cssi/SciSciGPT-SciSciNet huggingface dataset:
Histogram Sort with Sampling

To minimize data movement, state-of-the-art parallel sorting algorithms use techniques based on sampling and histogramming to partition keys prior to redistribution. Sampling enables partitioning to be done using a representative subset of the keys, while histogramming enables evaluation and iterative improvement of a given partition. We introduce Histogram sort with sampling (HSS), which combines sampling and iterative histogramming to find high quality partitions with minimal data movement and high practical performance. Compared to the best known (recently introduced) algorithm for finding these partitions, our algorithm requires a factor of O(log(p)/ log log(p)) less communication, and substantially less when compared to standard variants of Sample sort and Histogram sort. We provide a distributed memory implementation of the proposed algorithm, compare its performance to two existing implementations, and provide a brief application study showing benefit of the new algorithm.
PRACTICAL NUMBERS AND THE DISTRIBUTION OF DIVISORS

An integer $n$ is called practical if every $m\le n$ can be written as a sum of distinct divisors of $n$. We show that the number of practical numbers below $x$ is asymptotic to $c x/\log x$, as conjectured by Margenstern. We also give an asymptotic estimate for the number of integers below $x$ whose maximum ratio of consecutive divisors is at most $t$, valid uniformly for $t\ge 2$.
Commutators from a hyperplane of matrices

Denote by Mn(K) the algebra of n by n matrices with entries in the field K. A theorem of Albert and Muckenhoupt states that every trace zero matrix of Mn(K) can be expressed as AB − BA for some pair (A, B) ∈ Mn(K)2 . Assuming that n > 2 and that K has more than 3 elements, it is proved that the matrices A and B can be required to belong to an arbitrary given hyperplane of Mn(K).
Gibbs Measures on Mutually Interacting Brownian Paths under Singularities

We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in ℝd interacting through a mutual self-attraction. This is expressed by the Hamiltonian ∬ℝ2dV(x−y)μ(dx)ν(dy) with two probability measures μ and ν representing the occupation measures of two independent Brownian motions. We will be interested in a class of potentials V that are singular, e.g., Dirac- or Coulomb-type interactions in ℝ3, or the correlation function of the parabolic Anderson problem with white noise potential. The mutual interaction of the Brownian paths inspires a compactification of the quotient space of orbits of product measures, which is structurally different from the self-interacting case introduced in [27], owing to the lack of shift-invariant structure in the mutual interaction. We prove a strong large-deviation principle for the product measures of two Brownian occupation measures in such a compactification and derive asymptotic path behavior under Gibbs measures on Wiener paths arising from mutually attracting singular interactions. For the spatially smoothened parabolic Anderson model with white noise potential, our analysis allows a direct computation of the annealed Lyapunov exponents, and a strict ordering of them implies the intermittency effect present in the smoothened model. © 2017 Wiley Periodicals, Inc.
Polynomials Defined by Tableaux and Linear Recurrences

We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials , (also known as Demazure characters), and Demazure atoms . The same technique can be applied to Hall-Littlewood polynomials and dual Grothendieck polynomials. The motivation behind this is that such recurrences are strongly connected with other nice properties, such as interpretations in terms of lattice points in polytopes and divided difference operators.
High-Resolution, Three-Dimensional Reconstruction of the Outflow Tract Demonstrates Segmental Differences in Cleared Eyes.

Purpose The rate of conventional aqueous humor outflow is the highest nasally. We hypothesized that this is reflected in regionally different outflow structures and analyzed the entire limbus by high-resolution, full-thickness ribbon-scanning confocal microscopy (RSCM). Methods We perfused pig eyes by anterior chamber cannulation with eight lectin-fluorophore conjugates, followed by optical clearance with benzyl alcohol benzyl benzoate (BABB). RSCM and advanced analysis software (Imaris) were used to reconstruct a three-dimensional (3D), whole-specimen rendering of the perilimbal outflow structures. We performed morphometric analyses of the outflow tract from the level of the trabecular meshwork (TM) to the scleral vascular plexus (SVP). Results Except for pigmented structures, BABB cleared the entire eye. Rhodamine-conjugated Glycine max agglutinin (soybean [SBA]) labeled the outflow tract evenly and retained fluorescence for months. RSCM produced terabyte-sized files allowing for in silico dissection of outflow tract vessels at a high resolution and in 3D. Networks of interconnected lumens were traced from the TM to downstream drainage structures. The collector channel (CC) volumes were 10 times smaller than the receiving SVP vessels, the largest of which were in the inferior limbus. Proximal CC diameters were up to four times the size of distal diameters and more elliptical at their proximal ends. The largest CCs were found in the superonasal and inferonasal quadrants where the highest outflow occurs. Conclusion RSCM of cleared eyes enabled high-resolution, volumetric analysis of the outflow tract. The proximal structures had greater diameters nasally, whereas the SVP was larger in the inferior limbus.
A loop group extension of the odd Chern character

