cssi/SciSciGPT-SciSciNet huggingface dataset:
Sensor Assignment Algorithms to Improve Observability While Tracking Targets

In this paper, we study two sensor assignment problems for multitarget tracking with the goal of improving the observability of the underlying estimator. We consider various measures of the observability matrix as the assignment value function. We first study the general version where the sensors must form teams to track individual targets. If the value function is monotonically increasing and submodular, then a greedy algorithm yields a $1/2$ –approximation. We then study a restricted version where exactly two sensors must be assigned to each target. We present a $1/3$ –approximation algorithm for this problem, which holds for arbitrary value functions (not necessarily submodular or monotone). In addition to approximation algorithms, we also present various properties of observability measures. We show that the inverse of the condition number of the observability matrix is neither monotone nor submodular, but present other measures that are. Specifically, we show that the trace and rank of the symmetric observability matrix are monotone and submodular and the log determinant of the symmetric observability matrix is monotone and submodular when the matrix is nonsingular. If the target's motion model is not known, the inverse cannot be computed exactly. Instead, we present a lower bound for distance sensors. In addition to theoretical results, we evaluate our results empirically through simulations.
Holomorphic Line Bundles over a Tower of Coverings

We study a tower of normal coverings over a compact Kahler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution for zero currents of random holomorphic sections. Furthermore, we obtain a variance estimate for those random zero currents, which yields the almost sure convergence under some geometric condition.
An Optimization Approach to Learning Falling Rule Lists

A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a regular decision list, the order of rules in a falling rule list is important -- each example is classified by the first rule whose antecedent it satisfies. Unlike a regular decision list, a falling rule list requires the probabilities of the desired outcome ("1") to be monotonically decreasing down the list. We propose an optimization approach to learning falling rule lists and "softly" falling rule lists, along with Monte-Carlo search algorithms that use bounds on the optimal solution to prune the search space.
K-theoretic Chern class formulas for vexillary degeneracy loci

Abstract Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the loci where a generic matrix drops rank, and where a generic symmetric or skew-symmetric matrix drops rank. In an appendix, we construct a K-theoretic Euler class for even-rank vector bundles with quadratic form, refining the Chow-theoretic class introduced by Edidin and Graham. We also establish a relation between top Chern classes of maximal isotropic subbundles, which is used in proving the type D degeneracy locus formulas.
Directional and Causal Information Flow in EEG for Assessing Perceived Audio Quality

In this paper, electroencephalography (EEG) measurements are used to infer change in cortical functional connectivity in response to change in audio stimulus. Experiments are conducted wherein the EEG activity of human subjects is recorded as they listen to audio sequences whose quality varies with time. A causal information theoretic framework is then proposed to measure the information flow between EEG sensors appropriately grouped into different regions of interest (ROI) over the cortex. A new causal bidirectional information (CBI) measure is defined as an improvement over standard directed information measures for the purposes of identifying connectivity between ROIs in a generalized cortical network setting. CBI can be intuitively interpreted as a causal bidirectional modification of directed information, and inherently calculates the divergence of the observed data from a multiple access channel with feedback. Further, we determine the analytical relationship between the different causal measures and compare how well they are able to distinguish between the perceived audio quality. The connectivity results inferred indicate a significant change in the rate of information flow between ROIs as the subjects listen to different audio qualities, with CBI being the best in discriminating between the perceived audio quality, compared to using standard directed information measures.
Feature-based aggregation and deep reinforcement learning: a survey and some new implementations

In this paper we discuss policy iteration methods for approximate solution of a finite-state discounted Markov decision problem, with a focus on feature-based aggregation methods and their connection with deep reinforcement learning schemes. We introduce features of the states of the original problem, and we formulate a smaller &#x201C aggregate &#x201D Markov decision problem, whose states relate to the features. We discuss properties and possible implementations of this type of aggregation, including a new approach to approximate policy iteration. In this approach the policy improvement operation combines feature-based aggregation with feature construction using deep neural networks or other calculations. We argue that the cost function of a policy may be approximated much more accurately by the nonlinear function of the features provided by aggregation, than by the linear function of the features provided by neural network-based reinforcement learning, thereby potentially leading to more effective policy improvement.
Integrality gaps and approximation algorithms for dispersers and bipartite expanders

