cssi/SciSciGPT-SciSciNet huggingface dataset:
NUMERICAL ALGORITHMS FOR DUAL BASES OF POSITIVE-DIMENSIONAL IDEALS

An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However the usual standard basis algorithms are not numerically stable. A numerically stable approach to describing the ideal is by finding the space of dual functionals that annihilate it, which reduces the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.
On a surface formed by randomly gluing together polygonal discs

Starting with a collection of n oriented polygonal discs, with an even number N of sides in total, we generate a random oriented surface by randomly matching the sides of discs and properly gluing them together. Encoding the surface by a random permutation γ of N , we use the Fourier transform on S N to show that γ is asymptotic to the permutation distributed uniformly on the alternating group A N ( A N c resp.) if N - n and N / 2 are of the same (opposite resp.) parity. We use this to prove a local central limit theorem for the number of vertices on the surface, whence also for its Euler characteristic ?. We also show that with high probability (as N ? ∞ , uniformly in n) the random surface consists of a single component, and thus has a well-defined genus g = 1 - ? / 2 , which is asymptotic to a Gaussian random variable, with mean ( N / 2 - n - log ? N ) / 2 and variance ( log ? N ) / 4 .
A Catalog of Stars Observed Simultaneously by Kepler and TESS

The Kepler spacecraft provided the first long-baseline, high-precision photometry for large numbers of stars. This enabled the discovery of thousands of new exoplanets, and the characterization of myriad astrophysical phenomena. However, one of the challenges with interpreting Kepler data has been that no instrument has provided a comparison dataset. Therefore, the replication of Kepler time-series data has remained elusive. The Transiting Exoplanet Survey Satellite (TESS) launched in April 2018 and began science operations in July 2018. During the TESS primary mission, it will survey 85% of the sky. NASA's first two observatories dedicated to discovering exoplanets, Kepler and TESS, were simultaneously operating during 2018. While the Kepler's K2 mission surveyed the ecliptic plane, TESS targets fields outside the ecliptic. However, during September 2018, a small region of the sky was observed simultaneously by both TESS and Kepler as part of TESS's Sector 2 (Aug 22 - Sep 20, 2018) and K2 Campaign 19 (Sep 7 - Sep 26, 2018). The overlap region was 0.5 sq. deg. We identified 171 K2 targets that fell inside TESS Sector 2 field of view, all of which are observed at 30-minute cadence by both missions. The targets range in brightness in the TESS bandpass (Tmag) from 6.7-18.4, with 93 targets brighter than Tmag=15, and 17 brighter than Tmag=12. This dataset provides the first simultaneous, long-duration, high-precision observations of the same targets from different space-based observatories and presents an excellent opportunity to explore instrumental systematics present in the two telescopes.
Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories

We introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the e-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained for two-color QCD with quarks in the fundamental representation of the color group as well as any-color QCD with quarks in the adjoint representation. For Nc = 2 we also have obtained the lattice spacing dependence of the quenched average spectral density for a fixed value of the index of the Dirac operator. Comparisons with direct numerical simulations of the random matrix ensemble are shown.
Maximally Frobenius-destabilized vector bundles over smooth algebraic curves

Vector bundles in positive characteristics have a tendency to be destabilized after pulling back by the Frobenius morphism. In this paper, we closely examine vector bundles over curves that are, in an appropriate sense, maximally destabilized by the Frobenius morphism. Then we prove that such bundles of rank 2 exist over any curve in characteristic 3, and are unique up to twisting by a line bundle. We also give an application of such bundles to the study of ample vector bundles, which is valid in all characteristics.
Waving transport and propulsion in a generalized Newtonian fluid

