cssi/SciSciGPT-SciSciNet huggingface dataset:
Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.
Compendium of synovial signatures identifies pathologic characteristics for predicting treatment response in rheumatoid arthritis patients.

Rheumatoid arthritis (RA) is therapeutically challenging due to patient heterogeneity and variability. Herein we describe a novel integration of RA synovial genome-scale transcriptomic profiling of different patient cohorts that can be used to provide predictive insights on drug responses. A normalized compendium consisting of 256 RA synovial samples that cover an intersection of 11,769 genes from 11 datasets was build and compared with similar datasets derived from OA patients and healthy controls. Differentially expression genes (DEGs) that were identified in three independent methods were fed into functional network analysis, with subsequent grouping of the samples based on a non-negative matrix factorization method. RA-relevant pathway activation scores and four machine learning classification techniques supported the generation of a predictive model of patient treatment response. We identified 876 up-regulated DEGs including 24 known genetic risk factors and 8 drug targets. DEG-based subgrouping revealed 3 distinct RA patient clusters with distinct activity signatures for RA-relevant pathways. In the case of infliximab, we constructed a classifier of drug response that was highly accurate with an AUC/AUPR of 0.92/0.86. The most informative pathways in achieving this performance were the NFκB-, FceRI- TCR-, and TNF signaling pathways. Similarly, the expression of the HMMR, PRPF4B, EVI2A, RAB27A, MALT1, SNX6, and IFIH1 genes contributed in predicting the patient outcome. Construction and analysis of normalized synovial transcriptomic compendia can provide useful insights for understanding RA-related pathway involvement and drug responses for individual patients.
2-Deoxy-2-iodo- and 2-Deoxy-2-bromo-α-glucopyranosyl Trichloroacetimidates: Highly Reactive and Stereoselective Donors for the Synthesis of 2-Deoxy-β-glycosides

2-Deoxy-2-iodo- and 2-deoxy-2-bromoglucopyranosyl trichloroacetimidates 8−10 and 22 are extremely useful precursors of 2-deoxy-β-glycosides. These reactive glycosyl donors undergo highly stereosele...
Silicon Acceleration of a Tandem Alkene Isomerization/Electrocyclic Ring-opening of 2-Methyleneoxetanes to α,β-Unsaturated Methylketones

The first rearrangement of 2-methyleneoxetanes to α,β-unsaturated methylketones is reported. It is proposed that when these substrates are heated, the corresponding oxetenes are formed and subsequently undergo electrocyclic ring-opening to methyl vinylketones. In particular, α-silyl-α,β-unsaturated methylketones were isolated in moderate to high yields and with high stereoselectivities. Based on the proposed mechanism, density functional theory explains the differential kinetics and stereoselectivities among substrates.
Intermolecular Coupling Reaction of Cyclic Amines and Alkenes Catalyzed by a Ruthenium-Hydride Complex (PCy3)2(CO)RuHCl

The ruthenium-hydride complex (PCy3)2(CO)RuHCl (1) was found to be an effective catalyst for the dehydrogenative coupling reaction of cyclic amines and alkenes. The reaction of secondary cyclic ami...
Arylation of diethyl malonate and ethyl cyanoacetate catalyzed by palladium/di-tert-butylneopentylphosphine

α-Arylated carbonyl derivatives are important structural motifs in many natural products and pharmaceutically active compounds. Although arylation of simple monocarbonyl compounds is a well-established methodology, metal-catalyzed arylation of β-dicarbonyl derivatives is significantly more challenging. The ability of β-dicarbonyl anions to bind to palladium in a κ2-O,O mode, rather than the κ1-C-bound mode required for bond formation, often results in the deactivation of catalyst systems. The C-bound form of the enolate can be favored through the use of sterically demanding ligands. Herein, we report that the sterically demanding di-tert-butylneopentylphosphine (DTBNpP) ligand in combination with Pd(dba)2 provides an effective catalyst for the coupling of aryl bromides and chlorides with diethyl malonate. The Pd/DTBNpP system also catalyzes the coupling of aryl bromides with ethyl cyanoacetate.
Synthesis and resolution of 7-fluorotryptophans☆

