cssi/SciSciGPT-SciSciNet huggingface dataset:
Charge pair hopping and Bose-Einstein condensation in underdoped Mott insulators

Recently, a renormalized Hamiltonian has been derived by continuing spin states from the Mott limit of the $t$-$J$ model to the underdoped region. We show that it naturally leads to a pairing mechanism in which the pair has a dual character. Its spin part is a spinon singlet that condenses at ${T}^{*}$. The charge part is a real-space holon pair formed at ${T}_{p}l{T}^{*}$, which undergoes a Bose-Einstein condensation at ${T}_{c}l{T}_{p}$. While neither is observable separately, the combination is predicted to be observable as a sharp excitation above and below ${T}_{c}$. The mechanism is consistent with the small superfluid density, the decline of ${T}_{c}$ at small doping, and the existence of pairs above ${T}_{c}$ in cuprates, indicated by the observation of diamagnetism and Nernst effect.
Statistical characterization of microstructure evolution during compaction of granular systems composed of spheres with hardening plastic behavior

Abstract An extensive numerical campaign of particle mechanics calculations that predict microstructure formation and evolution during die compaction, up to solid fractions close to one, of monodisperse plastic spheres that exhibit power-law plastic hardening behavior is presented. The study is focused on elucidating the relationship between particle plastic properties, loading conditions, and statistical features of the resulting microstructure. This communication provides fundamental insight into the achievable space of microstructures through die compaction, for given plastic stiffness and hardening exponent at the particle scale.
Not So Many Non-Disjoint Translations

We show that, consistently, there is a Borel set which has uncountably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.
Riemannian Groupoids and Solitons for Three-Dimensional Homogeneous Ricci and Cross-Curvature Flows

In this paper, we investigate the behavior of three-dimensional homogeneous solutions of the cross-curvature flow using Riemannian groupoids. The Riemannian groupoid technique, originally introduced by J. Lott, allows us to investigate the long-term behavior of collapsing solutions of the flow, producing solitons in the limit. We also review Lott's results on the long-term behavior of three-dimensional homogeneous solutions of Ricci flow, demonstrating the coordinates we choose and reviewing the groupoid technique. We find cross-curvature soliton metrics on Sol and Nil, and show that the cross-curvature flow of SL(2,R) limits to Sol.
Causal inference in the context of an error prone exposure: Air pollution and mortality

We propose a new approach for estimating causal effects when the exposure is measured with error and confounding adjustment is performed via a generalized propensity score (GPS). Using validation data, we propose a regression calibration (RC)-based adjustment for a continuous error-prone exposure combined with GPS to adjust for confounding (RC-GPS). The outcome analysis is conducted after transforming the corrected continuous exposure into a categorical exposure. We consider confounding adjustment in the context of GPS subclassification, inverse probability treatment weighting (IPTW) and matching. In simulations with varying degrees of exposure error and confounding bias, RC-GPS eliminates bias from exposure error and confounding compared to standard approaches that rely on the error-prone exposure. We applied RC-GPS to a rich data platform to estimate the causal effect of long-term exposure to fine particles (PM2.5) on mortality in New England for the period from 2000 to 2012. The main study consists of 2202 zip codes covered by 217,660 1 km × 1 km grid cells with yearly mortality rates, yearly PM2.5 averages estimated from a spatio-temporal model (error-prone exposure) and several potential confounders. The internal validation study includes a subset of 83 1 km × 1 km grid cells within 75 zip codes from the main study with error-free yearly PM2.5 exposures obtained from monitor stations. Under assumptions of noninterference and weak unconfoundedness, using matching we found that exposure to moderate levels of PM2.5 (8 < PM2.5 ≤ 10 μg/m3) causes a 2.8% (95% CI: 0.6%, 3.6%) increase in all-cause mortality compared to low exposure (PM2.5 ≤ 8 μg/m3).
Robust Fruit Counting: Combining Deep Learning, Tracking, and Structure from Motion

