cssi/SciSciGPT-SciSciNet huggingface dataset:
A study of projections of 2-bouquet graphs

We extend the concepts of trivializing and knotting numbers for knots to spatial graphs and 2-bouquet graphs, in particular. Furthermore, we calculate the trivializing and knotting numbers for projections and pseudodiagrams of 2-bouquet spatial graphs based on the number of precrossings and the placement of the precrossings in the pseudodiagram of the spatial graph.
On constant gaps for the two-way Gaussian interference channel

We introduce the two-way Gaussian interference channel in which there are four nodes with four independent messages: two-messages to be transmitted over a Gaussian interference channel in the → direction, simultaneously with two-messages to be transmitted over an interference channel (in-band, full-duplex) in the ← direction. In such a two-way network, all nodes are transmitters and receivers of messages, allowing them to adapt current channel inputs to previously received channel outputs. We propose two new outer bounds on the symmetric sum-rate for the two-way Gaussian interference channel with complex channel gains: one under full adaptation (all 4 nodes are permitted to adapt inputs to previous outputs), and one under partial adaptation (only 2 nodes are permitted to adapt, the other 2 are restricted). We show that simple non-adaptive schemes such as the Han and Kobayashi scheme, where inputs are functions of messages only and not past outputs, utilized in each direction are sufficient to achieve within a constant gap of these fully or partially adaptive outer bounds for all channel regimes.
Computing the endomorphism ring of an ordinary abelian surface over a finite field

Abstract We present a new algorithm for computing the endomorphism ring of an ordinary abelian surface over a finite field which is subexponential and generalizes an algorithm of Bisson and Sutherland for elliptic curves. The correctness of this algorithm only requires the heuristic assumptions required by the algorithm of Biasse and Fieker [2] which computes the class group of an order in a number field in subexponential time. Thus we avoid the multiple heuristic assumptions on isogeny graphs and polarized class groups which were previously required. The output of the algorithm is an ideal in the maximal totally real subfield of the endomorphism algebra, generalizing the elliptic curve case.
Generalized opinion dynamics from local optimization rules

We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence depends on the distance of the agents' opinions. Under this setup, we identify conditions under which the opinions converge in finite time, and provide a qualitative characterization of the equilibrium. We interpret the HK model opinion update rule as a quadratic cost-minimization rule. This enables a second generalization: a family of update rules which possess different equilibrium properties.
The Yang-Mills Measure in the $SU(3)$ Skein Module

Let A be a nonzero complex number which is not a root of unity. Let F be a compact oriented surface, the SU(3)-skein space of F, SA(F), is the vector space over ℂ generated by framed oriented links (including framed oriented trivalent graphs in F×I) quotient by the SU(3)-skein relations due to Kuperberg [Spiders for rank 2 Lie algebra, Comm. Math. Phys. 180(1) (1996) 109–151]. For closed F, with genus greater than 1, we construct a local diffeomorphism invariant trace on SA(F) when A is a positive real number not equal to 1.
Vertical Trajectory Optimization to Minimize Environmental Impact in the Presence of Wind

The vertical trajectory optimization for the en route descent phase is studied in the presence of both along-track and cross winds, which are both modeled as functions of altitude. The flight range covers some portion of a cruise segment and ends at a meter fix. The descent trajectory is assumed as a flight idle descent. The problem is formulated as an optimal control problem with both mixed state path constraints and pure state constraints. For minimizing environmental impacts, we optimize descent trajectory with respect to two cost functionals: fuel and emissions costs. We analyze both singular arc and boundary arc using the necessary conditions of the optimality. From the analysis result, we propose the optimal trajectory generation method, in which the optimal trajectory is generated by the backward and forward integration. The trajectory from the proposed algorithm is compared with the numerical optimal solution of the original optimal control problem. The result shows that the proposed algorithm gen...
Fourier Frames for the Cantor-4 Set

The measure supported on the Cantor-4 set constructed by Jorgensen–Pedersen is known to have a Fourier basis, i.e. that it possess a sequence of exponentials which form an orthonormal basis. We construct Fourier frames for this measure via a dilation theory type construction. We expand the Cantor-4 set to a two dimensional fractal which admits a representation of a Cuntz algebra. Using the action of this algebra, an orthonormal set is generated on the larger fractal, which is then projected onto the Cantor-4 set to produce a Fourier frame.
Asynchronous Optimization over Weakly Coupled Renewal Systems

