cssi/SciSciGPT-SciSciNet huggingface dataset:
The Restriction Operator on Bergman Spaces

Motivated by questions related to the compactness of the $${\overline{\partial }}$$-Neumann operator, we study the restriction operator from the Bergman space of a domain in $$\mathbb {C}^n$$ to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the domain whose symbol is the characteristic function of the subset. Using the biholomorphic invariance of the spectrum of the associated Toeplitz operator, we study the restriction operator from the Bergman space of the unit disc to the Bergman space of subdomains with large symmetry groups, such as horodiscs and subdomains bounded by hypercycles. Furthermore, we prove a sharp estimate of the norm of the restriction operator in case the domain and the subdomain are balls. We also study various operator theoretic properties of the restriction operator such as compactness and essential norm estimates.
The unimodality of a polynomial coming from a rational integral. Back to the original proof

Abstract A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.
Small amplitude periodic solutions of Klein–Gordon equations

Abstract We consider a class of nonlinear Klein–Gordon equations u t t = u x x − u + f ( u ) and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales. The proof is based on a combination of Lyapunov–Schmidt reduction, averaging and Nash–Moser iteration.
Entropy of closed surfaces and min-max theory

Entropy is a natural geometric quantity measuring the complexity of a surface embedded in $\mathbb{R}^3$. For dynamical reasons relating to mean curvature flow, Colding–Ilmanen–Minicozzi–White conjectured (since proved by Bernstein–Wang) that the entropy of any closed surface is at least that of the self-shrinking two-sphere. In this paper we give an alternative proof of their conjecture for closed embedded 2-spheres. Our results can be thought of as the parabolic analog to the Willmore conjecture and our argument is analogous in many ways to that of Marques–Neves on the Willmore problem. The main tool is the min-max theory applied to the Gaussian area functional in $\mathbb{R}^3$ which we also establish. To any closed surface in $\mathbb{R}^3$ we associate a four parameter canonical family of surfaces and run a min-max procedure. The key step is ruling out the min-max sequence approaching a self-shrinking plane, and we accomplish this with a degree argument. To establish the min-max theory for $\mathbb{R}^3$ with Gaussian weight, the crucial ingredient is a tightening map that decreases the mass of nonstationary varifolds (with respect to the Gaussian metric of $\mathbb{R}^3$) in a continuous manner.
On Attractors of Isospectral Compressions of Networks

In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristics (attributes) of the network’s nodes (edges). Each isospectral compression (when a certain characteristic is fixed) defines a dynamical system on the space of all networks. It is shown that any orbit of such dynamical system which starts at any finite network (as the initial point of this orbit) converges to an attractor. This attractor is a smaller network where the chosen characteristic has the same value for all nodes (or edges). We demonstrate that isospectral compressions of one and the same network defined by different characteristics of nodes (or edges) may converge to the same as well as to different attractors. It is also shown that a collection of networks may be spectrally equivalent with respect to some network characteristic but nonequivalent with respect to another. These results suggest a new constructive approach which allows us to analyze and compare the topologies of different networks.
Global matrix factorizations

We study matrix factorization and curved module categories for Landau-Ginzburg models (X,W) with X a smooth variety, extending parts of the work of Dyckerhoff. Following Positselski, we equip these categories with model category structures. Using results of Rouquier and Orlov, we identify compact generators. Via To\"en's derived Morita theory, we identify Hochschild cohomology with derived endomorphisms of the diagonal curved module; we compute the latter and get the expected result. Finally, we show that our categories are smooth, proper when the singular locus of W is proper, and Calabi-Yau when the total space X is Calabi-Yau.
Virtual Legendrian isotopy

An elementary stabilization of a Legendrian link L in the spherical cotangent bundle ST M of a surface M is a surgery that results in attaching a handle to M along two discs away from the image in M of the projection of the link L. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies. We study virtual Legendrian isotopy classes of Legendrian links and show that every such class contains a unique irreducible representative. In particular we get a solution to the following conjecture of Cahn, Levi and the rst author: two Legendrian knots in ST S 2 that are isotopic as virtual Legendrian knots must be Legendrian isotopic in ST S 2 :
Learning-Based Single-Document Summarization with Compression and Anaphoricity Constraints

We present a discriminative model for single-document summarization that integrally combines compression and anaphoricity constraints. Our model selects textual units to include in the summary based on a rich set of sparse features whose weights are learned on a large corpus. We allow for the deletion of content within a sentence when that deletion is licensed by compression rules; in our framework, these are implemented as dependencies between subsentential units of text. Anaphoricity constraints then improve cross-sentence coherence by guaranteeing that, for each pronoun included in the summary, the pronoun's antecedent is included as well or the pronoun is rewritten as a full mention. When trained end-to-end, our final system outperforms prior work on both ROUGE as well as on human judgments of linguistic quality.
Provably safe and deadlock-free execution of multi-robot plans under delaying disturbances

