cssi/SciSciGPT-SciSciNet huggingface dataset:
Symmetric Disclosure: a Fresh Look at k-anonymity

We analyze how the sparsity of a typical aggregate social relation impacts the network overhead of online communication systems designed to provide k-anonymity. Once users are grouped in anonymity sets there will likely be few related pairs of users between any two particular sets, and so the sets need to be large in order to provide cover traffic between them. We can reduce the associated overhead by having both parties in a communication specify both the origin and the target sets of the communication. We propose to call this communication primitive “symmetric disclosure.” If in order to retrieve messages a user specifies a group from which he expects to receive them, the negative impact of the sparsity is offset.
Track and Transfer: Watching Videos to Simulate Strong Human Supervision for Weakly-Supervised Object Detection

The status quo approach to training object detectors requires expensive bounding box annotations. Our framework takes a markedly different direction: we transfer tracked object boxes from weakly-labeled videos to weakly-labeled images to automatically generate pseudo ground-truth boxes, which replace manually annotated bounding boxes. We first mine discriminative regions in the weakly-labeled image collection that frequently/rarely appear in the positive/ negative images. We then match those regions to videos and retrieve the corresponding tracked object boxes. Finally, we design a hough transform algorithm to vote for the best box to serve as the pseudo GT for each image, and use them to train an object detector. Together, these lead to state-of-the-art weakly-supervised detection results on the PASCAL 2007 and 2010 datasets.
Grid diagrams and the Ozsváth-Szabó tau-invariant

We use grid diagrams to investigate the Ozsvath-Szabo concordance invariant tau, and to prove that |tau(K_1)-tau(K_2)|<=g, whenever there is a genus g knot cobordism joining K_1 to K_2. This leads to an entirely grid diagram-based proof of Kronheimer-Mrowka's theorem, formerly known as the Milnor conjecture.
Étale homological stability and arithmetic statistics

We contribute to the arithmetic/topology dictionary by relating asymptotic point counts and arithmetic statistics over finite fields to homological stability and representation stability over $\Cb$ in the example of configuration spaces of $n$ points in smooth varieties. To do this, we import the method of homological stability from the realm of topology into the theory of etale cohomology; in particular we give the first examples of stability of etale cohomology groups as Galois representations where the Galois actions are not already explicitly known. We then establish subexponential bounds on the growth of the unstable cohomology, and we apply this and etale homological stability to compute the large $n$ limits of various arithmetic statistics of configuration spaces of varieties over $\F_q$.
Network Estimation From Point Process Data

Consider observing a collection of discrete events within a network that reflect how network nodes influence one another. Such data are common in spike trains recorded from biological neural networks, interactions within a social network, and a variety of other settings. Data of this form may be modeled as self-exciting point processes, in which the likelihood of future events depends on the past events. This paper addresses the problem of estimating self-excitation parameters and inferring the underlying functional network structure from self-exciting point process data. Past work in this area was limited by strong assumptions which are addressed by the novel approach here. Specifically, in this paper we 1) incorporate saturation in a point process model which both ensures stability and models non-linear thresholding effects; 2) impose general low-dimensional structural assumptions that include sparsity, group sparsity, and low-rankness that allows bounds to be developed in the high-dimensional setting; and 3) incorporate long-range memory effects through moving average and higher-order auto-regressive components. Using our general framework, we provide a number of novel theoretical guarantees for high-dimensional self-exciting point processes that reflect the role played by the underlying network structure and long-term memory. We also provide simulations and real data examples to support our methodology and main results.
Free-Space Optical Communication for Spacecraft and Satellites, Including CubeSats in Low Earth Orbit (LEO)

A static system is described, and computed results for it are shown for laser beam transmissions from a Cubstat in low Earth orbit. This system can replace current architectures which use dynamical systems (moving parts).
Good degeneration of Quot-schemes and coherent systems

We construct good degenerations of Quot-schemes and coherent systems using the stack of expanded degenerations. We show that these good degenerations are separated and proper DM stacks of finite type. Applying to the projective threefolds, we derive degeneration formulas for DT-invariants of ideal sheaves and PT stable pair invariants.
A Pyramid CNN for Dense-Leaves Segmentation

