cssi/SciSciGPT-SciSciNet huggingface dataset:
A New Series of Chalcohalide Semiconductors with Composite CdBr2/Sb2Se3 Lattices: Synthesis and Characterization of CdSb2Se3Br2 and Indium Derivatives InSb2S4X (X = Cl and Br) and InM2Se4Br (M = Sb and Bi)

A new series of mixed-framework compounds in the chalcohalide family has been synthesized using the conventional solid-state reactions. These include CdSb2Se3Br2 1 and its isoelectronic indium derivatives InSb2S4X (X = Cl 2 and Br 3) and InM2Se4Br (M = Sb 4 and Bi 5). Single crystals were grown from direct interaction of stoichiometric mixtures of respective elemental and binary compounds. The parent compound cadmium antimony selenobromide, CdSb2Se3Br2, was synthesized by heating the stoichiometric mixture of CdBr2 and Sb and Se at 450 °C followed by slow cooling. Single-crystal structure analysis was carried out by employing X-ray diffraction methods, showing that this compound crystallizes in the monoclinic crystal system (C2/m, No. 12) with a = 20.998(4) A, b = 4.0260(8) A, c = 12.149(2) A, β = 119.00(3)°, and V = 898.3(3) A3. The framework exhibits mixed CdBr2 and Sb2Se3 sublattices, respectively, adopting the (110) and (100) NaCl-type structures. The former consists of dual octahedral chains of Cd-ce...
Functionalized (Benzotriazol-1-yl)methanes as 1,1-Dipole Synthon Equivalents in Diverse Annulations to Aromatic and Heteroaromatic Rings

The title compounds 1a−e readily undergo deprotonation and subsequent reactions with the appropriate electrophiles to form intermediates of types 4 and 7 which, upon treatment with Lewis acids, cyc...
Inverted Regulation of Multidrug Efflux Pumps, Acid Resistance, and Porins in Benzoate-Evolved Escherichia coli K-12

Benzoic acid, a partial uncoupler of the proton motive force (PMF), selects for sensitivity to chloramphenicol and tetracycline during the experimental evolution of Escherichia coli K-12. Transcriptomes of E. coli isolates evolved with benzoate showed the reversal of benzoate-dependent regulation, including the downregulation of multidrug efflux pump genes, the gene for the Gad acid resistance regulon, the nitrate reductase genes narHJ, and the gene for the acid-consuming hydrogenase Hyd-3. However, the benzoate-evolved strains had increased expression of OmpF and other large-hole porins that admit fermentable substrates and antibiotics. Candidate genes identified from benzoate-evolved strains were tested for their roles in benzoate tolerance and in chloramphenicol sensitivity. Benzoate or salicylate tolerance was increased by deletion of the Gad activator ariR or of the acid fitness island from slp to the end of the gadX gene encoding Gad regulators and the multidrug pump genes mdtEF Benzoate tolerance was also increased by deletion of multidrug component gene emrA, RpoS posttranscriptional regulator gene cspC, adenosine deaminase gene add, hydrogenase gene hyc (Hyd-3), and the RNA chaperone/DNA-binding regulator gene hfq Chloramphenicol resistance was decreased by mutations in genes for global regulators, such as RNA polymerase alpha subunit gene rpoA, the Mar activator gene rob, and hfq Deletion of lipopolysaccharide biosynthetic kinase gene rfaY decreased the rate of growth in chloramphenicol. Isolates from experimental evolution with benzoate had many mutations affecting aromatic biosynthesis and catabolism, such as aroF (encoding tyrosine biosynthesis) and apt (encoding adenine phosphoribosyltransferase). Overall, benzoate or salicylate exposure selects for the loss of multidrug efflux pumps and of hydrogenases that generate a futile cycle of PMF and upregulates porins that admit fermentable nutrients and antibiotics.IMPORTANCE Benzoic acid is a common food preservative, and salicylic acid (2-hydroxybenzoic acid) is the active form of aspirin. At high concentrations, benzoic acid conducts a proton across the membrane, depleting the proton motive force. In the absence of antibiotics, benzoate exposure selects against proton-driven multidrug efflux pumps and upregulates porins that admit fermentable substrates but that also allow the entry of antibiotics. Thus, evolution with benzoate and related molecules, such as salicylates, requires a trade-off for antibiotic sensitivity, a trade-off that could help define a stable gut microbiome. Benzoate and salicylate are naturally occurring plant signal molecules that may modulate the microbiomes of plants and animal digestive tracts so as to favor fermenters and exclude drug-resistant pathogens.
Health co-benefits of sub-national renewable energy policy in the US