One of the standing challenges in multi-robot systems is the ability to reliably coordinate motions of multiple robots in environments where the robots are subject to disturbances. We consider disturbances that force the robot to temporarily stop and delay its advancement along its planned trajectory which can be used to model, e.g., passing-by humans for whom the robots have to yield. Although reactive collision-avoidance methods are often used in this context, they may lead to deadlocks between robots. We design a multi-robot control strategy for executing coordinated trajectories computed by a multi-robot trajectory planner and give a proof that the strategy is safe and deadlock-free even when robots are subject to delaying disturbances. Our simulations show that the proposed strategy scales significantly better with the intensity of disturbances than the naive liveness-preserving approach. The empirical results further confirm that the proposed approach is more reliable and also more efficient than state-of-the-art reactive techniques.
Age of information in a network of preemptive servers

A source submits status updates to a network for delivery to a destination monitor. Updates follow a route through a series of network nodes. Each node is a last-come-first-served queue supporting preemption in service. We characterize the average age of information at the input and output of each node in the route induced by the updates passing through. For Poisson arrivals to a line network of preemptive memoryless servers, we show that average age accumulates through successive network nodes.
Making “fetch” happen: The influence of social and linguistic context on nonstandard word growth and decline

In an online community, new words come and go: today’s “haha” may be replaced by tomorrow’s “lol.” Changes in online writing are usually studied as a social process, with innovations diffusing through a network of individuals in a speech community. But unlike other types of innovation, language change is shaped and constrained by the grammatical system in which it takes part. To investigate the role of social and structural factors in language change, we undertake a large-scale analysis of the frequencies of non-standard words in Reddit. Dissemination across many linguistic contexts is a predictor of success: words that appear in more linguistic contexts grow faster and survive longer. Furthermore, social dissemination plays a less important role in explaining word growth and decline than previously hypothesized.
Chip-Firing and Riemann-Roch Theory for Directed Graphs

Abstract Baker and Norine developed a graph theoretic analogue of the classical Riemann-Roch theorem. Amini and Manjunath extended their criteria to all full-dimensional lattices orthogonal to the all ones vector. We show that Amini and Manjunathʼs criteria holds for all full-dimensional lattices orthogonal to some positive vector and study some combinatorial examples of such lattices. Two distinct generalizations of the chip-firing game of Baker and Norine to directed graphs are provided. We describe how the “row” chip-firing game is related to the sandpile model and the “column” chip-firing game is related to directed G-parking functions. We finish with a discussion of arithmetical graphs, introduced by Lorenzini, viewing them as a class of vertex weighted graphs whose Laplacian is orthogonal to a positive vector and describe how they may be viewed as a special class of unweighted strongly connected directed graphs.
Hiding in Plain Sight: Insights about Health-Care Trends Gained through Open Health Data

The open data movement constitutes an approach to achieving accountability for government organizations. Government agencies at the Federal and State levels have released open health data consistin...
A Multiwavelength Study of Tadpole Galaxies in the Hubble Ultra Deep Field

Multiwavelength data are essential in order to provide a complete picture of galaxy evolution and to inform studies of galaxies' morphological properties across cosmic time. Here we present the results of a multiwavelength investigation of the morphologies of "tadpole" galaxies at intermediate redshift (0.314 < z < 3.175) in the Hubble Ultra Deep Field. These galaxies were previously selected from deep Hubble Space Telescope (HST) F775W data based on their distinct asymmetric knot-plus-tail morphologies. Here we use deep Wide Field Camera 3 near-infrared imaging in addition to the HST optical data in order to study the rest-frame UV/optical morphologies of these galaxies across the redshift range 0.3 < z < 3.2. This study reveals that the majority of these galaxies do retain their general asymmetric morphology in the rest-frame optical over this redshift range, if not the distinct "tadpole" shape. The average stellar mass of tadpole galaxies is lower than that of field galaxies, with the effect being slightly greater at higher redshift within the errors. Estimated from spectral energy distribution fits, the average age of tadpole galaxies is younger than that of field galaxies in the lower-redshift bin, and the average metallicity is lower (whereas the specific star formation rate for tadpoles is roughly the same as field galaxies across the redshift range probed here). These average effects combined support the conclusion that this subset of galaxies is in an active phase of assembly, either late-stage merging or cold gas accretion causing localized clumpy star formation.
Prediction of Individual Outcomes for Asthma Sufferers

