cssi/SciSciGPT-SciSciNet huggingface dataset:
Stochastic higher spin six vertex model and q-TASEPs

Abstract We present two new connections between the inhomogeneous stochastic higher spin six vertex model in a quadrant and integrable stochastic systems from the Macdonald processes hierarchy. First, we show how Macdonald q-difference operators with t = 0 (an algebraic tool crucial for studying the corresponding Macdonald processes) can be utilized to get q-moments of the height function h in the higher spin six vertex model first computed in [21] using Bethe ansatz. This result in particular implies that for the vertex model with the step Bernoulli boundary condition, the value of h at an arbitrary point ( N + 1 , T ) ∈ Z ≥ 2 × Z ≥ 1 has the same distribution as the last component λ N of a random partition under a specific t = 0 Macdonald measure. On the other hand, it is known that x N : = λ N − N can be identified with the location of the Nth particle in a certain discrete time q-TASEP started from the step initial configuration. The second construction we present is a coupling of this q-TASEP and the higher spin six vertex model (with the step Bernoulli boundary condition) along time-like paths providing an independent probabilistic explanation of the equality of h ( N + 1 , T ) and x N + N in distribution. As an illustration of our main results we obtain GUE Tracy–Widom asymptotics of a certain discrete time q-TASEP (with the step initial configuration and special jump parameters) by means of Schur measures (which are t = q Macdonald measures). This analysis combines our results with the identification of averages of observables between the stochastic higher spin six vertex model and Schur measures obtained recently in [8] .
Fundamental Limits of Budget-Fidelity Trade-off in Label Crowdsourcing

Digital crowdsourcing (CS) is a modern approach to perform certain large projects using small contributions of a large crowd. In CS, a taskmaster typically breaks down the project into small batches of tasks and assigns them to so-called workers with imperfect skill levels. The crowdsourcer then collects and analyzes the results for inference and serving the purpose of the project. In this work, the CS problem, as a human-in-the-loop computation problem, is modeled and analyzed in an information theoretic rate-distortion framework. The purpose is to identify the ultimate fidelity that one can achieve by any form of query from the crowd and any decoding (inference) algorithm with a given budget. The results are established by a joint source channel (de)coding scheme, which represent the query scheme and inference, over parallel noisy channels, which model workers with imperfect skill levels. We also present and analyze a query scheme dubbed k-ary incidence coding and study optimized query pricing in this setting.
Non interactive simulation of correlated distributions is decidable

A basic problem in information theory is the following: Let P = (X, Y) be an arbitrary distribution where the marginals X and Y are (potentially) correlated. Let Alice and Bob be two players where Alice gets samples {xi}i≥1 and Bob gets samples {yi}i≥1 and for all i, (xi, yi) ∼ P. What joint distributions Q can be simulated by Alice and Bob without any interaction? Classical works in information theory by Gacs-Korner and Wyner answer this question when at least one of P or Q is the distribution Eq (Eq is defined as uniform over the points (0, 0) and (1, 1)). However, other than this special case, the answer to this question is understood in very few cases. Recently, Ghazi, Kamath and Sudan showed that this problem is decidable for Q supported on {0, 1} × {0, 1}. We extend their result to Q supported on any finite alphabet. Moreover, we show that If Q can be simulated, our algorithm also provides a (non-interactive) simulation protocol. We rely on recent results in Gaussian geometry (by the authors) as well as a new smoothing argument inspired by the method of boosting from learning theory and potential function arguments from complexity theory and additive combinatorics.
Coregular spaces and genus one curves

A coregular space is a representation of an algebraic group for which the ring of polynomial invariants is free. In this paper, we show that the orbits of many coregular irreducible representations where the number of invariants is at least two, over a (not necessarily algebraically closed) field k, correspond to genus one curves over k together with line bundles, vector bundles, and/or points on their Jacobians. In forthcoming work, we use these orbit parametrizations to determine the average sizes of Selmer groups for various families of elliptic curves.
Improving LSTM-based Video Description with Linguistic Knowledge Mined from Text

This paper investigates how linguistic knowledge mined from large text corpora can aid the generation of natural language descriptions of videos. Specifically, we integrate both a neural language model and distributional semantics trained on large text corpora into a recent LSTM-based architecture for video description. We evaluate our approach on a collection of Youtube videos as well as two large movie description datasets showing significant improvements in grammaticality while modestly improving descriptive quality.
Comparing Models of Associative Meaning: An Empirical Investigation of Reference in Simple Language Games

