cssi/SciSciGPT-SciSciNet huggingface dataset:
A pseudo-Euclidean iteration for optimal recovery in noisy ICA

Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for ICA with Gaussian noise. The main technical innovation of the algorithm is to use a fixed point iteration in a pseudo-Euclidean (indefinite "inner product") space. The use of this indefinite "inner product" resolves technical issues common to several existing algorithms for noisy ICA. This leads to an algorithm which is conceptually simple, efficient and accurate in testing. Our second contribution is combining PEGI with the analysis of objectives for optimal recovery in the noisy ICA model. It has been observed that the direct approach of demixing with the inverse of the mixing matrix is suboptimal for signal recovery in terms of the natural Signal to Interference plus Noise Ratio (SINR) criterion. There have been several partial solutions proposed in the ICA literature. It turns out that any solution to the mixing matrix reconstruction problem can be used to construct an SINR-optimal ICA demixing, despite the fact that SINR itself cannot be computed from data. That allows us to obtain a practical and provably SINR-optimal recovery method for ICA with arbitrary Gaussian noise.
Universal state transfer on graphs

Abstract A continuous-time quantum walk on a graph G is given by the unitary matrix U ( t ) = exp ( − i t A ) , where A is the adjacency matrix of G . We say G has pretty good state transfer between vertices a and b if for any ϵ > 0 , there is a time t , where the ( a , b ) -entry of U ( t ) satisfies | U ( t ) a , b | ≥ 1 − ϵ . This notion was introduced by Godsil (2011). The state transfer is perfect if the above holds for ϵ = 0 . In this work, we study a natural extension of this notion called universal state transfer wherein state transfer exists between every pair of vertices of the graph. We prove the following results about graphs with this stronger property: (i) Graphs with universal state transfer have distinct eigenvalues and flat eigenbasis (each eigenvector has entries which are equal in magnitude). (ii) The switching automorphism group of a graph with universal state transfer is abelian and its order divides the size of the graph. Moreover, if the state transfer is perfect, the switching automorphism group is cyclic. (iii) There is a family of complex oriented prime-length cycles which has universal pretty good state transfer. This provides a concrete example of a family of graphs with this universal property. (iv) There exists a class of graphs with real symmetric adjacency matrices which has universal pretty good state transfer. In contrast, Kay (2011) proved that no graph with real-valued adjacency matrix can have universal perfect state transfer. Finally, we provide a spectral characterization of universal perfect state transfer for graphs switching equivalent to circulants.
Global well-posedness of the velocity–vorticity-Voigt model of the 3D Navier–Stokes equations

Abstract The velocity–vorticity formulation of the 3D Navier–Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We prove global well-posedness and regularity of this model under periodic boundary conditions. We prove convergence of the model's velocity and vorticity to their counterparts in the 3D Navier–Stokes equations as the Voigt modeling parameter tends to zero. We prove that the curl of the model's velocity converges to the model vorticity (which is solved for directly), as the Voigt modeling parameter tends to zero. Finally, we provide a criterion for finite-time blow-up of the 3D Navier–Stokes equations based on this inviscid regularization.
FIRST-ORDER OPTIMAL SEQUENTIAL SUBSPACE CHANGE-POINT DETECTION

We consider the sequential change-point detection problem of detecting changes that are characterized by a subspace structure. Such changes are frequent in high-dimensional streaming data altering the form of the corresponding covariance matrix. In this work we present a Subspace-CUSUM procedure and demonstrate its first-order asymptotic optimality properties for the case where the subspace structure is unknown and needs to be simultaneously estimated. To achieve this goal we develop a suitable analytical methodology that includes a proper parameter optimization for the proposed detection scheme. Numerical simulations corroborate our theoretical findings.
Reactive Trajectory Generation for Multiple Vehicles in Unknown Environments With Wind Disturbances

