cssi/SciSciGPT-SciSciNet huggingface dataset:
Domain Adversarial for Acoustic Emotion Recognition

The performance of speech emotion recognition is affected by the differences in data distributions between train (source domain) and test (target domain) sets used to build and evaluate the models. This is a common problem, as multiple studies have shown that the performance of emotional classifiers drops when they are exposed to data that do not match the distribution used to build the emotion classifiers. The difference in data distributions becomes very clear when the training and testing data come from different domains, causing a large performance gap between development and testing performance. Due to the high cost of annotating new data and the abundance of unlabeled data, it is crucial to extract as much useful information as possible from the available unlabeled data. This study looks into the use of adversarial multitask training to extract a common representation between train and test domains. The primary task is to predict emotional-attribute-based descriptors for arousal, valence, or dominance. The secondary task is to learn a common representation, where the train and test domains cannot be distinguished. By using a gradient reversal layer, the gradients coming from the domain classifier are used to bring the source and target domain representations closer. We show that exploiting unlabeled data consistently leads to better emotion recognition performance across all emotional dimensions. We visualize the effect of adversarial training on the feature representation across the proposed deep learning architecture. The analysis shows that the data representations for the train and test domains converge as the data are passed to deeper layers of the network. We also evaluate the difference in performance when we use a shallow neural network versus a deep neural network and the effect of the number of shared layers used by the task and domain classifiers.
Sample complexity of population recovery

The problem of population recovery refers to estimating a distribution based on incomplete or corrupted samples. Consider a random poll of sample size $n$ conducted on a population of individuals, where each pollee is asked to answer $d$ binary questions. We consider one of the two polling impediments: (a) in lossy population recovery, a pollee may skip each question with probability $\epsilon$, (b) in noisy population recovery, a pollee may lie on each question with probability $\epsilon$. Given $n$ lossy or noisy samples, the goal is to estimate the probabilities of all $2^d$ binary vectors simultaneously within accuracy $\delta$ with high probability. This paper settles the sample complexity of population recovery. For lossy model, the optimal sample complexity is $\tilde\Theta(\delta^{-2\max\{\frac{\epsilon}{1-\epsilon},1\}})$, improving the state of the art by Moitra and Saks in several ways: a lower bound is established, the upper bound is improved and the result depends at most on the logarithm of the dimension. Surprisingly, the sample complexity undergoes a phase transition from parametric to nonparametric rate when $\epsilon$ exceeds $1/2$. For noisy population recovery, the sharp sample complexity turns out to be more sensitive to dimension and scales as $\exp(\Theta(d^{1/3} \log^{2/3}(1/\delta)))$ except for the trivial cases of $\epsilon=0,1/2$ or $1$. For both models, our estimators simply compute the empirical mean of a certain function, which is found by pre-solving a linear program (LP). Curiously, the dual LP can be understood as Le Cam's method for lower-bounding the minimax risk, thus establishing the statistical optimality of the proposed estimators. The value of the LP is determined by complex-analytic methods.
M3: Scaling Up Machine Learning via Memory Mapping

To process data that do not fit in RAM, conventional wisdom would suggest using distributed approaches. However, recent research has demonstrated virtual memory's strong potential in scaling up graph mining algorithms on a single machine. We propose to use a similar approach for general machine learning. We contribute: (1) our latest finding that memory mapping is also a feasible technique for scaling up general machine learning algorithms like logistic regression and k-means, when data fits in or exceeds RAM (we tested datasets up to 190GB); (2) an approach, called M3, that enables existing machine learning algorithms to work with out-of-core datasets through memory mapping, achieving a speed that is significantly faster than a 4-instance Spark cluster, and comparable to an 8-instance cluster.
Computational Imaging for VLBI Image Reconstruction