Abstract We show that the universal odd Chern form, defined on the stable unitary group U , extends to the loop group L U as an equivariantly closed differential form. This provides an odd analogue to the Bismut–Chern form that appears in supersymmetric field theories. We also describe the associated transgression form, the so-called Bismut–Chern–Simons form, and explicate some properties it inherits as a differential form on the space of maps of a cylinder into the stable unitary group. As one corollary, we show that in a precise sense the spectral flow of a loop of self adjoint Fredholm operators equals the lowest degree component of the Bismut–Chern–Simons form, and the latter, when restricted to cylinders which are tori, is an equivariantly closed extension of spectral flow. As another corollary, we construct the Chern character homomorphism from odd K -theory to the periodic cohomology of the free loop space, represented geometrically on the level of differential forms.
celsr1a is essential for tissue homeostasis and onset of aging phenotypes in the zebrafish

The use of genetics has been invaluable in defining the complex mechanisms of aging and longevity. Zebrafish, while a prominent model for vertebrate development, have not been used systematically to address questions of how and why we age. In a mutagenesis screen focusing on late developmental phenotypes, we identified a new mutant that displays aging phenotypes at young adult stages. We find that the phenotypes are due to loss-of-function in the non-classical cadherin celsr1a. The premature aging is not associated with increased cellular senescence or telomere length but is a result of a failure to maintain progenitor cell populations. We show that celsr1a is essential for maintenance of stem cell progenitors in late stages. Caloric restriction can ameliorate celsr1a aging phenotypes. These data suggest that celsr1a function helps to mediate stem cell maintenance during maturation and homeostasis of tissues and thus regulates the onset or expressivity of aging phenotypes.
Tractable structure learning in radial physical flow networks

Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such networks, the flow on each edge is characterized by a function of the nodal potentials on either side of the edge. Further the net flow in and out of each node is conserved. Learning the structure and state of physical networks is necessary for optimal control as well as to quantify its privacy needs. We consider radial flow networks and study the problem of learning the operational network from a loopy graph of candidate edges using statistics of nodal potentials. Based on the monotonic properties of the flow functions, the key result in this paper shows that if variance of the difference of nodal potentials is used to weight candidate edges, the operational edges form the minimum spanning tree in the loopy graph. Under realistic conditions on the statistics of nodal injection (consumption or production), we provide a greedy structure learning algorithm with quasilinear computational complexity in the number of candidate edges in the network. Our learning framework is very general due to two significant attributes. First it is independent of the specific marginal distributions of nodal potentials and only uses order properties in their second moments. Second, the learning algorithm is agnostic to exact flow functions that relate edge flows to corresponding potential differences and is applicable for a broad class of networks with monotonic flow functions. We demonstrate the efficacy of our work through realistic simulations on diverse physical flow networks and discuss possible extensions of our work to other regimes.
Noncommutative homological projective duality

Abstract We generalize Kuznetsov's theory of homological projective duality to the setting of noncommutative algebraic geometry. Simultaneously, we develop the theory over general base schemes, and remove the usual smoothness, properness, and transversality hypotheses.
The critical group of the Kneser graph on 2-subsets of an n-element set

Abstract In this paper we compute the critical group of the Kneser graph K G ( n , 2 ) . This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph.
Sharp frequency bounds for eigenfunctions of the Ornstein–Uhlenbeck operator

We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein–Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.
Topic Independent Identification of Agreement and Disagreement in Social Media Dialogue

