cssi/SciSciGPT-SciSciNet huggingface dataset:
Optimal dynamic formation control of multi-agent systems in environments with obstacles

We address the optimal dynamic formation problem in mobile leader-follower networks where an optimal formation is generated to maximize a given objective function while continuously preserving connectivity. We show that in a convex mission space, the connectivity constraints can be satisfied by any feasible solution to a mixed integer nonlinear optimization problem. When the optimal formation objective is to maximize coverage in a mission space cluttered with obstacles, we separate the process into intervals with no obstacles detected and intervals where one or more obstacles are detected. In the latter case, we propose a minimum-effort reconfiguration approach for the formation which still optimizes the objective function while avoiding the obstacles and ensuring connectivity. We include simulation results illustrating this dynamic formation process.
VARIATIONAL STRUCTURE OF THE OPTIMAL ARTIFICIAL DIFFUSION METHOD FOR THE ADVECTION–DIFFUSION EQUATION

In this research note, we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional (1D) problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advective-diffusive system, and then derive a new stable weak formulation. When applied to 1D problems with constant coefficients and forcing function, this resulting weak formulation will be equivalent to the optimal artificial diffusion method. We present representative numerical results to corroborate our theoretical findings.
A note on Dehn colorings and invariant factors

If A is an abelian group and ϕ is an integer, let A(ϕ) be the subgroup of A consisting of elements a ∈ A such that ϕ ⋅ a = 0. We prove that if D is a diagram of a classical link L and 0 = ϕ0,ϕ1,…,ϕ...
Eigenfunctions and the Dirichlet problem for the Classical Kimura Diffusion Operator

We study the classical Kimura diffusion operator defined on the $n$-simplex, $\operatorname{L^{Kim}}=\sum_{1\leq i,j\leq n+1}x_i(\delta_{ij}-x_j)\partial_{x_i}\partial_{x_j},$ which has important applications in population genetics. Because it is a degenerate elliptic operator acting on a singular space, special tools are required to analyze and construct solutions to elliptic and parabolic problems defined by this operator. The natural boundary value problems are the “regular” problem and the Dirichlet problem. For the regular problem, one can only specify the regularity of the solution at the boundary. For the Dirichlet problem, one can specify the boundary values, but the solution is then not smooth at the boundary. In this paper we give a computationally effective recursive method to construct the eigenfunctions of the regular operator in any dimension, and a recursive method to use them to solve the inhomogeneous equation. As noted, the Dirichlet problem does not have a regular solution. We give an e...
Analyzing wireless communication network vulnerability with homological invariants

This article explains how homology theory can be applied to simplicial complex models of wireless communication networks to study their vulnerability to jamming. It develops two classes of invariants (one local and one global) for studying which nodes and links present more of a liability to the network's performance when under attack.
Roger and Yang's Kauffman Bracket ArcAlgebra is Finitely Generated

Generalizing the construction of the Kauffman bracket skein algebra, Roger and Yang defined the Kauffman bracket arc algebra of a punctured surface, so that it is a quantization of the decorated Teichmuller space. We provide an explicit, finite set of generators for their algebra.
Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer

We demonstrate a simple, robust, and ultrabright parametric down-conversion source of polarization-entangled photons based on a polarization Sagnac interferometer. Bidirectional pumping in type-II phase-matched periodically poled $\mathrm{K}\mathrm{Ti}\mathrm{O}\mathrm{P}{\mathrm{O}}_{4}$ yields a measured flux of 5000 polarization-entangled pairs/s/mW of pump power in a $1\text{\ensuremath{-}}\mathrm{nm}$ bandwidth at 96.8% quantum-interference visibility. The common-path arrangement of the Sagnac interferometer eliminates the need for phase stabilization for the biphoton output state.
Continuous user authentication via unlabeled phone movement patterns

In this paper, we propose a novel continuous authentication system for smartphone users. The proposed system entirely relies on unlabeled phone movement patterns collected through smartphone accelerometer. The data was collected in a completely unconstrained environment over five to twelve days. The contexts of phone usage were identified using k-means clustering. Multiple profiles, one for each context, were created for every user. Five machine learning algorithms were employed for classification of genuine and impostors. The performance of the system was evaluated over a diverse population of 57 users. The mean equal error rates achieved by Logistic Regression, Neural Network, kNN, SVM, and Random Forest were 13.7%, 13.5%, 12.1%, 10.7%, and 5.6% respectively. A series of statistical tests were conducted to compare the performance of the classifiers. The suitability of the proposed system for different types of users was also investigated using the failure to enroll policy.
Asymptotic Optimality of Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems

Dual-sourcing inventory systems, in which one supplier is faster i.e., express and more costly, while the other is slower i.e., regular and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize because of the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called tailored base-surge TBS policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the express source follows a simple order-up-to rule. Numerical experiments by several authors have suggested that such policies perform well as the lead time difference between the two sources grows large, which is exactly the setting in which the curse of dimensionality leads to the problem becoming intractable. However, providing a theoretical foundation for this phenomenon has remained a major open problem. In this paper, we provide such a theoretical foundation by proving that a simple TBS policy is indeed asymptotically optimal as the lead time of the regular source grows large, with the lead time of the express source held fixed. Our main proof technique combines novel convexity and lower-bounding arguments, an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes, and ideas from the theory of random walks and queues, significantly extending the methodology and applicability of a novel framework for analyzing inventory models with large lead times recently introduced by Goldberg and coauthors in the context of lost-sales models with positive lead times. This paper was accepted by Gad Allon, operations management.
A Light Touch for Heavily Constrained SGD

Minimizing empirical risk subject to a set of constraints can be a useful strategy for learning restricted classes of functions, such as monotonic functions, submodular functions, classifiers that guarantee a certain class label for some subset of examples, etc. However, these restrictions may result in a very large number of constraints. Projected stochastic gradient descent (SGD) is often the default choice for large-scale optimization in machine learning, but requires a projection after each update. For heavily-constrained objectives, we propose an efficient extension of SGD that stays close to the feasible region while only applying constraints probabilistically at each iteration. Theoretical analysis shows a compelling trade-off between per-iteration work and the number of iterations needed on problems with a large number of constraints.
The p-torsion subgroup scheme of an elliptic curve

Abstract Let k be a field of positive characteristic p. Question Does every twisted form of μ p over k occur as subgroup scheme of an elliptic curve over k? We show that this is true for most finite fields, for local fields and for fields of characteristic p ⩽ 11 . However, it is false in general for fields of characteristic p ⩾ 13 , which implies that there are also p-divisible and formal groups of height one over such fields that do not arise from elliptic curves. It also implies that the Hasse invariant does not obey the Hasse principle. Moreover, we also analyse twisted forms of p-torsion subgroup schemes of ordinary elliptic curves and the analogous questions for supersingular curves.
Sharper periodicity and stabilization maps for configuration spaces of closed manifolds

In this note we study the homology of configuration spaces of closed manifolds. We sharpen the eventual periodicity results of Nagpal and Cantero-Palmer, prove integral homological stability for configuration spaces of odd-dimensional manifolds and introduce a stabilization map on the homology with $Z[1/2]$-coefficients of configuration spaces of odd-dimensional manifolds.
Some 3-dimensional transverse C-links (Constructions of higher-dimensional C-links, I)

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3–manifolds are realized as transverse intersections of complex surfaces in C with strictly pseudoconvex 5–spheres. These manifolds not only inherit interesting intrinsic structures (eg, they have canonical Stein-fillable contact structures), they also have extrinsic structures of a knot-theoretical nature (eq, S arises in infinitely many distinct ways). This survey is not comprehensive; a number of questions are left open for future work.
Electromagnetic Wave Scattering by Many Small Particles and Creating Materials with a Desired Permeability

Scattering of electromagnetic (EM) waves by many small particles (bodies), embedded in a homogeneous medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the efiective EM fleld in the limiting medium, in the limit a ! 0, where a is the characteristic size of a particle and the number M(a) of the particles tends to inflnity at a suitable rate. The proposed theory allows one to create a medium with a desirable spatially inhomogeneous permeability. The main new physical result is the explicit analytical formula for the permeability "(x) of the limiting medium. While the initial medium has a constant permeability "0, the limiting medium, obtained as a result of embedding many small particles with prescribed boundary impedances, has a non-homogeneous permeability which is expressed analytically in terms of the density of the distribution of the small particles and their boundary impedances. Therefore, a new physical phenomenon is predicted theoretically, namely, appearance of a spatially inhomogeneous permeability as a result of embedding of many small particles whose physical properties are described by their boundary impedances.
Learning Global Features for Coreference Resolution