Very long baseline interferometry (VLBI) is a technique for imaging celestial radio emissions by simultaneously observing a source from telescopes distributed across Earth. The challenges in reconstructing images from fine angular resolution VLBI data are immense. The data is extremely sparse and noisy, thus requiring statistical image models such as those designed in the computer vision community. In this paper we present a novel Bayesian approach for VLBI image reconstruction. While other methods often require careful tuning and parameter selection for different types of data, our method (CHIRP) produces good results under different settings such as low SNR or extended emission. The success of our method is demonstrated on realistic synthetic experiments as well as publicly available real data. We present this problem in a way that is accessible to members of the community, and provide a dataset website (vlbiimaging.csail.mit.edu) that facilitates controlled comparisons across algorithms.
Robust detection of random events with spatially correlated data in wireless sensor networks via distributed compressive sensing

In this paper, we exploit the theory of compressive sensing to perform detection of a random source in a dense sensor network. When the sensors are densely deployed, observations at adjacent sensors are highly correlated while those corresponding to distant sensors are less correlated. Thus, the covariance matrix of the concatenated observation vector of all the sensors at any given time can be sparse where the sparse structure depends on the network topology and the correlation model. Exploiting the sparsity structure of the covariance matrix, we develop a robust nonparametric detector to detect the presence of the random event using a compressed version of the data collected at the distributed nodes. We employ the multiple access channel (MAC) model with distributed random projections for sensors to transmit observations so that a compressed version of the observations is available at the fusion center. Detection is performed by constructing a decision statistic based on the covariance information of uncompressed data which is estimated using compressed data. The proposed approach does not require any knowledge of the noise parameter to set the threshold, and is also robust when the distributed random projection matrices become sparse.
Triple crossing number and double crossing braid index

Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point,...
Syndecan-1 facilitates breast cancer metastasis to the brain

Although survival rates for patients with localized breast cancer have increased, patients with metastatic breast cancer still have poor prognosis. Understanding key factors involved in promoting breast cancer metastasis is imperative for better treatments. In this study, we investigated the role of syndecan-1 (Sdc1) in breast cancer metastasis. To assess the role of Sdc1 in breast cancer metastasis, we silenced Sdc1 expression in the triple-negative breast cancer human MDA-MB-231 cell line and overexpressed it in the mouse mammary carcinoma 4T1 cell line. Intracardiac injections were performed in an experimental mouse metastasis model using both cell lines. In vitro transwell blood–brain barrier (BBB) and brain section adhesion assays were utilized to specifically investigate how Sdc1 facilitates brain metastasis. A cytokine array was performed to evaluate differences in the breast cancer cell secretome when Sdc1 is silenced. Silencing expression of Sdc1 in breast cancer cells significantly reduced metastasis to the brain. Conversely, overexpression of Sdc1 increased metastasis to the brain. We found that silencing of Sdc1 expression had no effect on attachment of breast cancer cells to brain endothelial cells or astrocytes, but migration across the BBB was reduced as well as adhesion to the perivascular regions of the brain. Loss of Sdc1 also led to changes in breast cancer cell-secreted cytokines/chemokines, which may influence the BBB. Taken together, our study demonstrates a role for Sdc1 in promoting breast cancer metastasis to the brain. These findings suggest that Sdc1 supports breast cancer cell migration across the BBB through regulation of cytokines, which may modulate the BBB. Further elucidating this mechanism will allow for the development of therapeutic strategies to combat brain metastasis.
A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly \(\alpha \)-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.
Lasso adjustments of treatment effect estimates in randomized experiments

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the least absolute shrinkage and selection operator (Lasso) may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman-Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and ordinary least squares (OLS) for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS.
Loss-Proportional Subsampling for Subsequent ERM

We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the final excess risk will compare favorably with utilizing the entire original data set. We demonstrate the practical benefits of our approach on a large dataset which we subsample and subsequently fit with boosted trees.
Accelerating Greedy Coordinate Descent Methods

