cssi/SciSciGPT-SciSciNet huggingface dataset:
Separators in Region Intersection Graphs

For undirected graphs G=(V,E) and G_0=(V_0,E_0), say that G is a region intersection graph over G_0 if there is a family of connected subsets {R_u \subseteq V_0 : u \in V} of G_0 such that {u,v} \in E \iff R_u \cap R_v \neq \emptyset. We show if G_0 excludes the complete graph K_h as a minor for some h \geq 1, then every region intersection graph G over G_0 with m edges has a balanced separator with at most c_h \sqrt{m} nodes, where c_h is a constant depending only on h. If G additionally has uniformly bounded vertex degrees, then such a separator is found by spectral partitioning. A string graph is the intersection graph of continuous arcs in the plane. String graphs are precisely region intersection graphs over planar graphs. Thus the preceding result implies that every string graph with m edges has a balanced separator of size O(\sqrt{m}). This bound is optimal, as it generalizes the planar separator theorem. It confirms a conjecture of Fox and Pach (2010), and improves over the O(\sqrt{m} \log m) bound of Matousek (2013).
Nanopore occlusion: A biophysical mechanism for bipolar cancellation in cell membranes.

Abstract Extraordinarily large but short electric field pulses are reported by many experiments to cause bipolar cancellation (BPC). This unusual cell response occurs if a first pulse is followed by a second pulse with opposite polarity. Possibly universal, BPC presently lacks a mechanistic explanation. Multiple versions of the “standard model” of cell electroporation (EP) fail to account for BPC. Here we show, for the first time, how an extension of the standard model can account for a key experimental observation that essentially defines BPC: the amount of a tracer that enters a cell, and how tracer influx can be decreased by the second part of a bipolar pulse. The extended model can also account for the recovery of BPC wherein the extent of BPC is diminished if the spacing between the first and second pulses is increased. Our approach is reverse engineering, meaning that we identify and introduce an additional biophysical mechanism that allows pore transport to change. We hypothesize that occluding molecules from outside the membrane enter or relocate within a pore. Significantly, the additional mechanism is fundamental and general, involving a combination of partitioning and hindrance. Molecules near the membrane can enter pores to block transport of tracer molecules while still passing small ions (charge number ±1) that govern electrical behavior. Our extension of the standard model accounts for key BPC behavior.
Modeling sequence-specific polymers using anisotropic coarse-grained sites allows quantitative comparison with experiment.

Certain sequences of peptoid polymers (synthetic analogs of peptides) assemble into bilayer nanosheets via a nonequilibrium assembly pathway of adsorption, compression, and collapse at an air–water interface. As with other large-scale dynamic processes in biology and materials science, understanding the details of this supramolecular assembly process requires a modeling approach that captures behavior on a wide range of length and time scales, from those on which individual side chains fluctuate to those on which assemblies of polymers evolve. Here, we demonstrate that a new coarse-grained modeling approach is accurate and computationally efficient enough to do so. Our approach uses only a minimal number of coarse-grained sites but retains independently fluctuating orientational degrees of freedom for each site. These orientational degrees of freedom allow us to accurately parametrize both bonded and nonbonded interactions and to generate all-atom configurations with sufficient accuracy to perform atomic ...
Geometric divisors in normal local domains

Abstract Let A be the local ring at a point of a normal complex variety with completion R = A ˆ . Srinivas has asked about the possible images of the induced map Cl A → Cl R over all geometric local normal domains A with fixed completion R . We use Noether–Lefschetz theory to prove that all finitely generated subgroups are possible in some familiar cases. As a byproduct we show that every finitely generated abelian group appears as the class group of the local ring at the vertex of a cone over some smooth complex variety of each positive dimension.
The group of primitive almost pythagorean triples

We consider the triples of integer numbers that are solutions of the equation x 2 + qy 2 = z 2 , where q is a fixed, square-free arbitrary positive integer. The set of equivalence classes of these triples forms an abelian group under the operation coming from complex multiplication. We investigate the algebraic structure of this group and give a complete analysis when q ∈ {2,3,5,6}.
Downlink Coordinated Joint Transmission for Mutual Information Accumulation