This paper considers optimization over multiple renewal systems coupled by time-average constraints. These systems act asynchronously over variable length frames. When a particular system starts a new renewal frame, it chooses an action from a set of options for that frame. The action determines the duration of the frame, the penalty incurred during the frame (such as energy expenditure), and a vector of performance metrics (such as instantaneous number of job services). The goal is to minimize the time-average penalty subject to time-average overall constraints on the corresponding metrics. This problem has applications to task processing networks and coupled Markov decision processes. We propose a new algorithm so that each system can make its own decision after observing a global multiplier that is updated every slot. We show that this algorithm satisfies the desired constraints and achieves O(ϵ) near optimality with O(1/ϵ2) convergence time.
Probably certifiably correct k -means clustering

Recently, Bandeira (C R Math, 2015) introduced a new type of algorithm (the so-called probably certifiably correct algorithm) that combines fast solvers with the optimality certificates provided by convex relaxations. In this paper, we devise such an algorithm for the problem of k-means clustering. First, we prove that Peng and Wei’s semidefinite relaxation of k-means Peng and Wei (SIAM J Optim 18(1):186–205, 2007) is tight with high probability under a distribution of planted clusters called the stochastic ball model. Our proof follows from a new dual certificate for integral solutions of this semidefinite program. Next, we show how to test the optimality of a proposed k-means solution using this dual certificate in quasilinear time. Finally, we analyze a version of spectral clustering from Peng and Wei (SIAM J Optim 18(1):186–205, 2007) that is designed to solve k-means in the case of two clusters. In particular, we show that this quasilinear-time method typically recovers planted clusters under the stochastic ball model.
Unsupervised Facial Geometry Learning for Sketch to Photo Synthesis

Face sketch-photo synthesis is a critical application in law enforcement and digital entertainment industry where the goal is to learn the mapping between a face sketch image and its corresponding photo-realistic image. However, the limited number of paired sketch-photo training data usually prevents the current frameworks to learn a robust mapping between the geometry of sketches and their matching photo-realistic images. Consequently, in this work, we present an approach for learning to synthesize a photo-realistic image from a face sketch in an unsupervised fashion. In contrast to current unsupervised image-to-image translation techniques, our framework leverages a novel perceptual discriminator to learn the geometry of human face. Learning racial prior information empowers the network to remove the geometrical artifacts in the face sketch. We demonstrate that a simultaneous optimization of the face photo generator network, employing the proposed perceptual discriminator in combination with a texture-wise discriminator, results in a significant improvement in quality and recognition rate of the synthesized photos. We evaluate the proposed network by conducting extensive experiments on multiple baseline sketch-photo datasets.
Galois Conjugates of Pseudo-Anosov Stretch Factors are Dense in the Complex Plane

In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's construction of pseudo-Anosov mapping classes. As a consequence, we obtain that in a sense there is no restriction on the location of Galois conjugates of stretch factors arising from Penner's construction. This complements an earlier result of Shin and the author stating that Galois conjugates of stretch factors arising from Penner's construction may never lie on the unit circle.
Destination-Directed Trajectory Modeling and Prediction Using Conditionally Markov Sequences

In some problems there is information about the destination of a moving object. An example is an airliner flying from an origin to a destination. Such problems have three main components: an origin, a destination, and motion in between. To emphasize that the motion trajectories end up at the destination, we call them destination-directed trajectories. The Markov sequence is not flexible enough to model such trajectories. Given an initial density and an evolution law, the future of a Markov sequence is determined probabilistically. One class of conditionally Markov (CM) sequences, called the CM L sequence (including the Markov sequence as a special case), has the following main components: a joint endpoint density (i.e., an initial density and a final density conditioned on the initial) and a Markov-like evolution law. This paper proposes using the CM L sequence for modeling destination-directed trajectories. It is demonstrated how the CM L sequence enjoys several desirable properties for destination-directed trajectory modeling. Some simulations of trajectory modeling and prediction are presented for illustration.
A new proof of the noncommutative Banach-Stone theorem

Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate how our techniques may be applied to classify surjective isometries of noncommutative L spaces, extending the main results of [S1] to 0 < p ≤ 1.
pyLLE: a Fast and User Friendly Lugiato-Lefever Equation Solver

We present the development of pyLLE, a freely accessible and cross-platform Lugiato-Lefever equation solver programmed in Python and Julia and optimized for the simulation of microresonator frequency combs. Examples illustrating its operation, the simplicity of use, and performance against other programming language are presented. The documentation of the software can be found at this https URL
Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization

M arkov random fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms. Among those techniques, semidefinite programming (SDP) relaxations have been shown to provide accurate estimates, while scaling poorly with the problem size and being typically slow for practical applications. Our first contribution is to design a dual ascent method to solve standard SDP relaxations that takes advantage of the geometric structure of the problem to speed up computation. This technique, named dual ascent Riemannian staircase ( DARS ), is able to solve large problem instances in seconds . Our second contribution is to develop a second and faster approach. The backbone of this second approach is a novel SDP relaxation combined with a fast and scalable solver based on smooth Riemannian optimization. We show that this approach, named Fast Unconstrained SEmidefinite Solver ( FUSES ), can solve large problems in milliseconds . Contrarily to local MRF solvers, e.g., loopy belief propagation, our approaches do not require an initial guess. Moreover, we leverage recent results from optimization theory to provide per-instance sub-optimality guarantees. We demonstrate the proposed approaches in multi-class image segmentation problems. Extensive experimental evidence shows that: 1) FUSES and DARS produce near-optimal solutions, attaining an objective within 0.1% of the optimum; 2) FUSES and DARS are remarkably faster than general-purpose SDP solvers, and FUSES is more than two orders of magnitude faster than DARS while attaining similar solution quality; and 3) FUSES is faster than local search methods while being a global solver.
THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times\cdots {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre \cite{BS}. Since then the 2-ranks of compact Lie groups have been investigated by many mathematician. The 2-ranks of compact Lie groups relate closely with several important areas in mathematics. In this article, we survey important results concerning 2-ranks of compact Lie groups. In particular, we present the complete determination of 2-ranks of compact connected simple Lie groups $G$ via the maximal antipodal sets $A_{2}G$ of $G$ introduced in \cite{CN2,CN3}.
Cantor Set Arithmetic

Every element u of [0,1] can be written in the form u=x2y , where x, y are elements of the Cantor set C. In particular, every real number between zero and one is the product of three elements of th...
Multivariate Alexander colorings

We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module M over the Laurent polynomial ring Λμ = ℤ[t1±1,…,t μ±1]. If D is a diagram of a ...
Geometry Based Data Generation

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis.
Efficient First-Order Algorithms for Adaptive Signal Denoising.

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a certain convex optimization problem. Adaptive convolution-type estimators were demonstrated to have favorable statistical properties. However, the question of their computational complexity remains largely unexplored, and in fact we are not aware of any publicly available implementation of these estimators. Our first contribution is an efficient implementation of these estimators via some known first-order proximal algorithms. Our second contribution is a computational complexity analysis of the proposed procedures, which takes into account their statistical nature and the related notion of statistical accuracy. The proposed procedures and their analysis are illustrated on a simulated data benchmark.
The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled Chi-square

Logistic regression is used thousands of times a day to fit data, predict future outcomes, and assess the statistical significance of explanatory variables. When used for the purpose of statistical inference, logistic models produce p-values for the regression coefficients by using an approximation to the distribution of the likelihood-ratio test (LRT). Indeed, Wilks’ theorem asserts that whenever we have a fixed number p of variables, twice the log-likelihood ratio (LLR) $$2 \Lambda $$ is distributed as a $$\chi ^2_k$$ variable in the limit of large sample sizes n; here, $$\chi ^2_k$$ is a Chi-square with k degrees of freedom and k the number of variables being tested. In this paper, we prove that when p is not negligible compared to n, Wilks’ theorem does not hold and that the Chi-square approximation is grossly incorrect; in fact, this approximation produces p-values that are far too small (under the null hypothesis). Assume that n and p grow large in such a way that $$p/n \rightarrow \kappa $$ for some constant $$\kappa < 1/2$$ . (For $$\kappa > 1/2$$ , $$2\Lambda {\mathop {\rightarrow }\limits ^{{\mathbb {P}}}}0$$ so that the LRT is not interesting in this regime.) We prove that for a class of logistic models, the LLR converges to a rescaled Chi-square, namely, $$2\Lambda ~{\mathop {\rightarrow }\limits ^{\mathrm {d}}}~ \alpha (\kappa ) \chi _k^2$$ , where the scaling factor $$\alpha (\kappa )$$ is greater than one as soon as the dimensionality ratio $$\kappa $$ is positive. Hence, the LLR is larger than classically assumed. For instance, when $$\kappa = 0.3$$ , $$\alpha (\kappa ) \approx 1.5$$ . In general, we show how to compute the scaling factor by solving a nonlinear system of two equations with two unknowns. Our mathematical arguments are involved and use techniques from approximate message passing theory, from non-asymptotic random matrix theory and from convex geometry. We also complement our mathematical study by showing that the new limiting distribution is accurate for finite sample sizes. Finally, all the results from this paper extend to some other regression models such as the probit regression model.
A unitary ‘quantization commutes with reduction’ map for the adjoint action of a compact Lie group

Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its cotangent bundle. We consider the problem of "quantization commutes with reduction" for the adjoint action of $K$ on $T^{\ast}(K).$ We quantize both $T^{\ast}(K)$ and the reduced phase space using geometric quantization with half-forms. We then construct a geometrically natural map from the space of invariant elements in the quantization of $T^{\ast}(K)$ to the quantization of the reduced phase space. We show that this map is a constant multiple of a unitary map.
CLOSURE METHOD FOR SPATIALLY AVERAGED DYNAMICS OF PARTICLE CHAINS

Abstract We study the closure problem for continuum balance equations that model the mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the balance equations for spatial averages obtained earlier by a number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum balance equation contains a flux (stress), which is given by an exact function of particle positions and velocities. We propose a method for approximating this function by a sequence of operators applied to the average density and momentum. The resulting approximate mesoscopic models are systems in closed form. The closed form property allows one to work directly with the mesoscale equations without the need to calculate the underlying particle trajectories, which is useful for the modeling and simulation of large particle systems. The proposed closure method utilizes the theory of ill-posed problems, in particular iterative regularization methods for solving first order linear integral equations. The closed form approximations are obtained in two steps. First, we use Landweber regularization to (approximately) reconstruct the interpolants of the relevant microscale quantities from the average density and momentum. Second, these reconstructions are substituted into the exact formulas for stress. The developed general theory is then applied to non-linear oscillator chains. We conduct a detailed study of the simplest zero-order approximation, and show numerically that it works well as long as the fluctuations of velocity are nearly constant.
Iterative hard thresholding for low-rank recovery from rank-one projections

Abstract A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to succeed in situations where the standard rank-restricted isometry property fails, e.g. in case of subexponential unstructured measurements or of subgaussian rank-one measurements. The stability and robustness of the algorithm are established based on distinctive matrix-analytic ingredients and its performance is substantiated numerically.
Chemical Distances for Percolation of Planar Gaussian Free Fields and Critical Random Walk Loop Soups

We initiate the study on chemical distances of percolation clusters for level sets of two-dimensional discrete Gaussian free fields as well as loop clusters generated by two-dimensional random walk loop soups. One of our results states that the chemical distance between two macroscopic annuli away from the boundary for the random walk loop soup at the critical intensity is of dimension 1 with positive probability. Our proof method is based on an interesting combination of a theorem of Makarov, isomorphism theory, and an entropic repulsion estimate for Gaussian free fields in the presence of a hard wall.
nanoHUB.org: Experiences and Challenges in Software Sustainability for a Large Scientific Community

The science gateway nanoHUB.org , funded by the National Science Foundation (NSF), serves a large scientific community dedicated to research and education in nanotechnology with community-contributed simulation codes as well as a vast repository of other materials such as recorded presentations, teaching materials, and workshops and courses. Nearly 330,000 users annually access over 4400 items of content on nanoHUB, including 343 simulation tools. Arguably the largest nanotechnology facility in the world, nanoHUB has led the way not only in providing open access to scientific code in the nanotechnology community, but also in lowering barriers to the use of that code, by providing a platform where developers are able to easily and quickly deploy code written in a variety of languages with user-friendly graphical user interfaces and where users can run the latest versions of codes transparently on the grid or other powerful resources without ever having to download or update code. Being a leader in open access code deployment provides nanoHUB with opportunities and challenges as it meets the current and future needs of its community. This paper discusses the experiences of nanoHUB in addressing and adapting to the changing landscape of scientific software in ways that best serve its community and meet the needs of the largest portion of its user base.
Exceptional rays and bilipschitz geometry of real surface singularities

Abstract It is known that ambient bilipschitz equivalence preserves tangent cones. This paper explores the behavior of the Nash cone and, in particular, exceptional rays under ambient bilipschitz equivalence for real surfaces in R 3 with isolated singularity.
Technology Adoption, External Financing Frictions, and the Cross Sectional Returns

