cssi/SciSciGPT-SciSciNet huggingface dataset:
The dimensions of LU(3,q) codes

A family of LDPC codes, called LU(3,q) codes, has been constructed from q-regular bipartite graphs. Recently, P. Sin and Q. Xiang determined the dimensions of these codes in the case that q is a power of an odd prime. They also obtained a lower bound for the dimension of an LU(3,q) code when q is a power of 2. In this paper we prove that this lower bound is the exact dimension of the LU(3,q) code. The proof involves the geometry of symplectic generalized quadrangles, the representation theory of Sp(4,q), and the ring of polynomials.
The Bayesian Linear Information Filtering Problem

We present a Bayesian sequential decision-making formulation of the information filtering problem, in which an algorithm presents items (news articles, scientific papers, tweets) arriving in a stream, and learns relevance from user feedback on presented items. We model user preferences using a Bayesian linear model, similar in spirit to a Bayesian linear bandit. We compute a computational upper bound on the value of the optimal policy, which allows computing an optimality gap for implementable policies. We then use this analysis as motivation in introducing a pair of new Decompose-Then-Decide (DTD) heuristic policies, DTD-Dynamic-Programming(DTD-DP) and DTD-Upper-Confidence-Bound (DTD-UCB). We compare DTD-DP and DTD-UCB against several benchmarks on real and simulated data, demonstrating significant improvement, and show that the achieved performance is close to the upper bound.
Robust SAR STAP via Kronecker decomposition

This paper proposes a spatiotemporal decomposition for the detection of moving targets in multi-antenna synthetic aperture radar (SAR). As a high-resolution radar imaging modality, SAR detects and localizes nonmoving targets accurately, giving it an advantage over lower-resolution ground-moving target indication (GMTI) radars. Moving target detection is more challenging due to target smearing and masking by clutter. Space-time adaptive processing (STAP) is often used to remove the stationary clutter and enhance the moving targets. In this work, it is shown that the performance of STAP can be improved by modeling the clutter covariance as a space versus time Kronecker product with low-rank factors. Based on this model, a low-rank Kronecker product covariance estimation algorithm is proposed, and a novel separable clutter cancelation filter based on the Kronecker covariance estimate is introduced. The proposed method provides orders of magnitude reduction in the required number of training samples as well as improved robustness to corruption of the training data. Simulation results and experiments using the Gotcha SAR GMTI challenge dataset are presented that confirm the advantages of our approach relative to existing techniques.
3D Global Coronal Density Structure and Associated Magnetic Field near Solar Maximum

Measurement of the coronal magnetic field is a crucial ingredient in understanding the nature of solar coronal dynamic phenomena at all scales. We employ STEREO/COR1 data obtained near maximum of solar activity in December 2012 (Carrington rotation, CR 2131) to retrieve and analyze the three-dimensional (3D) coronal electron density in the range of heights from $1.5$ to $4\ R_\odot$ using a tomography method and qualitatively deduce structures of the coronal magnetic field. The 3D electron density analysis is complemented by the 3D STEREO/EUVI emissivity in 195 \AA \ band obtained by tomography for the same CR period. We find that the magnetic field configuration during CR 2131 has a tendency to become radially open at heliocentric distances below $\sim 2.5 \ R_\odot$. We compared the reconstructed 3D coronal structures over the CR near the solar maximum to the one at deep solar minimum. Results of our 3D density reconstruction will help to constrain solar coronal field models and test the accuracy of the magnetic field approximations for coronal modeling.
Methodological and computational aspects of parallel tempering methods in the infinite swapping limit

A variant of the parallel tempering method is proposed in terms of a stochastic switching process for the coupled dynamics of replica configuration and temperature permutation. This formulation is shown to facilitate the analysis of the convergence properties of parallel tempering by large deviation theory, which indicates that the method should be operated in the infinite swapping limit to maximize sampling efficiency. The effective equation for the replica alone that arises in this infinite swapping limit simply involves replacing the original potential by a mixture potential. The analysis of the geometric properties of this potential offers a new perspective on the issues of how to choose of temperature ladder, and why many temperatures should typically be introduced to boost the sampling efficiency. It is also shown how to simulate the effective equation in this many temperature regime using multiscale integrators. Finally, similar ideas are also used to discuss extensions of the infinite swapping limits to the technique of simulated tempering.
Estimating clique composition and size distributions from sampled network data

