cssi/SciSciGPT-SciSciNet huggingface dataset:
Systematic Design of Optimal Low-Thrust Transfers for the Three-Body Problem

We develop a computational approach for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The use of low thrust propulsion allows the spacecraft to depart from the natural dynamics and enables a wider range of transfers. We generate the reachable set of the spacecraft and use this to determine transfer opportunities, analogous to the intersection of control-free invariant manifolds. The reachable set is developed on a lower dimensional Poincare section and used to design transfer trajectories. This is solved numerically as a discrete optimal control problem using a variational integrator, which preserves the geometric structure of the motion in the three-body problem. We demonstrate our approach with two numerical simulations of transfers in the Earth-Moon three-body system.
Uncertainty quantification of electronic and photonic ICs with non-Gaussian correlated process variations

Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners. This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters, and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by 2500× to 3000× in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods. Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.
On regular 3-wise intersecting families

Ellis and the third author showed, verifying a conjecture of Frankl, that any $3$-wise intersecting family of subsets of $\{1,2,\dots,n\}$ admitting a transitive automorphism group has cardinality $o(2^n)$, while a construction of Frankl demonstrates that the same conclusion need not hold under the weaker constraint of being regular. Answering a question of Cameron, Frankl and Kantor from 1989, we show that the restriction of admitting a transitive automorphism group may be relaxed significantly: we prove that any $3$-wise intersecting family of subsets of $\{1,2,\dots,n\}$ that is regular and increasing has cardinality $o(2^n)$.
Voltage control using eigen value decomposition of fast decoupled load flow Jacobian

Voltage deviations occur frequently in power systems. If the violation at some buses falls outside the prescribed range, it will be necessary to correct the problem by controlling reactive power resources. In this paper, an optimal algorithm is proposed to solve this problem by identifying the voltage buses, that will have a maximum effect on the affected buses, and setting their new set-points. This algorithm is based on the Eigen-Value Decomposition of the fast decoupled load flow Jacobian matrix. Different Case studies including IEEE 9, 14, 30 and 57 bus systems have been used to verify the method.
Matrix weighted Triebel-Lizorkin bounds: A simple stopping time proof

In this paper we will give a simple stopping time proof in the $\mathbb{R}^d$ setting of the matrix weighted Triebel-Lizorkin bounds proved by F. Nazarov/S. Treil and A. Volberg, respectively. Furthermore, we provide explicit matrix A${}_p$ characteristic dependence and also discuss some interesting open questions.
On a Basis for the Framed Link Vector Space Spanned by Chord Diagrams

In view of the result of Kontsevich, now often called "the fundamental theorem of Vassiliev theory", identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the "4T-relation" (and in the unframed case, originally considered by Vassiliev, the "1T-" or "isolated chord relation"), it is a problem of some interest to provide a basis for the space of chord diagrams modulo the 4T-relation. We construct the basis for the vector space spanned by chord diagrams with n chords and m link components, modulo 4T relations for n ≤ 5.
Asynchronous Adaptation and Learning Over Networks—Part II: Performance Analysis

In Part I of this paper, also in this issue, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We performed a stability analysis and established the notable fact that the network is still able to converge in the mean-square-error sense to the desired solution. Once stable behavior is guaranteed, it becomes important to evaluate how fast the iterates converge and how close they get to the optimal solution. This is a demanding task due to the various asynchronous events and due to the fact that agents influence each other. In this Part II, we carry out a detailed analysis of the mean-square-error performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We derive analytical expressions for the mean-square convergence rate and the steady-state mean-square-deviation. The expressions reveal how the various parameters of the asynchronous behavior influence network performance. In the process, we establish the interesting conclusion that even under the influence of asynchronous events, all agents in the adaptive network can still reach an O(ν 1 + γo' ) near-agreement with some γo ' > 0 while approaching the desired solution within O(ν) accuracy, where ν is proportional to the small step-size parameter for adaptation.
On the convergence of a class of Adam-type algorithms for non-convex optimization

