cssi/SciSciGPT-SciSciNet huggingface dataset:
The Weil–Petersson Form on an Acyclic Cluster Variety

The Weil-Petersson form on a cluster variety is a 2-form on a certain open smooth subvariety; the union of the cluster tori. We show that for acyclic cluster varieties, the Weil-Petersson 2-form extends to a regular K\"ahler 2-form on the entire cluster variety.
Sequential optimal placement of distributed photovoltaics using downstream power index

The optimization of the size and location of Photovoltaic (PV) Distributed Generation (DG) is a method for reducing distribution networks loss, cutting costs for utilities, and integrating renewable energy into the power grid. However, this optimization problem is a difficult mixed continuous discrete problem that is difficult to solve efficiently. Herein, we propose a novel Sequential PVDG Placement algorithm which utilizes a Downstream Power Index (DPI) for PV allocation. We compare Sequential PVDG Placement results with those of Shuffled Frog Leaping Algorithm (SFLA), a memetic heuristic algorithm. Our algorithm demonstrates similar accuracy and drastically less computation time compared to SFLA. Given its high accuracy and low computation time, sequential PVDG allocation algorithm may be useful for rapid online power dispatch, long-term planning, and microgrid operations under high penetration of renewable sources.
Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ is represented as $UV^\top$, where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. In this paper, we complement recent findings on the non-convex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious local minima, under RIP.
Battery energy storage scheduling for optimal load variance minimization

Generation portfolio can be significantly altered due to the deployment of distributed energy resources (DER) in distribution networks and the concept of microgrid. Generally, distribution networks can operate in a more resilient and economic fashion through proper coordination of DER. However, due to the partially uncontrollable and stochastic nature of some DER, the variance of net load of distribution systems increases, which raises the operational cost and complicates operation for transmission companies. This motivates peak shaving and valley filling using energy storage units deployed in distribution systems. This paper aims at theoretical formulation of optimal load variance minimization, where the infinity norm of net load is minimized. Then, the problem is reformulated equivalently as a linear program. A case study is performed with capacity-limited battery energy storage model and the simplified power flow model of a radial distribution network. The influence of capacity limit and deployment location are studied.
The connected metric dimension at a vertex of a graph

Abstract The notion of metric dimension, dim ⁡ ( G ) , of a graph G, as well as a number of variants, is now well studied. In this paper, we begin a local analysis of this notion by introducing cdim G ( v ) , the connected metric dimension of G at a vertex v, which is defined as follows: a set of vertices S of G is a resolving set if, for any pair of distinct vertices x and y of G, there is a vertex z ∈ S such that the distance between z and x is distinct from the distance between z and y in G. We say that a resolving set S is connected if S induces a connected subgraph of G. Then, cdim G ( v ) is defined to be the minimum of the cardinalities of all connected resolving sets which contain the vertex v. The connected metric dimension of G, denoted by cdim ( G ) , is min ⁡ { cdim G ( v ) : v ∈ V ( G ) } . Noting that 1 ≤ dim ⁡ ( G ) ≤ cdim ( G ) ≤ cdim G ( v ) ≤ | V ( G ) | − 1 for any vertex v of G, we show the existence of a pair ( G , v ) such that cdim G ( v ) takes all positive integer values from dim ⁡ ( G ) to | V ( G ) | − 1 , as v varies in a fixed graph G. We characterize graphs G and their vertices v satisfying cdim G ( v ) ∈ { 1 , | V ( G ) | − 1 } . We show that cdim ( G ) = 2 implies G is planar, whereas it is well known that there is a non-planar graph H with dim ⁡ ( H ) = 2 . We also characterize trees and unicyclic graphs G satisfying cdim ( G ) = dim ⁡ ( G ) . We show that cdim ( G ) − dim ⁡ ( G ) can be arbitrarily large. We determine cdim ( G ) and cdim G ( v ) for some classes of graphs. We further examine the effect of vertex or edge deletion on the connected metric dimension. We conclude with some open problems.
Can you Trust the Trend?: Discovering Simpson's Paradoxes in Social Data

We investigate how Simpson»s paradox affects analysis of trends in social data. According to the paradox, the trends observed in data that has been aggregated over an entire population may be different from, and even opposite to, those of the underlying subgroups. Failure to take this effect into account can lead analysis to wrong conclusions. We present a statistical method to automatically identify Simpson»s paradox in data by comparing statistical trends in the aggregate data to those in the disaggregated subgroups. We apply the approach to data from Stack Exchange, a popular question-answering platform, to analyze factors affecting answerer performance, specifically, the likelihood that an answer written by a user will be accepted by the asker as the best answer to his or her question. Our analysis confirms a known Simpson»s paradox and identifies several new instances. These paradoxes provide novel insights into user behavior on Stack Exchange.
Provably correct algorithms for matrix column subset selection with selectively sampled data