7-Fluoro-DL-tryptophan (1a), 4,7-difluoro-DL-tryptophan (1b) and 5,7-difluoro-DL-tryptophan (1c) were prepared by Fischer indole cyclization. The resolution was achieved by treatment of the N-trifluoroacetly derivatices with carboxypeptidase A. All 7-fluorotryptophans are slow substrates for tryptophan indole-lyase from E. coli.
Approaches to Conjugated Polymers via New Solid State Polymerizations

Solid state polymerization is the most convenient approach for the synthesis of macroscopic polymer single crystals. Motivations for seeking fully crystalline specimens of conjugated polymers other than polydiacetylenes (PDA) are presented. The thermal reactivity of p-ethynylbenzoiic acid (EBA) is found to be a topochemically initiated solid state polymerization. The studies of EBA led to a new paradigm for solid state reactivity in such systems. Systems related to the paradigm, namely p-cyanobenzoic acid (CNBA) and p-cyanocinnamic acid (CNCA) have been studied. Sublimation competed with thermal processes in CNBA and CNCA, and a detailed product description has proved difficult to date. Thermochromism and charge-transfer transitions in PDA are discussed.
Palladium-Catalyzed Intramolecular Hydrosilylation of Alkenylsilanes: Selective Formation of Six-Membered Silicon Heterocycles

The cationic palladium complex (phen)Pd(Me)(OEt2)+BAr4- [phen = 1,10-phenanthroline; Ar = 3,5-C6H3(CF3)2] catalyzed the intramolecular hydrosilylation of 4-pentenylsilanes and 5-hexenylsilanes to form silacyclohexanes in 43−87% isolated yield and with excellent regioselectivity (typically ≥ 98:1).
Least-squares solution of a class of optimal space guidance problems via Theory of Connections

Abstract In this paper, we apply a newly developed method to solve boundary value problems for differential equations to solve optimal space guidance problems in a fast and accurate fashion. The method relies on the least-squares solution of differential equations via orthogonal polynomials expansion and constrained expression as derived via Theory of Connection (ToC). The application of the optimal control theory to derive the first order necessary conditions for optimality, yields a Two-Point Boundary Value Problem (TPBVP) that must be solved to find state and costate. Combining orthogonal polynomials expansion and ToC, we solve the TPBVP for a class of optimal guidance problems including energy-optimal landing on planetary bodies and fixed-time optimal intercept for a target-interceptor scenario. The performance analysis in terms of accuracy shows the potential of the proposed methodology as applied to optimal guidance problems.
The construction of high order convergent look-ahead finite difference formulas for Zhang Neural Networks

ABSTRACTZhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low ...
A novel approach to tricyclic pharmaceuticals via directed dilithiation of diaryl compounds

Abstract Tricyclic compounds were prepared using a novel approach based on the reaction between dilithio-diphenyl ether with appropriately substituted esters. The pharmaceutical drug, clopipazan, and its corresponding deschloro analog were synthesized utilizing this approach.
The chemistry of vicinal tricarbonyls and related systems.

In this Account, we survey our work on the chemistry of vicinal tricarbonyls and cyano analogues. Methods of preparing the vicinal functionalities are reviewed as well as the use in organic synthesis of these strongly electrophilic aggregates, readily available from carboxylic acids. By attaching neighboring electrophilic groups to the vicinal tricarbonyl, we have developed polyelectrophilic systems, which may be added to di- and trinucleophiles to create novel types of multistep reactivity. Application of tricarbonyl chemistry in synthesis is illustrated by the formation of various natural products or their precursors including fused-ring β-lactams, indole alkaloids, marine metabolites, enzyme inhibitors containing α-keto amides, and bioactive depsipeptides incorporating hydrated tricarbonyl units.
The Synthesis of Indoline and Benzofuran Scaffolds Using a Suzuki–Miyaura Coupling/Oxidative Cyclization Strategy

The generation of indolines and benzofurans from the combination of Suzuki–Miyaura coupling reactions with oxidative cyclizations is described.
Organozinc generation via the titanium-catalyzed activation of alkyl halides.