There is compelling evidence that coreference prediction would benefit from modeling global information about entity-clusters. Yet, state-of-the-art performance can be achieved with systems treating each mention prediction independently, which we attribute to the inherent difficulty of crafting informative cluster-level features. We instead propose to use recurrent neural networks (RNNs) to learn latent, global representations of entity clusters directly from their mentions. We show that such representations are especially useful for the prediction of pronominal mentions, and can be incorporated into an end-to-end coreference system that outperforms the state of the art without requiring any additional search.
Multiplicative relations for Fourier coefficients of degree 2 Siegel eigenforms

Abstract We prove multiplicative relations between certain Fourier coefficients of degree 2 Siegel eigenforms. These relations are analogous to those for elliptic eigenforms. We also provide two sets of formulas for the eigenvalues of degree 2 Siegel eigenforms. The first evaluates the eigenvalues in terms of the form's Fourier coefficients, in the case a ( I ) ≠ 0 . The second expresses the eigenvalues of index p and p 2 , for p prime, solely in terms of p and k, the weight of the form, in the case a ( 0 ) ≠ 0 . From this latter case, we give simple expressions for the eigenvalues associated to degree 2 Siegel Eisenstein series.
Slalom: Fast, Verifiable and Private Execution of Neural Networks in Trusted Hardware

As Machine Learning (ML) gets applied to security-critical or sensitive domains, there is a growing need for integrity and privacy for outsourced ML computations. A pragmatic solution comes from Trusted Execution Environments (TEEs), which use hardware and software protections to isolate sensitive computations from the untrusted software stack. However, these isolation guarantees come at a price in performance, compared to untrusted alternatives. This paper initiates the study of high performance execution of Deep Neural Networks (DNNs) in TEEs by efficiently partitioning DNN computations between trusted and untrusted devices. Building upon an efficient outsourcing scheme for matrix multiplication, we propose Slalom, a framework that securely delegates execution of all linear layers in a DNN from a TEE (e.g., Intel SGX or Sanctum) to a faster, yet untrusted, co-located processor. We evaluate Slalom by running DNNs in an Intel SGX enclave, which selectively delegates work to an untrusted GPU. For canonical DNNs (VGG16, MobileNet and ResNet variants) we obtain 6x to 20x increases in throughput for verifiable inference, and 4x to 11x for verifiable and private inference.
Data Streams with Bounded Deletions

Two prevalent models in the data stream literature are the insertion-only and turnstile models. Unfortunately, many important streaming problems require a Θ(log(n)) multiplicative factor more space for turnstile streams than for insertion-only streams. This complexity gap often arises because the underlying frequency vector f is very close to $0$, after accounting for all insertions and deletions to items. Signal detection in such streams is difficult, given the large number of deletions. In this work, we propose an intermediate model which, given a parameter α ≥ 1, lower bounds the norm |f|p by a 1/α-fraction of the Lp mass of the stream had all updates been positive. Here, for a vector f, |f|p = (∑i=1n |fi|p)1/p, and the value of p we choose depends on the application. This gives a fluid medium between insertion only streams (with α = 1), and turnstile streams (with α = poly(n)), and allows for analysis in terms of α. We show that for streams with this α-property, for many fundamental streaming problems we can replace a O(log(n)) factor in the space usage for algorithms in the turnstile model with a O(log(α)) factor. This is true for identifying heavy hitters, inner product estimation, L0 estimation, L1 estimation, L1 sampling, and support sampling. For each problem, we give matching or nearly matching lower bounds for α-property streams. We note that in practice, many important turnstile data streams are in fact α-property streams for small values of α. For such applications, our results represent significant improvements in efficiency for all the aforementioned problems.
Optimal strategies for the control of autonomous vehicles in data assimilation

Abstract We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for the locally optimal control algorithm presented here, with objective formed from the variance trace of the expected posterior distribution. We present results for linear flows near hyperbolic fixed points.
Stability structures of conjunctive Boolean networks

A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely used in modeling gene regulatory networks. We focus in this paper on a special class of Boolean networks, termed as conjunctive Boolean networks. A Boolean network is conjunctive if the associated value update rule is comprised of only AND operations. It is known that any trajectory of a finite dynamical system will enter a periodic orbit. We characterize in this paper all periodic orbits of a conjunctive Boolean network whose underlying graph is strongly connected. In particular, we establish a bijection between the set of periodic orbits and the set of binary necklaces of a certain length. We further investigate the stability of a periodic orbit. Specifically, we perturb a state in the periodic orbit by changing the value of a single entry of the state. The trajectory, with the perturbed state being the initial condition, will enter another (possibly the same) periodic orbit in finite time steps. We then provide a complete characterization of all such transitions from one periodic orbit to another. In particular, we construct a digraph, with the vertices being the periodic orbits, and the (directed) edges representing the transitions among the orbits. We call such a digraph the stability structure of the conjunctive Boolean network.
Strategyproof Mechanisms for One-Dimensional Hybrid and Obnoxious Facility Location.