In this letter, we propose a new coordinated multipoint technique based on mutual information (MI) accumulation using rateless codes. Using a stochastic geometry model for the cellular downlink, we quantify the performance enhancements in coverage probability and rate due to MI accumulation. By simulation and analysis, we show that MI accumulation using rateless codes leads to remarkable improvements in coverage and rate for general users and specific cell edge users.
Markov processes with spatial delay: Path space characterization, occupation time and properties

In this paper, we study one-dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one-dimensional, strong, homogeneous, continuous Markov process can be uniquely characterized via its infinitesimal generator and the generator’s domain of definition. Unlike standard diffusions like Brownian motion, processes with spatial delay spend positive time at a single point of space. Interestingly, the set of times that a delay process spends at its delay point is nowhere dense and forms a positive measure Cantor set. The domain of definition of the generator has restrictions involving second derivatives. In this paper we provide a pathwise characterization for processes with delay in terms of an SDE and an occupation time formula involving the symmetric local time. This characterization provides an explicit Doob–Meyer decomposition, demonstrating that such processes are semi-martingales and that all of stochastic calculus including Ito formula and Girsanov formula applies. We also establish an occupation time formula linking the time that the process spends at a delay point with its symmetric local time there. A physical example of a stochastic dynamical system with delay is lastly presented and analyzed.
On a 1D transport equation with nonlocal velocity and supercritical dissipation

Abstract We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global regularity for solutions when dissipation is slightly supercritical. Both results utilize a nonlocal maximum principle.
Optimal Rate Code Constructions for Computationally Simple Channels

We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter p and (b) the process that adds the errors can be described by a sufficiently “simple” circuit. Codes for such channel models are attractive since, like codes for standard adversarial errors, they can handle channels whose true behavior is unknown or varying over time.For two classes of channels, we provide explicit, efficiently encodable/decodable codes of optimal rate where only inefficiently decodable codes were previously known. In each case, we provide one encoder/decoder that works for every channel in the class. The encoders are randomized, and probabilities are taken over the (local, unknown to the decoder) coins of the encoder and those of the channel.Unique decoding for additive errors: We give the first construction of a polynomial-time encodable/decodable code for additive (a.k.a. oblivious) channels that achieve the Shannon capacity 1 − H(p). These are channels that add an arbitrary error vector e ∈ l0, 1rN of weight at most pN to the transmitted word; the vector e can depend on the code but not on the randomness of the encoder or the particular transmitted word. Such channels capture binary symmetric errors and burst errors as special cases.List decoding for polynomial-time channels: For every constant c > 0, we construct codes with optimal rate (arbitrarily close to 1 − H(p)) that efficiently recover a short list containing the correct message with high probability for channels describable by circuits of size at most Nc. Our construction is not fully explicit but rather Monte Carlo (we give an algorithm that, with high probability, produces an encoder/decoder pair that works for all time Nc channels). We are not aware of any channel models considered in the information theory literature other than purely adversarial channels, which require more than linear-size circuits to implement. We justify the relaxation to list decoding with an impossibility result showing that, in a large range of parameters (p > 1/4), codes that are uniquely decodable for a modest class of channels (online, memoryless, nonuniform channels) cannot have positive rate.
Large scale absolute extensors

Abstract This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting of creating analogs of small scale concepts using covers and the other amounting to the covering dimension of the Higson corona ν ( X ) of X. The first approach was used by M. Gromov when defining the asymptotic dimension asdim ( X ) of metric spaces X. The second approach was implicitly contained in the paper [6] by Dranishnikov on asymptotic topology. It is not known if the two approaches yield the same concept. However, Dranishnikov–Keesling–Uspenskiy proved dim ( ν ( X ) ) ≤ asdim ( X ) and Dranishnikov established that dim ( ν ( X ) ) = asdim ( X ) provided asdim ( X ) ∞ . We characterize asymptotic dimension (for spaces of finite asymptotic dimension) in terms of extensions of slowly oscillating functions to spheres. Our approach is specifically designed to relate asymptotic dimension to the covering dimension of the Higson corona ν ( X ) in case of proper metric spaces X. As an application, we recover the results of Dranishnikov–Keesling–Uspenskiy and Dranishnikov.
Fast property testing and metrics for permutations

