cssi/SciSciGPT-SciSciNet huggingface dataset:
Decreasing Flow Uncertainty in Bayesian Inverse Problems Through Lagrangian Drifter Control

Commonplace in oceanography is the collection of ocean drifter positions. Ocean drifters are devices that sit on the surface of the ocean and move with the flow, transmitting their position via GPS to stations on land. Using drifter data, it is possible to obtain a posterior on the underlying flow. This problem, however, is highly underdetermined. Through controlling an ocean drifter, we attempt to improve our knowledge of the underlying flow. We do this by instructing the drifter to explore parts of the flow currently uncharted, thereby obtaining fresh observations. The efficacy of a control is determined by its effect on the variance of the posterior distribution. A smaller variance is interpreted as a better understanding of the flow. We show that a systematic reduction in variance can be achieved by utilising controls that allow the drifter to navigate new or interesting flow structures, a good example of which are eddies.
Outage constrained secrecy rate maximization using cooperative jamming

1 We consider a Gaussian MISO wiretap channel, where a multi-antenna source communicates with a single-antenna destination in the presence of a single-antenna eavesdropper. The communication is assisted by multi-antenna helpers that act as jammers to the eavesdropper. Each helper independently transmits noise, which lies in the null space of the helper-destination channel, thus creating no interference to the destination. Under source-eavesdropper channel uncertainty, we derive the optimal source covariance matrix that maximizes the secrecy rate subject to probability of outage and power constraints. Further, for the case in which the helper-eavesdropper channels follow a zero-mean Gaussian model with known covariances, we derive the outage probability in a closed form. Simulation results in support of the analysis are provided.
Large Outgoing Solutions to Supercritical Wave Equations

We prove the existence of global solutions to the energy-supercritical wave equation in R^{3+1} u_{tt}-\Delta u + |u|^N u = 0, u(0) = u_0, u_t(0) = u_1, 4<N<\infty, for a large class of radially symmetric finite-energy initial data. Functions in this class are characterized as being outgoing under the linear flow --- for a specific meaning of "outgoing" defined below. In particular, we construct global solutions for initial data with large (even infinite) critical Sobolev, Besov, Lebesgue, and Lorentz norms and several other large critical norms.
Latent Fingerprint Recognition: Role of Texture Template

We propose a texture template approach, consisting of a set of virtual minutiae, to improve latent fingerprint recognition accuracy. To compensate for the lack of a sufficient number of minutiae in poor quality latent prints, we generate a set of virtual minutiae. However, due to a large number of these regularly placed virtual minutiae, texture based template matching has a large computational requirement compared to matching true minutiae templates. To improve both the accuracy and efficiency of the texture template matching, we investigate: i) both original and enhanced fingerprint patches for training convolutional neural networks (ConvNets) to improve the distinctiveness of descriptors associated with each virtual minutiae, ii) smaller patches around virtual minutiae and a fast ConvNet architecture to speed up descriptor extraction, iii) reducing the descriptor length, iv) a modified hierarchical graph matching strategy to improve the matching speed, and v) extraction of multiple texture templates to boost the performance. Experiments on NIST SD27 latent database show that the above strategies can improve the matching speed from 11 ms (24 threads) per comparison (between a latent and a reference print) to only 7.7 ms (single thread) per comparison while improving the rank1 accuracy by 8.9% against a gallery of 10K rolled prints.
Recovering communities in the general stochastic block model without knowing the parameters

The stochastic block model (SBM) has recently gathered significant attention due to new threshold phenomena. However, most developments rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet achieve the optimal information-theoretic tradeoffs identified in Abbe-Sandon FOCS15. In the constant degree regime, an algorithm is developed that requires only a lower-bound on the relative sizes of the communities and achieves the optimal accuracy scaling for large degrees. This lower-bound requirement is removed for the regime of arbitrarily slowly diverging degrees, and the model parameters are learned efficiently. For the logarithmic degree regime, this is further enhanced into a fully agnostic algorithm that achieves the CH-limit for exact recovery in quasi-linear time. These provide the first algorithms affording efficiency, universality and information-theoretic optimality for strong and weak consistency in the SBM.
Near-field coupling of gold plasmonic antennas for sub-100 nm magneto-thermal microscopy