We consider the problem of matrix column subset selection, which selects a subset of columns from an input matrix such that the input can be well approximated by the span of the selected columns. Column subset selection has been applied to numerous real-world data applications such as population genetics summarization, electronic circuits testing and recommendation systems. In many applications the complete data matrix is unavailable and one needs to select representative columns by inspecting only a small portion of the input matrix. In this paper we propose the first provably correct column subset selection algorithms for partially observed data matrices. Our proposed algorithms exhibit different merits and limitations in terms of statistical accuracy, computational efficiency, sample complexity and sampling schemes, which provides a nice exploration of the tradeoff between these desired properties for column subset selection. The proposed methods employ the idea of feedback driven sampling and are inspired by several sampling schemes previously introduced for low-rank matrix approximation tasks (Drineas et al., 2008; Frieze et al., 2004; Deshpande and Vempala, 2006; Krishnamurthy and Singh, 2014). Our analysis shows that, under the assumption that the input data matrix has incoherent rows but possibly coherent columns, all algorithms provably converge to the best low-rank approximation of the original data as number of selected columns increases. Furthermore, two of the proposed algorithms enjoy a relative error bound, which is preferred for column subset selection and matrix approximation purposes. We also demonstrate through both theoretical and empirical analysis the power of feedback driven sampling compared to uniform random sampling on input matrices with highly correlated columns.
On the average value of the canonical height in higher dimensional families of elliptic curves

Given an elliptic curve E over a function field K=Q(T_1,...,T_n), we study the behavior of the canonical height ^h_(E_w) of the specialized elliptic curve E_w with respect to the height of w in Q^n. In this paper, we prove that there exists a uniform non-zero lower bound for the average of the quotient ^h_(E_w)(P_w)/h(w) for all non-torsion P in E(K).
ComSens: Exploiting pilot diversity for pervasive integration of communication and sensing in MIMO-TDD-Frameworks

In this paper, we propose a fully-integrated radar and communication system — named ComSens. We utilize two different pilot sequences (one for uplink and one for downlink) with the condition that they must be uncorrelated to each other. Within such a framework, the signal received from end-user and the back-scattered signal from the desired objects have uncorrelated pilots. Thus, the base-station is able to distinguish data signal from user and back-scattered signal from object. We assume a time division duplex (TDD) framework. The pilot sequences are designed for MIMO channels. We evaluate channel MSE as a figure of merit for communication system. We also show that the designed pilots are uncorrelated for a range of time lags. Moreover, designed uplink pilot has negligable autocorrelation for a range of time lags leading to an impulse-like autocorrelation for radar sensing.
A Precise Analysis of PhaseMax in Phase Retrieval

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this problem, known as PhaseMax. Standard convex-relaxation-based methods in phase retrieval resort to the idea of “lifting” which makes them computationally inefficient, since the number of unknowns is effectively squared. In contrast, PhaseMax is a novel convex relaxation that does not increase the number of unknowns. Instead it relies on an initial estimate of the true signal which must be externally provided. In this paper, we investigate the required number of measurements for exact recovery of the signal in the large system limit and when the linear measurement matrix is random with iid standard normal entries. If $n$ denotes the dimension of the unknown complex signal and $m$ the number of phaseless measurements, then in the large system limit, $\frac{m}{n} > \frac{{4}}{\cos^{2}(\theta)}$ measurements is necessary and sufficient to recover the signal with high probability, where $\theta$ is the angle between the initial estimate and the true signal. Our result indicates a sharp phase transition in the asymptotic regime which matches the empirical result in numerical simulations.
A new realization of the Langlands correspondence for PGL(2,F)

In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic tori. Taking a cue from real groups, we propose that supercuspidal representations are naturally parameterized by characters of covers of tori. Over the reals, Harish-Chandra defined the discrete series representations by specifying their characters restricted to an elliptic torus, and these characters may naturally be expressed in terms of characters of a cover of the torus. We write down a natural analogue of Harish-Chandraʼs character for PGL(2,F), and show that it is the character of a unique supercuspidal representation, on a canonical subset of the elliptic torus. This paves the way for a realization of the local Langlands correspondence for PGL(2,F) that eliminates the need for any character twists.
Sharp constants in several inequalities on the Heisenberg group

We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Laplacian and conformally invariant fractional Laplacians. By considering limiting cases of these inequalities sharp constants for the analogues of the Onofri and log-Sobolev inequalities on H^n are obtained. The methodology is completely different from that used to obtain the R^n inequalities and can be (and has been) used to give a new, rearrangement free, proof of the HLS inequalities.
Undecidability of equations in free Lie algebras