The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are e-far from satisfying the property. There are now several general results in this area which show that natural properties of combinatorial objects can be tested with ‘constant’ query complexity, depending only on e and the property, and not on the size of the object being tested. The upper bound on the query complexity coming from the proof techniques is often enormous and impractical. It remains a major open problem if better bounds hold.Maybe surprisingly, for testing with respect to the rectangular distance, we prove there is a universal (not depending on the property), polynomial in 1/e query complexity bound for two-sided testing hereditary properties of sufficiently large permutations. We further give a nearly linear bound with respect to a closely related metric which also depends on the smallest forbidden subpermutation for the property. Finally, we show that several different permutation metrics of interest are related to the rectangular distance, yielding similar results for testing with respect to these metrics.
Unsupervised Discovery of Object Landmarks as Structural Representations

Deep neural networks can model images with rich latent representations, but they cannot naturally conceptualize structures of object categories in a human-perceptible way. This paper addresses the problem of learning object structures in an image modeling process without supervision. We propose an autoencoding formulation to discover landmarks as explicit structural representations. The encoding module outputs landmark coordinates, whose validity is ensured by constraints that reflect the necessary properties for landmarks. The decoding module takes the landmarks as a part of the learnable input representations in an end-to-end differentiable framework. Our discovered landmarks are semantically meaningful and more predictive of manually annotated landmarks than those discovered by previous methods. The coordinates of our landmarks are also complementary features to pretrained deep-neural-network representations in recognizing visual attributes. In addition, the proposed method naturally creates an unsupervised, perceptible interface to manipulate object shapes and decode images with controllable structures.
In Search of a Structural Model for a Thiolate-protected Au38 Cluster

The structure of thiolate-protected gold cluster Au38(SR)24 has not been experimentally determined, and the best available signature is its measured optical spectrum. Using this signature and energ...
Data-Driven Approximation of Transfer Operators: Naturally Structured Dynamic Mode Decomposition

In this paper, we provide a new algorithm for the finite dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time series data. We argue that existing approach for the finite dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose in this paper preserve these two properties. We call the proposed algorithm as naturally structured DMD since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite dimensional approximation play an important role for controller and estimator design of nonlinear systems.
Exploitation of Semantic Keywords for Malicious Event Classification

Learning an event classifier is challenging when the scenes are semantically different but visually similar. However, as humans, we typically handle such tasks painlessly by adding our background semantic knowledge. Motivated by this observation, we aim to provide an empirical study about how additional information such as semantic keywords can boost up the discrimination of such events. To demonstrate the validity of this study, we first construct a novel Malicious Crowd Dataset containing crowd images with two events, benign and malicious, which look visually similar. Note that the primary focus of this paper is not to provide the state-of-the-art performance on this dataset but to show the beneficial aspects of using semantically-driven keyword information. By leveraging crowd-sourcing platforms, such as Amazon Mechanical Turk, we collect semantic keywords associated with images and then subsequently identify a subset of keywords (e.g. police, fire, etc.) unique to specific events. We first show that by using recently introduced attention models, a naive CNN-based event classifier actually learns to primarily focus on local attributes associated with the discriminant semantic keywords identified by the Turks. We further show that incorporating the keyword-driven information into early-and late-fusion approaches can significantly enhance malicious event classification.
On Univariate Convex Regression

We find the local rate of convergence of the least squares estimator (LSE) of a one dimensional convex regression function when (a) a certain number of derivatives vanish at the point of interest, and (b) the true regression function is locally affine. In each case we derive the limiting distribution of the LSE and its derivative. The pointwise limiting distributions depend on the second and third derivatives at 0 of the “invelope function” of the integral of a two-sided Brownian motion with polynomial drifts. We also investigate the inconsistency of the LSE and the unboundedness of its derivative at the boundary of the domain of the covariate space. An estimator of the argmin of the convex regression function is proposed and its asymptotic distribution is derived. Further, we present some new results on the characterization of the convex LSE that may be of independent interest.
Multi-User Beam-Alignment for Millimeter-Wave Networks