Cliques are defined as complete graphs or subgraphs; they are the strongest form of cohesive subgroup, and are of interest in both social science and engineering contexts. In this paper we show how to efficiently estimate the distribution of clique sizes from a probability sample of nodes obtained from a graph (e.g., by independence or link-trace sampling). We introduce two types of unbiased estimators, one of which exploits labeling of sampled nodes neighbors and one of which does not require this information. This is the first work to present statistically principled design-based estimators for clique distributions in arbitrary graphs using sampled network data. We generalize our estimators to cases in which cliques are distinguished not only by size but also by node attributes, allowing us to estimate clique composition by size. Last, we compare our estimators on a variety of real-world graphs and provide suggestions for their use.
Auditing Black-Box Models for Indirect Influence

Data-trained predictive models see widespread use, but for the most part they are used as black boxes which output a prediction or score. It is therefore hard to acquire a deeper understanding of model behavior, and in particular how different features influence the model prediction. This is important when interpreting the behavior of complex models, or asserting that certain problematic attributes (like race or gender) are not unduly influencing decisions. In this paper, we present a technique for auditing black-box models, which lets us study the extent to which existing models take advantage of particular features in the dataset, without knowing how the models work. Our work focuses on the problem of indirect influence: how some features might indirectly influence outcomes via other, related features. As a result, we can find attribute influences even in cases where, upon further direct examination of the model, the attribute is not referred to by the model at all. Our approach does not require the black-box model to be retrained. This is important if (for example) the model is only accessible via an API, and contrasts our work with other methods that investigate feature influence like feature selection. We present experimental evidence for the effectiveness of our procedure using a variety of publicly available datasets and models. We also validate our procedure using techniques from interpretable learning and feature selection, as well as against other black-box auditing procedures.
Design Challenges in Named Entity Transliteration.

We analyze some of the fundamental design challenges that impact the development of a multilingual state-of-the-art named entity transliteration system, including curating bilingual named entity datasets and evaluation of multiple transliteration methods. We empirically evaluate the transliteration task using the traditional weighted finite state transducer (WFST) approach against two neural approaches: the encoder-decoder recurrent neural network method and the recent, non-sequential Transformer method. In order to improve availability of bilingual named entity transliteration datasets, we release personal name bilingual dictionaries mined from Wikidata for English to Russian, Hebrew, Arabic, and Japanese Katakana. Our code and dictionaries are publicly available.
On Almost-Planar Graphs

A nonplanar graph $G$ is called almost-planar if for every edge $e$ of $G$, at least one of $G\backslash e$ and $G/e$ is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small portion of it was published. The main purpose of this paper is to provide a short proof of this result. We also discuss the structure of almost-planar graphs that are not 3-connected.
Global solutions to nonlinear two-phase free boundary problems

We classify global Lipschitz solutions to two-phase free boundary problems governed by concave fully nonlinear equations, as either two-plane solutions or solutions to a one-phase problem.
On Multiplicative Functions with Bounded Partial Sums

Consider a multiplicative function f(n) taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that f(pn) = f(p)f(n) for all primes p in some finite set P, then the answer is yes. We also discuss a result of Bronstein that shows that functions modified from characters at a finite number of places must have unbounded partial sums.
The Information and Wave-Theoretic Limits of Analog Beamforming

The performance of broadband millimeter-wave (mmWave) RF architectures, is generally determined by mathematical concepts such as the Shannon capacity. These systems have also to obey physical laws such as the conservation of energy and the propagation laws. Taking the physical and hardware limitations into account is crucial for characterizing the actual performance of mm Wave systems under certain architecture such as analog beamforming. In this context, we consider a broadband frequency dependent array model that explicitly includes incremental time shifts instead of phase shifts between the individual antennas and incorporates a physically defined radiated power. As a consequence of this model, we present a novel joint approach for designing the optimal waveform and beamforming vector for analog beamforming. Our results show that, for sufficiently large array size, the achievable rate is mainly limited by the fundamental trade-off between the analog beamformina gain and siznal bandwidth.
Space–Time Metamaterials

Despite more than a decade of active research, the fundamental problem of material loss remains a major obstacle in fulfilling the promise of the recently emerged fields of metamaterials and plasmonics to bring in revolutionary practical applications. In the present work, we demonstrate that the problem of strong material absorption that is inherent to plasmonic systems and metamaterials based on plasmonic components, can be addressed by utilizing the time dimension. By matching the pulse profile to the actual response of a lossy metamaterial, this approach allows to offset the effect of the material absorption. The existence of the corresponding solution relies on the fundamental property of causality, that relates the absorption in the medium to the variations in the frequency-dependent time delay introduced by the material via the Kramers–Kronig relations. We demonstrate that the proposed space-time approach can be applied to a broad range of metamaterial-based and plasmonic systems, from hyperbolic me...
Bernstein polynomial model for grouped continuous data