We consider the problem of individual-specific medication level recommendation (initiation, removal, increase, or decrease) for asthma sufferers. Asthma is one of the most common chronic diseases in both adults and children, affecting 8% of the US population and costing $37-63 billion/year in the United States of America. Asthma is a complex disease, whose symptoms may wax and wane, making it difficult for clinicians to predict outcomes and prognosis. Improved ability to predict prognosis can inform decision making and may promote conversations between clinician and provider around optimizing medication therapy. Data from the US Medical Expenditure Panel Survey (MEPS) years 2000-2010 were used to fit a longitudinal model for a multivariate response of adverse events (Emergency Department or in-patient visits, excessive rescue inhaler use, and oral steroid use). To reduce bias in the estimation of medication effects, medication level was treated as a latent process which was restricted to be consistent with prescription refill data. This approach is demonstrated to be effective in the MEPS cohort via predictions on a validation hold out set and a synthetic data simulation study. This framework can be easily generalized to medication decisions for other conditions as well.
Chip-Firing on Trees of Loops

Cools, Draisma, Payne, and Robeva proved that generic metric graphs that are "paths of loops" are Brill-Noether general. We show that Brill-Noether generality does not hold for "trees of loops": the only trees of loops that are Brill-Noether general are paths of loops. We study various notions of generality and examine which of these graphs satisfy them.
Identifying causal effects with computer algebra

The long-standing identification problem for causal effects in graphical models has many partial results but lacks a systematic study. We show how computer algebra can be used to either prove that a causal effect can be identified, generically identified, or show that the effect is not generically identifiable. We report on the results of our computations for linear structural equation models, where we determine precisely which causal effects are generically identifiable for all graphs on three and four vertices.
Algebraic intersection spaces

We define a variant of intersection space theory that applies to many compact complex and real analytic spaces X, including all complex projective varieties; this is a significant extension to a th...
Exemplar-Centered Supervised Shallow Parametric Data Embedding

Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these approaches involve pairwise training data comparisons, and thus have quadratic computational complexity with respect to the size of training set, preventing them from scaling to fairly big datasets. Moreover, during testing, comparing test data against all the training data points is also expensive in terms of both computational cost and resources required. Furthermore, previous metrics are either too constrained or too expressive to be well learned. To effectively solve these issues, we present an exemplar-centered supervised shallow parametric data embedding model, using a Maximally Collapsing Metric Learning (MCML) objective. Our strategy learns a shallow high-order parametric embedding function and compares training/test data only with learned or precomputed exemplars, resulting in a cost function with linear computational complexity for both training and testing. We also empirically demonstrate, using several benchmark datasets, that for classification in two-dimensional embedding space, our approach not only gains speedup of kNN by hundreds of times, but also outperforms state-of-the-art supervised embedding approaches.
Resolving Language and Vision Ambiguities Together: Joint Segmentation & Prepositional Attachment Resolution in Captioned Scenes

We present an approach to simultaneously perform semantic segmentation and prepositional phrase attachment resolution for captioned images. Some ambiguities in language cannot be resolved without simultaneously reasoning about an associated image. If we consider the sentence "I shot an elephant in my pajamas", looking at language alone (and not using common sense), it is unclear if it is the person or the elephant wearing the pajamas or both. Our approach produces a diverse set of plausible hypotheses for both semantic segmentation and prepositional phrase attachment resolution that are then jointly reranked to select the most consistent pair. We show that our semantic segmentation and prepositional phrase attachment resolution modules have complementary strengths, and that joint reasoning produces more accurate results than any module operating in isolation. Multiple hypotheses are also shown to be crucial to improved multiple-module reasoning. Our vision and language approach significantly outperforms the Stanford Parser (De Marneffe et al., 2006) by 17.91% (28.69% relative) and 12.83% (25.28% relative) in two different experiments. We also make small improvements over DeepLab-CRF (Chen et al., 2015).
Active and passive learning of linear separators under log-concave distributions

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneouslinear separators under nearly log-concave distributions. Building on this, we provide a computationally efficient PAC algorithm with optimal (up to a constant factor) sample complexity for such problems. This resolves an open question of (Long, 1995, 2003; Bshouty et al., 2009) concerning the sample complexity of efficient PAC algorithms under the uniformdistribution in the unit ball. Moreover,it providesthe first bound for a polynomial-time PAC algorithm that is tight for an interesting infinite class of hypothesis functions under a general and natural class of data-distributions, providing significant progress towards a longstanding open question of (Ehrenfeucht et al., 1989; Blumer et al., 1989). We also provide new bounds for active and passive learning in the case that the data might not be linearly separable, both in the agnostic case and and underthe Tsybakovlow-noisecondition. To derive our results, we provide new structural results for (nearly) log-concave distributions, which might be of independent interest as well.
Stable Prehensile Pushing: In-Hand Manipulation with Alternating Sticking Contacts