In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in such free Lie algebras over a field of characteristic zero.
Enhancing robustness of machine learning systems via data transformations

We propose the use of data transformations as a defense against evasion attacks on ML classifiers. We present and investigate strategies for incorporating a variety of data transformations including dimensionality reduction via Principal Component Analysis to enhance the resilience of machine learning, targeting both the classification and the training phase. We empirically evaluate and demonstrate the feasibility of linear transformations of data as a defense mechanism against evasion attacks using multiple real-world datasets. Our key findings are that the defense is (i) effective against the best known evasion attacks from the literature, resulting in a two-fold increase in the resources required by a white-box adversary with knowledge of the defense for a successful attack, (ii) applicable across a range of ML classifiers, including Support Vector Machines and Deep Neural Networks, and (iii) generalizable to multiple application domains, including image classification and human activity classification.
RIOT: I/O-Efficient Numerical Computing without SQL

R is a numerical computing environment that is widely popular for statistical data analysis. Like many such environments, R performs poorly for large datasets whose sizes exceed that of physical mem- ory. We present our vision of RIOT (R with I/O Transparency), a system that makes R programs I/O-efficient in a way transpar- ent to the users. We describe our experience with RIOT-DB, an initial prototype that uses a relational database system as a back- end. Despite the overhead and inadequacy of generic database sys- tems in handling array data and numerical computation, RIOT-DB significantly outperforms R in many large-data scenarios, thanks to a suite of high-level, inter-operation optimizations that integrate seamlessly into R. While many techniques in RIOT are inspired by databases (and, for RIOT-DB, realized by a database system), RIOT users are insulated from anything database related. Compared with previous approaches that require users to learn new languages and rewrite their programs to interface with a database, RIOT will, we believe, be easier to adopt by the majority of the R users.
Large deviations for conditional guesswork

Abstract The guesswork problem was originally studied by Massey to quantify the number of guesses needed to ascertain a discrete random variable. It has been shown that for a large class of random processes the rescaled logarithm of the guesswork satisfies the large deviation principle and this has been extended to the case where k out m sequences are guessed. The study of conditional guesswork, where guessing of a sequence is aided by the observation of another one, was initiated by Arikan in his simple derivation of the upper bound of the cutoff rate for sequential decoding. In this note, we extend these large deviation results to the setting of conditional guesswork.
Energy-Dissipation Limits in Variance-Based Computing

Variance-based logic (VBL) uses the fluctuations or the variance in the state of a particle or a physical quantity to represent different logic levels. In this paper, we show that compared to the t...
Extended quandle spaces and shadow homotopy invariants of classical links

In 1993, Fenn, Rourke and Sanderson introduced rack spaces and rack homotopy invariants, and modifications to quandle spaces and quandle homotopy invariants were introduced by Nosaka in 2011. In this paper, we define the Cayley-type graph and the extended quandle space of a quandle in analogy to rack and quandle spaces. Moreover, we construct the shadow homotopy invariant of a classical link and prove that the shadow homotopy invariant is equal to the quandle homotopy invariant multiplied by the order of a quandle.
ConcurORAM: High-Throughput Stateless Parallel Multi-Client ORAM

ConcurORAM is a parallel, multi-client oblivious RAM (ORAM) that eliminates waiting for concurrent stateless clients and allows overall throughput to scale gracefully, without requiring trusted third party components (proxies) or direct inter-client coordination. A key insight behind ConcurORAM is the fact that, during multi-client data access, only a subset of the concurrently-accessed server-hosted data structures require access privacy guarantees. Everything else can be safely implemented as oblivious data structures that are later synced securely and efficiently during an ORAM "eviction". Further, since a major contributor to latency is the eviction - in which client-resident data is reshuffled and reinserted back encrypted into the main server database - ConcurORAM also enables multiple concurrent clients to evict asynchronously, in parallel (without compromising consistency), and in the background without having to block ongoing queries. As a result, throughput scales well with increasing number of concurrent clients and is not significantly impacted by evictions. For example, about 65 queries per second can be executed in parallel by 30 concurrent clients, a 2x speedup over the state-of-the-art. The query access time for individual clients increases by only 2x when compared to a single-client deployment.
Analytic Differential Operators on the Unit Disk

Formally symmetric differential operators on weighted Hardy–Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical Riemann and Heun equations. Symmetric minimal operators are characterized. A regular class whose leading coefficients have no zeros on the unit circle are shown to be essentially self-adjoint. Eigenvalue asymptotics are established. Some extensions to non-self-adjoint operators are also considered.
Talagrand concentration inequalities for stochastic partial differential equations

One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.
Connectivity of Wireless Sensor Networks Secured by Heterogeneous Key Predistribution Under an On/Off Channel Model