We consider a strategic variant of the facility location problem. We would like to locate a facility on a closed interval. There are n agents located on that interval, divided into two types: type 1 agents, who wish for the facility to be as far from them as possible, and type 2 agents, who wish for the facility to be as close to them as possible. Our goal is to maximize a form of aggregated social benefit: maxisum- the sum of the agents' utilities, or the egalitarian objective- the minimal agent utility. The strategic aspect of the problem is that the agents' locations are not known to us, but rather reported to us by the agents- an agent might misreport his location in an attempt to move the facility away from or towards to his true location. We therefore require the facility-locating mechanism to be strategyproof, namely that reporting truthfully is a dominant strategy for each agent. As simply maximizing the social benefit is generally not strategyproof, our goal is to design strategyproof mechanisms with good approximation ratios. For the maxisum objective, in the deterministic setting, we provide a best-possible 3- approximate strategyproof mechanism; in the randomized setting, we provide a 23/13- approximate strategyproof mechanism and a lower bound of \frac{2}{\sqrt{3}}. For the egalitarian objective, we provide a lower bound of 3/2 in the randomized setting, and show that no bounded approximation ratio is attainable in the deterministic setting. To obtain our deterministic lower bounds, we characterize all deterministic strategyproof mechanisms when all agents are of type 1. Finally, we consider a generalized model that allows an agent to control more than one location, and provide best-possible 3- and 3/2- approximate strategyproof mechanisms for maxisum, in the deterministic and randomized settings respectively, when only type 1 agents are present.
A characterization of almost universal ternary inhomogeneous quadratic polynomials with conductor 2

Abstract An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers. In this paper, we provide a characterization of almost universal ternary quadratic polynomials with conductor 2.
Policy Transfer with Strategy Optimization

Computer simulation provides an automatic and safe way for training robotic control policies to achieve complex tasks such as locomotion. However, a policy trained in simulation usually does not transfer directly to the real hardware due to the differences between the two environments. Transfer learning using domain randomization is a promising approach, but it usually assumes that the target environment is close to the distribution of the training environments, thus relying heavily on accurate system identification. In this paper, we present a different approach that leverages domain randomization for transferring control policies to unknown environments. The key idea that, instead of learning a single policy in the simulation, we simultaneously learn a family of policies that exhibit different behaviors. When tested in the target environment, we directly search for the best policy in the family based on the task performance, without the need to identify the dynamic parameters. We evaluate our method on five simulated robotic control problems with different discrepancies in the training and testing environment and demonstrate that our method can overcome larger modeling errors compared to training a robust policy or an adaptive policy.
Performance Bounds with Curvature for Batched Greedy Optimization

The batched greedy strategy is an approximation algorithm to maximize a set function subject to a matroid constraint. Starting with the empty set, the batched greedy strategy iteratively adds to the current solution set a batch of elements that results in the largest gain in the objective function while satisfying the matroid constraints. In this paper, we develop bounds on the performance of the batched greedy strategy relative to the optimal strategy in terms of a parameter called the total batched curvature. We show that when the objective function is a polymatroid set function, the batched greedy strategy satisfies a harmonic bound for a general matroid constraint and an exponential bound for a uniform matroid constraint, both in terms of the total batched curvature. We also study the behavior of the bounds as functions of the batch size. Specifically, we prove that the harmonic bound for a general matroid is nondecreasing in the batch size and the exponential bound for a uniform matroid is nondecreasing in the batch size under the condition that the batch size divides the rank of the uniform matroid. Finally, we illustrate our results by considering a task scheduling problem and an adaptive sensing problem.
Minimum Sparsity of Unobservable Power Network Attacks

Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $\kappa (\mathcal {G^M})+1$ , where $\kappa (\mathcal {G^M})$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.
Localisation and compactness properties of the Navier–Stokes global regularity problem