We study the problem of approximating the quality of a disperser. A bipartite graph G on ([N], [M]) is a (ρN, (1 - δ)M)-disperser if for any subset S ⊆ [N] of size ρN, the neighbor set Γ(S) contains at least (1 - δ)M distinct vertices. Our main results are strong integrality gaps in the Lasserre hierarchy and an approximation algorithm for dispersers.1. For any α > 0, δ > 0, and a random bipartite graph G with left degree D = O(log N), we prove that the Lasserre hierarchy cannot distinguish whether G is an (Nα, (1 - δ)M)-disperser or not an (N1-α,δM)-disperser.2. For any ρ > 0, we prove that there exist infinitely many constants d such that the Lasserre hierarchy cannot distinguish whether a random bipartite graph G with right degree d is a (ρN, (1 - (1 - ρ)d)M)-disperser or not a (ρN,(1 - Ω([EQUATION]))M)-disperser. We also provide an efficient algorithm to find a subset of size exact ρN that has an approximation ratio matching the integrality gap within an extra loss of [EQUATION].Our method gives an integrality gap in the Lasserre hierarchy for bipartite expanders with left degree D. G on ([N],[M]) is a (ρN,a)-expander if for any subset S ⊆ [N] of size ρN, the neighbor set Γ(S) contains at least a · ρN distinct vertices. We prove that for any constant e > 0, there exist constants e'
Singular vectors of orthogonally decomposable tensors

Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its singular vector tuples as a variety in a product of projective spaces.
The Natural Stories Corpus

It is now a common practice to compare models of human language processing by predicting participant reactions (such as reading times) to corpora consisting of rich naturalistic linguistic materials. However, many of the corpora used in these studies are based on naturalistic text and thus do not contain many of the low-frequency syntactic constructions that are often required to distinguish processing theories. Here we describe a new corpus consisting of English texts edited to contain many low-frequency syntactic constructions while still sounding fluent to native speakers. The corpus is annotated with hand-corrected parse trees and includes self-paced reading time data. Here we give an overview of the content of the corpus and release the data.
Learning topology of the power distribution grid with and without missing data

Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original loopy grid graph by opening switches on some lines. Due to limited presence of real-time switch monitoring devices, the operating structure needs to be estimated indirectly. This paper presents a new learning algorithm that uses only nodal voltage measurements to determine the operational radial structure. The algorithm is based on the key result stating that the correct operating structure is the optimal solution of the minimum-weight spanning tree problem over the original loopy graph where weights on all permissible edges/lines (open or closed) is the variance of nodal voltage difference at the edge ends. Compared to existing work, this spanning tree based approach has significantly lower complexity as it does not require information on line parameters. Further, a modified learning algorithm is developed for cases when the input voltage measurements are limited to only a subset of the total grid nodes. Performance of the algorithms (with and without missing data) is demonstrated by experiments on test cases.
On the Power of Truncated SVD for General High-rank Matrix Estimation Problems

We show that given an estimate $\widehat{\mat A}$ that is close to a general high-rank positive semi-definite (PSD) matrix $\mat A$ in spectral norm (i.e., $\|\widehat{\mat A}-\mat A\|_2 \leq \delta$), the simple truncated Singular Value Decomposition of $\widehat{\mat A}$ produces a multiplicative approximation of $\mat A$ in Frobenius norm. This observation leads to many interesting results on general high-rank matrix estimation problems: 1.High-rank matrix completion: we show that it is possible to recover a {general high-rank matrix} $\mat A$ up to $(1+\varepsilon)$ relative error in Frobenius norm from partial observations, with sample complexity independent of the spectral gap of $\mat A$. 2.High-rank matrix denoising: we design algorithms that recovers a matrix $\mat A$ with relative error in Frobenius norm from its noise-perturbed observations, without assuming $\mat A$ is exactly low-rank. 3.Low-dimensional estimation of high-dimensional covariance: given $N$ i.i.d.~samples of dimension $n$ from $\mathcal N_n(\mat 0,\mat A)$, we show that it is possible to estimate the covariance matrix $\mat A$ with relative error in Frobenius norm with $N\approx n$,improving over classical covariance estimation results which requires $N\approx n^2$.
Strong accessibility of Coxeter groups over minimal splittings