A protocol for the generation of organozinc reagents via catalytic activation of alkyl halides is described herein. Subsequent nucleophilic addition to carbonyl derivatives provided the desired products in good to excellent yields (76−99%). Evidence suggests that titanocene dichloride catalyzes the formation of an organozinc species. This discovery will have wide ranging applicability in the generation of highly reactive organometallic reagents.
Provider Responses to Online Price Transparency

Price transparency initiatives have recently emerged as a solution to the lack of health care price information available to consumers. This paper uses the staggered and nationwide diffusion of a leading internet-based price transparency platform to estimate the effects of price transparency on provider prices. I find a 1-4% reduction in provider prices for homogenous services, laboratory tests, but find no price response for differentiated services, office visits. Price responses are driven by active consumer use of price information. This paper demonstrates how reducing consumer search costs can spur limited firm price competition in health care markets.
Evolution-Driven Attenuation of Alphaviruses Highlights Key Glycoprotein Determinants Regulating Viral Infectivity and Dissemination.

Summary Understanding the fundamental mechanisms of arbovirus transmission and pathogenesis is essential to develop strategies for treatment and prevention. We previously took an in vivo evolution-based approach and identified the chikungunya virus E1 glycoprotein residue 80 to play a critical role in viral transmission and pathogenesis. In this study, we address the genetic conservation and function of position 80 and demonstrate that this residue is a key determinant in alphavirus infectivity and dissemination through modulation of viral fusion and cholesterol dependence. In addition, in studying the evolution of position 80, we identified a network of glycoprotein residues, including epidemic determinants, that regulate virus dissemination and infectivity. These studies underscore the importance of taking evolution-based approaches to not only identify key viral determinants driving arbovirus transmission and pathogenesis but also to uncover fundamental aspects of arbovirus biology.
Deep Convolutional Neural Networks For Imaging Data Based Survival Analysis Of Rectal Cancer

Recent radiomic studies have witnessed promising performance of deep learning techniques in learning radiomic features and fusing multimodal imaging data. Most existing deep learning based radiomic studies build predictive models in a setting of pattern classification, not appropriate for survival analysis studies where some data samples have incomplete observations. To improve existing survival analysis techniques whose performance is hinged on imaging features, we propose a deep learning method to build survival regression models by optimizing imaging features with deep convolutional neural networks (CNNs) in a proportional hazards model. To make the CNNs applicable to tumors with varied sizes, a spatial pyramid pooling strategy is adopted. Our method has been validated based on a simulated imaging dataset and a FDG-PET/CT dataset of rectal cancer patients treated for locally advanced rectal cancer. Compared with survival prediction models built upon hand-crafted radiomic features using Cox proportional hazards model and random survival forests, our method achieved competitive prediction performance.
Fermi acceleration of electrons inside foreshock transient cores

Foreshock transients upstream of Earth's bow shock have been recently observed to accelerate electrons to many times their thermal energy. How such acceleration occurs is unknown, however. Using THEMIS case studies, we examine a subset of acceleration events (31 of 247 events) in foreshock transients with cores that exhibit gradual electron energy increases accompanied by low background magnetic field strength and large-amplitude magnetic fluctuations. Using the evolution of electron distributions and the energy increase rates at multiple spacecraft, we suggest that Fermi acceleration between a converging foreshock transient's compressional boundary and the bow shock is responsible for the observed electron acceleration. We then show that a one-dimensional test particle simulation of an ideal Fermi acceleration model in fluctuating fields prescribed by the observations can reproduce the observed evolution of electron distributions, energy increase rate, and pitch-angle isotropy, providing further support for our hypothesis. Thus, Fermi acceleration is likely the principal electron acceleration mechanism in at least this subset of foreshock transient cores.
Limit Theorems for Empirical Density of Greatest Common Divisors

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. We study the large deviations of the empirical density. We will also obtain a rate of convergence to the normal distribution for the central limit theorem. Some generalisations are provided.
Learning local, quenched disorder in plasticity and other crackling noise phenomena

When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the material history. In plasticity modeling, the history is captured by a quenched, local and disordered flow stress distribution. While it is this disorder that causes avalanches that are commonly observed during nanoscale plastic deformation, the functional form and scaling properties have remained elusive. In this paper, a generic formalism is developed for deriving local disorder distributions from field-response (e.g., stress/strain) timeseries in models of crackling noise. We demonstrate the efficiency of the method in the hysteretic random-field Ising model and also, models of elastic interface depinning that have been used to model crystalline and amorphous plasticity. We show that the capacity to resolve the quenched disorder distribution improves with the temporal resolution and number of samples. Machine learning can estimate nanoscale local disorder distributions from crackling stress–strain curves, even with similar coexisting universal behavior. Stefanos Papanikolaou at The West Virginia University in West Virginia used unsupervised machine learning coupled with clustering to derive locally quenched disorder distributions from stress-strain curves that exhibit crackling noise over time. This method was successful in clustering and classifying data in two different models of crackling noise as well as in deriving the quenched disorder distribution for the experimental uniaxial compression of nickel micropillars. Extending the identification and classification of these quenched distributions to different materials, loading modes, and sample loading histories may help produce a library of stochastic yield distributions that can improve multiscale mechanics models.
Occluded Object Reconstruction for First Responders with Augmented Reality Glasses Using Conditional Generative Adversarial Networks