Automatic detection and segmentation of overlapping leaves in dense foliage can be a difficult task, particularly for leaves with strong textures and high occlusions. We present Dense-Leaves, an image dataset with ground truth segmentation labels that can be used to train and quantify algorithms for leaf segmentation in the wild. We also propose a pyramid convolutional neural network with multi-scale predictions that detects and discriminates leaf boundaries from interior textures. Using these detected boundaries, closed-contour boundaries around individual leaves are estimated with a watershed-based algorithm. The result is an instance segmenter for dense leaves. Promising segmentation results for leaves in dense foliage are obtained.
Computing conjugating sets and automorphism groups of rational functions

Abstract Let ϕ and ψ be endomorphisms of the projective line of degree at least 2, defined over a field F. From a dynamical perspective, a significant question is to determine whether ϕ and ψ are conjugate (or to answer the related question of whether a given rational function ϕ has a nontrivial automorphism). We construct efficient algorithms for computing the set of conjugating maps (resp., the group of automorphisms), with an emphasis on the case where F is a finite field or a number field. Each of our algorithms takes advantage of different dynamical structures, so context (e.g., field of definition and degree of the map) determines the preferred algorithm.
Chaotic dynamics of the Chaplygin sleigh with a passive internal rotor

The Chaplygin sleigh is a classic example of a nonholonomically constrained mechanical system. The sleigh’s motion always converges to a straight line whose slope is entirely determined by the initial configuration and velocity of the sleigh. We consider the motion of a modified Chaplygin sleigh that contains a passive internal rotor. We show that the presence of even a rotor with small inertia modifies the motion of the sleigh dramatically. A generic trajectory of the sleigh in a reduced velocity space exhibits two distinct transient phases before converging to a chaotic attractor. We demonstrate this through numerics. In recent work the dynamics of the Chaplygin sleigh have also been shown to be similar to that of a fish-like body in an inviscid fluid. The influence of a passive degree of freedom on the motion of the Chaplygin sleigh points to several possible applications in controlling the motion of the nonholonomically constrained terrestrial and aquatic robots.
Order three normalizers of 2-groups

ABSTRACTThis paper examines order three elements of finite groups which normalize no nontrivial 2-subgroup. The motivation for finding such elements arises out of a problem in modular representation theory. The question of when these elements appear in the almost simple groups was posed by Robinson in the context of studying 2-blocks of defect zero. For the almost simple groups, a complete classification of order three elements with this property is determined. On the basis of this result, necessary conditions are then given for the existence of such elements in a large class of finite groups.
Primitive geodesic lengths and (almost) arithmetic progressions

In this article we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every noncompact, locally symmetric, arithmetic manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also suggest an approach to a well known spectral rigidity problem based on the scarcity of manifolds with arithmetic progressions.
Regression-assisted inference for the average treatment effect in paired experiments

SummaryIn paired randomized experiments, individuals in a given matched pair may differ on prognostically important covariates despite the best efforts of practitioners. We examine the use of regression adjustment to correct for persistent covariate imbalances after randomization, and present two regression-assisted estimators for the sample average treatment effect in paired experiments. Using the potential outcomes framework, we prove that these estimators are consistent for the sample average treatment effect under mild regularity conditions even if the regression model is improperly specified, and describe how asymptotically conservative confidence intervals can be constructed. We demonstrate that the variances of the regression-assisted estimators are no larger than that of the standard difference-in-means estimator asymptotically, and illustrate the proposed methods by simulation. The analysis does not require a superpopulation model, a constant treatment effect, or the truth of the regression model, and hence provides inference for the sample average treatment effect with the potential to increase power without unrealistic assumptions.
Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot.

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines fidelity loss in spin transport from multiple perspectives. We first study incoherent fidelity loss due to hyperfine and spin-orbit interaction. We calculate fidelity loss due to the random Overhauser field from hyperfine interaction, and spin relaxation rate due to spin-orbit interaction in a wide range of experimental parameters with a focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We then analyze systematic errors due to non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-Stuckelberg interference to achieve high-fidelity spin transport at a higher speed. At last, we study another systematic error caused by the correction to the electron g-factor from the double dot potential, which can lead to a notable phase error. In all, our results should provide a useful guidance for future experiments on coherent electron spin transport.
Bohr inequalities for free holomorphic functions on polyballs