Research on the structure of dialogue has been hampered for years because large dialogue corpora have not been available. This has impacted the dialogue research community’s ability to develop better theories, as well as good off-the-shelf tools for dialogue processing. Happily, an increasing amount of information and opinion exchange occur in natural dialogue in online forums, where people share their opinions about a vast range of topics. In particular we are interested in rejection in dialogue, also called disagreement and denial, where the size of available dialogue corpora, for the first time, offers an opportunity to empirically test theoretical accounts of the expression and inference of rejection in dialogue. In this paper, we test whether topic-independent features motivated by theoretical predictions can be used to recognize rejection in online forums in a topic-independent way. Our results show that our theoretically motivated features achieve 66% accuracy, an improvement over a unigram baseline of an absolute 6%.
Convolutional Dictionary Learning through Tensor Factorization

Author(s): Huang, Furong; Anandkumar, Animashree | Abstract: Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional invariances such as shift invariances exist, enforced via models such as convolutional dictionary learning. In this paper, we develop novel tensor decomposition algorithms for parameter estimation of convolutional models. Our algorithm is based on the popular alternating least squares method, but with efficient projections onto the space of stacked circulant matrices. Our method is embarrassingly parallel and consists of simple operations such as fast Fourier transforms and matrix multiplications. Our algorithm converges to the dictionary much faster and more accurately compared to the alternating minimization over filters and activation maps.
Convergence Rate of Stochastic k-means

We analyze online and mini-batch k-means variants. Both scale up the widely used Lloyd 's algorithm via stochastic approximation, and have become popular for large-scale clustering and unsupervised feature learning. We show, for the first time, that they have global convergence towards local optima at $O(\frac{1}{t})$ rate under general conditions. In addition, we show if the dataset is clusterable, with suitable initialization, mini-batch k-means converges to an optimal k-means solution with $O(\frac{1}{t})$ convergence rate with high probability. The k-means objective is non-convex and non-differentiable: we exploit ideas from non-convex gradient-based optimization by providing a novel characterization of the trajectory of k-means algorithm on its solution space, and circumvent its non-differentiability via geometric insights about k-means update.
Calibrate: Frequency Estimation and Heavy Hitter Identification with Local Differential Privacy via Incorporating Prior Knowledge

Estimating frequencies of certain items among a population is a basic step in data analytics, which enables more advanced data analytics (e.g., heavy hitter identification, frequent pattern mining), client software optimization, and detecting unwanted or malicious hijacking of user settings in browsers. Frequency estimation and heavy hitter identification with local differential privacy (LDP) protect user privacy as well as the data collector. Existing LDP algorithms cannot leverage 1) prior knowledge about the noise in the estimated item frequencies and 2) prior knowledge about the true item frequencies. As a result, they achieve suboptimal performance in practice. In this work, we aim to design LDP algorithms that can leverage such prior knowledge. Specifically, we design Calibrate to incorporate the prior knowledge via statistical inference. Calibrate can be appended to an existing LDP algorithm to reduce its estimation errors. We model the prior knowledge about the noise and the true item frequencies as two probability distributions, respectively. Given the two probability distributions and an estimated frequency of an item produced by an existing LDP algorithm, our Calibrate computes the conditional probability distribution of the item’s frequency and uses the mean of the conditional probability distribution as the calibrated frequency for the item. It is challenging to estimate the two probability distributions due to data sparsity. We address the challenge via integrating techniques from statistics and machine learning. Our empirical results on two real-world datasets show that Calibrate significantly outperforms state-of-the-art LDP algorithms for frequency estimation and heavy hitter identification.
Modeling Individual Cyclic Variation in Human Behavior