We present a novel fruit counting pipeline that combines deep segmentation, frame to frame tracking, and 3D localization to accurately count visible fruits across a sequence of images. Our pipeline works on image streams from a monocular camera, both in natural light, as well as with controlled illumination at night. We first train a Fully Convolutional Network (FCN) and segment video frame images into fruit and non-fruit pixels. We then track fruits across frames using the Hungarian Algorithm where the objective cost is determined from a Kalman Filter corrected Kanade-Lucas-Tomasi (KLT) Tracker. In order to correct the estimated count from tracking process, we combine tracking results with a Structure from Motion (SfM) algorithm to calculate relative 3D locations and size estimates to reject outliers and double counted fruit tracks. We evaluate our algorithm by comparing with ground-truth human-annotated visual counts. Our results demonstrate that our pipeline is able to accurately and reliably count fruits across image sequences, and the correction step can significantly improve the counting accuracy and robustness. Although discussed in the context of fruit counting, our work can extend to detection, tracking, and counting of a variety of other stationary features of interest such as leaf-spots, wilt, and blossom.
Bregman Parallel Direction Method of Multipliers for Distributed Optimization via Mirror Averaging

Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and $O$ ( $1/T$ ) convergence rate of the Bregman PDMM, along with its $O$ ( $n/\ln n$ ) improvement over existing PDMM, where $T$ denotes the number of iterations and $n$ the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.
Nonparametric Estimation of Multi-View Latent Variable Models

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to mixtures of discrete or Gaussian distributions. In this paper, we propose a kernel method for learning multi-view latent variable models, allowing each mixture component to be nonparametric and learned from data in an unsupervised fashion. The key idea of our method is to embed the joint distribution of a multi-view latent variable model into a reproducing kernel Hilbert space, and then the latent parameters are recovered using a robust tensor power method. We establish that the sample complexity for the proposed method is quadratic in the number of latent components and is a low order polynomial in the other relevant parameters. Thus, our nonparametric tensor approach to learning latent variable models enjoys good sample and computational efficiencies. As a special case of our framework, we also obtain a first unsupervised conditional density estimator of the kind with provable guarantees. In both synthetic and real world datasets, the nonparametric tensor power method compares favorably to EM algorithm and other spectral algorithms.
Tropicalization is a non-Archimedean analytic stack quotient

For a complex toric variety $X$ the logarithmic absolute value induces a natural retraction of $X$ onto the set of its non-negative points and this retraction can be identified with a quotient of $X(\mathbb{C})$ by its big real torus. We prove an analogous result in the non-Archimedean world: The Kajiwara-Payne tropicalization map is a non-Archimedean analytic stack quotient of $X^{an}$ by its big affinoid torus. Along the way, we provide foundations for a geometric theory of non-Archimedean analytic stacks, particularly focussing on analytic groupoids and their quotients, the process of analytification, and the underlying topological spaces of analytic stacks.
A Boo(n) for Evaluating Architecture Performance

We point out important problems with the common practice of using the best single model performance for comparing deep learning architectures, and we propose a method that corrects these flaws. Each time a model is trained, one gets a different result due to random factors in the training process, which include random parameter initialization and random data shuffling. Reporting the best single model performance does not appropriately address this stochasticity. We propose a normalized expected best-out-of-$n$ performance ($\text{Boo}_n$) as a way to correct these problems.
Using Ramsey's Theorem Once

We show that $$\mathsf {RT} (2,4)$$ cannot be proved with one typical application of $$\mathsf {RT} (2,2)$$ in an intuitionistic extension of $${\mathsf {RCA}}_{0}$$ to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach’s axiomatization of higher order reverse mathematics, results related to modified reducibility, and a formalization of Weihrauch reducibility.
Distance-Penalized Active Learning Using Quantile Search

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb {R}^d$ with an optimal number of samples. We generalize this problem to the case of spatial signals, where the sampling cost is a function of both the number of samples taken and the distance traveled during estimation. This is motivated by our work studying regions of low oxygen concentration in the Great Lakes. We show that for one-dimensional threshold classifiers, a tradeoff between the number of samples taken and distance traveled can be achieved using a generalization of binary search, which we refer to as quantile search . We characterize both the estimation error after a fixed number of samples and the distance traveled in the noiseless case, as well as the estimation error in the case of noisy measurements. We illustrate our results in both simulations and experiments and show that our method outperforms existing algorithms in a large range of sampling scenarios.
Learning Word Representations with Hierarchical Sparse Coding

We propose a new method for learning word representations using hierarchical regularization in sparse coding inspired by the linguistic study of word meanings. We show an efficient learning algorithm based on stochastic proximal methods that is significantly faster than previous approaches, making it possible to perform hierarchical sparse coding on a corpus of billions of word tokens. Experiments on various benchmark tasks--word similarity ranking, syntactic and semantic analogies, sentence completion, and sentiment analysis--demonstrate that the method out-performs or is competitive with state-of-the-art methods.
Scalable Anomaly Ranking of Attributed Neighborhoods