Abstract Multivariable operator theory is used to provide Bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball B n , n = ( n 1 , … , n k ) ∈ N k , which is a noncommutative analogue of the scalar polyball ( C n 1 ) 1 × ⋯ × ( C n k ) 1 . The Bohr radius K m h ( B n ) (resp. K h ( B n ) ) associated with the multi-homogeneous (resp. homogeneous) power series expansions of the free holomorphic functions are the main objects of study in this paper. We extend a theorem of Bombieri and Bourgain for the disc D : = { z ∈ C : | z | 1 } to the polyball, and obtain the estimations 1 3 k K m h ( B n ) 2 log ⁡ k k if k > 1 , extending Boas-Khavinson result for the scalar polydisc D k . With respect to the homogeneous power series expansion, we prove that K h ( B n ) = 1 / 3 , extending the classical result, and obtain analogues of Caratheodory, Fejer, and Egervary-Szasz inequalities for free holomorphic functions with operator coefficients and positive real parts on the polyball. These results are used to provide multivariable analogues of Landau's inequality and Bohr's inequality when the norm is replaced by the numerical radius of an operator. When specialized to the regular polydisc D k (which corresponds to the case n 1 = ⋯ = n k = 1 ), we obtain new results concerning Bohr, Landau, Fejer, and Harnack inequalities for operator-valued holomorphic functions and k-pluriharmonic functions on the scalar polydisc D k . The results of the paper can be used to obtain Bohr type inequalities for the noncommutative ball algebra A n , the Hardy algebra F n ∞ , and the C ⁎ -algebra C ⁎ ( S ) , generated by the universal model S of the polyball B n .
Paneitz operator for metrics near $$S^{3}$$

We derive the first and second variation formula for the Green’s function pole’s value of Paneitz operator on the standard three sphere. In particular it is shown that the first variation vanishes and the second variation is nonpositively definite. Moreover, the second variation vanishes only at the direction of conformal deformation. We also introduce a new invariant of the Paneitz operator and illustrate its close relation with the second eigenvalue and Sobolev inequality of Paneitz operator.
Testing against a linear regression model using ideas from shape‐restricted estimation

Summary A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large dimensional, non-parametric double-cone alternative. For example, the test against a constant function uses the alternative of increasing or decreasing regression functions, and the test against a linear function uses the convex or concave alternative. The test proposed is exact and unbiased and the critical value is easily computed. The power of the test increases to 1 as the sample size increases, under very mild assumptions—even when the alternative is misspecified, i.e. the power of the test converges to 1 for any true regression function that deviates (in a non-degenerate way) from the parametric null hypothesis. We also formulate tests for the linear versus partial linear model and consider the special case of the additive model. Simulations show that our procedure behaves well consistently when compared with other methods. Although the alternative fit is non-parametric, no tuning parameters are involved. Supplementary materials with proofs and technical details are available on line.
A game-theoretic formulation of the homogeneous self-reconfiguration problem

In this paper we formulate the homogeneous two- and three-dimensional self-reconfiguration problem over discrete grids as a constrained potential game. We develop a game-theoretic learning algorithm based on the Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a globally optimal fashion. Both a centralized and a fully decentralized algorithm are presented and we show that the only stochastically stable state is the potential function maximizer, i.e. the desired target configuration. These algorithms compute transition probabilities in such a way that even though each agent acts in a self-interested way, the overall collective goal of self-reconfiguration is achieved. Simulation results confirm the feasibility of our approach and show convergence to desired target configurations.
Detecting clusters of anomalies on low-dimensional feature subsets with application to network traffic flow data

In a variety of applications, one desires to detect groups of anomalous data samples, with a group potentially manifesting its atypicality (relative to a reference model) on a low-dimensional subset of the full measured set of features. Samples may only be weakly atypical individually, whereas they may be strongly atypical when considered jointly. What makes this group anomaly detection problem quite challenging is that it is a priori unknown which subset of features jointly manifests a particular group of anomalies. Moreover, it is unknown how many anomalous groups are present in a given data batch. In this work, we develop a group anomaly detection (GAD) scheme to identify subsets of samples and subsets of features that jointly specify anomalous clusters. We apply our approach to network intrusion detection to detect botnet and peer-to-peer flow clusters. Unlike previous studies, our approach captures and exploits statistical dependencies that may exist between the measured features. Experiments on real world network traffic data demonstrate the advantage of our proposed system, and highlight the importance of exploiting feature dependency structure, compared to the feature (or test) independence assumption made in previous studies.
Equidistribution of sparse sequences on nilmanifolds