Cycles are fundamental to human health and behavior. Examples include mood cycles, circadian rhythms, and the menstrual cycle. However, modeling cycles in time series data is challenging because in most cases the cycles are not labeled or directly observed and need to be inferred from multidimensional measurements taken over time. Here, we present Cyclic Hidden Markov Models (CyHMMs) for detecting and modeling cycles in a collection of multidimensional heterogeneous time series data. In contrast to previous cycle modeling methods, CyHMMs deal with a number of challenges encountered in modeling real-world cycles: they can model multivariate data with both discrete and continuous dimensions; they explicitly model and are robust to missing data; and they can share information across individuals to accommodate variation both within and between individual time series. Experiments on synthetic and real-world health-tracking data demonstrate that CyHMMs infer cycle lengths more accurately than existing methods, with 58% lower error on simulated data and 63% lower error on real-world data compared to the best-performing baseline. CyHMMs can also perform functions which baselines cannot: they can model the progression of individual features/symptoms over the course of the cycle, identify the most variable features, and cluster individual time series into groups with distinct characteristics. Applying CyHMMs to two real-world health-tracking datasets -- of human menstrual cycle symptoms and physical activity tracking data -- yields important insights including which symptoms to expect at each point during the cycle. We also find that people fall into several groups with distinct cycle patterns, and that these groups differ along dimensions not provided to the model. For example, by modeling missing data in the menstrual cycles dataset, we are able to discover a medically relevant group of birth control users even though information on birth control is not given to the model.
RACK SHADOWS AND THEIR INVARIANTS

A rack shadow or rack set is a set X with a rack action by a rack R, analogous to a vector space over a field. We use shadow colorings of classical link diagrams to define enhanced rack counting invariants and show that the enhanced invariants are stronger than unenhanced counting invariants.
Interception in distance-vector routing networks

Despite the large effort devoted to cybersecurity research over the last decades, cyber intrusions and attacks are still increasing. With respect to routing networks, route hijacking has highlighted the need to reexamine the existing protocols that govern traffic routing. In particular, our pri- mary question is how the topology of a network affects the susceptibility of a routing protocol to endogenous route misdirection. In this paper we define and analyze an abstract model of traffic interception (i.e. eavesdropping) in distance-vector routing networks. Specifically, we study al- gorithms that measure the potential of groups of dishonest agents to divert traffic through their infrastructure under the constraint that messages must reach their intended destinations. We relate two variants of our model based on the allowed kinds of lies, define strategies for colluding agents, and prove optimality in special cases. In our main theorem we derive a provably optimal monitoring strategy for subsets of agents in which no two are adjacent, and we extend this strategy to the general case. Finally, we use our results to analyze the susceptibility of real and synthetic networks to endogenous traffic interception. In the Autonomous Systems (AS) graph of the United States, we show that compromising only 18 random nodes in the AS graph surprisingly captures 10% of all traffic paths in the network in expectation when a distance-vector routing protocol is in use.
Selection Problems in the Presence of Implicit Bias

Over the past two decades, the notion of implicit bias has come to serve as an important com- ponent in our understanding of bias and discrimination in activities such as hiring, promotion, and school admissions. Research on implicit bias posits that when people evaluate others - for example, in a hiring context - their unconscious biases about membership in particular demo- graphic groups can have an effect on their decision-making, even when they have no deliberate intention to discriminate against members of these groups. A growing body of experimental work has demonstrated the effect that implicit bias can have in producing adverse outcomes. Here we propose a theoretical model for studying the effects of implicit bias on selection decisions, and a way of analyzing possible procedural remedies for implicit bias within this model. A canonical situation represented by our model is a hiring setting, in which recruiters are trying to evaluate the future potential of job applicants, but their estimates of potential are skewed by an unconscious bias against members of one group. In this model, we show that measures such as the Rooney Rule, a requirement that at least one member of an underrepresented group be selected, can not only improve the representation of the affected group, but also lead to higher payoffs in absolute terms for the organization performing the recruiting. However, identifying the conditions under which such measures can lead to improved payoffs involves subtle trade- offs between the extent of the bias and the underlying distribution of applicant characteristics, leading to novel theoretical questions about order statistics in the presence of probabilistic side information.
Equilibrium states in dynamical systems via geometric measure theory

Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds. We extend this geometric construction to the substantially broader class of equilibrium states corresponding to Holder continuous potentials; these states arise naturally in statistical physics and play a crucial role in studying stochastic behavior of dynamical systems. The key step in our construction is to replace leaf volume with a reference measure that is obtained from a Caratheodory dimension structure via an analogue of the construction of Hausdorff measure. In particular, we give a new proof of existence and uniqueness of equilibrium states that does not use standard techniques based on Markov partitions or the specification property; our approach can be applied to systems that do not have Markov partitions and do not satisfy the specification property.
Low energy properties of the random displacement model

