cssi/SciSciGPT-SciSciNet huggingface dataset:
Morphological Control in Colloidal Crystal Templating of Inverse Opals, Hierarchical Structures, and Shaped Particles†

Inverse opals or three-dimensionally ordered macroporous (3DOM) materials, prepared by colloidal crystal templating (CCT) methods, possess distinctive structural features that are important for the design of photonic crystals, sensors, power sources, catalysts, and various other applications. In the past decade, vast progress has been made in shaping these materials at various length scales. It is now possible to prepare 3DOM materials in a variety of simple and complex compositions, in which pore sizes, pore shapes, and skeletal geometries can be adjusted statically and sometimes even dynamically to alter the physical properties of the material. Hierarchical pore structures can be achieved by combining CCT with additional templating techniques. Furthermore, shaped porous nanoparticles may be synthesized using CCT methods. This review will highlight recent advances in controlling both the internal structure of inverse opals and their external morphology, enhancing compositional complexity, endowing these ...
Reactivity of hindered 1,1-dimethylbutadienes towards α,β-unsaturated enones

Abstract The reactivity of several hindered 1,1-dimethylbutadienes towards α,β-unsaturated enones were studied and compared. Computational and experimental results suggest that substituents at C-2 and C-3 of the dienes significantly effect the reactivities. A synthetic application of this reaction is also described.
Unusual degree of selectivity in diamantane derivatizations

Abstract Direct, selective functionalization of diamantane to 1- and 4-aminodiamantanes was obtained with NCl 3 /AlCl 3 . 1- and 4-diamantanethiols were prepared from their respective bromides without rearrangement.
Hydrogen bond directed highly regioselective palladium-catalyzed allylic substitution.

The palladium-catalyzed allylic substitution of 5-vinyloxazolidinones and derivatives was investigated. Unusual and high regioselectivity for the branched product was observed. The regioselectivity...
Cyclic vinylogous triflate hemiacetals as new surrogates for alkynyl aldehydes

Abstract Cyclic vinylogous triflate hemiacetals can serve as ‘synthetic equivalents’ for alkynyl aldehydes: treatment of a vinylogous triflate hemiacetal with excess amounts of Grignard reagents produces acyclic alkynyl alcohols in good to high yields. This transformation likely involves the Grob-type C–C bond cleaving fragmentation to form the alkynyl aldehyde in situ. Subsequent nucleophilic attack of the Grignard reagent furnishes secondary alkynols. Vinylogous triflate hemiacetals are easily prepared by DIBALH reduction of vinylogous acyl triflates, which are derived from cyclic 1,3-diketones.
Steric control of chemoselectivity in the reaction of ynamine esters with heterodienes

Abstract Ynamine esters undergo regioselective formal hetero-Diels-Alder reactions with α,β-unsaturated-1,3-dicarbonyl compounds yielding functionalised pyrans. The chemoselectivity of the reaction appears to be governed by steric factors.
Polynomial pass lower bounds for graph streaming algorithms

We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a weighted minimum s-t cut in an n-vertex undirected graph requires n2−o(1) space unless it makes nΩ(1) passes over the stream. To prove our lower bounds, we introduce and analyze a new four-player communication problem that we refer to as the hidden-pointer chasing problem. This is a problem in spirit of the standard pointer chasing problem with the key difference that the pointers in this problem are hidden to players and finding each one of them requires solving another communication problem, namely the set intersection problem. Our lower bounds for graph problems are then obtained by reductions from the hidden-pointer chasing problem. Our hidden-pointer chasing problem appears flexible enough to find other applications and is therefore interesting in its own right. To showcase this, we further present an interesting application of this problem beyond streaming algorithms. Using a reduction from hidden-pointer chasing, we prove that any algorithm for submodular function minimization needs to make n2−o(1) value queries to the function unless it has a polynomial degree of adaptivity.
Sensitized mutagenesis screen in Factor V Leiden mice identifies thrombosis suppressor loci