State and local policy-makers in the U.S. have shown interest in transitioning electricity systems toward renewable energy sources and in mitigating harmful air pollution. However, the extent to which sub-national renewable energy policies can improve air quality remains unclear. To investigate this issue, we develop a systemic modeling framework that combines economic and air pollution models to assess the projected sub-national impacts of Renewable Portfolio Standards (RPSs) on air quality and human health, as well as on the economy and on climate change. We contribute to existing RPS cost-benefit literature by providing a comprehensive assessment of economic costs and estimating economy-wide changes in emissions and their impacts, using a general equilibrium modeling approach. This study is also the first to our knowledge to directly compare the health co-benefits of RPSs to those of carbon pricing. We estimate that existing RPSs in the "Rust Belt" region generate a health co-benefit of $94 per ton CO2 reduced ($2-477/tCO2) in 2030, or 8? for each kWh of renewable energy deployed (0.2- 40?/kWh) in 2015 dollars. Our central estimate is 34% larger than total policy costs. We estimate that the central marginal benefit of raising renewable energy requirements exceeds the marginal cost, suggesting that strengthening RPSs increases net societal benefits. We also calculate that carbon pricing delivers health co-benefits of $211/tCO2 in 2030, 63% greater than the health co-benefit of reducing the same amount of CO2 through an RPS approach.
Characters of equivariant D-modules on Veronese cones

For d > 1, we consider the Veronese map of degree d on a complex vector space W , Ver_d : W -> Sym^d W , w -> w^d , and denote its image by Z. We describe the characters of the simple GL(W)-equivariant holonomic D-modules supported on Z. In the case when d is 2, we obtain a counterexample to a conjecture of Levasseur by exhibiting a GL(W)-equivariant D-module on the Capelli type representation Sym^2 W which contains no SL(W)-invariant sections. We also study the local cohomology modules H_Z^j(S), where S is the ring of polynomial functions on the vector space Sym^d W. We recover a result of Ogus showing that there is only one local cohomology module that is non-zero (namely in degree j = codim(Z)), and moreover we prove that it is a simple D-module and determine its character.
ADAGIO: Fast Data-Aware Near-Isometric Linear Embeddings

Many important applications, including signal reconstruction, parameter estimation, and signal processing in a compressed domain, rely on a low-dimensional representation of the dataset that preserves all pairwise distances between the data points and leverages the inherent geometric structure that is typically present. Recently Hedge, Sankaranarayanan, Yin and Baraniuk [19] proposed the first data-aware near-isometric linear embedding which achieves the best of both worlds. However, their method NuMax does not scale to large-scale datasets. Our main contribution is a simple, data-aware, near-isometric linear dimensionality reduction method which significantly outperforms a state-of-the-art method [19] with respect to scalability while achieving high quality near-isometries. Furthermore, our method comes with strong worst-case theoretical guarantees that allow us to guarantee the quality of the obtained nearisometry. We verify experimentally the efficiency of our method on numerous real-world datasets, where we find that our method (9 hours) on medium scale datasets with 60 000 datapoints in 784 dimensions. Finally, we use our method as a preprocessing step to increase the computational efficiency of a classification application and for speeding up approximate nearest neighbor queries.
Heat flows on hyperbolic spaces

In this paper we develop new methods for studying the convergence problem for the heat flow on negatively curved spaces and prove that any quasiconformal map of the sphere S^(n−1), n ≥ 3, can be extended to the n-dimensional hyperbolic space such that the heat flow starting with this extension converges to a quasi-isometric harmonic map. This implies the Schoen-Li-Wang conjecture that every quasiconformal map of S^(n−1), n ≥ 3, can be extended to a harmonic quasi-isometry of the n-dimensional hyperbolic space.
Convergence Rate of Distributed ADMM Over Networks