Abstract We study low-energy properties of the random displacement model, a random Schrodinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are characterized. While this configuration is essentially unique for dimension greater than one, there are infinitely many different minimizing configurations in the one-dimensional case. The latter leads to unusual low energy asymptotics for the integrated density of states of the one-dimensional random displacement model. For symmetric Bernoulli-distributed displacements it has a 1 / log 2 -singularity at the bottom of the spectrum. In particular, it is not Holder-continuous.
Information-theoretic lower bounds for recovery of diffusion network structures

We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order Ω(k log p), for directed graphs of p nodes, and at most k parents per node. Next, we introduce a continuous-time diffusion model, for which a similar lower bound of order Ω(k log p) is obtained. Our results show that the algorithm of [1] is statistically optimal for the discrete-time regime. Our work also opens the question of whether it is possible to devise an optimal algorithm for the continuous-time regime.
A big-data approach to handle process variations: Uncertainty quantification by tensor recovery

Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters. However, their computational cost significantly increases as the number of random parameters increases. This paper presents a big-data approach to solve high-dimensional uncertainty quantification problems. Specifically, we simulate integrated circuits and MEMS at only a small number of quadrature samples; then, a huge number of (e.g., 1.5×1027) solution samples are estimated from the available small-size (e.g., 500) solution samples via a low-rank and tensor-recovery method. Numerical results show that our algorithm can easily extend the applicability of tensor-product stochastic collocation to IC and MEMS problems with over 50 random parameters, whereas the traditional algorithm can only handle several random parameters.
Electrical neurostimulation for chronic pain: On selective relay of sensory neural activities in myelinated nerve fibers

Chronic pain affects about 100 million adults in the US. Despite their great need, neuropharmacology and neurostimulation therapies for chronic pain have been associated with suboptimal efficacy and limited long-term success, as their mechanisms of action are unclear. Yet current computational models of pain transmission suffer from several limitations. In particular, dorsal column models do not include the fundamental underlying sensory activity traveling in these nerve fibers. We developed a (simple) simulation test bed of electrical neurostimulation of myelinated nerve fibers with underlying sensory activity. This paper reports our findings so far. Interactions between stimulation-evoked and underlying activities are mainly due to collisions of action potentials and losses of excitability due to the refractory period following an action potential. In addition, intuitively, the reliability of sensory activity decreases as the stimulation frequency increases. This first step opens the door to a better understanding of pain transmission and its modulation by neurostimulation therapies.
Comprehensive Evaluation of Statistical Speech Waveform Synthesis

Statistical TTS systems that directly predict the speech waveform have recently reported improvements in synthesis quality. This investigation evaluates Amazon’s statistical speech waveform synthesis (SSWS) system. An in-depth evaluation of SSWS is conducted across a number of domains to better understand the consistency in quality. The results of this evaluation are validated by repeating the procedure on a separate group of testers. Finally, an analysis of the nature of speech errors of SSWS compared to hybrid unit selection synthesis is conducted to identify the strengths and weaknesses of SSWS. Having a deeper insight into SSWS allows us to better define the focus of future work to improve this new technology.
Data Recombination for Neural Semantic Parsing

Modeling crisp logical regularities is crucial in semantic parsing, making it difficult for neural models with no task-specific prior knowledge to achieve good results. In this paper, we introduce data recombination, a novel framework for injecting such prior knowledge into a model. From the training data, we induce a high-precision synchronous context-free grammar, which captures important conditional independence properties commonly found in semantic parsing. We then train a sequence-to-sequence recurrent network (RNN) model with a novel attention-based copying mechanism on datapoints sampled from this grammar, thereby teaching the model about these structural properties. Data recombination improves the accuracy of our RNN model on three semantic parsing datasets, leading to new state-of-the-art performance on the standard GeoQuery dataset for models with comparable supervision.
Explicit Formulas for GJMS-Operators and Q-Curvatures

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincare–Einstein metrics and renormalized volume coefficients. As special cases, we derive explicit formulas for conformally covariant third and fourth powers of the Laplacian. Moreover, we prove related formulas for all Branson’s Q-curvatures. The results settle and refine conjectural statements in earlier works. The proofs rest on the theory of residue families introduced in Juhl (Progress in Mathematics, vol. 275. Birkhauser Verlag, Basel, 2009).
FlyNetSim: An Open Source Synchronized UAV Network Simulator based on ns-3 and Ardupilot