This paper studies a class of adaptive gradient based momentum algorithms that update the search directions and learning rates simultaneously using past gradients. This class, which we refer to as the "Adam-type", includes the popular algorithms such as the Adam, AMSGrad and AdaGrad. Despite their popularity in training deep neural networks, the convergence of these algorithms for solving nonconvex problems remains an open question. This paper provides a set of mild sufficient conditions that guarantee the convergence for the Adam-type methods. We prove that under our derived conditions, these methods can achieve the convergence rate of order $O(\log{T}/\sqrt{T})$ for nonconvex stochastic optimization. We show the conditions are essential in the sense that violating them may make the algorithm diverge. Moreover, we propose and analyze a class of (deterministic) incremental adaptive gradient algorithms, which has the same $O(\log{T}/\sqrt{T})$ convergence rate. Our study could also be extended to a broader class of adaptive gradient methods in machine learning and optimization.
Weighted Tensor Decomposition for Learning Latent Variables with Partial Data

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always observed---common in applied settings, where not all measurements may be taken for all observations---resulting in moment estimates of varying quality. We derive a weighted tensor decomposition approach that is computationally as efficient as the non-weighted approach, and demonstrate that it outperforms methods that do not appropriately leverage these less-observed dimensions.
Generalized pseudolikelihood methods for inverse covariance estimation

Author(s): Ali, A; Khare, K; Oh, SY; Rajaratnam, B | Editor(s): Singh, Aarti; Zhu, Xiaojin Jerry | Abstract: Copyright 2017 by the author(s). We introduce PseudoNet, a new pseudolikelihood-based estimator of the inverse covariance matrix, that has a number of useful statistical and computational properties. We show, through detailed experiments with synthetic as well as real-world finance and wind power data, that PseudoNet outperforms related methods in terms of estimation error and support recovery, making it well-suited for use in a downstream application, where obtaining low estimation error can be important. We also show, under regularity conditions, that PseudoNet is consistent. Our proof assumes the existence of accurate estimates of the diagonal entries of the underlying inverse covariance matrix; we additionally provide a two-step method to obtain these estimates, even in a high-dimensional setting, going beyond the proofs for related methods. Unlike other pseudolikelihood-based methods, we also show that PseudoNet does not saturate, i.e., in high dimensions, there is no hard limit on the number of nonzero entries in the PseudoNet estimate. We present a fast algorithm as well as screening rules that make computing the PseudoNet estimate over a range of tuning parameters tractable.
Transformations of matrix structures work again

Abstract Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering, and Signal and Image Processing. These four matrix classes have distinct features, but in our 1990 paper in Mathematics of Computation we showed that Vandermonde and Hankel multipliers can be applied to transform each class into the others, and then we demonstrated how by using these transforms we can readily extend any successful matrix inversion algorithm from one of these classes to all the others. The power of this approach was widely recognized later, when novel numerically stable algorithms solved nonsingular Toeplitz linear systems of equations in quadratic (versus classical cubic) arithmetic time based on transforming Toeplitz into Cauchy matrix structures. More recent papers combined the same transformation with a link of the Cauchy matrices to the Hierarchical Semiseparable matrix structure, which is a specialization of matrix representations employed by the Fast Multipole Method. This produced numerically stable algorithms that approximated the solution of a nonsingular Toeplitz linear system of equations in nearly linear arithmetic time. We first revisit the successful method of structure transformation, covering it comprehensively. Then we analyze the latter approximation algorithms for Toeplitz linear systems and extend them to approximate multiplication of Vandermonde and Cauchy matrices by a vector and to approximate solution of Vandermonde and Cauchy linear systems of equations provided that they are nonsingular and well-conditioned. We decrease the arithmetic cost of the known numerical approximation algorithms for these tasks from quadratic to nearly linear, and similarly for the computations with the matrices having structures that generalize the structures of Vandermonde and Cauchy matrices and for polynomial and rational evaluation and interpolation. We also accelerate a little further the known numerical approximation algorithms for a nonsingular Toeplitz or Toeplitz-like linear system by employing distinct transformations of matrix structures, and we briefly comment on some natural research challenges, particularly some promising applications of our techniques to high precision computations.
The mass of quasars