Simple reference games are of central theoretical and empirical importance in the study of situated language use. Although language provides rich, compositional truth-conditional semantics to facilitate reference, speakers and listeners may sometimes lack the overall lexical and cognitive resources to guarantee successful reference through these means alone. However, language also has rich associational structures that can serve as a further resource for achieving successful reference. Here we investigate this use of associational information in a setting where only associational information is available: a simplified version of the popular game Codenames. Using optimal experiment design techniques, we compare a range of models varying in the type of associative information deployed and in level of pragmatic sophistication against human behavior. In this setting we find that listeners’ behavior reflects direct bigram collocational associations more strongly than word-embedding or semantic knowledge graph-based associations and that there is little evidence for pragmatically sophisticated behavior on the part of either speakers or listeners. More generally, we demonstrate the effective use of simple tasks to derive insights into the nature of complex linguistic phenomena.
Comparing skein and quantum group representations and their application to asymptotic faithfulness

We generalize the asymptotic faithfulness of the skein quantum $SU(2)$ representations of mapping class groups of orientable closed surfaces to skein $SU(3)$. Skein quantum representations of mapping class groups are different from the Reshetikin-Turaev ones from quantum groups or geometric quantization because they are given by different modular tensor categories. We conjecture asymptotic faithfulness holds for skein quantum $G$ representations when $G$ is a simply-connected simple Lie group. The difficulty for such a generalization lies in the lack of an explicit description of the fusion spaces with multiplicities to define an appropriate complexity of state vectors.
Kleinian groups of small Hausdorff dimension are classical Schottky groups. I

It has been conjectured that the Hausdorff dimensions of nonclassical Schottky groups are strictly bounded from below. In this first part of our work on this conjecture, we prove that there exists a universal positive number λ greater than 0 such that any 2–generated nonelementary Kleinian group with limit set of Hausdorff dimension less than λ is a classical Schottky group.
Fine-Grained Recognition in the Wild: A Multi-task Domain Adaptation Approach

While fine-grained object recognition is an important problem in computer vision, current models are unlikely to accurately classify objects in the wild. These fully supervised models need additional annotated images to classify objects in every new scenario, a task that is infeasible. However, sources such as e-commerce websites and field guides provide annotated images for many classes. In this work, we study fine-grained domain adaptation as a step towards overcoming the dataset shift between easily acquired annotated images and the real world. Adaptation has not been studied in the fine-grained setting where annotations such as attributes could be used to increase performance. Our work uses an attribute based multi-task adaptation loss to increase accuracy from a baseline of 4:1% to 19:1% in the semi-supervised adaptation case. Prior domain adaptation works have been benchmarked on small datasets such as [46] with a total of 795 images for some domains, or simplistic datasets such as [41] consisting of digits. We perform experiments on a subset of a new challenging fine-grained dataset consisting of 1; 095; 021 images of 2; 657 car categories drawn from e-commerce websites and Google Street View.
Freudenthal triple systems by root system methods

Abstract For certain Lie algebras g , we can use a grading g = g − 2 ⊕ g − 1 ⊕ g 0 ⊕ g 1 ⊕ g 2 and define a quartic form and a skew-symmetric bilinear form on g 1 , thereby constructing a Freudenthal triple system. The structure of the Freudenthal triple system is examined using root system methods available in the Lie algebra context. In the cases g = E 8 (where g 1 is the minuscule representation of E 7 ) and g = D 4 , we determine the groups stabilizing the quartic form and both the quartic and bilinear forms.
Unsupervised Grammar Induction with Depth-bounded PCFG

There has been recent interest in applying cognitively- or empirically-motivated bounds on recursion depth to limit the search space of grammar induction models (Ponvert et al., 2011; Noji and John...
Asymptotic Estimates for the Number of Contingency Tables, Integer Flows, and Volumes of Transportation Polytopes

We prove an asymptotic estimate for the number of m × n non-negative integer matrices (contingency tables) with prescribed row and column sums and, more generally, for the number of integer-feasible flows in a network. Similarly, we estimate the volume of the polytope of m × n non-negative real matrices with prescribed row and column sums. Our estimates are solutions of convex optimization problems, and hence can be computed efficiently. As a corollary, we show that if row sums R = (r 1 , …, r m ) and column sums C = (c 1 , …, c n ) with r 1 + ⋯ + r m = c 1 + ⋯ + c n = Nare sufficiently far from constant vectors, then, asymptotically, in the uniform probability space of the m × nnon-negative integer matrices with the total sum N of entries, the event consisting of the matrices with row sums R and the event consisting of the matrices with column sums C are positively correlated.
Optimal geographic caching in finite wireless networks