Grouped data are commonly encountered in applications. All data from a continuous population are grouped due to rounding of the individual observations. The Bernstein polynomial model is proposed a...
Knowledge Base Completion: Baselines Strike Back

Many papers have been published on the knowledge base completion task in the past few years. Most of these introduce novel architectures for relation learning that are evaluated on standard datasets like FB15k and WN18. This paper shows that the accuracy of almost all models published on the FB15k can be outperformed by an appropriately tuned baseline — our reimplementation of the DistMult model. Our findings cast doubt on the claim that the performance improvements of recent models are due to architectural changes as opposed to hyper-parameter tuning or different training objectives. This should prompt future research to re-consider how the performance of models is evaluated and reported.
Market-based power allocation for a differentially priced FDMA system

In this paper, we study the problem of differential pricing and QoS assignment by a broadband data provider. In our model, the broadband data provider decides on the power allocated to an end-user not only based on parameters of the transmission medium, but also based on the price the user is willing to pay. In addition, end-users bid the price that they are willing to pay to the BTS based on their channel condition, the throughput they require, and their belief about other users' parameters. We will characterize the optimum power allocation by the BTS which turns out to be a modification of the solution to the well-known water-filling problem. We also characterize the optimum bidding strategy of end-users using the belief of each user about the cell condition.
The Physical Systems Behind Optimization Algorithms

We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient descent, coordinate gradient descent, proximal coordinate gradient, and Newton's methods as well as their Nesterov's accelerated variants in a unified framework motivated by a natural connection of optimization algorithms to physical systems. Our analysis is applicable to more general algorithms and optimization problems {\it \textbf{beyond}} convexity and strong convexity, e.g. Polyak-\L ojasiewicz and error bound conditions (possibly nonconvex).
A combinatorial proof of Sun's “curious” identity.

A binomial coefficient identity due to Zhi-Wei Sun is the subject of half a dozen recent papers that prove it by various analytic techniques and establish a generalization. Here we give a simple proof that uses weight-reversing involutions on suitable configurations involving dominos and colorings. With somewhat more work, the method extends to the generalization also.
A general asymptotic framework for distribution‐free graph‐based two‐sample tests

Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution-free, are based either on geometric graphs constructed using inter-point distances between the observations (multivariate generalizations of the Wald-Wolfowitz's runs test) or on multivariate data-depth (generalizations of the Mann-Whitney rank test). This paper introduces a general notion of distribution-free graph-based two-sample tests, and provides a unified framework for analyzing and comparing their asymptotic properties. The asymptotic (Pitman) efficiency of a general graph-based test is derived, which include tests based on geometric graphs, such as the Friedman-Rafsky test (1979), the test based on the $K$-nearest neighbor graph, the cross-match test (2005), the generalized edge-count test (2017), as well as tests based on multivariate depth functions (the Liu-Singh rank sum statistic (1993)). The results show how the combinatorial properties of the underlying graph effect the performance of the associated two-sample test, and can be used to validate and decide which tests to use in practice. Applications of the results are illustrated both on synthetic and real datasets.
Monitoring dynamic spatio-temporal ecological processes optimally.

Population dynamics vary in space and time. Survey designs that ignore these dynamics may be inefficient and fail to capture essential spatio-temporal variability of a process. Alternatively, dynamic survey designs explicitly incorporate knowledge of ecological processes, the associated uncertainty in those processes, and can be optimized with respect to monitoring objectives. We describe a cohesive framework for monitoring a spreading population that explicitly links animal movement models with survey design and monitoring objectives. We apply the framework to develop an optimal survey design for sea otters in Glacier Bay. Sea otters were first detected in Glacier Bay in 1988 and have since increased in both abundance and distribution; abundance estimates increased from 5 otters to >5,000 otters, and they have spread faster than 2.7 km/yr. By explicitly linking animal movement models and survey design, we are able to reduce uncertainty associated with forecasting occupancy, abundance, and distribution compared to other potential random designs. The framework we describe is general, and we outline steps to applying it to novel systems and taxa.
Existence, uniqueness, analyticity, and Borel summability for Boussinesq equations