Given a graph with node attributes, what neighborhoods are anomalous? To answer this question, one needs a quality score that utilizes both structure and attributes. Popular existing measures either quantify the structure only and ignore the attributes (e.g., conductance), or only consider the connectedness of the nodes inside the neighborhood and ignore the cross-edges at the boundary (e.g., density). In this work we propose normality, a new quality measure for attributed neighborhoods. Normality utilizes structure and attributes together to quantify both internal consistency and external separability. It exhibits two key advantages over other measures: (1) It allows many boundary-edges as long as they can be "exonerated"; i.e., either (i) are expected under a null model, and/or (ii) the boundary nodes do not exhibit the subset of attributes shared by the neighborhood members. Existing measures, in contrast, penalize boundary edges irrespectively. (2) Normality can be efficiently maximized to automatically infer the shared attribute subspace (and respective weights) that characterize a neighborhood. This efficient optimization allows us to process graphs with millions of attributes. We capitalize on our measure to present a novel approach for Anomaly Mining of Entity Neighborhoods (AMEN). Experiments on real-world attributed graphs illustrate the effectiveness of our measure at anomaly detection, outperforming popular approaches including conductance, density, OddBall, and SODA. In addition to anomaly detection, our qualitative analysis demonstrates the utility of normality as a powerful tool to contrast the correlation between structure and attributes across different graphs.
Metric uniformization and spectral bounds for graphs

We present a method for proving upper bounds on the eigenvalues of the graph Laplacian. A main step involves choosing an appropriate “Riemannian” metric to uniformize the geometry of the graph. In many interesting cases, the existence of such a metric is shown by examining the combinatorics of special types of flows. This involves proving new inequalities on the crossing number of graphs.
Sequential Adaptive Detection for In-Situ Transmission Electron Microscopy (TEM)

We develop new efficient online algorithms for detecting transient sparse signals in TEM video sequences, by adopting the recently developed framework for sequential detection jointly with online convex optimization [1]. We cast the problem as detecting an unknown sparse mean shift of Gaussian observations, and develop adaptive CUSUM and adaptive SSRS procedures, which are based on likelihood ratio statistics with post-change mean vector being online maximum likelihood estimators with $\ell_{1}$ . We demonstrate the meritorious performance of our algorithms for TEM imaging using real data.
Thermodynamic Model of Criticality in the Cortex Based on EEG/ECoG Data

Author(s): Kozma, Robert; Puljic, Marko; Freeman, Walter J, III | Abstract: Criticality in the cortex emerges from the seemingly random interaction of microscopic components and produces higher cognitive functions at mesoscopic and macroscopic scales. Random graphs and percolation theory provide natural means to describe critical regions in the behavior of the cortex and they are proposed here as novel mathematical tools helping us deciphering the language of the brain.
Approximability of Discriminators Implies Diversity in GANs

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al. suggests a dilemma about GANs' statistical properties: powerful discriminators cause overfitting, whereas weak discriminators cannot detect mode collapse. By contrast, we show in this paper that GANs can in principle learn distributions in Wasserstein distance (or KL-divergence in many cases) with polynomial sample complexity, if the discriminator class has strong distinguishing power against the particular generator class (instead of against all possible generators). For various generator classes such as mixture of Gaussians, exponential families, and invertible and injective neural networks generators, we design corresponding discriminators (which are often neural nets of specific architectures) such that the Integral Probability Metric (IPM) induced by the discriminators can provably approximate the Wasserstein distance and/or KL-divergence. This implies that if the training is successful, then the learned distribution is close to the true distribution in Wasserstein distance or KL divergence, and thus cannot drop modes. Our preliminary experiments show that on synthetic datasets the test IPM is well correlated with KL divergence or the Wasserstein distance, indicating that the lack of diversity in GANs may be caused by the sub-optimality in optimization instead of statistical inefficiency.
An observation on (-1)-curves on rational surfaces

We give an effective iterative characterization of the classes of (smooth, rational) (-1)-curves on the blowup of the projective plane at general points. Such classes are characterized as having self-intersection -1, arithmetic genus 0, and intersecting every (-1)-curve of smaller degree nonnegatively.
Galois branched covers with fixed ramification locus