Abstract Cilia and flagella are hair-like appendages that protrude from the surface of a variety of eukaryotic cells and deform in a wavelike fashion to transport fluids and propel cells. Motivated by the ubiquity of non-Newtonian fluids in biology, we address mathematically the role of shear-dependent viscosities on both the waving flagellar locomotion and ciliary transport by metachronal waves. Using a two-dimensional waving sheet as model for the kinematics of a flagellum or an array of cilia, and allowing for both normal and tangential deformation of the sheet, we calculate the flow field induced by a small-amplitude deformation of the sheet in a generalized Newtonian Carreau fluid up to order four in the dimensionless waving amplitude. The net flow induced far from the sheet can be interpreted either as a net pumping flow or, in the frame moving with the sheet, as a swimming velocity. At leading order (square in the waving amplitude), the net flow induced by the waving sheet and the rate of viscous dissipation is the same as the Newtonian case, but is different at the next nontrivial order (four in the waving amplitude). If the sheet deforms both in the directions perpendicular and parallel to the wave progression, the shear-dependence of the viscosity leads to a nonzero flow induced in the far field while if the sheet is inextensible, the non-Newtonian influence is exactly zero. Shear-thinning and shear-thickening fluids are seen to always induce opposite effects. When the fluid is shear-thinning, the rate of working of the sheet against the fluid is always smaller than in the Newtonian fluid, and the largest gain is obtained for antiplectic metachronal waves. Considering a variety of deformation kinematics for the sheet, we further show that in all cases transport by the sheet is more efficiency in a shear-thinning fluid, and in most cases the transport speed in the fluid is also increased. Comparing the order of magnitude of the shear-thinning contributions with past work on elastic effects as well as the magnitude of the Newtonian contributions, our theoretical results, which beyond the Carreau model are valid for a wide class of generalized Newtonian fluids, suggest that the impact of shear-dependent viscosities on transport could play a major biological role.
Geo-neutrinos: recent developments

Abstract Radiogenic heating is a key component of the energy balance and thermal evolution of the Earth. It contributes to mantle convection, plate tectonics, volcanoes, and mountain building. Geo-neutrino observations estimate the present radiogenic power of our planet. This estimate depends on the quantity and distribution of heat-producing elements in various Earth reservoirs. Of particular geological importance is radiogenic heating in the mantle. This quantity informs the origin and thermal evolution of our planet. Here we present: currently reported geo-neutrino observations; estimates of the mantle geo-neutrino signal, mantle radiogenic heating, and mantle cooling; a comparison of chemical Earth model predictions of the mantle geo-neutrino signal and mantle radiogenic heating; a brief discussion of radiogenic heating in the core, including calculations of geo-neutrino signals per pW/kg; and finally a discussion of observational strategy.
Variation of the Liouville measure of a hyperbolic surface

For a compact Riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the Riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, which does depend on the metric. For a surface S , we show that the map which to a hyperbolic metric on S associates its Liouville transverse measure is differentiable, in an appropriate sense. Its tangent map is valued in the space of transverse Holder distributions for the geodesic foliation.
AN ASYMPTOTICALLY TIGHT BOUND ON THE Q-INDEX OF GRAPHS WITH FORBIDDEN CYCLES

Communicated by Slobodan Simic Abstract. Let G be a graph of order n and let q(G) be the largest eigenvalue of the signless Laplacian of G. It is shown that if k > 2, n > 5k 2 , and q(G) > n + 2k 2, then G contains a cycle of length l for each l 2 {3, 4, . . . , 2k + 2}. This bound on q(G) is asymptotically tight, as the graph Kk _ Kn k contains no cycles longer than 2k and q(Kk _ Kn k) > n + 2k 2 2k(k 1) n + 2k 3 . The main result gives an asymptotic solution to a recent conjecture about the maximum q(G) of a graph G with forbidden cycles. The proof of the main result and the tools used therein could serve as a guidance to the proof of the full conjecture.
Rate of convergence of the mean for sub-additive ergodic sequences

Abstract For sub-additive ergodic processes { X m , n } with weak dependence, we analyze the rate of convergence of E X 0 , n / n to its limit g. We define an exponent γ given roughly by E X 0 , n ∼ n g + n γ , and, assuming existence of a fluctuation exponent χ that gives Var X 0 , n ∼ n 2 χ , we provide a lower bound for γ of the form γ ≥ χ . The main requirement is that χ ≠ 1 / 2 . In the case χ = 1 / 2 and under the assumption Var X 0 , n = O ( n / ( log ⁡ n ) β ) for some β > 0 , we prove γ ≥ χ − c ( β ) for a β-dependent constant c ( β ) . These results show in particular that non-diffusive fluctuations are associated to non-trivial γ. Various models, including first-passage percolation, directed polymers, the minimum of a branching random walk and bin packing, fall into our general framework, and the results apply assuming χ exists. In the case of first-passage percolation in Z d , we provide a version of γ ≥ − 1 / 2 without assuming existence of χ.
The New Superconductor tP-SrPd2Bi2: Structural Polymorphism and Superconductivity in Intermetallics

