cssi/SciSciGPT-SciSciNet huggingface dataset:
Contrasting Determinants of Mutation Rates in Germline and Soma

Recent studies of somatic and germline mutations have led to the identification of a number of factors that influence point mutation rates, including CpG methylation, expression levels, replication timing, and GC content. Intriguingly, some of the effects appear to differ between soma and germline: in particular, whereas mutation rates have been reported to decrease with expression levels in tumors, no clear effect has been detected in the germline. Distinct approaches were taken to analyze the data, however, so it is hard to know whether these apparent differences are real. To enable a cleaner comparison, we considered a statistical model in which the mutation rate of a coding region is predicted by GC content, expression levels, replication timing, and two histone repressive marks. We applied this model to both a set of germline mutations identified in exomes and to exonic somatic mutations in four types of tumors. Most determinants of mutations are shared: notably, we detected an effect of expression levels on both germline and somatic mutation rates. Moreover, in all tissues considered, higher expression levels are associated with greater strand asymmetry of mutations. However, mutation rates increase with expression levels in testis (and, more tentatively, in ovary), whereas they decrease with expression levels in somatic tissues. This contrast points to differences in damage or repair rates during transcription in soma and germline.
Efficient synthesis of 5-alkyl amino and thioether substituted pyrazoles

Nucleophilic substitution reactions of 1-(4-methylsulfonyl-2-pyridyl)-5-chloro pyrazoles with various substitutions at the 4 position with amine nucleophiles and thiols occur under mild conditions to provide the 5-alkyl amino and thioether pyrazoles in high yields.
Phylogenomics offers resolution of major tunicate relationships.

Abstract Tunicata, a diverse clade of approximately 3000 described species of marine, filter-feeding chordates, is of great interest to researchers because tunicates are the closest living relatives of vertebrates and they facilitate comparative studies of our own biology. The group also includes numerous invasive species that cause considerable economic damage and some species of tunicates are edible. Despite their diversity and importance, relationships among major lineages of Tunicata are not completely resolved. Here, we supplemented public data with transcriptomes from seven species spanning the diversity of Tunicata and conducted phylogenomic analyses on data sets of up to 798 genes. Sensitivity analyses were employed to examine the influences of reducing compositional heterogeneity and branch-length heterogeneity. All analyses maximally supported a monophyletic Tunicata within Olfactores (Vertebrata + Tunicata). Within Tunicata, all analyses recovered Appendicularia sister to the rest of Tunicata and confirmed (with maximal support) that Thaliacea is nested within Ascidiacea. Stolidobranchia is the sister taxon to all other tunicates except Appendicularia. In most analyses, phlebobranch tunicates were recovered paraphyletic with respect to Aplousobranchia. Support for this topology varied but was strong in some cases. However, when only the 50 best genes based on compositional heterogeneity were analysed, we recovered Phlebobranchia and Aplousobranchia reciprocally monophyletic with strong support, consistent with most traditional morphology-based hypotheses. Examination of internode certainty also cast doubt on results of phlebobranch paraphyly, which may be due to limited taxon sampling. Taken together, these results provide a higher-level phylogenetic framework for our closest living invertebrate relatives.
Antigen structure affects cellular routing through DC-SIGN

Dendritic cell (DC) lectins mediate the recognition, uptake, and processing of antigens, but they can also be coopted by pathogens for infection. These distinct activities depend upon the routing of antigens within the cell. Antigens directed to endosomal compartments are degraded, and the peptides are presented on major histocompatibility complex class II molecules, thereby promoting immunity. Alternatively, HIV-1 can avoid degradation, as virus engagement with C-type lectin receptors (CLRs), such as DC-SIGN (DC-specific ICAM-3–grabbing nonintegrin) results in trafficking to surface-accessible invaginated pockets. This process appears to enable infection of T cells in trans . We sought to explore whether antigen fate upon CLR-mediated internalization was affected by antigen physical properties. To this end, we employed the ring-opening metathesis polymerization to generate glycopolymers that each display multiple copies of mannoside ligand for DC-SIGN, yet differ in length and size. The rate and extent of glycopolymer internalization depended upon polymer structure—longer polymers were internalized more rapidly and more efficiently than were shorter polymers. The trafficking, however, did not differ, and both short and longer polymers colocalized with transferrin-labeled early endosomes. To explore how DC-SIGN directs larger particles, such as pathogens, we induced aggregation of the polymers to access particulate antigens. Strikingly, these particulate antigens were diverted to the invaginated pockets that harbor HIV-1. Thus, antigen structure has a dramatic effect on DC-SIGN–mediated uptake and trafficking. These findings have consequences for the design of synthetic vaccines. Additionally, the results suggest strategies for targeting DC reservoirs that harbor viral pathogens.
INTERNATIONAL DEAL EXPERIENCE AND CROSS‐BORDER ACQUISITIONS