We propose a new distributed algorithm based on alternating direction method of multipliers (ADMM) to minimize sum of locally known convex functions using communication over a network. This optimization problem emerges in many applications in distributed machine learning and statistical estimation. Our algorithm allows for a general choice of the communication weight matrix, which is used to combine the iterates at different nodes. We show that when functions are convex, both the objective function values and the feasibility violation converge with rate $O(1/T)$ , where $T$ is the number of iterations. We then show that when functions are strongly convex and have Lipschitz continuous gradients, the sequence generated by our algorithm converges linearly to the optimal solution. In particular, an $\epsilon$ -optimal solution can be computed with $O\left(\sqrt{\kappa _f} \log (1/\epsilon) \right)$ iterations, where $\kappa _f$ is the condition number of the problem. Our analysis highlights the effect of network and communication weights on the convergence rate through degrees of the nodes, the smallest nonzero eigenvalue, and operator norm of the communication matrix.
Structurable equivalence relations

For a class K of countable relational structures, a countable Borel equivalence relation E is said to be K-structurable if there is a Borel way to put a structure in K on each E-equivalence class. We study in this paper the global structure of the classes of K-structurable equivalence relations for various K. We show that K-structurability interacts well with several kinds of Borel homomorphisms and reductions commonly used in the classification of countable Borel equivalence relations. We consider the poset of classes of K-structurable equivalence relations for various K, under inclusion, and show that it is a distributive lattice; this implies that the Borel reducibility preordering among countable Borel equivalence relations contains a large sublattice. Finally, we consider the effect on K-structurability of various model-theoretic properties of K. In particular, we characterize the K such that every K-structurable equivalence relation is smooth, answering a question of Marks.
Nonparametric Distributed Learning Architecture for Big Data: Algorithm and Applications

Dramatic increases in the size and complexity of modern datasets have made traditional “centralized” statistical inference prohibitive. In addition to computational challenges associated with big data learning, the presence of numerous data types (e.g., discrete, continuous, categorical, etc.) makes automation and scalability difficult. A question of immediate concern is how to design a data-intensive statistical inference architecture without changing the basic statistical modeling principles developed for “small” data over the last century. To address this problem, we present MetaLP, a flexible, distributed statistical modeling framework suitable for large-scale data analysis, where statistical inference meets big data computing. This framework consists of three key components that work together to provide a holistic solution for big data learning: (i) partitioning massive data into smaller datasets for parallel processing and efficient computation, (ii) modern nonparametric learning based on a specially designed, orthonormal data transformation leading to mixed data algorithms, and finally (iii) combining heterogeneous “local” inferences from partitioned data using meta-analysis techniques to arrive at the “global” inference for the original big data. We present an application of this general theory in the context of a nonparametric two-sample inference algorithm for Expedia personalized hotel recommendations based on 10 million search result records.
Convex Relaxation of Bilinear Matrix Inequalities Part I: Theoretical Results

This two-part paper is concerned with the problem of minimizing a linear objective function subject to a bilinear matrix inequality (BMI) constraint. In this part, we first consider a family of convex relaxations which transform BMI optimization problems into polynomial-time solvable surrogates. As an alternative to the state-of-the-art semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations, a computationally efficient parabolic relaxation is developed, which relies on convex quadratic constraints only. Next, we developed a family of penalty functions, which can be incorporated into the objective of SDP, SOCP, and parabolic relaxations to facilitate the recovery of feasible points for the original non-convex BMI optimization. Penalty terms can be constructed using any arbitrary initial point. We prove that if the initial point is sufficiently close to the feasible set, then the penalized relaxations are guaranteed to produce feasible points for the original BMI. In Part II of the paper, the efficacy of the proposed penalized convex relaxations is demonstrated on benchmark instances of $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ optimal control synthesis problems.
Streaming Verification of Graph Properties.

Streaming interactive proofs (SIPs) are a framework for outsourced computation. A computationally limited streaming client (the verifier) hands over a large data set to an untrusted server (the prover) in the cloud and the two parties run a protocol to confirm the correctness of result with high probability. SIPs are particularly interesting for problems that are hard to solve (or even approximate) well in a streaming setting. The most notable of these problems is finding maximum matchings, which has received intense interest in recent years but has strong lower bounds even for constant factor approximations. In this paper, we present efficient streaming interactive proofs that can verify maximum matchings exactly. Our results cover all flavors of matchings (bipartite/non-bipartite and weighted). In addition, we also present streaming verifiers for approximate metric TSP. In particular, these are the first efficient results for weighted matchings and for metric TSP in any streaming verification model.
Points on Elliptic Curves Parametrizing Dynamical Galois Groups