Cache-enabled device-to-device (D2D) networks turn memory of the devices at the network edge, such as smart phones and tablets, into bandwidth by enabling asynchronous content sharing directly between proximate devices. Limited storage capacity of the mobile devices necessitates the determination of optimal set of contents to be cached on each device. In order to study the problem of optimal cache placement, we model the locations of devices in a finite region (e.g., coffee shop, sports bar, library) as a uniform binomial point process (BPP). For this setup, we first develop a generic framework to analyze the coverage probability of the target receiver (target-Rx) when the requested content is available at the kth closest device to it. Using this coverage probability result, we evaluate optimal caching probability of the popular content to maximize the total hit probability. Our analysis concretely demonstrates that optimal caching probability strongly depends on the number of simultaneously active devices in the network.
Fast Counting in Machine Learning Applications

We propose scalable methods to execute counting queries in machine learning applications. To achieve memory and computational efficiency, we abstract counting queries and their context such that the counts can be aggregated as a stream. We demonstrate performance and scalability of the resulting approach on random queries, and through extensive experimentation using Bayesian networks learning and association rule mining. Our methods significantly outperform commonly used ADtrees and hash tables, and are practical alternatives for processing large-scale data.
Entanglement-enhanced lidars for simultaneous range and velocity measurements

Lidar is a well-known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurements of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurements of range and radial velocity from the detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the round-trip loss incurred by the signal photons. The second entanglement-enhanced lidar---which requires a lossless, noiseless environment---realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to $1/M$ when $M$ signal photons are transmitted. These two lidars derive their entanglement-based enhancements from the use of a unitary transformation that takes a signal-idler photon pair with frequencies ${\ensuremath{\omega}}_{S}$ and ${\ensuremath{\omega}}_{I}$ and converts it to a signal-idler photon pair whose frequencies are $({\ensuremath{\omega}}_{S}+{\ensuremath{\omega}}_{I})/2$ and $({\ensuremath{\omega}}_{S}\ensuremath{-}{\ensuremath{\omega}}_{I})/2$. Insight into how this transformation provides its benefits is provided through an analogy to continuous-variable superdense coding.
From Grassmann Necklaces to Restricted Permutations and Back Again

We study the commutative algebras ZJK appearing in Brown and Goodearl’s extension of the \(\mathcal {H}\)-stratification framework, and show that if A is the single parameter quantized coordinate ring of Mm,n, GLn or SLn, then the algebras ZJK can always be constructed in terms of centres of localizations. The main purpose of the ZJK is to study the structure of the topological space spec(A), which remains unknown for all but a few low-dimensional examples. We explicitly construct the required denominator sets using two different techniques (restricted permutations and Grassmann necklaces) and show that we obtain the same sets in both cases. As a corollary, we obtain a simple formula for the Grassmann necklace associated to a cell of totally nonnegative real m × n matrices in terms of its restricted permutation.
Responses to Remixing on a Social Media Sharing Website

In this paper we describe the ways participants of the Scratch online community, primarily young people, engage in remixing of each others' shared animations, games, and interactive projects. In particular, we try to answer the following questions: How do users respond to remixing in a social media environment where remixing is explicitly permitted? What qualities of originators and their projects correspond to a higher likelihood of plagiarism accusations? Is there a connection between plagiarism complaints and similarities between a remix and the work it is based on? Our findings indicate that users have a very wide range of reactions to remixing and that as many users react positively as accuse remixers of plagiarism. We test several hypotheses that might explain the high number of plagiarism accusations related to original project complexity, cumulative remixing, originators' integration into remixing practice, and remixee-remixer project similarity, and find support for the first and last explanations.
A minimal lamination with Cantor set-like singularities

Given a compact closed subset $M$ of a line segment in $\mathbb{R}^3$, we construct a sequence of minimal surfaces $\Sigma_k$ embedded in a neighborhood $C$ of the line segment that converge smoothly to a limit lamination of $C$ away from $M$. Moreover, the curvature of this sequence blows up precisely on $M$, and the limit lamination has non-removable singularities precisely on the boundary of $M$.
Algorithmic Bidding for Virtual Trading in Electricity Markets