This paper presents an approach to in-hand manipulation planning that exploits the mechanics of alternating sticking contact. Particularly, we consider the problem of manipulating a grasped object using external pushes for which the pusher sticks to the object. Given the physical properties of the object, frictional coefficients at contacts and a desired regrasp on the object, we propose a sampling-based planning framework that builds a pushing strategy concatenating different feasible stable pushes to achieve the desired regrasp. An efficient dynamics formulation allows us to plan in-hand manipulations 100–1000 times faster than our previous work which builds upon a complementarity formulation. Experimental observations for the generated plans show that the object precisely moves in the grasp as expected by the planner. Video Summary – youtu.be/qOTKRJMx6Ho
A homotopy method for computing the largest eigenvalue of an irreducible nonnegative tensor

Abstract In this paper we propose a homotopy method to compute the largest eigenvalue and a corresponding eigenvector of a nonnegative tensor. We prove that it converges to the desired eigenpair when the tensor is irreducible. We also implement the method using a prediction–correction approach for path following. Some numerical results are provided to illustrate the efficiency of the method.
The typical structure of maximal triangle-free graphs

Recently, settling a question of Erd} os, Balogh and Pet r ckov a showed that there are at most 2 n 2 =8+o(n 2 ) n-vertex maximal triangle-free graphs, matching the previously known lower bound. Here we characterize the typical structure of maximal trianglefree graphs. We show that almost every maximal triangle-free graph G admits a vertex partition X[ Y such that G[X] is a perfect matching and Y is an independent set. Our proof uses the Ruzsa-Szemer edi removal lemma, the Erd} os-Simonovits stability theorem, and recent results of Balogh-Morris-Samotij and Saxton-Thomason on characterization of the structure of independent sets in hypergraphs. The proof also relies on a new bound on the number of maximal independent sets in triangle-free graphs with many vertex-disjoint P3’s, which is of independent interest.
The application of distributed control algorithms using VOLTTRON-based software platform

This paper gives an insight into the applications of an open-source control system platform named VOLTTRON. This platform was developed by the Pacific Northwest National Laboratory. A brief introduction is given on the functionality and key features of the platform. Potential applications in the areas of building control and electric vehicle charging are stated, along with an overview of existing projects. A comparison is also made between VOLTTRON and other related software. An actual implementation case of VOLTTRON is then presented in the case study. The demonstration uses the VOLTTRON platform as a message bus. Decentralized generators and consumers are simulated by 16 single-board computers.
Finite Sample Prediction and Recovery Bounds for Ordinal Embedding

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints like ``item $i$ is closer to item $j$ than item $k$''. Ordinal constraints like this often come from human judgments. The classic approach to solving this problem is known as non-metric multidimensional scaling. To account for errors and variation in judgments, we consider the noisy situation in which the given constraints are independently corrupted by reversing the correct constraint with some probability. The ordinal embedding problem has been studied for decades, but most past work pays little attention to the question of whether accurate embedding is possible, apart from empirical studies. This paper shows that under a generative data model it is possible to learn the correct embedding from noisy distance comparisons. In establishing this fundamental result, the paper makes several new contributions. First, we derive prediction error bounds for embedding from noisy distance comparisons by exploiting the fact that the rank of a distance matrix of points in $\R^d$ is at most $d+2$. These bounds characterize how well a learned embedding predicts new comparative judgments. Second, we show that the underlying embedding can be recovered by solving a simple convex optimization. This result is highly non-trivial since we show that the linear map corresponding to distance comparisons is non-invertible, but there exists a nonlinear map that is invertible. Third, two new algorithms for ordinal embedding are proposed and evaluated in experiments.
Conceptions of topological transitivity

Abstract There are several different common definitions of a property in topological dynamics called “topological transitivity,” and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various equivalences are proved in different places, but the full story is difficult to find. This note provides a complete description of the relationships among the different properties.
Vanishing and injectivity theorems for Hodge modules