We show how rational points on certain varieties parametrize phenomena arising in the Galois theory of iterates of quadratic polynomials. As an example, we characterize completely the set of quadratic polynomials $x^2+c$ whose third iterate has a "small" Galois group by determining the rational points on some elliptic curves. It follows as a corollary that the only such integer value with this property is $c=3$, answering a question of Rafe Jones. Furthermore, using a result of Granville's on the rational points on quadratic twists of a hyperelliptic curve, we indicate how the ABC conjecture implies a finite index result, suggesting a geometric interpretation of this problem.
Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation

Abstract We summarize several decades of work in finding values for the percolation threshold pc for site percolation on the square lattice, the universal correction-to-scaling exponent, and the susceptibility amplitude ratio C + /C – , in two dimensions. Recent studies have yielded the precise values pc = 0:59274602(4), = 72=91 _ 0:791, and C + /C – = 161:5(2:0), resolving long-standing controversies about the last two quantities and verifying the widely used value pc = 0:592746 for the first.
Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems

Abstract We study pullback attractors of non-autonomous non-compact dynamical systems generated by differential equations with non-autonomous deterministic as well as stochastic forcing terms. We first introduce the concepts of pullback attractors and asymptotic compactness for such systems. We then prove a sufficient and necessary condition for existence of pullback attractors. We also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors. For random systems containing periodic deterministic forcing terms, we show the pullback attractors are also periodic under certain conditions. As an application of the abstract theory, we prove the existence of a unique pullback attractor for Reaction–Diffusion equations on R n with both deterministic and random external terms. Since Sobolev embeddings are not compact on unbounded domains, the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions.
Robust dequantized compressive sensing

Abstract We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation errors (from being outside the range of representable values). Our formulation has an objective of weighted l 2 – l 1 type, along with constraints that account explicitly for quantization and saturation errors, and is solved with an augmented Lagrangian method. We prove a consistency result for the recovered solution, stronger than those that have appeared to date in the literature, showing in particular that asymptotic consistency can be obtained without oversampling. We present extensive computational comparisons with formulations proposed previously, and variants thereof.
Staggered t-structures on toric varieties

Abstract Achar has recently introduced a family of t-structures on the derived category of equivariant coherent sheaves on a G -scheme, generalizing the perverse coherent t-structures of Bezrukavnikov and Deligne. They are called staggered t-structures, and one of their points of interest is that they are more often self-dual. In this paper we investigate these t-structures on the T -equivariant derived category of a toric variety.
The Mathematics of the Flip and Horseshoe Shuffles

We consider new types of perfect shuffles wherein a deck is split in half, one half of the deck is “reversed,” and then the cards are interlaced. Flip shuffles are when the reversal comes from turn...
A Knowledge Gradient Policy for Sequencing Experiments to Identify the Structure of RNA Molecules Using a Sparse Additive Belief Model

We present a sparse knowledge gradient (SpKG) algorithm for adaptively selecting the targeted regions within a large RNA molecule to identify which regions are most amenable to interactions with ot...
Stack-Pointer Networks for Dependency Parsing.

We introduce a novel architecture for dependency parsing: stack-pointer networks (StackPtr). Combining pointer networks (Vinyals et al., 2015) with an internal stack, the proposed model first reads and encodes the whole sentence, then builds the dependency tree top-down (from root-to-leaf) in a depth-first fashion. The stack tracks the status of the depth-first search and the pointer networks select one child for the word at the top of the stack at each step. The StackPtr parser benefits from the information of whole sentence and all previously derived subtree structures, and removes the left-to-right restriction in classical transition-based parsers. Yet the number of steps for building any (non-projective) parse tree is linear in the length of the sentence just as other transition-based parsers, yielding an efficient decoding algorithm with O(n2) time complexity. We evaluate our model on 29 treebanks spanning 20 languages and different dependency annotation schemas, and achieve state-of-the-art performances on 21 of them
Belle II iTOP Optics: Design, Construction and Performance

The imaging-Time-of-Propogation (iTOP) counter is a new type of ring-imaging Cherenkov counter developed for particle identification at the Belle II experiment. It consists of 16 modules arranged azimuthally around the beam line. Each module consists of one mirror, one prism and two quartz bar radiators. Here we describe the design, acceptance test, alignment, gluing and assembly of the optical components. All iTOP modules have been successfully assembled and installed in the Belle II detector by the middle of 2016. After installation, laser and cosmic ray data have been taken to test the performance of the modules. First results from these tests are presented.
Parallel Range, Segment and Rectangle Queries with Augmented Maps

