cssi/SciSciGPT-SciSciNet huggingface dataset:
Additive approximations in high dimensional nonparametric regression via the SALSA

High dimensional nonparametric regression is an inherently difficult problem with known lower bounds depending exponentially in dimension. A popular strategy to alleviate this curse of dimensionality has been to use additive models of first order, which model the regression function as a sum of independent functions on each dimension. Though useful in controlling the variance of the estimate, such models are often too restrictive in practical settings. Between non-additive models which often have large variance and first order additive models which have large bias, there has been little work to exploit the trade-off in the middle via additive models of intermediate order. In this work, we propose SALSA, which bridges this gap by allowing interactions between variables, but controls model capacity by limiting the order of interactions. SALSA minimises the residual sum of squares with squared RKHS norm penalties. Algorithmically, it can be viewed as Kernel Ridge Regression with an additive kernel. When the regression function is additive, the excess risk is only polynomial in dimension. Using the Girard-Newton formulae, we efficiently sum over a combinatorial number of terms in the additive expansion. Via a comparison on 15 real datasets, we show that our method is competitive against 21 other alternatives.
Learning sparse representations in reinforcement learning with sparse coding

A variety of representation learning approaches have been investigated for reinforcement learning; much less attention, however, has been given to investigating the utility of sparse coding. Outside of reinforcement learning, sparse coding representations have been widely used, with non-convex objectives that result in discriminative representations. In this work, we develop a supervised sparse coding objective for policy evaluation. Despite the non-convexity of this objective, we prove that all local minima are global minima, making the approach amenable to simple optimization strategies. We empirically show that it is key to use a supervised objective, rather than the more straightforward unsupervised sparse coding approach. We compare the learned representations to a canonical fixed sparse representation, called tile-coding, demonstrating that the sparse coding representation outperforms a wide variety of tile-coding representations.
Digital Stylometry: Linking Profiles Across Social Networks

There is an ever growing number of users with accounts on multiple social media and networking sites. Consequently, there is increasing interest in matching user accounts and profiles across different social networks in order to create aggregate profiles of users. In this paper, we present models for Digital Stylometry, which is a method for matching users through stylometry inspired techniques. We experimented with linguistic, temporal, and combined temporal-linguistic models for matching user accounts, using standard and novel techniques. Using publicly available data, our best model, a combined temporal-linguistic one, was able to correctly match the accounts of 31% of 5,612 distinct users across Twitter and Facebook.
The Signature of the Chern Coefficients of Local Rings

This paper considers the following conjecture: If $R$ is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal $J$ generated by a system of parameters, the Chern coefficient $e_1(J)< 0$ is equivalent to $R$ being non Cohen-Macaulay. The conjecture is established if $R$ is a homomorphic image of a Gorenstein ring, and for all universally catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived.
VLSI design of a nonparametric equalizer for massive MU-MIMO

Linear minimum mean-square error (L-MMSE) equalization is among the most popular methods for data detection in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. While L-MMSE equalization enables near-optimal spectral efficiency, accurate knowledge of the signal and noise powers is necessary. Furthermore, corresponding VLSI designs must solve linear systems of equations, which requires high arithmetic precision, exhibits stringent data dependencies, and results in high circuit complexity. This paper proposes the first VLSI design of the NOnParametric Equalizer (NOPE), which avoids knowledge of the transmit signal and noise powers, provably delivers the performance of L-MMSE equalization for massive MU-MIMO systems, and is resilient to numerous system and hardware impairments due to its parameter-free nature. Moreover, NOPE avoids computation of a matrix inverse and only requires hardware-friendly matrix-vector multiplications. To showcase the practical advantages of NOPE, we propose a parallel VLSI architecture and provide synthesis results in 28 nm CMOS. We demonstrate that NOPE performs on par with existing data detectors for massive MU-MIMO that require accurate knowledge of the signal and noise powers.
Circular law for random discrete matrices of given row sum