Factor V Leiden (F5L ) is a common genetic risk factor for venous thromboembolism in humans. We conducted a sensitized N-ethyl-N-nitrosourea (ENU) mutagenesis screen for dominant thrombosuppressor genes based on perinatal lethal thrombosis in mice homozygous for F5L (F5L/L ) and haploinsufficient for tissue factor pathway inhibitor (Tfpi+/- ). F8 deficiency enhanced the survival of F5L/LTfpi+/- mice, demonstrating that F5L/LTfpi+/- lethality is genetically suppressible. ENU-mutagenized F5L/L males and F5L/+Tfpi+/- females were crossed to generate 6,729 progeny, with 98 F5L/LTfpi+/- offspring surviving until weaning. Sixteen lines, referred to as "modifier of Factor 5 Leiden (MF5L1-16)," exhibited transmission of a putative thrombosuppressor to subsequent generations. Linkage analysis in MF5L6 identified a chromosome 3 locus containing the tissue factor gene (F3). Although no ENU-induced F3 mutation was identified, haploinsufficiency for F3 (F3+/- ) suppressed F5L/LTfpi+/- lethality. Whole-exome sequencing in MF5L12 identified an Actr2 gene point mutation (p.R258G) as the sole candidate. Inheritance of this variant is associated with suppression of F5L/LTfpi+/- lethality (P = 1.7 × 10-6), suggesting that Actr2p.R258G is thrombosuppressive. CRISPR/Cas9 experiments to generate an independent Actr2 knockin/knockout demonstrated that Actr2 haploinsufficiency is lethal, supporting a hypomorphic or gain-of-function mechanism of action for Actr2p.R258G Our findings identify F8 and the Tfpi/F3 axis as key regulators in determining thrombosis balance in the setting of F5L and also suggest a role for Actr2 in this process.
Discovery of potential urine-accessible metabolite biomarkers associated with muscle disease and corticosteroid response in the mdx mouse model for Duchenne.

Urine is increasingly being considered as a source of biomarker development in Duchenne Muscular Dystrophy (DMD), a severe, life-limiting disorder that affects approximately 1 in 4500 boys. In this study, we considered the mdx mice—a murine model of DMD—to discover biomarkers of disease, as well as pharmacodynamic biomarkers responsive to prednisolone, a corticosteroid commonly used to treat DMD. Longitudinal urine samples were analyzed from male age-matched mdx and wild-type mice randomized to prednisolone or vehicle control via liquid chromatography tandem mass spectrometry. A large number of metabolites (869 out of 6,334) were found to be significantly different between mdx and wild-type mice at baseline (Bonferroni-adjusted p-value < 0.05), thus being associated with disease status. These included a metabolite with m/z = 357 and creatine, which were also reported in a previous human study looking at serum. Novel observations in this study included peaks identified as biliverdin and hypusine. These four metabolites were significantly higher at baseline in the urine of mdx mice compared to wild-type, and significantly changed their levels over time after baseline. Creatine and biliverdin levels were also different between treated and control groups, but for creatine this may have been driven by an imbalance at baseline. In conclusion, our study reports a number of biomarkers, both known and novel, which may be related to either the mechanisms of muscle injury in DMD or prednisolone treatment.
The Proof of the Removable Pair Conjecture for Fractional Dimension

In 1971 Trotter (or Bogart and Trotter) conjectured that every finite poset on at least 3 points has a pair whose removal does not decrease the dimension by more than 1. In 1992 Brightwell and Scheinerman introduced fractional dimension of posets, and they made a similar conjecture for fractional dimension. This paper settles this latter conjecture.
On the average uncertainty for systems with nonlinear coupling

Abstract The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions. The Shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities. For the exponential and Gaussian distributions, we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale (i.e. at the width of the distribution). The average uncertainty is generalized via the weighted generalized mean, in which the moment is a function of the nonlinear source. Both the Renyi and Tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain. For the generalized Pareto and Student’s t-distributions, which are the maximum entropy distributions for these generalized entropies, the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale. A coupled entropy function is proposed, which is equal to the normalized Tsallis entropy divided by one plus the coupling.
Rubel's problem on bounded analytic functions

The paper shows that for any Gδ set F of Lebesgue measure zero on the unit circle T there exists a function f ∈ H∞ such that the radial limits of f exist at each point of T and vanish precisely on F . This solves a problem proposed by Rubel in 1973.
Finding Stable Matchings That Are Robust to Errors in the Input.