We study ways to accelerate greedy coordinate descent in theory and in practice, where "accelerate" refers either to $O(1/k^2)$ convergence in theory, in practice, or both. We introduce and study two algorithms: Accelerated Semi-Greedy Coordinate Descent (ASCD) and Accelerated Greedy Coordinate Descent (AGCD). While ASCD takes greedy steps in the $x$-updates and randomized steps in the $z$-updates, AGCD is a straightforward extension of standard greedy coordinate descent that only takes greedy steps. On the theory side, our main results are for ASCD: we show that ASCD achieves $O(1/k^2)$ convergence, and it also achieves accelerated linear convergence for strongly convex functions. On the empirical side, we observe that both AGCD and ASCD outperform Accelerated Randomized Coordinate Descent on a variety of instances. In particular, we note that AGCD significantly outperforms the other accelerated coordinate descent methods in numerical tests, in spite of a lack of theoretical guarantees for this method. To complement the empirical study of AGCD, we present a Lyapunov energy function argument that points to an explanation for why a direct extension of the acceleration proof for AGCD does not work; and we also introduce a technical condition under which AGCD is guaranteed to have accelerated convergence. Last of all, we confirm that this technical condition holds in our empirical study.
Fibered stable varieties

Reference EPFL-ARTICLE-231103doi:10.1090/tran/6386 URL: http://dx.doi.org/10.1090/tran/6386 Record created on 2017-09-19, modified on 2017-10-02
Mapping schemes realizable by obstructed topological polynomials

In 1985, Levy used a theorem of Berstein to prove that all hyperbolic topological polynomials are equivalent to complex polynomials. We prove a partial converse to the Berstein-Levy Theorem: given post-critical dynamics that are in a sense strongly non-hyperbolic, we prove the existence of topological polynomials which are not equivalent to any complex polynomial that realize these post-critical dynamics. This proof employs the theory of self-similar groups to demonstrate that a topological polynomial admits an obstruction and produces a wealth of examples of obstructed topological polynomials.
Simulating the Spread of Influenza Pandemic of 1918- 1919 Considering the Effect of the First World War

The Influenza Pandemic of 1918-1919, also called Spanish Flu Pandemic, was one of the severest pandemics in history. It is thought that the First World War much influenced the spread of the pandemic. In this paper, we model the pandemic considering both civil and military traffic. We propose a hybrid model to determine how the pandemic spread through the world. Our approach considers both the SEIR-based model for local areas and the network model for global connection between countries. First, we reproduce the situation in 12 countries. Then, we simulate another scenario: there was no military traffic during the pandemic, to determine the influence of the influenced of the war on the pandemic. By considering the simulation results, we find that the influence of the war varies in countries; in countries which were deeply involved in the war, the infections were much influenced by the war, while in countries which were not much engaged in the war, the infections were not influenced by the war. Keywords-Simulation, Pandemic, Influenza, SEIR, Social Network, Spanish Flu, International Traffic, Infectious Disease
Differential Geometric Approach to Trajectory Planning: Cooperative Transport by a Team of Autonomous Marine Vehicles

In this paper we addressed the cooperative transport problem for a team of autonomous surface vehicles (ASVs) towing a single buoyant load. We consider the dynamics of the constrained system and decompose the cooperative transport problem into a collection of subproblems. Each subproblem consists of an ASV and load pair where each ASV is attached to the load at the same point. Since the system states evolve on a smooth manifold, we use the tools from differential geometry to model the holonomic constraint arising from the cooperative transport problem and the non-holonomic constraints arising from the ASV dynamics. We then synthesize distributed feedback control strategies using the proposed mathematical modeling framework to enable the team transport the load on a desired trajectory. We experimentally validate the proposed strategy using a team of micro ASVs.
Developing Bug-Free Machine Learning Systems With Formal Mathematics.

Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We demonstrate a methodology in which developers use an interactive proof assistant to both implement their system and to state a formal theorem defining what it means for their system to be correct. The process of proving this theorem interactively in the proof assistant exposes all implementation errors since any error in the program would cause the proof to fail. As a case study, we implement a new system, Certigrad, for optimizing over stochastic computation graphs, and we generate a formal (i.e. machine-checkable) proof that the gradients sampled by the system are unbiased estimates of the true mathematical gradients. We train a variational autoencoder using Certigrad and find the performance comparable to training the same model in TensorFlow.
Two-faced families of non-commutative random variables having bi-free infinitely divisible distributions