We consider a system where structural polymorphism suggests the possible existence of superconductivity through the implied structural instability. SrPd2Bi2 has two polymorphs, which can be controlled by the synthesis temperature: a tetragonal form (CaBe2Ge2-type) and a monoclinic form (BaAu2Sb2-type). Although the crystallographic difference between the two forms may, at first, seem trivial, we show that tetragonal SrPd2Bi2 is superconducting at 2.0 K, whereas monoclinic SrPd2Bi2 is not. We rationalize this finding and place it in context with other 1–2–2 phases.
A gap theorem for the complex geometry of convex domains

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain must be strongly pseudoconvex. One consequence of our general result is the following: for any dimension there exists some $\epsilon > 0$ so that if the squeezing function on a smoothly bounded convex domain is greater than $1-\epsilon$ outside a compact set, then the domain is strongly pseudoconvex (and hence the squeezing function limits to one on the boundary). Another consequence is the following: for any dimension $d$ there exists some $\epsilon > 0$ so that if the holomorphic sectional curvature of the Bergman metric on a smoothly bounded convex domain is within $\epsilon$ of $-4/(d+1)$ outside a compact set, then the domain is strongly pseudoconvex (and hence the holomorphic sectional curvature limits to $-4/(d+1)$ on the boundary).
Counting generic measures for a subshift of linear growth

In 1984 Boshernitzan proved an upper bound on the number of ergodic measures for a minimal subshift of linear block growth and asked if it could be lowered without further assumptions on the shift. We answer this question, showing that Boshernitzan's bound is sharp. We further prove that the same bound holds for the, a priori, larger set of nonatomic generic measures, and that this bound remains valid even if one drops the assumption of minimality. Applying these results to interval exchange transformations, we give an upper bound on the number of nonatomic generic measures of a minimal IET, answering a question recently posed by Chaika and Masur.
Convexified convolutional neural networks

We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a reproducing kernel Hilbert space, the CNN parameters can be represented in terms of a low-rank matrix, and the rank constraint can be relaxed so as to obtain a convex optimization problem. For learning two-layer convolutional neural networks, we prove that the generalization error obtained by a convexified CNN converges to that of the best possible CNN. For learning deeper networks, we train CCNNs in a layer-wise manner. Empirically, we find that CC-NNs achieve competitive or better performance than CNNs trained by backpropagation, SVMs, fully-connected neural networks, stacked denoising auto-encoders, and other baseline methods.
CUBE NUMBER CAN DETECT CHIRALITY AND LEGENDRIAN TYPE OF KNOTS

For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. Examples of knots for which the cube number detects chirality are presented. An example is also presented of two Legendrian knots that, while topologically isotopic, are distinguished as Legendrian knots by cube number.
Accelerated development of CuSbS2 thin film photovoltaic device prototypes

Development of alternative thin film photovoltaic technologies is an important research topic because of the potential of low-cost, high-efficiency solar cells to produce terawatt levels of clean power. However, this development of unexplored yet promising absorbers can be hindered by complications that arise during solar cell fabrication. Here, a high-throughput combinatorial method is applied to accelerate development of photovoltaic devices, in this case, using the novel CuSbS2 absorber via a newly developed three-stage self-regulated growth process to control absorber purity and orientation. Photovoltaic performance of the absorber, using the typical substrate CuInxGa1 − xSe2 (CIGS) device architecture, is explored as a function of absorber quality and thickness using a variety of back contacts. This study yields CuSbS2 device prototypes with ~1% conversion efficiency, suggesting that the optimal CuSbS2 device fabrication parameters and contact selection criteria are quite different than for CIGS, despite the similarity of these two absorbers. The CuSbS2 device efficiency is at present limited by low short-circuit current because of bulk recombination related to defects, and a small open-circuit voltage because of a theoretically predicted cliff-type conduction band offset between CuSbS2 and CdS. Overall, these results illustrate both the potential and limits of combinatorial methods to accelerate the development of thin film photovoltaic devices using novel absorbers. Copyright © 2016 John Wiley & Sons, Ltd.
Livšic Theorem for matrix cocycles

We prove the Liv sic Theorem for arbitrary GL( m;R) cocycles. We con- sider a hyperbolic dynamical system f : X! X and a Holder continuous function A : X! GL(m;R). We show that if A has trivial periodic data, i.e. A(f n 1 p) A(fp)A(p) = Id for each periodic point p = f n p, then there exists a Holder continuous function C : X ! GL(m;R) satisfying A(x) = C(fx)C(x) 1 for all x2 X. The main new ingredients in the proof are results of independent interest on relations between the periodic data, Lyapunov exponents, and uniform estimates on growth of products along orbits for an arbitrary Holder function A.
Heterogeneous MPSoCs for Mixed-Criticality Systems: Challenges and Opportunities