Let Mn be a random matrix of size n×n and let λ1, . . . , λn be the eigenvalues of Mn. The empirical spectral distribution μMn of Mn is defined as μMn(s, t) = 1 n #{k ≤ n,<(λk) ≤ s;=(λk) ≤ t}. The circular law theorem in random matrix theory asserts that if the entries of Mn are i.i.d. copies of a random variable with mean zero and variance σ, then the empirical spectral distribution of the normalized matrix 1 σ √ n Mn of Mn converges almost surely to the uniform distribution μcir over the unit disk as n tends to infinity. In this paper we show that the empirical spectral distribution of the normalized matrix of Mn, a random matrix whose rows are independent random (−1, 1) vectors of given row-sum s with some fixed integer s satisfying |s| ≤ (1 − o(1))n, also obeys the circular law. The key ingredient is a new polynomial estimate on the least singular value of Mn.
Projections and dyadic Parseval frame MRA wavelets

Abstract A classical theorem attributed to Naimark states that, given a Parseval frame B in a Hilbert space H , one can embed H in a larger Hilbert space K so that the image of B is the projection of an orthonormal basis for K . In the present work, we revisit the notion of Parseval frame MRA wavelets from [12] and [13] and produce an analog of Naimark's theorem for these wavelets at the level of their scaling functions. We aim to make this discussion as self-contained as possible and provide a different point of view on Parseval frame MRA wavelets than that of [12] and [13] .
Dropout with Expectation-linear Regularization

Dropout, a simple and effective way to train deep neural networks, has led to a number of impressive empirical successes and spawned many recent theoretical investigations. However, the gap between dropout's training and inference phases, introduced due to tractability considerations, has largely remained under-appreciated. In this work, we first formulate dropout as a tractable approximation of some latent variable model, leading to a clean view of parameter sharing and enabling further theoretical analysis. Then, we introduce (approximate) expectation-linear dropout neural networks, whose inference gap we are able to formally characterize. Algorithmically, we show that our proposed measure of the inference gap can be used to regularize the standard dropout training objective, resulting in an \emph{explicit} control of the gap. Our method is as simple and efficient as standard dropout. We further prove the upper bounds on the loss in accuracy due to expectation-linearization, describe classes of input distributions that expectation-linearize easily. Experiments on three image classification benchmark datasets demonstrate that reducing the inference gap can indeed improve the performance consistently.
Guided acoustic and optical waves in silicon-on-insulator for Brillouin scattering and optomechanics

We numerically study silicon waveguides on silica showing that it is possible to simultaneously guide optical and acoustic waves in the technologically important silicon on insulator (SOI) material system. Thin waveguides, or fins, exhibit geometrically softened mechanical modes at gigahertz frequencies with phase velocities below the Rayleigh velocity in glass, eliminating acoustic radiation losses. We propose slot waveguides on glass with telecom optical frequencies and strong radiation pressure forces resulting in Brillouin gains on the order of 500 and 50 000 W−1m−1 for backward and forward Brillouin scattering, respectively.
Existence, bifurcation, and geometric evolution of quasi-bilayers in the multicomponent functionalized Cahn–Hilliard equation

Multicomponent bilayer structures arise as the ubiquitous plasma membrane in cellular biology and as blends of amphiphilic copolymers used in electrolyte membranes, drug delivery, and emulsion stabilization within the context of synthetic chemistry. We present the multicomponent functionalized Cahn–Hilliard (mFCH) free energy as a model which allows competition between bilayers with distinct composition and between bilayers and higher codimensional structures, such as co-dimension two filaments and co-dimension three micelles. We construct symmetric and asymmetric homoclinic bilayer profiles via a billiard limit potential and show that co-dimensional bifurcation is driven by the experimentally observed layer-by-layer pearling mechanism. We investigate the stability and slow geometric evolution of multicomponent bilayer interfaces within the context of an $$H^{-1}$$ gradient flow of the mFCH, addressing the impact of aspect ratio of the amphiphile (lipid or copolymer unit) on the intrinsic curvature and the codimensional bifurcation. In particular we derive a Canham–Helfrich sharp interface energy whose intrinsic curvature arises through a Melnikov parameter associated to amphiphile aspect ratio.
Dual Hodge decompositions and derived Poisson brackets

We study general properties of Hodge-type decompositions of cyclic and Hochschild homology of universal enveloping algebras of (DG) Lie algebras. Our construction generalizes the operadic construction of cyclic homology of Lie algebras due to Getzler and Kapranov. We give a topological interpretation of such Lie Hodge decompositions in terms of $$S^1$$ -equivariant homology of the free loop space of a simply connected topological space. We prove that the canonical derived Poisson structure on a universal enveloping algebra arising from a cyclic pairing on the Koszul dual coalgebra preserves the Hodge filtration on cyclic homology. As an application, we show that the Chas–Sullivan Lie algebra of any simply connected closed manifold carries a natural Hodge filtration. We conjecture that the Chas–Sullivan Lie algebra is actually graded, i.e. the string topology bracket preserves the Hodge decomposition.
A matrix model for random nilpotent groups