I show that corporate directors' human capital facilitates international investments. Directors' experience with cross-border transactions positively influences firms' decisions to conduct their first cross-border acquisitions. Cross-border acquirers are more likely to buy firms headquartered in countries with which the directors have prior deal experience. This effect is strongest for target firms headquartered in culturally and institutionally dissimilar countries. Announced cross-border acquisitions are received more favorably by financial markets and are more likely to be completed successfully when the announcing firm has a director with cross-border acquisition experience. These effects are not driven by investment bank involvement in the deal process or by other forms of directors' human capital, and they are robust to endogeneity of director hires. (JEL F23, F21, J24, L23)
DeepLens: Towards a Visual Data Management System.

Advances in deep learning have greatly widened the scope of automatic computer vision algorithms and enable users to ask questions directly about the content in images and video. This paper explores the necessary steps towards a future Visual Data Management System (VDMS), where the predictions of such deep learning models are stored, managed, queried, and indexed. We propose a query and data model that disentangles the neural network models used, the query workload, and the data source semantics from the query processing layer. Our system, DeepLens, is based on dataflow query processing systems and this research prototype presents initial experiments to elicit important open research questions in visual analytics systems. One of our main conclusions is that any future "declarative" VDMS will have to revisit query optimization and automated physical design from a unified perspective of performance and accuracy tradeoffs. Physical design and query optimization choices can not only change performance by orders of magnitude, they can potentially affect the accuracy of results.
Estimating Information Flow in Deep Neural Networks

We study the flow of information and the evolution of internal representations during deep neural network (DNN) training, aiming to demystify the compression aspect of the information bottleneck theory. The theory suggests that DNN training comprises a rapid fitting phase followed by a slower compression phase, in which the mutual information $I(X;T)$ between the input $X$ and internal representations $T$ decreases. Several papers observe compression of estimated mutual information on different DNN models, but the true $I(X;T)$ over these networks is provably either constant (discrete $X$) or infinite (continuous $X$). This work explains the discrepancy between theory and experiments, and clarifies what was actually measured by these past works. To this end, we introduce an auxiliary (noisy) DNN framework for which $I(X;T)$ is a meaningful quantity that depends on the network's parameters. This noisy framework is shown to be a good proxy for the original (deterministic) DNN both in terms of performance and the learned representations. We then develop a rigorous estimator for $I(X;T)$ in noisy DNNs and observe compression in various models. By relating $I(X;T)$ in the noisy DNN to an information-theoretic communication problem, we show that compression is driven by the progressive clustering of hidden representations of inputs from the same class. Several methods to directly monitor clustering of hidden representations, both in noisy and deterministic DNNs, are used to show that meaningful clusters form in the $T$ space. Finally, we return to the estimator of $I(X;T)$ employed in past works, and demonstrate that while it fails to capture the true (vacuous) mutual information, it does serve as a measure for clustering. This clarifies the past observations of compression and isolates the geometric clustering of hidden representations as the true phenomenon of interest.
Brownian Motion and the Dirichlet Problem at Infinity on Two-dimensional Cartan-Hadamard Manifolds

After recalling the Dirichlet problem at infinity on a Cartan-Hadamard manifold, we describe what is known under various curvature assumptions and the difference between the two-dimensional and the higher-dimensional cases. We discuss the probabilistic formulation of the problem in terms of the asymptotic behavior of the angular component of Brownian motion. We then introduce a new (and appealing) probabilistic approach that allows us to prove that the Dirichlet problem at infinity on a two-dimensional Cartan-Hadamard manifold is solvable under the curvature condition K ≤ (1 + e)/(r 2 logr) outside of a compact set, for some e> 0, in polar coordinates around some pole. This condition on the curvature is sharp, and improves upon the previously known case of quadratic curvature decay. Finally, we briefly discuss the issues which arise in trying to extend this method to higher dimensions.
A second order estimate for general complex Hessian equations

We consider the general complex Hessian equations with right-hand sides depending on gradients, which are motivated by the Fu–Yau equations arising from the study of Strominger systems. The second order estimate for the solution is crucial to solving the equation by the method of continuity. We obtain such an estimate for the χ-plurisubharmonic solutions.
Granular bed consolidation, creep, and armoring under subcritical fluid flow

Internal imaging shows that a granular bed consolidates and creeps under the action of fluid flow well below the bedload transport critical rate. The bed is shown to be armored with a systematic increase in erosion threshold depending on the duration and strength of applied subcritical shear.
Luminous and Dark Matter Profiles from Galaxies to Clusters: Bridging the Gap with Group-scale Lenses