We investigate the connectivity of a wireless sensor network (WSN) secured by the heterogeneous key predistribution scheme under an independent on/off channel model. The heterogeneous scheme induces an inhomogeneous random key graph, denoted by $\mathbb {K}(n;\boldsymbol {\mu },\boldsymbol {K},P)$ and the on/off channel model induces an Erdős-Renyi graph, denoted by $\mathbb {H}(n,\alpha)$ . Hence, the overall random graph modeling the WSN is obtained by the intersection of $\mathbb {K}(n;\boldsymbol {\mu },\boldsymbol {K},P)$ and $\mathbb {H}(n,\alpha)$ . We present conditions on how to scale the parameters of the intersecting graph with respect to the network size $n$ such that the graph i) has no isolated nodes and ii) is connected, both with high probability (whp) as the number of nodes gets large. Our results are supported by a simulation study demonstrating that i) despite their asymptotic nature, our results can in fact be useful in designing finite -node WSNs so that they achieve secure connectivity whp; and ii) despite the simplicity of the on/off communication model, the probability of connectivity in the resulting WSN approximates very well the case where the disk model is used.
Unexpected spectral asymptotics for wave equations on certain compact spacetimes

We study the spectral asymptotics of wave equations on certain compact spacetimes, where some variant of the Weyl asymptotic law is valid. The simplest example is the spacetime S1×S2. For the Laplacian on S1×S2, theWeyl asymptotic law gives a growth rate O(s3/2) for the eigenvalue counting function N(s) = #{λj: 0 ≤ λj ≤ s}. For the wave operator, there are two corresponding eigenvalue counting functions: N±(s) = #{λj: 0 < ±λj ≤ s}, and they both have a growth rate of O(s2). More precisely, there is a leading term π2s2/4 and a correction term of as3/2, where the constant a is different for N±. These results are not robust in that if we include a speed of propagation constant to the wave operator, the result depends on number theoretic properties of the constant, and generalizations to S1 × Sq are valid for q even but not q odd. We also examine some related examples.
Intrinsic Localized Lattice Modes and Thermal Transport: Potential Application in a Thermal Rectifier

Recent experiments provide evidence of intrinsic localized modes (ILMs) in the lattice dynamics of conventional 3D materials. Here evidence that ILMs in uranium metal enhance the thermal conductivity is presented along with speculation on how thermal transport by ILMs might be used to improve a reported design for a solid-state thermal rectifier.
#SarcasmDetection Is Soooo General! Towards a Domain-Independent Approach for Detecting Sarcasm.

Automatic sarcasm detection methods have traditionally been designed for maximum performance on a specific domain. This poses challenges for those wishing to transfer those approaches to other existing or novel domains, which may be typified by very different language characteristics. We develop a general set of features and evaluate it under different training scenarios utilizing in-domain and/or out-of-domain training data. The best-performing scenario, training on both while employing a domain adaptation step, achieves an F1 of 0.780, which is well above baseline F1-measures of 0.515 and 0.345. We also show that the approach outperforms the best results from prior work on the same target domain.
Initialization and Coordinate Optimization for Multi-way Matching

We consider the problem of consistently matching multiple sets of elements to each other, which is a common task in fields such as computer vision. To solve the underlying NP-hard objective, existing methods often relax or approximate it, but end up with unsatisfying empirical performance due to a misaligned objective. We propose a coordinate update algorithm that directly optimizes the target objective. By using pairwise alignment information to build an undirected graph and initializing the permutation matrices along the edges of its Maximum Spanning Tree, our algorithm successfully avoids bad local optima. Theoretically, with high probability our algorithm guarantees an optimal solution under reasonable noise assumptions. Empirically, our algorithm consistently and significantly outperforms existing methods on several benchmark tasks on real datasets.
Social Learning and Distributed Hypothesis Testing

This paper considers a problem of distributed hypothesis testing over a network. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypothesis). The marginals of the joint observation distribution conditioned on each hypothesis are known locally at the nodes, but the true parameter/hypothesis is not known. An update rule is analyzed in which nodes first perform a Bayesian update of their belief (distribution estimate) of each hypothesis based on their local observations, communicate these updates to their neighbors, and then perform a “non-Bayesian” linear consensus using the log-beliefs of their neighbors. Under mild assumptions, we show that the belief of any node on a wrong hypothesis converges to zero exponentially fast. We characterize the exponential rate of learning, which we call the network divergence, in terms of the nodes’ influence of the network and the divergences between the observations’ distributions. For a broad class of observation statistics which includes distributions with unbounded support such as Gaussian mixtures, we show that rate of rejection of wrong hypothesis satisfies a large deviation principle, i.e., the probability of sample paths on which the rate of rejection of wrong hypothesis deviates from the mean rate vanishes exponentially fast and we characterize the rate function in terms of the nodes’ influence of the network and the local observation models.
Near-optimal estimation of simultaneously sparse and low-rank matrices from nested linear measurements