I review the current status of quasar black hole (BH) mass estimations. Spectroscopic methods have been developed to estimate BH mass in broad line quasars to an accuracy of ~0.5 dex. Despite their popularity, significant issues and confusion remain regarding these mass estimators. I provide an in-depth discussion on the merits and caveats of the single-epoch (SE) virial BH mass estimators, and a detailed derivation of the statistical biases of these SE mass estimates resulting from their errors. I show that error-induced sample biases on the order of a factor of several are likely present in the SE mass estimates for flux-limited, statistical quasar samples, and the distribution of SE masses in finite luminosity bins can be narrower than the nominal uncertainty of these mass estimates. I then discuss the latest applications of SE virial masses in quasar studies, including the early growth of supermassive black holes, quasar demography in the mass-luminosity plane, and the evolution of the BH-host scaling relations, with specific emphases on selection effects and sample biases in the SE masses. I conclude that there is a pressing need to understand and deal with the errors in these BH mass estimates, and to improve these BH weighing methods with substantially more and better reverberation mapping data.
On the capacity of memoryless adversary

In this paper, we study a model of communication under adversarial noise. In this model, the adversary makes online decisions on whether to corrupt a transmitted bit based on only the value of that bit. Like the usual binary symmetric channel of information theory or the fully adversarial channel of combinatorial coding theory, the adversary can, with high probability, introduce at most a given fraction of error. It is shown that, the capacity (maximum rate of reliable information transfer) of such memoryless adversary is strictly below that of the binary symmetric channel. We give new upper bound on the capacity of such channel – the tightness of this upper bound remains an open question. The main component of our proof is the careful examination of error-correcting properties of a code with skewed distance distribution.
Learning to Decompose and Disentangle Representations for Video Prediction

Our goal is to predict future video frames given a sequence of input frames. Despite large amounts of video data, this remains a challenging task because of the high-dimensionality of video frames. We address this challenge by proposing the Decompositional Disentangled Predictive Auto-Encoder (DDPAE), a framework that combines structured probabilistic models and deep networks to automatically (i) decompose the high-dimensional video that we aim to predict into components, and (ii) disentangle each component to have low-dimensional temporal dynamics that are easier to predict. Crucially, with an appropriately specified generative model of video frames, our DDPAE is able to learn both the latent decomposition and disentanglement without explicit supervision. For the Moving MNIST dataset, we show that DDPAE is able to recover the underlying components (individual digits) and disentanglement (appearance and location) as we would intuitively do. We further demonstrate that DDPAE can be applied to the Bouncing Balls dataset involving complex interactions between multiple objects to predict the video frame directly from the pixels and recover physical states without explicit supervision.
A Dynamic Power Management Schema for Multi-tier Data Centers

Data centers play an important role in the operation and management of IT infrastructures but because of their huge power consumption it raises issue of great concern as it relates to global warming. This paper explores the sleep state of data centers’ servers under specific conditions such as setup time and identifies an optimal number of servers potentially to increase energy efficiency. We use a Dynamic Power Management policy based model with the optimal number of servers that is required in each tier while increasing servers’ setup time after sleep mode. The Reactive approach is used to validate the results and energy efficiency by calculating the average power consumption of each server under specific sleep mode and setup time. Our method uses average power consumption to calculate the Normalized- Performance-Per-Watt in order to evaluate the power efficiency. The results indicate that the schema reported in this paper can improve power efficiency in data centers with high setup time servers.
Quadratic nonresidues below the Burgess bound

For any odd prime number p, let (⋅|p) be the Legendre symbol, and let n1(p) 0. In this paper, we prove that the stronger bound nk(p) ≪ p(4e)−1exp(e−1 log plog log p) holds for all odd primes p provided that k ≪ p(8e)−1exp 1 2e−1 log plog log p −1 2loglog p, where the implied constants are absolute. For fixed e ∈0, π−2 9π−2, we also show that there is a number c = c(e) > 0 such that for all odd primes p, there are ≫ey/(log y)e natural numbers n ≤ y with (n|p) = −1 provided that y ≥ p(4e)−1exp(c(log p)1−e).
Recurrence and Ergodicity of Switching Diffusions with Past-Dependent Switching Having A Countable State Space