Through Borel summation methods, we analyze the Boussinesq equations for coupled fluid velocity and temperature fields: (1) ut−νΔu=−P[u⋅∇u−ae2Θ]+f Θt−μΔΘ=−u⋅∇Θ. We prove that an equivalent system of integral equations in the Borel variable p∈R+ dual to 1/t has a unique solution in a class of exponentially bounded functions, implying the existence of a classical solution to (1) in a complex t-region that includes a real positive time axis segment. For analytic initial data and forcing, it is shown that the solution is Borel summable, implying that formal series in powers of t is Gevrey-1 asymptotic, and within the time interval of existence, the solution remains analytic with the same analyticity strip width as the initial data and forcing. We also determine conditions on the integral equation solution that improve the estimate for existence time.
Geometry of the Sample Frequency Spectrum and the Perils of Demographic Inference

The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to zero or diverge to infinity, and show undesirable sensitivity to perturbations in the data. The goal of this article is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographies and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model, and generalize our intuition to arbitrary sample sizes using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only [Formula: see text] epochs, where [Formula: see text] is between [Formula: see text] and [Formula: see text] The set of expected SFS for piecewise-constant demographies with fewer than [Formula: see text] epochs is open and nonconvex, which causes the above phenomena for inference from data.
Some Properties and Examples of Triangular Pointed Hopf Algebras

A fundamental problem in the theory of Hopf algebras is the classification and construction of finite-dimensional (minimal) triangular Hopf algebras (A,R) introduced by Drinfeld. Only recently Etingof and the author completely solved this problem for semisimple A over algebraically closed fields of characteristics 0 and p>>dim(A) (any p if one assumes that A is also cosemisimple). In this paper we take the first step towards solving this problem for finite-dimensional pointed Hopf algebras over an algebraically closed field k of characteristic 0. We first prove that the fourth power of the antipode of any triangular pointed Hopf algebra A is the identity. We do that by focusing on minimal triangular pointed Hopf algebras (A,R) (every triangular Hopf algebra contains a minimal triangular sub Hopf algebra) and proving that the group algebra of the group of grouplike elements of A (which must be abelian) admits a minimal triangular structure and consequently that A has the structure of a biproduct. We also generalize our result on the order of the antipode to any finite-dimensional quasitriangular Hopf algebra A whose Drinfeld element u acts as a scalar in any irreducible representation of A (e.g. when A^* is pointed). Second, we describe a method of construction of finite-dimensional pointed Hopf algebras which admit a minimal triangular structure, and classify all their minimal triangular structures. We conclude the paper by proving that any minimal triangular Hopf algebra which is generated as an algebra by grouplike elements and skew primitive elements is isomorphic to a minimal triangular Hopf algebra constructed using our method.
Multiscale methods for model order reduction of non-linear multiphase flow problems

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order reduction approaches are available in the existing literature that alleviate this issue by approximating the solution at a coarse scale preserving fine scale features. We attempt to present a comparison between two such model order reduction techniques, namely (1) adaptive numerical homogenization and (2) generalized multiscale basis functions. We rely upon a non-linear, multi-phase, black-oil model formulation, commonly encountered in the oil and gas industry, as the basis for comparing the aforementioned two approaches. An expanded mixed finite element formulation is used to separate the spatial scales between non-linear, flow, and transport problems. A numerical benchmark is setup using fine scale property information from the 10th SPE comparative project dataset for the purpose of comparing accuracies of these two schemes. An adaptive criterion is employed by both the schemes for local enrichment that allows us to preserve solution accuracy compared to the fine scale benchmark problem. The numerical results indicate that both schemes are able to adequately capture the fine scale features of the model problem at hand.
Algebra properties for Besov spaces on unimodular Lie groups

We consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group G equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property for $B^{p,q}_\alpha(G)$ for $\alpha>0$, $1\leq p,q \leq +\infty$. These results hold for polynomial as well as for exponential volume growth of balls.
Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant of AGD, and shows that it escapes saddle points and finds a second-order stationary point in $\tilde{O}(1/\epsilon^{7/4})$ iterations, faster than the $\tilde{O}(1/\epsilon^{2})$ iterations required by GD. To the best of our knowledge, this is the first Hessian-free algorithm to find a second-order stationary point faster than GD, and also the first single-loop algorithm with a faster rate than GD even in the setting of finding a first-order stationary point. Our analysis is based on two key ideas: (1) the use of a simple Hamiltonian function, inspired by a continuous-time perspective, which AGD monotonically decreases per step even for nonconvex functions, and (2) a novel framework called improve or localize, which is useful for tracking the long-term behavior of gradient-based optimization algorithms. We believe that these techniques may deepen our understanding of both acceleration algorithms and nonconvex optimization.
Representation of units in cyclotomic function fields