We study two-faced families of non-commutative random variables having bi-free (additive) infinitely divisible distributions. We prove a limit theorem of the sums of bi-free two-faced families of random variables within a triangular array. As a corollary of our limit theorem, we get Voiculescu’s bi-free central limit theorem. Using the full Fock space operator model, we show that a two-faced pair of random variables has a bi-free (additive) infinitely divisible distribution if and only if its distribution is the limit distribution in our limit theorem. Finally, we characterize the bi-free (additive) infinite divisibility of the distribution of a two-faced pair of random variables in terms of bi-free Levy processes.
Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases

Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.
The Apollonian structure of Bianchi groups

We study the orbit of $\widehat{\mathbb{R}}$ under the Mobius action of the Bianchi group $\operatorname{PSL}_2(\mathcal{O}_K)$ on $\widehat{\mathbb{C}}$, where $\mathcal{O}_K$ is the ring of integers of an imaginary quadratic field $K$. The orbit $\mathcal{S}_K$, called a Schmidt arrangement, is a geometric realisation, as an intricate circle packing, of the arithmetic of $K$. We give a simple geometric characterisation of certain subsets of $\mathcal{S}_K$ generalizing Apollonian circle packings, and show that $\mathcal{S}_K$, considered with orientations, is a disjoint union of all primitive integral such $K$-Apollonian packings. These packings are described by a new class of thin groups of arithmetic interest called $K$-Apollonian groups. We make a conjecture on the curvatures of these packings, generalizing the local-to-global conjecture for Apollonian circle packings.
Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials

We study the two-point correlation functions for the zeroes of systems of SO(n + 1)-invariant Gaussian random polynomials on RP and systems of Isom(Rn)-invariant Gaussian analytic functions. Our result reflects the same “repelling,” “neutral,” and “attracting” short-distance asymptotic behavior, depending on the dimension, as was discovered in the complex case by Bleher, Shiffman, and Zelditch. We then prove that the correlation function for the Isom(Rn)-invariant Gaussian analytic functions is “universal,” describing the scaling limit of the correlation function for the restriction of systems of the SO(k + 1)-invariant Gaussian random polynomials to any n-dimensional C2 submanifold M ⊂ RP . This provides a real counterpart to the universality results that were proved in the complex case by Bleher, Shiffman, and Zelditch.
Loop-Closure and Gaussian Models of Collective Structural Characteristics of Capped PEO Oligomers in Water.

Parallel-tempering MD results for a CH3(CH2–O–CH2)mCH3 chain in water are exploited as a database for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in null water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple k → ∞ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting and scaling the discrete-Gaussian model helps to identify the low-k to high-k transition near k ≈ 2π/0.6 nm when an empirically matched number of Gaussian links is about one-third of the total number of effective atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the r space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distrib...
On the Positivity of Propagator Differences

We discuss positivity properties of certain‘distinguished propagators’, i.e., distinguished inverses of operators that frequently occur in scattering theory and wave propagation. We relate this to the work of Duistermaat and Hormander on distinguished parametrices (approximate inverses), which has played a major role in quantum field theory on curved spacetimes recently.
Evidential confirmation as transformed probability

A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several researchers have gone so far as to invent new formalisms and methods. Some of these have become widely used and theoretically explored [17, 15). We show how to represent two major approaches to evidential confirmation not only in terms of transformed (Bayesian) probability, but also in terms of each other; which: • unifies two of the leading approaches to confirmation theory, by showing that a revised MYCIN Certainty Factor method [12] is equivalent to a special case of Dempster-Shafer theory; • gives us a well-understood axiomatic basis, i.e. conditional independence, to interpret previous work on quantitative confirmation theory; in particular, • provides a new axiomatic analysis and interpretation of Dempster's Rule for an important special case; • which gives a firmer epistemological basis for acquiring, and for using in decisions, Dempster-Shafer belief functions aggregated via Dempster's Rule; • substantially resolves the "take-them-or-leave-them" problem of priors: MYCIN had to leave them out, while PROSPECTOR had to have them in; • recasts some of confirmation theory's advantages in terms of the psychological accessibility of probabilistic information in different (transformed) formats; • helps to unify the representation of plausible/inexact/uncertain reasoning (see also [11]); • clarifies the place of evidential confirmation in a general scheme for probabilistic reasoning: as concerned with aggregating "parallel" updates or changes in probability; and • in particular marries evidential confirmation to the strengths of Bayesian, arbitrary-conditional, probability: especially, if-then rules and forward and backward chaining.
Optimal Covariance Control for Stochastic Systems Under Chance Constraints