Abstract We examine conditions under which there exists a non-constant family of Galois branched covers of curves over an algebraically closed field k of fixed degree and fixed ramification locus, under a notion of equivalence derived from considering linear series on a fixed smooth proper source curve X . We show such a family exists precisely when the following conditions are satisfied: char ( k ) = p > 0 , X is isomorphic to P k 1 , there is a unique ramification point, and the Galois group is ( Z / p Z ) m for some integer m > 0 .
Fibrations and higher products in cohomology

This paper is a continuation of [2]. Working in the context of commutative differential graded algebras, we study the ideal of the cohomology classes which can be annihilated by fibrations whose fiber has finite homological dimension. In this paper we identify these classes with certain higher products in cohomology.
Uniqueness of solutions to the 3D quintic Gross–Pitaevskii hierarchy

Abstract In this paper, we study solutions to the three-dimensional quintic Gross–Pitaevskii hierarchy. We prove unconditional uniqueness among all small solutions in the critical space H 1 (which corresponds to H 1 on the NLS level). With slight modifications to the proof, we also prove unconditional uniqueness of solutions to the Hartree hierarchy without a smallness condition. Our proof uses the quantum de Finetti theorem, and is an extension of the work by Chen, Hainzl, Pavlovic, and Seiringer [9] , and our previous work [32] .
Gap structure in Fe-based superconductors with accidental nodes: The role of hybridization

We study the effects of hybridization between the two electron pockets in Fe-based superconductors with $s$-wave gap with accidental nodes. We argue that hybridization reconstructs the Fermi surfaces and also induces an additional interpocket pairing component. We analyze how these two effects modify the gap structure by tracing the position of the nodal points of the energy dispersions in the superconducting state. We find three possible outcomes. In the first, the nodes simply shift their positions in the Brillouin zone; in the second, the nodes merge and disappear, in which case the gap function has either equal or opposite signs on the electron pockets; in the third, a new set of nodal points emerges, doubling the original number of nodes.
Parallelized Kalman-Filter-Based Reconstruction of Particle Tracks on Many-Core Architectures

Faced with physical and energy density limitations on clock speed, contemporary microprocessor designers have increasingly turned to on-chip parallelism for performance gains. Algorithms should accordingly be designed with ample amounts of fine-grained parallelism if they are to realize the full performance of the hardware. This requirement can be challenging for algorithms that are naturally expressed as a sequence of small-matrix operations, such as the Kalman filter methods widely in use in high-energy physics experiments. In the High-Luminosity Large Hadron Collider (HL-LHC), for example, one of the dominant computational problems is expected to be finding and fitting charged-particle tracks during event reconstruction; today, the most common track-finding methods are those based on the Kalman filter. Experience at the LHC, both in the trigger and offline, has shown that these methods are robust and provide high physics performance. Previously we reported the significant parallel speedups that resulted from our efforts to adapt Kalman-filter-based tracking to many-core architectures such as Intel Xeon Phi. Here we report on how effectively those techniques can be applied to more realistic detector configurations and event complexity.
Linear-time learning on distributions with approximate kernel embeddings

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Most previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an approach is fine for smaller datasets, the computation of an N × N Gram matrix is prohibitive in large datasets. Recent scalable estimators that work over pdfs have done so only with kernels that use Euclidean metrics, like the L2 distance. However, there are a myriad of other useful metrics available, such as total variation, Hellinger distance, and the Jensen-Shannon divergence. This work develops the first random features for pdfs whose dot product approximates kernels using these non-Euclidean metrics. These random features allow estimators to scale to large datasets by working in a primal space, without computing large Gram matrices. We provide an analysis of the approximation error in using our proposed random features, and show empirically the quality of our approximation both in estimating a Gram matrix and in solving learning tasks in real-world and synthetic data.
On Weyl’s Embedding Problem in Riemannian Manifolds

We consider a priori estimates of Weyl's embedding problem of $(\mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, \bar g)$. We establish interior $C^2$ estimate under natural geometric assumption. Together with a recent work by Li and Wang, we obtain an isometric embedding of $(\mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's embedding theorem in space form under the condition that $g\in C^2$ with $D^2g$ Dini continuous.
Sentence-Level Grammatical Error Identification as Sequence-to-Sequence Correction

We demonstrate that an attention-based encoder-decoder model can be used for sentence-level grammatical error identification for the Automated Evaluation of Scientific Writing (AESW) Shared Task 2016. The attention-based encoder-decoder models can be used for the generation of corrections, in addition to error identification, which is of interest for certain end-user applications. We show that a character-based encoder-decoder model is particularly effective, outperforming other results on the AESW Shared Task on its own, and showing gains over a word-based counterpart. Our final model--a combination of three character-based encoder-decoder models, one word-based encoder-decoder model, and a sentence-level CNN--is the highest performing system on the AESW 2016 binary prediction Shared Task.
Twisted Alexander polynomials with the adjoint action for some classes of knots