In this paper, we prove a refinement of Hilbert’s Satz 90 for the ℘-cyclotomic function fields, where ℘ is a monic prime in &#x1d53d;q[T]. Our result can be viewed as a function field analogue of Newman’s ...
Multiscale Topology of Chromatin Folding

The three dimensional structure of DNA in the nucleus (chromatin) plays an important role in many cellular processes. Recent experimental advances have led to high-throughput methods of capturing information about chromatin conformation on genome-wide scales. New models are needed to quantitatively interpret this data at a global scale. Here we introduce the use of tools from topological data analysis to study chromatin conformation. We use persistent homology to identify and characterize conserved loops and voids in contact map data and identify scales of interaction. We demonstrate the utility of the approach on simulated data and then look data from both a bacterial genome and a human cell line. We identify substantial multiscale topology in these datasets.
Testing Contextuality in Cyclic Psychophysical Systems of High Ranks

Contextuality-by-Default (CbD) is a mathematical framework for understanding the role of context in systems with deterministic inputs and random outputs. A necessary and sufficient condition for contextuality was derived for cyclic systems with binary outcomes. In quantum physics, the cyclic systems of ranks \(n=\) 5, 4, and 3 are known as systems of Klyachko-type, EPR-Bell-type, and Leggett-Garg-type, respectively. In earlier publications, we examined data collected in various behavioral and social scenarios, from polls of public opinion to our own experiments with psychophysical matching. No evidence of contextuality was found in these data sets. However, those studies were confined to cyclic systems of lower ranks (\(n\le 4\)). In this paper, contextuality of higher ranks (\(n=6,8\)) was tested on our data with psychophysical matching, and again, no contextuality was found. This may indicate that many if not all of the seemingly contextual effects observed in behavioral sciences are merely violations of consistent connectedness (selectiveness of influences).
Detection of Cooperative Interactions in Logistic Regression Models

An important problem in the field of bioinformatics is to identify interactive effects among profiled variables for outcome prediction. In this paper, a logistic regression model with pairwise interactions among a set of binary covariates is considered. Modeling the structure of the interactions by a graph, our goal is to recover the interaction graph from independently identically distributed (i.i.d.) samples of the covariates and the outcome. When viewed as a feature selection problem, a simple quantity called influence is proposed as a measure of the marginal effects of the interaction terms on the outcome. For the case when the underlying interaction graph is known to be acyclic, it is shown that a simple algorithm that is based on a maximum-weight spanning tree with respect to the plug-in estimates of the influences not only has strong theoretical performance guarantees, but can also outperform generic feature selection algorithms for recovering the interaction graph from i.i.d. samples of the covariates and the outcome. Our results can also be extended to the model that includes both individual effects and pairwise interactions via the help of an auxiliary covariate.
Vanishing of the negative homotopy K-theory of quotient singularities

Making use of Gruson–Raynaud’s technique of ‘platification par eclatement’, Kerz and Strunk proved that the negative homotopy -theory group.
A Frobenius–Schur Theorem for Hopf Algebras

We prove a version of the Frobenius–Schur theorem for a finite-dimensional semisimple Hopf algebra H over an algebraically closed field; if the field has characteristic p not 0, H is also assumed to be cosemisimple. Then for each irreducible representation V of H, we define a Schur indicator for V, which reduces to the classical Schur indicator when H is the group algebra of a finite group. We prove that this indicator is 0 if and only if V is not self-dual. If V is self dual, then the indicator is positive (respectively, negative) if and only if V admits a nondegenerate bilinear symmetric (resp., skew-symmetric) H-invariant form. A more general result is proved for algebras with involution.
Cascade Source Coding With a Side Information Vending Machine

The model of a side information vending machine (VM) accounts for scenarios in which the measurement of side information sequences can be controlled via the selection of cost-constrained actions. In this paper, the three-node cascade source coding problem is studied under the assumption that a side information VM is available at the intermediate and/or end node of the cascade. A single-letter characterization of the achievable tradeoff among the transmission rates, distortions in the reconstructions at the intermediate and end node, and cost for acquiring the side information is derived for a number of relevant special cases. It is shown that a joint design of the description, source, and control signals used to guide the selection of the actions at downstream nodes is generally necessary for an efficient use of the available communication links. In particular, for all the considered models, layered coding strategies prove to be optimal, whereby the base layer fulfills two network objectives: 1) determining the actions of downstream nodes and 2) simultaneously providing a coarse description of the source. Design of the optimal coding strategy is shown via examples to depend on both the network topology and action costs. Examples also illustrate the involved performance tradeoffs across the network.
G-character varieties for G=SO(n,C) and other not simply connected groups