In this paper we establish a number of implications between various qualitative and quantitative versions of the global regularity problem for the Navier–Stokes equations in the periodic, smooth finite energy, smooth H1, Schwartz, and mild H1 categories, and with or without a forcing term. In particular, we show that if one has global well-posedness in H1 for the periodic Navier–Stokes problem with a forcing term, then one can obtain global regularity both for periodic and for Schwartz initial data (thus yielding a positive answer to both official formulations of the problem for the Clay Millennium Prize), and can also obtain global almost smooth solutions from smooth H1 data or smooth finite energy data, although we show in this category that fully smooth solutions are not always possible. Our main new tools are localised energy and enstrophy estimates to the Navier–Stokes equation that are applicable for large data or long times, and which may be of independent interest.
Exploring features for predicting policy citations

In this study we performed an initial investigation and evaluation of altmetrics and their relationship with public policy citation of research papers. We examined methods for using altmetrics and other data to predict whether a research paper is cited in public policy and applied receiver operating characteristic curve on various feature groups in order to evaluate their potential usefulness. From the methods we tested, classifying based on tweet count provided the best results, achieving an area under the ROC curve of 0.91.
The non-convex Burer-Monteiro approach works on smooth semidefinite programs

Semidefinite programs (SDP's) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and Monteiro proposed to solve SDP's with few equality constraints via rank-restricted, non-convex surrogates. Remarkably, for some applications, local optimization methods seem to converge to global optima of these non-convex surrogates reliably. Although some theory supports this empirical success, a complete explanation of it remains an open question. In this paper, we consider a class of SDP's which includes applications such as max-cut, community detection in the stochastic block model, robust PCA, phase retrieval and synchronization of rotations. We show that the low-rank Burer-Monteiro formulation of SDP's in that class almost never has any spurious local optima.
From Virtual Demonstration to Real-World Manipulation Using LSTM and MDN.

Robots assisting the disabled or elderly must perform complex manipulation tasks and must adapt to the home environment and preferences of their user. Learning from demonstration is a promising choice, that would allow the non-technical user to teach the robot different tasks. However, collecting demonstrations in the home environment of a disabled user is time consuming, disruptive to the comfort of the user, and presents safety challenges. It would be desirable to perform the demonstrations in a virtual environment. In this paper we describe a solution to the challenging problem of behavior transfer from virtual demonstration to a physical robot. The virtual demonstrations are used to train a deep neural network based controller, which is using a Long Short Term Memory (LSTM) recurrent neural network to generate trajectories. The training process uses a Mixture Density Network (MDN) to calculate an error signal suitable for the multimodal nature of demonstrations. The controller learned in the virtual environment is transferred to a physical robot (a Rethink Robotics Baxter). An off-the-shelf vision component is used to substitute for geometric knowledge available in the simulation and an inverse kinematics module is used to allow the Baxter to enact the trajectory. Our experimental studies validate the three contributions of the paper: (1) the controller learned from virtual demonstrations can be used to successfully perform the manipulation tasks on a physical robot, (2) the LSTM+MDN architectural choice outperforms other choices, such as the use of feedforward networks and mean-squared error based training signals and (3) allowing imperfect demonstrations in the training set also allows the controller to learn how to correct its manipulation mistakes.
Shortest path in a polygon using sublinear space

We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon $P$ with $n$ vertices in a read only memory, and additional working memory of size $m$, the new algorithm computes the shortest path (in $P$) in $O( n^2 / m )$ expected time, assuming $m = O(n/\log^2 n)$. This requires several new tools, which we believe to be of independent interest. Specifically, we show that violator space problems, an abstraction of low dimensional linear-programming (and LP-type problems), can be solved using constant space and expected linear time, by modifying Seidel's linear programming algorithm and using pseudo-random sequences.
An effective Lie–Kolchin Theorem for quasi-unipotent matrices

Abstract We establish an effective version of the classical Lie–Kolchin Theorem. Namely, let A , B ∈ GL m ( C ) be quasi-unipotent matrices such that the Jordan Canonical Form of B consists of a single block, and suppose that for all k ⩾ 0 the matrix A B k is also quasi-unipotent. Then A and B have a common eigenvector. In particular, 〈 A , B 〉 GL m ( C ) is a solvable subgroup. We give applications of this result to the representation theory of mapping class groups of orientable surfaces.
On the sum capacity of K-user cascade Gaussian Z-interference channel

A K-user cascade Gaussian Z-interference channel is a subclass of the general K-user Gaussian interference channel, where each user, except the first one, experiences interference only from the previous user. Under simple Han-Kobayashi schemes assuming Gaussian inputs and no time sharing, it is shown that the maximum sum rate is achieved by each user transmitting either common or private signals. For K = 3, channel conditions under which the achieved sum rate is either equal to or within 0.5 bits to the sum capacity are identified.
Levy Measure Decompositions for the Beta and Gamma Processes