We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in [J. Dubois, Nonabelian twisted Reidemeister torsion for fibered knots, Canad. Math. Bull.49(1) (2006) 55–71] and a formula for the nonabelian Reidemeister torsion of twist knots that is better than the one in [J. Dubois, V. Huynh and Y. Yamaguchi, Nonabelian Reidemeister torsion for twist knots, J. Knot Theory Ramifications18(3) (2009) 303–341].
Equiangular tight frames with centroidal symmetry

Abstract An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.
Planar Graphs have Independence Ratio at least 3/13

The 4 Color Theorem (4CT) implies that every $n$-vertex planar graph has an independent set of size at least $\frac{n}4$; this is best possible, as shown by the disjoint union of many copies of $K_4$. In 1968, Erdős asked whether this bound on independence number could be proved more easily than the full 4CT. In 1976 Albertson showed (independently of the 4CT) that every $n$-vertex planar graph has an independent set of size at least $\frac{2n}9$. Until now, this remained the best bound independent of the 4CT. Our main result improves this bound to $\frac{3n}{13}$.
Newton slopes for twisted Artin–Schreier–Witt towers

We fix a monic polynomial f(x) ∈ &#x1d53d;q[x] over a finite field of characteristic p of degree relatively prime to p. Let a↦ω(a) be the Teichmuller lift of &#x1d53d;q, and let χ : ℤp → ℂp× be a finite character ...
Cubic planar graphs and Legendrian surface theory

We study Legendrian surfaces determined by cubic planar graphs. Graphs with distinct chromatic polynomials determine surfaces that are not Legendrian isotopic, thus giving many examples of non-isotopic Legendrian surfaces with the same classical invariants. The Legendrians have no exact Lagrangian fillings, but have many interesting non-exact fillings. We obtain these results by studying sheaves on a three-ball with microsupport in the surface. The moduli of such sheaves has a concrete description in terms of the graph and a beautiful embedding as a holomorphic Lagrangian submanifold of a symplectic period domain, a Lagrangian that has appeared in the work of Dimofte-Gabella-Goncharov [DGGo]. We exploit this structure to find conjectural open Gromov-Witten invariants for the non-exact filling, following Aganagic-Vafa [AV, AV2].
On the Effect of Task-to-Worker Assignment in Distributed Computing Systems with Stragglers

We study the expected completion time of some recently proposed algorithms for distributed computing which redundantly assign computing tasks to multiple machines in order to tolerate a certain number of machine failures. We analytically show that not only the amount of redundancy but also the task-to-machine assignments affect the latency in a distributed system. We study systems with a fixed number of computing tasks that are split in possibly overlapping batches, and independent exponentially distributed machine service times. We show that, for such systems, the uniform replication of non-overlapping (disjoint) batches of computing tasks achieves the minimum expected computing time.
On Calabi’s extremal metric and properness

In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar K\"ahler metric on a compact K\"ahler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates needed, but rather there are necessary modifications adapted to the extremal case. We prove that there exists an extremal metric with extremal vector $V$ if and only if the modified Mabuchi energy is proper, modulo the action the subgroup in the identity component of automorphism group which commutes with the flow of $V$. We introduce two essentially equivalent notions, called \emph{reductive properness} and \emph{reduced properness}. We observe that one can test reductive properness/reduced properness only for invariant metrics. We prove that existence of an extremal metric is equivalent to reductive properness/reduced properness of the modified Mabuchi energy.
The KP Approximation Under a Weak Coriolis Forcing

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq–Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev–Petviashvili equation (also called Grimshaw–Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev–Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.
Relaxing Integrity Requirements for Attack-Resilient Cyber-Physical Systems