Observations of strong gravitational lensing, stellar kinematics, and larger-scale tracers enable accurate measures of the distribution of dark matter (DM) and baryons in massive early-type galaxies (ETGs). While such techniques have been applied to galaxy-scale and cluster-scale lenses, the paucity of intermediate-mass systems with high-quality data has precluded a uniform analysis of mass-dependent trends. With the aim of bridging this gap, we present new observations and analyses of 10 group-scale lenses at 〈z 〉= 0.36 characterized by Einstein radii θ_(Ein) = 2".5 − 5".1 and a mean halo mass of M_(200) = 10^(14.0)M_⊙. For these groups, we find a mean halo concentration c_(200) = 5.0 ± 0.8 consistent with unmodified cold dark matter halos. By combining our data with other lens samples, we analyze the mass structure of ETGs in halos spanning the mass range 10^(13) M_⊙ − 10^(15)M_⊙ halos using homogeneous techniques. We show that the slope of the total density profile γtot within the effective radius depends on the stellar surface density, as demonstrated previously, but also on the halo mass. We analyze these trends using halo occupation models and resolved stellar kinematics with the goal of testing the universality of the DM profile. Whereas the central galaxies of clusters require a shallow inner DM density profile, group-scale lenses are consistent with a Navarro–Frenk–White profile or one that is slightly contracted. The largest uncertainties arise from the sample size and likely radial gradients in stellar populations. We conclude that the net effect of baryons on the DM distribution may not be universal, but more likely varies with halo mass due to underlying trends in star formation efficiency and assembly history.
Algebraic statistical models

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the parameter space of a reference model with nice properties, such as for example a regular exponential family. This observation leads to the definition of an ‘algebraic exponential family’. This new definition provides a unified framework for the study of statistical models with algebraic structure. In this paper we review the ingredients to this definition and illustrate in examples how computational algebraic geometry can be used to solve problems arising in statistical inference in algebraic models.
On the spectral distribution of large weighted random regular graphs

McKay proved the limiting spectral measures of the ensembles of d-regular graphs with N vertices converge to Kesten's measure as N → ∞. Given a large d-regular graph we assign random weights, drawn from some distribution , to its edges. We study the relationship between and the associated limiting spectral distribution obtained by averaging over the weighted graphs. We establish the existence of a unique "eigendistribution" (a weight distribution such that the associated limiting spectral distribution is a rescaling of ). Initial investigations suggested that the eigendistribution was the semi-circle distribution, which by Wigner's Law is the limiting spectral measure for real symmetric matrices. We prove this is not the case, though the deviation between the eigendistribution and the semi-circular density is small (the first seven moments agree, and the difference in each higher moment is O(1/d2)). Our analysis uses combinatorial results about closed acyclic walks in large trees, which may be of independent interest.
COTANGENT BUNDLE TO THE GRASSMANN VARIETY

We show that there is an affine Schubert variety in the infinite-dimensional partial Flag variety (associated to the two-step parabolic subgroup of the Kac–Moody group , corresponding to omitting α 0; α d ) which is a natural compactification of the cotangent bundle to the Grassmann variety.
Combining Fully Convolutional and Recurrent Neural Networks for 3D Biomedical Image Segmentation

Segmentation of 3D images is a fundamental problem in biomedical image analysis. Deep learning (DL) approaches have achieved the state-of-the-art segmentation performance. To exploit the 3D contexts using neural networks, known DL segmentation methods, including 3D convolution, 2D convolution on the planes orthogonal to 2D slices, and LSTM in multiple directions, all suffer incompatibility with the highly anisotropic dimensions in common 3D biomedical images. In this paper, we propose a new DL framework for 3D image segmentation, based on a combination of a fully convolutional network (FCN) and a recurrent neural network (RNN), which are responsible for exploiting the intra-slice and inter-slice contexts, respectively. To our best knowledge, this is the first DL framework for 3D image segmentation that explicitly leverages 3D image anisotropism. Evaluating using a dataset from the ISBI Neuronal Structure Segmentation Challenge and in-house image stacks for 3D fungus segmentation, our approach achieves promising results, comparing to the known DL-based 3D segmentation approaches.
Efficient free-energy-profile reconstruction using adaptive stochastic perturbation protocols

The Jarzynski-relation-based free-energy calculation is limited by the very slow convergence of the estimate when dissipation is high. We present two novel perturbation protocols able to significantly improve the quality of the potential of mean force (PMF) calculation by reducing the estimate's bias without increasing the number of samples. The protocols are directly applicable with both numerical simulations and real-life experiments. The improvement is achieved through the intentional but controlled widening of the distribution of the external work used to perturb a given system. Our protocols can achieve the same accuracy in PMF estimation as the normal constant velocity pulling with less than 10% of the required samples.
Fast Black-box Variational Inference through Stochastic Trust-Region Optimization