Firefighters suffer a variety of life-threatening risks, including line-of-duty deaths, injuries, and exposures to hazardous substances. Support for reducing these risks is important. We built a partially occluded object reconstruction method on augmented reality glasses for first responders. We used a deep learning based on conditional generative adversarial networks to train associations between the various images of flammable and hazardous objects and their partially occluded counterparts. Our system then reconstructed an image of a new flammable object. Finally, the reconstructed image was superimposed on the input image to provide "transparency". The system imitates human learning about the laws of physics through experience by learning the shape of flammable objects and the flame characteristics.
Bergman interpolation on finite Riemann surfaces. Part I: asymptotically flat case

The article considers the Bergman space interpolation problem on open Riemann surfaces obtained from a compact Riemann surface by removing a finite number of points. Such a surface is equipped with what we call an asymptotically flat conformal metric, i.e., a complete metric with zero curvature outside a compact subset. Sufficient conditions for interpolation in weighted Bergman spaces over asymptotically flat Riemann surfaces are then established. When the weights have curvature that is quasi-isometric to the asymptotically flat boundary metric, these sufficient conditions are shown to be necessary, unless the surface has at least one cylindrical end, in which case, the necessary conditions are slightly weaker than the sufficient conditions.
The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model.

Cognitive diagnosis models (CDMs) are useful statistical tools in cognitive diagnosis assessment. However, as many other latent variable models, the CDMs often suffer from the non-identifiability issue. This work gives the sufficient and necessary condition for identifiability of the basic DINA model, which not only addresses the open problem in Xu and Zhang (Psychometrika 81:625–649, 2016) on the minimal requirement for identifiability, but also sheds light on the study of more general CDMs, which often cover DINA as a submodel. Moreover, we show the identifiability condition ensures the consistent estimation of the model parameters. From a practical perspective, the identifiability condition only depends on the Q-matrix structure and is easy to verify, which would provide a guideline for designing statistically valid and estimable cognitive diagnosis tests.
Estimating Learnability in the Sublinear Data Regime

We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this ``learnability'' even when given an amount of data that is too small to reliably learn any accurate model. Our first result applies to the setting where the data is drawn from a $d$-dimensional distribution with isotropic covariance, and the label of each datapoint is an arbitrary noisy function of the datapoint. In this setting, we show that with $O(\sqrt{d})$ samples, one can accurately estimate the fraction of the variance of the label that can be explained via the best linear function of the data. We extend these techniques to a binary classification, and show that the prediction error of the best linear classifier can be accurately estimated given $O(\sqrt{d})$ labeled samples. For comparison, in both the linear regression and binary classification settings, even if there is no noise in the labels, a sample size linear in the dimension, $d$, is required to \emph{learn} any function correlated with the underlying model. We further extend our estimation approach to the setting where the data distribution has an (unknown) arbitrary covariance matrix, allowing these techniques to be applied to settings where the model class consists of a linear function applied to a nonlinear embedding of the data. We demonstrate the practical viability of our approaches on synthetic and real data. This ability to estimate the explanatory value of a set of features (or dataset), even in the regime in which there is too little data to realize that explanatory value, may be relevant to the scientific and industrial settings for which data collection is expensive and there are many potentially relevant feature sets that could be collected.
Large-Scale Optimization Algorithms for Sparse Conditional Gaussian Graphical Models