Unmanned aerial vehicle use continues to increase, including operating beyond line of sight in unknown environments where the vehicle must autonomously generate a trajectory to safely navigate. In this article, we develop a trajectory generation algorithm for vehicles with second-order dynamics in unknown environments with bounded wind disturbances in which the vehicle only relies on its on-board distance sensors and communication with other vehicles to navigate. The proposed algorithm generates smooth trajectories and can be used with high-level planners and low-level motion controllers. The algorithm computes a maximum safe cruise velocity for the vehicle in the environment and guarantees that the trajectory does not violate the vehicle's thrust limitation, sensor constraints, or user-defined clearance radius around other vehicles and obstacles. Additionally, the trajectories are guaranteed to reach a stationary goal position in finite time given a finite number of bounded obstacles. Simulation results demonstrate the algorithm properties through two scenarios. First, a quadrotor navigating through a moving obstacle field to a goal position and, second, multiple quadrotors navigating into a building to different goal positions.
Fractional Poincaré and logarithmic Sobolev inequalities for measure spaces

Abstract We prove generalizations of the Poincare and logarithmic Sobolev inequalities corresponding to the case of fractional derivatives in measure spaces with only a minimal amount of geometric structure. The class of such spaces includes (but is not limited to) spaces of homogeneous type with doubling measures. Several examples and applications are given, including Poincare inequalities for graph Laplacians, fractional Poincare inequalities of Mouhot, Russ, and Sire (2011) [17] , and implications for recent work of the author and R.M. Strain on the Boltzmann collision operator (Gressman and Strain, 2010, 2011, 2011 [9] , [10] , [11] ).
BLOWUPS AND FIBERS OF MORPHISMS

Our object of study is a rational map defined by homogeneous forms , of the same degree , in the homogeneous coordinate ring of . Our goal is to relate properties of , of the homogeneous coordinate ring of the variety parameterized by , and of the Rees algebra , the bihomogeneous coordinate ring of the graph of . For a regular map , for instance, we prove that satisfies Serre’s condition , for some , if and only if satisfies and is birational onto its image. Thus, in particular, is birational onto its image if and only if satisfies . Either condition has implications for the shape of the core, namely, is the multiplier ideal of and Conversely, for , either equality for the core implies birationality. In addition, by means of the generalized rows of the syzygy matrix of , we give an explicit method to reduce the nonbirational case to the birational one when .
Variational multiscale proper orthogonal decomposition: Navier‐stokes equations

We develop a variational multiscale proper orthogonal decomposition (POD) reduced-order model (ROM) for turbulent incompressible Navier-Stokes equations. Under two assumptions on the underlying finite element approximation and the generation of the POD basis, the error analysis of the full discretization of the ROM is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the POD truncation error. Numerical tests for a three-dimensional turbulent flow past a cylinder at Reynolds number show the improved physical accuracy of the new model over the standard Galerkin and mixing-length POD ROMs. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two-dimensional Navier-Stokes problem. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 641–663, 2014
Deep learning ensembles for melanoma recognition in dermoscopy images

Melanoma is the deadliest form of skin cancer. While curable with early detection, only highly trained specialists are capable of accurately recognizing the disease. As expertise is in limited supply, automated systems capable of identifying disease could save lives, reduce unnecessary biopsies, and reduce costs. Toward this goal, we propose a system that combines recent developments in deep learning with established machine learning approaches, creating ensembles of methods that are capable of segmenting skin lesions, as well as analyzing the detected area and surrounding tissue for melanoma detection. The system is evaluated using the largest publicly available benchmark dataset of dermoscopic images, containing 900 training and 379 testing images. New state-of-the-art performance levels are demonstrated, leading to an improvement in the area under receiver operating characteristic curve of 7.5% (0.843 versus 0.783), in average precision of 4% (0.649 versus 0.624), and in specificity measured at the clinically relevant 95% sensitivity operating point 2.9 times higher than the previous state of the art (36.8% specificity compared to 12.5%). Compared to the average of eight expert dermatologists on a subset of 100 test images, the proposed system produces a higher accuracy (76% versus 70.5%), and specificity (62% versus 59%) evaluated at an equivalent sensitivity (82%).
Scalability of frames generated by dynamical operators

Let H be a separable Hilbert space, let G be a subset of H, and let A be an operator on H. Under appropriate conditions on A and G, it is known that the set of iterations F_G(A) is a frame for H. We call F_G(A) a dynamical frame for H, and explore further its properties; in particular, we show that its canonical dual frame also has an iterative set structure. We explore the relations between the operator A, the set G and the number of iterations L which ensure that the system F_G(A) is a scalable frame. We give a general statement on frame scalability, and study in detail the case when A is a normal operator, utilizing the unitary diagonalization. In addition, we answer the question of when F_G(A) is a scalable frame in several special cases involving block-diagonal and companion operators.
Fibered and primitive/Seifert twisted torus knots