We explore the asset pricing implications of technological change in a model with costly technology adoption and external financing frictions. Firms adopt the latest technology embodied in new capital to reach the technology frontier, but entail adoption costs and external financing costs. The central finding is that optimal technology adoption is an important determinant of the cross section of stock returns. The model predicts that technology adopting firms are less risky than non-adopting firms. Intuitively, by restricting firms from freely upgrading the existing vintage capital to the technology frontier, costly technology adoption and external financing frictions reduce firms' real and financial flexibilities, and hence generate the risk dispersion between technology adopting firms and non-adopting firms. The model is qualitatively and in many cases quantitatively consistent with the key empirical regularities in the cross sectional returns.
A Note on Maximality of Ideal-independent Sets

We give a solution to a problem originally posed in a draft of J.D. Monk [4]. This result is now listed as further fact 4 after theorem 2.16. In doing so, we will consider some subsets of boolean algebras. We will follow S. Koppelberg [2] for notation. In particular +, ·, and − will used as the Boolean operators, and 0 and 1 as the least and greatest element. By extension, the least upper bound of a set M will be denoted ∑ M
Ex vivo mouse brain microscopy at 15T with loop-gap RF coil.

The design of a loop-gap-resonator RF coil optimized for ex vivo mouse brain microscopy at ultra high fields is described and its properties characterized using simulations, phantoms and experimental scans of mouse brains fixed in 10% formalin containing 4 mM Magnevist™. The RF (B1) and magnetic field (B0) homogeneities are experimentally quantified and compared to electromagnetic simulations of the coil. The coil's performance is also compared to a similarly sized surface coil and found to yield double the sensitivity. A three-dimensional gradient-echo (GRE) sequence is used to acquire high resolution mouse brain scans at (47 μm)3 resolution in 1.8 h and a 20 × 20 × 19 μm3 resolution in 27 h. The high resolution obtained permitted clear visualization and identification of multiple structures in the ex vivo mouse brain and represents, to our knowledge, the highest resolution ever achieved for a whole mouse brain. Importantly, the coil design is simple and easy to construct.
On the efficiency and fairness of multiplayer HTTP-based adaptive video streaming

User-perceived quality-of-experience (QoE) is critical in Internet video delivery systems. Many previous efforts have studied the design of client-side bitrate adaptation algorithms to maximize single-player QoE. However, multiplayer QoE fairness becomes critical as the growth of video traffic makes it more likely that multiple players share a bottleneck in the network. Despite several recent proposals, there are still a series of open questions. In this paper, we shed light to the problem space from a control theory perspective by formalizing the multiplayer QoE fairness problem and address two key questions. First, we derive the sufficient conditions of convergence to steady state QoE fairness under a TCP-based bandwidth sharing scheme. Based on the insight from this analysis that in-network active bandwidth allocation is needed, we propose a non-linear MPC-based, router-assisted bandwidth allocation algorithm that regards each player as a closed-loop system. We use trace-driven simulations to show the improvement over existing approaches. We identify several research directions enabled by the control theoretic modeling and envision that control theory can play an important role on guiding real system design in adaptive video streaming.
Solving the Likelihood Equations to Compute Euler Obstruction Functions

Macpherson defined Chern-Schwartz-Macpherson classes by introducing the (local) Euler obstruction function, which is an integer valued function on the variety that is constant on each stratum of a Whitney stratification. By understanding the Euler obstruction, one gains insights about a singular algebraic variety. It was recently shown by the author and B. Wang, how to compute these functions using maximum likelihood degrees. This paper discusses a symbolic and a numerical implementation of algorithms to compute the Euler obstruction at a point.
Convergence of Cauchy sequences for the covariant Gromov–Hausdorff propinquity

Abstract The covariant Gromov–Hausdorff propinquity is a distance on Lipschitz dynamical systems over quantum compact metric spaces, up to equivariant full quantum isometry. It is built from the dual Gromov–Hausdorff propinquity which, as its classical counterpart, is complete. We prove in this paper several sufficient conditions for convergence of Cauchy sequences for the covariant propinquity and apply it to show that many natural classes of dynamical systems are complete for this metric.
Steklov approximations of harmonic boundary value problems on planar regions

Abstract Error estimates for approximations of solutions of Laplace’s equation with Dirichlet, Robin or Neumann boundary value conditions are described. The solutions are represented by orthogonal series using the harmonic Steklov eigenfunctions. Error bounds for partial sums involving the lowest eigenfunctions are found. When the region is a rectangle, explicit formulae for the Steklov eigenfunctions and eigenvalues are known. These were used to find approximations for problems with known explicit solutions. Results about the accuracy of these solutions, as a function of the number of eigenfunctions used, are given.
PERIODIC ORBITS OF A DYNAMICAL SYSTEM RELATED TO A KNOT