We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new structural question concerning the stable matching problem, namely finding relationships between the lattices of solutions of two "nearby" instances. Our main algorithmic result is the following: We identify a polynomially large class of errors, $D$, that can be introduced in a stable matching instance. Given an instance $A$ of stable matching, let $B$ be the random variable that represents the instance that results after introducing {\em one} error from $D$, chosen via a given discrete probability distribution. The problem is to find a stable matching for $A$ that maximizes the probability of being stable for $B$ as well. Via new structural properties of the type described in the question stated above, we give a combinatorial polynomial time algorithm for this problem. We also show that the set of robust stable matchings for instance $A$, under probability distribution $p$, forms a sublattice of the lattice of stable matchings for $A$. We give an efficient algorithm for finding a succinct representation for this set; this representation has the property that any member of the set can be efficiently retrieved from it.
A radial basis function method for computing Helmholtz–Hodge decompositions

A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is specified on the boundary, and one where the tangential component of the curl-free part of the field specified. These two decompositions can then be combined to obtain a full Helmholtz-Hodge decomposition of the field, i.e. the sum of divergence-free, curl-free, and harmonic fields. All decompositions are computed from samples of the field at (possibly scattered) nodes over the domain, and all boundary conditions are imposed on the vector fields, not their potentials, distinguishing this technique from many current methods. Sobolev-type error estimates for the various decompositions are provided and demonstrated with numerical examples.
Convergence of empirical distributions in an interpretation of quantum mechanics

From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the interaction of finitely many classical "worlds." The wave function is then recovered (as a secondary object) from observations of particles in these worlds, without knowing the world from which any particular observation originates. Hall, Deckert and Wiseman [Physical Review X 4 (2014) 041013] have introduced an explicit many-interacting-worlds harmonic oscillator model to provide support for this approach. In this note we provide a proof of their claim that the particle configuration is asymptotically Gaussian, thus matching the stationary ground-state solution of Schrodinger's equation when the number of worlds goes to infinity. We also construct a Markov chain based on resampling from the particle configuration and show that it converges to an Ornstein-Uhlenbeck process, matching the time-dependent solution as well.
Networked Microgrids for Improving Economics and Resiliency

In this paper, we propose networked microgrids to facilitate the integration of variable renewable generation and improve the economics and resiliency of electricity supply in microgrids. A new concept, probability of successful islanding (PSI) is used to quantify the islanding capability of a microgrid considering the uncertainty of renewable energy resources and load as well as exchanged power at PCC. With the goal of min-imizing the total operating cost while preserving user specified PSI, a chance-constrained optimization problem is formulated for the optimal scheduling of both individual microgrid and networked microgrids. Numerical simulation results show significant saving in electricity cost can be achieved by proposed networked microgrids without compromising the resiliency. The impact of correlation coefficients among the renewable generation and load of adjacent microgrids has been studied as well.
One-class slab support vector machine

This work introduces the one-class slab SVM (OCSSVM), a one-class classifier that aims at improving the performance of the one-class SVM. The proposed strategy reduces the false positive rate and increases the accuracy of detecting instances from novel classes. To this end, it uses two parallel hyperplanes to learn the normal region of the decision scores of the target class. OCSSVM extends one-class SVM since it can scale and learn non-linear decision functions via kernel methods. The experiments on two publicly available datasets show that OCSSVM can consistently outperform the one-class SVM and perform comparable to or better than other state-of-the-art one-class classifiers.
The convexity radius of a Riemannian manifold

The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.
Collaborative multi-bitrate video caching and processing in Mobile-Edge Computing networks

Recently, Mobile-Edge Computing (MEC) has arisen as an emerging paradigm that extends cloud-computing capabilities to the edge of the Radio Access Network (RAN) by deploying MEC servers right at the Base Stations (BSs). In this paper, we envision a collaborative joint caching and processing strategy for on-demand video streaming in MEC networks. Our design aims at enhancing the widely used Adaptive BitRate (ABR) streaming technology, where multiple bitrate versions of a video can be delivered so as to adapt to the heterogeneity of user capabilities and the varying of network condition. The proposed strategy faces two main challenges: (i) not only the videos but their appropriate bitrate versions have to be effectively selected to store in the caches, and (ii) the transcoding relationships among different versions need to be taken into account to effectively utilize the processing capacity at the MEC servers. To this end, we formulate the collaborative joint caching and processing problem as an Integer Linear Program (ILP) that minimizes the backhaul network cost, subject to the cache storage and processing capacity constraints. Due to the NP-completeness of the problem and the impractical overheads of the existing offline approaches, we propose a novel online algorithm that makes cache placement and video scheduling decisions upon the arrival of each new request. Extensive simulations results demonstrate the significant performance improvement of the proposed strategy over traditional approaches in terms of cache hit ratio increase, backhaul traffic and initial access delay reduction.
Collagen hydrogel confinement of amyloid-β accelerates aggregation and reduces cytotoxic effects