This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to model the output network influenced by conditioning input variables. While highly scalable optimization methods exist for sparse Gaussian graphical model estimation, state-of-the-art methods for conditional Gaussian graphical models are not efficient enough and more importantly, fail due to memory constraints for very large problems. In this paper, we propose a new optimization procedure based on a Newton method that efficiently iterates over two sub-problems, leading to drastic improvement in computation time compared to the previous methods. We then extend our method to scale to large problems under memory constraints, using block coordinate descent to limit memory usage while achieving fast convergence. Using synthetic and genomic data, we show that our methods can solve one million dimensional problems to high accuracy in a little over a day on a single machine.
Parallelizing greedy for submodular set function maximization in matroids and beyond

We consider parallel, or low adaptivity, algorithms for submodular function maximization. This line of work was recently initiated by Balkanski and Singer and has already led to several interesting results on the cardinality constraint and explicit packing constraints. An important open problem is the classical setting of matroid constraint, which has been instrumental for developments in submodular function maximization. In this paper we develop a general strategy to parallelize the well-studied greedy algorithm and use it to obtain a randomized (1 / 2 − є)-approximation in O( log2(n) / 2 ) rounds of adaptivity. We rely on this algorithm, and an elegant amplification approach due to Badanidiyuru and Vondrak to obtain a fractional solution that yields a near-optimal randomized ( 1 − 1/e − є )-approximation in O( log2(n) / є3 ) rounds of adaptivity. For non-negative functions we obtain a ( 3−2√2 − є )-approximation and a fractional solution that yields a ( 1 / e − є)-approximation. Our approach for parallelizing greedy yields approximations for intersections of matroids and matchoids, and the approximation ratios are comparable to those known for sequential greedy.
Computing Optimal Control of Cascading Failure in DC Networks

We consider discrete-time dynamics for cascading failure in DC networks whose map is a composition of failure rule with control actions. Supply–demand at the nodes is monotonically nonincreasing under admissible control. Under the failure rule, a link is removed permanently if its flow exceeds capacity. We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply–demand at the nodes, to a feasible state, i.e., a state which is invariant under the failure rule. There is no running cost and the reward associated with a feasible terminal state is the associated cumulative supply–demand. We propose two approaches for computing optimal control. The first approach, geared toward tree reducible networks, decomposes the global problem into a system of coupled local problems, which can be solved to optimality in two iterations. When restricted to the class of one-shot control actions, the optimal solutions to the local problems possess a piecewise affine property, which facilitates analytical solutions. The second approach computes optimal control by searching over the reachable set, which is shown to admit an equivalent finite representation by aggregation of control actions leading to the same reachable active link set. An algorithmic procedure to construct this representation is provided by leveraging and extending tools for arrangement of hyperplanes and polytopes. Illustrative simulations, including showing the effectiveness of projection-based approximation algorithms, are also presented.
Analysis of the U.S. patient referral network

In this paper, we analyze the US Patient Referral Network (also called the Shared Patient Network) and various subnetworks for the years 2009 to 2015. In these networks, two physicians are linked if a patient encounters both of them within a specified time interval, according to the data made available by the Centers for Medicare and Medicaid Services. We find power law distributions on most state-level data as well as a core-periphery structure. On a national and state level, we discover a so-called small-world structure as well as a "gravity law" of the type found in some large-scale economic networks. Some physicians play the role of hubs for interstate referral. Strong correlations between certain network statistics with health care system statistics at both the state and national levels are discovered. The patterns in the referral network evinced using several statistical analyses involving key metrics derived from the network illustrate the potential for using network analysis to provide new insights into the health care system and opportunities or mechanisms for catalyzing improvements.
DEPTH-ZERO BASE CHANGE FOR RAMIFIED U(2, 1)

We give an explicit description of L-packets and quadratic base change for depth-zero representations of ramified unitary groups in two and three variables. We show that this base change lifting is compatible with a certain lifting of families of representations of finite groups. We conjecture that such a compatibility is valid in much greater generality.
Semimartingales on rays, Walsh diffusions, and related problems of control and stopping

Abstract We introduce a class of continuous planar processes, called “semimartingales on rays”, and develop for them a change-of-variable formula involving quite general classes of test functions. Special cases of such processes are diffusions which choose, once at the origin, the rays for their subsequent voyage according to a fixed probability measure in the manner of Walsh (1978). We develop existence and uniqueness results for these “Walsh diffusions”, study their asymptotic behavior, and develop tests for explosions in finite time. We use these results to find an optimal strategy, in a problem of stochastic control with discretionary stopping involving Walsh diffusions.
Spinor pairs and the concentration principle for Dirac operators