In this paper we consider the problem of estimating simultaneously low-rank and row-wise sparse matrices from nested linear measurements where the linear operator consists of the product of a linear operator $\mathcal{W}$ and a matrix $\mathbf{\varPsi}$. Leveraging the nested structure of the measurement operator, we propose a computationally efficient two-stage algorithm for estimating the simultaneously structured target matrix. Assuming that $\mathcal{W}$ is a restricted isometry for low-rank matrices and $\mathbf{\varPsi}$ is a restricted isometry for row-wise sparse matrices, we establish an accuracy guarantee that holds uniformly for all sufficiently low-rank and row-wise sparse matrices with high probability. Furthermore, using standard tools from information theory, we establish a minimax lower bound for estimation of simultaneously low-rank and row-wise sparse matrices from linear measurements that need not be nested. The accuracy bounds established for the algorithm, that also serve as a minimax upper bound, differ from the derived minimax lower bound merely by a polylogarithmic factor of the dimensions. Therefore, the proposed algorithm is nearly minimax optimal. We also discuss some applications of the proposed observation model and evaluate our algorithm through numerical simulation.
Multiple messengers of fast radio bursts

Multi-wavelength and multi-messenger astronomy will reveal the phenomena that produce fast radio bursts, turning fast radio bursts into sharper tools with which to probe extragalactic plasma.
Perceptual quality prediction on authentically distorted images using a bag of features approach

Current top-performing blind perceptual image quality prediction models are generally trained on legacy databases of human quality opinion scores on synthetically distorted images. Therefore, they learn image features that effectively predict human visual quality judgments of inauthentic and usually isolated (single) distortions. However, real-world images usually contain complex composite mixtures of multiple distortions. We study the perceptually relevant natural scene statistics of such authentically distorted images in different color spaces and transform domains. We propose a "bag of feature maps" approach that avoids assumptions about the type of distortion(s) contained in an image and instead focuses on capturing consistencies-or departures therefrom-of the statistics of real-world images. Using a large database of authentically distorted images, human opinions of them, and bags of features computed on them, we train a regressor to conduct image quality prediction. We demonstrate the competence of the features toward improving automatic perceptual quality prediction by testing a learned algorithm using them on a benchmark legacy database as well as on a newly introduced distortion-realistic resource called the LIVE In the Wild Image Quality Challenge Database. We extensively evaluate the perceptual quality prediction model and algorithm and show that it is able to achieve good-quality prediction power that is better than other leading models.
BourGAN: Generative Networks with Metric Embeddings

This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an arbitrary metric space into the L2 space, while preserving their pairwise distance distribution. Not only does this metric embedding determine the dimensionality of the latent space automatically, it also enables us to construct a mixture of Gaussians to draw latent space random vectors. We use the Gaussian mixture model in tandem with a simple augmentation of the objective function to train GANs. Every major step of our method is supported by theoretical analysis, and our experiments on real and synthetic data confirm that the generator is able to produce samples spreading over most of the modes while avoiding unwanted samples, outperforming several recent GAN variants on a number of metrics and offering new features.
Tangles and links: A view with trees

A result about spanning forests for graphs yields a short proof of Krebes’s theorem concerning embedded tangles in links.
Enumeration of Bipartite Graphs and Bipartite Blocks

We use the theory of combinatorial species to count unlabelled bipartite graphs and bipartite blocks (nonseparable or 2-connected graphs). We start with bicolored graphs, which are bipartite graphs that are properly colored in two colors. The two-element group $\mathfrak{S}_2$ acts on these graphs by switching the colors, and connected bipartite graphs are orbits of connected bicolored graphs under this action. From first principles we compute the $\mathfrak{S}_2$-cycle index for bicolored graphs, an extension of the ordinary cycle index, introduced by Henderson, that incorporates the $\mathfrak{S}_2$-action. From this we can compute the $\mathfrak{S}_2$-cycle index for connected bicolored graphs, and then the ordinary cycle index for connected bipartite graphs. The cycle index for connected bipartite graphs allows us, by standard techniques, to count unlabeled bipartite graphs and bipartite blocks.
Finite representations for two small relation algebras

In this note, we prove that two different finite relation algebras are representable over finite sets. We give an explicit group representation of $$52_{65}$$ over $$ (\mathbb {Z}/2\mathbb {Z})^{10}$$ . We also give a representation of $$59_{65}$$ over $$\mathbb {Z}/113\mathbb {Z}$$ using a technique due to Comer.
Finite time blowup for high dimensional nonlinear wave systems with bounded smooth nonlinearity