Alzheimer9s disease (AD) is the most common form of dementia and is associated with the accumulation of amyloid-β (A-β), a peptide whose aggregation has been associated with neurotoxicity. Drugs targeting A-β have shown great promise in 2D in vitro models and mouse models, yet preclinical and clinical trials for AD have been highly disappointing. We propose that current in vitro culture systems for discovering and developing AD drugs have significant limitations; specifically, that A-β aggregation is vastly different in these 2D cultures carried out on flat plastic or glass substrates vs. in a 3D environment, such as brain tissue, where A-β confinement very likely alters aggregation kinetics and thermodynamics. In this work, we identified attenuation of A-β cytotoxicity in 3D hydrogel culture compared to 2D cell culture. We investigated A-β structure and aggregation in solution vs. hydrogel using Transmission Electron Microscopy (TEM), Fluorescence Correlation Spectroscopy (FCS), and Thioflavin T (ThT) assays. Our results reveal that the equilibrium is shifted to stable β-sheet aggregates in hydrogels and away from the relatively unstable/unstructured presumed toxic oligomeric A-β species in solution. Volume exclusion imparted by hydrogel confinement stabilizes unfolded, presumably toxic species, promoting stable extended β-sheet fibrils. These results, taken together with the many recent reports that 3D hydrogel cell cultures enable cell morphologies and epigenetic changes that are more similar to cells in vivo compared to 2D cultures, strongly suggest that AD drugs should be tested in 3D culture systems as a step along the development pathway towards new, more effective therapeutics.
Amorphous intergranular films act as ultra-efficient point defect sinks during collision cascades

Atomistic simulations are used to explore the effect of interfacial structure on residual radiation damage. Specifically, an ordered grain boundary is compared to a disordered amorphous intergranular film, to investigate how interface thickness and free volume impacts point defect recombination. Collision cascades are simulated and residual point defect populations are analyzed as a function of boundary type and primary knock on atom energy. While ordered grain boundaries easily absorb interstitials, these interfaces are inefficient vacancy sinks. Alternatively, amorphous intergranular films act as ultra-efficient, unbiased defect sinks, providing a path for the creation of radiation-tolerant materials.
Visualizing Sensor Network Coverage with Location Uncertainty

We present an interactive visualization system for exploring the coverage in sensor networks with uncertain sensor locations. We consider a simple case of uncertainty where the location of each sensor is confined to a discrete number of points sampled uniformly at random from a region with a fixed radius. Employing techniques from topological data analysis, we model and visualize network coverage by quantifying the uncertainty defined on its simplicial complex representations. We demonstrate the capabilities and effectiveness of our tool via the exploration of randomly distributed sensor networks.
Uniform asymptotics for kernel density estimators with variable bandwidths

It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), ‘Improved Variable Window Kernel Estimates of Probability Densities’, Annals of Statistics, 23, 1–10] modification of Abramson's [Abramson, I. (1982), ‘On Bandwidth Variation in Kernel Estimates – A Square-root Law’, Annals of Statistics, 10, 1217–1223] variable bandwidth kernel density estimator satisfies the optimal asymptotic properties for estimating densities with four uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero.
The arithmetic Kuznetsov formula on GL(3), I: The Whittaker case

The original formulae of Kuznetsov for SL(2, Z) allowed one to study either a spectral average via Kloosterman sums or to study an average of Kloosterman sums via a spectral interpretation. In previous papers, we have developed the spectral Kuznetsov formulae at the minimal weights for SL(3, Z), and in these formulae, the big-cell Kloosterman sums occur with weight functions attached to four different integral kernels, according to the choice of signs of the indices. These correspond to the J- and K-Bessel functions in the case of GL(2). In this paper, we demonstrate a linear combination of the spherical and weight-one SL(3, Z) Kuznetsov formulae that isolates one particular integral kernel, which is the spherical GL(3) Whittaker function. Using the known inversion formula of Wallach, we give the first arithmetic Kuznetsov formula for SL(3, Z) and use it to study smooth averages and the Kloosterman zeta function attached to this particular choice of signs.
The singular values of the GUE (less is more)

Some properties that nominally involve the eigenvalues of the Gaussian Unitary Ensemble (GUE) can instead be phrased in terms of singular values. By discarding the signs of the eigenvalues, we gain access to a surprising decomposition: the singular values of the GUE are distributed as the union of the singular values of two independent ensembles of Laguerre type. This independence is remarkable given the well-known phenomenon of eigenvalue repulsion. The structure of this decomposition reveals that several existing observations about large n limits of the GUE are in fact manifestations of phenomena that are already present for finite random matrices. We relate the semicircle law to the quarter-circle law by connecting Hermite polynomials to generalized Laguerre polynomials with parameter ± 1/2. Similarly, we write the absolute value of the determinant of the n × n GUE as a product n independent random variables to gain new insight into its asymptotic log-normality. The decomposition also provides a description of the distribution of the smallest singular value of the GUE, which in turn permits the study of the leading order behavior of the condition number of GUE matrices. The study is motivated by questions involving the enumeration of orientable maps, and is related to questions involving powers of complex Ginibre matrices. The inescapable conclusion of this work is that the singular values of the GUE play an unpredictably important role that had gone unnoticed for decades even though, in hindsight, so many clues had been around.
Coverage and field estimation on bounded domains by diffusive swarms