We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based on minibatches of draws from the variational distribution. The algorithm provably converges to a stationary point. We implemented TrustVI in the Stan framework and compared it to two alternatives: Automatic Differentiation Variational Inference (ADVI) and Hessian-free Stochastic Gradient Variational Inference (HFSGVI). The former is based on stochastic first-order optimization. The latter uses second-order information, but lacks convergence guarantees. TrustVI typically converged at least one order of magnitude faster than ADVI, demonstrating the value of stochastic second-order information. TrustVI often found substantially better variational distributions than HFSGVI, demonstrating that our convergence theory can matter in practice.
A 2D Parallel Triangle Counting Algorithm for Distributed-Memory Architectures

Triangle counting is a fundamental graph analytic operation that is used extensively in network science and graph mining. As the size of the graphs that needs to be analyzed continues to grow, there is a requirement in developing scalable algorithms for distributed-memory parallel systems. To this end, we present a distributed-memory triangle counting algorithm, which uses a 2D cyclic decomposition to balance the computations and reduce the communication overheads. The algorithm structures its communication and computational steps such that it reduces its memory overhead and includes key optimizations that leverage the sparsity of the graph and the way the computations are structured. Experiments on synthetic and real-world graphs show that our algorithm obtains an average relative speedup range between 3.24 to 7.22 out of 10.56 across the datasets using 169 MPI ranks over the performance achieved by 16 MPI ranks. Moreover, we obtain an average speedup of 10.2 times on comparison with previously developed distributed-memory parallel algorithms.
Bayesian Social Learning in a Dynamic Environment

Bayesian agents learn about a moving target, such as a commodity price, using private signals and their network neighbors' estimates. The weights agents place on these sources of information are endogenously determined by the precisions and correlations of the sources; the weights, in turn, determine future correlations. We study stationary equilibria\textemdash ones in which all of these quantities are constant over time. Equilibria in linear updating rules always exist, yielding a Bayesian learning model as tractable as the commonly-used DeGroot heuristic. Equilibria and the comparative statics of learning outcomes can be readily computed even in large networks. Substantively, we identify pervasive inefficiencies in Bayesian learning. In any stationary equilibrium where agents put positive weights on neighbors' actions, learning is Pareto inefficient in a generic network: agents rationally overuse social information and underuse their private signals.
Limited information strategies and discrete selectivity

Abstract We relate the property of discrete selectivity and its corresponding game, both recently introduced by V.V. Tkachuk, to a variety of selection principles and point-picking games. In particular we show that player II can win the discrete selectivity game on C p ( X ) if and only if player II can win a variant of the point-open game on X. We also show that the existence of limited information strategies in the discrete selectivity game on C p ( X ) for either player are equivalent to other well-known topological properties.
Duality and nonlinear graph Laplacians

Abstract In this paper we show that a recent nearly linear time algorithm for solving a system of equations arising from a graph Laplacian can be extended to a large class of nonlinear systems of equations, based on a nonlinear generalization of the graph Laplacian. This result follows from a nonlinear generalization of the notable duality between graph Laplacians and electrical flows. Beyond providing a fast algorithm for a class of nonlinear sets of equations, our work highlights the robustness of spectral graph theory and suggests new directions for research in spectral graph theory. Specifically, we present an iterative algorithm for solving a class of nonlinear system of equations arising from a nonlinear generalization of the graph Laplacian in O ˜ ( k 2 m log ⁡ ( k n / ϵ ) ) iterations, where k is a measure of nonlinearity, n is the number of variables, m is the number of nonzero entries in the generalized graph Laplacian L, ϵ is the solution accuracy and O ˜ ( ) neglects (non-leading) logarithmic terms. This algorithm is a natural nonlinear extension of the one in Kelner et al. (2013), which solves a linear Laplacian system of equations in nearly linear time. Unlike the linear case, in the nonlinear case each iteration takes O ˜ ( n ) time so the total running time is O ˜ ( k 2 m n log ⁡ ( k n / ϵ ) ) . For sparse graphs with m = O ( n ) and fixed k this nonlinear algorithm is O ˜ ( n 2 log ⁡ ( n / ϵ ) ) which is slightly faster than standard methods for solving linear equations, which require approximately O ( n 2.38 ) time.
Inverse Scattering Transform and the Theory of Solitons

A review of the inverse scattering transform is given, and an introduction to solitons is provided.
Transversely stable soliton trains in photonic lattices