Following [6] we consider a knot group G, its commutator subgroup K = [G, G], a finite group Σ and the space Hom(K, Σ) of all representations ρ : K → Σ, endowed with the weak topology. We choose a meridian x ∈ G of the knot and consider the homeomorphism σx of Hom(K, Σ) onto itself: σxρ(a) = ρ(xax-1) ∀ a ∈ K, ρ ∈ Hom(K, Σ). As proven in [5], the dynamical system (Hom(K, Σ), σx) is a shift of finite type. In the case when Σ is abelian, Hom(K, Σ) is finite. In this paper we calculate the periods of orbits of (Hom(K, ℤ/p), σx), where p is prime, in terms of the roots of the Alexander polynomial of the knot. In the case of two-bridge knots we give a complete description of the set of periods.
Multi-Task Learning for Contextual Bandits

Contextual bandits are a form of multi-armed bandit in which the agent has access to predictive side information (known as the context) for each arm at each time step, and have been used to model personalized news recommendation, ad placement, and other applications. In this work, we propose a multi-task learning framework for contextual bandit problems. Like multi-task learning in the batch setting, the goal is to leverage similarities in contexts for different arms so as to improve the agent's ability to predict rewards from contexts. We propose an upper confidence bound-based multi-task learning algorithm for contextual bandits, establish a corresponding regret bound, and interpret this bound to quantify the advantages of learning in the presence of high task (arm) similarity. We also describe an effective scheme for estimating task similarity from data, and demonstrate our algorithm's performance on several data sets.
How well can we estimate a sparse vector

The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix being used and regardless of the estimation procedure. This lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an l1 estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved.
The Henchman Problem: Measuring Secrecy by the Minimum Distortion in a List

We introduce a new measure of information-theoretic secrecy based on rate-distortion theory and study it in the context of the Shannon cipher system. Whereas rate-distortion theory is traditionally concerned with a single reconstruction sequence, in this paper, we suppose that an eavesdropper produces a list of $2^{nR_{\sf L}}$ reconstruction sequences and measure secrecy by the minimum distortion over the entire list. We show that this setting is equivalent to one in which an eavesdropper must reconstruct a single sequence, but also receives side information about the source sequence and public message from a rate-limited henchman (a helper for an adversary). We characterize the optimal tradeoff of secret key rate, list rate, and eavesdropper distortion. The solution hinges on a problem of independent interest: lossy compression of a codeword uniformly drawn from a random codebook. We also characterize the solution to the lossy communication version of the problem in which distortion is allowed at the legitimate receiver. The analysis in both the settings is greatly aided by a recent technique for proving source coding results with the use of a likelihood encoder.
Lifted polymatroid inequalities for mean-risk optimization with indicator variables

We investigate a mixed 0–1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities by lifting the polymatroid inequalities on the binary variables. Computational experiments demonstrate the effectiveness of the inequalities in strengthening the convex relaxations and, thereby, improving the solution times for mean-risk problems with fixed charges and cardinality constraints significantly.
Multi-lingual Common Semantic Space Construction via Cluster-consistent Word Embedding

We construct a multilingual common semantic space based on distributional semantics, where words from multiple languages are projected into a shared space via which all available resources and knowledge can be shared across multiple languages. Beyond word alignment, we introduce multiple cluster-level alignments and enforce the word clusters to be consistently distributed across multiple languages. We exploit three signals for clustering: (1) neighbor words in the monolingual word embedding space; (2) character-level information; and (3) linguistic properties (e.g., apposition, locative suffix) derived from linguistic structure knowledge bases available for thousands of languages. We introduce a new cluster-consistent correlational neural network to construct the common semantic space by aligning words as well as clusters. Intrinsic evaluation on monolingual and multilingual QVEC tasks shows our approach achieves significantly higher correlation with linguistic features which are extracted from manually crafted lexical resources than state-of-the-art multi-lingual embedding learning methods do. Using low-resource language name tagging as a case study for extrinsic evaluation, our approach achieves up to 14.6% absolute F-score gain over the state of the art on cross-lingual direct transfer. Our approach is also shown to be robust even when the size of bilingual dictionary is small.
End-to-End Learning of Keypoint Detector and Descriptor for Pose Invariant 3D Matching