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.
Sockpuppet Detection in Wikipedia: A Corpus of Real-World Deceptive Writing for Linking Identities

This paper describes a corpus of sockpuppet cases from Wikipedia. A sockpuppet is an online user account created with a fake identity for the purpose of covering abusive behavior and/or subverting the editing regulation process. We used a semi-automated method for crawling and curating a dataset of real sockpuppet investigation cases. To the best of our knowledge, this is the first corpus available on real-world deceptive writing. We describe the process for crawling the data and some preliminary results that can be used as baseline for benchmarking research. The dataset has been released under a Creative Commons license from our project website (http://docsig.cis.uab.edu/tools-and-datasets/).
A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models

Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large $K$) under a high-dimensional (large $p$) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult non-smooth optimizations. We propose a novel approach, FASJEM for \underline{fa}st and \underline{s}calable \underline{j}oint structure-\underline{e}stimation of \underline{m}ultiple sGGMs at a large scale. As the first study of joint sGGM using the Elementary Estimator framework, our work has three major contributions: (1) We solve FASJEM through an entry-wise manner which is parallelizable. (2) We choose a proximal algorithm to optimize FASJEM. This improves the computational efficiency from $O(Kp^3)$ to $O(Kp^2)$ and reduces the memory requirement from $O(Kp^2)$ to $O(K)$. (3) We theoretically prove that FASJEM achieves a consistent estimation with a convergence rate of $O(\log(Kp)/n_{tot})$. On several synthetic and four real-world datasets, FASJEM shows significant improvements over baselines on accuracy, computational complexity, and memory costs.
Intelligent Environments Based on Ultra-massive Mimo Platforms for Wireless Communication in Millimeter Wave and Terahertz Bands

Millimeter-wave (30-300 GHz) and Terahertz-band communications (0.3-10 THz) are envisioned as key wireless technologies to satisfy the demand for Terabit-per-second (Tbps) links in the 5G and beyond eras. The very large available bandwidth in this ultra-broadband frequency range comes at the cost of a very high propagation loss, which combined with the low power of mm-wave and THz-band transceivers limits the communication distance and data-rates. In this paper, the concept of intelligent communication environments enabled by Ultra-Massive MIMO platforms is proposed to increase the communication distance and data-rates at mm-wave and THz-band frequencies. An end-to-end physical model is developed by taking into account the capabilities of novel intelligent plasmonic antenna arrays which can operate in transmission, reception, reflection and waveguiding, as well as the peculiarities of the mm-wave and THz-band multi-path channel. Based on the developed model, extensive quantitative results for different scenarios are provided to illustrate the performance improvements in terms of both achievable distance and data-rate in Ultra-Massive MIMO environments.
Defining Equitable Geographic Districts in Road Networks via Stable Matching

We introduce a novel method for defining geographic districts in road networks using stable matching. In this approach, each geographic district is defined in terms of a center, which identifies a location of interest, such as a post office or polling place, and all other network vertices must be labeled with the center to which they are associated. We focus on defining geographic districts that are equitable, in that every district has the same number of vertices and the assignment is stable in terms of geographic distance. That is, there is no unassigned vertex-center pair such that both would prefer each other over their current assignments. We solve this problem using a version of the classic stable matching problem, called symmetric stable matching, in which the preferences of the elements in both sets obey a certain symmetry. We show that, for a planar graph or road network with n nodes and k centers, the problem can be solved in O(n √ n log n) time, which improves upon the O(nk) runtime of using the classic Gale--Shapley stable matching algorithm when k is large. Finally, we provide experimental results on road networks for these algorithms and a heuristic algorithm that performs better than the Gale--Shapley algorithm for any range of values of k.
The Asymptotic Distribution of The Pathwise Mean Squared Displacement in Single Particle Tracking Experiments

Microrheology is the study of the properties of biological complex fluids through the anomalous diffusion of small embedded particles. The main statistic for characterizing anomalous diffusion is the so-named mean squared displacement (MSD) of the particles. Notwithstanding the central statistical role of the MSD, its asymptotic distribution has not yet been established. In this paper, we assume that the particle motion is a Gaussian, stationary-increment stochastic process. We show that as the sample and the increment lag sizes go to infinity, the MSD displays Gaussian or non-Gaussian limiting distributions, as well as distinct convergence rates, depending on the diffusion exponent parameter.
Empirical Reference Distributions for Networks of Different Size.