We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on differences between day-ahead and real-time market prices that are random and unknown to market participants. An online learning algorithm is proposed to maximize the cumulative payoff over a finite number of trading sessions by allocating the trader's budget among his bids for $K$ options in each session. It is shown that the expected payoff of the proposed algorithm converges, with an almost optimal convergence rate, to the expected payoff of the global optimal corresponding to the case when the underlying price distribution is known. The proposed algorithm is also generalized for trading strategies with a risk measure. By using both cumulative payoff and Sharpe ratio as performance metrics, evaluations were performed based on the historical data spanning ten year period of NYISO and PJM markets. It was shown that the proposed strategy outperforms standard benchmarks and the S&P 500 index over the same period.
The Cohen-Macaulay property of affine semigroup rings in dimension 2

Consider the subring R=k[xa,xp1yq1,…,xptyqt,yb] of k[x,y], where k is a field and x, y indeterminates over k. We calculate the Hilbert polynomial of (xa,yb). The multiplicity of this ideal provides...
A free boundary problem for the parabolic Poisson kernel

Abstract We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystrom [14] , and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel has logarithm in VMO must in fact be a vanishing chord arc domain (i.e. satisfies a vanishing Carleson measure condition). This generalizes, to the parabolic setting, a result of Kenig and Toro [26] and answers in the affirmative a question left open in the aforementioned paper of Hofmann et al. A key step in this proof is a classification of “flat” blowups for the parabolic problem.
Leveraging edge caching in NOMA systems with QoS requirements

Non-Orthogonal Multiple Access (NOMA) and caching are two proposed approaches to increase the capacity of future 5G wireless systems. Typically in NOMA systems, signals at the receiver are decoded using successive interference cancellation in order to achieve capacity in multi-user systems. The leveraging of caching in the physical layer to further improve on the benefits of NOMA is investigated, which is termed cache-aided NOMA. Specific attention is given to the caching cases where the users with weaker channel conditions possess a cache of the information requested by a user with a stronger channel condition. The probability that any of the users is in outage for any of the rates required for this NOMA system, defined as the “union-outage,” is derived for the case of fixed-power allocation, and the power allocation strategy that minimizes the union-outage probability is derived. Simulation results confirm the analytical results, which demonstrate the benefits of cache-aided NOMA on reducing the union-outages probability.
Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction

Based on the reported data until 18 March 2015 and numerical fitting via a simple formula of cumulative case number, we provide real-time estimation on basic reproduction number, inflection point, peak time and final outbreak size of ongoing Ebola outbreak in West Africa. From our simulation, we conclude that the first wave has passed its inflection point and predict that a second epidemic wave may appear in the near future.
A note on degree vs gap of Min-Rep Label Cover and improved inapproximability for connectivity problems

Abstract This note concerns the trade-off between the degree of the constraint graph and the gap in hardness of approximating the Min-Rep variant of Label Cover (aka Projection Game). We make a very simple observation that, for NP-hardness with gap g, the degree can be made as small as O ( g log ⁡ g ) , which improves upon the previous O ˜ ( g 2 ) bound from the work of Laekhanukit [15] . Note that our bound is optimal up to a logarithmic factor since there is a trivial Δ-approximation for Min-Rep where Δ is the maximum degree of the constraint graph. Thanks to known reductions [10] , [8] , [11] , [15] , this improvement implies better hardness of approximation results for Rooted k-Connectivity, Vertex-Connectivity Survivable Network Design and Vertex-Connectivity k-Route Cut.
A 3-D Spatial Model for In-Building Wireless Networks With Correlated Shadowing

Consider orthogonal planes in the 3-D space representing floors and walls in a large building. These planes divide the space into rooms, where a wireless infrastructure is deployed. This paper is focused on the analysis of the correlated shadowing field created by this wireless infrastructure through the set of walls and floors. When the locations of the planes and wireless nodes are governed by Poisson processes, we obtain a simple stochastic model which captures the non-uniform nature of node deployment and room sizes. This model, which we propose to call the Poisson building , captures the complex in-building shadowing correlations, is scalable in the number of dimensions, and can be used for network performance analysis. It allows an exact mathematical characterization of the interference distribution in both infinite and finite buildings, which further leads to closed-form expressions for the coverage probabilities in in-building cellular networks and the success probability of in-building underlay D2D transmissions.
Fairness Without Demographics in Repeated Loss Minimization

Machine learning models (e.g., speech recognizers) are usually trained to minimize average loss, which results in representation disparity---minority groups (e.g., non-native speakers) contribute less to the training objective and thus tend to suffer higher loss. Worse, as model accuracy affects user retention, a minority group can shrink over time. In this paper, we first show that the status quo of empirical risk minimization (ERM) amplifies representation disparity over time, which can even make initially fair models unfair. To mitigate this, we develop an approach based on distributionally robust optimization (DRO), which minimizes the worst case risk over all distributions close to the empirical distribution. We prove that this approach controls the risk of the minority group at each time step, in the spirit of Rawlsian distributive justice, while remaining oblivious to the identity of the groups. We demonstrate that DRO prevents disparity amplification on examples where ERM fails, and show improvements in minority group user satisfaction in a real-world text autocomplete task.
Approximations of semicontinuous functions with applications to stochastic optimization and statistical estimation

Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc function is the limit of a hypo-converging sequence of piecewise affine functions of the difference-of-max type and illustrate resulting algorithmic possibilities in the context of approximate solution of infinite-dimensional optimization problems. In an effort to quantify the ease with which classes of usc functions can be approximated by finite collections, we provide upper and lower bounds on covering numbers for bounded sets of usc functions under the Attouch-Wets distance. The result is applied in the context of stochastic optimization problems defined over spaces of usc functions. We establish confidence regions for optimal solutions based on sample average approximations and examine the accompanying rates of convergence. Examples from nonparametric statistics illustrate the results.
Classifier Risk Estimation under Limited Labeling Resources

Evaluating a trained system is an important component of machine learning. Labeling test data for large scale evaluation of a trained model can be extremely time consuming and expensive. In this paper we propose strategies for estimating performance of a classifier using as little labeling resource as possible. Specifically, we assume a labeling budget is given and the goal is to get a good estimate of the classifier performance using the provided labeling budget. We propose strategies to get a precise estimate of classifier accuracy under this restricted labeling budget scenario. We show that these strategies can reduce the variance in estimation of classifier accuracy by a significant amount compared to simple random sampling (over \(\mathbf {65\%}\) in several cases). In terms of labeling resource, the reduction in number of samples required (compared to random sampling) to estimate the classifier accuracy with only \(1\%\) error is high as \(\mathbf {60\%}\) in some cases.
Unipotent classes and special Weyl group representations

Abstract We show that various invariants of a unipotent conjugacy class in a connected semisimple group can be recovered purely in terms of data involving the Weyl group.
Strichartz estimates for convex co-compact hyperbolic surfaces

Using recent work of Bourgain-Dyatlov we show that for any convex co-compact hyperbolic surface Strichartz estimates for the Schrodinger equation hold with an arbitrarily small loss of regularity.
Primordial Nucleosynthesis: The Predicted and Observed Abundances and Their Consequences

For a brief time in its early evolution the Universe was a cosmic nuclear reactor. The expansion and cooling of the Universe limited this epoch to the first few minutes, allowing time for the synthesis in astrophysically interesting abundances of on ly the lightest nuclides (D, 3 He, 4 He, 7 Li). For big bang nucleosynthesis (BBN) in the standard models of cosmology and particle physics (SBBN), the SBBN-predicted abundances depend on only one adjustable parameter, the baryon density parameter (the ratio by number of baryons (nucleons) to photons). The predicted and observed abundances of the relic light elements are revi ewed, testing the internal consistency of primordial nucleosynthesis. The consistency of BBN is also explored by comparing the values of the cosmological parameters inferred from primordial nu cleosynthesis for the standard model and for models with non-standard early Universe expansion rates with those determined from studies of the cosmic background radiation, which provides a snapshot of the Universe some 400 thousand years after BBN ended.
Level Spacings and Nodal Sets at Infinity for Radial Perturbations of the Harmonic Oscillator

We study properties of the nodal sets of high frequency eigenfunctions and quasimodes for radial perturbations of the Harmonic Oscillator. In particular, we consider nodal sets on spheres of large radius (in the classically forbidden region) for quasimodes with energies lying in intervals around a fixed energy $E$. For well chosen intervals we show that these nodal sets exhibit quantitatively different behavior compared to those of the unperturbed Harmonic Oscillator. These energy intervals are defined via a careful analysis of the eigenvalue spacings for the perturbed operator, based on analytic perturbation theory and linearization formulas for Laguerre polynomials.
Nonreciprocal cavities and the time–bandwidth limit

The time–bandwidth limit inherently relates the lifetime of a resonance and its spectral bandwidth, with direct implications for the maximum storage time of a pulse versus its frequency content. Recently, it has been argued that nonreciprocal cavities may overcome this constraint by breaking the strict equality of their incoupling and outcoupling coefficients. Here, we study the implications of nonreciprocity on resonant linear, time-invariant cavities and derive general relations, stemming from microscopic reversibility, that govern their dynamics. We show that nonreciprocal cavities do not provide specific advantages in terms of the time–bandwidth limit, but enable other attractive properties for nanophotonic systems.
Conformal dimension and boundaries of planar domains