We study random torsion-free nilpotent groups generated by a pair of random words of length $\ell$ in the standard generating set of $U_n(\mathbb{Z})$. Specifically, we give asymptotic results about the step properties of the group when the lengths of the generating words are functions of $n$. We show that the threshold function for asymptotic abelianness is $\ell = c \sqrt{n}$, for which the probability approaches $e^{-2c^2}$, and also that the threshold function for having full-step, the same step as $U_n(\mathbb{Z})$, is between $c n^2$ and $c n^3$.
Testing Separability of Functional Time Series

We derive and study a significance test for determining whether a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one depending only on time and the other depending only on the coordinates of the panel. Separability is a property that can dramatically improve computational efficiency by substantially reducing model complexity. It is especially useful for functional data, as it implies that the functional principal components are the same for each member of the panel. However, such an assumption must be verified before proceeding with further inference. Our approach is based on functional norm differences and provides a test with well‐controlled size and high power. We establish our procedure quite generally, allowing one to test separability of autocovariances as well. In addition to an asymptotic justification, our methodology is validated by a simulation study. It is applied to functional panels of particulate pollution and stock market data.
On a Fractional Version of Haemers’ Bound

In this paper, we present a fractional version of Haemers’ bound on the Shannon capacity of a graph, which is originally due to Blasiak. This bound is a common strengthening of both Haemers’ bound and the fractional chromatic number of a graph. We show that this fractional version outperforms any bound on the Shannon capacity that could be attained through Haemers’ bound. We show also that this bound is multiplicative, unlike Haemers’ bound.
Examining the Effects of Objective Hurricane Risks and Community Resilience on Risk Perceptions of Hurricanes at the County Level in the U.S. Gulf Coast: An Innovative Approach

Communities' risk perceptions can influence their abilities to cope with coastal hazards such as hurricanes and coastal flooding. Our study presents an initial effort to examine the relationship be...
The maximum number of cliques in graphs without long cycles

Abstract The Erdős–Gallai Theorem states that for k ≥ 3 every graph on n vertices with more than 1 2 ( k − 1 ) ( n − 1 ) edges contains a cycle of length at least k. Kopylov proved a strengthening of this result for 2-connected graphs with extremal examples H n , k , t and H n , k , 2 . In this note, we generalize the result of Kopylov to bound the number of s-cliques in a graph with circumference less than k. Furthermore, we show that the same extremal examples that maximize the number of edges also maximize the number of cliques of any fixed size. Finally, we obtain the extremal number of s-cliques in a graph with no path on k-vertices.
GO Gradient for Expectation-Based Objectives

Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\gammav$ for expectation-based objectives $\Ebb_{q_{\gammav} (\yv)} [f(\yv)]$. Most existing methods either (i) suffer from high variance, seeking help from (often) complicated variance-reduction techniques; or (ii) they only apply to reparameterizable continuous random variables and employ a reparameterization trick. To address these limitations, we propose a General and One-sample (GO) gradient that (i) applies to many distributions associated with non-reparameterizable continuous or discrete random variables, and (ii) has the same low-variance as the reparameterization trick. We find that the GO gradient often works well in practice based on only one Monte Carlo sample (although one can of course use more samples if desired). Alongside the GO gradient, we develop a means of propagating the chain rule through distributions, yielding statistical back-propagation, coupling neural networks to common random variables.
Multigrid methods for saddle point problems: Darcy systems

We design and analyze multigrid methods for the saddle point problems resulting from Raviart–Thomas–Nedelec mixed finite element methods for the Darcy system in porous media flow. Uniform convergence of the W-cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.
Copula variational inference

We develop a general variational inference method that preserves dependency among the latent variables. Our method uses copulas to augment the families of distributions used in mean-field and structured approximations. Copulas model the dependency that is not captured by the original variational distribution, and thus the augmented variational family guarantees better approximations to the posterior. With stochastic optimization, inference on the augmented distribution is scalable. Furthermore, our strategy is generic: it can be applied to any inference procedure that currently uses the mean-field or structured approach. Copula variational inference has many advantages: it reduces bias; it is less sensitive to local optima; it is less sensitive to hyperparameters; and it helps characterize and interpret the dependency among the latent variables.
Sparse exchangeable graphs and their limits via graphon processes