This letter addresses the optimal covariance control problem for stochastic discrete-time linear systems subject to chance constraints. To the best of our knowledge, covariance steering problems with probabilistic chance constraints have not been discussed previously in the literature, although their treatment seems to be a natural extension. In this letter, we first show that, unlike the case with no chance constraints, the covariance steering problem with chance constraints cannot be decoupled to mean and covariance steering sub-problems. We then propose an approach to solve the covariance steering problem with chance constraints by converting it to a convex programming problem. The proposed algorithm is verified using a numerical example.
CapProNet: Deep Feature Learning via Orthogonal Projections onto Capsule Subspaces

In this paper, we formalize the idea behind capsule nets of using a capsule vector rather than a neuron activation to predict the label of samples. To this end, we propose to learn a group of capsule subspaces onto which an input feature vector is projected. Then the lengths of resultant capsules are used to score the probability of belonging to different classes. We train such a Capsule Projection Network (CapProNet) by learning an orthogonal projection matrix for each capsule subspace, and show that each capsule subspace is updated until it contains input feature vectors corresponding to the associated class. With low dimensionality of capsule subspace as well as an iterative method to estimate the matrix inverse, only a small negligible computing overhead is incurred to train the network. Experiment results on image datasets show the presented network can greatly improve the performance of state-of-the-art Resnet backbones by $10-20\%$ with almost the same computing cost.
Dyson's Partition Ranks and their Multiplicative Extensions

We study the Dyson rank function N(r, 3; n), the number of partitions of n with rank \(\equiv r \pmod 3\). We investigate the convexity of these functions. We extend N(r, 3; n) multiplicatively to the set of partitions, and we determine the maximum value when taken over all partitions of size n.
Paradigm and Paradox in Topology Control of Power Grids

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of “greedy” heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using IEEE 118-bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched.
Meta-Learning with Latent Embedding Optimization

Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter spaces in extreme low-data regimes. We show that it is possible to bypass these limitations by learning a data-dependent latent generative representation of model parameters, and performing gradient-based meta-learning in this low-dimensional latent space. The resulting approach, latent embedding optimization (LEO), decouples the gradient-based adaptation procedure from the underlying high-dimensional space of model parameters. Our evaluation shows that LEO can achieve state-of-the-art performance on the competitive miniImageNet and tieredImageNet few-shot classification tasks. Further analysis indicates LEO is able to capture uncertainty in the data, and can perform adaptation more effectively by optimizing in latent space.
Evidence Accumulation in a Laplace Domain Decision Space

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially; across neurons there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform; these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a "decision axis." This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.
Homology operations on homology of quandles

Abstract We introduce the concept of the quandle partial derivatives, and use them to define extreme chains that yield homological operations. We apply this to a large class of finite and infinite quandles to show, in particular, that they have nontrivial elements in the third and fourth quandle homology.
Lightweight Unsupervised Deep Loop Closure