Editor’s note: This article presents the challenges and the opportunities in designing mixed-criticality systems with heterogeneous Multiple-Processor System-on-Chip (MPSoC) architectures. —Tulika Mitra, National University of Singapore —Jurgen Teich, Friedrich-Alexander-Universitat Erlangen-Nurnberg—Lothar Thiele, ETH Zurich
Renormalization of Einstein gravity through a derivative-dependent field redefinition

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-...
Federated multi-task learning

Federated learning poses new statistical and systems challenges in training machine learning models over distributed networks of devices. In this work, we show that multi-task learning is naturally suited to handle the statistical challenges of this setting, and propose a novel systems-aware optimization method, MOCHA, that is robust to practical systems issues. Our method and theory for the first time consider issues of high communication cost, stragglers, and fault tolerance for distributed multi-task learning. The resulting method achieves significant speedups compared to alternatives in the federated setting, as we demonstrate through simulations on real-world federated datasets.
Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Abstract Guided by theoretical predictions, we have demonstrated experimentally the existence of negative refraction on the two lowest acoustic-branch passbands (shear and longitudinal modes) of a simple two-dimensional phononic crystal consisting of an isotropic stiff (aluminum) matrix and square-patterned isotropic compliant (PMMA) circular inclusions. We experimentally distinguished the shear and longitudinal modes to ensure that there are no couplings between the two modes and that the shear-mode negative refraction is an inherent property of periodic composites with stiff matrix and compliant inclusions. We have also discovered that a composite with compliant (PMMA) matrix and stiff (aluminum) inclusions does not display negative shear-mode refraction on its first branch. At frequencies and wave vectors where the refraction on the acoustic-branch passbands is negative, the effective mass-density and the effective stiffness tensors of the crystal are positive-definite, and this is an inherent property of such phononic crystals.The equi-frequency contours and energy flux vectors as functions of the phase-vector components, reveal a rich body of refractive properties that can be exploited to realize, for example, beam splitting, focusing, and frequency filtration on the lowest passbands of the crystal where the dissipation is minimum. By proper selection of material and geometric parameters these phenomena can be realized at remarkably low frequencies (large wave lengths) using rather small simple two-phase unit cells.
Section problems for configuration spaces of surfaces

In this paper, we give a close-to-sharp answer to the basic questions: When is there a continuous way to add a point to a configuration of n ordered points on a surface S of finite type so that all...
A cubic algorithm for computing gaussian volume

We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of the integration algorithm is O*(n3) while the complexity of the sampling algorithm is O*(n3) for the first sample and O*(n2) for every subsequent sample. These bounds improve on the corresponding state-of-the-art by a factor of n. Our improvement comes from several aspects: better isoperimetry, smoother annealing, avoiding transformation to isotropic position and the use of the "speedy walk" in the analysis. .
Support varieties for Hecke algebras

Let ${\mathcal H}_{q}(d)$ be the Iwahori-Hecke algebra for the symmetric group, where $q$ is a primitive $l$th root of unity. In this paper we develop a theory of support varieties which detects natural homological properties such as the complexity of modules. The theory the authors develop has a canonical description in an affine space where computations are tractable. The ideas involve the interplay with the computation of the cohomology ring due to Benson, Erdmann and Mikaelian, the theory of vertices due to Dipper and Du, and branching results for cohomology by Hemmer and Nakano. Calculations of support varieties and vertices are presented for permutation, Young and classes of Specht modules. Furthermore, a discussion of how the authors' results can be extended to other Hecke algebras for other classical groups is presented at the end of the paper.
Lipschitz Continuity in Model-based Reinforcement Learning

We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the Wasserstein metric. We go on to prove an error bound for the value-function estimate arising from Lipschitz models and show that the estimated value function is itself Lipschitz. We conclude with empirical results that show the benefits of controlling the Lipschitz constant of neural-network models.
On Birman's sequence of Hardy–Rellich-type inequalities