Given a class of groups C, a group G is strongly accessible over C if there is a bound on the number of terms in a sequence Λ1,Λ2,…,Λn of graph of groups decompositions of G with edge groups in C such that Λ1 is the trivial decomposition (with 1-vertex) and for i>1, Λi is obtained from Λi−1 by non-trivially and compatibly splitting a vertex group of Λi−1 over a group in C, replacing this vertex group by the splitting and then reducing. If H and K are subgroups of a group G then H is smaller than K if H∩K has finite index in H and infinite index in K. The minimal splitting subgroups of G, are the subgroups H of G, such that G splits non-trivially (as an amalgamated product or HNN-extension) over H and for any other splitting subgroup K of W, K is not smaller than H. When G is a finitely generated Coxeter group, minimal splitting subgroups are always finitely generated. Minimal splittings are explicitly or implicitly important aspects of Dunwoody’s work on accessibility and the JSJ results of Rips–Sela, Dunwoody–Sageev and Mihalik. Our main results are that Coxeter groups are strongly accessible over minimal splittings and if Λ is an irreducible graph of groups decomposition of a Coxeter group with minimal splitting edge groups, then the vertex and edge groups of Λ are Coxeter.
The Particle–Hole Map: A Computational Tool To Visualize Electronic Excitations

We introduce the particle-hole map (PHM), which is a visualization tool to analyze electronic excitations in molecules in the time or frequency domain, to be used in conjunction with time-dependent density-functional theory (TDDFT) or other ab initio methods. The purpose of the PHM is to give detailed insight into electronic excitation processes that is not obtainable from local visualization methods, such as transition densities, density differences, or natural transition orbitals. The PHM is defined as a nonlocal function of two spatial variables and provides information about the origins, destinations, and connections of charge fluctuations during an excitation process; it is particularly valuable to analyze charge-transfer excitonic processes. In contrast with the transition density matrix, the PHM has a statistical interpretation involving joint probabilities of individual states and their transitions; it satisfies several sum rules and exact conditions, and it is easier to read and interpret. We discuss and illustrate the properties of the PHM and give several examples and applications to excitations in one-dimensional model systems, in a hydrogen chain, and in a benzothiadiazole (BT)-based molecule.
Generic mean curvature flow I; generic singularities

It has long been conjectured that starting at a generic smooth closed embedded surface in R 3 , the mean curvature ow remains smooth until it arrives at a singularity in a neighborhood of which the ow looks like concentric spheres or cylinders. That is, the only singularities of a generic ow are spherical or cylindrical. We will address this conjecture here and in a sequel. The higher dimensional case will be addressed elsewhere. The key to showing this conjecture is to show that shrinking spheres, cylinders, and planes are the only stable self-shrinkers under the mean curvature ow. We prove this here in all dimensions. An easy consequence of this is that every singularity other than spheres and cylinders can be perturbed away.
Springer Fibers for the Minimal and the Minimal Special Nilpotent Orbits

We describe Springer fibers corresponding to the minimal and minimal special nilpotent orbits of simple Lie algebras. As a result, we give an answer to the conjecture of Humphreys regarding some graphs attached to Springer fibers.
Consciousness viewed in the framework of brain phase space dynamics, criticality, and the Renormalization Group

Abstract The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations.
The life and death of unwanted bits: Towards proactive waste data management in digital ecosystems

Our everyday data processing activities create massive amounts of data. Like physical waste and trash, unwanted and unused data also pollutes the digital environment by degrading the performance and capacity of storage systems and requiring costly disposal. In this paper, we propose using the lessons from real life waste management in handling waste data. We show the impact of waste data on the performance and operational costs of our computing systems. To allow better waste data management, we define a waste hierarchy for digital objects and provide insights into how to identify and categorize waste data. Finally, we introduce novel ways of reusing, reducing, and recycling data and software to minimize the impact of data wastage.
A universal first-order formula defining the ring of integers in a number field

We show that the complement of the ring of integers in a number field K is Diophantine. This means the set of ring of integers in K can be written as {t in K | for all x_1, ..., x_N in K, f(t,x_1, ..., x_N) is not 0}. We will use global class field theory and generalize the ideas originating from Koenigsmann's recent result giving a universal first order formula for Z in Q.
DUALITY IN FILTERED FLOER–NOVIKOV COMPLEXES

We prove that a certain bilinear pairing (analogous to the Poincare–Lefschetz intersection pairing) between filtered sub- and quotient complexes of a Floer-type chain complex and of its "opposite complex" is always nondegenerate on homology. This implies a duality relation for the Oh–Schwarz-type spectral invariants of these complexes which (in Hamiltonian Floer theory) was established in the special case that the period map has discrete image by Entov and Polterovich. The duality relation served as a key lemma in Entov and Polterovich's construction of a Calabi quasimorphism on certain rational symplectic manifolds, and the result that we prove here implies that their construction remains valid when the rationality hypothesis is dropped. Apart from this, we also use the nondegeneracy of the pairing to establish a new formula for what we have previously called the boundary depth of a Floer chain complex; this formula shows that the boundary depth is unchanged under passing to the opposite complex.
Constraining Roche-Lobe Overflow Models Using the Hot-Subdwarf Wide Binary Population