We prove a surjectivity theorem for the Deligne canonical extension of a polarizable variation of Hodge structure with quasi-unipotent monodromy at infinity along the lines of Esnault-Viehweg. We deduce from it several injectivity theorems and vanishing theorems for pure Hodge modules. We also give an inductive proof of Kawamata-Viehweg vanishing for the lowest graded piece of the Hodge filtration of a pure Hodge module using mixed Hodge modules of nearby cycles.
Learning Populations of Parameters

Consider the following estimation problem: there are $n$ entities, each with an unknown parameter $p_i \in [0,1]$, and we observe $n$ independent random variables, $X_1,\ldots,X_n$, with $X_i \sim $ Binomial$(t, p_i)$. How accurately can one recover the ``histogram'' (i.e. cumulative density function) of the $p_i$'s? While the empirical estimates would recover the histogram to earth mover distance $\Theta(\frac{1}{\sqrt{t}})$ (equivalently, $\ell_1$ distance between the CDFs), we show that, provided $n$ is sufficiently large, we can achieve error $O(\frac{1}{t})$ which is information theoretically optimal. We also extend our results to the multi-dimensional parameter case, capturing settings where each member of the population has multiple associated parameters. Beyond the theoretical results, we demonstrate that the recovery algorithm performs well in practice on a variety of datasets, providing illuminating insights into several domains, including politics, sports analytics, and variation in the gender ratio of offspring.
Random matrices: Probability of Normality

Abstract We consider a random n × n matrix, M n , whose entries are independent and identically distributed (i.i.d.) Rademacher random variables (taking values { ± 1 } with probability 1/2) and prove 2 − ( 0.5 + o ( 1 ) ) n 2 ≤ P ( M n is normal ) ≤ 2 − ( 0.302 + o ( 1 ) ) n 2 . We conjecture that the lower bound is sharp.
The $q = -1$ phenomenon via homology concentration

We introduce a homological approach to exhibiting instances of Stembridge's q=-1 phenomenon. This approach is shown to explain two important instances of the phenomenon, namely that of partitions whose Ferrers diagrams fit in a rectangle of fixed size and that of plane partitions fitting in a box of fixed size. A more general framework of invariant and coinvariant complexes with coefficients taken mod 2 is developed, and as a part of this story an analogous homological result for necklaces is conjectured.
Fair Forests: Regularized Tree Induction to Minimize Model Bias

The potential lack of fairness in the outputs of machine learning algorithms has recently gained attention both within the research community as well as in society more broadly. Surprisingly, there is no prior work developing tree-induction algorithms for building fair decision trees or fair random forests. These methods have widespread popularity as they are one of the few to be simultaneously interpretable, non-linear, and easy-to-use. In this paper we develop, to our knowledge, the first technique for the induction of fair decision trees.We show that our "Fair Forest" retains the benefits of the tree-based approach, while providing both greater accuracy and fairness than other alternatives, for both "group fairness'' and "individual fairness.'' We also introduce new measures for fairness which are able to handle multinomial and continues attributes as well as regression problems, as opposed to binary attributes and labels only. Finally, we demonstrate a new, more robust evaluation procedure for algorithms that considers the dataset in its entirety rather than only a specific protected attribute.
Learning Factorized Multimodal Representations

Learning multimodal representations is a fundamentally complex research problem due to the presence of multiple heterogeneous sources of information. Although the presence of multiple modalities provides additional valuable information, there are two key challenges to address when learning from multimodal data: 1) models must learn the complex intra-modal and cross-modal interactions for prediction and 2) models must be robust to unexpected missing or noisy modalities during testing. In this paper, we propose to optimize for a joint generative-discriminative objective across multimodal data and labels. We introduce a model that factorizes representations into two sets of independent factors: multimodal discriminative and modality-specific generative factors. Multimodal discriminative factors are shared across all modalities and contain joint multimodal features required for discriminative tasks such as sentiment prediction. Modality-specific generative factors are unique for each modality and contain the information required for generating data. Experimental results show that our model is able to learn meaningful multimodal representations that achieve state-of-the-art or competitive performance on six multimodal datasets. Our model demonstrates flexible generative capabilities by conditioning on independent factors and can reconstruct missing modalities without significantly impacting performance. Lastly, we interpret our factorized representations to understand the interactions that influence multimodal learning.
Acoustic Feature Learning via Deep Variational Canonical Correlation Analysis.