The twisted torus knots lie on the standard genus 2 Heegaard surface for S3, as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knots are fibered, and that not all primitive/Seifert knots are fibered. Since there is a wealth of primitive/Seifert knots that are twisted torus knots, we consider the twisted torus knots to partially answer the question of which primitive/Seifert knots are fibered. A braid computation shows that a particular family of twisted torus knots is fibered, and that computation is then used to generalize the results of a previous paper by the author.
Occupation and Parkinson disease in the Women's Health Initiative Observational Study

Author(s): Burstyn, Igor; LaCroix, Andrea Z; Litvan, Irene; Wallace, Robert B; Checkoway, Harvey | Abstract: IntroductionThere is a lack of consistent study findings on associations between workplace exposures and the risk of Parkinson disease (PD) and a paucity of such data on women. We assessed PD risk among occupational groups to derive insights about potential occupation-specific exposures in a large cohort of women.MethodsThe Women's Health Initiative Observational Study (WHI-OS) is a prospective cohort that enrolled 91 627 postmenopausal women, 50 to 79 years of age, from 01 October 1993 through 31 December 1998, at 40 clinical centers across the United States, with average follow-up interval of 11 years. These women reported up to three paid jobs, held the longest since age 18; these jobs were coded and duration of employment calculated. We defined a case by self-report of doctor-diagnosed PD (at baseline or follow-up), death attributed to PD, or taking medication consistent with PD.ResultsAmong 2590 PD cases, we found evidence of excess risk among "counselors, social workers, and other community and social service specialists," and there was a suggestion of increased in risk among postsecondary teachers, and "building and grounds cleaning and maintenance" workers. There was also evidence of a deficit in risk among women who worked in sales. Results according to ever-employed and job duration were similar, except for evidence of excess risk among "health technologists and technicians" with more than 20 years of employment. Longer duration of life on a farm was associated with higher risk.ConclusionOur findings paint a largely reassuring picture of occupational risks for PD among US women.
On the character varieties of finitely generated groups

We establish three results dealing with the character varieties of finitely generated groups. The first two are concerned with the behavior of $\dim X_n(\Gamma)$ as a function of $n$, and the third addresses the problem of realizing a $\mathbb{Q}$-defined complex affine algebraic variety as a character variety.
The instability of the Hocking-Stewartson pulse and its geometric phase in the Hopf bundle

This work demonstrates an innovative numerical method for counting and locating eigenvalues with the Evans function. Utilizing the geometric phase in the Hopf bundle, the technique calculates the winding of the Evans function about a contour in the spectral plane, describing the eigenvalues enclosed by the contour for the Hocking-Stewartson pulse of the complex Ginzburg-Landau equation. Locating eigenvalues with the geometric phase in the Hopf bundle was proposed by Way (2009), and proven by Grudzien etźal. (2016). Way demonstrated his proposed method for the Hocking-Stewartson pulse, and this manuscript redevelops this example as in the proof of the method in Grudzien etźal. (2016), modifying his numerical shooting argument, and introduces new numerical results concerning the phase transition.
Fast Lexically Constrained Decoding with Dynamic Beam Allocation for Neural Machine Translation

The end-to-end nature of neural machine translation (NMT) removes many ways of manually guiding the translation process that were available in older paradigms. Recent work, however, has introduced a new capability: lexically constrained or guided decoding, a modification to beam search that forces the inclusion of pre-specified words and phrases in the output. However, while theoretically sound, existing approaches have computational complexities that are either linear (Hokamp and Liu, 2017) or exponential (Anderson et al., 2017) in the number of constraints. We present a algorithm for lexically constrained decoding with a complexity of O(1) in the number of constraints. We demonstrate the algorithm’s remarkable ability to properly place these constraints, and use it to explore the shaky relationship between model and BLEU scores. Our implementation is available as part of Sockeye.
Generative Code Modeling with Graphs.