We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from $X$-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band ($\ensuremath{\Gamma}$ and $M$ points) still suffer transverse instability. These results are obtained in the continuous lattice model and are further corroborated by the discrete model.
On the first homology of Peano continua

We show that the first homology group of a locally connected compact metric space is either uncountable or is finitely generated. This is related to Shelah's well-known result which shows that the fundamental group of such a space satisfies a similar criterion. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result doesn't follow from Shelah's. We clarify a claim made by Pawlikowski and offer a proof of the clarification.
Regularity of solutions to the parabolic fractional obstacle problem

In recent years, there has been an increasing interest in studying constrained variational problems with a fractional diffusion. One of the motivations comes from mathematical finance: jumpdiffusion processes where incorporated by Merton [14] into the theory of option evaluation to introduce discontinuous paths in the dynamics of the stock’s prices, in contrast with the classical lognormal diffusion model of Black and Scholes [2]. These models allow to take into account large price changes, and they have become increasingly popular for modeling market fluctuations, both for risk management and option pricing purposes. Let us recall that an American option gives its holder the right to buy a stock at a given price prior (but not later) than a given time T > 0. If v(τ, x) represents the rational price of an American option with a payoff ψ at time T > 0, then v will solve (in the viscosity sense) the following obstacle problem: { min{Lv, v − ψ} = 0, v(T ) = ψ.
Variance component score test for time-course gene set analysis of longitudinal RNA-seq data

As gene expression measurement technology is shifting from microarrays to sequencing, the statistical tools available for their analysis must be adapted since RNA-seq data are measured as counts. It has been proposed to model RNA-seq counts as continuous variables using nonparametric regression to account for their inherent heteroscedasticity. In this vein, we propose tcgsaseq, a principled, model-free, and efficient method for detecting longitudinal changes in RNA-seq gene sets defined a priori. The method identifies those gene sets whose expression varies over time, based on an original variance component score test accounting for both covariates and heteroscedasticity without assuming any specific parametric distribution for the (transformed) counts. We demonstrate that despite the presence of a nonparametric component, our test statistic has a simple form and limiting distribution, and both may be computed quickly. A permutation version of the test is additionally proposed for very small sample sizes. Applied to both simulated data and two real datasets, tcgsaseq is shown to exhibit very good statistical properties, with an increase in stability and power when compared to state-of-the-art methods ROAST (rotation gene set testing), edgeR, and DESeq2, which can fail to control the type I error under certain realistic settings. We have made the method available for the community in the R package tcgsaseq.
Are facial attributes adversarially robust

Facial attributes are emerging soft biometrics that have the potential to reject non-matches, for example, based on mismatching gender. To be usable in stand-alone systems, facial attributes must be extracted from images automatically and reliably. In this paper, we propose a simple yet effective solution for automatic facial attribute extraction by training a deep convolutional neural network (DCNN) for each facial attribute separately, without using any pre-training or dataset augmentation, and we obtain new state-of-the-art facial attribute classification results on the CelebA benchmark. To test the stability of the networks, we generated adversarial images - formed by adding imperceptible non-random perturbations to original inputs which result in classification errors - via a novel fast flipping attribute (FFA) technique. We show that FFA generates more adversarial examples than other related algorithms, and that DCNNs for certain attributes are generally robust to adversarial inputs, while DCNNs for other attributes are not. This result is surprising because no DCNNs tested to date have exhibited robustness to adversarial images without explicit augmentation in the training procedure to account for adversarial examples. Finally, we introduce the concept of natural adversarial samples, i.e., images that are misclassified but can be easily turned into correctly classified images by applying small perturbations. We demonstrate that natural adversarial samples commonly occur, even within the training set, and show that many of these images remain misclassified even with additional training epochs. This phenomenon is surprising because correcting the misclassification, particularly when guided by training data, should require only a small adjustment to the DCNN parameters.
Timescales of Kozai–Lidov oscillations at quadrupole and octupole order in the test particle limit

Kozai-Lidov (KL) oscillations in hierarchical triple systems have found application to many astrophysical contexts, including planet formation, type Ia supernovae, and supermassive black hole dynamics. The period of these oscillations is known at the order-of-magnitude level, but dependencies on the initial mutual inclination or inner eccentricity are not typically included. In this work I calculate the period of KL oscillations (tKL) exactly in the test particle limit at quadrupole order (TPQ). I explore the parameter space of all hierarchical triples at TPQ and show that except for triples on the boundary between libration and rotation, the period of KL oscillations does not vary by more than a factor of a few. The exact period may be approximated to better than 2 per cent for triples with mutual inclinations between 60 ◦ and 120 ◦ and initial eccentricities less than �0.3. In addition, I derive an analytic expression for the period of octupole-order oscillations due to the ‘eccentric KL mechanism’ (EKM). I show that the timescale for EKM oscillations is proportional to ǫ −1/2 oct , where ǫoct measures the strength of octupole perturbations relative to quadrupole perturbations.
Direct Scattering for the Benjamin–Ono Equation with Rational Initial Data

We compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.
Periodicity in the stable representation theory of crystallographic groups

Deformation K–theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2–periodic above the rational cohomological dimension of G (minus 2), in the sense that T. Lawson’s Bott map is an isomorphism on homotopy in these dimensions. We establish a periodicity theorem for crystallographic subgroups of the isometries of k–dimensional Euclidean space. For a certain subclass of torsion-free crystallographic groups, we prove a vanishing result for the homotopy groups of the stable moduli space of representations, and we provide examples relating these homotopy groups to the cohomology of G. These results are established as corollaries of the fact that for each n > 0, the one-point compactification of the moduli space of irreducible n–dimensional representations of G is a CW complex of dimension at most k. This is proven using real algebraic geometry and projective representation theory.
Soul theorem for 4-dimensional topologically regular open nonnegatively curved Alexandrov spaces

In this paper, we study the topology of topologically regular 4-dimensional open non-negatively curved Alexandrov spaces. These spaces occur naturally as the blow-up limits of compact Riemannian manifolds with lower curvature bound. These manifolds have also been studied by Yamaguchi in his preprint [Yam2002]. Our main tools are gradient flows of semi-concave functions and critical point theory for distance functions, which have been used to study the 3-dimensional collapsing theory in the paper [CaoG2010]. The results of this paper will be used in our future studies of collapsing 4-manifolds, which will be discussed elsewhere.
Notes On Supermanifolds and Integration

These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
Localization Properties of Chern Insulators

We study the localization properties of the equal-time electron Green’s function in a Chern insulator in an arbitrary dimension and with an arbitrary number of bands. We prove that the Green’s function cannot decay super-exponentially if the Hamiltonian is finite-range and the quantum Hall response is nonzero. For a general band Hamiltonian (possibly infinite-range), we prove that the Green’s function cannot be finite-range if the quantum Hall response is nonzero. The proofs use methods of algebraic geometry.
Null mean curvature flow and outermost MOTS

We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface $\partial \Omega$, we show that there exists a weak solution to the null mean curvature flow, given as a limit of approximate solutions that are defined using the $\varepsilon$-regularization method. We show that the approximate solutions blow up on the outermost MOTS and the weak solution converges (as boundaries of finite perimeter sets) to a generalized MOTS.
Depth Extraction from Videos Using Geometric Context and Occlusion Boundaries

© 2014. The copyright of this document resides with its authors. It may be distributed unchanged freely in print or electronic forms
Lorentz-Conformal Transformations in the Plane

Abstract While conformal transformations of the plane preserve Laplace’s equation, Lorentz-conformal mappings preserve the wave equation. This property gives rise to a rich Lorentzian geometry in dimension 1 + 1 . In elucidating the geometry of the Lorentzian plane, this work provides a window into the field of pseudo-Riemannian geometry, where the Lorentzian plane is of fundamental importance. In the Lorentzian plane, curvilinear quadrilaterals and pairs of crossing curves are transformed under nonlinear Lorentz-conformal mappings via geometric constructions that can be expressed also by functional formulas. Classes of Lorentz-conformal maps are characterized by their symmetries under subgroups of the dihedral group of order eight, and unfoldings of non-invertible mappings into invertible ones are reflected in a change of the symmetry group. The questions are simple; but the answers are not obvious, yet have beautiful geometric, algebraic, and functional descriptions and proofs. This is due to the simple form of nonlinear Lorentz-conformal transformations in dimension 1 + 1 , provided by characteristic coordinates.
Risk limiting dispatch with ramping constraints

The increasing penetration of renewable resources poses a challenge to the reliable operation of power systems. In particular, operators face the risk of not scheduling enough traditional generators when renewable generation becomes lower than expected. This paper studies the optimal trade-off between the system risk and the cost of scheduling reserve generators. The problem is modeled as a multi-period stochastic control problem, and in particular the ramping constraints on the generators are explicitly considered. The structure of the optimal dispatch control is identified. Based on the derived structure results, two types of control policies are proposed to efficiently compute the optimal dispatch: (i) a chance constrained policy, and (ii) efficient look-ahead policies. Utilizing real system data, the chance constrained dispatch is shown to outperform the look-ahead policies and to be robust to changes in the probability distribution of the uncertainties involved in the problem.
Dual Attention Network for Product Compatibility and Function Satisfiability Analysis