ABSTRACTWe consider the global regularity problem for nonlinear wave systems on Minkowski spacetime ℝ1+d with d'Alembertian , where the field u: ℝ1+d → ℝm is vector valued, and the nonlinearity f: ℝm → ℝm is a smooth function with f(0) = 0 and all derivatives bounded; the higher dimensional sine-Gordon equation □u = sin u is a model example of this class of nonlinear wave system. For dimensions d ≤ 9, it follows from the work of Heinz, Pecher, Brenner, and von Wahl that one has smooth solutions to this equation for any smooth choice of initial data. Perhaps surprisingly, we show that this result is almost sharp, in the sense that for any d ≥ 11, there exists an m (in fact we can take m = 2) and a nonlinearity f: ℝm → ℝm with all derivatives bounded, for which the above equation admits solutions that blow up in finite time. The intermediate case d = 10 remains open.
Paradox of peroxy defects and positive holes in rocks. Part I: Effect of temperature

Abstract Most non-seismic, non-geodesic pre-earthquake phenomena are believed to be controlled by the stress-activation of peroxy defects in rocks, which release highly mobile electric charges. Though ubiquitous in minerals of igneous and high-grade metamorphic rocks, peroxy defects have been widely overlooked in the past. The charge carriers of interest are positive holes, chemically equivalent to O− in a matrix of O2−, physically defect electrons in the O2− sublattice, highly mobile, able to propagate fast and far. O− are oxidized relative to O2−. As such O− are not supposed to exist in minerals and rocks that come from deep within the Earth’s crust, where the environments are overwhelmingly reduced. The presence of O− appears to contradict thermodynamics. However, there is no conflict. In order to understand how peroxy defects are introduced into common rock-forming minerals, over which temperature window they release positive holes, and how this may be related to pre-earthquake phenomena, we look at peroxy defects in a crystallographically and compositionally well characterized model system: single crystals of nominally high-purity MgO, grown from the melt under highly reducing conditions. During crystallization the MgO crystals incorporate OH− through dissolution of traces of H2O in the MgO matrix, leading to a solid solution (ss) Mg1−δ(OH)2δO1−2δ, where δ ≪ 1. During cooling, the ss leaves thermodynamic equilibrium, turning into a metastable supersaturated solid solution (sss). Using infrared (IR) spectroscopy it is shown that, during further cooling, OH− pairs at Mg2+ vacancy sites rearrange their electrons, undergoing a redox conversion, which leads to peroxy anions, O22−, plus molecular H2. Being diffusively mobile, the H2 molecules can leave the Mg2+ vacancy sites, leaving behind cation-deficient Mg1−δO. During reheating, but in the sss range, the O22− break up, releasing positive hole charge carriers, which profoundly affect the electrical conductivity behavior. In igneous mafic and ultramafic rocks, similar changes in the electrical conductivity are observed in the temperature window, where peroxy defects of the type O3Si-OO-SiO3 break up. They release positive holes, which control the electrical conductivity response. Deciphering these processes helps understanding the stress-activation of positive holes along the geotherm.
Weyl closure of hypergeometric systems

We show that $A$-hypergeometric systems and Horn hypergeometric systems are Weyl closed for very generic parameters.
Toward Foraging for Understanding of StarCraft Agents: An Empirical Study

Assessing and understanding intelligent agents is a difficult task for users that lack an AI background. A relatively new area, called "Explainable AI," is emerging to help address this problem, but little is known about how users would forage through information an explanation system might offer. To inform the development of Explainable AI systems, we conducted a formative study -- using the lens of Information Foraging Theory -- into how experienced users foraged in the domain of StarCraft to assess an agent. Our results showed that participants faced difficult foraging problems. These foraging problems caused participants to entirely miss events that were important to them, reluctantly choose to ignore actions they did not want to ignore, and bear high cognitive, navigation, and information costs to access the information they needed.
An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an important role in generating efficient solutions in these multi-scale problems. Under conditions of scale separation, one can rescale Maxwell's equations in such a way as to give a magneto static limit known as the Darwin approximation of electromagnetics. In this work, we present a new approach to solve Maxwell's equations based on a Method of Lines Transpose ($$\hbox {MOL}^T$$MOLT) formulation, combined with a fast summation method with computational complexity $$O(N\log {N})$$O(NlogN), where N is the number of grid points (particles). Under appropriate scaling, we show that the proposed schemes result in asymptotic preserving methods that can recover the Darwin limit of electrodynamics.
Rigidity of Complete Entire Self-Shrinking Solutions to Kähler–Ricci Flow