Unmanned Aerial Vehicle (UAV) systems are being increasingly used in a broad range of applications requiring extensive communications, either to interconnect the UAVs with each other or with ground resources. Focusing either on the modeling of UAV operations or communication and network dynamics, available simulation tools fail to capture the complex interdependencies between these two aspects of the problem. The main contribution of this paper is a flexible and scalable open source simulator -- FlyNetSim -- bridging the two domains. The overall objective is to enable simulation and evaluation of UAV swarms operating within articulated multi-layered technological ecosystems, such as the Urban Internet of Things (IoT). To this aim, FlyNetSim interfaces two open source tools, ArduPilot and ns-3, creating individual data paths between the devices operating in the system using a publish and subscribe-based middleware. The capabilities of FlyNetSim are illustrated through several case-study scenarios including UAVs interconnecting with a multi-technology communication infrastructure and intra-swarm ad-hoc communications.
Neural Discrete Representation Learning

Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector Quantised-Variational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt rather than static. In order to learn a discrete latent representation, we incorporate ideas from vector quantisation (VQ). Using the VQ method allows the model to circumvent issues of ``posterior collapse'' -— where the latents are ignored when they are paired with a powerful autoregressive decoder -— typically observed in the VAE framework. Pairing these representations with an autoregressive prior, the model can generate high quality images, videos, and speech as well as doing high quality speaker conversion and unsupervised learning of phonemes, providing further evidence of the utility of the learnt representations.
PhyShare: Sharing Physical Interaction in Virtual Reality

We present PhyShare, a new haptic user interface based on actuated robots. Virtual reality has recently been gaining wide adoption, and an effective haptic feedback in these scenarios can strongly support user's sensory in bridging virtual and physical world. Since participants do not directly observe these robotic proxies, we investigate the multiple mappings between physical robots and virtual proxies that can utilize the resources needed to provide a well rounded VR experience. PhyShare bots can act either as directly touchable objects or invisible carriers of physical objects, depending on different scenarios. They also support distributed collaboration, allowing remotely located VR collaborators to share the same physical feedback.
Complete characterization by multistationarity of fully open networks with one non-flow reaction

This article characterizes certain small multistationary chemical reaction networks. We consider the set of fully open networks, those for which all chemical species participate in inflow and outflow, containing one non-flow (reversible or irreversible) reaction. We show that such a network admits multiple positive mass-action steady states if and only if the stoichiometric coefficients in the non-flow reaction satisfy a certain simple arithmetic relation. The multistationary fully open one-reaction networks are identified with the chemical process of autocatalysis. Using the notion of 'embedded network' defined recently by Joshi and Shiu, we provide new sufficient conditions for establishing multistationarity of fully open networks, applicable well beyond the one-reaction setting.
Minimum Circuit Size, Graph Isomorphism, and Related Problems

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions from supposedly-intractable problems to MCSP / MKTP hinged on the power of MCSP / MKTP to distinguish random distributions from distributions produced by hardness-based pseudorandom generator constructions. We develop a fundamentally different approach inspired by the well-known interactive proof system for the complement of Graph Isomorphism (GI). It yields a randomized reduction with zero-sided error from GI to MKTP. We generalize the result and show that GI can be replaced by any isomorphism problem for which the underlying group satisfies some elementary properties. Instantiations include Linear Code Equivalence, Permutation Group Conjugacy, and Matrix Subspace Conjugacy. Along the way we develop encodings of isomorphism classes that are efficiently decodable and achieve compression that is at or near the information-theoretic optimum; those encodings may be of independent interest.
The Weights of the Tautological Classes of Character Varieties

I calculate the weights of the tautological classes of character varieties using the functorial mixed Hodge structure on simplicial schemes.
Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones

Abstract We define upper bound and lower bounds for order-preserving homogeneous of degree one maps on a proper closed cone in R n in terms of the cone spectral radius. We also define weak upper bounds for these maps. For a proper closed cone C ⊂ R n , we prove that any order-preserving homogeneous of degree one map f : int C → int C has a lower bound. If C is polyhedral, we prove that the map f has a weak upper bound. We give examples of weak upper bounds for certain order-preserving homogeneous of degree one maps defined on the interior of R + n .
ON MUTATION AND KHOVANOV HOMOLOGY