We study equidistribution properties of nil-orbits (b n x)n∈ℕ when the parameter n is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if X = G/Γ is a nilmanifold, b ∈ G is an ergodic nilrotation, and c ∈ ℝ \ ℤ is positive, then the sequence $$ (b^{[n^c ]} x)_{n \in \mathbb{N}} $$ is equidistributed in X for every x ∈ X. This is also the case when n c is replaced with a(n), where a(t) is a function that belongs to some Hardy field, has polynomial growth, and stays logarithmically away from polynomials, and when it is replaced with a random sequence of integers with sub-exponential growth. Similar results have been established by Boshernitzan when X is the circle.
Adversarial Image Registration with Application for MR and TRUS Image Fusion

Robust and accurate alignment of multimodal medical images is a very challenging task, which however is very useful for many clinical applications. For example, magnetic resonance (MR) and transrectal ultrasound (TRUS) image registration is a critical component in MR-TRUS fusion guided prostate interventions. However, due to the huge difference between the image appearances and the large variation in image correspondence, MR-TRUS image registration is a very challenging problem. In this paper, an adversarial image registration (AIR) framework is proposed. By training two deep neural networks simultaneously, one being a generator and the other being a discriminator, we can obtain not only a network for image registration, but also a metric network which can help evaluate the quality of image registration. The developed AIR-net is then evaluated using clinical datasets acquired through image-fusion guided prostate biopsy procedures and promising results are demonstrated.
Optimal multi-object segmentation with novel gradient vector flow based shape priors

Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing self-intersection or mesh folding. Those problems require complex and expensive algorithms to mitigate. In this paper, we propose a novel shape prior directly embedded in the voxel grid space, based on gradient vector flows of a pre-segmentation. The flexible and powerful prior shape representation is ready to be extended to simultaneously segmenting multiple interacting objects with minimum separation distance constraint. The segmentation problem of multiple interacting objects with shape priors is formulated as a Markov Random Field problem, which seeks to optimize the label assignment (objects or background) for each voxel while keeping the label consistency between the neighboring voxels. The optimization problem can be efficiently solved with a single minimum s-t cut in an appropriately constructed graph. The proposed algorithm has been validated on two multi-object segmentation applications: the brain tissue segmentation in MRI images and the bladder/prostate segmentation in CT images. Both sets of experiments showed superior or competitive performance of the proposed method to the compared state-of-the-art methods.
Algorithms for structured matrix-vector product of optimal bilinear complexity

We present explicit algorithms for computing structured matrix-vector products that are optimal in the sense of Strassen, i.e., using a provably minimum number of multiplications. These structures include Toeplitz/Hankel/circulant, symmetric, Toeplitz-plus-Hankel, sparse, and multilevel structures. The last category include BTTB, BHHB, BCCB but also any arbitrarily complicated nested structures built out of other structures.
Gibbs measures and phase transitions on sparse random graphs

Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. We review this approach and provide some results towards a rigorous treatment of these problems.
Resilient Distributed Estimation: Sensor Attacks

This paper studies multiagent distributed estimation under sensor attacks. Individual agents make sensor measurements of an unknown parameter belonging to a compact set, and, at every time step, a fraction of the agents’ sensor measurements may fall under attack and take arbitrary values. We present the saturated innovation update ( $\mathcal{SIU}$ ) algorithm for distributed estimation resilient to sensor attacks. Under the iterative $\mathcal{SIU}$ algorithm, if less than one half of the agent sensors fall under attack, then, all of the agents’ estimates converge at a polynomial rate (with respect to the number of iterations) to the true parameter. The resilience of $\mathcal{SIU}$ to sensor attacks does not depend on the topology of the interagent communication network, as long as it remains connected. We demonstrate the performance of $\mathcal{SIU}$ with numerical examples.
Characteristics of On-time and Late Reward Delivery Projects

The crowdfunding market size has increased exponentially, reaching tens of billions of dollars and showing the popularity of crowdfunding. However, according to Kickstarter, 35% backers did not receive rewards on time. To maintain the trust between creators and backers, and sustain the crowdfunding business growth, it is crucial to understand how on-time and late reward delivery projects are different. In this paper, we analyze characteristics of on-time and late reward delivery projects, especially, focusing on project descriptions, creator profiles, and activeness and linguistic patterns of creators and backers. Our analysis reveals that the less complicated a project is and more actively a creator responds to backers, the higher an on-time reward delivery probability is. It shows there are significant differences between on-time and late reward delivery projects.
Active Testing: An Efficient and Robust Framework for Estimating Accuracy