Building off of techniques that were recently developed by M. Carrasco, S. Keith, and B. Kleiner to study the conformal dimension of boundaries of hyperbolic groups, we prove that uniformly perfect boundaries of John domains in the Riemann sphere have conformal dimension equal to 0 or 1. Our proof uses a discretized version of Carrasco's "uniformly well-spread cut point" condition, which we call the discrete UWS property, that is well-suited to deal with metric spaces that are not linearly connected. More specifically, we prove that boundaries of John domains have the discrete UWS property and that any compact, doubling, uniformly perfect metric space with the discrete UWS property has conformal dimension equal to 0 or 1. In addition, we establish other geometric properties of metric spaces with the discrete UWS property, including connectivity properties of their weak tangents.
Thorup–Zwick emulators are universally optimal hopsets

Abstract A ( β , ϵ ) -hopset is, informally, a weighted edge set that, when added to a graph, allows one to get from point a to point b using a path with at most β edges (“hops”) and length ( 1 + ϵ ) dist ( a , b ) . In this paper we observe that Thorup and Zwick's sublinear additive emulators are also actually ( O ( k / ϵ ) k , ϵ ) -hopsets for every ϵ > 0 , and that with a small change to the Thorup–Zwick construction, the size of the hopset can be made O ( n 1 + 1 2 k + 1 − 1 ) . As corollaries, we also shave “k” factors off the size of Thorup and Zwick's [20] sublinear additive emulators and the sparsest known ( 1 + ϵ , O ( k / ϵ ) k − 1 ) -spanners, due to Abboud, Bodwin, and Pettie [1] .
Fubini-Griffiths-Harris rigidity and Lie algebra cohomology

We prove a general extrinsic rigidity theorem for homogeneous varieties in $\mathbb{CP}^N$. The theorem is used to show that the adjoint variety of a complex simple Lie algebra $\mathfrak{g}$ (the unique minimal G orbit in $\mathbb{P}\mathfrak{g}$) is extrinsically rigid to third order. In contrast, we show that the adjoint variety of $SL_3\mathbb{C}$, and the Segre product $\mathit{Seg}(\mathbb{P}^1\times \mathbb{P}^n)$, both varieties with osculating sequences of length two, are flexible at order two. In the $SL_3\mathbb{C}$ example we discuss the relationship between the extrinsic projective geometry and the intrinsic path geometry. We extend machinery developed by Hwang and Yamaguchi, Se-ashi, Tanaka and others to reduce the proof of the general theorem to a Lie algebra cohomology calculation. The proofs of the flexibility statements use exterior differential systems techniques.
Cohomology classes of interval positroid varieties and a conjecture of Liu

To each finite subset of $\mathbb{Z}^2$ (a diagram), one can associate a subvariety of a complex Grassmannian (a diagram variety), and a representation of a symmetric group (a Specht module). Liu has conjectured that the cohomology class of a diagram variety is represented by the Frobenius characteristic of the corresponding Specht module. We give a counterexample to this conjecture. However, we show that for the diagram variety of a permutation diagram, Liu's conjectured cohomology class $\sigma$ is at least an upper bound on the actual class $\tau$, in the sense that $\sigma - \tau$ is a nonnegative linear combination of Schubert classes. To do this, we exhibit the appropriate diagram variety as a component in a degeneration of one of Knutson's interval positroid varieties (up to Grassmann duality). A priori, the cohomology classes of these interval positroid varieties are represented by affine Stanley symmetric functions. We give a different formula for these classes as ordinary Stanley symmetric functions, one with the advantage of being Schur-positive and compatible with inclusions between Grassmannians.
Convolutional networks on graphs for learning molecular fingerprints

We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.
Principal component projection without principal component analysis

We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependence on the number of top principal components. We show that it can be used to give a fast iterative method for the popular principal component regression problem, giving the first major runtime improvement over the naive method of combining PCA with regression. To achieve our results, we first observe that ridge regression can be used to obtain a "smooth projection" onto the top principal components. We then sharpen this approximation to true projection using a low-degree polynomial approximation to the matrix step function. Step function approximation is a topic of long-term interest in scientific computing. We extend prior theory by constructing polynomials with simple iterative structure and rigorously analyzing their behavior under limited precision.
On Factoring an Operator Using Elements of its Kernel

A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to ot...
Benchmarking and Error Diagnosis in Multi-instance Pose Estimation

We propose a new method to analyze the impact of errors in algorithms for multi-instance pose estimation and a principled benchmark that can be used to compare them. We define and characterize three classes of errors - localization, scoring, and background - study how they are influenced by instance attributes and their impact on an algorithm’s performance. Our technique is applied to compare the two leading methods for human pose estimation on the COCO Dataset, measure the sensitivity of pose estimation with respect to instance size, type and number of visible keypoints, clutter due to multiple instances, and the relative score of instances. The performance of algorithms, and the types of error they make, are highly dependent on all these variables, but mostly on the number of keypoints and the clutter. The analysis and software tools we propose offer a novel and insightful approach for understanding the behavior of pose estimation algorithms and an effective method for measuring their strengths and weaknesses.
Feature-Augmented Neural Networks for Patient Note De-identification.