Product compatibility and functionality are of utmost importance to customers when they purchase products, and to sellers and manufacturers when they sell products. Due to the huge number of products available online, it is infeasible to enumerate and test the compatibility and functionality of every product. In this paper, we address two closely related problems: product compatibility analysis and function satisfiability analysis, where the second problem is a generalization of the first problem (e.g., whether a product works with another product can be considered as a special function). We first identify a novel question and answering corpus that is up-to-date regarding product compatibility and functionality information. To allow automatic discovery product compatibility and functionality, we then propose a deep learning model called Dual Attention Network (DAN). Given a QA pair for a to-be-purchased product, DAN learns to 1) discover complementary products (or functions), and 2) accurately predict the actual compatibility (or satisfiability) of the discovered products (or functions). The challenges addressed by the model include the briefness of QAs, linguistic patterns indicating compatibility, and the appropriate fusion of questions and answers. We conduct experiments to quantitatively and qualitatively show that the identified products and functions have both high coverage and accuracy, compared with a wide spectrum of baselines.
Higher-level canonical subgroups for p-divisible groups

Let R be a complete rank-1 valuation ring of mixed characteristic (0, p), and let K be its field of fractions. A g-dimensional truncated Barsotti–Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G ⊗RK with geometric structure (Z/pnZ)g consisting of points ‘closest to zero’. We give a non-trivial condition on the Hasse invariant of G that guarantees the existence of the canonical subgroup, analogous to a result of Katz and Lubin for elliptic curves. The bound is independent of the height and dimension of G.
Linear Algebraic Structure of Word Senses, with Applications to Polysemy

Word embeddings are ubiquitous in NLP and information retrieval, but it is unclear what they represent when the word is polysemous. Here it is shown that multiple word senses reside in linear super...
Average Pace and Horizontal Chords

On November 16, 2013, Molly Huddle ran 37:49 for 12 kilometers, a world record for that distance. People applauded this fine performance, but some pointed out that Mary Keitany’s world record of 65:50 for the half marathon, which is 21.1 kilometers, is actually faster than Huddle’s record: Keitany averaged 3:07 per kilometer, while Huddle averaged 3:09 per kilometer [IAAF] [NYRR]. Therefore, Keitany must have run some 12 km subset of the race faster than Huddle − right?
Numerical Techniques for Finding the Distances of Quantum Codes

We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces complexity exponent of all existing deterministic techniques designed for codes with small relative distances (which include all known families of quantum LDPC codes), and also surpasses the probabilistic technique for sufficiently high code rates.
Analysis of models for viscoelastic wave propagation

We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the coupling of different models within the same solid are covered as well. Stability of each model is investigated in the Laplace domain, and these are then translated to time-domain estimates. With the use of semigroup theory, some time-domain results are also given which avoid using the Laplace transform and give sharper estimates. We take the time to develop and explain the theory necessary to understand the relation between the equations we solve in the Laplace domain and those in the time-domain which are written using the language of causal tempered distributions. Finally we offer some numerical experiments that highlight some of the differences between the models and how different parameters effect the results.
The history of the muon (g-2) experiments

I discuss the history of the muon $(g-2)$ measurements, beginning with theColumbia-Nevis measurement that observed parity violation in muon decay, andalso measured the muon $g$-factor for the first time, finding $g_\mu=2$. Thetheoretical (Standard Model) value contains contributions from quantumelectrodynamics, the strong interaction through hadronic vacuum polarizationand hadronic light-by-light loops, as well as the electroweak contributionsfrom the $W$, $Z$ and Higgs bosons. The subsequent experiments, first at Nevisand then with increasing precision at CERN, measured the muon anomaly $a_\mu =(g_\mu-2)/2$ down to a precision of 7.3 parts per million (ppm) The BrookhavenNational Laboratory experiment E821 increased the precision to 0.54 ppm, andobserved for the first time the electroweak contributions. Interestingly, thevalue of $a_\mu$ measured at Brookhaven appears to be larger than the StandardModel value by greater than three standard deviations. A new experiment,Fermilab E989, aims to improve on the precision by a factor of four, to clarifywhether this result is a harbinger of new physics entering through loops, orfrom some experimental, statistical or systematic issue.
Perishability of data: dynamic pricing under varying-coefficient models

We consider a firm that sells a large number of products to its customers in an online fashion. Each product is described by a high dimensional feature vector, and the market value of a product is assumed to be linear in the values of its features. Parameters of the valuation model are unknown and can change over time. The firm sequentially observes a product's features and can use the historical sales data (binary sale/no sale feedbacks) to set the price of current product, with the objective of maximizing the collected revenue. We measure the performance of a dynamic pricing policy via regret, which is the expected revenue loss compared to a clairvoyant that knows the sequence of model parameters in advance. We propose a pricing policy based on projected stochastic gradient descent (PSGD) and characterize its regret in terms of time T, features dimension d, and the temporal variability in the model parameters, δt. We consider two settings. In the first one, feature vectors are chosen antagonistically by nature and we prove that the regret of PSGD pricing policy is of order O(√T + Σt=1T √tδt). In the second setting (referred to as stochastic features model), the feature vectors are drawn independently from an unknown distribution. We show that in this case, the regret of PSGD pricing policy is of order O(d2 log T + Σt=1T tδt/d).
Life equations for the senescence process.