Abstract Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features, across multiple networks that differ in size. Although “normalized” versions of some network statistics exist, we demonstrate via simulation why direct comparison is often inappropriate. We consider normalizing network statistics relative to a simple fully parameterized reference distribution and demonstrate via simulation how this is an improvement over direct comparison, but still sometimes problematic. We propose a new adjustment method based on a reference distribution constructed as a mixture model of random graphs which reflect the dependence structure exhibited in the observed networks. We show that using simple Bernoulli models as mixture components in this reference distribution can provide adjusted network statistics that are relatively comparable across different network sizes but still describe interesting features of networks, and that this can be accomplished at relatively low computational expense. Finally, we apply this methodology to a collection of ecological networks derived from the Los Angeles Family and Neighborhood Survey activity location data.
Optimal parameter identification for discrete mechanical systems with application to flexible object manipulation

We present a method for system identification of flexible objects by measuring forces and displacement during interaction with a manipulating arm. We model the object's structure and flexibility by a chain of rigid bodies connected by torsional springs. Unlike previous work, the proposed optimal control approach using variational integrators allows identification of closed loops, which include the robot arm itself. This allows using the resulting models for planning in configuration space of the robot. In order to solve the resulting problem efficiently, we develop a novel method for fast discrete-time adjoint-based gradient calculation. The feasibility of the approach is demonstrated using full physics simulation in trep and using data recorded from a 7-DOF series elastic robot arm.
A distributed-memory hierarchical solver for general sparse linear systems

Abstract We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We present various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
On the construction of unbiased estimators for the group testing problem

Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential binomial sampling. Previous research, however, has focused heavily on the simple case where no misclassification is assumed and only one trait is to be tested. In this paper, we consider the problem of unbiased estimation in these broader areas, giving constructions of such estimators for several cases. We show that, outside of the standard case addressed previously in the literature, it is impossible to find any proper unbiased estimator, that is, an estimator giving only values in the parameter space. This is shown to hold generally under any binomial or multinomial sampling plans.
Analytic cohomology groups of infinite dimensional complex manifolds

Abstract Given a cohesive sheaf S over a complex Banach manifold M, we endow the cohomology groups H q ( M , S ) of M and H q ( U , S ) of open covers U of M with a locally convex topology. Under certain assumptions we prove that the canonical map H q ( U , S ) → H q ( M , S ) is an isomorphism of topological vector spaces.
Finite index theorems for iterated Galois groups of cubic polynomials

Let K be a number field or a function field. Let $$f\in K(x)$$ be a rational function of degree $$d\ge 2$$ , and let $$\beta \in {\mathbb {P}}^1(\overline{K})$$ . For all $$n\in \mathbb {N}\cup \{\infty \}$$ , the Galois groups $$G_n(\beta )={{\mathrm{Gal}}}(K(f^{-n}(\beta ))/K(\beta ))$$ embed into $${{\mathrm{Aut}}}(T_n)$$ , the automorphism group of the d-ary rooted tree of level n. A major problem in arithmetic dynamics is the arboreal finite index problem: determining when $$[{{\mathrm{Aut}}}(T_\infty ):G_\infty (\beta )]<\infty $$ . When f is a cubic polynomial and K is a function field of transcendence degree 1 over an algebraic extension of $${\mathbb {Q}}$$ , we resolve this problem by proving a list of necessary and sufficient conditions for finite index. This is the first result that gives necessary and sufficient conditions for finite index, and can be seen as a dynamical analog of the Serre Open Image Theorem. When K is a number field, our proof is conditional on both the abc conjecture for K and Vojta’s conjecture for blowups of $${\mathbb {P}}^1 \times {\mathbb {P}}^1$$ . We also use our approach to solve some natural variants of the finite index problem for modified trees.
Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds

Abstract The main results of this article provide asymptotics at infinity of the Green's functions near and at the spectral gap edges for “generic” periodic second-order, self-adjoint, elliptic operators on noncompact Riemannian co-compact coverings with abelian deck groups. Previously, analogous results have been known for the case of R n only. One of the interesting features discovered is that the rank of the deck group plays more important role than the dimension of the manifold.
Generalized Euler classes, differential forms and commutative DGAs