We show that every complete entire self-shrinking solution on complex Euclidean space to the Kahler-Ricci flow must be generated from a quadratic potential.
Randomized Wagering Mechanisms

Wagering mechanisms are one-shot betting mechanisms that elicit agents’ predictions of an event. For deterministic wagering mechanisms, an existing impossibility result has shown incompatibility of some desirable theoretical properties. In particular, Pareto optimality (no profitable side bet before allocation) can not be achieved together with weak incentive compatibility, weak budget balance and individual rationality. In this paper, we expand the design space of wagering mechanisms to allow randomization and ask whether there are randomized wagering mechanisms that can achieve all previously considered desirable properties, including Pareto optimality. We answer this question positively with two classes of randomized wagering mechanisms: i) one simple randomized lottery-type implementation of existing deterministic wagering mechanisms, and ii) another family of randomized wagering mechanisms, named surrogate wagering mechanisms, which are robust to noisy ground truth. Surrogate wagering mechanisms are inspired by an idea of learning with noisy labels (Natarajan et al. 2013) as well as a recent extension of this idea to the information elicitation without verification setting (Liu and Chen 2018). We show that a broad set of randomized wagering mechanisms satisfy all desirable theoretical properties.
Combining Online Learning Guarantees

We show how to take any two parameter-free online learning algorithms with different regret guarantees and obtain a single algorithm whose regret is the minimum of the two base algorithms. Our method is embarrassingly simple: just add the iterates. This trick can generate efficient algorithms that adapt to many norms simultaneously, as well as providing diagonal-style algorithms that still maintain dimension-free guarantees. We then proceed to show how a variant on this idea yields a black-box procedure for generating optimistic online learning algorithms. This yields the first optimistic regret guarantees in the unconstrained setting and generically increases adaptivity. Further, our optimistic algorithms are guaranteed to do no worse than their non-optimistic counterparts regardless of the quality of the optimistic estimates provided to the algorithm.
Approximate Guarantees for Dictionary Learning.

In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \ll n$), and $Y$ has columns that are $k$-sparse (typically $k \ll d$). Most of the known theoretical results involve assuming that the columns of the unknown $A$ have certain incoherence properties, and that the coefficient matrix $Y$ has random (or partly random) structure. The goal of our work is to understand what can be said in the absence of such assumptions. Can we still find $A$ and $Y$ such that $X \approx AY$? We show that this is possible, if we allow violating the bounds on $m$ and $k$ by appropriate factors that depend on $k$ and the desired approximation. Our results rely on an algorithm for what we call the threshold correlation problem, which turns out to be related to hypercontractive norms of matrices. We also show that our algorithmic ideas apply to a setting in which some of the columns of $X$ are outliers, thus giving similar guarantees even in this challenging setting.
Metformin and Sulfonylurea Use and Risk of Incident Dementia

Abstract Objective To compare incident dementia risk among patients who initiated treatment with metformin or sulfonylurea in Veterans Health Affairs (VHA) patients with replication in Kaiser Permanente Washington (KPW) patients to determine whether first-choice antidiabetic medications are associated with reduced risk of dementia. Patients and Methods Cohorts contained 75,187 VHA patients and 10,866 KPW patients, 50 years and older, who initiated monotherapy with metformin or sulfonylurea. Patients were free of dementia diagnoses and any diabetes treatment for 2 years before cohort entry. Variables were extracted from electronic health data from VHA (1999-2015) and KPW (1996-2015), which included diagnosis codes, pharmacy data, laboratory values, and demographic characteristics. Propensity scores and inverse probability of treatment weighting controlled for confounding. Results Veterans Health Affairs patients were 60.8±6.8 years of age on average, and KPW patients were 63.1±9.5 years of age. In the VHA sample, 72,769 (96.8%) were male; and in the KPW sample, 5480 (50.4%). After adjusting for confounding, metformin initiation was associated with a significantly (P=.02) lower risk of dementia in VHA (hazard ratio, 0.9; 95% CI, 0.9-1.0), with a similar point estimate in KPW (hazard ratio, 0.9; 95% CI, 0.7-1.1). Metformin was not associated with dementia risk in patients 75 years and older. Conclusion Existing epidemiological studies of metformin and incident dementia have been inconsistent. Using a similar study design in 2 patient populations that differed in clinical and demographic characteristics, our results provide robust evidence that metformin use is associated with a modestly lower risk of incident dementia.
Growth after War in Syria

This paper addresses three questions: 1) what would have been the growth and income trajectory of Syria in the absence of war; 2) given the war, what explains the reduction in economic growth in terms physical capital, labor force, human capital, and productivity; and 3) what potential growth scenarios for Syria there could be in the aftermath of war. Estimates of the impact of conflict point to negative gross domestic product (GDP) growth of -12 percent on average over 2011-18, resulting in a GDP contraction to about one-third of the 2010 level. In post-conflict simulation scenarios, the growth drivers are affected by the assumed levels of reconstruction assistance, repatriation of refugees, and productivity improvements associated with three plausible political settlement outcomes: a baseline (Sochi-plus) moderate scenario, an optimistic (robust political settlement) scenario, and a pessimistic (de facto balance of power) scenario. Respectively for these scenarios, GDP per capita average growth in the next two decades is projected to be 6.1, 8.2, or 3.1 percent, assuming that a final and stable resolution of the conflict is achieved.
Quality of life changes after lumbar decompression in patients with tandem spinal stenosis.