The increase in network connectivity has also resulted in several high-profile attacks on cyber-physical systems. An attacker that manages to access a local network could remotely affect control performance by tampering with sensor measurements delivered to the controller. Recent results have shown that with network-based attacks, such as man-in-the-middle attacks, the attacker can introduce an unbounded state estimation error if measurements from a suitable subset of sensors contain false data when delivered to the controller. While these attacks can be addressed with the standard cryptographic tools that ensure data integrity, their continuous use would introduce significant communication and computation overhead. Consequently, we study effects of intermittent data integrity guarantees on system performance under stealthy attacks. We consider linear estimators equipped with a general type of residual-based intrusion detectors (including, e.g., widely used $\chi ^2$ detectors) and show that even when integrity of sensor measurements is enforced only intermittently, the attack impact is significantly limited; specifically, the state estimation error is bounded or the attacker cannot remain stealthy. Furthermore, we present methods to: 1) evaluate the effects of any given integrity enforcement policy in terms of reachable state estimation errors for any type of stealthy attacks; and 2) design an enforcement policy that provides the desired estimation error guarantees under attack. Finally, on three automotive case studies, we show that even with less than 10% of authenticated messages, we can ensure satisfiable control performance in the presence of attacks.
Group symmetries of complementary code matrices

Complementary code matrices (CCMs) generalize Golay pairs and Hadamard matrices. In this paper, we describe new group relations satisfied by CCM-preserving symmetries and use its symmetry group to classify CCMs in terms of their equivalence classes. We also give an upper bound on the order of this group, determine the number of equivalence classes of N × 4 quad-phase CCMs where N = 2, 3, 4, 5, 6, and present a new construction to generate quad-phase CCMs from ternary CCM dual pairs.
Deconstruction, holography and emergent supersymmetry

We study a gauge theory in a 5D warped space via the dimensional deconstruction that a higher dimensional gauge theory is constructed from a moose of 4D gauge groups. By the AdS/CFT correspondence, a 5D warped gauge theory is dual to a 4D conformal field theory (CFT) with a global symmetry. As far as physics of the gauge theory, we obtain the one-to-one correspondence between each component of a moose of gauge groups and that of a CFT. We formulate a supersymmetric extension of deconstruction and explore the framework of natural supersymmetry in a 5D warped space — the super-symmetric Randall-Sundrum model with the IR-brane localized Higgs and bulk fermions — via the gauge moose. In this model, a supersymmetry breaking source is located at the end of the moose corresponding to the UV brane and the first two generations of squarks are decoupled. With left-right gauge symmetries in the bulk of the moose, we demonstrate realization of accidental or emergent supersymmetry of the Higgs sector in comparison with the proposed “Moose/CFT correspondence.”
Simultaneous policy learning and latent state inference for imitating driver behavior

Human driving depends on latent states, such as aggression and intent, that cannot be directly observed. In this work, we propose a method for learning driver models that can account for unobserved states. When trained on a synthetic dataset, our model is able to learn encodings for vehicle trajectories that distinguish between four distinct classes of driver behavior. Such encodings are learned without any knowledge of the number of driver classes or any objective that directly requires the model to learn encodings for each class. We show that latent state driving policies outperform baseline methods at replicating driver behavior. Furthermore, we demonstrate that the actions chosen by our policy are heavily influenced by its assigned latent state.
Divisors of secant planes to curves

Abstract Inside the symmetric product of a very general curve, we consider the codimension-one subvarieties of symmetric tuples of points imposing exceptional secant conditions on linear series on the curve of fixed degree and dimension. We compute the classes of such divisors, and thus obtain improved bounds for the slope of the cone of effective divisor classes on symmetric products of a very general curve. By letting the moduli of the curve vary, we study more generally the classes of the related divisors inside the moduli space of stable pointed curves.
Generalized Colonel Blotto Game

Competitive resource allocation between adversarial decision makers arises in a wide spectrum of realworld applications such as in communication systems, cyber-physical systems security, as well as financial and political competition. Hence, developing analytical tools to model and analyze competitive resource allocation is crucial for devising optimal allocation strategies and anticipating the potential outcomes of the competition. To this end, the Colonel Blotto game is one of the most popular game-theoretic frameworks for modeling and analyzing such competitive resource allocation problems. However, in many practical competitive situations, the Colonel Blotto game does not admit solutions in deterministic strategies and, hence, one must rely on analytically complex mixed-strategies with their associated tractability, applicability, and practicality challenges. In this regard, in this paper, a generalization of the Colonel Blotto game which enables the derivation of deterministic, practical, and implementable equilibrium strategies is proposed while accounting for scenarios with heterogeneous battlefields. In addition, the proposed generalized game factors in the consumed/destroyed resources in each battlefield, a feature that is not considered in the classical Blotto game. For this generalized game, the existence of a Nash equilibrium in pure strategies is shown. Then, closed-form analytical expressions of the equilibrium strategies are derived and the outcome of the game is characterized, based on the number of each player's resources and each battlefield's valuation. The generated results provide invaluable insights on the outcome of the competition. For example, the results show that, when both players are fully rational, the more resourceful player can achieve a better total payoff at the Nash equilibrium, a result that is not mimicked in the classical Blotto game.
Rate-Maximizing OFDM Pilot Patterns for UAV Communications in Nonstationary A2G Channels