Robust efficient loop closure detection is essential for large-scale real-time SLAM. In this paper, we propose a novel unsupervised deep neural network architecture of a feature embedding for visual loop closure that is both reliable and compact. Our model is built upon the autoencoder architecture, tailored specifically to the problem at hand. To train our network, we inflict random noise on our input data as the denoising autoencoder does, but, instead of applying random dropout, we warp images with randomized projective transformations to emulate natural viewpoint changes due to robot motion. Moreover, we utilize the geometric information and illumination invariance provided by histogram of oriented gradients (HOG), forcing the encoder to reconstruct a HOG descriptor instead of the original image. As a result, our trained model extracts features robust to extreme variations in appearance directly from raw images, without the need for labeled training data or environment-specific training. We perform extensive experiments on various challenging datasets, showing that the proposed deep loop-closure model consistently outperforms the state-of-the-art methods in terms of effectiveness and efficiency. Our model is fast and reliable enough to close loops in real time with no dimensionality reduction, and capable of replacing generic off-the-shelf networks in state-of-the-art ConvNet-based loop closure systems.
The Lovász-Bregman divergence and connections to rank aggregation, clustering, and web ranking

We extend the recently introduced theory of Lovasz Bregman (LB) divergences [19] in several ways. We show that they represent a distortion between a "score" and an "ordering", thus providing a new view of rank aggregation and order based clustering with interesting connections to web ranking. We show how the LB divergences have a number of properties akin to many permutation based metrics, and in fact have as special cases forms very similar to the Kendall-τ metric. We also show how the LB divergences subsume a number of commonly used ranking measures in information retrieval, like NDCG [22] and AUC [35]. Unlike the traditional permutation based metrics, however, the LB divergence naturally captures a notion of "confidence" in the orderings, thus providing a new representation to applications involving aggregating scores as opposed to just orderings. We show how a number of recently used web ranking models are forms of Lovasz Bregman rank aggregation and also observe that a natural form of Mallow's model using the LB divergence has been used as conditional ranking models for the "Learning to Rank" problem.
The period-index problem for fields of transcendence degree 2

Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over Fp.
Pixels, Voxels, and Views: A Study of Shape Representations for Single View 3D Object Shape Prediction

The goal of this paper is to compare surface-based and volumetric 3D object shape representations, as well as viewer-centered and object-centered reference frames for single-view 3D shape prediction. We propose a new algorithm for predicting depth maps from multiple viewpoints, with a single depth or RGB image as input. By modifying the network and the way models are evaluated, we can directly compare the merits of voxels vs. surfaces and viewer-centered vs. object-centered for familiar vs. unfamiliar objects, as predicted from RGB or depth images. Among our findings, we show that surface-based methods outperform voxel representations for objects from novel classes and produce higher resolution outputs. We also find that using viewer-centered coordinates is advantageous for novel objects, while object-centered representations are better for more familiar objects. Interestingly, the coordinate frame significantly affects the shape representation learned, with object-centered placing more importance on implicitly recognizing the object category and viewer-centered producing shape representations with less dependence on category recognition.
Adversarial deep structured nets for mass segmentation from mammograms

Mass segmentation provides effective morphological features which are important for mass diagnosis. In this work, we propose a novel end-to-end network for mammographic mass segmentation which employs a fully convolutional network (FCN) to model a potential function, followed by a conditional random field (CRF) to perform structured learning. Because the mass distribution varies greatly with pixel position, the FCN is combined with a position priori. Further, we employ adversarial training to eliminate over-fitting due to the small sizes of mammogram datasets. Multi-scale FCN is employed to improve the segmentation performance. Experimental results on two public datasets, IN breast and DDSM-BCRP, demonstrate that our end-to-end network achieves better performance than state-of-the-art approaches.1
Differentiability of the Arrival Time

For a monotonically advancing front, the arrival time is the time when the front reaches a given point. We show that it is twice differentiable everywhere with uniformly bounded second derivative. It is smooth away from the critical points where the equation is degenerate. We also show that the critical set has finite codimensional two Hausdorff measure. For a monotonically advancing front, the arrival time is equivalent to the level set method; a priori not even differentiable but only satisfies the equation in the viscosity sense. Using that it is twice differentiable and that we can identify the Hessian at critical points, we show that it satisfies the equation in the classical sense. The arrival time has a game theoretic interpretation. For the linear heat equation, there is a game theoretic interpretation that relates to Black-Scholes option pricing. From variations of the Sard and Lojasiewicz theorems, we relate differentiability to whether or not singularities all occur at only finitely many times for flows.
Iterated Function Systems, Moments, and Transformations of Infinite Matrices