This work focuses on recurrence and ergodicity of switching diffusions consisting of continuous and discrete components, in which the discrete component takes values in a countably infinite set and the rates of switching at current time depend on the value of the continuous component over an interval including certain past history. Sufficient conditions for recurrence and ergodicity are given. Moreover, the relationship between systems of partial differential equations and recurrence when the switching is past-independent is established under suitable conditions.
Impact of the Food-Labeling and Advertising Law Banning Competitive Food and Beverages in Chilean Public Schools, 2014–2016

Objectives. To evaluate the impact of a national law banning sales of competitive food and beverages (CF&B) in schools on the availability of CF&B sold at school kiosks.Methods. This study was unco...
Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes

Abstract Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and statistical properties of the multivariate process. In this paper, under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators of bivariate fractal indices. Our main results quantitatively describe the effect of the cross-dependence structure on the performance of the estimators.
Rigged Configurations for all Symmetrizable Types

In an earlier work, the authors developed a rigged configuration model for the crystal $B(\infty)$ (which also descends to a model for irreducible highest weight crystals via a cutting procedure). However, the result obtained was only valid in finite types, affine types, and simply-laced indefinite types. In this paper, we show that the rigged configuration model proposed does indeed hold for all symmetrizable types. As an application, we give an easy combinatorial condition that gives a Littlewood-Richardson rule using rigged configurations which is valid in all symmetrizable Kac-Moody types.
Linkage classes of grade 3 perfect ideals

Abstract While every grade 2 perfect ideal in a regular local ring is linked to a complete intersection ideal, it is known not to be the case for ideals of grade 3. We soften the blow by proving that every grade 3 perfect ideal in a regular local ring is linked to a complete intersection or a Golod ideal. Our proof is indebted to a homological classification of Cohen–Macaulay local rings of codimension 3. That debt is swiftly repaid, as we use linkage to reveal some of the finer structures of this classification.
Weak bounded negativity conjecture

In this paper, we prove the following "Weak Bounded Negativity Conjecture", which says that given a complex smooth projective surface $X$, for any reduced curve $C$ in $X$ and integer $g$, assume that the geometric genus of each component of $C$ is bounded from above by $g$, then the self-intersection number $C^2$ is bounded from below.
The density of primes dividing a term in the Somos-5 sequence

The Somos-5 sequence is defined by $a_{0} = a_{1} = a_{2} = a_{3} = a_{4} = 1$ and $a_{m} = \frac{a_{m-1} a_{m-4} + a_{m-2} a_{m-3}}{a_{m-5}}$ for $m \geq 5$. We relate the arithmetic of the Somos-5 sequence to the elliptic curve $E : y^{2} + xy = x^{3} + x^{2} - 2x$ and use properties of Galois representations attached to $E$ to prove the density of primes $p$ dividing some term in the Somos-5 sequence is equal to $\frac{5087}{10752}$.
Neural Cross-Lingual Entity Linking

A major challenge in Entity Linking (EL) is making effective use of contextual information to disambiguate mentions to Wikipedia that might refer to different entities in different contexts. The problem exacerbates with cross-lingual EL which involves linking mentions written in non-English documents to entries in the English Wikipedia: to compare textual clues across languages we need to compute similarity between textual fragments across languages. In this paper, we propose a neural EL model that trains fine-grained similarities and dissimilarities between the query and candidate document from multiple perspectives, combined with convolution and tensor networks. Further, we show that this English-trained system can be applied, in zero-shot learning, to other languages by making surprisingly effective use of multi-lingual embeddings. The proposed system has strong empirical evidence yielding state-of-the-art results in English as well as cross-lingual: Spanish and Chinese TAC 2015 datasets.
Animal-inspired agile flight using optical flow sensing

There is evidence that flying animals such as pigeons, goshawks, and bats use optical flow sensing to enable high-speed flight through forest clutter. This paper discusses the elements of a theory of controlled flight through obstacle fields in which motion control laws are based on optical flow sensing. Performance comparison is made with feedback laws that use distance and bearing measurements, and practical challenges of implementation on an actual robotic air vehicle are described. The related question of fundamental performance limits due to clutter density is addressed.
Theory of Optical Leaky-Wave Antenna Integrated in a Ring Resonator for Radiation Control