Millimeter-wave communications is the most promising technology for next-generation cellular wireless systems, thanks to the large bandwidth available compared to sub-6 GHz networks. Nevertheless, communication at these frequencies requires narrow beams via massive MIMO and beamforming to overcome the strong signal attenuation, and thus precise beam-alignment between transmitter and receiver is needed. The resulting signaling overhead may become a severe impairment, especially in mobile networks with high users density. Therefore, it is imperative to optimize the beam-alignment protocol to minimize the signaling overhead. In this paper, the design of energy efficient joint beam-alignment protocols for two users is addressed, with the goal to minimize the power consumption during data transmission, subject to rate constraints for both users, under analog beamforming constraints. It is proved that a bisection search algorithm is optimal. Additionally, the optimal scheduling strategy of the two users in the data communication phase is optimized based on the outcome of beam-alignment, according to a time division multiplexing scheme. The numerical results show significant decrease in the power consumption for the proposed joint beam-alignment scheme compared to exhaustive search and a single-user beam-alignment scheme taking place separately for each user.
An approximation to Wiener measure and quantization of the Hamiltonian on manifolds with non-positive sectional curvature☆

This paper gives a rigorous interpretation of a Feynman path integral on a Riemannian manifold M with non-positive sectional curvature. An L2 Riemannian metric GP is given on the space of piecewise geodesic paths HP(M) adapted to the partition P of [0,1], whence a finite-dimensional approximation of Wiener measure is developed. It is proved that, as mesh(P)→0, the approximate Wiener measure converges in an L1 sense to the measure exp{−2+3203∫01Scal(σ(s))ds}dν(σ) on the Wiener space W(M) with Wiener measure ν. This gives a possible prescription for the path integral representation of the quantized Hamiltonian, as well as yielding such a result for the natural geometric approximation schemes originating in Andersson and Driver (1999) [3] and followed by Lim (2007) [34].
Model-based Reinforcement Learning and the Eluder Dimension

We consider the problem of learning to optimize an unknown Markov decision process (MDP). We show that, if the MDP can be parameterized within some known function class, we can obtain regret bounds that scale with the dimensionality, rather than cardinality, of the system. We characterize this dependence explicitly as O(√dKdET) where T is time elapsed, dK is the Kolmogorov dimension and dE is the eluder dimension. These represent the first unified regret bounds for model-based reinforcement learning and provide state of the art guarantees in several important settings. Moreover, we present a simple and computationally efficient algorithm posterior sampling for reinforcement learning (PSRL) that satisfies these bounds.
Strange, charm, and bottom flavors in CTEQ global analysis

I discuss advances in the determination of strange, charm, and bottom quark parton distribution functions obtained in the CTEQ6.5 and CTEQ6.6 global analyses. These results affect electroweak precision observables and certain new physics searches at the Large Hadron Collider. I focus, in particular, on high-energy implications of the consistent treatment of heavy-quark threshold effects in DIS in the general-mass factorization scheme; an independent parametrization for the strangeness PDF; and the possible presence of nonperturbative ("intrinsic") charm.
Distributed Online Optimization in Dynamic Environments Using Mirror Descent

This work addresses decentralized online optimization in nonstationary environments. A network of agents aim to track the minimizer of a global, time-varying, and convex function. The minimizer follows a known linear dynamics corrupted by unknown unstructured noise. At each time, the global function (which could be a tracking error) can be cast as a sum of a finite number of local functions, each of which is assigned to one agent in the network. Moreover, the local functions become available to agents sequentially, and agents do not have prior knowledge of the future cost functions. Therefore, agents must communicate with each other to build an online approximation of the global function. We propose a decentralized variation of the celebrated mirror descent algorithm, according to which agents perform a consensus step to follow the global function and take into account the dynamics of the global minimizer. In order to measure the performance of the proposed online algorithm, we compare it to its offline counterpart, where the global functions are available a priori . The gap between the two losses is defined as dynamic regret. We establish a regret bound that scales inversely in the spectral gap of the network and represents the deviation of minimizer sequence with respect to the given dynamics. We show that our framework subsumes a number of results in distributed optimization.
The topology of toric origami manifolds

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin and Pires, who classified toric origami manifolds by combinatorial origami templates. In this paper, we examine the topology of toric origami manifolds that have acyclic origami template and co-orientable folding hypersurface. We prove that the cohomology is concentrated in even degrees, and that the equivariant cohomology satisfies the GKM description. Finally we show that toric origami manifolds with co-orientable folding hypersurface provide a class of examples of Masuda and Panov's torus manifolds.
SnapToGrid: From Statistical to Interpretable Models for Biomedical Information Extraction