It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtration and a spectral sequence that converges to the reduced Khovanov homology of K. We show that the E2-term of this spectral sequence is a matroid invariant and hence invariant under mutation.
Differential-flatness and control of quadrotor(s) with a payload suspended through flexible cable(s)

We present the coordinate-free dynamics of three different quadrotor systems : (a) single quadrotor with a pointmass payload suspended through a flexible cable; (b) multiple quadrotors with a shared point-mass payload suspended through flexible cables; and (c) multiple quadrotors with a shared rigid-body payload suspended through flexible cables. We model the flexible cable(s) as a finite series of links with spherical joints with mass concentrated at the end of each link. The resulting systems are thus high-dimensional with high degree-of-underactuation. For each of these systems, we show that the dynamics are differentially-flat, enabling planning of dynamically feasible trajectories. For the single quadrotor with a point-mass payload suspended through a flexible cable with five links (16 degrees-of-freedom and 12 degrees-of-underactuation), we use the coordinate-free dynamics to develop a geometric variation-based linearized equations of motion about a desired trajectory. We show that a finite-horizon linear quadratic regulator can be used to track a desired trajectory with a relatively large region of attraction.
Sparse matrix inversion with scaled Lasso

We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the target matrix by the scaled Lasso and then adjusts the matrix estimator to be symmetric. The penalty level of the scaled Lasso for each column is completely determined by data via convex minimization, without using cross-validation. We prove that this scaled Lasso method guarantees the fastest proven rate of convergence in the spectrum norm under conditions of weaker form than those in the existing analyses of other l1 regularized algorithms, and has faster guaranteed rate of convergence when the ratio of the l1 and spectrum norms of the target inverse matrix diverges to infinity. A simulation study demonstrates the computational feasibility and superb performance of the proposed method. Our analysis also provides new performance bounds for the Lasso and scaled Lasso to guarantee higher concentration of the error at a smaller threshold level than previous analyses, and to allow the use of the union bound in column-by-column applications of the scaled Lasso without an adjustment of the penalty level. In addition, the least squares estimation after the scaled Lasso selection is considered and proven to guarantee performance bounds similar to that of the scaled Lasso.
Distributionally Robust Chance-Constrained Optimal Power Flow Assuming Unimodal Distributions With Misspecified Modes

Chance-constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs, while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of distributions called the ambiguity set. Commonly, ambiguity sets are only based on moment information (e.g., mean and covariance) of the random variables; however, specifying additional characteristics of the random variables reduces conservatism and cost. Here, we consider ambiguity sets that additionally incorporate unimodality information. In practice, it is difficult to estimate the mode location from the data and so we allow it to be potentially misspecified. We formulate the problem and derive a separation-based algorithm to efficiently solve it. Finally, we evaluate the performance of the proposed approach on a modified IEEE-30 bus network with wind uncertainty and compare it with other distributionally robust approaches. We find that a misspecified mode significantly affects the reliability of the solution, and the proposed model demonstrates a good tradeoff between cost and reliability.
Estimating perimeter using graph cuts

We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For Ω ⊆ D = (0, 1) d with d ≥ 2, we are given n random independent and identically distributed points on D whose membership in Ω is known. We consider the sample as a random geometric graph with connection distance e > 0. We estimate the perimeter of Ω (relative to D) by the, appropriately rescaled, graph cut between the vertices in Ω and the vertices in D ∖ Ω. We obtain bias and variance estimates on the error, which are optimal in scaling with respect to n and e. We consider two scaling regimes: the dense (when the average degree of the vertices goes to ∞) and the sparse one (when the degree goes to 0). In the dense regime, there is a crossover in the nature of the approximation at dimension d = 5: we show that in low dimensions d = 2, 3, 4 one can obtain confidence intervals for the approximation error, while in higher dimensions one can obtain only error estimates for testing the hypothesis that the perimeter is less than a given number.
STATISTICAL INFERENCE ON TRANSFORMATION MODELS: A SELF-INDUCED SMOOTHING APPROACH