Generative models for source code are an interesting structured prediction problem, requiring to reason about both hard syntactic and semantic constraints as well as about natural, likely programs. We present a novel model for this problem that uses a graph to represent the intermediate state of the generated output. The generative procedure interleaves grammar-driven expansion steps with graph augmentation and neural message passing steps. An experimental evaluation shows that our new model can generate semantically meaningful expressions, outperforming a range of strong baselines.
On the variational formulation of systems with non-holonomic constraints

In a previous article by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems by starting with the first variation functional instead of an action functional. In this article, it is shown that this same approach will also allow one to give a variational formulation to systems with non-holonomic constraints. The key is to use an adapted anholonomic local frame field in the formulation, which then implies the replacement of ordinary derivatives with covariant ones. The method is then applied to the case of a vertical disc rolling without slipping or friction on a plane.
Large-degree asymptotics of rational Painleve-IV functions associated to generalized Hermite polynomials

The Painleve-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers m and n. These functions have applications to nonlinear wave equations, random matrices, fluid dynamics, and quantum mechanics. Numerical studies suggest the zeros and poles form a deformed n by m rectangular grid. Properly scaled, the zeros and poles appear to densely fill certain curvilinear rectangles as m and n tend to infinity with r=m/n fixed. Generalizing a method of Bertola and Bothner used to study rational Painleve-II functions, we express the generalized Hermite rational Painleve-IV functions in terms of certain orthogonal polynomials on the unit circle. Using the Deift-Zhou nonlinear steepest-descent method, we asymptotically analyze the associated Riemann-Hilbert problem in the limit as n tends to infinity with m=r*n for r fixed. We obtain an explicit characterization of the boundary curve and determine the leading-order asymptotic expansion of the functions in the pole-free region.
Breuil-Kisin Modules via crystalline cohomology

For a perfect field $k$ of characteristic $p>0$ and a smooth and proper formal scheme $\mathscr{X}$ over the ring of integers of a finite and totally ramified extension $K$ of $W(k)[1/p]$, we propose a cohomological construction of the Breuil-Kisin modules attached to the $p$-adic etale cohomology $H^i_{\mathrm{et}}(\mathscr{X}_{\overline{K}},\mathbf{Z}_p)$. We then prove that our proposal works when $p>2$, $i < p-1$, and the crystalline cohomology of the special fiber of $\mathscr{X}$ is torsion-free in degrees $i$ and $i+1$.
A PAC-Bayesian Analysis of Randomized Learning with Application to Stochastic Gradient Descent

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all posterior distributions on an algorithm's random hyperparameters, including distributions that depend on the training data. This inspires an adaptive sampling algorithm for SGD that optimizes the posterior at runtime. We analyze this algorithm in the context of our generalization bounds and evaluate it on a benchmark dataset. Our experiments demonstrate that adaptive sampling can reduce empirical risk faster than uniform sampling while also improving out-of-sample accuracy.
The Anomaly Flow and the Fu-Yau Equation

The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter $$\alpha '$$ . This implies both results of Fu and Yau on the existence of solutions for Hull-Strominger systems, which they proved using different methods depending on the sign of $$\alpha '$$ . It is also the first case where the Anomaly flow can even be shown to exist for all time. This is in itself remarkable from the point of view of the theory of fully nonlinear partial differential equations, as the elliptic terms in the flow are not concave.
Slopes of modular forms and the ghost conjecture, II

We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the boundary of weight space".
Managed Blockchain Based Cryptocurrencies with Consensus Enforced Rules and Transparency

Blockchain based cryptocurrencies are usually unmanaged, distributed, consensus-based systems in which no single entity has control. Managed cryptocurrencies can be implemented using private blockchains but are fundamentally different as the owners have complete control to do arbitrary activity without transparency (since they control the mining). In this work we explore a hybrid approach where a managed cryptocurrency is maintained through distributed consensus based methods. The currency administrator can perform ongoing management functions while the consensus methods enforce the rules of the cryptocurrency and provide transparency for all management actions. This enables the introduction of money management features common in fiat currencies but where the managing entity cannot perform arbitrary actions and transparency is enforced. We thus eliminate the need for users to trust the currency administrator but also to enable the administrator to manage the cryptocurrency. We demonstrate how to implement our approach through modest modifications to the implicit Bitcoin specification, however, our approach can be applied to most any blockchain based cryptocurrency using a variety of consensus methods.
Negative (and positive) circles in signed graphs: A problem collection