In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in R+. Here we show that by generalizing the classical definition of graphons as functions over probability spaces to functions over σ-finite measure spaces, we can model a large family of exchangeable graphs, including the Caron-Fox graphs and the traditional exchangeable dense graphs as special cases. Explicitly, modelling the underlying space of features by a σ-finite measure space (S, S, µ) and the connection probabilities by an integrable function W : S × S → [0, 1], we construct a random family (Gt)t≥0 of growing graphs such that the vertices of Gt are given by a Poisson point process on S with intensity tµ, with two points x, y of the point process connected with probability W(x, y). We call such a random family a graphon process. We prove that a graphon process has convergent subgraph frequencies (with possibly infinite limits) and that, in the natural extension of the cut metric to our setting, the sequence converges to the generating graphon. We also show that the underlying graphon is identifiable only as an equivalence class over graphons with cut distance zero. More generally, we study metric convergence for arbitrary (not necessarily random) sequences of graphs, and show that a sequence of graphs has a convergent subsequence if and only if it has a subsequence satisfying a property we call uniform regularity of tails. Finally, we prove that every graphon is equivalent to a graphon on R+ equipped with Lebesgue measure.
Fast Mixing for Discrete Point Processes

We investigate the systematic mechanism for designing fast mixing Markov chain Monte Carlo algorithms to sample from discrete point processes under the Dobrushin uniqueness condition for Gibbs measures. Discrete point processes are defined as probability distributions μ(S) ∝ exp(βf(S)) over all subsets S ∈ 2 of a finite set V through a bounded set function f : 2 → R and a parameter β > 0. A subclass of discrete point processes characterized by submodular functions (which include log-submodular distributions, submodular point processes, and determinantal point processes) has recently gained a lot of interest in machine learning and shown to be effective for modeling diversity and coverage. We show that if the set function (not necessarily submodular) displays a natural notion of decay of correlation, then, for β small enough, it is possible to design fast mixing Markov chain Monte Carlo methods that yield error bounds on marginal approximations that do not depend on the size of the set V . The sufficient conditions that we derive involve a control on the (discrete) Hessian of set functions, a quantity that has not been previously considered in the literature. We specialize our results for submodular functions, and we discuss canonical examples where the Hessian can be easily controlled.
Subsampling for Ridge Regression via Regularized Volume Sampling

Given $n$ vectors $\mathbf{x}_i\in \mathbb{R}^d$, we want to fit a linear regression model for noisy labels $y_i\in\mathbb{R}$. The ridge estimator is a classical solution to this problem. However, when labels are expensive, we are forced to select only a small subset of vectors $\mathbf{x}_i$ for which we obtain the labels $y_i$. We propose a new procedure for selecting the subset of vectors, such that the ridge estimator obtained from that subset offers strong statistical guarantees in terms of the mean squared prediction error over the entire dataset of $n$ labeled vectors. The number of labels needed is proportional to the statistical dimension of the problem which is often much smaller than $d$. Our method is an extension of a joint subsampling procedure called volume sampling. A second major contribution is that we speed up volume sampling so that it is essentially as efficient as leverage scores, which is the main i.i.d. subsampling procedure for this task. Finally, we show theoretically and experimentally that volume sampling has a clear advantage over any i.i.d. sampling when labels are expensive.
Object Detectors Emerge in Deep Scene CNNs

Abstract: With the success of new computational architectures for visual processing, such as convolutional neural networks (CNN) and access to image databases with millions of labeled examples (e.g., ImageNet, Places), the state of the art in computer vision is advancing rapidly. One important factor for continued progress is to understand the representations that are learned by the inner layers of these deep architectures. Here we show that object detectors emerge from training CNNs to perform scene classification. As scenes are composed of objects, the CNN for scene classification automatically discovers meaningful objects detectors, representative of the learned scene categories. With object detectors emerging as a result of learning to recognize scenes, our work demonstrates that the same network can perform both scene recognition and object localization in a single forward-pass, without ever having been explicitly taught the notion of objects.
Large deviations and averaging for systems of slow-fast stochastic reaction–diffusion equations