ABSTRACTThis paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in simultaneous point and variance estimation. The self-induced smoothing does not require bandwidth selection, yet provides the right amount of smoothness so that the estimator is asymptotically normal with mean zero (unbiased) and variance–covariance matrix consistently estimated by the usual sandwich-type estimator. An iterative algorithm is given for the variance estimation and shown to numerically converge to a consistent limiting variance estimator. The approach is applied to a data set involving survival times of primary biliary cirrhosis patients. Simulation results are reported, showing that the new method performs well under a variety of scenarios.
Effective Field Theories and Lattice QCD

I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the twoand three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
“Rapid” regions-of-interest detection in big histopathological images

The sheer volume and size of histopathological images (e.g., 106 MPixel) underscores the need for faster and more accurate Regions-of-interest (ROI) detection algorithms. In this paper, we propose such an algorithm, which has four main components that help achieve greater accuracy and faster speed: First, while using coarse-to-fine topology preserving segmentation as the baseline, the proposed algorithm uses a superpixel regularity optimization scheme for avoiding irregular and extremely small superpixels. Second, the proposed technique employs a prediction strategy to focus only on important superpixels at finer image levels. Third, the algorithm reuses the information gained from the coarsest image level at other finer image levels. Both the second and the third components drastically lower the complexity. Fourth, the algorithm employs a highly effective parallelization scheme using adaptive data partitioning, which gains high speedup. Experimental results, conducted on the BSD500 [1] and 500 whole-slide histological images from the National Lung Screening Trial (NLST)1 dataset, confirm that the proposed algorithm gained 13 times speedup compared with the baseline, and around 160 times compared with SLIC [11], without losing accuracy.
Stability of entire solutions to supercritical elliptic problems involving advection

Abstract We examine the equation given by (1) − Δ u + a ( x ) ⋅ ∇ u = u p in R N , where p > 1 and a ( x ) is a smooth vector field satisfying some decay conditions. We show that for p p c , the Joseph–Lundgren exponent, there is no positive stable solution of (1) provided one imposes a smallness condition on a along with a divergence free condition. In the other direction we show that for N ≥ 4 and p > N − 1 N − 3 there exists a positive solution of (1) provided a satisfies a smallness condition. For p > p c we show the existence of a positive stable solution of (1) provided a is divergence free and satisfies a smallness condition.
Galois groups of some iterated polynomials over cyclotomic extensions

Let \(\varphi _p(z)=(z-1)^p+2-\zeta _p\), where \(\zeta _p\in \bar{\mathbb {Q}}\) is a primitive pth root of unity. Building on previous work, we show that the nth iterate \(\varphi _p^n(z)\) has Galois group \([C_p]^n\), an iterated wreath product of cyclic groups, whenever p is not a Wieferich prime.
Fundamental limits of weak recovery with applications to phase retrieval

In phase retrieval, we want to recover an unknown signal $${{\varvec{x}}}\in {{\mathbb {C}}}^d$$ from n quadratic measurements of the form $$y_i = |\langle {{\varvec{a}}}_i,{{\varvec{x}}}\rangle |^2+w_i$$ , where $${{\varvec{a}}}_i\in {{\mathbb {C}}}^d$$ are known sensing vectors and $$w_i$$ is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n needed to produce an estimator $${\hat{{{\varvec{x}}}}}({{\varvec{y}}})$$ that is positively correlated with the signal $${{\varvec{x}}}$$ ? We consider the case of Gaussian vectors $${{\varvec{a}}}_i$$ . We prove that—in the high-dimensional limit—a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For $$n\le d-o(d)$$ , no estimator can do significantly better than random and achieve a strictly positive correlation. For $$n\ge d+o(d)$$ , a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theoretic arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper bound and lower bound generalize beyond phase retrieval to measurements $$y_i$$ produced according to a generalized linear model. As a by-product of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm.
A Blackbox Polynomial System Solver on Parallel Shared Memory Computers

A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods are applied to compute a numerical irreducible decomposition. Load balancing and pipelining are techniques in a parallel implementation on a computer with multicore processors. The application of the parallel algorithms is illustrated on solving the cyclic n-roots problems, in particular for \(n = 8, 9\), and 12.
Cardinal invariants of closed graphs

We study several cardinal characteristics of closed graphs G on compact metrizable spaces. In particular, we address the question when it is consistent for the bounding number to be strictly smaller than the smallest size of a set not covered by countably many compact G-anticliques. We also provide a descriptive set theoretic characterization of the class of analytic graphs with countable coloring number.