Abstract A signed graph is a graph whose edges are labeled positive or negative. The sign of a circle (cycle, circuit) is the product of the signs of its edges. Most of the essential properties of a signed graph depend on the signs of its circles. Here I describe several questions regarding negative circles and their cousins the positive circles. Topics include incidence between signed circles and edges or vertices, characterizing signed graphs with special circle properties, counting negative circles, signed-circle packing and covering, signed circles and eigenvalues, and directed cycles in signed digraphs. A few of the questions come with answers.
Online, interactive user guidance for high-dimensional, constrained motion planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics.
Some special families of hyperelliptic curves

Let denote the locus of hyperelliptic curves of genus g whose automorphism group contains a subgroup isomorphic to G. We study spaces for G≅ℤn, ℤ2⊕ℤn, ℤ2⊕A4, or SL2(3). We show that for G≅ℤn, ℤ2⊕ℤn, the space is a rational variety and find generators of its function field. For G≅ℤ2⊕A4, SL2(3) we find a necessary condition in terms of the coefficients, whether or not the curve belongs to . Further, we describe algebraically the loci of such curves for g≤12 and show that for all curves in these loci, the field of moduli is a field of definition.
Maximal green sequences for quivers of finite mutation type

Abstract In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers of finite mutation type. In particular, we show that a mutation finite cluster quiver has a maximal green sequence unless it arises from a once-punctured closed marked surface, or one of the two quivers in the mutation class of X 7 . We develop a procedure to explicitly find maximal green sequences for cluster quivers associated to arbitrary triangulations of closed marked surfaces with at least two punctures. As a corollary, it follows that any triangulation of a marked surface with boundary has a maximal green sequence. We also compute explicit maximal green sequences for exceptional quivers of finite mutation type.
On the dimension of the Hilbert scheme of curves

Consider an irreducible component of the Hilbert scheme whose general point parameterizes a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such components when X is P, P or a smooth quadric threefold in P, respectively. Those bounds make sense from the asymptotic viewpoint if we fix d and let g vary. Some examples are constructed using determinantal varieties to show the sharpness of the bounds for d and g in a certain range. The results can be applied to study rigid curves.
NESTT: A Nonconvex Primal-Dual Splitting Method for Distributed and Stochastic Optimization

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into $N$ subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves $\epsilon$-stationary solution using $\mathcal{O}((\sum_{i=1}^N\sqrt{L_i/N})^2/\epsilon)$ gradient evaluations, which can be up to $\mathcal{O}(N)$ times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex $\ell_1$ penalized quadratic problems with polyhedral constraints. Further, we reveal a fundamental connection between {\it primal-dual} based methods and a few {\it primal only} methods such as IAG/SAG/SAGA.
On the Density of the Odd Values of the Partition Function

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely, the conjecture that the partition function p(n) is equidistributed modulo 2. Our main result will relate the densities, say, $${\delta_t}$$ , of the odd values of the t-multipartition functions $${p_t(n)}$$ , for several integers t. In particular, we will show that if $${\delta_t > 0}$$ for some $${t \in \{5, 7, 11, 13, 17, 19, 23, 25\}}$$ , then (assuming it exists) $${\delta_1 > 0}$$ ; that is, p(n) itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that p(n) is odd for $${\sqrt{x}}$$ values of $${n \leq x}$$ . In general, we conjecture that $${\delta_t = 1/2}$$ for all t odd, i.e., that similarly to the case of p(n), all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.
Metric recovery from directed unweighted graphs

We analyze directed, unweighted graphs obtained from xi 2 R d by connecting vertex i to j i jxi xjj < "(xi). Examples of such graphs include k-nearest neighbor graphs, where "(xi) varies from point to point, and, arguably, many real-world graphs such as copurchasing graphs. We ask whether we can recover the underlying Euclidean metric"(xi) and the associated density p(xi) given only the directed graph and d. We show that consistent recovery is possible up to isometric scaling when the vertex degree is at least!(n 2=(2+d) log(n) d=(d+2) ). Our estimator is based on a careful characterization of a random walk over the directed graph and the associated continuum limit. As an algorithm, it resembles the PageRank centrality metric. We demonstrate empirically that the estimator performs well on simulated examples as well as on real-world co-purchasing graphs even with a small number of points and degree scaling as low as log(n).
Matrix Completion for Structured Observations