Much recent work on visual recognition aims to scale up learning to massive, noisily-annotated datasets. We address the problem of scaling- up the evaluation of such models to large-scale datasets with noisy labels. Current protocols for doing so require a human user to either vet (re-annotate) a small fraction of the test set and ignore the rest, or else correct errors in annotation as they are found through manual inspection of results. In this work, we re-formulate the problem as one of active testing, and examine strategies for efficiently querying a user so as to obtain an accu- rate performance estimate with minimal vetting. We demonstrate the effectiveness of our proposed active testing framework on estimating two performance metrics, Precision@K and mean Average Precision, for two popular computer vision tasks, multi-label classification and instance segmentation. We further show that our approach is able to save significant human annotation effort and is more robust than alternative evaluation protocols.
Recognizing Surgical Activities with Recurrent Neural Networks

We apply recurrent neural networks to the task of recognizing surgical activities from robot kinematics. Prior work in this area focuses on recognizing short, low-level activities, or gestures, and has been based on variants of hidden Markov models and conditional random fields. In contrast, we work on recognizing both gestures and longer, higher-level activites, or maneuvers, and we model the mapping from kinematics to gestures/maneuvers with recurrent neural networks. To our knowledge, we are the first to apply recurrent neural networks to this task. Using a single model and a single set of hyperparameters, we match state-of-the-art performance for gesture recognition and advance state-of-the-art performance for maneuver recognition, in terms of both accuracy and edit distance. Code is available at https://github.com/rdipietro/miccai-2016-surgical-activity-rec.
Online Continuous Submodular Maximization

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe algorithm that has access to the full gradient of the objective functions. We show that it achieves a regret bound of $O(\sqrt{T})$ (where $T$ is the horizon of the online optimization problem) against a $(1-1/e)$-approximation to the best feasible solution in hindsight. However, in many scenarios, only an unbiased estimate of the gradients are available. For such settings, we then propose an online stochastic gradient ascent algorithm that also achieves a regret bound of $O(\sqrt{T})$ regret, albeit against a weaker $1/2$-approximation to the best feasible solution in hindsight. We also generalize our results to $\gamma$-weakly submodular functions and prove the same sublinear regret bounds. Finally, we demonstrate the efficiency of our algorithms on a few problem instances, including non-convex/non-concave quadratic programs, multilinear extensions of submodular set functions, and D-optimal design.
Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems

We propose methods to solve time-varying, sensor and actuator (SaA) selection problems for uncertain cyber-physical systems. We show that many SaA selection problems for optimizing a variety of control and estimation metrics can be posed as semidefinite optimization problems with mixed-integer bilinear matrix inequalities (MIBMIs). Although this class of optimization problems is computationally challenging, we present tractable approaches that directly tackle MIBMIs, providing both upper and lower bounds, and that lead to effective heuristics for SaA selection. The upper and lower bounds are obtained via successive convex approximations and semidefinite programming relaxations, respectively, and selections are obtained with a slicing algorithm from the solutions of the bounding problems. Custom branch-and-bound and combinatorial greedy approaches are also developed for a broad class of systems for comparison. Finally, comprehensive numerical simulations are performed to compare the different methods and illustrate their effectiveness.
Avoiding algebraic integers of bounded house in orbits of rational functions over cyclotomic closures

Let $k$ be a number field with cyclotomic closure $k^{\mathrm{cyc}}$, and let $h \in k^{\mathrm{cyc}}(x)$. For $A \ge 1$ a real number, we show that \[ \{ \alpha \in k^{\mathrm{cyc}} : h(\alpha) \in \overline{\mathbb Z} \text{ has house at most } A \} \] is finite for many $h$. We also show that for many such $h$ the same result holds if $h(\alpha)$ is replaced by orbits $h(h(\cdots h(\alpha)))$. This generalizes a result proved by Ostafe that concerns avoiding roots of unity, which is the case $A=1$.
Localization of quantum states and landscape functions