We study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Our main object of study is the infinite matrix which encodes all the moment data of a Borel measure on R^d or C. To encode the salient features of a given IFS into precise moment data, we establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, our aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them. We first examine the classical existence problem for moments, culminating in a new proof of the existence of a Borel measure on R or C with a specified list of moments. Next, we consider moment problems associated with affine and non-affine IFSs. Our main goal is to determine conditions under which an intertwining relation is satisfied by the moment matrix of an equilibrium measure of an IFS. Finally, using the famous Hilbert matrix as our prototypical example, we study boundedness and spectral properties of moment matrices viewed as Kato-Friedrichs operators on weighted l^2 spaces.
Practical Contextual Bandits with Regression Oracles

A major challenge in contextual bandits is to design general-purpose algorithms that are both practically useful and theoretically well-founded. We present a new technique that has the empirical and computational advantages of realizability-based approaches combined with the flexibility of agnostic methods. Our algorithms leverage the availability of a regression oracle for the value-function class, a more realistic and reasonable oracle than the classification oracles over policies typically assumed by agnostic methods. Our approach generalizes both UCB and LinUCB to far more expressive possible model classes and achieves low regret under certain distributional assumptions. In an extensive empirical evaluation, compared to both realizability-based and agnostic baselines, we find that our approach typically gives comparable or superior results.
IHT dies hard: Provable accelerated Iterative Hard Thresholding

We study --both in theory and practice-- the use of momentum motions in classic iterative hard thresholding (IHT) methods. By simply modifying plain IHT, we investigate its convergence behavior on convex optimization criteria with non-convex constraints, under standard assumptions. In diverse scenaria, we observe that acceleration in IHT leads to significant improvements, compared to state of the art projected gradient descent and Frank-Wolfe variants. As a byproduct of our inspection, we study the impact of selecting the momentum parameter: similar to convex settings, two modes of behavior are observed --"rippling" and linear-- depending on the level of momentum.
Nearly Optimal Distinct Elements and Heavy Hitters on Sliding Windows.

We study the distinct elements and l_p-heavy hitters problems in the sliding window model, where only the most recent n elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the exponential (Datar et al., SODA 2002) and smooth histograms (Braverman and Ostrovsky, FOCS 2007) that may be of independent interest. We then show that the composable histogram{} along with a careful combination of existing techniques to track either the identity or frequency of a few specific items suffices to obtain algorithms for both distinct elements and l_p-heavy hitters that are nearly optimal in both n and epsilon. Applying our new composable histogram framework, we provide an algorithm that outputs a (1+epsilon)-approximation to the number of distinct elements in the sliding window model and uses O{1/(epsilon^2) log n log (1/epsilon)log log n+ (1/epsilon) log^2 n} bits of space. For l_p-heavy hitters, we provide an algorithm using space O{(1/epsilon^p) log^2 n (log^2 log n+log 1/epsilon)} for 0<p <=2, improving upon the best-known algorithm for l_2-heavy hitters (Braverman et al., COCOON 2014), which has space complexity O{1/epsilon^4 log^3 n}. We also show complementing nearly optimal lower bounds of Omega ((1/epsilon) log^2 n+(1/epsilon^2) log n) for distinct elements and Omega ((1/epsilon^p) log^2 n) for l_p-heavy hitters, both tight up to O{log log n} and O{log 1/epsilon} factors.
Generalized notions of sparsity and restricted isometry property. Part I: a unified framework

The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and noncommutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high order tensor products.
A new characterization of Elfving's method for high dimensional computation

Abstract We give a new characterization of Elfving's (1952) method for computing c -optimal designs in k dimensions which gives explicit formulae for the k unknown optimal weights and k unknown signs in Elfving's characterization. This eliminates the need to search over these parameters to compute c -optimal designs, and thus reduces the computational burden from solving a family of optimization problems to solving a single optimization problem for the optimal finite support set. We give two illustrative examples: a high dimensional polynomial regression model and a logistic regression model, the latter showing that the method can be used for locally optimal designs in nonlinear models as well.
Rapid Mass Segregation in Massive Star Clusters