The need to predict or fill-in missing data, often referred to as matrix completion, is a common challenge in today's data-driven world. Previous strategies typically assume that no structural difference between observed and missing entries exists. Unfortunately, this assumption is woefully unrealistic in many applications. For example, in the classic Netflix challenge, in which one hopes to predict user-movie ratings for unseen films, the fact that the viewer has not watched a given movie may indicate a lack of interest in that movie, thus suggesting a lower rating than otherwise expected. We propose adjusting the standard nuclear norm minimization strategy for matrix completion to account for such structural differences between observed and unobserved entries by regularizing the values of the unobserved entries. We show that the proposed method outperforms nuclear norm minimization in certain settings.
Fubini–Griffiths–Harris Rigidity of Homogeneous Varieties

Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.
$U(3)_C \times Sp(1)_L \times U(1)_L \times U(1)_R$

We outline the basic setting of the U(3)_C \times Sp(1)_L \times U(1)_L \times U(1)_R gauge theory and review the associated phenomenological aspects related to experimental searches for new physics at hadron colliders.
Debloating Software through Piece-Wise Compilation and Loading

Programs are bloated. Our study shows that only 5% of libc is used on average across the Ubuntu Desktop environment (2016 programs); the heaviest user, vlc media player, only needed 18%. In this paper: (1) We present a debloating framework built on a compiler toolchain that can successfully debloat programs (shared/static libraries and executables). Our solution can successfully compile and load most libraries on Ubuntu Desktop 16.04. (2) We demonstrate the elimination of over 79% of code from coreutils and 86% of code from SPEC CPU 2006 benchmark programs without affecting functionality. We show that even complex programs such as Firefox and curl can be debloated without a need to recompile. (3) We demonstrate the security impact of debloating by eliminating over 71% of reusable code gadgets from the coreutils suite and show that unused code that contains real-world vulnerabilities can also be successfully eliminated without adverse effects on the program. (4) We incur a low load time overhead.
Oriented and degree-generated block models: generating and inferring communities with inhomogeneous degree distributions

The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. The degree-corrected block model can accommodate arbitrary degree distributions within communities. But since it takes the vertex degrees as parameters rather than generating them, it cannot use them to help it classify the vertices, and its natural generalization to directed graphs cannot even use the orientations of the edges. In this paper, we present variants of the block model with the best of both worlds: they can use vertex degrees and edge orientations in the classification process, while tolerating heavy-tailed degree distributions within communities. We show that for some networks, including synthetic networks and networks of word adjacencies in English text, these new block models achieve a higher accuracy than either standard or degree-corrected block models.
A New Ensemble Learning Framework for 3D Biomedical Image Segmentation.

3D image segmentation plays an important role in biomedical image analysis. Many 2D and 3D deep learning models have achieved state-of-the-art segmentation performance on 3D biomedical image datasets. Yet, 2D and 3D models have their own strengths and weaknesses, and by unifying them together, one may be able to achieve more accurate results. In this paper, we propose a new ensemble learning framework for 3D biomedical image segmentation that combines the merits of 2D and 3D models. First, we develop a fully convolutional network based meta-learner to learn how to improve the results from 2D and 3D models (base-learners). Then, to minimize over-fitting for our sophisticated meta-learner, we devise a new training method that uses the results of the baselearners as multiple versions of “ground truths”. Furthermore, since our new meta-learner training scheme does not depend on manual annotation, it can utilize abundant unlabeled 3D image data to further improve the model. Extensive experiments on two public datasets (the HVSMR 2016 Challenge dataset and the mouse piriform cortex dataset) show that our approach is effective under fully-supervised, semisupervised, and transductive settings, and attains superior performance over state-of-the-art image segmentation methods.
Improved Range in the Return Times Theorem

We prove that the Return Times Theorem holds true for pairs of $L^p-L^q$ functions, whenever $\frac{1}{p}+\frac{1}{q}<{3/2}$.
Eigenvalue Decay Implies Polynomial-Time Learnability for Neural Networks

We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural distributional assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g. feed-forward networks of ReLUs). We make no assumptions on the structure of the network or the labels. Given sufficiently-strong eigenvalue decay, we obtain {\em fully}-polynomial time algorithms in {\em all} the relevant parameters with respect to square-loss. This is the first purely distributional assumption that leads to polynomial-time algorithms for networks of ReLUs. Further, unlike prior distributional assumptions (e.g., the marginal distribution is Gaussian), eigenvalue decay has been observed in practice on common data sets.
A note on the Schur-finiteness of linear sections