In the context of commutative differential graded algebras over ℚ, we show that an iteration of “odd spherical fibration” creates a “total space” commutative differential graded algebra with only o...
Triangle singularities and XYZ quarkonium peaks

We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. We show that this effect only occurs if masses of resonances in the crossed channel are in a specific, narrow range. We estimate the size of threshold enhancements originating from these anomalous singularities in reactions where the Zc(3900) and the Zb(10610) peaks have been observed.
Bloom Filters, Adaptivity, and the Dictionary Problem

An approximate membership query data structure (AMQ)—such as a Bloom, quotient, or cuckoo filter—maintains a compact, probabilistic representation of a set S of keys from a universe U. It supports lookups and inserts. Some AMQs also support deletes. A query for x in S returns "present." A query for x not in S returns "present" with a tunable false positive probability epsilon, and otherwise returns "absent." AMQs are widely used to speed up dictionaries that are stored remotely (e.g., on disk or across a network). The AMQ is stored locally (e.g., in memory). The remote dictionary is only accessed when the AMQ returns "present." Thus, the primary performance metric of an AMQ is how often it returns "absent" for negative queries. Existing AMQs offer weak guarantees on the number of false positives in a sequence of queries. The false-positive probability epsilon holds only for a single query. It is easy for an adversary to drive an AMQ's false-positive rate towards 1 by simply repeating false positives. This paper shows what it takes to get strong guarantees on the number of false positives. We say that an AMQ is adaptive if it guarantees a false-positive probability of epsilon for every query, regardless of answers to previous queries. We establish upper and lower bounds for adaptive AMQs. Our lower bound shows that it is impossible to build a small adaptive AMQ, even when the AMQ is immediately told whenever a query is a false positive. On the other hand, we show that it is possible to maintain an AMQ that uses the same amount of local space as a non-adaptive AMQ (up to lower order terms), performs all queries and updates in constant time, and guarantees that each negative query to the dictionary accesses remote storage with probability epsilon, independent of the results of past queries. Thus, we show that adaptivity can be achieved effectively for free.
A note on nearly platonic graphs

A nearly platonic graph is a k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for a finite graph to have exactly one disparate face, and offer some conjectures, including the conjecture that graphs with two disparate faces come in a small set of families.
Zero-density estimate for modular form $L$-functions in weight aspect

Considering the family of $L$-functions $\{L(s,f)\}_{f \in H_k}$ where $H_k$ is the set of weight $k$ Hecke-eigen cusp forms for $SL_2(\mathbb{Z})$, we prove a zero density estimate near the central point, valid as the weight $k \to \infty$. This is an ingredient in the author's related paper, which gives an unconditional upper bound on the distribution of the central values.
Exploiting an oracle that reports AUC scores in machine learning contests

In machine learning contests such as the ImageNet Large Scale Visual Recognition Challenge (Russakovsky et al. 2015) and the KDD Cup, contestants can submit candidate solutions and receive from an oracle (typically the organizers of the competition) the accuracy of their guesses compared to the ground-truth labels. One of the most commonly used accuracy metrics for binary classification tasks is the Area Under the Receiver Operating Characteristics Curve (AUC). In this paper we provide proofs-of-concept of how knowledge of the AUC of a set of guesses can be used, in two different kinds of attacks, to improve the accuracy of those guesses. On the other hand, we also demonstrate the intractability of one kind of AUC exploit by proving that the number of possible binary labelings of n examples for which a candidate solution obtains a AUC score of c grows exponentially in n, for every c ∈ (0, 1).
Covering numbers for bounded variation functions

Abstract In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to L 1 -distance.
On Chatbots Exhibiting Goal-Directed Autonomy in Dynamic Environments.

Conversation interfaces (CIs), or chatbots, are a popular form of intelligent agents that engage humans in task-oriented or informal conversation. In this position paper and demonstration, we argue that chatbots working in dynamic environments, like with sensor data, can not only serve as a promising platform to research issues at the intersection of learning, reasoning, representation and execution for goal-directed autonomy; but also handle non-trivial business applications. We explore the underlying issues in the context of Water Advisor, a preliminary multi-modal conversation system that can access and explain water quality data.
Covers of stacky curves and limits of plane quintics

We construct a well-behaved compactification of the space of finite covers of a stacky curve using admissible cover degenerations. Using our construction, we compactify the space of tetragonal curves on Hirzebruch surfaces. As an application, we explicitly describe the boundary divisors of the closure inM6 of the locus of smooth plane quintic curves.
A sufficient condition for a rational differential operator to generate an integrable system