We study the problem of acoustic feature learning in the setting where we have access to another (non-acoustic) modality for feature learning but not at test time. We use deep variational canonical correlation analysis (VCCA), a recently proposed deep generative method for multi-view representation learning. We also extend VCCA with improved latent variable priors and with adversarial learning. Compared to other techniques for multi-view feature learning, VCCA's advantages include an intuitive latent variable interpretation and a variational lower bound objective that can be trained end-to-end efficiently. We compare VCCA and its extensions with previous feature learning methods on the University of Wisconsin X-ray Microbeam Database, and show that VCCA-based feature learning improves over previous methods for speaker-independent phonetic recognition.
Hybrid Voltage Control in Distribution Networks Under Limited Communication Rates

Voltage regulation in distribution networks is challenged by increasing penetration of distributed energy resources (DERs). Thanks to advancement in power electronics, DERs can be leveraged to regulate the grid voltage by quickly changing their reactive power outputs. This paper develops a hybrid voltage control (HVC) strategy that can seamlessly integrate both local and distributed designs to effectively coordinate the network-wide DERs. By minimizing a special voltage mismatch objective, we achieve the proposed HVC design by adopting partial primal-dual gradient updates that can allow for a distributed and online implementation. The proposed HVC design improves over existing distributed approaches by reliably integrating local voltage feedback. As a result, it can dynamically adapt to varying system operating conditions while being fully cognizant of the instantaneous availability of communication links. Under the worst-case scenario of total link outages, the proposed design naturally boils down to a surrogate local control implementation. Numerical tests on realistic feeder cases have been made to corroborate our analytical results and demonstrate the algorithmic performance.
Distance to the nearest stable Metzler matrix

This paper considers the non-convex problem of finding the nearest Metzler matrix to a given possibly unstable matrix. Linear systems whose state vector evolves according to a Metzler matrix have many desirable properties in analysis and control with regard to scalability. This motivates the question, how close (in the Frobenius norm of coefficients) to the nearest Metzler matrix are we? Dropping the Metzler constraint, this problem has recently been studied using the theory of dissipative Hamiltonian (DH) systems, which provide a helpful characterization of the feasible set of stable matrices. This work uses the DH theory to provide a block coordinate descent algorithm consisting of a quadratic program with favourable structural properties and a semidefinite program for which recent diagonal dominance results can be used to improve tractability.
Enumeration of lozenge tilings of a hexagon with a shamrock missing on the symmetry axis

Abstract In their paper about a dual of MacMahon’s classical theorem on plane partitions, Ciucu and Krattenthaler proved a closed form product formula for the tiling number of a hexagon with a “shamrock”, a union of four adjacent triangles, removed in the center (Ciucu and Krattenthaler, 2013). Lai later presented a q -enumeration for lozenge tilings of a hexagon with a shamrock removed from the boundary (Lai, 2017). It appears that the above are the only two positions of the shamrock hole that yield nice tiling enumerations. In this paper, we show that in the case of symmetric hexagons, we always have a simple product formula for the number of tilings when removing a shamrock at any position along the symmetry axis. Our result also generalizes Eisenkolbl’s related work about lozenge tilings of a hexagon with two unit triangles missing on the symmetry axis (Eisenkolbl, 1999).
Tight Lower Bounds on the Contact Distance Distribution in Poisson Hole Process

In this letter, we derive new lower bounds on the cumulative distribution function (CDF) of the contact distance in the Poisson hole process (PHP) for two cases: 1) reference point is selected uniformly at random from $\mathbb {R}^{\boldsymbol {2}}$ independently of the PHP and 2) reference point is located at the center of a hole selected uniformly at random from the PHP. While one can derive upper bounds on the CDF of contact distance by simply ignoring the effect of holes, deriving lower bounds is known to be relatively more challenging. As a part of our proof, we introduce a tractable way of bounding the effect of all the holes in a PHP, which can be used to study other properties of a PHP as well.
Correlation Clustering and Biclustering With Locally Bounded Errors

We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with + or −, we wish to partition the graph into clusters while trying to avoid errors: + edges between clusters or − edges within clusters. Classically, one seeks to minimize the total number of such errors. We introduce a new framework that allows the objective to be a more general function of the number of errors at each vertex (for example, we may wish to minimize the number of errors at the worst vertex) and provides a rounding algorithm which converts “fractional clusterings” into discrete clusterings while causing only a constant-factor blowup in the number of errors at each vertex. This rounding algorithm yields constant-factor approximation algorithms for the discrete problem under a wide variety of objective functions.
Subspace Learning From Bits

Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and internet-of-things. To reduce the communication, sensing, and storage complexity, this paper proposes a simple sensing and estimation framework to faithfully recover the principal subspace of high-dimensional data streams using a collection of binary measurements from distributed sensors, without transmitting the whole data. The binary measurements are designed to indicate comparison outcomes of aggregated energy projections of the data samples over pairs of randomly selected directions. When the covariance matrix is a low-rank matrix, we propose a spectral estimator that recovers the principal subspace of the covariance matrix as the subspace spanned by the top eigenvectors of a properly designed surrogate matrix, which is provably accurate as soon as the number of binary measurements is sufficiently large. An adaptive rank selection strategy based on soft thresholding is also presented. Furthermore, we propose a tailored spectral estimator when the covariance matrix is additionally Toeplitz, and show that the reliable estimation can be obtained from a substantially smaller number of binary measurements. Our results hold even when a constant fraction of the binary measurements is randomly flipped. Finally, we develop a low-complexity online algorithm to track the principal subspace when new measurements arrive sequentially. Numerical experiments are provided to validate the proposed approach.
A Statistical Method for Parking Spaces Occupancy Detection via Automotive Radars

Real-time parking occupancy information is valuable for guiding drivers' searching for parking spaces. Recently many parking detection systems using on-vehicle range- based sensors are invented. However, they disregard the practical difficulty of obtaining access to raw sensory data which are required for feature-based algorithms. In this paper, we focus on transforming short-range radars (SRR) embedded in Advanced Driver Assistance System (ADAS) to collect occupancy information, and broadcast it through a connected vehicle network. The challenge that raw data transmitted through ADAS unit has been encoded to sparse points is overcome by analyzing the cumulative data by statistical techniques instead of direct feature extractions. We propose a two-step classification algorithm combining Mean-Shift clustering and Support Vector Machine, and evaluate it through field experiments. The results show that the average Type I error rate for off-street parking is $15.23 \%$ and for on-street parking is $32.62\%$. In both cased the Type II error rates are less than $20 \%$, and Bayesian updating can recursively improve the mapping results. This paper provides a comprehensive method to leverage on ADAS sensors for the parking detection function.
On the proportionality of Chern and Riemannian scalar curvatures

On a Kahler manifold there is a clear connection between the complex geometry and underlying Riemannian geometry. In some ways, this can be used to characterize the Kahler condition. While such a link is not so obvious in the non-Kahler setting, one can seek to understand extensions of these characterizations to general Hermitian manifolds. This idea has been the subject of much study from the cohomological side, however, the focus here is to address such a question from the perspective of curvature relationships. In particular, on compact manifolds the Kahler condition is characterized by the relationship that the Chern scalar curvature is equal to half the Riemannian scalar curvature. What we study here is the existence, or lack thereof, of non-Kahler Hermitian metrics for which a more general proportionality relationship between these scalar curvatures holds.
Onsager's energy conservation for inhomogeneous Euler equations

Abstract This paper addresses the problem of energy conservation for the two- and three-dimensional density-dependent Euler equations. Two types of sufficient conditions on the regularity of solutions are provided to ensure the conservation of total kinetic energy on the entire time interval including the initial time. The first class of data assumes integrability on the spatial gradient of the density, and hence covers the classical result of Constantin–E–Titi [4] for the homogeneous Euler equations. The other type of data imposes extra time Besov regularity on the velocity profile, and the corresponding result can be applied to deal with a wide class of rough density profiles.
Machine Self-confidence in Autonomous Systems via Meta-analysis of Decision Processes

Algorithmic assurances assist human users in trusting advanced autonomous systems appropriately. This work explores one approach to creating assurances in which systems self-assess their decision-making capabilities, resulting in a ‘self-confidence’ measure. We present a framework for self-confidence assessment and reporting using meta-analysis factors, and then develop a new factor pertaining to ‘solver quality’ in the context of solving Markov decision processes (MDPs), which are widely used in autonomous systems. A novel method for computing solver quality self-confidence is derived, drawing inspiration from empirical hardness models. Numerical examples show our approach has desirable properties for enabling an MDP-based agent to self-assess its performance for a given task under different conditions. Experimental results for a simulated autonomous vehicle navigation problem show significantly improved delegated task performance outcomes in conditions where self-confidence reports are provided to users.
Breakdown of Carr-Purcell Meiboom-Gill spin echoes in inhomogeneous fields

The Carr-Purcell Meiboom-Gill (CPMG) experiment has been used for decades to measure nuclear-spin transverse (T2) relaxation times. In the presence of magnetic field inhomogeneities, the limit of short interpulse spacings yields the intrinsic T2 time. Here, we show that the signal decay in such experiments exhibits fundamentally different behaviors between liquids and gases. In gases, the CPMG unexpectedly fails to eliminate the inhomogeneous broadening due to the non-Fickian nature of the motional averaging.
Minimal fields of definition for Galois action