Finding correspondences between images or 3D scans is at the heart of many computer vision and image retrieval applications and is often enabled by matching local keypoint descriptors. Various learning approaches have been applied in the past to different stages of the matching pipeline, considering detection, description, or metric learning objectives. These objectives were typically addressed separately and most previous work has focused on image data. This paper proposes an end-to-end learning framework for keypoint detection and its representation (descriptor) for 3D depth maps or 3D scans, where the two can be jointly optimized towards task-specific objectives without a need for separate annotations. We employ a Siamese architecture augmented by a sampling layer and a novel score loss function which in turn affects the selection of region proposals. The positive and negative examples are obtained automatically by sampling corresponding region proposals based on their consistency with known 3D pose labels. Matching experiments with depth data on multiple benchmark datasets demonstrate the efficacy of the proposed approach, showing significant improvements over state-of-the-art methods.
Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning

Very deep convolutional networks have been central to the largest advances in image recognition performance in recent years. One example is the Inception architecture that has been shown to achieve very good performance at relatively low computational cost. Recently, the introduction of residual connections in conjunction with a more traditional architecture has yielded state-of-the-art performance in the 2015 ILSVRC challenge; its performance was similar to the latest generation Inception-v3 network. This raises the question: Are there any benefits to combining Inception architectures with residual connections? Here we give clear empirical evidence that training with residual connections accelerates the training of Inception networks significantly. There is also some evidence of residual Inception networks outperforming similarly expensive Inception networks without residual connections by a thin margin. We also present several new streamlined architectures for both residual and non-residual Inception networks. These variations improve the single-frame recognition performance on the ILSVRC 2012 classification task significantly. We further demonstrate how proper activation scaling stabilizes the training of very wide residual Inception networks. With an ensemble of three residual and one Inception-v4 networks, we achieve 3.08% top-5 error on the test set of the ImageNet classification (CLS) challenge.
Budget-Constrained Edge Service Provisioning With Demand Estimation via Bandit Learning

Shared edge computing platforms, which enable Application Service Providers (ASPs) to deploy applications in close proximity to mobile users are providing ultra-low latency and location-awareness to a rich portfolio of services. Though ubiquitous edge service provisioning, i.e., deploying the application at all possible edge sites, is always preferable, it is impractical due to often limited operational budget of ASPs. In this case, an ASP has to cautiously decide where to deploy the edge service and how much budget it is willing to use. A central issue here is that the service demand received by each edge site, which is the key factor of deploying benefit, is unknown to ASPs a priori. What’s more complicated is that this demand pattern varies temporally and spatially across geographically distributed edge sites. In this paper, we investigate an edge resource rental problem where the ASP learns service demand patterns for individual edge sites while renting computation resource at these sites to host its applications for edge service provisioning. An online algorithm, called Context-aware Online Edge Resource Rental (COERR), is proposed based on the framework of Contextual Combinatorial Multi-armed Bandit (CC-MAB). COERR observes side-information (context) to learn the demand patterns of edge sites and decides rental decisions (including where to rent the computation resource and how much to rent) to maximize ASP’s utility given a limited budget. COERR provides a provable performance achieving sublinear regret compared to an Oracle algorithm that knows exactly the expected service demand of edge sites. Experiments are carried out on a real-world dataset and the results show that COERR significantly outperforms other benchmarks.
Visualizing structural transitions of ligand-dependent gating of the TRPM2 channel

The transient receptor potential melastatin 2 (TRPM2) channel plays a key role in redox sensation in many cell types. Channel activation requires binding of both ADP-ribose (ADPR) and Ca2+. The recently published TRPM2 structures from Danio rerio in the ligand-free and the ADPR/Ca2+-bound conditions represent the channel in closed and open states, which uncovered substantial tertiary and quaternary conformational rearrangements. However, it is unclear how these rearrangements are achieved within the tetrameric channel during channel gating. Here we report the cryo-electron microscopy structures of Danio rerio TRPM2 in the absence of ligands, in complex with Ca2+ alone, and with both ADPR and Ca2+, resolved to ~4.3 A, ~3.8 A, and ~4.2 A, respectively. In contrast to the published results, our studies capture ligand-bound TRPM2 structures in two-fold symmetric intermediate states, offering a glimpse of the structural transitions that bridge the closed and open conformations. The transient receptor potential channel member 2 (TRPM2) ion channel has a function in redox-dependent signaling. Here the authors present the cryo-EM structures of zebrafish TRPM2 in the ligand-free form, with Ca2+ and both ADP-ribose/Ca2+ and observe two-fold symmetric quaternary structure rearrangements in the ligand-bound structures that likely represent intermediate gating states.
Towards Controllable and Personalized Review Generation