Patient notes contain a wealth of information of potentially great interest to medical investigators. However, to protect patients’ privacy, Protected Health Information (PHI) must be removed from the patient notes before they can be legally released, a process known as patient note de-identification. The main objective for a de-identification system is to have the highest possible recall. Recently, the first neural-network-based de-identification system has been proposed, yielding state-of-the-art results. Unlike other systems, it does not rely on human-engineered features, which allows it to be quickly deployed, but does not leverage knowledge from human experts or from electronic health records (EHRs). In this work, we explore a method to incorporate human-engineered features as well as features derived from EHRs to a neural-network-based de-identification system. Our results show that the addition of features, especially the EHR-derived features, further improves the state-of-the-art in patient note de-identification, including for some of the most sensitive PHI types such as patient names. Since in a real-life setting patient notes typically come with EHRs, we recommend developers of de-identification systems to leverage the information EHRs contain.
Performance Analysis of a Mission-Critical Portable LTE System in Targeted RF Interference

Mission-critical wireless networks are being upgraded to 4G long-term evolution (LTE). These networks require very high reliability and security as well as easy deployment and operation in the field. Wireless communications systems have been vulnerable to jamming, spoofing and other radio frequency (RF) attacks since the early days of analog systems. Although wireless systems have evolved, important security and reliability concerns still exist. This paper presents our methodology for testing 4G LTE operating in harsh signaling environments. We use software-defined radio technology and open-source software to develop a fully configurable protocol-aware interference waveform. We define several test cases that target the entire LTE signal or part of it and evaluate the performance of a mission- critical production LTE system. Our RF experiments show that LTE synchronization signal interference causes significant throughput degradation at low interference power. By dynamically evaluating the performance measurement counters, the k-nearest neighbor classification method can detect the specific RF signaling attack to aid in effective mitigation.
Geometry in the Courtroom

There has been a recent media blitz on a cohort of mathematicians valiantly working to fix the democratic system in the United States by combatting gerrymandering with geometry. While statistics co...
Using micro-collections in social media to generate seeds for web archive collections

In a Web plagued by disappearing resources, Web archive collections provide a valuable means of preserving Web resources important to the study of past events ranging from elections to disease outbreaks. These archived collections start with seed URIs (Uniform Resource Identifiers) hand-selected by curators. Curators produce high quality seeds by removing non-relevant URIs and adding URIs from credible and authoritative sources, but this ability comes at a cost: it is time consuming to collect these seeds. Two main strategies adopted by curators for discovering seeds include scraping Web (e.g., Google) Search Engine Result Pages (SERPs) and social media (e.g., Twitter) SERPs. In this work, we studied three social media platforms in order to provide some insight on the characteristics of seeds generated from different sources. First, we developed a simple vocabulary for describing social media posts across different platforms. Second, we introduced a novel source for generating seeds from URIs in the threaded conversations of social media posts created by single or multiple users. Users on social media sites routinely create and share posts about news events consisting of hand-selected URIs of news stories, tweets, videos, etc. In this work, we call these posts micro-collections, whether shared on Reddit or Twitter, and we consider them as an important source for seeds. This is because, the effort taken to create micro-collections is an indication of editorial activity and a demonstration of domain expertise. Third, we generated 23,112 seed collections with text and hashtag queries from 449,347 social media posts from Reddit, Twitter, and Scoop.it. We collected in total 120,444 URIs from the conventional scraped SERP posts and micro-collections. We characterized the resultant seed collections across multiple dimensions including the distribution of URIs, precision, ages, diversity of webpages, etc. We showed that seeds generated by scraping SERPs had a higher median probability (0.63) of producing relevant URIs than micro-collections (0.5). However, micro-collections were more likely to produce seeds with a higher precision than conventional SERP collections for Twitter collections generated with hashtags. Also, micro-collections were more likely to produce older webpages and more non-HTML documents.
Robust Model Predictive Control for Linear Systems with State and Input Dependent Uncertainties