Abstract In 1961, Birman proved a sequence of inequalities { I n } , for n ∈ N , valid for functions in C 0 n ( ( 0 , ∞ ) ) ⊂ L 2 ( ( 0 , ∞ ) ) . In particular, I 1 is the classical (integral) Hardy inequality and I 2 is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space H n ( [ 0 , ∞ ) ) of functions defined on [ 0 , ∞ ) . Moreover, f ∈ H n ( [ 0 , ∞ ) ) implies f ′ ∈ H n − 1 ( [ 0 , ∞ ) ) ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite b > 0 , these inequalities hold on the standard Sobolev space H 0 n ( ( 0 , b ) ) . Furthermore, in all cases, the Birman constants [ ( 2 n − 1 ) ! ! ] 2 / 2 2 n in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in L 2 ( ( 0 , ∞ ) ) (resp., L 2 ( ( 0 , b ) ) ). We also show that these Birman constants are related to the norm of a generalized continuous Cesaro averaging operator whose spectral properties we determine in detail.
Pseudo-locality for a coupled Ricci flow

Let $(M,g,\phi)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $\phi$. We show that a complete, $\kappa$-noncollapsed solution $(M,g,\phi)$ to this coupled Ricci flow with a Type I singularity at time $T<\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow.
On Blow-Ups and Injectivity of Quivers

This work connects the idea of a "blow-up" of a quiver with that of injectivity, showing that for a class of monic maps $\Phi$, a quiver is $\Phi$-injective if and only if all blow-ups of it are as well. This relationship is then used to characterize all quivers that are injective with respect to the natural embedding of $P_{n}$ into $C_{n}$.
Homological stability for symmetric complements

A conjecture of Vakil and Wood (2015) states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the case of connected manifolds of dimension at least 2 and give an explicit homological stability range.
Calabi–Yau Frobenius algebras

Abstract We define Calabi–Yau Frobenius algebras over arbitrary base commutative rings. We define a Hochschild analogue of Tate cohomology, and show that this “stable Hochschild cohomology” of periodic CY Frobenius algebras has a Batalin–Vilkovisky and Frobenius algebra structure. Such algebras include (centrally extended) preprojective algebras of (generalized) Dynkin quivers, and group algebras of classical periodic groups. We use this theory to compute (for the first time) the Hochschild cohomology of many algebras related to quivers, and to simplify the description of known results. Furthermore, we compute the maps on cohomology from extended Dynkin preprojective algebras to the Dynkin ones, which relates our CY property (for Frobenius algebras) to that of Ginzburg (for algebras of finite Hochschild dimension).
Zero Shot Learning for Code Education: Rubric Sampling with Deep Learning Inference.

In modern computer science education, massive open online courses (MOOCs) log thousands of hours of data about how students solve coding challenges. Being so rich in data, these platforms have garnered the interest of the machine learning community, with many new algorithms attempting to autonomously provide feedback to help future students learn. But what about those first hundred thousand students? In most educational contexts (i.e. classrooms), assignments do not have enough historical data for supervised learning. In this paper, we introduce a human-in-the-loop “rubric sampling” approach to tackle the “zero shot” feedback challenge. We are able to provide autonomous feedback for the first students working on an introductory programming assignment with accuracy that substantially outperforms data-hungry algorithms and approaches human level fidelity. Rubric sampling requires minimal teacher effort, can associate feedback with specific parts of a student’s solution and can articulate a student’s misconceptions in the language of the instructor. Deep learning inference enables rubric sampling to further improve as more assignment specific student data is acquired. We demonstrate our results on a novel dataset from Code.org, the world’s largest programming education platform.
Affine Grassmannians and the geometric Satake in mixed characteristic

We endow the set of lattices in Q^n_p with a reasonable algebro-geometric structure. As a result, we prove the representability of affine Grassmannians and establish the geometric Satake equivalence in mixed characteristic. We also give an application of our theory to the study of Rapoport-Zink spaces.
A geometric proof of the Feigin-Frenkel theorem

We reprove the theorem of Feigin and Frenkel relating the center of the critical level enveloping algebra of the Kac-Moody algebra for a semisimple Lie algebra to opers (which are certain de Rham local systems with extra structure) for the Langlands dual group. Our proof incorporates a construction of Beilinson and Drinfeld relating the Feigin-Frenkel isomorphism to (more classical) Langlands duality through the geometric Satake theorem.
Gain function approximation in the feedback particle filter

This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to approximate this solution using only particles sampled from the probability distribution. Two algorithms are presented: a Galerkin algorithm and a kernel-based algorithm. Both the algorithms are adapted to the samples and do not require approximation of the probability distribution as an intermediate step. The paper contains a preliminary error analysis for the algorithms as well as some comparative numerical results for a non-Gaussian distribution. These algorithms are also applied and illustrated for a simple nonlinear filtering example.
Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization

Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantees and impressive numerical performance. In this paper, we generalize HTP from compressed sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard truncation step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods when applied to learning tasks of sparse logistic regression and sparse support vector machines.
Retrofitting Distributional Embeddings to Knowledge Graphs with Functional Relations

Knowledge graphs are a versatile framework to encode richly structured data relationships, but it can be challenging to combine these graphs with unstructured data. Methods for retrofitting pre-trained entity representations to the structure of a knowledge graph typically assume that entities are embedded in a connected space and that relations imply similarity. However, useful knowledge graphs often contain diverse entities and relations (with potentially disjoint underlying corpora) which do not accord with these assumptions. To overcome these limitations, we present Functional Retrofitting, a framework that generalizes current retrofitting methods by explicitly modeling pairwise relations. Our framework can directly incorporate a variety of pairwise penalty functions previously developed for knowledge graph completion. Further, it allows users to encode, learn, and extract information about relation semantics. We present both linear and neural instantiations of the framework. Functional Retrofitting significantly outperforms existing retrofitting methods on complex knowledge graphs and loses no accuracy on simpler graphs (in which relations do imply similarity). Finally, we demonstrate the utility of the framework by predicting new drug–disease treatment pairs in a large, complex health knowledge graph.
Geometric aspects of representation theory for DG algebras: answering a question of Vasconcelos

We apply geometric techniques from representation theory to the study of homologically finite differential graded (DG) modules M over a finite dimensional, positively graded, commutative DG algebra U. In particular, in this setting we prove a version of a theorem of Voigt by exhibiting an isomorphism between the Yoneda Ext group YExtU1(M,M) and a quotient of tangent spaces coming from an algebraic group action on an algebraic variety. As an application, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many semidualizing complexes up to shift-isomorphism in the derived category D(R).
Multilinear embedding estimates for the fractional Laplacian

Three novel multilinear embedding estimates for the fractional Laplacian are obtained in terms of trace integrals restricted to the diagonal. The resulting sharp inequalities may be viewed as extensions of the Hardy-Littlewood-Sobolev inequality, the Gagliardo-Nirenberg inequality and Pitt's inequality.
Variations on average character degrees and p -nilpotence

We prove that if p is an odd prime, G is a solvable group, and the average value of the irreducible characters of G whose degrees are not divisible by p is strictly less than 2(p + 1)/(p + 3), then G is p-nilpotent. We show that there are examples that are not p-nilpotent where this bound is met for every prime p. We then prove a number of variations of this result.
The shape of cubic fields

We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the quantitative equidistribution of the shape of cubic fields when the fields are ordered by discriminant.
Mitchell's theorem revisited

Abstract Mitchell's theorem on the approachability ideal states that it is consistent relative to a greatly Mahlo cardinal that there is no stationary subset of ω 2 ∩ cof ( ω 1 ) in the approachability ideal I [ ω 2 ] . In this paper we give a new proof of Mitchell's theorem, deriving it from an abstract framework of side condition methods.
Eigenfunctions of Periodic Differential Operators Analytic in a Strip

Ordinary differential operators with periodic coefficients analytic in a strip act on a Hardy–Hilbert space of analytic functions with inner product defined by integration over a period on the boundary of the strip. Simple examples show that eigenfunctions may form a complete set for a narrow strip, but completeness may be lost for a wide strip. Completeness of the eigenfunctions in the Hardy–Hilbert space is established for regular second order operators with matrix-valued coefficients when the leading coefficient satisfies a positive real part condition throughout the strip.
Monolayer adsorption of noble gases on graphene

Abstract We report our results of simulations of the adsorption of noble gases (Kr, Ar, Xe) on graphene. For Kr, we consider two configurations: supported and free-standing graphene, where atoms are adsorbed only on one or two sides of the graphene. For Ar and Xe, we studied only the case of supported graphene. For the single-side adsorption, we calculated the two-dimensional gas-liquid critical temperature for each adsorbate. We determined the different phases of the monolayers and constructed the phase diagrams. We found two-dimensional incommensurate solid phases for krypton, argon and xenon, and a two-dimensional commensurate solid phase for krypton. For double side adsorption of Kr, we do not see evidence of an ordering transition driven by the interlayer forces.
Secure Transmission of Delay-Sensitive Data Over Wireless Fading Channels