We study a large deviation principle for a system of stochastic reaction–diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to characterize the limiting process via a “viable pair” that captures the limiting controlled dynamics and the effective invariant measure simultaneously. The characterization of the limit of the controlled slow-fast processes in terms of viable pair enables us to obtain a variational representation of the large deviation action functional. Due to the infinite-dimensional nature of our set-up, the proof of tightness as well as the analysis of the limit process and in particular the proof of the large deviations lower bound is considerably more delicate here than in the finite-dimensional situation. Smoothness properties of optimal controls in infinite dimensions (a necessary step for the large deviations lower bound) need to be established. We emphasize that many issues that are present in the infinite dimensional case, are completely absent in finite dimensions.
Distributed Subgradient Projection Algorithm Over Directed Graphs

We propose Directed-Distributed Projected Subgradient (D-DPS) to solve a constrained optimization problem over a multi-agent network, where the goal of agents is to collectively minimize the sum of locally known convex functions. Each agent in the network owns only its local objective function, constrained to a commonly known convex set. We focus on the circumstance when communications between agents are described by a directed network. The D-DPS combines surplus consensus to overcome the asymmetry caused by the directed communication network. The analysis shows the convergence rate to be $O(\frac{\ln k}{\sqrt{k}})$ .
Sliding Bidirectional Recurrent Neural Networks for Sequence Detection in Communication Systems

The design and analysis of communication systems typically rely on the development of mathematical models that describe the underlying communication channel. However, in some systems, such as molecular communication systems where chemical signals are used for transfer of information, the underlying channel models are unknown. In these scenarios, a completely new approach to design and analysis is required. In this work, we focus on one important aspect of communication systems, the detection algorithms, and demonstrate that by using tools from deep learning, it is possible to train detectors that perform well without any knowledge of the underlying channel models. We propose a technique we call sliding bidirectional recurrent neural network (SBRNN) for real-time sequence detection. We evaluate this algorithm using experimental data that is collected by a chemical communication platform, where the channel model is unknown and difficult to model analytically. We show that deep learning algorithms perform significantly better than a detector proposed in previous works, and the SBRNN outperforms other techniques considered in this work.
View-Volume Network for Semantic Scene Completion from a Single Depth Image

We introduce a View-Volume convolutional neural network (VVNet) for inferring the occupancy and semantic labels of a volumetric 3D scene from a single depth image. The VVNet concatenates a 2D view CNN and a 3D volume CNN with a differentiable projection layer. Given a single RGBD image, our method extracts the detailed geometric features from the input depth image with a 2D view CNN and then projects the features into a 3D volume according to the input depth map via a projection layer. After that, we learn the 3D context information of the scene with a 3D volume CNN for computing the result volumetric occupancy and semantic labels. With combined 2D and 3D representations, the VVNet efficiently reduces the computational cost, enables feature extraction from multi-channel high resolution inputs, and thus significantly improves the result accuracy. We validate our method and demonstrate its efficiency and effectiveness on both synthetic SUNCG and real NYU dataset.
Limit linear series and the Amini–Baker construction

We draw comparisons between the author’s recent construction of limit linear series for curves not of compact type and the Amini–Baker theory of limit linear series on metrized complexes, as well as the related theories of divisors on discrete graphs and on metric graphs. From these we conclude that the author’s theory (like the others) satisfies the Riemann and Clifford inequalities. Motivated by our comparisons, we also develop negative results on Brill–Noether generality for certain families of metric graphs. Companion work of He develops our comparisons further and uses them to prove new results on smoothability of Amini–Baker limit linear series and of divisors on metric graphs.
Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.
Inverter Probing for Power Distribution Network Topology Processing

Knowing the connectivity and line parameters of the underlying electric distribution network is a prerequisite for solving any grid optimization task. Although distribution grids lack observability and comprehensive metering, inverters with advanced cyber capabilities currently interface solar panels and energy storage devices to the grid. Smart inverters have been widely used for grid control and optimization, yet the fresh idea here is to engage them towards network topology inference. With an electric circuit, a distribution grid can be intentionally probed by instantaneously perturbing inverter injections. Collecting and processing the incurred voltage deviations across nodes can potentially unveil the grid topology even without knowing loads. Using grid probing data and under an approximate grid model, the tasks of topology recovery and line status verification are posed, respectively, as nonconvex estimation and detection problems. Leveraging the features of the Laplacian matrix of a tree graph, probing terminal nodes is analytically shown to be sufficient for exact topology recovery if voltage data are collected at all buses. The related nonconvex problems are surrogated to convex ones, which are iteratively solved via closed-form updates based on the alternating direction method of multipliers and projected gradient descent. Numerical tests on benchmark feeders demonstrate that grid probing can yield line status error probabilities of $10^{-3}$ by probing 40% of the nodes.
Co-Occuring Directions Sketching for Approximate Matrix Multiply