The development of spintronic technology with increasingly dense, high-speed, and complex devices will be accelerated by accessible microscopy techniques capable of probing magnetic phenomena on picosecond time scales and at deeply sub-micron length scales. A recently developed time-resolved magneto-thermal microscope provides a path towards this goal if it is augmented with a picosecond, nanoscale heat source. We theoretically study adiabatic nanofocusing and near-field heat induction using conical gold plasmonic antennas to generate sub-100 nm thermal gradients for time-resolved magneto-thermal imaging. Finite element calculations of antenna-sample interactions reveal focused electromagnetic loss profiles that are either peaked directly under the antenna or are annular, depending on the sample’s conductivity, the antenna’s apex radius, and the tip-sample separation. We find that the thermal gradient is confined to 40 nm to 60 nm full width at half maximum for realistic ranges of sample conductivity and ...
Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category

Let $\mathfrak{g}$ be a real or complex (finite dimensional) simple Lie algebra and $\sigma\in\mathrm{Aut}\mathfrak{g}$. The authors study automorphisms of the twisted loop algebra $L(\mathfrak{g},\sigma)$ of smooth $\sigma$-periodic maps from $\mathbb{R}$ to $\mathfrak{g}$ as well as of the ``smooth'' affine Kac-Moody algebra $\hat L(\mathfrak{g},\sigma)$, which is a $2$-dimensional extension of $L(\mathfrak{g},\sigma)$. It turns out that these automorphisms which either preserve or reverse the orientation of loops, and are correspondingly called to be of first and second kind, can be described essentially by curves of automorphisms of $\mathfrak{g}$. If the order of the automorphisms is finite, then the corresponding curves in $\mathrm{Aut}\mathfrak{g}$ allow us to define certain invariants and these turn out to parametrize the conjugacy classes of the automorphisms. If their order is $2$ the authors carry this out in detail and deduce a complete classification of involutions and real forms (which correspond to conjugate linear involutions) of smooth affine Kac-Moody algebras. The resulting classification can be seen as an extension of Cartan's classification of symmetric spaces, i.e. of involutions on $\mathfrak{g}$. If $\mathfrak{g}$ is compact, then conjugate linear extensions of involutions from $\hat L(\mathfrak{g},\sigma)$ to conjugate linear involutions on $\hat L(\mathfrak{g}_{\mathbb{C}},\sigma_{\mathbb{C}})$ yield a bijection between their conjugacy classes and this gives existence and uniqueness of Cartan decompositions of real forms of complex smooth affine Kac-Moody algebras. The authors show that their methods work equally well also in the algebraic case where the loops are assumed to have finite Fourier expansions.
Carbon Nanotube-Based Black Coatings

Coatings comprising carbon nanotubes are very black, that is, characterized by uniformly low reflectance over a broad range of wavelengths from the visible to far infrared. Arguably, there is no other material that is comparable. This is attributable to the intrinsic properties of graphitic material as well as the morphology (density, thickness, disorder, and tube size). We briefly describe a history of other coatings such as nickel phosphorous, gold black, and carbon-based paints and the comparable structural morphology that we associate with very black coatings. The need for black coatings is persistent for a variety of applications ranging from baffles and traps to blackbodies and thermal detectors. Applications for space-based instruments are of interest and we present a review of space qualification and the results of outgassing measurements. Questions of nanoparticle safety depend on the nanotube size and aspect ratio as well as the nature and route of exposure. We describe the growth of carbon nano...
Fast convergence of regularized learning in games

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at O(T-3/4), while the sum of utilities converges to an approximate optimum at O(T-1)-an improvement upon the worst case O(T-1/2) rates. We show a black-box reduction for any algorithm in the class to achieve O(T-1/2) rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of Rakhlin and Shridharan [17] and Daskalakis et al. [4], who only analyzed two-player zero-sum games for specific algorithms.
Nonlinear Muckenhoupt–Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations

Abstract A weighted norm inequality of Muckenhoupt–Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source term of arbitrary power law growth.
HP-GAN: Probabilistic 3D Human Motion Prediction via GAN

Predicting and understanding human motion dynamics has many applications, such as motion synthesis, augmented reality, security, and autonomous vehicles. Due to the recent success of generative adversarial networks (GAN), there has been much interest in probabilistic estimation and synthetic data generation using deep neural network architectures and learning algorithms. We propose a novel sequence-to-sequence model for probabilistic human motion prediction, trained with a modified version of improved Wasserstein generative adversarial networks (WGAN-GP), in which we use a custom loss function designed for human motion prediction. Our model, which we call HP-GAN, learns a probability density function of future human poses conditioned on previous poses. It predicts multiple sequences of possible future human poses, each from the same input sequence but a different vector z drawn from a random distribution. Furthermore, to quantify the quality of the non-deterministic predictions, we simultaneously train a motion-quality-assessment model that learns the probability that a given skeleton sequence is a real human motion. We test our algorithm on two of the largest skeleton datasets: NTURGB-D and Human3.6M. We train our model on both single and multiple action types. Its predictive power for long-term motion estimation is demonstrated by generating multiple plausible futures of more than 30 frames from just 10 frames of input. We show that most sequences generated from the same input have more than 50% probabilities of being judged as a real human sequence. We published all the code used in this paper to https://github.com/ebarsoum/hpgan.
Species trees from gene trees despite a high rate of lateral genetic transfer: a tight bound

Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes which can complicate the reconstruction problem due to the fact that different genes may undergo different evolutionary histories. This is the case in particular in the presence of lateral genetic transfer (LGT), whereby a gene is inherited from a distant species rather than an immediate ancestor. Such an event produces a gene tree which is distinct from (but related to) the species phylogeny. In previous work, a stochastic model of LGT was introduced and it was shown that the species phylogeny can be reconstructed from gene trees despite surprisingly high rates of LGT. Both lower and upper bounds on this rate were obtained, but a large gap remained. Here we close this gap, up to a constant. Specifically, we show that the species phylogeny can be reconstructed perfectly even when each edge of the tree has a constant probability of being the location of an LGT event. Our new reconstruction algorithm builds the tree recursively from the leaves. We also provide a matching bound in the negative direction (up to a constant).
Quantum ergodicity of Wigner induced spherical harmonics

We show that a Wigner induced random orthonormal basis of spherical harmonics is almost surely quantum ergodic. Here, a random basis is identified with an element of the product probability space of unitary groups, each endowed with the measure induced by the generalized Wigner ensemble. This yields a semi-classical realization of the probabilistic quantum unique ergodicity result for Wigner eigenvectors of Bourgade-Yau. At the same time, this generalizes a similar result due to Zelditch, who uses Haar measure on the unitary groups in defining the notion of a random basis.
Theoretical and Numerical Analysis of Approximate Dynamic Programming with Approximation Errors

This study is aimed at answering the question of how the approximation errors at each iteration of approximate dynamic programming affect the quality of the final results, considering the fact that errors at each iteration affect the next iteration. To this goal, convergence of value iteration scheme of approximate dynamic programming for deterministic nonlinear optimal control problems with discrete-time known dynamics subject to an undiscounted known cost functions is investigated while considering the errors existing in approximating respective functions. The boundedness of the results around the optimal solution is obtained based on quantities that are known in a general optimal control problem and assumptions that are verifiable. Moreover, because the presence of the approximation errors leads to the deviation of the results from optimality, sufficient conditions for stability of the system operated by the result obtained after a finite number of value iterations, along with an estimation of its regi...
Singular integral operators with kernels associated to negative powers of real-analytic functions

Abstract Given a real-analytic function b ( x ) defined on a neighborhood of the origin with b ( 0 ) = 0 , we consider local convolutions with kernels which are bounded by | b ( x ) | − a , where a > 0 is the smallest number for which | b ( x ) | − a is not integrable on any neighborhood of the origin. Under appropriate first derivative bounds and a cancellation condition, we prove L p boundedness theorems for such operators including when the kernel is not integrable. We primarily (but not exclusively) consider the p = 2 situation. The operators considered generalize both local versions of Riesz transforms and some local multiparameter singular integrals. Generalizations of our results to nontranslation-invariant versions as well as singular Radon transform versions are also proven.
Defending Against Saddle Point Attack in Byzantine-Robust Distributed Learning.

We study robust distributed learning that involves minimizing a non-convex loss function with saddle points. We consider the Byzantine setting where some worker machines have abnormal or even arbitrary and adversarial behavior. In this setting, the Byzantine machines may create fake local minima near a saddle point that is far away from any true local minimum, even when robust gradient estimators are used. We develop ByzantinePGD, a robust first-order algorithm that can provably escape saddle points and fake local minima, and converge to an approximate true local minimizer with low iteration complexity. As a by-product, we give a simpler algorithm and analysis for escaping saddle points in the usual non-Byzantine setting. We further discuss three robust gradient estimators that can be used in ByzantinePGD, including median, trimmed mean, and iterative filtering. We characterize their performance in concrete statistical settings, and argue for their near-optimality in low and high dimensional regimes.
Time-Delay Origins of Fundamental Tradeoffs Between Risk of Large Fluctuations and Network Connectivity