Let K be a field, and let f:X→Y be a finite etale cover between reduced and geometrically irreducible K-schemes of finite type such that fKs is Galois. Assuming f admits a Galois K-form f¯:X¯→Y, we use it to analyze fields of definition over K for the Galois property of f and the presence of K-points in general K-forms f′:X′→Y over Y(K). Additionally, we show that if K is Hilbertian, the group G is non-abelian, and the base variety is rational, then there are finite separable extensions L/K such that some L-form of fL does not descend to a cover of Y.
A Unified Framework for Multi-view Multi-class Object Pose Estimation

One[NOSPACE] [NOSPACE][SPACE]core challenge in object pose estimation is to ensure accurate and robust performance for large numbers of diverse foreground objects amidst complex background clutter. In this work, we present a scalable framework for accurately inferring six Degree-of-Freedom (6-DoF) pose for a large number of object classes from single or multiple views. To learn discriminative pose features, we integrate three new capabilities into a deep Convolutional Neural Network (CNN): an inference scheme that combines both classification and pose regression based on a uniform tessellation of the Special Euclidean group in three dimensions (SE(3)), the fusion of class priors into the training process via a tiled class map, and an additional regularization using deep supervision with an object mask. Further, an efficient multi-view framework is formulated to address single-view ambiguity. We show that this framework consistently improves the performance of the single-view network. We evaluate our method on three large-scale benchmarks: YCB-Video, JHUScene-50 and ObjectNet-3D. Our approach achieves competitive or superior performance over the current state-of-the-art methods.
Singular vectors under random perturbation

Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, an exact calculation is hard to achieve, and the following problem is of importance: How much does a small perturbation to the matrix change the singular vectors? Answering this question, classical theorems, such as those of Davis-Kahan and Wedin, give tight estimates for the worst-case scenario. In this paper, we show that if the perturbation (noise) is random and our matrix has low rank, then better estimates can be obtained. Our method relies on high dimensional geometry and is different from those used in earlier papers. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 © 2011 Wiley Periodicals, Inc.
Harmonic Analysis on the Positive Rationals. Determination of the Group Generated by the Ratios $(an+b)/(An+B)$

The multiplicative group generated by a certain sequence of rationals is determined, settling a 30-year conjecture.
Robust graphical modeling with t -distributions

Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent progress includes the development of fitting methodology involving penalization of the likelihood function. In this paper we advocate the use of the multivariate t and related distributions for more robust inference of graphs. In particular, we demonstrate that penalized likelihood inference combined with an application of the EM algorithm provides a simple and computationally efficient approach to model selection in the t-distribution case.
Submonoids of groups, and group-representability of restricted relation algebras

Marek Kuczma asked in 1980 whether for every positive integer n, there exists a subsemigroup M of a group G, such that G is equal to the n-fold product $$M\,M^{-1} M\,M^{-1} \ldots \,M^{(-1)^{n-1}}$$ , but not to any proper initial subproduct of this product. We answer his question affirmatively, and prove a more general result on representing a certain sort of relation algebra by a family of subsets of a group. We also sketch several variants of the latter result.
Polyhedral geometry for lecture hall partitions

Lecture hall partitions are a fundamental combinatorial structure which have been studied extensively over the past two decades. These objects have produced new results, as well as reinterpretations and generalizations of classicial results, which are of interest in combinatorial number theory, enumerative combinatorics, and convex geometry. In a recent survey of Savage \cite{Savage-LHP-Survey}, a wide variety of these results are nicely presented. However, since the publication of this survey, there have been many new developments related to the polyhedral geometry and Ehrhart theory arising from lecture hall partitions. Subsequently, in this survey article, we focus exclusively on the polyhedral geometric results in the theory of lecture hall partitions in an effort to showcase these new developments. In particular, we highlight results on lecture hall cones, lecture hall simplices, and lecture hall order polytopes. We conclude with an extensive list of open problems and conjectures in this area.
Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow

Distribution system operators (DSOs) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This paper describes a decomposable approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov decision process (MDP). The MDP model is then integrated with a chance constrained optimal power flow that accounts for the uncertainty of photovoltaic resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative spatio-temporal dual decomposition algorithm (ST-D2). We demonstrate the merits of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system.
On the Convergence Rate of Decomposable Submodular Function Minimization

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an easy-to-use, parallelizable algorithm for minimizing submodular functions that decompose as the sum of "simple" submodular functions. Empirically, this algorithm performs extremely well, but no theoretical analysis was given. In this paper, we show that the algorithm converges linearly, and we provide upper and lower bounds on the rate of convergence. Our proof relies on the geometry of submodular polyhedra and draws on results from spectral graph theory.