The Gompertz law of mortality quantitatively describes the mortality rate of humans and almost all multicellular animals. However, its underlying kinetic mechanism is unclear. The Gompertz law cannot explain the mortality plateau at advanced ages and cannot give an explicit relationship between temperature and mortality. In this study a reaction kinetics model with a time dependent rate coefficient is proposed to describe the survival and senescence processes. A temperature-dependent mortality function was derived. The new mortality function becomes the Gompertz mortality function with the same relationship of parameters prescribed by the Strehler–Mildvan correlation when age is smaller than a characteristic value δ, and reaches the mortality plateau when age is greater than δ. A closed-form analytical expression for describing the relationship of average lifespan with temperature and other equations are derived from the new mortality function. The derived equations can be used to estimate the limit of average lifespan, predict the maximal longevity, calculate the temperature coefficient of lifespan, and explain the tendency of the survival curve. This prediction is consistent with the most recently reported mortality trajectories for single-year birth cohorts. This study suggests that the senescence process results from the imbalance between damaging energy and protecting energy for the critical chemical substance in the body. The rate of senescence of the organism increases while the protecting energy decreases. The mortality plateau is reached when the protecting energy decreases to its minimal levels. The decreasing rate of the protecting energy is temperature-dependent. This study is exploring the connection between the biochemical mechanism and demography.
Biologically Motivated Algorithms for Propagating Local Target Representations.

Finding biologically plausible alternatives to back-propagation of errors is a fundamentally important challenge in artificial neural network research. In this paper, we propose a learning algorithm called error-driven Local Representation Alignment (LRA-E), which has strong connections to predictive coding, a theory that offers a mechanistic way of describing neurocomputational machinery. In addition, we propose an improved variant of Difference Target Propagation, another procedure that comes from the same family of algorithms as LRA-E. We compare our procedures to several other biologicallymotivated algorithms, including two feedback alignment algorithms and Equilibrium Propagation. In two benchmarks, we find that both of our proposed algorithms yield stable performance and strong generalization compared to other competing back-propagation alternatives when training deeper, highly nonlinear networks, with LRA-E performing the best overall.
ON THE NUMBER OF COMPATIBLY FROBENIUS SPLIT SUBVARIETIES, PRIME F-IDEALS, AND LOG CANONICAL CENTERS

Let X be a projective Frobenius split variety over an algebraically closed field with splitting � : FOX ! OX. In this paper we give a sharp bound on the number of subvarieties of X compatibly split by �. In particular, suppose L is a sufficiently ample line bundle onX (for example, if L induces a projectively normal embedding) with n = dimH 0 (X, L ). We show that the number of d-dimensional irreducible subvarieties of X that are compatibly split byis less than or equal ton d+1 ´ . This generalizes a well known result on the number of closed points compatibly split by a fixed splitting �. Similarly, we give a bound on the number of prime F-ideals of an F-finite F-pure local ring. Compatibly split subvarieties are closely related to log canonical centers. Our methods apply in any characteristic, and so we are also able to bound the possible number of log canonical centers of a log canonical pair (X,�) passing through a closed point x 2 X. Specifically, if n is the embedding dimension of X at x, then the number of d-dimensional log canonical centers of (X,�) through x is less than or equal ton ´ .
Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives

Abstract I. Panin proved in the nineties that the algebraic K-theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras. Later, Merkurjev and Panin described the algebraic K-theory of toric varieties as a direct summand of the algebraic K-theory of separable algebras. In this article, making use of the recent theory of noncommutative motives, we extend Panin and Merkurjev–Panin's computations from algebraic K-theory to every additive invariant. As a first application, we fully compute the cyclic homology (and all its variants) of twisted projective homogeneous varieties. As a second application, we show that the noncommutative motive of a twisted projective homogeneous variety is trivial if and only if the Brauer classes of the associated central simple algebras are trivial. Along the way we construct a fully-faithful ⊗-functor from Merkurjev–Panin's motivic category to Kontsevich's category of noncommutative Chow motives, which is of independent interest.