One of the important issues regarding the final evolution of stars is the impact of binarity. A rich zoo of peculiar, evolved objects are born from the interaction between the loosely bound envelope of a giant, and the gravitational pull of a companion. However, binary interactions are not understood from first principles, and the theoretical models are subject to many assumptions. It is currently agreed upon that hot subdwarf stars can only be formed through binary interaction, either through common envelope ejection or stable Roche-lobe overflow (RLOF) near the tip of the red giant branch (RGB). These systems are therefore an ideal testing ground for binary interaction models. With our long term study of wide hot subdwarf (sdB) binaries we aim to improve our current understanding of stable RLOF on the RGB by comparing the results of binary population synthesis studies with the observed population. In this article we describe the current model and possible improvements, and which observables can be used to test different parts of the interaction model.
A further note on the concordance invariants epsilon and Upsilon

Hom gives an example of a knot with vanishing Upsilon invariant but nonzero epsilon invariant. We build more such knots that are linearly independent in the smooth concordance group.
Bubble impact on a tilted wall: Removing bacteria using bubbles

An investigation into the dynamics of bubble-wall interaction---to assess its potential to remove bacteria on surfaces---finds that the shear stress generated by an impacting bubble is more than the bacterium adhesion force.
Fair Prediction with Disparate Impact: A Study of Bias in Recidivism Prediction Instruments

Abstract Recidivism prediction instruments (RPIs) provide decision-makers with an assessment of the likelihood that a criminal defendant will reoffend at a future point in time. Although such instruments are gaining increasing popularity across the country, their use is attracting tremendous controversy. Much of the controversy concerns potential discriminatory bias in the risk assessments that are produced. This article discusses several fairness criteria that have recently been applied to assess the fairness of RPIs. We demonstrate that the criteria cannot all be simultaneously satisfied when recidivism prevalence differs across groups. We then show how disparate impact can arise when an RPI fails to satisfy the criterion of error rate balance.
Monochromatic sums and products in $\mathbb N$

An old question in Ramsey theory asks whether any finite coloring of the natural numbers admits a monochromatic pair $\{x+y,xy\}$. We answer this question affirmatively in a strong sense by exhibiting a large new class of non-linear patterns which can be found in a single cell of any finite partition of $\mathbb{N}$. Our proof involves a correspondence principle which transfers the problem into the language of topological dynamics. As a corollary of our main theorem we obtain partition regularity for new types of equations, such as $x^2-y^2=z$ and $x^2+2y^2-3z^2=w$.
Nearly Euclidean Thurston maps

We introduce and study a class of Thurston maps from the 2-sphere to itself which we call nearly Euclidean Thurston (NET) maps. These are simple generalizations of Euclidean Thurston maps.
Prediction-adaptation-correction recurrent neural networks for low-resource language speech recognition

In this paper, we investigate the use of prediction-adaptation-correction recurrent neural networks (PAC-RNNs) for low-resource speech recognition. A PAC-RNN is comprised of a pair of neural networks in which a correction network uses auxiliary information given by a prediction network to help estimate the state probability. The information from the correction network is also used by the prediction network in a recurrent loop. Our model outperforms other state-of-the-art neural networks (DNNs, LSTMs) on IARPA-Babel tasks. Moreover, transfer learning from a language that is similar to the target language can help improve performance further.
Corralling a Band of Bandit Algorithms

We study the problem of combining multiple bandit algorithms (that is, online learning algorithms with partial feedback) with the goal of creating a master algorithm that performs almost as well as the best base algorithm \it if it were to be run on its own. The main challenge is that when run with a master, base algorithms unavoidably receive much less feedback and it is thus critical that the master not starve a base algorithm that might perform uncompetitively initially but would eventually outperform others if given enough feedback. We address this difficulty by devising a version of Online Mirror Descent with a special mirror map together with a sophisticated learning rate scheme. We show that this approach manages to achieve a more delicate balance between exploiting and exploring base algorithms than previous works yielding superior regret bounds. Our results are applicable to many settings, such as multi-armed bandits, contextual bandits, and convex bandits. As examples, we present two main applications. The first is to create an algorithm that enjoys worst-case robustness while at the same time performing much better when the environment is relatively easy. The second is to create an algorithm that works simultaneously under different assumptions of the environment, such as different priors or different loss structures.
F -invariants of diagonal hypersurfaces