We study perturbed Dirac operators of the form $ D_s= D + s{\cal A} :\Gamma(E)\rightarrow \Gamma(F)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps ${\cal A} : E\rightarrow F$ for $s>>0$. Under a simple algebraic criterion on the pair $(c, {\cal A})$, solutions of $D_s\psi=0$ concentrate as $s\to\infty$ around the singular set $Z_\A\subset X$ of ${\cal A}$. We give many examples, the most interesting ones arising from a general ``spinor pair'' construction.
Complexity Classes and Completeness in Algebraic Geometry

We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the NP-completeness of a sequence called the universal circuit resultant. This is the first family of compact spaces shown to be NP-complete in a geometric setting.
Partial regularity of weak solutions to a PDE system with cubic nonlinearity

Abstract In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.
Individual performance and leader's laterality in interactive contests.

ABSTRACTLeft-handedness is known to provide an intrinsic and tactical advantage at top level in many sports involving interactive contests. Again, most of the renowned leaders of the world are known to have been left-handed. Leadership plays an important role in politics, sports and mentorship. In this paper we show that Cricket captains who bat left-handed have a strategic advantage over the right-handed captains in One Day International (ODI) and Test matches. The present study involving 46 left-handed captains and 148 right-handed captains in ODI matches, reveal a strong relation between leader’s laterality and team member performance, demonstrating the critical importance of left-handedness and successful leadership. The odds for superior batting performance in an ODI match under left-handed captains are 89% higher than the odds under right-handed captains. Our study shows that left-handed captains are more successful in extracting superior performance from the batsmen and bowlers in ODI and Test matc...
Determining tournament payout structures for daily fantasy sports

With an exploding global market and the recent introduction of online cash prize tournaments, fantasy sports contests are quickly becoming a central part of the social gaming and sports industries. For sports fans and online media companies, fantasy sports contests are an opportunity for large financial gains. However, they present a host of technical challenges that arise from the complexities involved in running a web-scale, prize driven fantasy sports platform. We initiate the study of these challenges by examining one concrete problem in particular: how to algorithmically generate contest payout structures that are 1) economically motivating and appealing to contestants and 2) reasonably structured and succinctly representable. We formalize this problem and present a general two-staged approach for producing satisfying payout structures given constraints on contest size, entry fee, prize bucketing, etc. We then propose and evaluate several potential algorithms for solving the payout problem efficiently, including methods based on dynamic programming, integer programming, and heuristic techniques. Experimental results show that a carefully designed heuristic scales very well, even to contests with over 100,000 prize winners. Our approach extends beyond fantasy sports -- it is suitable for generating engaging payout structures for any contest with a large number of entrants and a large number of prize winners, including other massive online games, poker tournaments, and real-life sports tournaments.
Equivalence of Additive-Combinatorial Linear Inequalities for Shannon Entropy and Differential Entropy

This paper addresses the correspondence between linear inequalities for Shannon entropy and differential entropy for sums of independent group-valued random variables. We show that any balanced (with the sum of coefficients being zero) linear inequality for Shannon entropy holds if and only if its differential entropy counterpart also holds; moreover, any linear inequality for differential entropy must be balanced. In particular, our result shows that recently proved differential entropy inequalities by Kontoyiannis and Madiman can be deduced from their discrete counterparts due to Tao in a unified manner. Generalizations to certain abelian groups are also obtained. Our proof of extending inequalities for Shannon entropy to differential entropy relies on a result of Renyi which relates the Shannon entropy of a finely discretized random variable to its differential entropy and also helps in establishing that the entropy of the sum of quantized random variables is asymptotically equal to that of the quantized sum; the converse uses the asymptotics of the differential entropy of convolutions with weak additive noise.
The Bruss-Robertson Inequality:Elaborations, Extensions, and Applications

The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither requires the independence of the summands nor requires the equality of their marginal distributions. A review is also given of the applications of the Bruss-Robertson inequality,especially the applications to problems of combinatorial optimization such as the sequential knapsack problem and the sequential monotone subsequence selection problem.
Exact exponent in optimal rates for crowdsourcing

In many machine learning applications, crowd-sourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent mI(π) in which m is the number of workers and I(π) the average Chernoff information that characterizes the workers' collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement m > 1/I(π) log 1/e in order to achieve an e misclassification error. In addition, our results imply the optimality of various EM algorithms for crowd-sourcing initialized by consistent estimators.
Benefits of over-parameterization with EM

Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid spurious local optima in the log-likelihood. We consider the problem of estimating the mean vectors of a Gaussian mixture model in a scenario where the mixing weights are known. Our study shows that the global behavior of EM, when one uses an over-parameterized model in which the mixing weights are treated as unknown, is better than that when one uses the (correct) model with the mixing weights fixed to the known values. For symmetric Gaussians mixtures with two components, we prove that introducing the (statistically redundant) weight parameters enables EM to find the global maximizer of the log-likelihood starting from almost any initial mean parameters, whereas EM without this over-parameterization may very often fail. For other Gaussian mixtures, we provide empirical evidence that shows similar behavior. Our results corroborate the value of over-parameterization in solving non-convex optimization problems, previously observed in other domains.
Twisting functors and generalized Verma modules

Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie superalgebras, and generalize a result from \cite{CM} about twisting Verma modules.
Enriched $K$ -Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing $K$ -tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process , where the locations of the users around BSs are Gaussian distributed and 2) Matern cluster process , where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers.
The Degasperis–Procesi equation on the half-line

Abstract We analyze a class of initial-boundary value problems for the Degasperis–Procesi equation on the half-line. Assuming that the solution u ( x , t ) exists, we show that it can be recovered from its initial and boundary values via the solution of a Riemann–Hilbert problem formulated in the plane of the complex spectral parameter k .
The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit

We study the Benjamin-Ono hierarchy with positive initial data of a general type, in the limit when the dispersion parameter tends to zero. We establish simple formulae for the limits (in appropriate weak or distributional senses) of an infinite family of simultaneously conserved densities in terms of alternating sums of branches of solutions of the inviscid Burgers hierarchy.
Learning Topics Using Semantic Locality

The topic modeling discovers the latent topic probability of the given text documents. To generate the more meaningful topic that better represents the given document, we proposed a new feature extraction technique which can be used in the data preprocessing stage. The method consists of three steps. First, it generates the word/word-pair from every single document. Second, it applies a two-way TF-IDF algorithm to word/word-pair for semantic filtering. Third, it uses the K-means algorithm to merge the word pairs that have the similar semantic meaning. Experiments are carried out on the Open Movie Database (OMDb), Reuters Dataset and 20NewsGroup Dataset. The mean Average Precision score is used as the evaluation metric. Comparing our results with other state-of-the-art topic models, such as Latent Dirichlet allocation and traditional Restricted Boltzmann Machines. Our proposed data preprocessing can improve the generated topic accuracy by up to 12.99 %.
Inherent Symmetry and Microstructure Ambiguity in Micromechanics

Abstract The computational cost of micromechanics for heterogeneous materials can be reduced in certain cases where symmetric boundary conditions are applicable. We derived an eighth symmetric formulation of the Generalized Method of Cells for triply periodic microstructures. During this endeavor, an inherent symmetry was discovered. This implied that all repeating unit cells may be quarter symmetric representations of other microstructures. Additionally, it was discovered that a repeating unit cell can have columns of subcells swapped with no changes to the local or global fields. We concluded that first-order micromechanics are not well suited for capturing detailed or complex microstructures; however, higher-order theories, such as High Fidelity Generalized Method of Cells, can adequately model these microstructures.
Random matrices and the average topology of the intersection of two quadrics

Let XR be the zero locus in RP n of one or two independently and Weyl distributed random real quadratic forms. Denoting by XC the complex part in CP n of XR and by b(XR) and b(XC) the sums of their Betti numbers, we prove that: (1) lim n→∞ Eb(XR) n = 1. In particular for one quadric hypersurface asymptotically Smith’s inequality b(XR) ≤ b(XC) is expected to be sharp. The methods we use combine Random Matrix Theory, Integral Geometry and spectral sequences.
Divergence of combinatorial averages and the unboundedness of the trilinear Hilbert transform

We consider multilinear averages in ergodic theory and harmonic analysis and prove their divergence in some range of Lp spaces. This contrasts with the positive behavior exhibited by these averages in a different range, as proved in Demeter et al [Maximal multilinear operators. Trans. Amer. Math. Soc.360(9) (2008), 4989–5042]. We also prove that the trilinear Hilbert transform is unbounded in a similar range of Lp spaces. The principle underlying these constructions is stated, setting the stage for more general results.
On Classification of Modular Categories by Rank