For the class of noisy time-delay linear consensus networks, we obtain explicit formulas for risk of large fluctuations of a scalar observable as a function of Laplacian eigenspectrum. It is shown that there is an intrinsic tradeoff between risk and effective resistance of the underlying coupling graph of the network. The main implication is that increasing network connectivity, increases the risk of large fluctuations. For vector-valued observables, we obtain computationally tractable lower and upper bounds for joint risk measures. Then, we study behavior of risk measures for networks with specific graph topologies and show how risk scales with the network size.
Licensed and Unlicensed Spectrum Allocation in Heterogeneous Networks

In future networks, an operator may employ a wide range of access points using diverse radio access technologies (RATs) over multiple licensed and unlicensed frequency bands. This paper studies centralized user association and spectrum allocation across many access points in such a heterogeneous network. Such centralized control is on a relatively slow timescale to allow information exchange and joint optimization over multiple cells. This is in contrast and complementary to distributed scheduling on a fast timescale. A queueing model is introduced to capture the lower spectral efficiency, reliability, and additional delays of data transmission over the unlicensed bands due to contention and/or listen-before-talk requirements. Two optimization-based spectrum allocation schemes are proposed along with efficient algorithms for computing the allocations. The proposed solutions take into account traffic loads, network topology, as well as external interference levels in the unlicensed bands. Packet-level simulation results show that the proposed schemes significantly outperform orthogonal and full-frequency-reuse allocations under all traffic conditions.
Equivariant quantum cohomology of the odd symplectic Grassmannian

The odd symplectic Grassmannian $$\mathrm {IG}:=\mathrm {IG}(k, 2n+1)$$ parametrizes k dimensional subspaces of $${\mathbb {C}}^{2n+1}$$ which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on $$\mathrm {IG}$$ with two orbits, and $$\mathrm {IG}$$ is itself a smooth Schubert variety in the submaximal isotropic Grassmannian $$\mathrm {IG}(k, 2n+2)$$ . We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of $$\mathrm {IG}$$ , i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case $$k=2$$ , and it gives an algorithm to calculate any multiplication in the equivariant quantum cohomology ring.
The Sharp Corner Formation in 2D Euler Dynamics of Patches: Infinite Double Exponential Rate of Merging

For the 2D Euler dynamics of patches, we investigate the convergence to the singular stationary solution in the presence of a regular strain. It is proved that the rate of merging can be double exponential infinitely in time and the estimates we obtain are sharp.
Ten Steps of EM Suffice for Mixtures of Two Gaussians

Presented on March 6, 2017 at 11:00 a.m. in the Klaus Advanced Computing Building, Room 1116E.
Flexible Market for Smart Grid: Coordinated Trading of Contingent Contracts

A coordinated trading process is proposed as a design for an electricity market with significant uncertainty, perhaps from renewables. In this process, groups of agents propose to the system operator (SO) a contingent trade that is balanced, that is, the sum of demand bids and the sum of supply bids are equal. The SO accepts the proposed trade if no network constraint is violated or curtails it until no violation occurs. Each proposed trade is accepted or curtailed as it is presented. The SO also provides guidance to help future proposed trades meet network constraints. The SO does not set prices, and there is no requirement that different trades occur simultaneously or clear at uniform prices. Indeed, there is no price-setting mechanism. However, if participants exploit opportunities for gain, the trading process will lead to an efficient allocation of energy and to the discovery of locational marginal prices. The great flexibility in the proposed trading process and the low communication and control burden on the SO may make the process suitable for coordinating producers and consumers in the distribution system.
GIT-equivalence and semi-stable subcategories of quiver representations

Abstract In this paper, we answer the question of when the subcategory of semi-stable representations is the same for two rational vectors for an acyclic quiver. This question has been previously answered by Ingalls, Paquette, and Thomas in the tame case in [14] . Here we take a more invariant theoretic approach , to answer this question in general. We recover the known result in the tame case.
Primitively generated Hopf orders in characteristic p

ABSTRACTLet R be a characteristic p discrete valuation ring with field of fractions K. Let H be a commutative, cocommutative K-Hopf algebra of p-power rank which is generated as a K-algebra by primitive elements. We construct all of the R-Hopf orders of H in K; each Hopf order corresponds to a solution to a single matrix equation. For R complete, we greatly simplify the matrix equation and give explicit examples of Hopf orders in some rank p2 K-Hopf algebras.
On the time for Brownian motion to visit every point on a circle

Abstract Consider a Wiener process W on a circle of circumference L . We prove the rather surprising result that the Laplace transform of the distribution of the first time, θ L , when the Wiener process has visited every point of the circle can be solved in closed form using a continuous recurrence approach.
Proton-induced cross sections relevant to production of 225Ac and 223Ra in natural thorium targets below 200 MeV.