In this note, we derive a formula for the F-pure threshold of diagonal hypersurfaces over a perfect field of prime characteristic. We also calculate the associated test ideal at the F-pure threshold, and give formulas for higher jumping numbers of Fermat hypersurfaces.
Classification of generalized multiresolution analyses

Abstract We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions m and matrix-valued filter functions H . Given a natural number valued function m and a system of functions encoded in a matrix H satisfying certain conditions, a construction procedure is described that produces an abstract GMRA with multiplicity function m and filter system H . An equivalence relation on GMRAs is defined and described in terms of their associated pairs ( m , H ) . This classification system is applied to MRAs and other classical examples in L 2 ( R d ) as well as to previously studied abstract examples.
Spatial structure and scaling of agricultural networks

Abstract Considering agricultural landscapes as networks can provide information about spatial connectivity relevant for a wide range of applications including pollination, pest management, and ecology. At global scales, spatial networks of agricultural land use inferred from land cover products are well-described by power law rank-size distributions. However, regional analyses of agricultural land use typically focus on subsets of the total global network. In this paper, we seek to address the following questions: Does the globally observed scale-free property of agricultural networks hold over smaller spatial domains? Can similar properties be observed at kilometer to meter scales? Does the observed scale-free structure persist as agricultural networks evolve over the growing season? We analyze 9 intensively cultivated Landsat scenes on 5 continents with a wide range of vegetation distributions. We find that networks of vegetation fraction within the domain of each of these Landsat scenes exhibit substantial variability – but generally still possess similar scaling properties to the global distribution of agriculture. We also find similar results when comparing Landsat and Sentinel-2 imagery for 3 agricultural regions in Europe, as well as in an IKONOS image of an agricultural region of China. To illustrate an application of spatial network analysis, we show an example of network disruption. We compare two networks with similar rank-size distributions that behave differently when nodes are progressively removed. We suggest that treating agricultural land cover as spatial networks can provide a straightforward way of characterizing the connectivity and evolution of complex spatial distributions of agriculture across a wide range of landscapes and at spatial scales relevant for practical agricultural applications.
Learning discrete Bayesian networks from continuous data

Learning Bayesian networks from raw data can help provide insights into the relationships between variables. While real data often contains a mixture of discrete and continuous-valued variables, many Bayesian network structure learning algorithms assume all random variables are discrete. Thus, continuous variables are often discretized when learning a Bayesian network. However, the choice of discretization policy has significant impact on the accuracy, speed, and interpretability of the resulting models. This paper introduces a principled Bayesian discretization method for continuous variables in Bayesian networks with quadratic complexity instead of the cubic complexity of other standard techniques. Empirical demonstrations show that the proposed method is superior to the established minimum description length algorithm. In addition, this paper shows how to incorporate existing methods into the structure learning process to discretize all continuous variables and simultaneously learn Bayesian network structures.
Timely Lossless Source Coding for Randomly Arriving Symbols

We consider a real-time streaming source coding system in which an encoder observes a sequence of randomly arriving symbols from an i.i.d. source, and feeds binary code-words to a FIFO buffer that outputs one bit per time unit to a decoder. Each source symbol represents a status update by the source, and the timeliness of the system is quantified by the age of information (AoI), defined as the time difference between the present time and the generation time of the most up-to-date symbol at the output of the decoder. When the FIFO buffer is allowed to be empty, we propose an optimal prefix-free lossless coding scheme that minimizes the average peak age based on the analysis of discrete-time Geo/G/1 queue. For more practical scenarios in which a special codeword is reserved for indicating an empty buffer, we propose an encoding scheme that assigns a codeword to the empty buffer state based on an estimate of the buffer idle time.
Sampled-Data Reachability Analysis Using Sensitivity and Mixed-Monotonicity

This letter over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing over-approximation result based on the sign-stability of the sensitivity matrices and a discretetime approach relying on a mixed-monotonicity property. We then present a new over-approximation result which scales at worst linearly with the state dimension and is applicable to any continuous-time system with bounded sensitivity. Finally, we provide a simulation-based approach to estimate these bounds through sampling and falsification. The results are illustrated with numerical examples on traffic networks and satellite orbits.
An overdetermined problem in Riesz-potential and fractional Laplacian