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=5 modular categories and describe the corresponding monoidal equivalence classes.
On the complete intersection conjecture of Murthy

Abstract Suppose A = k [ X 1 , X 2 , … , X n ] is a polynomial ring over a field k and I is an ideal in A. M.P. Murthy conjectured that μ ( I ) = μ ( I / I 2 ) , where μ denotes the minimal number of generators. Recently, Fasel [3] settled this conjecture, affirmatively, when k is an infinite perfect field, with 1 / 2 ∈ k (always). We are able to do the same, when k is an infinite field. In fact, we prove similar results for ideals I in a polynomial ring A = R [ X ] , that contains a monic polynomial and R is essentially smooth algebra over an infinite field k, or R is a regular ring over a perfect field k.
Recovery of compactly supported functions from spectrogram measurements via lifting

A novel phase retrieval method, motivated by ptychographic imaging, is proposed for the approximate recovery of a compactly supported specimen function f : ℝ → ℂ from its continuous short time Fourier transform (STFT) spectrogram measurements. The method, partially inspired by the well known PhaseLift [1] algorithm, is based on a lifted formulation of the infinite dimensional problem which is then later truncated for the sake of computation. Numerical experiments demonstrate the promise of the proposed approach.
Updating Content in Cache-Aided Coded Multicast

Motivated by applications to delivery of dynamically updated, but correlated data in settings such as content distribution networks, and distributed file sharing systems, we study a single source multiple destination network coded multicast problem in a cache-aided network. We focus on models where the caches are primarily located near the destinations and the source has no cache. The source observes a sequence of correlated frames and is expected to do frame-by-frame encoding with no access to prior frames. We present a novel scheme that shows how the caches can be advantageously used to decrease the overall cost of multicast, even though the source encodes without access to past data. Our cache design and update scheme works with any choice of network code designed for a corresponding cache-less network, is largely decentralized, and works for an arbitrary network. We study a convex relation of the optimization problem that results from the overall cost function. The results of the optimization problem determine the rate allocation and caching strategies. Numerous simulation results are presented to substantiate the theory developed.
On the averaged Colmez conjecture

The Colmez conjecture, proposed by Colmez, is a conjecture expressing the Faltings height of a CM abelian variety in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture.
Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups

We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.
Ginzburg‐Landau vortex dynamics driven by an applied boundary current

In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain Ω C ℝ 2, subject to an electrical current applied on the boundary. The dynamics with an applied current are nondissipative, but via the identification of a special structure in an interaction energy, we are able to derive a precise upper bound for the energy growth. We then turn to the study of the dynamics of the vortices of the solutions in the limit e → 0. We first consider the original time scale in which the vortices do not move and the solutions undergo a "phase relaxation." Then we study an accelerated time scale in which the vortices move according to a derived dynamical law. In the dynamical law, we identify a novel Lorentz force term induced by the applied boundary current. © 2010 Wiley Periodicals, Inc.
Flexion in Abell 2744

We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing "cosmic telescope" galaxy clusters, observed as part of the Hubble Frontier Fields initiative. Using HST observations of Abell 2744 (z = 0.308), we apply a modified Analytic Image Model (AIM) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin$^{-2}$. By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43' from the cluster core. We generate two types of nonparametric reconstructions: a flexion aperture mass map, which identifies the central potential and substructure peak with mass signal-to-noise of 3.5$\sigma$ and 2.3$\sigma$ respectively; and a convergence map derived directly from the smoothed flexion field. For the primary peak we find a mass of $1.93\times10^{14}\,h^{-1}\,M_{\odot}$ within a 45" (145h$^{-1}$ kpc) aperture, and for the western substructure we find a mass of $7.12\times10^{13}\,h^{-1}\,M_{\odot}$ within a 25" (80h$^{-1}$ kpc) aperture. The associated peak velocity dispersions were determined to be $\sigma_v$ = 1630 km/s and $\sigma_v$ = 766 km/s, respectively, by fitting nonsingular isothermal sphere profiles to the flexion data. Additionally, we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure, and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions. Finally, we perform the same analysis on the Abell 2744 parallel sky field, and find no strong phantom signals in the noise reconstructions.