In this paper, we propose and evaluate rate-maximizing pilot configurations for Unmanned Aerial Vehicle (UAV) communications employing OFDM waveforms. OFDM relies on pilot symbols for effective communications. We formulate a rate-maximization problem in which the pilot spacing (in the time-frequency resource grid) and power is varied as a function of the time-varying channel statistics. The receiver solves this rate-maximization problem, and the optimal pilot spacing and power are explicitly fed back to the transmitter to adapt to the time-varying channel statistics in an air-to-ground (A2G) environment. We show the enhanced throughput performance of this scheme for UAV communications in sub-6 GHz bands. These performance gains are achieved at the cost of very low computational complexity and feedback requirements, making it attractive for A2G UAV communications in 5G.
Equivalence of Edge Bicolored Graphs on Surfaces

Consider the collection of edge bicolorings of a graph that are cellularly embedded on an orientable surface. In this work, we count the number of equivalence classes of such colorings under two relations: reversing colors around a face and reversing colors around a vertex. In the case of the plane, this is well studied, but for other surfaces, the computation is more subtle. While this question can be stated purely graph theoretically, it has interesting applications in knot theory.
On the Exponent of Finite-Dimensional Hopf Algebras

One of the classical notions of group theory is the notion of the exponent of a group. The exponent of a group is the least common multiple of orders of its elements. In this paper we generalize the notion of exponent to Hopf algebras. We give five equivalent definitions of the exponent. Two of them are: 1) the exponent of H equals the order of the Drinfeld element u of the quantum double D(H); 2) the exponent of H is the order of the squared brading acting in the tensor square of the regular representation of D(H). We show that the exponent is invariant under twisting. We prove that for semisimple and cosemisimple Hopf algebras H, the exponent is finite and divides dim(H)^3. For triangular Hopf algebras in characteristic zero, we show that the exponent divides dim(H). We conjecture that if H is semisimple and cosemisimple then the exponent always divides dim(H). At the end we formulate some open questions, in particular suggest a formulation for a possible Hopf algebraic analogue of Sylow's theorem.
Random permutations fix a worst case for cyclic coordinate descent

Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of $x$ in order; randomized (RCD), in which the component to update is selected randomly and independently at each iteration; and random-permutations cyclic (RPCD), which differs from CCD only in that a random permutation is applied to the variables at the start of each cycle. Known convergence guarantees are weaker for CCD and RPCD than for RCD, though in most practical cases, computational performance is similar among all these variants. There is a certain type of quadratic function for which CCD is significantly slower than for RCD; a recent paper by \cite{SunY16a} has explored the poor behavior of CCD on functions of this type. The RPCD approach performs well on these functions, even better than RCD in a certain regime. This paper explains the good behavior of RPCD with a tight analysis.
Interactive Full Image Segmentation by Considering All Regions Jointly

We address interactive full image annotation, where the goal is to accurately segment all object and stuff regions in an image. We propose an interactive, scribble-based annotation framework which operates on the whole image to produce segmentations for all regions. This enables sharing scribble corrections across regions, and allows the annotator to focus on the largest errors made by the machine across the whole image. To realize this, we adapt Mask-RCNN [22] into a fast interactive segmentation framework and introduce an instance-aware loss measured at the pixel-level in the full image canvas, which lets predictions for nearby regions properly compete for space. Finally, we compare to interactive single object segmentation on the COCO panoptic dataset [11, 27, 34]. We demonstrate that our interactive full image segmentation approach leads to a 5% IoU gain, reaching 90% IoU at a budget of four extreme clicks and four corrective scribbles per region
Knottedness is in NP, modulo GRH

Abstract Given a tame knot K presented in the form of a knot diagram, we show that the problem of determining whether K is knotted is in the complexity class NP , assuming the generalized Riemann hypothesis (GRH). In other words, there exists a polynomial-length certificate that can be verified in polynomial time to prove that K is non-trivial. GRH is not needed to believe the certificate, but only to find a short certificate. This result complements the result of Hass, Lagarias, and Pippenger that unknottedness is in NP . Our proof is a corollary of major results of others in algebraic geometry and geometric topology.
Third order WENO scheme on sparse grids for hyperbolic equations