We propose an approach for biomedical information extraction that marries the advantages of machine learning models, e.g., learning directly from data, with the benefits of rule-based approaches, e.g., interpretability. Our approach starts by training a feature-based statistical model, then converts this model to a rule-based variant by converting its features to rules, and “snapping to grid” the feature weights to discrete votes. In doing so, our proposal takes advantage of the large body of work in machine learning, but it produces an interpretable model, which can be directly edited by experts. We evaluate our approach on the BioNLP 2009 event extraction task. Our results show that there is a small performance penalty when converting the statistical model to rules, but the gain in interpretability compensates for that: with minimal effort, human experts improve this model to have similar performance to the statistical model that served as starting point.
The Design of Arbitrage-Free Data Pricing Schemes

Motivated by a growing market that involves buying and selling data over the web, we study pricing schemes that assign value to queries issued over a database. Previous work studied pricing mechanisms that compute the price of a query by extending a data seller’s explicit prices on certain queries, or investigated the properties that a pricing function should exhibit without detailing a generic construction. In this work, we present a formal framework for pricing queries over data that allows the construction of general families of pricing functions, with the main goal of avoiding arbitrage. We consider two types of pricing schemes: instance-independent schemes, where the price depends only on the structure of the query, and answer-dependent schemes, where the price also depends on the query output. Our main result is a complete characterization of the structure of pricing functions in both settings, by relating it to properties of a function over a lattice. We use our characterization, together with information-theoretic methods, to construct a variety of arbitrage-free pricing functions. Finally, we discuss various tradeoffs in the design space and present techniques for efficient computation of the proposed pricing functions.
Flow cytometry based state aggregation of a stochastic model of protein expression

In this article, we introduce the new approach fluorescence grid based aggregation (FGBA) to justify a dynamical model of protein expression using experimental fluorescence histograms. First, we describe the dynamics of the geneprotein system by a chemical master equation (CME), while the protein production rates are unknown. Second, we aggregate the states of the CME into unknown group sizes. Then, we show that these unknown values can be replaced by the data from the experimental fluorescence histograms. Consequently, final probability distributions correspond to the experimental fluorescence histograms.
Stratified Bayesian Optimization

We consider derivative-free black-box global optimization of expensive noisy functions, when most of the randomness in the objective is produced by a few influential scalar random inputs. We present a new Bayesian global optimization algorithm, called Stratified Bayesian Optimization (SBO), which uses this strong dependence to improve performance. Our algorithm is similar in spirit to stratification, a technique from simulation, which uses strong dependence on a categorical representation of the random input to reduce variance. We demonstrate in numerical experiments that SBO outperforms state-of-the-art Bayesian optimization benchmarks that do not leverage this dependence.
Design of policy-aware differentially private algorithms

The problem of designing error optimal differentially private algorithms is well studied. Recent work applying differential privacy to real world settings have used variants of differential privacy that appropriately modify the notion of neighboring databases. The problem of designing error optimal algorithms for such variants of differential privacy is open. In this paper, we show a novel transformational equivalence result that can turn the problem of query answering under differential privacy with a modified notion of neighbors to one of query answering under standard differential privacy, for a large class of neighbor definitions.We utilize the Blowfish privacy framework that generalizes differential privacy. Blowfish uses a policy graph to instantiate different notions of neighboring databases. We show that the error incurred when answering a workload W on a database x under a Blowfish policy graph G is identical to the error required to answer a transformed workload fG(W) on database gG(x) under standard differential privacy, where fG and gG are linear transformations based on G. Using this result, we develop error efficient algorithms for releasing histograms and multidimensional range queries under different Blowfish policies. We believe the tools we develop will be useful for finding mechanisms to answer many other classes of queries with low error under other policy graphs.
A faster pseudopolynomial time algorithm for subset sum

Given a multiset S of n positive integers and a target integer t, the subset sum problem is to decide if there is a subset of S that sums up to t. We present a new divide-and-conquer algorithm that computes all the realizable subset sums up to an integer u in [EQUATION], where σ is the sum of all elements in S and O hides polylogarithmic factors. This result improves upon the standard dynamic programming algorithm that runs in O(nu) time. To the best of our knowledge, the new algorithm is the fastest general deterministic algorithm for this problem. We also present a modified algorithm for finite cyclic groups, which computes all the realizable subset sums within the group in [EQUATION] time, where m is the order of the group.
Monocular Vision based Collaborative Localization for Micro Aerial Vehicle Swarms