We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occuring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a $1 + \epsilon$ -approximation of the optimal low rank approximation of a matrix product. Empirically our algorithm outperforms competing methods for AMM, for a small sketch size. We validate empirically our theoretical findings and algorithms
A characterization of Markov equivalence classes for directed acyclic graphs with latent variables

Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly identify all arrow orientations shared by all DAGs in a Markov equivalence class, given a member of that class. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to construct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is particularly useful for causal inference.
Computational study of shock waves propagating through air-plastic-water interfaces

The following study ismotivated by experimental studies in traumatic brain injury (TBI). Recent research has demonstrated that low intensity non-impact blast wave exposure frequently leads to mild traumatic brain injury (mTBI); however, the mechanisms connecting the blast waves and the mTBI remain unclear. Collaborators at the Seattle VA Hospital are doing experiments to understand how blast waves can produce mTBI. In order to gain insight that is hard to obtain by experimental means, we have developed conservative finite volume methods for interface-shock wave interaction to simulate these experiments. A 1D model of their experimental setup has been implemented using Euler equations for compressible fluids. These equations are coupled with a Tammann equation of state (EOS) that allows us to model compressible gas along with almost incompressible fluids or elastic solids. A hybrid HLLC-exact Eulerian-Lagrangian Riemann solver for Tammann EOS with a jump in the parameters has been developed. The model has shown that if the plastic interface is very thin, it can be neglected. This result might be very helpful to model more complicated setups in higher dimensions.
Learning Simple Auctions

We present a general framework for proving polynomial sample complexity bounds for the problem of learning from samples the best auction in a class of “simple” auctions. Our framework captures the most prominent examples of “simple” auctions, including anonymous and non-anonymous item and bundle pricings, with either a single or multiple buyers. The first step of the framework is to show that the set of auction allocation rules have a low-dimensional representation. The second step shows that, across the subset of auctions that share the same allocations on a given set of samples, the auction revenue varies in a lowdimensional way. Our results imply that in typical scenarios where it is possible to compute a near-optimal simple auction with a known prior, it is also possible to compute such an auction with an unknown prior, given a polynomial number of samples.
Improved Dropout for Shallow and Deep Learning

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptimal for the sake of convergence. In this paper, we propose to use multinomial sampling for dropout, i.e., sampling features or neurons according to a multinomial distribution with different probabilities for different features/neurons. To exhibit the optimal dropout probabilities, we analyze the shallow learning with multinomial dropout and establish the risk bound for stochastic optimization. By minimizing a sampling dependent factor in the risk bound, we obtain a distribution-dependent dropout with sampling probabilities dependent on the second order statistics of the data distribution. To tackle the issue of evolving distribution of neurons in deep learning, we propose an efficient adaptive dropout (named \textbf{evolutional dropout}) that computes the sampling probabilities on-the-fly from a mini-batch of examples. Empirical studies on several benchmark datasets demonstrate that the proposed dropouts achieve not only much faster convergence and but also a smaller testing error than the standard dropout. For example, on the CIFAR-100 data, the evolutional dropout achieves relative improvements over 10\% on the prediction performance and over 50\% on the convergence speed compared to the standard dropout.
Actin Dynamics Drive Microvillar Motility and Clustering during Brush Border Assembly.

Summary Transporting epithelial cells generate arrays of microvilli, known as a brush border, to enhance functional capacity. To understand brush border formation, we used live cell imaging to visualize apical remodeling early in this process. Strikingly, we found that individual microvilli exhibit persistent active motility, translocating across the cell surface at ∼0.2 μm/min. Perturbation with inhibitors and photokinetic experiments revealed that microvillar motility is driven by actin assembly at the barbed ends of core bundles, which in turn is linked to robust treadmilling of these structures. Actin regulatory factors IRTKS and EPS8 localize to the barbed ends of motile microvilli, where they control the kinetics and nature of movement. As the apical surface of differentiating epithelial cells is crowded with nascent microvilli, persistent motility promotes collisions between protrusions and ultimately clustering and consolidation into higher-order arrays. Thus, microvillar motility represents a previously unrecognized driving force for apical surface remodeling and maturation during epithelial differentiation.
Disproportionate Effect of Sub-Micron Topography on Osteoconductive Capability of Titanium