Eigenfunctions in inhomogeneous media can have strong localization properties. Filoche \& Mayboroda showed that the function $u$ solving $(-\Delta + V)u = 1$ controls the behavior of eigenfunctions $(-\Delta + V)\phi = \lambda\phi$ via the inequality $$|\phi(x)| \leq \lambda u(x) \|\phi\|_{L^{\infty}}.$$ This inequality has proven to be remarkably effective in predicting localization and recently Arnold, David, Jerison, Mayboroda \& Filoche connected $1/u$ to decay properties of eigenfunctions. We aim to clarify properties of the landscape: the main ingredient is a localized variation estimate obtained from writing $\phi(x)$ as an average over Brownian motion $\omega(\cdot)$ in started in $x$ $$\phi(x) = \mathbb{E}_{x}\left(\phi(\omega(t)) e^{\lambda t-\int_{0}^{t}{V(\omega(z))dz}} \right).$$ This variation estimate will guarantee that $\phi$ has to change at least by a factor of 2 in a small ball, which implicitly creates a landscape whose relationship with $1/u$ we discuss.
Light scattering in pseudo-passive media with uniformly balanced gain and loss

We demonstrate that a family of metamaterials, with a designed complex permittivity and permeability such that their index of refraction is real, have anomalous scattering features as opposed to their lossless passive counterparts with the same index of refraction.
Towards a Mathematical Theory of Super-resolution

This paper develops a mathematical theory of super-resolution. Broadly speaking, superresolution is the problem of recovering the ne details of an object|the high end of its spectrum| from coarse scale information only|from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in [0; 1] and with unknown complex-valued amplitudes. We only observe Fourier samples of this object up until a frequency cut-o fc. We show that one can super-resolve these point sources with innite precision|i.e. recover the exact locations and amplitudes|by solving a simple convex optimization problem, which can essentially be reformulated as a semidenite program. This holds provided that the distance between sources is at least 2=fc. This result extends to higher dimensions and other models. In one dimension for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with innite precision as well. We also show that the theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super-resolved signal is expected to degrade when both the noise level and the super-resolution factor vary.
Randomized Iterative Algorithms for Fisher Discriminant Analysis

Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is regularized Fisher discriminant analysis (RFDA). In this paper, we present a simple, iterative, sketching-based algorithm for RFDA that comes with provable accuracy guarantees when compared to the conventional approach. Our analysis builds upon two simple structural results that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized linear algebra. We analyze the behavior of RFDA when the ridge leverage and the standard leverage scores are used to select predictor variables and we prove that accurate approximations can be achieved by a sample whose size depends on the effective degrees of freedom of the RFDA problem. Our results yield significant improvements over existing approaches and our empirical evaluations support our theoretical analyses.
Electron pairing in the pseudogap state revealed by shot noise in copper oxide junctions

In the quest to understand high-temperature superconductivity in copper oxides, debate has been focused on the pseudogap—a partial energy gap that opens over portions of the Fermi surface in the ‘normal’ state above the bulk critical temperature1. The pseudogap has been attributed to precursor superconductivity, to the existence of preformed pairs and to competing orders such as charge-density waves1–4. A direct determination of the charge of carriers as a function of temperature and bias could help resolve among these alternatives. Here we report measurements of the shot noise of tunnelling current in high-quality La2−xSrxCuO4/La2CuO4/La2−xSrxCuO4 (LSCO/LCO/LSCO) heterostructures fabricated using atomic layer-by-layer molecular beam epitaxy at several doping levels. The data delineate three distinct regions in the bias voltage–temperature space. Well outside the superconducting gap region, the shot noise agrees quantitatively with independent tunnelling of individual charge carriers. Deep within the superconducting gap, shot noise is greatly enhanced, reminiscent of multiple Andreev reflections5–7. Above the critical temperature and extending to biases much larger than the superconducting gap, there is a broad region in which the noise substantially exceeds theoretical expectations for single-charge tunnelling, indicating pairing of charge carriers. These pairs are detectable deep into the pseudogap region of temperature and bias. The presence of these pairs constrains current models of the pseudogap and broken symmetry states, while phase fluctuations limit the domain of superconductivity. Shot-noise measurements in copper oxides reveal paired charge carriers existing in the pseudogap above the superconducting critical temperature, shedding light on the properties of high-temperature superconductivity in these materials.
Three-dimensional cephalometric analysis of the maxilla: Analysis of new landmarks.