In this paper, we present a vision based collaborative localization framework for groups of micro aerial vehicles (MAV). The vehicles are each assumed to be equipped with a forward-facing monocular camera, and to be capable of communicating with each other. This collaborative localization approach is built upon a distributed algorithm where individual and relative pose estimation techniques are combined for the group to localize against surrounding environments. The MAVs initially detect and match salient features between each other to create a sparse reconstruction of the observed environment, which acts as a global map. Once a map is available, each MAV performs feature detection and tracking with a robust outlier rejection process to estimate its own six degree-of-freedom pose. Occasionally, the MAVs can also fuse relative measurements with individual measurements through feature matching and multiple-view geometry based relative pose computation. We present the implementation of this algorithm for MAVs and environments simulated within Microsoft AirSim, and discuss the results and the advantages of collaborative localization.
A utility proportional fairness radio resource block allocation in cellular networks

This paper presents a radio resource block allocation optimization problem for cellular communications systems with users running delay-tolerant and real-time applications, generating elastic and inelastic traffic on the network and being modelled as logarithmic and sigmoidal utilities respectively. The optimization is cast under a utility proportional fairness framework aiming at maximizing the cellular systems utility whilst allocating users the resource blocks with an eye on application quality of service requirements and on the procedural temporal and computational efficiency. Ultimately, the sensitivity of the proposed modus operandi to the resource variations is investigated.
A note on quasi-positive curvature conditions

Abstract We classify the triples H ⊂ K ⊂ G of nested compact Lie groups which satisfy the “positive triple” condition that was shown in [17] to ensure that G / H admits a metric with quasi-positive curvature. A few new examples of spaces that admit quasi-positively curved metrics emerge from this classification; namely, a CP 2 -bundle over S 6 , a B 7 -bundle over HP 2 , a CP 2 n − 1 -bundle over HP n for each n ⩾ 2 , and a family of finite quotients of T 1 S 6 .
Archimedean zeta integrals on U(2,1)

It is known that for a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain au- tomorphic L-functions, which have applications to arithmetic. In this paper we explicitly calculate archimedean zeta integrals of this type for U(2,1). In particular we compute the matrix coefficients of Weil representations using joint harmonics in the Fock model, and those of discrete series using Schmid operators. In the theory of automorphic forms, to obtain deep arithmetic applications it is often necessary to have effectively computable results locally at each place of a number field. In particular, at archimedean places we need some detailed calculations on the harmonic analysis of real Lie groups, and have to face certain combinatorial complexity. In (L1, L2) the author works out the local archimedean theory for cohomological rep- resentations and the connection to special values of L-functions in the stable range. The local theory of theta correspondence for unitary groups is developed in (HKS) for p-adic fields and in (P) for field of real numbers. It is made more precise in (H1, H2) and applied to obtain results about special values of L-functions. The article (HLS) outlines the general global theory of theta correspondence for cuspidal automorphic representations of unitary groups, in which the authors obtain a general formula for the local zeta integral on unitary groups and show that the central L-value is non-negative. We shall explain the motivation and background of this paper by a brief review for above context, following (HLS). Let F + be a totally real number field, F a totally imaginary quadratic extension of F + , A = A F + the adele ring of F + . Let V (resp. V ' ) be a hermitian (resp. skew-hermitian) vector space of dimension n over F, and W = V ⊗F V ' , a symplectic space over F + . Fixing an additive character ψ and a complete polarization W = X⊕Y , we have the Schrodinger model of the oscillator representation ω of f Sp(W)(A), realized on the space S(X(A)) of Schwartz-Bruhat functions on X(A). Let G = U(V ), G ' = U(V ' ). By choosing a global splitting character χ of A × /F × (cf. (HLS)), ω then defines a Weil representation ωV,V ',� of G(A) ×G ' (A) on S(X(A)). As usual, for � ∈ S(X(A)) we have the theta kernel θ�(g,g ' ) = X ∈X(F +)
Noncommutative Geometry and Arithmetic

This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with complex multiplication for imaginary quadratic fields. This talk concentrates on two main aspects: the relation of Stark numbers to the geometry of noncommutative tori with real multiplication, and the shadows of modular forms on the noncommutative boundary of modular curves, that is, the moduli space of on commutative tori.
Continuous adaptation of multi-camera person identification models through sparse non-redundant representative selection