Titanium micro-scale topography offers excellent osteoconductivity and bone–implant integration. However, the biological effects of sub-micron topography are unknown. We compared osteoblastic phenotypes and in vivo bone and implant integration abilities between titanium surfaces with micro- (1–5 µm) and sub-micro-scale (0.1–0.5 µm) compartmental structures and machined titanium. The calculated average roughness was 12.5 ± 0.65, 123 ± 6.15, and 24 ± 1.2 nm for machined, micro-rough, and sub-micro-rough surfaces, respectively. In culture studies using bone marrow-derived osteoblasts, the micro-rough surface showed the lowest proliferation and fewest cells attaching during the initial stage. Calcium deposition and expression of osteoblastic genes were highest on the sub-micro-rough surface. The bone–implant integration in the Sprague–Dawley male rat femur model was the strongest on the micro-rough surface. Thus, the biological effects of titanium surfaces are not necessarily proportional to the degree of roughness in osteoblastic cultures or in vivo. Sub-micro-rough titanium ameliorates the disadvantage of micro-rough titanium by restoring cell attachment and proliferation. However, bone integration and the ability to retain cells are compromised due to its lower interfacial mechanical locking. This is the first report on sub-micron topography on a titanium surface promoting osteoblast function with minimal osseointegration.
On the Downstream Performance of Compressed Word Embeddings.

Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression quality often fail to distinguish between embeddings that perform well and those that do not. We thus propose the eigenspace overlap score as a new measure. We relate the eigenspace overlap score to downstream performance by developing generalization bounds for the compressed embeddings in terms of this score, in the context of linear and logistic regression. We then show that we can lower bound the eigenspace overlap score for a simple uniform quantization compression method, helping to explain the strong empirical performance of this method. Finally, we show that by using the eigenspace overlap score as a selection criterion between embeddings drawn from a representative set we compressed, we can efficiently identify the better performing embedding with up to 2x lower selection error rates than the next best measure of compression quality, and avoid the cost of training a separate model for each task of interest.
Elpasolite Planetary Ice and Composition Spectrometer (EPICS): A Low-Resource Combined Gamma-Ray and Neutron Spectrometer for Planetary Science

Neutron and gamma-ray spectroscopy (NGRS) is a well established technique for studying the geochemical composition and volatile abundance relevant to planetary structure and evolution of planetary bodies. Previous NGRS instruments have used separate gamma-ray and neutron spectrometers. The Elpasolite Planetary Ice and Composition Spectrometer (EPICS) instrument is an innovative and fully integrated NGRS with low resource requirements. EPICS utilizes elpasolite scintillator read out by silicon photomultipliers to combine the gamma-ray and neutron spectrometer into a single instrument, leading to a significant reduction in instrument size, weight, and power. An overview and motivation for the EPICS instrument, current status of the EPICS development, and a discussion of the expected sensitivity and performance are presented.
Coverage Probability Analysis Under Clustered Ambient Backscatter Nodes

In this letter, we consider a new large-scale communication scheme where randomly distributed backscatter nodes are involved as secondary users to primary transmitter and primary receiver pairs. The secondary communication between a backscatter transmitter and a backscatter receiver introduces additional double fading channels and has a two-side effect to the primary communications. We derive the signal-to-interference-plus-noise ratio and signal-to-interference ratio based coverage probabilities for two network configuration scenarios.
SMALL SCALES AND SINGULARITY FORMATION IN FLUID DYNAMICS

We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.
Should Good People be Doctors? A Comment on Paul Butler and Anonymous

A much-discussed essay by Paul Butler argues that good people should not be prosecutors, because working in a prosecutor's office can do harm to one's personal commitments and soul. A recent note in Harvard Law Review arrives at the same conclusion based on systemic considerations--the work strengthens and legitimizes a wicked system. I argue that part of these authors' incisive critiques is sound, but another stands on infirm footing. Except for those willing to serve as "double agents," prepared to live with daily ambiguity, prosecution should not be a high career choice. My argument rests not so much on the politics of putting people in prison for a living, nor on the psychological effects of the work on those doing it--but on the nature of the work itself.
Localization for Anderson models on metric and discrete tree graphs