In this paper, we propose a novel model RevGAN that automatically generates controllable and personalized user reviews based on the arbitrarily given sentimental and stylistic information. RevGAN utilizes the combination of three novel components, including self-attentive recursive autoencoders, conditional discriminators, and personalized decoders. We test its performance on the several real-world datasets, where our model significantly outperforms state-of-the-art generation models in terms of sentence quality, coherence, personalization, and human evaluations. We also empirically show that the generated reviews could not be easily distinguished from the organically produced reviews and that they follow the same statistical linguistics laws.
An associative search language for data management

Recent years have witnessed a widespread and intensive effort to develop systems to store, maintain and access data bases of varied size. Such systems are referred to as DBMS— D ata B ase Management S ystems. In different areas, such as artificial intelligence, management information systems, military and corporate logistics and medical diagnosis, a wide variety of DBMS exist. All these systems have generally been implemented on conventional computers, which are based on the von Neumann design. In this design, operations will be performed on the information in the memory by means of their addresses. Because of the size of typical data bases and costs of memory, we cannot hold all information in the main memory and swapping converts the search problem to a transportation problem. Present-day systems have to transfer large sets of data from their mass storage to the CPU, where simple compare-functions are performed in order to separate relevant data from irrelevant data. The transfer channels with their limited capacity form the main bottleneck of this system and as a result, great efforts have been made to reduce the necessary data flow by means of sophisticated software systems and additional redundancy such as index tables and inverted files. By these techniques, address of information will be obtained from a directory. Although directory partially solved the bottleneck problem, it nevertheless created some problems. The directory should logically be kept in the main memory. If we are dealing with large data bases, naturally we are dealing also with large directories, and large directories occupy a large portion of the memory. Also, the use of directories will create some complexity in the search, update and delete algorithms. Conventional computers are all based on numerical operations. The necessity of designing new hardware based on non-numerical operations has been discussed in detail by one of the authors. 1 In contrast, use of associative or content addressable memories and hardware design based on non-numerical operations as well as numerical operations causes information stored at unknown locations to be processed efficiently on the basis of some knowledge of its content.
Quantification of IGF-1 Receptor is Useful in the Differential Diagnosis of Essential Thrombocytosis from Reactive Thrombocytosis

Background To make a definite diagnosis of essential thrombocytosis (ET) from reactive thrombocytosis (RT), the most reliable criteria are the presence of driver mutations, namely JAK2, CALR, or MPL gene mutations. In the absence of these driver mutations, so-called triple-negative ET, the differential diagnosis could be difficult. Although bone marrow biopsy could be helpful, it may be difficult in some cases, to do gene sequence analysis to identify other clonal marker gene mutations than the driver mutations, as only very few were found. Methods IGF-1R quantification by flow cytometry in mononuclear cells (MNC) from peripheral blood was performed in 33 patients with ET (untreated or off treatment with hydroxyurea), 28 patients with RT, and 16 normal volunteer controls. Results We found IGF-1R levels were significantly elevated in ET patients compared to RT patients or controls. A cutoff value of 253 was chosen from the logistic regression to predict each patient's group, a value ≥253 meant that a patient belonged to the ET group (sensitivity 96.4% and specificity 68.6%). Conclusion We suggest that adding quantification of IGF-1R in blood MNC by flow cytometry is useful in differentiating ET from RT.
Ethics for Contingent Classifications: Rorty’s Pragmatic Ethics and Postmodern Knowledge Organization

There is potential disconnect between a view of classification as historically and culturally contingent and the ethics of KO. For instance, Mai (2011) urges a shift away from the ‘modernity’ of received classification theory, towards a more pluralistic view that acknowledges the social, political, and historical contingency of classification as a practice. While this is a view shared by many, it is not evident how such an approach can support an ethics which prioritizes a commitment to truth, fairness, democracy, and the common good. A view of such values as merely contingent factors in classification activities would seem to undermine their use as ethical ideals, posing a choice between abandoning modernist tendencies and a workable ethics of KO. An ethics that is consonant with core methodological commitments is critical if we seek to preserve both disciplinary rigor and claim to serve the common good. Rorty's thought is presented as an ethics compatible with a view of classification as contingent. His suggestion of an ironic ethics is presented and distinguished from cynicism, which is a common misinterpretation of this aspect of his thought. Finally, his ethical principle of solidarity is shown to be broadly compatible with the traditional values of the field of LIS, while approaching it from a philosophical standpoint that doesn’t demand or encourage the universalizing tendencies which Mai and others have exhorted us to abandon. In short, this paper attempts to preserve the baby of a workable ethics while discarding the bathwater of universalism in knowledge organization.