Abstract The main purpose of this paper is to address two open questions raised by Reichel (2009) in [2] on characterizations of balls in terms of the Riesz potential and fractional Laplacian. For a bounded C 1 domain Ω ⊂ R N , we consider the Riesz-potential u ( x ) = ∫ Ω 1 ∣ x − y ∣ N − α d y for 2 ≤ α ≠ N . We show that u = constant on ∂ Ω if and only if Ω is a ball. In the case of α = N , the similar characterization is established for the logarithmic potential u ( x ) = ∫ Ω log 1 ∣ x − y ∣ d y . We also prove that such a characterization holds for the logarithmic Riesz potential u ( x ) = ∫ Ω ∣ x − y ∣ α − N log 1 ∣ x − y ∣ d y when the diameter of the domain Ω is less than e 1 N − α in the case when α − N is a nonnegative even integer. This provides a characterization for the overdetermined problem of the fractional Laplacian. These results answer two open questions in Reichel (2009) [2] to some extent. Moreover, we also establish some nonexistence result of positive solutions to a class of integral equations in an exterior domain.
Waring's problem in finite rings

Abstract In this paper we obtain explicit results for Waring's problem over general finite rings, especially matrix rings over finite fields by building on analogous results over finite fields. Commutative algebra, in particular the Jacobson radical and nilpotent ideals, plays an important role in our proofs.
Quasiconformal mappings on the Grushin plane

We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal. As the main step in our argument, we show that a quasisymmetric parametrization of the Grushin plane by the Euclidean plane must also be geometrically quasiconformal. We also discuss some aspects of the Euclidean theory of quasiconformal maps, such as absolute continuity on almost every compact curve, not satisfied in the Grushin case.
Improved Bilinear Pooling with CNNs.

Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering tasks among others. The resulting representation captures second-order statistics of convolutional features in a translationally invariant manner. In this paper we investigate various ways of normalizing these statistics to improve their representation power. In particular we find that the matrix square-root normalization offers significant improvements and outperforms alternative schemes such as the matrix logarithm normalization when combined with elementwise square-root and l2 normalization. This improves the accuracy by 2-3% on a range of fine-grained recognition datasets leading to a new state of the art. We also investigate how the accuracy of matrix function computations effect network training and evaluation. In particular we compare against a technique for estimating matrix square-root gradients via solving a Lyapunov equation that is more numerically accurate than computing gradients via a Singular Value Decomposition (SVD). We find that while SVD gradients are numerically inaccurate the overall effect on the final accuracy is negligible once boundary cases are handled carefully. We present an alternative scheme for computing gradients that is faster and yet it offers improvements over the baseline model. Finally we show that the matrix square-root computed approximately using a few Newton iterations is just as accurate for the classification task but allows an order-of-magnitude faster GPU implementation compared to SVD decomposition.
Testing Mixtures of Discrete Distributions

There has been significant study on the sample complexity of testing properties of distributions over large domains. For many properties, it is known that the sample complexity can be substantially smaller than the domain size. For example, over a domain of size $n$, distinguishing the uniform distribution from distributions that are far from uniform in $\ell_1$-distance uses only $O(\sqrt{n})$ samples. However, the picture is very different in the presence of arbitrary noise, even when the amount of noise is quite small. In this case, one must distinguish if samples are coming from a distribution that is $\epsilon$-close to uniform from the case where the distribution is $(1-\epsilon)$-far from uniform. The latter task requires nearly linear in $n$ samples [Valiant 2008, Valian and Valiant 2011]. In this work, we present a noise model that on one hand is more tractable for the testing problem, and on the other hand represents a rich class of noise families. In our model, the noisy distribution is a mixture of the original distribution and noise, where the latter is known to the tester either explicitly or via sample access; the form of the noise is also known a priori. Focusing on the identity and closeness testing problems leads to the following mixture testing question: Given samples of distributions $p, q_1,q_2$, can we test if $p$ is a mixture of $q_1$ and $q_2$? We consider this general question in various scenarios that differ in terms of how the tester can access the distributions, and show that indeed this problem is more tractable. Our results show that the sample complexity of our testers are exactly the same as for the classical non-mixture case.
Differential Expression of Mucins in Murine Olfactory Versus Respiratory Epithelium