We develop new representations for the Levy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these infinite sums may be truncated in practice, and explicitly characterize truncation errors. We also perform an analysis of the characteristics of posterior distributions, based on the proposed decompositions. The decompositions provide new insights into the beta and gamma processes (and their generalizations), and we demonstrate how the proposed representation unifies some properties of the two. This paper is meant to provide a rigorous foundation for and new perspectives on Levy processes, as these are of increasing importance in machine learning.
Resonant leading term geometric optics expansions with boundary layers for quasilinear hyperbolic boundary problems

We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to show approximate solutions tend to the exact solutions in the small wavelength limit. Recent work [2] by Coulombel et al. studied the case of reflecting wave trains whose expansions involve only real phases. We treat generic boundary frequencies by incorporating into our expansions both real and nonreal phases. Nonreal phases introduce difficulties such as approximately solving complex transport equations and result in the addition of boundary layers with exponential decay. This also prevents us from doing an error analysis based on almost periodic profiles as in [2].
INFRARED TIME LAGS FOR THE PERIODIC QUASAR PG 1302-102

The optical light curve of the quasar PG 1302-102 at z = 0.278 shows a strong, smooth 5.2 year periodic signal, detectable over a period of ~20 years. Although the interpretation of this phenomenon is still uncertain, the most plausible mechanisms involve a binary system of two supermassive black holes with a subparsec separation. At this close separation, the nuclear black holes in PG 1302-102 will likely merge within ~ 10^5 years due to gravitational wave emission alone. Here, we report the rest-frame near-infrared time lags for PG 1302-102. Compiling data from WISE and Akari, we confirm that the periodic behavior reported in the optical light curve from Graham et al. is reproduced at infrared wavelengths, with best-fit observed-frame 3.4 and 4.6 µm time lags of (2219 ± 153, 2408 ± 148) days for a near face-on orientation of the torus, or (4103 ± 153, 4292 ± 148) days for an inclined system with relativistic Doppler boosting in effect. The periodicity in the infrared light curves and the light-travel time of the accretion disk photons to reach the dust glowing regions support that a source within the accretion disk is responsible for the optical variability of PG 1302-102, echoed at the farther out dusty regions. The implied distance of this dusty, assumed toroidal region is ~1.5 pc for a near face-on geometry or ~1.1 pc for the relativistic Doppler-boosted case.
Robust AC Optimal Power Flow

There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow (RAC-OPF) problem as a two-stage robust optimization problem with recourse. This problem amounts to a nonconvex infinite-dimensional optimization problem that is computationally intractable, in general. Under the assumption that there is adjustable generation or load at every bus in the power transmission network, we develop a technique to approximate RAC-OPF from within by a finite-dimensional semidefinite program by restricting the space of recourse policies to be affine in the uncertain problem data. We establish a sufficient condition under which the semidefinite program returns an affine recourse policy that is guaranteed to be feasible for the original RAC-OPF problem. We illustrate the effectiveness of the proposed optimization method on the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable resource penetration and uncertainty.
Vision-based preharvest yield mapping for apple orchards

Abstract We present an end-to-end computer vision system for yield mapping in apple orchards. Our proposed system is platform independent and does not require any specific lighting conditions. Our main technical contributions are (1) a semi-supervised clustering algorithm that utilizes colors to identify apples and (2) an unsupervised clustering method that utilizes spatial properties to estimate fruit counts from apple clusters having arbitrarily complex geometry. Additionally, we utilize camera motion to merge the counts across multiple views. We verified the performance of our algorithms by conducting multiple field trials. Results indicate that the detection method achieves F 1 -measure .95–.97 for multiple color varieties and lighting conditions. The counting method achieves an accuracy of 89–98%. Additionally, we report merged fruit counts from both sides of the tree rows. Our yield estimation method achieves an overall accuracy of 91.98–94.81% across different datasets.
Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods

Quartet trees displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets in many practical problems with large numbers of taxa. We introduce the notion of an Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via an EQS contains all of the combinatorial information of the tree itself. Using performance tests on simulated datasets, we also demonstrate that using an EQS to reduce the number of quartets in both summary method pipelines for species tree inference as well as methods for supertree inference results in only small reductions in accuracy.
Bayesian Nonparametric Functional Mixture Estimation for Time-Series Data, With Application to Estimation of State Employment Totals