This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being non-convex, we are able to handle it as a second-order cone program. Both open-loop and semi-feedback planning strategies are presented. The formulation has linear complexity in the planning horizon length. The approach is thus amenable to efficient real-time implementation with a guarantee on recursive feasibility and global optimality. Robust position control of a satellite is considered as an illustrative example.
Demonstrating predictive wavefront control with the Keck II near-infrared pyramid wavefront sensor

The success of ground-based instruments for high contrast exoplanet imaging depends on the degree to which adaptive optics (AO) systems can mitigate atmospheric turbulence. While modern AO systems typically suffer from millisecond time lags between wavefront measurement and control, predictive wavefront control (pWFC) is a means of compensating for those time lags using previous wavefront measurements, thereby improving the raw contrast in the post-coronagraphic science focal plane. A method of predictive control based on Empirical Orthogonal Functions (EOF) has previously been proposed and demonstrated on Subaru/SCExAO. In this paper we present initial tests of this method for application to the near-infrared pyramid wavefront sensor (PYWFS) recently installed in the Keck II AO system. We demonstrate the expected root-mean-square (RMS) wavefront error and contrast benefits of pWFC based on simulations, applying pWFC to on-sky telemetry data saved during commissioning of the PYWFS. We discuss how the performance varies as different temporal and spatial scales are included in the computation of the predictive filter. We further describe the implementation of EOF pWFC within the PYWFS dedicated real-time controller (RTC), and, via daytime testing at the observatory, we demonstrate the performance of pWFC in real time when pre-computed phase screens are applied to the deformable mirror (DM).
A population balance model for large eddy simulation of polydisperse droplet evolution

In the context of many applications of turbulent multi-phase flows, knowledge of the dispersed phase size distribution and its evolution is critical to predicting important macroscopic features. We develop a large eddy simulation (LES) model that can predict the turbulent transport and evolution of size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, and occurring at low volume fraction. We use a population dynamics model for polydisperse droplet distributions specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. We model the number density fields using an Eulerian approach for each bin of the discretized droplet size distribution. Following earlier methods used in the Reynolds-averaged Navier–Stokes framework, the droplet breakup due to turbulent fluctuations is modelled by treating droplet–eddy collisions as in kinetic theory of gases. Existing models assume the scale of droplet–eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. After initial comparisons of the one-dimensional model to measurements of oil droplets in an axisymmetric jet, it is then applied in a three-dimensional LES of a jet in cross-flow with large oil droplets of a single size being released at the source of the jet. We model the concentration fields using bins of discrete droplet sizes and solve scalar transport equations for each bin. The resulting droplet size distributions are compared with published experimental data, and good agreement for the relative size distribution is obtained. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behaviour.
Recovery of the fetal electrocardiogram for morphological analysis from two trans-abdominal channels via optimal shrinkage.

Objective We propose a novel algorithm to recover fetal electrocardiogram (ECG) for both the fetal heart rate analysis and morphological analysis of its waveform from two or three trans-abdominal maternal ECG channels. Approach We design an algorithm based on the optimal-shrinkage under the wave-shape manifold model. For the fetal heart rate analysis, the algorithm is evaluated on publicly available database, 2013 PhyioNet/Computing in Cardiology Challenge, set A (CinC2013). For the morphological analysis, we analyze CinC2013 and another publicly available database, non-invasive fetal ECG arrhythmia database (nifeadb), and propose to simulate semi-real databases by mixing the MIT-BIH normal sinus rhythm database and MITDB arrhythmia database. Main results For the fetal R peak detection, the proposed algorithm outperforms all algorithms under comparison. For the morphological analysis, the algorithm provides an encouraging result in recovery of the fetal ECG waveform, including PR, QT and ST intervals, even when the fetus has arrhythmia, both in real and simulated databases. Significance To the best of our knowledge, this is the first work focusing on recovering the fetal ECG for morphological analysis from two or three channels with an algorithm potentially applicable for continuous fetal electrocardiographic monitoring, which creates the potential for long term monitoring purpose.
Single-cell q-PCR derived expression profiles of identified sensory neurons.

Sensory neurons are chemically and functionally heterogeneous, and this heterogeneity has been examined extensively over the last several decades. These studies have employed a variety of different...
Using Machine Learning to Construct Velocity Fields from OH-PLIF Images

This work utilizes data-driven methods to morph a series of time-resolved experimental OH-PLIF images into corresponding three-component planar PIV fields in the closed domain of a premixed swirl c...