We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This level of generality, in particular, allows us to treat radial trees with disordered geometry as well as Schrodinger operators with Bernoulli-type singular potentials. Our methods are based on an interplay between graph-theoretical properties of radial trees and spectral analysis of the associated random differential and difference operators on the half-line.
Modeling Communication Processes in the Human Connectome through Cooperative Learning

Communication processes within the human brain at different cognitive states are neither well understood nor completely characterized. We assess communication processes in the human connectome using ant colony-inspired cooperative learning algorithm, starting from a source with no a priori information about the network topology, and cooperatively searching for the target through a pheromone-inspired model. This framework relies on two parameters, namely pheromone perception and edge perception , to define the cognizance and subsequent behaviour of the ants on the network and, overall, the communication processes happening between source and target nodes. Simulations obtained through different configurations allow the identification of path-ensembles that are involved in the communication between node pairs. These path-ensembles may contain different number of paths depending on the perception parameters and the node pair. In order to assess the different communication regimes displayed on the simulations and their associations with functional connectivity, we introduce two network measurements, effective path-length and arrival rate. These communication features are tested as individual as well as combined descriptors of functional connectivity during different tasks. Finally, different communication regimes are found in different specialized functional networks. Overall, this framework may be used as a test-bed for different communication regimes on top of an underlaying topology.
Estimating statistical power for event-related potential studies using the late positive potential.

The late positive potential (LPP) is a common measurement used to study emotional processes of subjects in ERP paradigms. Despite its extensive use in affective neuroscience, there is presently no gold standard for how to appropriately power ERP studies using the LPP. The present study investigates how the number of trials, number of subjects, and magnitude of the effect size affect statistical power in analyses of the LPP. Using Monte Carlo simulations of ERP experiments with varying numbers of trials, subjects, and synthetic effects of known magnitude, we measured the probability of obtaining a statistically significant effect in 1,489 experiments repeated 1,000 times each. Predictably, our results showed that statistical power increases with increasing numbers of trials and subjects and at larger effect sizes. We also found that higher levels of statistical power can be achieved with lower numbers of subjects and trials and at lower effect sizes in within-subject than in between-subjects designs. Furthermore, we found that, as subjects are added to an experiment, the slope of the relationship between effect size and statistical power increased and shifted to the left until the power asymptoted to nearly 100% at higher effect sizes. This suggests that adding more subjects greatly increases statistical power at lower effect sizes ( 1.5 µV) effect sizes. We confirmed the results from the simulations based on the synthetic effects by running a new series of simulated experiments based on real data collected while participants looked at emotional images.
Automated data‐intensive forecasting of plant phenology throughout the United States

Phenology, the timing of cyclical and seasonal natural phenomena such as flowering and leaf out, is an integral part of ecological systems with impacts on human activities like environmental management, tourism, and agriculture. As a result, there are numerous potential applications for actionable predictions of when phenological events will occur. However, despite the availability of phenological data with large spatial, temporal, and taxonomic extents, and numerous phenology models, there have been no automated species-level forecasts of plant phenology. This is due in part to the challenges of building a system that integrates large volumes of climate observations and forecasts, uses that data to fit models and make predictions for large numbers of species, and consistently disseminates the results of these forecasts in interpretable ways. Here, we describe a new near-term phenology-forecasting system that makes predictions for the timing of budburst, flowers, ripe fruit, and fall colors for 78 species across the United States up to 6 months in advance and is updated every four days. We use the lessons learned in developing this system to provide guidance developing large-scale near-term ecological forecast systems more generally, to help advance the use of automated forecasting in ecology.
Massive on-shell supersymmetric scattering amplitudes

We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible $$ \mathcal{N} $$ = 1 three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.
Unsupervised Learning of Dislocation Motion

Abstract The unsupervised learning technique, locally linear embedding (LLE), is applied to the analysis of X-ray diffraction data measured in-situ during the uniaxial plastic deformation of an additively manufactured nickel-based superalloy. With the aid of a physics-based material model, we find that the lower-dimensional coordinates determined using LLE appear to be physically significant and reflect the evolution of the defect densities that dictate strength and plastic flow behavior in the alloy. The implications of the findings for future constitutive model development are discussed, with a focus on wider applicability to microstructure evolution and phase transformation studies during in-situ materials processing.