The U.S. Bureau of Labor Statistics use monthly, by-state employment totals from the Current Population Survey (CPS) as a key input to develop employment estimates for counties within the states. The monthly CPS by-state totals, however, express high levels of volatility that compromise the accuracy of resulting estimates composed for the counties. Typically-employed models for small area estimation produce de-noised, state-level employment estimates by borrowing information over the survey months, but assume independence among the collection of by-state time series, which is typically violated due to similarities in their underlying economies. We construct Gaussian process and Gaussian Markov random field alternative functional prior specifications, each in a mixture of multivariate Gaussian distributions with a Dirichlet process (DP) mixing measure over the parameters of their covariance or precision matrices. Our DP mixture of functions models allow the data to simultaneously estimate a dependence among the months and between states. A feature of our models is that those functions assigned to the same cluster are drawn from a distribution with the same covariance parameters, so that they are similar, but don't have to be identical. We compare the performances of our two alternatives on synthetic data and apply them to recover de-noised, by-state CPS employment totals for data from $2000-2013$.
Maximizing the Smallest Eigenvalue of a Symmetric Matrix: A Submodular Optimization Approach

This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input nodes in order to guarantee consensus of networks with negative edges as well as maximizing the convergence rate of distributed systems. We develop a submodular optimization approach to maximizing the smallest eigenvalue by first proving that positivity of the eigenvalues of a submatrix can be characterized using the probability distribution of the quadratic form induced by the submatrix. We then exploit that connection to prove that positive-definiteness of a submatrix can be expressed as a constraint on a submodular function. We prove that our approach results in polynomial-time algorithms with provable bounds on the size of the submatrix. We also present generalizations to non-symmetric matrices, alternative sufficient conditions for the smallest eigenvalue to exceed a desired bound that are valid for Laplacian matrices, and a numerical evaluation.
Protecting JPEG Images Against Adversarial Attacks

As deep neural networks (DNNs) have been integrated into critical systems, several methods to attack these systems have been developed. These adversarial attacks make imperceptible modifications to an image that fool DNN classifiers. We present an adaptive JPEG encoder which defends against many of these attacks. Experimentally, we show that our method produces images with high visual quality while greatly reducing the potency of state-of- the-art attacks. Our algorithm requires only a modest increase in encoding time, produces a compressed image which can be decompressed by an off-the-shelf JPEG decoder, and classified by an unmodified classifier.
A projective analogue of Napoleon's and Varignon's theorems

What do Napoleon's and Varignon's theorems have in common? We claim that they both are examples of immediately regularizing natural polygon iterations in different planar geometries and present a new and analogous result in projective geometry.
Rates of Convergence of Spectral Methods for Graphon Estimation

This paper studies the problem of estimating the grahpon model - the underlying generating mechanism of a network. Graphon estimation arises in many applications such as predicting missing links in networks and learning user preferences in recommender systems. The graphon model deals with a random graph of $n$ vertices such that each pair of two vertices $i$ and $j$ are connected independently with probability $\rho \times f(x_i,x_j)$, where $x_i$ is the unknown $d$-dimensional label of vertex $i$, $f$ is an unknown symmetric function, and $\rho$ is a scaling parameter characterizing the graph sparsity. Recent studies have identified the minimax error rate of estimating the graphon from a single realization of the random graph. However, there exists a wide gap between the known error rates of computationally efficient estimation procedures and the minimax optimal error rate. Here we analyze a spectral method, namely universal singular value thresholding (USVT) algorithm, in the relatively sparse regime with the average vertex degree $n\rho=\Omega(\log n)$. When $f$ belongs to Holder or Sobolev space with smoothness index $\alpha$, we show the error rate of USVT is at most $(n\rho)^{ -2 \alpha / (2\alpha+d)}$, approaching the minimax optimal error rate $\log (n\rho)/(n\rho)$ for $d=1$ as $\alpha$ increases. Furthermore, when $f$ is analytic, we show the error rate of USVT is at most $\log^d (n\rho)/(n\rho)$. In the special case of stochastic block model with $k$ blocks, the error rate of USVT is at most $k/(n\rho)$, which is larger than the minimax optimal error rate by at most a multiplicative factor $k/\log k$. This coincides with the computational gap observed for community detection. A key step of our analysis is to derive the eigenvalue decaying rate of the edge probability matrix using piecewise polynomial approximations of the graphon function $f$.
How does bribery affect a firm’s future growth? Empirical evidence from transition economies

Although economists have long studied the impact of bribery on firms’ development, the debate continues as to whether bribery ‘greases’ or ‘sands’ the growth of businesses. For this investigation, ...
Additive genetic variance for lifetime fitness and the capacity for adaptation in an annual plant.