Making use of the recent theory of noncommutative motives, we prove that Schur-finiteness in the setting of Voevodsky's mixed motives is invariant under homological projective duality. As an application, we show that the mixed motives of smooth linear sections of certain (Lagrangian) Grassmannians, spinor varieties, and determinantal varieties, are Schur-finite. Finally, we upgrade our applications from Schur-finiteness to Kimura-finiteness.
Approximating Flexibility in Distributed Energy Resources: A Geometric Approach

With increasing availability of communication and control infrastructure at the distribution systems, it is expected that the distributed energy resources (DERs) will take an active part in future power systems operations. One of the main challenges associated with integration of DERs in grid planning and control is in estimating the available flexibility in a collection of (heterogeneous) DERs, each of which may have local constraints that vary over time. In this work, we present a geometric approach for approximating the flexibility of a DER in modulating its active and reactive power consumption. The proposed method is agnostic about the type and model of the DERs, thereby facilitating a plug-and-play approach, and allows scalable aggregation of the flexibility of a collection of (heterogeneous) DERs at the distributed system level. Simulation results are presented to demonstrate the performance of the proposed method.
Algorithms and complexity of range clustering

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called clusters or classes, consisting of similar objects so that different clusters are as dissimilar as possible. We propose a number of objective functions that employ the range of the clusters as part of the objective function. Several of the proposed objectives mimic objectives based on sums of similarities. These objective functions are motivated by image segmentation problems, where the diameter, or range of values associated with objects in each cluster, should be small. It is demonstrated that range-based problems are in general easier, in terms of their complexity, than the analogous similarity-sum problems. Several of the problems we present could therefore be viable alternatives to existing clustering problems which are NP-hard, offering the advantage of efficient algorithms.
Positional effects on citation and readership in arXiv

arXiv.org mediates contact with the literature for entire scholarly communities, providing both archival access and daily email and web announcements of new materials. We confirm and extend a surprising correlation between article position in these initial announcements and later citation impact, due primarily to intentional “self-promotion” by authors. There is, however, also a pure “visibility” effect: the subset of articles accidentally in early positions fared measurably better in the long-term citation record. Articles in astrophysics (astro-ph) and two large subcommunities of theoretical high energy physics (hep-th and hep-ph) announced in position 1, for example, respectively received median numbers of citations 83p, 50p, and 100p higher than those lower down, while the subsets there accidentally had 44p, 38p, and 71p visibility boosts. We also consider the positional effects on early readership. The median numbers of early full text downloads for astro-ph, hep-th, and hep-ph articles announced in position 1 were 82p, 61p, and 58p higher than for lower positions, respectively, and those there accidentally had medians visibility-boosted by 53p, 44p, and 46p. Finally, we correlate a variety of readership features with long-term citations, using machine learning methods, and conclude with some observations on impact metrics and the dangers of recommender mechanisms. © 2009 Wiley Periodicals, Inc.
Striations in PageRank-ordered matrices

Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small-world phenomenon in social networks. The discovery and modeling of such regular patterns has a wide application from disease propagation to financial markets. In this work, we describe a newly discovered regularly occurring striation pattern found in the PageRank ordering of adjacency matrices that encode real-world networks. We demonstrate that these striations are the result of well-known graph-generation processes resulting in regularities that are manifested in the typical neighborhood distribution. The spectral view explored in this paper encodes a tremendous amount about the explicit and implicit topology of a given network, so we also discuss the interesting network properties, outliers and anomalies that a viewer can determine from a brief look at the re-ordered matrix.
Tree-Residue Vertex-Breaking: a new tool for proving hardness.