Abstract We describe the relation between G -character varieties, X G ( Γ ) , and G / H -character varieties, where H is a finite, central subgroup of G . In particular, we find finite generating sets for C [ X G / H ( Γ ) ] for classical groups G and H as above. By applying this approach to SO ( 4 , C ) = ( SL ( 2 , C ) × SL ( 2 , C ) ) / Z / 2 we find an explicit description of C [ X SO ( 4 , C ) ( F 2 ) ] for the free group on two generators, F 2 . In the second part of the paper, we prove several properties of SO ( 2 n , C ) -character varieties. This is a particularly interesting class of character varieties because unlike for all other classical groups G , the coordinate rings C [ X G ( Γ ) ] are generally not generated by the trace functions, τ γ , for γ ∈ Γ , for G = SO ( 2 n , C ) . In fact, we prove that the coordinate ring C [ X SO ( 2 n , C ) ( Γ ) ] is not even generated by “generalized trace functions,” τ γ , V , for all γ ∈ Γ and all representations V of SO ( 2 n , C ) for n = 2 and groups Γ of corank ≥2.
Grid topology identification using electricity prices

The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LMPs) correspond to the Lagrange multipliers of the linear program involved. The interesting observation here is that the matrix of spatiotemporally varying LMPs exhibits the following property: Once premultiplied by the weighted grid Laplacian, it yields a low-rank and sparse matrix. Leveraging this rich structure, a regularized maximum likelihood estimator (MLE) is developed to recover the grid Laplacian from the LMPs. The convex optimization problem formulated includes low rank-and sparsity-promoting regularizers, and it is solved using a scalable algorithm. Numerical tests on prices generated for the IEEE 14-bus benchmark provide encouraging topology recovery results.
Data-Driven Learning-Based Optimization for Distribution System State Estimation

Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used algorithms such as Gauss–Newton perform poorly with the limited number of measurements typically available for DSSE, often require many iterations to obtain reasonable results, and sometimes fail to converge. DSSE is a non-convex problem, and working with a limited number of measurements further aggravates the situation, as indeterminacy induces multiple global (in addition to local) minima. Gauss–Newton is also known to be sensitive to initialization. Hence, the situation is far from ideal. It is therefore natural to ask if there is a smart way of initializing Gauss–Newton that will avoid these DSSE-specific pitfalls. This paper proposes using historical or simulation-derived data to train a shallow neural network to “learn to initialize,” that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss–Newton. It is shown that this hybrid machine learning/optimization approach yields superior performance in terms of stability, accuracy, and runtime efficiency, compared to conventional optimization-only approaches. It is also shown that judicious design of the neural network training cost function helps to improve the overall DSSE performance.
Partitioned Factors in Christoffel and Sturmian Words

Abstract Borel and Reutenauer (2006) [3] showed, inter alia, that a word w of length n > 1 is conjugate to a Christoffel word if and only if for k = 0 , 1 , … , n − 1 , w has k + 1 distinct circular factors of length k. Sturmian words are the infinite counterparts to Christoffel words, characterized as aperiodic but of minimal complexity, i.e., for all n ∈ N there are n + 1 factors of length n. Berthe (1996) [2] showed that the factors of a given length in the Sturmian case have at most three frequencies (probabilities). In this paper we extend to results on factors of both Christoffel words and Sturmian words under fixed partitionings (decompositions of factors of length m into concatenations of words whose lengths are given by a composition of m into k components). Any factor of a Sturmian word (respectively, circular factor of a Christoffel word) thus partitioned into k elements belongs to one of k + 1 equivalence classes (varieties). We show how to compute the sizes of the equivalence classes determined by a composition in the case of Christoffel word, and show how to compute the frequencies of the classes in the case of Sturmian words. A version of the finitary case was proved in a very different context (expressed in musical and number-theoretical terms) by Clough and Myerson (1985, 1986) [5] , [6] ; we use their terminology, variety and multiplicity.
The Roots of Bias on Uber

In the last decade, there has been a growth in, what we call, digitally mediated workplaces. A digitally mediated workplace is one where interactions between stakeholders are primarily managed by proprietary, algorithmically managed digital platform. The replacement of the relationships between the stakeholders by the platform is a key feature of these workplaces, and is a contributing factor to the decrease in contractual responsibilities each stakeholder has to one another. In this paper, we discuss some of the ways in which this structure and lack of accountability serves as a root of, or at least an enabler to, the realization of biases in the ridesharing application Uber, a digitally mediated workplace.
Okounkov bodies on projectivizations of rank two toric vector bundles