Abstract Cross sections for 223,225Ra, 225Ac and 227Th production by the proton bombardment of natural thorium targets were measured at proton energies below 200 MeV. Our measurements are in good agreement with previously published data and offer a complete excitation function for 223,225Ra in the energy range above 90 MeV. Comparison of theoretical predictions with the experimental data shows reasonable-to-good agreement. Results indicate that accelerator-based production of 225Ac and 223Ra below 200 MeV is a viable production method.
Zero-Shot Deep Domain Adaptation

Domain adaptation is an important tool to transfer knowledge about a task (e.g. classification) learned in a source domain to a second, or target domain. Current approaches assume that task-relevant target-domain data is available during training. We demonstrate how to perform domain adaptation when no such task-relevant target-domain data is available. To tackle this issue, we propose zero-shot deep domain adaptation (ZDDA), which uses privileged information from task-irrelevant dual-domain pairs. ZDDA learns a source-domain representation which is not only tailored for the task of interest but also close to the target-domain representation. Therefore, the source-domain task of interest solution (e.g. a classifier for classification tasks) which is jointly trained with the source-domain representation can be applicable to both the source and target representations. Using the MNIST, Fashion-MNIST, NIST, EMNIST, and SUN RGB-D datasets, we show that ZDDA can perform domain adaptation in classification tasks without access to task-relevant target-domain training data. We also extend ZDDA to perform sensor fusion in the SUN RGB-D scene classification task by simulating task-relevant target-domain representations with task-relevant source-domain data. To the best of our knowledge, ZDDA is the first domain adaptation and sensor fusion method which requires no task-relevant target-domain data. The underlying principle is not particular to computer vision data, but should be extensible to other domains.
Distributed Strategies for Generating Weight-Balanced and Doubly Stochastic Digraphs

This paper deals with the design and analysis of dynamical systems on directed graphs (digraphs) that achieve weight-balanced and doubly stochastic assignments. Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of coordination problems, including formation control, agreement, and distributed optimization. We refer to a digraph as doubly stochasticable (weight-balanceable) if it admits a doubly stochastic (weight-balanced) adjacency matrix. This paper studies the characterization of both classes of digraphs, and introduces distributed dynamical systems to compute the appropriate set of weights in each case. It is known that semiconnectedness is a necessary and sufficient condition for a digraph to be weight-balanceable. The first main contribution is a characterization of doubly-stochasticable digraphs. As a by-product, we unveil the connection of this class of digraphs with weight-balanceable digraphs. The second main contribution is the synthesis of a distributed strategy running synchronously on a directed communication network that allows individual agents to balance their in- and out-degrees. We show that a variation of our distributed procedure over the mirror graph has a much smaller time complexity than the currently available centralized algorithm based on the computation of the graph cycles. The final main contribution is the design of two cooperative strategies for finding a doubly stochastic weight assignment. One algorithm works under the assumption that individual agents are allowed to add self-loops. For the case when this assumption does not hold, we introduce an algorithm distributed over the mirror digraph which allows the agents to compute a doubly stochastic weight assignment if the digraph is doubly stochasticable and announce otherwise if it is not. Various examples illustrate the results.
Generalized Fisher score for feature selection

Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.
Learning a Multi-View Stereo Machine

We present a learnt system for multi-view stereopsis. In contrast to recent learning based methods for 3D reconstruction, we leverage the underlying 3D geometry of the problem through feature projection and unprojection along viewing rays. By formulating these operations in a differentiable manner, we are able to learn the system end-to-end for the task of metric 3D reconstruction. End-to-end learning allows us to jointly reason about shape priors while conforming to geometric constraints, enabling reconstruction from much fewer images (even a single image) than required by classical approaches as well as completion of unseen surfaces. We thoroughly evaluate our approach on the ShapeNet dataset and demonstrate the benefits over classical approaches and recent learning based methods.
Estimation of the Szlenk index of Banach spaces via Schreier spaces

For each ordinal $\alpha<\omega_1$, we prove the existence of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of spaces with Szlenk index not exceeding $\omega^\alpha$. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates.
The Apollonian structure of integer superharmonic matrices

We prove that the set of quadratic growths attainable by integer-valued superharmonic functions on the lattice $\mathbb{Z}^2$ has the structure of an Apollonian circle packing. This completely characterizes the PDE which determines the continuum scaling limit of the Abelian sandpile on the lattice $\mathbb{Z}^2$.
An Instability in Variational Inference for Topic Models

Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instance each item in a collection of scientific articles) is regarded as a convex combination of a small number of vectors corresponding to `topics' or `components'. The weights are assumed to have a Dirichlet prior distribution. The standard approach towards approximating the posterior is to use variational inference algorithms, and in particular a mean field approximation. We show that this approach suffers from an instability that can produce misleading conclusions. Namely, for certain regimes of the model parameters, variational inference outputs a non-trivial decomposition into topics. However --for the same parameter values-- the data contain no actual information about the true decomposition, and hence the output of the algorithm is uncorrelated with the true topic decomposition. Among other consequences, the estimated posterior mean is significantly wrong, and estimated Bayesian credible regions do not achieve the nominal coverage. We discuss how this instability is remedied by more accurate mean field approximations.
A Fast Parameterized Algorithm for Co-Path Set

The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time, randomized fpt algorithm with complexity O^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where tw(G) denotes treewidth. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.
Level raising mod 2 and arbitrary 2-Selmer ranks

We prove a level raising mod theorem for elliptic curves over . It generalizes theorems of Ribet and Diamond–Taylor and also explains different sign phenomena compared to odd . We use it to study the 2-Selmer groups of modular abelian varieties with common mod 2 Galois representation. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families.
Calculating Power by Bootstrap, with an Application to Cluster-Randomized Trials.

Background: A key requirement for a useful power calculation is that the calculation mimic the data analysis that will be performed on the actual data, once it is observed. Close approximations may be difficult to achieve using analytic solutions, however, and thus Monte Carlo approaches, including both simulation and bootstrap resampling, are often attractive. One setting in which this is particularly true is cluster-randomized trial designs. However, Monte Carlo approaches are useful in many additional settings as well. Calculating power for cluster-randomized trials using analytic or simulation-based methods is frequently unsatisfactory due to the complexity of the data analysis methods to be employed and to the sparseness of data to inform the choice of important parameters in these methods. Methods: We propose that among Monte Carlo methods, bootstrap approaches are most likely to generate data similar to the observed data. In bootstrap approaches, real data are re-sampled to build complete data sets based on real data that resemble the data for the intended analyses. In contrast, simulation methods would use the real data to estimate parameters for the data and then simulate data using these parameters. Means of implementing bootstrap power calculation are described. Results: We demonstrate bootstrap power calculation for a cluster-randomized trial with a censored survival outcome and a baseline observation period. Conclusions: Bootstrap power calculation is a natural application of resampling methods. It provides a relatively simple solution to power calculation that is likely to be more accurate than analytic solutions or simulation-based calculations, in the sense that the bootstrap approach does not rely on the assumptions inherent in analytic calculations. It has several important strengths. Notably, it is simple to achieve great fidelity to the proposed data analysis method and there is no requirement for parameter estimates, or estimates of their variability, from outside settings. So, for example, for cluster-randomized trials, power calculations need not depend on intracluster correlation coefficient estimates from outside studies. In contrast, bootstrap power calculation requires initial data resembling data to be used in the planned study. We are not aware of bootstrap power calculation being previously proposed or explored for cluster-randomized trials, but it can also be applied for other study designs. We show with a simulation study that bootstrap power calculation can replicate analytic power in cases where analytic power can be accurately calculated. We also demonstrate power calculations for correlated censored survival outcomes in a cluster randomized trial setting, for which we are unaware of an analytic alternative. The method can easily be used when preliminary data is available, as is likely to be the case when research is performed in health delivery systems or other settings where electronic medical records can be obtained.
Support and adic finiteness for complexes

Let X be a chain complex over a commutative noetherian ring R, that is, an object in the derived category &#x1d49f;(R). We investigate the small support and co-support of X, introduced by Foxby and Benson,...
Verification of Turbulence Models for Flow in a Constricted Pipe at Low Reynolds Number

Computational fluid dynamics (CFD) is a useful tool for prediction of turbulence in aerodynamic and biomedical applications. The choice of appropriate turbulence models is key to reaching accurate predictions. The present investigation concentrated on the comparison of different turbulence models for predicting the flow field downstream of a constricted pipe. This geometry is relevant to arterial stenosis in patients with vascular diseases. More specifically, the results of Unsteady Reynolds-Averaged Navier-Stokes (URANS) and scale resolving simulation (SRS) turbulence models such as Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) were compared with experimental measurements. Comparisons included the mean flow and fluctuations downstream of the constriction. Results showed that the LES model was in better agreement with the velocity measurements performed using a Laser Doppler Anemometry (LDA). In addition, although URANS models predicted a wake region size and mean flow velocities comparable to SRS turbulence models, no small-scale vortical structures can be observed in the URANS solution due to the nature of these models. Modeling of these structures would, however, be helpful when more detailed flow behavior is needed such as in studies of acoustic sources. Hence, LES would be an optimal turbulence model for the flow under consideration, especially when sound generation would be of interest.
Theoretical Bounds and Constructions of Codes in the Generalized Cayley Metric