The range, segment and rectangle query problems are fundamental problems in computational geometry, and have extensive applications in many domains. Despite the significant theoretical work on these problems, efficient implementations can be complicated. We know of very few practical implementations of the algorithms in parallel, and most implementations do not have tight theoretical bounds. We focus on simple and efficient parallel algorithms and implementations for these queries, which have tight worst-case bound in theory and good parallel performance in practice. We propose to use a simple framework (the augmented map) to model the problem. Based on the augmented map interface, we develop both multi-level tree structures and sweepline algorithms supporting range, segment and rectangle queries in two dimensions. For the sweepline algorithms, we propose a parallel paradigm and show corresponding cost bounds. All of our data structures are work-efficient to build in theory and achieve a low parallel depth. The query time is almost linear to the output size. We have implemented all the data structures described in the paper using a parallel augmented map library. Based on the library each data structure only requires about 100 lines of C++ code. We test their performance on large data sets (up to $10^8$ elements) and a machine with 72-cores (144 hyperthreads). The parallel construction achieves 32-68x speedup. Speedup numbers on queries are up to 126-fold. Our sequential implementation outperforms the CGAL library by at least 2x in both construction and queries. Our sequential implementation can be slightly slower than the R-tree in the Boost library in some cases (0.6-2.5x), but has significantly better query performance (1.6-1400x) than Boost.
Quantum lower bounds for approximate counting via laurent polynomials

We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative integer exponents). Specifically, we resolve the complexity of approximate counting, the problem of multiplicatively estimating the size of a nonempty set S ⊆ [N], in two natural generalizations of quantum query complexity.Our first result holds in the standard Quantum Merlin-Arthur (QMA) setting, in which a quantum algorithm receives an untrusted quantum witness. We show that, if the algorithm makes T quantum queries to S, and also receives an (untrusted) m-qubit quantum witness, then either [MATH HERE]. This is optimal, matching the straightforward protocols where the witness is either empty, or specifies all the elements of S. As a corollary, this resolves the open problem of giving an oracle separation between SBP, the complexity class that captures approximate counting, and QMA.In our second result, we ask what if, in addition to a membership oracle for S, a quantum algorithm is also given "QSamples"- i.e., copies of the state [MATH HERE] - or even access to a unitary transformation that enables QSampling? We show that, even then, the algorithm needs either [MATH HERE] queries or else [MATH HERE] QSamples or accesses to the unitary.Our lower bounds in both settings make essential use of Laurent polynomials, but in different ways.
Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications

Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces whose intersection contains a fixed vector space $$\mathscr {D}$$ . In the case when $$\mathscr {D}$$ is dense in one of the Hilbert spaces (but not necessarily in the other), we make precise an operator-theoretic linking between the two Hilbert spaces. No relative boundedness is assumed. Nonetheless, under natural assumptions (motivated by potential theory), we prove a theorem where a comparison between the two Hilbert spaces is made via a specific selfadjoint semibounded operator. Applications include physical Hamiltonians, both continuous and discrete (infinite network models), and the operator theory of reflection positivity.
Lifting Private Information Retrieval from Two to any Number of Messages

We study private information retrieval (PIR) on coded data with possibly colluding servers. Devising PIR schemes with optimal download rate in the case of collusion and coded data is still open in general. We provide a lifting operation that can transform what we call one-shot PIR schemes for two messages into schemes for any number of messages. We apply this lifting operation on existing PIR schemes and describe two immediate implications. First, we obtain novel PIR schemes with improved download rate in the case of MDS coded data and server collusion. Second, we provide a simplified description of existing optimal PIR schemes on replicated data as lifted secret sharing based PIR.
Tracial state space with non-compact extreme boundary

Let A be a unital simple separable C*-algebra. If A is nuclear and infinite-dimensional, it is known that strict comparison of positive elements is equivalent to Z-stability if the extreme boundary of its tracial state space is compact and of finite covering dimension. Here we provide the first proof of this result in the case of certain non-compact extreme boundaries. Additionally, if A has strict comparison of positive elements, it is known that the Cuntz semigroup of this C*-algebra is recovered functorially from the Murray–von Neumann semigroup and the tracial state space whenever the extreme boundary of the tracial state space is compact and of finite covering dimension. We extend this result to the case of a countable extreme boundary with finitely many cluster points.
Explainable Entity-based Recommendations with Knowledge Graphs.