Abstract Objective Tandem spinal stenosis (TSS) is a degenerative spinal condition characterized by spinal canal narrowing at 2 or more distinct spinal levels. It is an aging-related condition that is likely to increase as the population ages, but which remains poorly described in the literature. Here we sought to determine the impact of primary lumbar decompression on quality-of-life (QOL) outcomes in patients with symptomatic TSS. Patients and methods We retrospectively reviewed 803 patients with clinical and radiographic evidence of TSS treated between 2008 and 2014 with a minimum 2-year follow-up. The records of patients with clinical and radiographic evidence of concurrent cervical and lumbar stenosis were reviewed. Prospectively gathered QOL data, including the Pain Disability Questionnaire (PDQ), Patient Health Questionnaire-9 (PHQ-9), EuroQOL-5 Dimensions (EQ-5D), and Visual Analogue Scale (VAS) for low back pain, were assessed at the 6-month, 1-year, and 2-year follow-ups. Results Of 803 identified patients (mean age 66.2 years; 46.9% male), 19.6% underwent lumbar decompression only, 14.1% underwent cervical + lumbar decompression, and 66.4% underwent conservative management only. Baseline VAS scores were similar across all groups, but patients undergoing conservative management had better baseline QOL scores on all other measures. Both surgical cohorts experienced significant improvements in the VAS, PDQ, and EQ-5D at all time points; patients in the cervical + lumbar cohort also had significant improvement in the PHQ-9. Conservatively managed patients showed no significant improvement in QOL scores at any follow-up interval. Conclusion Lumbar decompression with or without cervical decompression improves low back pain and QOL outcomes in patients with TSS. The decision to prioritize lumbar decompression is therefore unlikely to adversely affect long-term quality-of-life improvements.
Class IIa HDACs regulate learning and memory through dynamic experience-dependent repression of transcription

The formation of new memories requires transcription. However, the mechanisms that limit signaling of relevant gene programs in space and time for precision of information coding remain poorly understood. We found that, during learning, the cellular patterns of expression of early response genes (ERGs) are regulated by class IIa HDACs 4 and 5, transcriptional repressors that transiently enter neuronal nuclei from cytoplasm after sensory input. Mice lacking these repressors in the forebrain have abnormally broad experience-dependent expression of ERGs, altered synaptic architecture and function, elevated anxiety, and severely impaired memory. By acutely manipulating the nuclear activity of class IIa HDACs in behaving animals using a chemical-genetic technique, we further demonstrate that rapid induction of transcriptional programs is critical for memory acquisition but these programs may become dispensable when a stable memory is formed. These results provide new insights into the molecular basis of memory storage.
Robust Optimal Design of Energy Efficient Series Elastic Actuators: Application to a Powered Prosthetic Ankle

Design of rehabilitation and physical assistance robots that work safely and efficiently despite uncertain operational conditions remains an important challenge. Current methods for the design of energy efficient series elastic actuators use an optimization formulation that typically assumes known operational requirements. This approach could lead to actuators that cannot satisfy elongation, speed, or torque requirements when the operation deviates from nominal conditions. Addressing this gap, we propose a convex optimization formulation to design the stiffness of series elastic actuators to minimize energy consumption and satisfy actuator constraints despite uncertainty due to manufacturing of the spring, unmodeled dynamics, efficiency of the transmission, and the kinematics and kinetics of the load. To achieve convexity, we write energy consumption as a scalar convex-quadratic function of compliance. As actuator constraints, we consider peak motor torque, peak motor velocity, limitations due to the speed-torque relationship of DC motors, and peak elongation of the spring. We apply our formulation to the robust design of a series elastic actuator for a powered prosthetic ankle. Our simulation results indicate that a small trade-off between energy efficiency and robustness is justified to design actuators that can operate with uncertainty.
What is made-in-China feminism(s)? Gender discontent and class friction in post-socialist China

Contemporary Chinese feminism has drawn much attention in academe and popular media, yet its ontological roots and the politics of naming has largely escaped scrutiny. This paper first demonstrates...