Permutation codes have recently garnered substantial research interest due to their potential in various applications, including cloud storage systems, genome resequencing, and flash memories. In this paper, we study the theoretical bounds and constructions of permutation codes in the generalized Cayley metric. The generalized Cayley metric captures the number of generalized transposition errors in a permutation and subsumes previously studied error types, including transpositions and translocations, without imposing restrictions on the lengths and positions of the translocated segments. Based on the so-called breakpoint analysis method proposed by Chee and Vu, we first present a coding framework that leads to order-optimal constructions, thus improving upon the existing constructions that are not order-optimal. We then use this framework to also develop an order-optimal coding scheme that is additionally explicit and systematic.
Fukaya categories and bordered Heegaard- Floer homology

We outline an interpretation of Heegaard-Floer homology of 3-manifolds (closed or with boundary) in terms of the symplectic topology of symmetric products of Riemann surfaces, as suggested by recent work of Tim Perutz and Yanko Lekili. In particular we discuss the connection between the Fukaya category of the symmetric prod- uct and the bordered algebra introduced by Robert Lipshitz, Peter Ozsvath and Dylan Thurston, and recast bordered Heegaard-Floer homology in this language. Mathematics Subject Classification (2000). 53D40 (57M27, 57R58)
A remark about supramenability and the Macaev norm

We show that a finitely generated group G which satisfies a certain condition with respect to the Macaev norm is supramenable. The condition is equivalent to the existence of quasicentral approximate unit with respect to the Macaev norm relative to the left regular representation of the group and has been studied by the author in connection with perturbation questions for Hilbert space operators. The condition can be also viewed as an analogue with respect to the Macaev norm of Yamasaki parabolicity. We also show that existence of quasicentral approximate units relative to the Macaev norm for n-tuples of operators is not preserved when taking tensor products.
Performance of optimal data shaping codes

Data shaping is a coding technique that has been proposed to increase the lifetime of flash memory devices. Several data shaping codes have been described in recent work, including endurance codes [2] and direct shaping codes for structured data [8], [4], [5]. In this paper, we study information-theoretic properties of a general class of data shaping codes and prove a separation theorem stating that optimal data shaping can be achieved by the concatenation of optimal lossless compression with optimal endurance coding. We also determine the expansion factor that minimizes the total wear cost. Finally, we analyze the performance of direct shaping codes and establish a condition for their optimality.
Elastic metasurfaces for splitting SV- and P-waves in elastic solids

Although recent advances have made it possible to manipulate electromagnetic and acoustic wavefronts with sub-wavelength metasurface slabs, the design of elastodynamic counterparts remains challenging. We introduce a novel but simple design approach to control SV-waves in elastic solids. The proposed metasurface can be fabricated by cutting an array of aligned parallel cracks in a solid such that the materials between the cracks act as plate-like waveguides in the background medium. The plate array is capable of modulating the phase change of SV-wave while keeping the phase of P-wave unchanged. An analytical model for SV-wave incidence is established to calculate the transmission coefficient and the transmitted phase through the plate-like waveguide explicitly. A complete 2π range of phase delay is achieved by selecting different thicknesses for the plates. An elastic metasurface for splitting SV- and P-waves is designed and demonstrated using full wave finite element simulations. Two metasurfaces for focusing plane and cylindrical SV-waves are also presented.
Testing Identity of Multidimensional Histograms