Explainable recommendation is an important task. Many methods have been proposed which generate explanations from the content and reviews written for items. When review text is unavailable, generating explanations is still a hard problem. In this paper, we illustrate how explanations can be generated in such a scenario by leveraging external knowledge in the form of knowledge graphs. Our method jointly ranks items and knowledge graph entities using a Personalized PageRank procedure to produce recommendations together with their explanations.
A free boundary problem related to thermal insulation: flat implies smooth

We study the regularity of the interface for a new free boundary problem introduced in Caffarelli and Kriventsov (A free boundary problem related to thermal insulation, 2015). We show that for minimizers of the functional $$\begin{aligned} F_1(A,u) = \int _A |\nabla u|^2 d{{\mathcal {L}}}^n + \int _{\partial A} u^2 + \bar{C} {{\mathcal {L}}}^n(A) \end{aligned}$$ over all pairs (A, u) of open sets A containing a fixed set $$\Omega $$ and functions $$u\in H^1(A)$$ which equal 1 on $$\Omega $$ , the boundary $$\partial A$$ locally coincides with the union of the graphs of two $$C^{1,\alpha }$$ functions near most points. Specifically, this happens at all points where the interface is trapped between two planes which are sufficiently close together. The proof combines ideas introduced by Ambrosio, Fusco, and Pallara for the Mumford–Shah functional with new arguments specific to the problem considered.
The CR Paneitz operator and the stability of CR pluriharmonic functions

Abstract We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a real analytic deformation. As an application, we show that the real ellipsoids in C 2 are such that the CR Paneitz operator is nonnegative with kernel consisting only of the CR pluriharmonic functions.
A Fundamental Limitation on Maximum Parameter Dimension for Accurate Estimation With Quantized Data

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization-induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and, moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system.
A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity

Abstract We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth.
Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues

There are various parametric models for analyzing pairwise comparison data, including the Bradley–Terry–Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this paper, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are required only to satisfy a natural form of stochastic transitivity. This class includes parametric models, including the BTL and Thurstone models as special cases, but is considerably more general. We provide various examples of models in this broader stochastically transitive class for which classical parametric models provide poor fits. Despite this greater flexibility, we show that the matrix of probabilities can be estimated at the same rate as in standard parametric models up to logarithmic terms. On the other hand, unlike in the BTL and Thurstone models, computing the minimax-optimal estimator in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives. We show that a simple singular value thresholding algorithm is statistically consistent but does not achieve the minimax rate. We then propose and study algorithms that achieve the minimax rate over interesting sub-classes of the full stochastically transitive class. We complement our theoretical results with thorough numerical simulations.
Weighted interpolation from certain singular affine hypersurfaces

We prove that square integrable (with respect to a plurisubharmonic weight) holomorphic functions can be extended in a square integrable manner from certain singular hypersurfaces (which include uniformly flat, normal crossing divisors) to entire functions in affine space. This gives evidence to a conjecture regarding the positivity of the curvature of the weight under consideration.
Deformation of quintic threefolds to the chordal variety

We consider a family of quintic threefolds specializing to a certain reducible threefold. We describe the space of genus zero stable morphisms to the central fiber (as defined by J. Li). As an elementary application of an extension of the analysis, we prove the existence of rigid stable maps of arbitrary genus and sufficiently high degree to very general quintics.
Efficient approaches for escaping higher order saddle points in non-convex optimization

Author(s): Anandkumar, Anima; Ge, Rong | Abstract: Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures in high dimensions. Many functions have degenerate saddle points such that the first and second order derivatives cannot distinguish them with local optima. In this paper we use higher order derivatives to escape these saddle points: we design the first efficient algorithm guaranteed to converge to a third order local optimum (while existing techniques are at most second order). We also show that it is NP-hard to extend this further to finding fourth order local optima.
Pattern-avoiding permutations and Brownian excursion, part II: fixed points

Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study fixed points of both 123- and 231-avoiding permutations. We find an exact description for a scaling limit of the empirical distribution of fixed points in terms of Brownian excursion. This builds on the connections between pattern-avoiding permutations and Brownian excursion developed in Hoffman et al. (Pattern-avoiding permutations and Brownian excursion, Part 1: Shapes and fluctuations. to appear Random Structures and Algorithms. arXiv:1406.5156 , 2016) and strengthens the recent results of Elizalde (Electron J Comb 18(2):17, 2011) and Miner and Pak (Adv Appl Math 55:86–130, 2014) on fixed points of pattern-avoiding permutations.
Single- and multi-level network sparsification by algebraic distance

Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required. We propose a method of network sparsification that preserves a wide range of structural properties. Depending on the analysis goals, the method allows to distinguish between local and global range edges that can be filtered out during the sparsification. First we rank edges by their algebraic distances and then we sample them. We also introduce a multilevel framework for sparsification that can be used to control the sparsification process at various coarse-grained resolutions. Based primarily on the matrix-vector multiplications, our method is easily parallelized for different architectures.
The Epistemology of Nondeterminism

This paper proposes new semantics for propositional dynamic logic (PDL), replacing the standard relational semantics. Under these new semantics, program execution is represented as fundamentally deterministic (i.e., functional), while nondeterminism emerges as an epistemic relationship between the agent and the system: intuitively, the nondeterministic outcomes of a given process are precisely those that cannot be ruled out in advance. We formalize these notions using topology and the framework of dynamic topological logic (DTL) [1]. We show that DTL can be used to interpret the language of PDL in a manner that captures the intuition above, and moreover that continuous functions in this setting correspond exactly to deterministic processes. We also prove that certain axiomatizations of PDL remain sound and complete with respect to the corresponding classes of dynamic topological models. Finally, we extend the framework to incorporate knowledge using the machinery of subset space logic [2], and show that the topological interpretation of public announcements as given in [3] coincides exactly with a natural interpretation of test programs.
Extension Theorems for Large Scale Spaces via Coarse Neighbourhoods

We introduce the notion of (hybrid) large scale normal space and prove coarse geometric analogues of Urysohn’s Lemma and the Tietze Extension Theorem for these spaces, where continuous maps are replaced by (continuous and) slowly oscillating maps. To do so, we first prove a general form of each of these results in the context of a set equipped with a neighbourhood operator satisfying certain axioms, from which we obtain both the classical topological results and the (hybrid) large scale results as corollaries. We prove that all metric spaces are hybrid large scale normal, and characterize those locally compact abelian groups which (as hybrid large scale spaces) are hybrid large scale normal. Finally, we look at some properties of the Higson compactifications and coronas of hybrid large scale normal spaces.
Radio Galaxy Zoo: host galaxies and radio morphologies for large surveys from visual inspection

We present a description and early results from Radio Galaxy Zoo, a web-based citizen science project for visual inspection and classification of all-sky radio surveys. The goals of the project are to classify individual radio sources (particularly galaxies with multiple lobes and/or complex morphologies) as well as matching the continuum radio emission to the host galaxy. Radio images come from the FIRST and ATLAS surveys, while matches to potential hosts are performed with infrared imaging from WISE and SWIRE. The first twelve months of classification have yielded more than 1 million classifications of more than 60,000 sources. For images with at least 75% consensus by the volunteer classifiers, the accuracy is comparable to visual inspection by the expert science team. Based on mid-infrared colors, the hosts associated with radio emission are primarily a mixture of elliptical galaxies, QSOs, and LIRGs, which is in good agreement with previous studies. The full catalog of radio lobes and their host galaxies will measure the relative populations of host types as a function of radio morphology and power. Radio Galaxy Zoo has also been an effective method for detecting extremely rare objects, such as HyMORs and giant radio galaxies. Results from the project are being used to train automatic algorithms for host matching for use in future large continuum surveys such as EMU, as well as establishing roles for citizen science in projects such as the SKA.
Controlling Sources of Inaccuracy in Stochastic Kriging

ABSTRACTScientists and engineers commonly use simulation models to study real systems for which actual experimentation is costly, difficult, or impossible. Many simulations are stochastic in the se...
Statistical translation, heat kernels and expected distances

High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore novel connections between statistical translation, heat kernels on manifolds and graphs, and expected distances. These connections provide a new framework for unsupervised metric learning for text documents. Experiments indicate that the resulting distances are generally superior to their more standard counterparts.
On Schauder equivalence relations