In this paper, throughput and energy efficiency of secure wireless transmission of delay sensitive data generated by random sources is studied. A fading broadcast model in which the transmitter sends confidential and common messages to two receivers is considered. It is assumed that the common and confidential data, generated from Markovian sources, are stored in buffers prior to transmission, and the transmitter operates under constraints on buffer/delay violation probability. Under such statistical quality-of-service constraints, effective capacity of time-varying wireless transmissions and effective bandwidth of Markovian sources are employed to determine the throughput. In particular, secrecy capacity is used to describe the service rate of buffers containing confidential messages. Moreover, energy per bit is used as the energy efficiency metric and energy efficiency is studied in the low signal-to-noise regime. Specifically, minimum energy per bit required for the reliable communication of common and confidential messages is determined and wideband slope expressions are identified. The impact of buffer/delay constraints, correlation between channels, source characteristics/burstiness, channel knowledge at the transmitter, power allocation, and secrecy requirements on the throughput and energy efficiency of common and confidential message transmissions is identified.
Quantum cognition: The possibility of processing with nuclear spins in the brain

Abstract The possibility that quantum processing with nuclear spins might be operative in the brain is explored. Phosphorus is identified as the unique biological element with a nuclear spin that can serve as a qubit for such putative quantum processing–a neural qubit–while the phosphate ion is the only possible qubit-transporter. We identify the “Posner molecule”, Ca 9 ( PO 4 ) 6 , as the unique molecule that can protect the neural qubits on very long times and thereby serve as a (working) quantum-memory. A central requirement for quantum-processing is quantum entanglement. It is argued that the enzyme catalyzed chemical reaction which breaks a pyrophosphate ion into two phosphate ions can quantum entangle pairs of qubits. Posner molecules, formed by binding such phosphate pairs with extracellular calcium ions, will inherit the nuclear spin entanglement. A mechanism for transporting Posner molecules into presynaptic neurons during vesicle endocytosis is proposed. Quantum measurements can occur when a pair of Posner molecules chemically bind and subsequently melt, releasing a shower of intra-cellular calcium ions that can trigger further neurotransmitter release and enhance the probability of post-synaptic neuron firing. Multiple entangled Posner molecules, triggering non-local quantum correlations of neuron firing rates, would provide the key mechanism for neural quantum processing. Implications, both in vitro and in vivo, are briefly mentioned.
A touch of sleep: biophysical model of contact-mediated dormancy of archaea by viruses.

The canonical view of the interactions between viruses and their microbial hosts presumes that changes in host and virus fate requires the initiation of infection of a host by a virus. Infection may lead to the death of the host cell and release of viruses, to the elimination of the viral genome through cellular defence mechanisms or the integration of the viral genome with the host as a chromosomal or extrachromosomal element. Here, we revisit this canonical view, inspired by recent experimental findings in which the majority of target host cells can be induced into a dormant state when exposed to either active or deactivated viruses, even when viruses are present at low relative titre. We propose that both the qualitative phenomena and the quantitative timescales of dormancy induction are consistent with the hypothesis that cellular physiology can be altered by contact on the surface of host cells rather than strictly by infection . In order to test this hypothesis, we develop and study a biophysical model of contact-mediated dynamics involving virus particles and target cells. We show how virus particles can catalyse cellular transformations among many cells, even if they ultimately infect only one (or none). We also find that population-scale dormancy is robust to variation in the representation of model dynamics, including cell growth, death and recovery.
On the Characterization of Local Nash Equilibria in Continuous Games

We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria . Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.
Ab initio calculations of the atomic and electronic structures of crystalline PEO3:LiCF3SO3 electrolytes

Abstract The PEO3:LiCF3SO3 polymer electrolyte has attracted significant research due to its enhanced stability at the lithium/polymer interface of high conductivity polymer batteries. Experimental studies have shown that, depending on the preparation conditions, both the PEO3:LiCF3SO3 crystalline complex and the PEO3:LiCF3SO3 amorphous phase can be formed. However, previous theoretical investigations focused on the short chain amorphous PEO3:LiCF3SO3 system. We report ab initio density-functional-theory calculations of crystalline PEO3:LiCF3SO3. The calculated results about the bonding configuration, electronic structures, and conductivity properties are in good agreement with the experimental measurements.
Splitting tower and degree of tt-rings

After constructing a splitting tower for separable commutative ring objects in tensor-triangulated categories, we define and study their degree.
Enhancing Underwater Imagery Using Generative Adversarial Networks