Abstract The global Okounkov body of a projective variety is a closed convex cone that encodes asymptotic information about every big line bundle on the variety. In the case of a rank two toric vector bundle E on a smooth projective toric variety, we use its Klyachko filtrations to give an explicit description of the global Okounkov body of P ( E ) . In particular, we show that this is a rational polyhedral cone and that P ( E ) is a Mori dream space.
First-Order Adaptive Sample Size Methods to Reduce Complexity of Empirical Risk Minimization

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic methods. In contrast to traditional methods that attempt to solve the ERM problem corresponding to the full dataset directly, adaptive sample size schemes start with a small number of samples and solve the corresponding ERM problem to its statistical accuracy. The sample size is then grown geometrically -- e.g., scaling by a factor of two -- and use the solution of the previous ERM as a warm start for the new ERM. Theoretical analyses show that the use of adaptive sample size methods reduces the overall computational cost of achieving the statistical accuracy of the whole dataset for a broad range of deterministic and stochastic first-order methods. The gains are specific to the choice of method. When particularized to, e.g., accelerated gradient descent and stochastic variance reduce gradient, the computational cost advantage is a logarithm of the number of training samples. Numerical experiments on various datasets confirm theoretical claims and showcase the gains of using the proposed adaptive sample size scheme.
Creation of a Virtual Nutrition Support Team to Improve Quality of Care for Patients Receiving Parenteral Nutrition in a Multisite Healthcare System

BACKGROUND Parenteral nutrition (PN) is a complicated therapy in which having specially trained clinicians can provide benefit, but it can be difficult to provide this level of expertise to all patients requiring PN. Creation of a virtual nutrition support team (NST) model allows patients across multiple hospitals to receive care from NST clinicians using remote conferencing technology on a daily basis. This study reviewed retrospective data from before and after implementation of the virtual model to assess quality indicators. METHODS The NST was developed including a team of dietitians and pharmacists with a physician medical director. Practice guidelines were developed to provide consistent methods for ordering and monitoring patients receiving PN. Patient charts in both the preintervention and postintervention groups were reviewed for indication for PN, duration of therapy, blood glucose levels, and demographic data. RESULTS A greater proportion of patients in the postintervention period had appropriate orders (97.2%) compared with patients in the preintervention period (58.9%) (P < 0.001). A greater proportion of patients in the postintervention period had blood glucose levels within the range 65-180 mg/dL (83.5%) compared with patients in the preintervention period (62.2%) (P < 0.001). CONCLUSION A virtual team model was applied to remotely manage patients receiving PN in a large healthcare system. This resulted in optimized care of patients by reducing inappropriately prescribed therapy and improving blood glucose control.
Two weight L p estimates for paraproducts in non-homogeneous settings

Abstract We give a necessary and sufficient condition for the two weight L p -estimates for paraproducts in non-homogeneous settings, 1 p ∞ . We are mainly interested in the case p ≠ 2 , since the case p = 2 is a well-known and easy corollary of the Carleson embedding theorem. The necessary and sufficient condition is given in terms of testing conditions of Sawyer type: for p ≤ 2 only one (“direct”) testing condition is required, but for p > 2 both “direct” and “adjoint” testing conditions are needed. An interesting feature is that the “adjoint” testing condition is that it is a testing condition not for the adjoint of the paraproduct, but for some auxiliary operator.
Using weighting algorithms to refine source direction determinations in all-sky gravitational wave burst searches with two-detector networks

I explore the possibility of resurrecting an old, non-Bayesian computational approach for inferring the source direction of a gravitational wave from the output of a two-detector network. The method gives the beam pattern response functions and time delay, and performs well even in the presence of noise and unexpected signal forms. I further suggest an improvement to this method in the form of a weighting algorithm that usefully improves its accuracy beyond what can be achieved with simple best-fit methods, validating the new procedure with several small-scale simulations. The approach is identified as complementary to --rather than in competition with-- the now-standard Bayesian approach typically used by the LIGO network in parameter determination. Finally, I briefly discuss the possible applications of this method in the world of three-or-more-detector networks and some directions for future work.
Residential demand response targeting using machine learning with observational data