We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \rightarrow \mathbb{R}_+$, where $D \subseteq \mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the domain into $k$ axis-aligned rectangles such that $p$ is constant within each such rectangle. Histograms are one of the most fundamental nonparametric families of distributions and have been extensively studied in computer science and statistics. We give the first identity tester for this problem with {\em sub-learning} sample complexity in any fixed dimension and a nearly-matching sample complexity lower bound. In more detail, let $q$ be an unknown $d$-dimensional $k$-histogram distribution in fixed dimension $d$, and $p$ be an explicitly given $d$-dimensional $k$-histogram. We want to correctly distinguish, with probability at least $2/3$, between the case that $p = q$ versus $\|p-q\|_1 \geq \epsilon$. We design an algorithm for this hypothesis testing problem with sample complexity $O((\sqrt{k}/\epsilon^2) 2^{d/2} \log^{2.5 d}(k/\epsilon))$ that runs in sample-polynomial time. Our algorithm is robust to model misspecification, i.e., succeeds even if $q$ is only promised to be {\em close} to a $k$-histogram. Moreover, for $k = 2^{\Omega(d)}$, we show a sample complexity lower bound of $(\sqrt{k}/\epsilon^2) \cdot \Omega(\log(k)/d)^{d-1}$ when $d\geq 2$. That is, for any fixed dimension $d$, our upper and lower bounds are nearly matching. Prior to our work, the sample complexity of the $d=1$ case was well-understood, but no algorithm with sub-learning sample complexity was known, even for $d=2$. Our new upper and lower bounds have interesting conceptual implications regarding the relation between learning and testing in this setting.
Computational Limitations in Robust Classification and Win-Win Results.

We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust classifier exists, in the small-perturbation regime; (b) a non-robust classifier can be learned efficiently; but (c) it is computationally hard to learn a robust classifier, assuming the hardness of factoring large numbers. The question of whether a robust classifier for their task exists in the large perturbation regime seems related to important open questions in computational number theory. In this work, we extend their work in three directions. First, we demonstrate classification tasks where computationally efficient robust classification is impossible, even when computationally unbounded robust classifiers exist. For this, we rely on the existence of average-case hard functions. Second, we show hard-to-robustly-learn classification tasks in the large-perturbation regime. Namely, we show that even though an efficient classifier that is robust to large perturbations exists, it is computationally hard to learn any non-trivial robust classifier. Our first construction relies on the existence of one-way functions, and the second on the hardness of the learning parity with noise problem. In the latter setting, not only does a non-robust classifier exist, but also an efficient algorithm that generates fresh new labeled samples given access to polynomially many training examples (termed as generation by Kearns et. al. (1994)). Third, we show that any such counterexample implies the existence of cryptographic primitives such as one-way functions. This leads us to a win-win scenario: either we can learn an efficient robust classifier, or we can construct new instances of cryptographic primitives.
MicroED with the Falcon III direct electron detector

Microcrystal electron diffraction (MicroED) combines crystallography and electron cryo-microscopy (cryo-EM) into a method that is applicable to high-resolution structure determination. In MicroED, nanosized crystals, which are often intractable using other techniques, are probed by high-energy electrons in a transmission electron microscope. Diffraction data are recorded by a camera in movie mode: the nanocrystal is continuously rotated in the beam, thus creating a sequence of frames that constitute a movie with respect to the rotation angle. Until now, diffraction-optimized cameras have mostly been used for MicroED. Here, the use of a direct electron detector that was designed for imaging is reported. It is demonstrated that data can be collected more rapidly using the Falcon III for MicroED and with markedly lower exposure than has previously been reported. The Falcon III was operated at 40 frames per second and complete data sets reaching atomic resolution were recorded in minutes. The resulting density maps to 2.1 A resolution of the serine protease proteinase K showed no visible signs of radiation damage. It is thus demonstrated that dedicated diffraction-optimized detectors are not required for MicroED, as shown by the fact that the very same cameras that are used for imaging applications in electron microscopy, such as single-particle cryo-EM, can also be used effectively for diffraction measurements.
Attenuated Amiloride-Sensitive Current and Augmented Calcium-Activated Chloride Current in Marsh Rice Rat (Oryzomys palustris) Airways

Prolonged heat and sea salt aerosols pose a challenge for the mammalian airway, placing the protective airway surface liquid (ASL) at risk for desiccation. Thus, mammals inhabiting salt marshes might have acquired adaptations for ASL regulation. We studied the airways of the rice rat, a rodent that inhabits salt marshes. We discovered negligible Na+ transport through the epithelial sodium channel (ENaC). In contrast, carbachol induced a large Cl- secretory current that was blocked by the calcium-activated chloride channel (CaCC) inhibitor CaCCinhi-A01. Decreased mRNA expression of α, β, and γ ENaC, and increased mRNA expression of the CaCC transmembrane member 16A, distinguished the rice rat airway. Rice rat airway cultures also secreted fluid in response to carbachol and displayed an exaggerated expansion of the ASL volume when challenged with 3.5% NaCl. These data suggest that the rice rat airway might possess unique ion transport adaptations to facilitate survival in the salt marsh environment.