In this paper, we introduce a new problem called Tree-Residue Vertex-Breaking (TRVB): given a multigraph $G$ some of whose vertices are marked "breakable," is it possible to convert $G$ into a tree via a sequence of "vertex-breaking" operations (replacing a degree-$k$ breakable vertex by $k$ degree-$1$ vertices, disconnecting the $k$ incident edges)? We characterize the computational complexity of TRVB with any combination of the following additional constraints: $G$ must be planar, $G$ must be a simple graph, the degree of every breakable vertex must belong to an allowed list $B$, and the degree of every unbreakable vertex must belong to an allowed list $U$. The two results which we expect to be most generally applicable are that (1) TRVB is polynomially solvable when breakable vertices are restricted to have degree at most $3$; and (2) for any $k \ge 4$, TRVB is NP-complete when the given multigraph is restricted to be planar and to consist entirely of degree-$k$ breakable vertices. To demonstrate the use of TRVB, we give a simple proof of the known result that Hamiltonicity in max-degree-$3$ square grid graphs is NP-hard. We also demonstrate a connection between TRVB and the Hypergraph Spanning Tree problem. This connection allows us to show that the Hypergraph Spanning Tree problem in $k$-uniform $2$-regular hypergraphs is NP-complete for any $k \ge 4$, even when the incidence graph of the hypergraph is planar.
The multiplicative eigenvalue problem and deformed quantum cohomology

Abstract We construct deformations of the small quantum cohomology rings of homogeneous spaces G / P , and obtain an irredundant set of inequalities determining the multiplicative eigen polytope for the compact form K of G .
Nonparametric risk bounds for time-series forecasting

We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space models. These nonasymptotic bounds need only weak assumptions on the data-generating process, yet allow forecasters to select among competing models and to guarantee, with high probability, that their chosen model will perform well. We motivate our techniques with and apply them to standard economic and financial forecasting tools--a GARCH model for predicting equity volatility and a dynamic stochastic general equilibrium model (DSGE), the standard tool in macroeconomic forecasting. We demonstrate in particular how our techniques can aid forecasters and policy makers in choosing models which behave well under uncertainty and mis-specification.
Dehn filling and the Thurston norm

For a compact, orientable, irreducible $3$-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary torus has a finite set of slopes such that, if avoided, the Thurston norm of a Dehn filling behaves predictably. More precisely, for all but finitely many slopes, the Thurston norm of a class in the second homology of the filled manifold plus the so-called winding norm of the class will be equal to the Thurston norm of the corresponding class in the second homology of the unfilled manifold. This generalizes a result of Sela and is used to answer a question of Baker–Motegi concerning the Seifert genus of knots obtained by twisting a given initial knot along an unknot which links it.
Analytical modeling for rapid design of bistable buckled beams

Abstract Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics, energy harvesting, and microelectromechanical system (MEMS). However, their design often requires time-consuming and expensive computations. In this work, we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force. Based on the Euler–Bernoulli beam theory, we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties. This model is verified against the results from a finite element analysis (FEA) model, with maximum discrepancy less than 7%. By analyzing and simplifying our theoretical model, we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam. These behavioral values include critical force, critical displacement, and travel, which are generally sufficient for characterizing the snap-through properties of a bistable buckled beam. Based on these analytical formulas, we investigate the influence of a bistable buckled beam's key design parameters, including its actuation position and precompression, on its critical behavioral values, with our results validated by FEA simulations. Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.
Efficient Constellation-Based Map-Merging for Semantic SLAM

Data association in SLAM is fundamentally challenging, and handling ambiguity well is crucial to achieve robust operation in real-world environments. When ambiguous measurements arise, conservatism often mandates that the measurement is discarded or a new landmark is initialized rather than risking an incorrect association. To address the inevitable “duplicate” landmarks that arise, we present an efficient map-merging framework to detect duplicate constellations of landmarks, providing a high-confidence loopclosure mechanism well-suited for object-level SLAM. This approach uses an incrementally-computable approximation of landmark uncertainty that only depends on local information in the SLAM graph, avoiding expensive recovery of the full system covariance matrix. This enables a search based on geometric consistency (GC) (rather than full joint compatibility (JC)) that inexpensively reduces the search space to a handful of “best” hypotheses. Furthermore, we reformulate the commonly-used interpretation tree to allow for more efficient integration of clique-based pairwise compatibility, accelerating the branch-and-bound max-cardinality search. Our method is demonstrated to match the performance of full JC methods at significantly-reduced computational cost, facilitating robust object-based loop-closure over large SLAM problems.
Selecting the independent coordinates of manifolds with large aspect ratios

Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized. Mathematically, success is possible under very broad conditions, provided that embedding is done by carefully selected eigenfunctions of the Laplace-Beltrami operator $\Delta_\M$. Hence, we propose a bicriterial Independent Eigencoordinate Selection (IES) algorithm that selects smooth embeddings with few eigenvectors. The algorithm is grounded in theory, has low computational overhead, and is successful on synthetic and large real data.