Abstract The problem of image-base person identification/recognition is to provide an identity to the image of an individual based on learned models that describe his/her appearance. Most traditional person identification systems rely on learning a static model on tediously labeled training data. Though labeling manually is an indispensable part of a supervised framework, for a large scale identification system labeling huge amount of data is a significant overhead. For large multi-sensor data as typically encountered in camera networks, labeling a lot of samples does not always mean more information, as redundant images are labeled several times. In this work, we propose a convex optimization based iterative framework that progressively and judiciously chooses a sparse but informative set of samples for labeling, with minimal overlap with previously labeled images. We also use a structure preserving sparse reconstruction based classifier to reduce the training burden typically seen in discriminative classifiers. The two stage approach leads to a novel framework for online update of the classifiers involving only the incorporation of new labeled data rather than any expensive training phase. We demonstrate the effectiveness of our approach on multi-camera person re-identification datasets, to demonstrate the feasibility of learning online classification models in multi-camera big data applications. Using three benchmark datasets, we validate our approach and demonstrate that our framework achieves superior performance with significantly less amount of manual labeling.
Optimal Stopping for Interval Estimation in Bernoulli Trials

We propose an optimal sequential methodology for obtaining confidence intervals for a binomial proportion $\theta$ . Assuming that an independent and identically distributed sequence of Bernoulli ( $\theta$ ) trials is observed sequentially, we are interested in designing: 1) a stopping time $T$ that will decide the best time to stop sampling the process and 2) an optimum estimator $\hat{{\theta}}_{{T}}$ that will provide the optimum center of the interval estimate of $\theta$ . We follow a semi-Bayesian approach, where we assume that there exists a prior distribution for $\theta$ , and our goal is to minimize the average number of samples while we guarantee a minimal specified coverage probability level. The solution is obtained by applying standard optimal stopping theory and computing the optimum pair $(T,\hat{{\theta }}_{{T}})$ numerically. Regarding the optimum stopping time component $T$ , we demonstrate that it enjoys certain very interesting characteristics not commonly encountered in solutions of other classical optimal stopping problems. In particular, we prove that, for a particular prior (beta density), the optimum stopping time is always bounded from above and below; it needs to first accumulate a sufficient amount of information before deciding whether or not to stop, and it will always terminate before some finite deterministic time. We also conjecture that these properties are present with any prior. Finally, we compare our method with the optimum fixed-sample-size procedure as well as with existing alternative sequential schemes.
Dynamical Models and tracking regret in online convex programming

This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total accumulated loss comparable to that of the best comparator sequence, and existing tracking or shifting regret bounds scale with the overall variation of the comparator sequence. In many practical scenarios, however, the environment is non-stationary and comparator sequences with small variation are quite weak, resulting in large losses. The proposed Dynamic Mirror Descent method, in contrast, can yield low regret relative to highly variable comparator sequences by both tracking the best dynamical model and forming predictions based on that model. This concept is demonstrated empirically in the context of sequential compressive observations of a dynamic scene and tracking a dynamic social network.
Operadic multiplications in equivariant spectra, norms, and transfers

We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N∞ operads, equivariant generalizations of E∞ operads. Algebras in equivariant spectra over an N∞ operad model homotopically commutative equivariant ring spectra that only admit certain collections of Hill–Hopkins–Ravenel norms, determined by the operad. Analogously, algebras in equivariant spaces over an N∞ operad provide explicit constructions of certain transfers. This characterization yields a conceptual explanation of the structure of equivariant infinite loop spaces. To explain the relationship between norms, transfers, and N∞ operads, we discuss the general features of these operads, linking their properties to families of finite sets with group actions and analyzing their behavior under norms and geometric fixed points. A surprising consequence of our study is that in stark contract to the classical setting, equivariantly the little disks and linear isometries operads for a general incomplete universe U need not determine the same algebras. Our work is motivated by the need to provide a framework to describe the flavors of commutativity seen in recent work of the second author and Hopkins on localization of equivariant commutative ring spectra.
Aligning Biomedical Metadata with Ontologies Using Clustering and Embeddings