The integration of a leaky-wave antenna with a ring resonator is presented based on the leaky-wave theory and integrated waveguide models. The device consists of a ring resonator fed by a directional coupler, where the ring resonator path includes a segment that is turned into a leaky-wave antenna. We devise an analytical model of the guided wave propagation along a directional coupler and the ring resonator path, including the antenna and non-radiating segments. The resonator integration provides two main advantages: 1) the high-quality factor resonance ensures effective control of radiation intensity by controlling the resonance conditions and 2) the efficient radiation from a leaky-wave antenna even when its length is much smaller than the propagation length of the leaky wave. The tradeoffs regarding the quality factor of resonance and the antenna efficiency of such a design are reported in terms of the coupler parameters, leaky-wave constant, and radiation length. Finally, a CMOS-compatible OLWA suitable for the ring resonator integration is designed where silicon is utilized as the waveguide material for a possible electronic control of radiation intensity. The simulation results together with the analytical model show that slight variations in the leaky wave's propagation constant, realized through excitation of excess carriers in the Si domain, is sufficient to control the far-field radiation modulation with high extinction ratio.
Communication Model–Task Pairing in Artificial Swarm Design

Unraveling the nature of the communication model that governs which two individuals in a swarm interact with each other is an important line of inquiry in the collective behavior sciences. A number of models have been proposed in the biological swarm literature, with the leading models being the metric, topological, and visual models. The hypothesis evaluated in this letter is whether the choice of a communication model impacts the performance of a tasked artificial swarm. The biological models are used to design coordination algorithms for a simulated swarm, which are evaluated over a range of six swarm robotics tasks. Each task has an associated set of performance metrics that are used to evaluate how the communication models fare against each other. The general findings demonstrate that the communication model significantly affects the swarm's performance for individual tasks, and this result implies that the communication model–task pairing is an important consideration when designing artificial swarms. Further analysis of each tasks’ performance metrics reveals instances in which pairwise considerations of model and one of the various experimental factors become relevant. The reported research demonstrates that the artificial swarm's task performance can be increased through the careful selection of a communication model.
Epidemic spread in human networks

One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the Susceptible-Infected-Susceptible (SIS) model has been widely used. In the SIS model, each node can be susceptible, become infected with a given infection rate, and become again susceptible with a given curing rate. In this paper, we add a new compartment to the classic SIS model to account for human response to epidemic spread. In our model, each individual can be infected, susceptible, or alert. Susceptible individuals can become alert with an alerting rate if infected individuals exist in their neighborhood. Due to a newly adopted cautious behavior, an individual in the alert state is less probable to become infected. The problem is modeled as a continuous-time Markov process on a generic graph and then formulated as a set of ordinary differential equations. The model is then studied using results from spectral graph theory and center manifold theorem. We analytically show that our model exhibits two distinct thresholds in the dynamics of epidemic spread. Below the first threshold, infection dies out exponentially. Beyond the second threshold, infection persists in the steady state. Between the two thresholds, infection spreads at the first stage but then dies out asymptotically as the result of increased alertness in the network. Finally, simulations are provided to support our findings.
A Unified Analytical Framework for Trustable Machine Learning and Automation Running with Blockchain

Traditional machine learning algorithms use data from databases that are mutable, and therefore the data cannot be fully trusted. Also, the machine learning process is difficult to automate. This paper proposes building a trustable machine learning system by using blockchain technology, which can store data in a permanent and immutable way. In addition, smart contracts are used to automate the machine learning process. This paper makes three contributions. First, it establishes a link between machine learning technology and blockchain technology. Previously, machine learning and blockchain have been considered two independent technologies without an obvious link. Second, it proposes a unified analytical framework for trustable machine learning by using blockchain technology. This unified framework solves both the trustability and automation issues in machine learning. Third, it enables a computer to translate core machine learning implementation from a single thread on a single machine to multiple threads on multiple machines running with blockchain by using a unified approach. The paper uses association rule mining as an example to demonstrate how trustable machine learning can be implemented with blockchain, and it shows how this approach can be used to analyze opioid prescriptions to help combat the opioid crisis.
Modified Mixed Realizations, New Additive Invariants, and Periods of DG Categories