Introduction Clinical evaluation of the midface including the paranasal and upper lip regions is highly subjective and complex. Traditional and 3-dimensional cephalometrics were not developed with the clinical appearance of these midfacial areas in mind and are therefore inappropriate surrogates for the clinical appearance of the midface, making them unsuitable as aids in diagnosing dentofacial deformities. The aim of this study was to evaluate traditional as well as newly defined landmarks and measurements and their correlation with clinical appearance of the midface. Methods Fifty-two subjects who underwent full-field cone-beam computed tomography were recruited for this study. A single examiner assessed each subject's midfacial region (paranasal and upper lip), and a second examiner obtained traditional and newly defined cephalometric measurements for each subject. Both examiners were blinded to each other's data throughout the study. Statistical analysis was performed to assess the correlations of the traditional and novel cephalometric measurements with clinical midfacial findings. The impact of the soft tissue thickness in the paranasal region was also analyzed. The performance of any classification derived from statistically significant variables was analyzed with the use of micro-F scores and area under the receiver operating characteristic curve (AUC). Results Both traditional (SNA) and newly defined measurements (SNANS, SNPR, SNNP, SNh) had no statistically significant correlation with clinical paranasal diagnosis. However, in the absence of upper lip procumbency or protrusion, SNNP and SNh had statistically significant correlations with clinical paranasal diagnosis (P = 0.047 and P = 0.003, respectively). For upper lip analysis, both traditional (SNA) and newly defined measurements (SNCEJ) had strong correlations with clinical upper lip diagnosis (P Conclusions Newly defined measurements SNh and SNNP correlated with clinical paranasal diagnosis only in the absence of upper lip procumbency and protrusion. SNA and SNCEJ were strongly correlated with clinical upper lip diagnosis. However, fitted models based on this study sample yielded low micro-F scores, making the fitted models currently unsuitable for anything besides correlation with clinical findings. A larger sample size will be necessary to further clarify the potential roles of these measurements, especially given the reasonable AUC values. The findings of this study demonstrate the highly subjective and relative nature of midfacial diagnosis and the importance of clinical judgment despite the potential utility of some traditional and new measurements.
Hierarchical and Safe Motion Control for Cooperative Locomotion of Robotic Guide Dogs and Humans: A Hybrid Systems Approach

This letter presents a hierarchical control strategy based on hybrid systems theory, nonlinear control, and safety-critical systems to enable cooperative locomotion of robotic guide dogs and visually impaired people. We address high-dimensional and complex hybrid dynamical models that represent collaborative locomotion. At the high level of the control scheme, local and nonlinear controllers, based on the virtual constraints approach, are designed to induce exponentially stable dynamic gaits. The local controller for the leash is assumed to be a nonlinear controller that keeps the human in a safe distance from the dog while following it. At the lower level, a real-time quadratic programming (QP) is solved for modifying the local controllers of the robot as well as the leash to avoid obstacles. In particular, the QP framework is set up based on control barrier functions (CBFs) to compute optimal control inputs that guarantee safety while being close to the local controllers. The stability of the complex periodic gaits is investigated through the Poincare return map. To demonstrate the power of the analytical foundation, the control algorithms are transferred into an extensive numerical simulation of a complex model that represents cooperative locomotion of a quadrupedal robot, referred to as Vision 60, and a human model. The complex model has 16 continuous-time domains with 60 state variables and 20 control inputs.
Designing Power Grid Topologies for Minimizing Network Disturbances: An Exact MILP Formulation

The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the $H$ 2 -norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial (tree) and meshed (loopy) topologies for new networks. Although the design task can be posed as a mixed-integer semidefinite program (MI-SDP), its performance does not scale well with network size. Using McCormick relaxation, the topology design problem can be reformulated as a mixed-integer linear program (MILP). To improve the computation time, graphical properties are exploited to provide tighter bounds on the continuous optimization variables. Numerical tests on the IEEE 39-bus feeder demonstrate the efficacy of the optimal topology in minimizing disturbances.
Chromatin conformation remains stable upon extensive transcriptional changes driven by heat shock

Heat shock (HS) initiates rapid, extensive, and evolutionarily conserved changes in transcription that are accompanied by chromatin decondensation and nucleosome loss at HS loci. Here we have employed in situ Hi-C to determine how heat stress affects long-range chromatin conformation in human and Drosophila cells. We found that compartments and topologically associating domains (TADs) remain unchanged by an acute HS. Knockdown of Heat Shock Factor 1 (HSF1), the master transcriptional regulator of the HS response, identified HSF1-dependent genes and revealed that up-regulation is often mediated by distal HSF1 bound enhancers. HSF1-dependent genes were usually found in the same TAD as the nearest HSF1 binding site. Although most interactions between HSF1 binding sites and target promoters were established in the nonheat shock (NHS) condition, a subset increased contact frequency following HS. Integrating information about HSF1 binding strength, RNA polymerase abundance at the HSF1 bound sites (putative enhancers), and contact frequency with a target promoter accurately predicted which up-regulated genes were direct targets of HSF1 during HS. Our results suggest that the chromatin conformation necessary for a robust HS response is preestablished in NHS cells of diverse metazoan species.
Trajectory Generation for Robotic Systems with Contact Force Constraints