Autonomous underwater vehicles (AUVs) rely on a variety of sensors - acoustic, inertial and visual - for intelligent decision making. Due to its non-intrusive, passive nature and high information content, vision is an attractive sensing modality, particularly at shallower depths. However, factors such as light refraction and absorption, suspended particles in the water, and color distortion affect the quality of visual data, resulting in noisy and distorted images. AUVs that rely on visual sensing thus face difficult challenges and consequently exhibit poor performance on vision-driven tasks. This paper proposes a method to improve the quality of visual underwater scenes using Generative Adversarial Networks (GANs), with the goal of improving input to vision-driven behaviors further down the autonomy pipeline. Furthermore, we show how recently proposed methods are able to generate a dataset for the purpose of such underwater image restoration. For any visually-guided underwater robots, this improvement can result in increased safety and reliability through robust visual perception. To that effect, we present quantitative and qualitative data which demonstrates that images corrected through the proposed approach generate more visually appealing images, and also provide increased accuracy for a diver tracking algorithm.
Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.
Discretized conformal prediction for efficient distribution‐free inference

In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training and test data are assumed to be exchangeable. However, these methods bear a heavy computational cost-and, to be carried out exactly, the regression algorithm would need to be fitted infinitely many times. In practice, the conformal prediction method is run by simply considering only a finite grid of finely spaced values for the response variable. This paper develops discretized conformal prediction algorithms that are guaranteed to cover the target value with the desired probability, and that offer a tradeoff between computational cost and prediction accuracy.
Dependence upon initial conditions

Abstract This article discusses dependence on initial conditions in natural and social sciences with focus on physical science. The main focus is on the newly discovered rough dependence on initial data.
GROUP ACTIONS ON ALGEBRAS AND THE GRADED LIE STRUCTURE OF HOCHSCHILD COHOMOLOGY

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a nite group acting on an al- gebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and polynomial algebras that arise in orbifold theory and representation theory; deformations in this context include graded Hecke alge- bras and symplectic reection algebras. We give some general results describing when brackets are zero for polynomial skew group algebras, which allow us in particular to nd noncommutative Poisson structures. For abelian groups, we express the bracket using inner products of group characters. Lastly, we inter- pret results for graded Hecke algebras.
Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities.

Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen as a generic technique to round a fractional solution in the matroid polytope in an online fashion. It has found applications in several stochastic combinatorial problems where there is a commitment constraint: on seeing the value of a stochastic element, the algorithm has to immediately and irrevocably decide whether to select it while always maintaining an independent set in the matroid. Although OCRSs immediately lead to prophet inequalities, these prophet inequalities are not optimal. Can we instead use prophet inequalities to design optimal OCRSs? We design the first optimal $1/2$-OCRS for matroids by reducing the problem to designing a matroid prophet inequality where we compare to the stronger benchmark of an ex-ante relaxation. We also introduce and design optimal $(1-1/e)$-random order CRSs for matroids, which are similar to OCRSs but the arrival is chosen uniformly at random.
An asymptotic formula for the number of non-negative integer matrices with prescribed row and column sums

We count m×n non-negative integer matrices (contingency tables) with prescribed row and column sums (margins). For a wide class of smooth margins we establish a computationally efficient asymptotic formula approximating the number of matrices within a relative error which approaches 0 as m and n grow.
Degree bounds for semi-invariant rings of quivers

Abstract We use recent results on matrix semi-invariants to give degree bounds on generators for the ring of semi-invariants for quivers with no oriented cycles.
Hierarchical Long-term Video Prediction without Supervision

Much of recent research has been devoted to video prediction and generation, yet most of the previous works have demonstrated only limited success in generating videos on short-term horizons. The hierarchical video prediction method by Villegas et al. (2017) is an example of a state-of-the-art method for long-term video prediction, but their method is limited because it requires ground truth annotation of high-level structures (e.g., human joint landmarks) at training time. Our network encodes the input frame, predicts a high-level encoding into the future, and then a decoder with access to the first frame produces the predicted image from the predicted encoding. The decoder also produces a mask that outlines the predicted foreground object (e.g., person) as a by-product. Unlike Villegas et al. (2017), we develop a novel training method that jointly trains the encoder, the predictor, and the decoder together without highlevel supervision; we further improve upon this by using an adversarial loss in the feature space to train the predictor. Our method can predict about 20 seconds into the future and provides better results compared to Denton and Fergus (2018) and Finn et al. (2016) on the Human 3.6M dataset.