Mucins are a key component of the surface mucus overlying airway epithelium. Given the different functions of the olfactory and respiratory epithelia, we hypothesized that mucins would be differentially expressed between these 2 areas. Secondarily, we evaluated for potential changes in mucin expression with radiation exposure, given the clinical observations of nasal dryness, altered mucus rheology, and smell loss in radiated patients. Immunofluorescence staining was performed to evaluate expression of mucins 1, 2, 5AC, and 5B in nasal respiratory and olfactory epithelia of control mice and 1 week after exposure to 8 Gy of radiation. Mucins 1, 5AC, and 5B exhibited differential expression patterns between olfactory and respiratory epithelium (RE) while mucin 2 showed no difference. In the olfactory epithelium (OE), mucin 1 was located in a lattice-like pattern around gaps corresponding to dendritic knobs of olfactory sensory neurons, whereas in RE it was intermittently expressed by surface goblet cells. Mucin 5AC was expressed by subepithelial glands in both epithelial types but to a higher degree in the OE. Mucin 5B was expressed by submucosal glands in OE and by surface epithelial cells in RE. At 1-week after exposure to single-dose 8 Gy of radiation, no qualitative effects were seen on mucin expression. Our findings demonstrate that murine OE and RE express mucins differently, and characteristic patterns of mucins 1, 5AC, and 5B can be used to define the underlying epithelium. Radiation (8 Gy) does not appear to affect mucin expression at 1 week. LEVEL OF EVIDENCE N/A (Basic Science Research).IACUC-approved study [Protocol 200065].
Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium

In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may co...
Self-Supervised Audio Spatialization with Correspondence Classifier

Spatial audio is an essential medium to audiences for 3D visual and auditory experience. However, the recording devices and techniques are expensive or inaccessible to the general public. In this work, we propose a self-supervised audio spatialization network that can generate spatial audio given the corresponding video and monaural audio. To enhance spatialization performance, we use an auxiliary classifier to classify ground-truth videos and those with audio where the left and right channels are swapped. We collect a large-scale video dataset with spatial audio to validate the proposed method. Experimental results demonstrate the effectiveness of the proposed model on the audio spatialization task.
First order expansion of convex regularized estimators

We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function $h$ and the corresponding penalized estimator $\hbeta$, we construct a quantity $\eta$, the first order expansion of $\hbeta$, such that the distance between $\hbeta$ and $\eta$ is an order of magnitude smaller than the estimation error $\|\hat{\beta} - \beta^*\|$. In this sense, the first order expansion $\eta$ can be thought of as a generalization of influence functions from the mathematical statistics literature to regularized estimators in high-dimensions. Such first order expansion implies that the risk of $\hat{\beta}$ is asymptotically the same as the risk of $\eta$ which leads to a precise characterization of the MSE of $\hbeta$; this characterization takes a particularly simple form for isotropic design. Such first order expansion also leads to inference results based on $\hat{\beta}$. We provide sufficient conditions for the existence of such first order expansion for three regularizers: the Lasso in its constrained form, the lasso in its penalized form, and the Group-Lasso. The results apply to general loss functions under some conditions and those conditions are satisfied for the squared loss in linear regression and for the logistic loss in the logistic model.
Online Gambling of Pure Chance: Wager Distribution, Risk Attitude, and Anomalous Diffusion

Online gambling sites offer many different gambling games. In this work we analyse the gambling logs of numerous solely probability-based gambling games and extract the wager and odds distributions. We find that the log-normal distribution describes the wager distribution at the aggregate level. Viewing the gamblers’ net incomes as random walks, we study the mean-squared displacement of net income and related quantities and find different diffusive behaviors for different games. We discuss possible origins for the observed anomalous diffusion.
Equality's Understudies

Robert L. Tsai’s Practical Equality: Forging Justice in a Divided Nation proposes to discard equality as an otiose criterion for legal and political strategy. The idea is at once surprising and provocative. That it should come from a respected and accomplished progressive scholar is even more noteworthy. I critique Tsai’s claim by evaluating his use of equality and the adequacy of his proposed understudies. None of these understudies, I suggest, can do the salutary work Tsai hopes. In particular, I argue that the failures of human sympathy that consistently undermine the progressive equality project will equally puncture the proposed understudies. A final, brief conclusion reconsiders how equality might be analyzed and deployed as a regulative ideal in modern American politics and law notwithstanding Tsai's well-founded concerns.
Computational Convergence Analysis of Distributed Gradient Tracking for Smooth Convex Optimization Using Dissipativity Theory