For a rational differential operator \({L=AB^{-1}}\), the Lenard–Magri scheme of integrability is a sequence of functions \({F_n, n \geq 0}\), such that (1) \({B(F_{n+1})=A(F_n)}\) for all \({n \geq 0}\) and (2) the functions \({B(F_n)}\) pairwise commute. We show that, assuming that property (1) holds and that the set of differential orders of \({B(F_n)}\) is unbounded, property (2) holds if and only if L belongs to a class of rational operators that we call integrable. If we assume moreover that the rational operator L is weakly non-local and preserves a certain splitting of the algebra of functions into even and odd parts, we show that one can always find such a sequence (Fn) starting from any function in Ker B. This result gives some insight in the mechanism of recursion operators, which encode the hierarchies of the corresponding integrable equations.
On the Vanishing Ranges for the Cohomology of Finite Groups of Lie Type

Abstract. The computation of the cohomology for ﬁnite groups of Lie type in the describing characteristicis a challenging and diﬃcult problem. In [BNP], the authors constructed an induction functor which takesmodules over the ﬁnite group of Lie type, G(F q ), to modules for the ambient algebraic group G. In particularthis functor when applied to the trivial module yields a natural G-ﬁltration. This ﬁltration was utilized in[BNP] to determine the ﬁrst non-trivial cohomology class when the underlying root system is of type A n orC n . In this paper the authors extend these results toward locating the ﬁrst non-trivial cohomology classesfor the remaining ﬁnite groups of Lie type (i.e., the underlying root system is of type B n , C n , D n , E 6 , E 7 ,E 8 , F 4 , and G 2 ) when the prime is larger than the Coxeter number. 1. Introduction1.1. Let Gbe a simple algebraic group scheme over a ﬁeld kof prime characteristic pwhich is deﬁnedand split over the prime ﬁeld F p , and F : G→ Gdenote the Frobenius map. The ﬁxed points of therth iterate of the Frobenius map, denoted G(F
Optimal cooperative inference

Cooperative transmission of data fosters rapid accumulation of knowledge by efficiently combining experiences across learners. Although well studied in human learning and increasingly in machine learning, we lack formal frameworks through which we may reason about the benefits and limitations of cooperative inference. We present such a framework. We introduce novel indices for measuring the effectiveness of probabilistic and cooperative information transmission. We relate our indices to the well-known Teaching Dimension in deterministic settings. We prove conditions under which optimal cooperative inference can be achieved, including a representation theorem that constrains the form of inductive biases for learners optimized for cooperative inference. We conclude by demonstrating how these principles may inform the design of machine learning algorithms and discuss implications for human and machine learning.
Homological Stability For The Moduli Spaces of Products of Spheres

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p 4$, with respect to forming connected sums with $S^{n}\times S^{n}$.
Composition operators on noncommutative Hardy spaces

Abstract In this paper we initiate the study of composition operators on the noncommutative Hardy space H ball 2 , which is the Hilbert space of all free holomorphic functions of the form f ( X 1 , … , X n ) = ∑ k = 0 ∞ ∑ | α | = k a α X α , ∑ α ∈ F n + | a α | 2 1 , where the convergence is in the operator norm topology for all ( X 1 , … , X n ) in the noncommutative operatorial ball [ B ( H ) n ] 1 and B ( H ) is the algebra of all bounded linear operators on a Hilbert space H . When the symbol φ is a free holomorphic self-map of [ B ( H ) n ] 1 , we show that the composition operator C φ f : = f ∘ φ , f ∈ H ball 2 , is bounded on H ball 2 . Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness, similarity) have free analogues in our noncommutative multivariable setting. The most prominent feature of this paper is the interaction between the noncommutative analytic function theory in the unit ball of B ( H ) n , the operator algebras generated by the left creation operators on the full Fock space with n generators, and the classical complex function theory in the unit ball of C n . In a more general setting, we establish basic properties concerning the composition operators acting on Fock spaces associated with noncommutative varieties V P 0 ( H ) ⊆ [ B ( H ) n ] 1 generated by sets P 0 of noncommutative polynomials in n indeterminates such that p ( 0 ) = 0 , p ∈ P 0 . In particular, when P 0 consists of the commutators X i X j − X j X i for i , j = 1 , … , n , we show that many of our results have commutative counterparts for composition operators on the symmetric Fock space and, consequently, on spaces of analytic functions in the unit ball of C n .