The metadata about scientific experiments published in online repositories have been shown to suffer from a high degree of representational heterogeneity—there are often many ways to represent the same type of information, such as a geographical location via its latitude and longitude. To harness the potential that metadata have for discovering scientific data, it is crucial that they be represented in a uniform way that can be queried effectively. One step toward uniformly-represented metadata is to normalize the multiple, distinct field names used in metadata (e.g., lat lon, lat and long) to describe the same type of value. To that end, we present a new method based on clustering and embeddings (i.e., vector representations of words) to align metadata field names with ontology terms. We apply our method to biomedical metadata by generating embeddings for terms in biomedical ontologies from the BioPortal repository. We carried out a comparative study between our method and the NCBO Annotator, which revealed that our method yields more and substantially better alignments between metadata and ontology terms.
Conversational Markers of Constructive Discussions

Group discussions are essential for organizing every aspect of modern life, from faculty meetings to senate debates, from grant review panels to papal conclaves. While costly in terms of time and organization effort, group discussions are commonly seen as a way of reaching better decisions compared to solutions that do not require coordination between the individuals (e.g. voting)—through discussion, the sum becomes greater than the parts. However, this assumption is not irrefutable: anecdotal evidence of wasteful discussions abounds, and in our own experiments we find that over 30% of discussions are unproductive. We propose a framework for analyzing conversational dynamics in order to determine whether a given task-oriented discussion is worth having or not. We exploit conversational patterns reflecting the flow of ideas and the balance between the participants, as well as their linguistic choices. We apply this framework to conversations naturally occurring in an online collaborative world exploration game developed and deployed to support this research. Using this setting, we show that linguistic cues and conversational patterns extracted from the first 20 seconds of a team discussion are predictive of whether it will be a wasteful or a productive one.
EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION

This paper builds on work of Hochster and Yao that provides nice embeddings for finitely generated modules of finite G-dimension, finite projective dimension or locally finite injective dimension. We extend these results by providing similar embeddings in the relative setting, that is, for certain modules of finite G C -dimension, finite C -projective dimension, locally finite C -injective dimension or locally finite C -injective dimension where C is a semidualizing module. Along the way, we extend some results for modules of finite homological dimension to modules of locally finite homological dimension in the relative setting.
Power system supplementary damping controllers in the presence of saturation

This paper presents the analysis and a method to design supplementary damping controllers (SDCs) for synchronous generators considering the effects of saturation limits. Usually such saturations of control signals are imposed in order to enforce practical limitations such as component ratings. However, to guarantee the stability in the presence of saturation limits, the state trajectories must remain inside the domain of attraction (DA). In this paper, the domain of attraction of a single-machine infinite-bus (SMIB) power system with saturation nonlinearity is estimated and compared with the exact description of the null controllable region. Then, state-feedback controllers are designed to enlarge the DA. Our analysis shows that nonlinear effects of saturation should be considered to guarantee stability and satisfactory performance. Simulation results on a detailed nonlinear model of a synchronous generator indicate that the DA enlarges with the proposed controller. The results also indicate that Critical Clearing Time (CCT) and damping of the system with saturation can be improved by the proposed method.
Skein theory for the ADE planar algebras

Abstract We give generators and relations for the planar algebras corresponding to the E 8 subfactor. We also give an explicit basis, and an algorithm to express an arbitrary diagram as a linear combination of basis diagrams. We summarize the analogous results for the other A D E subfactors, which can be obtained by the same methods.
Combinatorial restrictions on the tree class of the Auslander–Reiten quiver of a triangulated category

We show that if a connected, Hom-finite, Krull–Schmidt triangulated category has an Auslander–Reiten quiver component with Dynkin tree class then the category has Auslander–Reiten triangles and that component is the entire quiver. This is an analogue for triangulated categories of a theorem of Auslander, and extends a previous result of Scherotzke. We also show that if there is a quiver component with extended Dynkin tree class, then other components must also have extended Dynkin class or one of a small set of infinite trees, provided there is a non-zero homomorphism between the components. The proofs use the theory of additive functions.
Learning Latent Permutations with Gumbel-Sinkhorn Networks

Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator. Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms.
Constrained geometric attitude control on SO(3)

This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the controlled attitude trajectory avoids undesired regions defined by an inequality constraint. In addition, we develop an adaptive update law that enables attitude stabilization in the presence of unknown disturbances. The attitude dynamics and the proposed control systems are developed on the special orthogonal group such that singularities and ambiguities of other attitude parameterizations, such as Euler angles and quaternions are completely avoided. The effectiveness of the proposed control system is demonstrated through numerical simulations and experimental results.