We present a computational analysis that establishes the O(1/K) convergence of the distributed gradient tracking method when the objective function is smooth and convex but not strongly convex. The analysis is inspired by recent work on applying dissipativity theory to the analysis of centralized optimization algorithms, in which convergence is proved by searching for a numerical certificate consisting of a storage function and a supply rate. We derive a base supply rate that can be used to analyze distributed optimization with non-strongly convex objective functions. The base supply rate is then used to create a class of supply rates by combining with integral quadratic constraints. Provided that the class of supply rates is rich enough, a numerical certificate of convergence can be automatically generated following a standard procedure that involves solving a linear matrix inequality. Our computational analysis is found capable of certifying convergence under a broader range of step sizes than what is given by the original analytic result.
A Computer-Aided System for Determining the Application Range of a Warfarin Clinical Dosing Algorithm Using Support Vector Machines with a Polynomial Kernel Function

Determining the optimal initial dose for warfarin is a critically important task. Several factors have an impact on the therapeutic dose for individual patients, such as patients’ physical attributes (Age, Height, etc medication profile, co-morbidities, and metabolic genotypes (CYP2C9 and VKORCI). These wide range factors influencing therapeutic dose, create a complex environment for clinicians to determine the optimal initial dose. Using a sample of 4,237 patients, we have proposed a companion classification model to one of the most popular dosing algorithms (International Warfarin Pharmacogenetics Consortium (IWPC) clinical model), which identifies the appropriate cohort of patients for applying this model. The proposed model functions as a clinical decision support system that assists clinicians in dosing. We have developed a classification model using Support Vector Machines, with a polynomial kernel function to determine if applying the dose prediction model is appropriate for a given patient. The IWPC clinical model will only be used if the patient is classified as "Safe for model". By using the proposed methodology, the dosing model’s prediction accuracy increases by 15% in terms of Root Mean Squared Error and 17% in terms of Mean Absolute Error in dose estimates of patients classified as "Safe for model".
“WHAT'S WRONG WITH THE WAY I TALK?” THE EFFECT OF SOUND MOTION PICTURES ON ACTOR CAREERS

The development of sound motion pictures in the late 1920s provides one of history’s most evocative examples of how new technology can affect employment – film historians have long believed that the transition to sound cut short the careers of a number of silent film stars. But whether this was due to the transition itself (actor careers are unpredictable at the best of times), and if so, whether more than a small number of famous stars were affected, has not been explored systematically. In this paper, I analyze a data set of nearly 10,000 actors who played in motion pictures from 1920 through 1940, inclusive. I find that the transition period is associated with a substantial increase in career terminations, not only among major stars, but also among more minor actors. However, I also find that sound films raised hazard rates generally, so that whereas the silent era is associated with a hazard rate that is 30-to-50 percent lower than that of the transition period, the sound era it is associated with only a 10 percent lower hazard rate. This means that some of the increase in career terminations attributed to the transition process may in fact simply reflect the higher rate of exit that became the norm during the first decade of sound motion pictures.
On the structure of limiting flocks in hydrodynamic Euler Alignment models

The goal of this paper is to study limiting behavior of a self-organized continuous flock evolving according to the 1D hydrodynamic Euler Alignment model. We provide a series of quantitative estima...
A $q$-Queens Problem. IV. Attacking Configurations and Their Denominators

Abstract In Parts I–III we showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q . In this part we focus on the periods of those quasipolynomials. We calculate denominators of vertices of the inside-out polytope, since the period is bounded by, and conjecturally equal to, their least common denominator. We find an exact formula for that denominator of every piece with one move and of two-move pieces having a horizontal move. For pieces with three or more moves, we produce geometrical constructions related to the Fibonacci numbers that show the denominator grows at least exponentially with q .
FilterReg: Robust and Efficient Probabilistic Point-Set Registration Using Gaussian Filter and Twist Parameterization

Probabilistic point-set registration methods have been gaining more attention for their robustness to noise, outliers and occlusions. However, these methods tend to be much slower than the popular iterative closest point (ICP) algorithms, which severely limits their usability. In this paper, we contribute a novel probabilistic registration method that achieves state-of-the-art robustness as well as substantially faster computational performance than modern ICP implementations. This is achieved using a rigorous yet computationally-efficient probabilistic formulation. Point-set registration is cast as a maximum likelihood estimation and solved using the EM algorithm. We show that with a simple augmentation, the E step can be formulated as a filtering problem, allowing us to leverage advances in efficient Gaussian filtering methods. We also propose a customized permutohedral filter to improve its performance while retaining sufficient accuracy for our task. Additionally, we present a simple and efficient twist parameterization that generalizes our method to the registration of articulated and deformable objects. For articulated objects, the complexity of our method is almost independent of the Degrees Of Freedom (DOFs), which makes it highly efficient even for high DOF systems. The results demonstrate the proposed method consistently outperforms many competitive baselines on a variety of registration tasks.