Several dynamical scenarios have been proposed that can lead to prompt mass segregation on the crossing time scale of a young cluster. They generally rely on cool and/or clumpy initial conditions, and are most relevant to small systems. As a counterpoint, we present a novel dynamical mechanism that can operate in relatively large, homogeneous, cool or cold systems. This mechanism may be important in understanding the assembly of large mass-segregated clusters from smaller clumps.
Equal But Not The Same: Understanding the Implicit Relationship Between Persuasive Images and Text

Images and text in advertisements interact in complex, non-literal ways. The two channels are usually complementary, with each channel telling a different part of the story. Current approaches, such as image captioning methods, only examine literal, redundant relationships, where image and text show exactly the same content. To understand more complex relationships, we first collect a dataset of advertisement interpretations for whether the image and slogan in the same visual advertisement form a parallel (conveying the same message without literally saying the same thing) or non-parallel relationship, with the help of workers recruited on Amazon Mechanical Turk. We develop a variety of features that capture the creativity of images and the specificity or ambiguity of text, as well as methods that analyze the semantics within and across channels. We show that our method outperforms standard image-text alignment approaches on predicting the parallel/non-parallel relationship between image and text.
A Probabilistic Approach to Power System State Estimation using a Linear Algorithm

An equivalent circuit formulation for power system analysis was demonstrated to improve robustness of Power Flow and enable more generalized modeling, including that for RTUs (Remote Terminal Units) and PMUs (Phasor Measurement Units). These measurement device models, together with an adjoint circuit based optimization framework, enable an alternative formulation to Power System State Estimation (SE) that can be solved within the equivalent circuit formulation. In this paper, we utilize a linear RTU model to create a fully linear SE algorithm that includes PMU and RTU measurements to enable a probabilistic approach to SE. Results demonstrate that this is a practical approach that is well suited for real-world applications.
Thompson Sampling on Symmetric Alpha-Stable Bandits

Thompson Sampling provides an efficient technique to introduce prior knowledge in the multi-armed bandit problem, along with providing remarkable empirical performance. In this paper, we revisit the Thompson Sampling algorithm under rewards drawn from symmetric $\alpha$-stable distributions, which are a class of heavy-tailed probability distributions utilized in finance and economics, in problems such as modeling stock prices and human behavior. We present an efficient framework for posterior inference, which leads to two algorithms for Thompson Sampling in this setting. We prove finite-time regret bounds for both algorithms, and demonstrate through a series of experiments the stronger performance of Thompson Sampling in this setting. With our results, we provide an exposition of symmetric $\alpha$-stable distributions in sequential decision-making, and enable sequential Bayesian inference in applications from diverse fields in finance and complex systems that operate on heavy-tailed features.
What Do Employees Know? Evidence from a Social Media Platform

ABSTRACT We use employee predictions of their companies' six-month business outlook from Glassdoor.com to assess the information content of employee social media disclosures. We find that average e...
Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature

We exhibit the first examples of closed 4-manifolds with nonnegative sectional curvature that lose this property when evolved via Ricci flow.
Stochastic meshless analysis of elastic–plastic cracked structures

This paper presents a stochastic mesh-free method for probabilistic fracture-mechanics analysis of nonlinear cracked structures. The method involves enriched element-free Galerkin formulation for calculating the J-integral; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method (FORM) for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique. Numerical examples based on mode-I fracture problems have been presented to illustrate the proposed method. The results from sensitivity analysis indicate that the maximum difference between sensitivity of the J-integral calculated using the proposed method and reference solutions obtained by the finite-difference method is about three percent. The results from reliability analysis show that the probability of fracture initiation using the proposed sensitivity and meshless-based FORM are very accurate when compared with either the finite-element-based Monte Carlo simulation or finite-element-based FORM. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently using meshless methods.
Perspectives on CUR decompositions

Abstract This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization of CUR decompositions which synergizes these viewpoints and shows that they are indeed the same in the exact decomposition case.