We study Schauder equivalence relations, which are Borel equivalence relations induced by actions of Banach spaces with Schauder bases. Firstly, we show that Rω/l1 and Rω/c0 are minimal Schauder equivalence relations. Then, we prove that neither of them is Borel reducible to the quotient Rω/T where T is the Tsirelson space. This implies that they cannot form a basis for the Schauder equivalence relations. In addition, we apply an argument of Farah to show that every basis for the Schauder equivalence relations, if such exist, has to be of cardinality 2ℵ0.
A finiteness theorem for positive definite strictly n-regular quadratic forms

An integral quadratic form is called strictly n-regular if it primitively represents all quadratic forms in n variables that are primitively represented by its genus. For any $$n \ge 2$$ , it will be shown that there are only finitely many similarity classes of positive definite strictly n-regular integral quadratic forms in $$n + 4$$ variables. This extends the recent finiteness results for strictly regular quaternary quadratic forms by Earnest et al. (J Number Theory 144: 256–266, 2014).
The quadrifocal variety

Abstract Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 8 (and partially in degree 9) using the representations of GL ( 3 ) × 4 in the polynomial ring on the space of 3 × 3 × 3 × 3 tensors. Further representation-theoretic analysis gives a lower bound for the number of minimal generators.
Sparse Hierarchical Solvers with Guaranteed Convergence

Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners, such as incomplete LU factorization, provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low-frequency errors, we propose a novel hierarchical solver with improved robustness with respect to the condition number of the linear system. This solver retains the linear computational cost and memory footprint of the original algorithm.
A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices

Abstract We prove a Saad's type bound for harmonic Ritz vectors of a Hermitian matrix. The new bound reveals a dependence of the harmonic Rayleigh–Ritz procedure on the condition number of a shifted problem operator. Several practical implications are discussed. In particular, the bound motivates incorporation of preconditioning into the harmonic Rayleigh–Ritz scheme.
Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for prestressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.
Straggler Mitigation by Delayed Relaunch of Tasks

Redundancy for straggler mitigation, originally in data download and more recently in distributed computing context, has been shown to be effective both in theory and practice. Analysis of systems with redundancy has drawn significant attention and numerous papers have studied pain and gain of redundancy under various service models and assumptions on the straggler characteristics. We here present a cost (pain) vs. latency (gain) analysis of using simple replication or erasure coding for straggler mitigation in executing jobs with many tasks. We quantify the effect of the tail of task execution times and discuss tail heaviness as a decisive parameter for the cost and latency of using redundancy. Specifically, we find that coded redundancy achieves better cost vs. latency tradeoff than simple replication and can yield reduction in both cost and latency under less heavy tailed execution times. We show that delaying redundancy is not effective in reducing cost and that delayed relaunch of stragglers can yield significant reduction in cost and latency. We validate these observations by comparing with the simulations that use empirical distributions extracted from Google cluster data.
Risk-Averse Stochastic Convex Bandit

Motivated by applications in clinical trials and finance, we study the problem of online convex optimization (with bandit feedback) where the decision maker is risk-averse. We provide two algorithms to solve this problem. The first one is a descent-type algorithm which is easy to implement. The second algorithm, which combines the ellipsoid method and a center point device, achieves (almost) optimal regret bounds with respect to the number of rounds. To the best of our knowledge this is the first attempt to address risk-aversion in the online convex bandit problem.
A Stochastic Programming Approach for Electric Vehicle Charging Network Design

The advantages of electric vehicles (EVs) include reduction of greenhouse gas and other emissions, energy security, and fuel economy. The societal benefits of large-scale adoption of EVs cannot be realized without adequate deployment of publicly accessible charging stations. We propose a two-stage stochastic programming model to determine the optimal network of charging stations for a community, considering uncertainties in the arrival and dwell times of vehicles, the state of charge of arriving vehicles’ batteries, drivers’ walking ranges and charging preferences, demand during weekdays and weekends, and the community’s rate of EV adoption. We conducted studies using the sample average approximation method, which asymptotically converges to an optimal solution for a two-stage stochastic problem. However, this method is computationally expensive for large-scale instances. Therefore, we also developed a heuristic to produce nearly optimal solutions quickly for our data instances. We conducted computational experiments using various publicly available data sources and evaluated the benefits of the solutions for a given community, both quantitatively and qualitatively.