The immediate capacity for adaptation under current environmental conditions is directly proportional to the additive genetic variance for fitness, VA (W). Mean absolute fitness, W¯ , is predicted to change at the rate VA(W)W¯ , according to Fisher's Fundamental Theorem of Natural Selection. Despite ample research evaluating degree of local adaptation, direct assessment of VA (W) and the capacity for ongoing adaptation is exceedingly rare. We estimated VA (W) and W¯ in three pedigreed populations of annual Chamaecrista fasciculata, over three years in the wild. Contrasting with common expectations, we found significant VA (W) in all populations and years, predicting increased mean fitness in subsequent generations (0.83 to 6.12 seeds per individual). Further, we detected two cases predicting "evolutionary rescue," where selection on standing VA (W) was expected to increase fitness of declining populations ( W¯ < 1.0) to levels consistent with population sustainability and growth. Within populations, inter-annual differences in genetic expression of fitness were striking. Significant genotype-by-year interactions reflected modest correlations between breeding values across years, indicating temporally variable selection at the genotypic level that could contribute to maintaining VA (W). By directly estimating VA (W) and total lifetime W¯ , our study presents an experimental approach for studies of adaptive capacity in the wild.
Resonantly enhanced nonreciprocal silicon Brillouin amplifier

The ability to amplify light within silicon waveguides is central to the development of high-performance silicon photonic device technologies. To this end, the large optical nonlinearities made possible through stimulated Brillouin scattering offer a promising avenue for power-efficient all-silicon amplifiers, with recent demonstrations producing several dB of net amplification. However, scaling the degree of amplification to technologically compelling levels (>10 dB), necessary for everything from filtering to small signal detection, remains an important goal. Here, we significantly enhance the Brillouin amplification process by harnessing an intermodal Brillouin interaction within a multi-spatial-mode silicon racetrack resonator. Using this approach, we demonstrate more than 20 dB of net Brillouin amplification in silicon, advancing state-of-the-art performance in silicon waveguides by a factor of 30. This level of amplification is achieved with modest (∼15 mW) continuous-wave pump powers and produces low out-of-band noise. Moreover, we show that this same system behaves as a unidirectional amplifier, providing more than 28 dB of optical nonreciprocity without insertion loss in an all-silicon platform. Building on these results, this device concept opens the door to new types of all-silicon injection-locked Brillouin lasers, high-performance photonic filters, and waveguide-compatible distributed optomechanical phenomena.
On the Optimality of Perturbations in Stochastic and Adversarial Multi-armed Bandit Problems

We investigate the optimality of perturbation based algorithms in the stochastic and adversarial multi-armed bandit problems. For the stochastic case, we provide a unified regret analysis for both sub-Weibull and bounded perturbations when rewards are sub-Gaussian. Our bounds are instance optimal for sub-Weibull perturbations with parameter 2 that also have a matching lower tail bound, and all bounded support perturbations where there is sufficient probability mass at the extremes of the support. For the adversarial setting, we prove rigorous barriers against two natural solution approaches using tools from discrete choice theory and extreme value theory. Our results suggest that the optimal perturbation, if it exists, will be of Frechet-type.
Learning Risk Level Set Parameters from Data Sets for Safer Driving

This paper examines how vehicles can quickly quantify the level of congestion in their environment for planning. We use risk level sets to define a metric of congestion for the vehicles. Using this metric, we can quickly identify distributions of environment and driver features, such as velocities and number of neighbors, based on risk within human driving data sets. We use the NGSIM and highD data sets to study how risk influences behaviors in city and highway driving. From these data sets, we learn common risk thresholds for classifying low, medium, and high-risk situations. Using these thresholds, we develop simulations of an autonomous vehicle driving along a highway, and demonstrate how the chosen risk threshold influences the autonomous vehicle behavior.
Symplectic Instanton Homology: naturality, and maps from cobordisms

We prove that Manolescu and Woodward's Symplectic Instanton homology, and its twisted versions are natural, and define maps associated to four dimensional cobordisms within this theory. This allows one to define representations of the mapping class group and the fundamental group of a 3-manifold, and to have a geometric interpretation of the maps appearing in the long exact sequence for symplectic instanton homology, together with vanishing criterions.