This paper presents a trajectory generation method for contact-constrained robotic systems such as manipulators and legged robots. Contact-constrained systems are affected by the interaction forces between the robot and the environment. In turn, these forces determine and constrain state reachability of the robot parts or end-effectors. Our study subdivides the trajectory generation problem and the supporting reachability analysis into tractable subproblems consisting of a sampling problem, a convex optimization problem, and a nonlinear programming problem. Our method leads to significant reduction of computational cost. The proposed approach is validated using a realistic simulated contact-constrained robotic system.
Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a computational framework for learning Koopman operators of nonlinear dynamical systems using deep learning. We show that this novel method automatically selects efficient deep dictionaries, requiring much lower dimensional dictionaries while outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict on test data quantitatively 100 steps into the future, using only a single timepoint as an initial condition, and quantitative oscillatory behavior 400 steps into the future.
Waveform Design using Multi-Tone Feedback Frequency Modulation

This paper introduces a waveform design method using Multi-Tone Feedback Frequency Modulation (MT-FFM), a generalization of the single oscillator feedback FM method developed by Tomisawa [1]. The MT-FFM utilizes a collection of $K$ harmonically related oscillators each governed by a design parameter $z_{k}$ . These are in turn utilized as a discrete set of design parameters that may be modified to generate a richer set of modulation functions than in the single oscillator case. The waveforms resulting from these modulation functions can be designed to possess user defined properites by modifying the design parameters $z_{k}$ . The MT-FFM's modulation function is represented in exact closed-form using a Kapteyn series composed of Generalized Bessel Functions (GBF). This paper describes the structure of the MT-FFM waveform, derives the Kapteyn series representation of the waveform's modulation function, and demonstrates the design method with a waveform design example.
Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

We revisit the successive refinement problem with causal decoder side information considered by Maor and Merhav (2008) and strengthen their result by deriving an exponential strong converse theorem. To be specific, we show that for any rate-distortion tuple outside the rate-distortion region of the successive refinement problem with causal decoder side information, the excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and Holder’s inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result.
Cost-Aware Learning for Improved Identifiability with Multiple Experiments

We analyze the sample complexity of learning from multiple experiments where the experimenter has a total budget for obtaining samples. In this problem, the learner should choose a hypothesis that performs well with respect to multiple experiments, and their related data distributions. Each collected sample is associated with a cost which depends on the particular experiments. In our setup, a learner performs m experiments, while incurring a total cost C. We first show that learning from multiple experiments allows to improve identifiability. Additionally, by using a Rademacher complexity approach, we show that the gap between the training and generalization error is $O\left({C^{ - \frac{1}{2}}}\right)$. We also provide some examples for linear prediction, two-layer neural networks and kernel methods.
Adversarial Influence Maximization

We consider the problem of influence maximization in fixed networks for contagion models in an adversarial setting. The goal is to select an optimal set of nodes to seed the influence process, such that the number of influenced nodes at the conclusion of the campaign is as large as possible. We formulate the problem as a repeated game between a player and adversary, where the adversary specifies the edges along which the contagion may spread, and the player chooses sets of nodes to influence in an online fashion. We establish upper and lower bounds on the minimax pseudo-regret in both undirected and directed networks.
Reduced tree growth in the semiarid United States due to asymmetric responses to intensifying precipitation extremes.

Earth’s hydroclimatic variability is increasing, with changes in the frequency of extreme events that may negatively affect forest ecosystems. We examined possible consequences of changing precipitation variability using tree rings in the conterminous United States. While many growth records showed either little evidence of precipitation limitation or linear relationships to precipitation, growth of some species (particularly those in semiarid regions) responded asymmetrically to precipitation such that tree growth reductions during dry years were greater than, and not compensated by, increases during wet years. The U.S. Southwest, in particular, showed a large increase in precipitation variability, coupled with asymmetric responses of growth to precipitation. Simulations suggested roughly a twofold increase in the probability of large negative growth anomalies across the Southwest resulting solely from 20th century increases in variability of cool-season precipitation. Models project continued increases in precipitation variability, portending future growth reductions across semiarid forests of the western United States.