than the scaled test. The new test can accommodate multiple predictors. Compared with various other widely used tests, simulation experiments demonstrate remarkable finite-sample performance. We reexamine the predictive ability of various popular predictors for aggregate equity premium.Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.
High-resolution absorption coefficient and refractive index spectra of carbon monoxide gas at millimeter and submillimeter wavelengths

The use of dispersive Fourier transform techniques in interferometry allows the measurement of absorption coefficient and refractive index spectra with great precision. This paper presents the absorption coefficient and refractive index spectra of carbon monoxide (CO) gas at millimeter and submillimeter wavelengths. To assess rotational lines of CO, the gas was measured at four different pressures, giving insight into the behavior of the spectral lines with varying parameters. The measurements in this study demonstrate that varying the pressure of the gas affects only the amplitude of the absorption lines and not their exact position. This is critical in air pollution studies when trying to single out a specific gas from a field sample with unknown constituents
Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices

We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\R^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies log-Sobolev inequality and $f$ has bounded Hessian. Notably, we do not assume convexity or bounds on higher derivatives. We also prove convergence guarantees in R\'enyi divergence of order $q > 1$ assuming the limit of ULA satisfies either log-Sobolev or Poincar\'e inequality.
Absolutely Localized Projection-Based Embedding for Excited States

We present a quantum embedding method that allows for calculation of local excited states embedded in a Kohn–Sham density functional theory (DFT) environment. Projection-based quantum embedding met...
Fast estimation of genetic correlation for biobank-scale data.

This research was conducted using the UK Biobank Resource under applications 33127. We thank the participants of UK Biobank for making this work possible. SS was supported in part by is supported in part by NIH grants R35GM125055, NSF Grant III-1705121, an Alfred P. Sloan Research Fellowship, and a gift from the Okawa Foundation.
Design and performance of hafnium optical and near-IR kinetic inductance detectors

We report on the design and performance of microwave kinetic inductance detectors (MKIDs) sensitive to single photons in the optical to near-infrared range using hafnium as the sensor material. Our test device had a superconducting transition temperature of 395 mK and a room temperature normal state resistivity of 97 μ Ω cm with RRR = 1.6. Resonators on the device displayed internal quality factors of around 200 000. Similar to the analysis of MKIDs made from other highly resistive superconductors, we find that modeling the temperature response of the detector requires an extra broadening parameter in the superconducting density of states. Finally, we show that this material and design is compatible with a full-array fabrication process, which resulted in pixels with decay times of about 40 μs and resolving powers of ∼9 at 800 nm.We report on the design and performance of microwave kinetic inductance detectors (MKIDs) sensitive to single photons in the optical to near-infrared range using hafnium as the sensor material. Our test device had a superconducting transition temperature of 395 mK and a room temperature normal state resistivity of 97 μ Ω cm with RRR = 1.6. Resonators on the device displayed internal quality factors of around 200 000. Similar to the analysis of MKIDs made from other highly resistive superconductors, we find that modeling the temperature response of the detector requires an extra broadening parameter in the superconducting density of states. Finally, we show that this material and design is compatible with a full-array fabrication process, which resulted in pixels with decay times of about 40 μs and resolving powers of ∼9 at 800 nm.
Structural Remodeling Of Fibrous Astrocytes After Axonal Injury

Reactive astrocytes are a pathological hallmark of many CNS injuries and neurodegenerations. They are characterized by hypertrophy of the soma and processes and an increase in the expression of glial fibrillary acidic protein. Because the cells obscure each other in immunostaining, little is known about the behavior of a single reactive astrocyte, nor how single astrocytes combine to form the glial scar. We have investigated the reaction of fibrous astrocytes to axonal degeneration using a transgenic mouse strain expressing enhanced green fluorescent protein in small subsets of astrocytes. Fibrous astrocytes in the optic nerve and corpus callosum initially react to injury by hypertrophy of the soma and processes. They retract their primary processes, simplifying their shape and dramatically reducing their spatial coverage. At 3 d after crush, quantitative analysis revealed nearly a twofold increase in the thickness of the primary processes, a halving of the number of primary processes leaving the soma and an eightfold reduction in the spatial coverage. In the subsequent week, they partially reextend long processes, returning to a near-normal morphology and an extensive spatial overlap. The resulting glial scar consists of an irregular array of astrocyte processes, contrasting with their original orderly arrangement. These changes are in distinct contrast to those reported for reactive protoplasmic astrocytes of the gray matter, in which the number of processes and branchings increase, but the cells continue to maintain nonoverlapping individual territories throughout their response to injury.
Zhong–Yang type eigenvalue estimate with integral curvature condition

We prove a sharp Zhong–Yang type eigenvalue lower bound for closed Riemannian manifolds with control on integral Ricci curvature.