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). The computational cost of such schemes increases significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points and nonlinearity of high order accuracy WENO schemes. How to achieve fast computations by WENO methods for high spatial dimension PDEs is a challenging and important question. Recently, sparse-grid has become a major approximation tool for high dimensional problems. The open question is how to design WENO computations on sparse grids such that comparable high order accuracy of WENO schemes in smooth regions and essentially non-oscillatory stability in non-smooth regions of the solutions can still be achieved as that for computations on regular single grids? In this paper, we combine the third order finite difference WENO method with sparse-grid combination technique and solve high spatial dimension hyperbolic equations on sparse grids. WENO interpolation is proposed for the prolongation part in sparse grid combination techniques to deal with discontinuous solutions of hyperbolic equations. Numerical examples are presented to show that significant computational times are saved while both high order accuracy and stability of the WENO scheme are maintained for simulations on sparse grids.
Equivariant quantum cohomology of cotangent bundle of G/P

Abstract Let G denote a complex semisimple linear algebraic group, P a parabolic subgroup of G and P = G / P . We identify the quantum multiplication by divisors in T ⁎ P in terms of stable basis, which is introduced in [9] . Using this and the restriction formula for stable basis [17] , we show that the G × C ⁎ -equivariant quantum multiplication formula in T ⁎ P is conjugate to the formula conjectured by Braverman.
Tight bounds for the distribution-free testing of monotone conjunctions

We improve both upper and lower bounds for the distribution-free testing of monotone conjunctions. Given oracle access to an unknown Boolean function f: {0, 1}n → {0, 1} and sampling oracle access to an unknown distribution D over {0, 1}n, we present an O(n1/3/e5)-query algorithm that tests whether f is a monotone conjunction versus e-far from any monotone conjunction with respect to D. This improves the previous best upper bound of O(n1/2/e) by Dolev and Ron [DR11], when 1/e is small compared to n. For some constant e0 > 0, we also prove a lower bound of Ω(n1/3) for the query complexity, improving the previous best lower bound of Ω(n1/5) by Glasner and Servedio [GS09]. Our upper and lower bounds are tight, up to a poly-logarithmic factor, when the distance parameter e is a constant. Furthermore, the same upper and lower bounds can be extended to the distribution-free testing of general conjunctions, and the lower bound can be extended to that of decision lists and linear threshold functions.
The reactive-telegraph equation and a related kinetic model

We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model a population density, does not preserve positivity in higher dimensions. In view of this, in dimensions larger than one, we consider a reactive-kinetic model and investigate the long-range, long-time limit of the solutions. We provide a general characterization of the speed of propagation and we compute it explicitly in one and two dimensions. We show that a phase transition between parabolic and hyperbolic behavior takes place only in one dimension. Finally, we investigate the hydrodynamic limit of the limiting problem.
On the Spectral Sequence from Khovanov Homology to Heegaard Floer Homology

Ozsvath and Szabo [“On the Heegaard Floer homology of branched double-covers.” Advances in Mathematics 194, no. 1 (2005): 1–33.] show that there is a spectral sequence the E 2 term of which is and which converges to . We prove that the E k term of this spectral sequence is an invariant of the link L for all k≥2. If L is a transverse link in (S 3 ,ξ std ), then we show that Plamenevskaya’s transverse invariant ψ(L) gives rise to a transverse invariant, ψ k (L), in the E k term for each k≥2. We use this fact to compute each term in the spectral sequences associated to the torus knots T(3,4) and T(3,5).
Efficient Nonparametric Smoothness Estimation

Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They also include, as special cases, L^2 quantities which are used in many applications. We propose and analyze a family of estimators for Sobolev quantities of unknown probability density functions. We bound the finite-sample bias and variance of our estimators, finding that they are generally minimax rate-optimal. Our estimators are significantly more computationally tractable than previous estimators, and exhibit a statistical/computational trade-off allowing them to adapt to computational constraints. We also draw theoretical connections to recent work on fast two-sample testing and empirically validate our estimators on synthetic data.
Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials

The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric multilayer stack. In contrast to the local effective medium theory, our proposed nonlocal effective medium theory can accurately predict measured incident angle-dependent reflection spectra from a fabricated multilayer stack and provide nonlocal dispersion relations. Moreover, the bulk plasmon polaritons with large wave vectors supported in the multilayer stack are also investigated with the nonlocal effective medium theory through the analysis of the dispersion relation and eigenmode.