The large-scale deployment of Advanced Metering Infrastructure among residential energy customers has served as a boon for energy systems research relying on granular consumption data. Residential Demand Response aims to utilize the flexibility of consumers to reduce their energy usage during times when the grid is strained. Suitable incentive mechanisms to encourage customers to deviate from their usual behavior have to be implemented to correctly control the bids into the wholesale electricity market as a Demand Response provider. In this paper, we present a framework for shortterm load forecasting on an individual user level, and relate non-experimental estimates of Demand Response efficacy (the estimated reduction of consumption during Demand Response events) to the variability of a user's consumption. We apply our framework on a dataset from a residential Demand Response program in the Western United States. Our results suggest that users with more variable consumption patterns are more likely to reduce their consumption compared to users with a more regular consumption behavior.
Multi-task Spatiotemporal Neural Networks for Structured Surface Reconstruction

Deep learning methods have surpassed the performance of traditional techniques on a wide range of problems in computer vision, but nearly all of this work has studied consumer photos, where precisely correct output is often not critical. It is less clear how well these techniques may apply on structured prediction problems where fine-grained output with high precision is required, such as in scientific imaging domains. Here we consider the problem of segmenting echogram radar data collected from the polar ice sheets, which is challenging because segmentation boundaries are often very weak and there is a high degree of noise. We propose a multi-task spatiotemporal neural network that combines 3D ConvNets and Recurrent Neural Networks (RNNs) to estimate ice surface boundaries from sequences of tomographic radar images. We show that our model outperforms the state-of-the-art on this problem by (1) avoiding the need for hand-tuned parameters, (2) extracting multiple surfaces (ice-air and ice-bed) simultaneously, (3) requiring less non-visual metadata, and (4) being about 6 times faster.
Eigenvalues of non-regular linear quasirandom hypergraphs

Abstract Chung, Graham, and Wilson proved that a graph is quasirandom if and only if there is a large gap between its first and second largest eigenvalue. Recently, the authors extended this characterization to coregular k -uniform hypergraphs with loops. However, for k ≥ 3 no k -uniform hypergraph is coregular. In this paper we remove the coregular requirement. Consequently, the characterization can be applied to k -uniform hypergraphs; for example it is used in Lenz and Mubayi (2015) [5] to show that a construction of a k -uniform hypergraph sequence has some quasirandom properties. The specific statement that we prove here is that if a k -uniform hypergraph satisfies the correct count of a specially defined four-cycle, then its second largest eigenvalue is much smaller than its largest one.
How the medium shapes the message: Printing and the rise of the arts and sciences.

Communication technologies, from printing to social media, affect our historical records by changing the way ideas are spread and recorded. Yet, finding statistical evidence of this fact has been challenging. Here we combine a common causal inference technique (instrumental variable estimation) with a dataset on nearly forty thousand biographies from Wikipedia (Pantheon 2.0), to study the effect of the introduction of printing in European cities on Wikipedia’s digital biographical records. By using a city’s distance to Mainz as an instrument for the adoption of the movable type press, we show that European cities that adopted printing earlier were more likely to become the birthplace of a famous scientist or artist during the years following the invention of printing. We bring these findings to recent communication technologies by showing that the number of radios and televisions in a country correlates with the number of globally famous performing artists and sports players born in that country, even after controlling for GDP, population, and including country and year fixed effects. These findings support the hypothesis that the introduction of communication technologies can bias historical records in the direction of the content that is best suited for each technology.
Derived-Equivalent Rational Threefolds

We describe an infinite set of smooth projective threefolds that have equivalent derived categories but are not isomorphic, contrary to a conjecture of Kawamata. These arise as blow-ups of P at various configurations of 8 points, which are related by Cremona transformations.
On Channel Sounding With Switched Arrays in Fast Time-Varying Channels

Time-division multiplexed (TDM) channel sounders, in which a single RF chain is connected sequentially via an electronic switch to different elements of an array, are widely used for the measurement of double-directional/MIMO propagation channels. This paper investigates the impact of array switching patterns on the accuracy of parameter estimation of multipath components (MPC) for a time-division multiplexed (TDM) channel sounder. The commonly-used sequential (uniform) switching pattern poses a fundamental limit on the number of antennas that a TDM channel sounder can employ in fast time-varying channels. We thus aim to design improved patterns that relax these constraints. To characterize the performance, we introduce a novel spatio-temporal ambiguity function, which can handle the non-idealities of real-world arrays. We formulate the sequence design problem as an optimization problem and propose an algorithm based on simulated annealing to obtain the optimal sequence. As a result, we can extend the estimation range of Doppler shifts by eliminating ambiguities in parameter estimation. We show through Monte Carlo simulations that the root mean square errors of both direction of departure and Doppler are reduced significantly with the new switching sequence. The results are also verified with actual vehicle-to-vehicle (V2V) channel measurements.