To every scheme, not necessarily smooth neither proper, we can associate its different mixed realizations (de Rham, Betti, etale, Hodge, etc) as well as its ring of periods. In this note, following an insight of Kontsevich, we prove that, after suitable modifications, these classical constructions can be extended from schemes to the broad setting of dg categories. This leads to new additive invariants, which we compute in the case of differential operators, as well as to a theory of periods of dg categories. Among other applications, we prove that the ring of periods of a scheme is invariant under projective homological duality. Along the way, we explicitly describe the modified mixed realizations using the Tannakian formalism.
A review of dielectric optical metasurfaces for wavefront control

During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here, we review some of these recent developments, with a focus on dielectric structures for shaping optical wavefronts. We discuss the mechanisms for achieving steep phase gradients with high efficiency, simultaneous polarization and phase control, controlling the chromatic dispersion, and controlling the angular response. Then, we review applications in imaging, conformal optics, tunable devices, and optical systems. We conclude with an outlook on future potentials and challenges that need to be overcome.
Refining Enumeration Schemes to Count According to Permutation Statistics

We develop algorithmic tools to compute quickly the distribution of permutation statistics over sets of pattern-avoiding permutations. More specfically, the algorithms are based on enumeration schemes, the permutation statistics are based on the number of occurrences of certain vincular patterns, and the permutations avoid sets of vincular patterns. We prove that whenever a finite enumeration scheme exists to count the number of pattern-avoiding permutations, then the distribution of statistics like the number of descents can also be computed based on the same scheme. Statistics such as the number of peaks, right-to-left maxima, and the major index are also investigated, as well as multi-statistics.
Compositions colored by simplicial polytopic numbers

For a given integer $d\ge 1$, we consider $\binom{n+d-1}{d}$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $\binom{n+d-1}{d}$ colors. We give explicit formulas for the enumeration of such compositions, generalizing existing results for $n$-color compositions (case $d=1$) and $\binom{n+1}{2}$-color compositions (case $d=2$). In addition, we give bijections from the set of $\binom{n+d-1}{d}$-color compositions of $\nu$ to the set of compositions of $(d+1)\nu - 1$ having only parts of size $1$ and $d+1$, the set of compositions of $(d+1)\nu$ having only parts of size congruent to $1$ modulo $d+1$, and the set of compositions of $(d+1)\nu + d$ having no parts of size less than $d+1$. Our results rely on basic properties of partial Bell polynomials and on a suitable adaptation of known bijections for $n$-color compositions.
Linear Codes, Target Function Classes, and Network Computing Capacity

We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, semi-injective, and linear target functions over finite fields. Computing capacity bounds and achievability are given with respect to these target function classes for network codes that use routing, linear coding, or nonlinear coding.
Playing anonymous games using simple strategies

We investigate the complexity of computing approximate Nash equilibria in anonymous games. Our main algorithmic result is the following: For any n-player anonymous game with a bounded number of strategies and any constant δ > 0, an O(1/n1−δ)-approximate Nash equilibrium can be computed in polynomial time. Complementing this positive result, we show that if there exists any constant δ > 0 such that an O(1/n1+δ)-approximate equilibrium can be computed in polynomial time, then there is a fully polynomial-time approximation scheme (FPTAS) for this problem.We also present a faster algorithm that, for any n-player k-strategy anonymous game, runs in time O((n + k)knk) and computes an O(n−1/3k11/3)-approximate equilibrium. This algorithm follows from the existence of simple approximate equilibria of anonymous games, where each player plays one strategy with probability 1 − δ, for some small δ, and plays uniformly at random with probability δ.Our approach exploits the connection between Nash equilibria in anonymous games and Poisson multinomial distributions (PMDs). Specifically, we prove a new probabilistic lemma establishing the following: Two PMDs, with large variance in each direction, whose first few moments are approximately matching are close in total variation distance. Our structural result strengthens previous work by providing a smooth tradeoff between the variance bound and the number of matching moments.
Interactive Channel Capacity Revisited

We provide the first capacity approaching coding schemes that robustly simulate any interactive protocol over an adversarial channel that corrupts any eps fraction of the transmitted symbols. Our coding schemes achieve a communication rate of 1 -- O(a#x221A;aepsi; log log 1/aepsi;) over any adversarial channel. This can be improved to 1 -- O(a#x221A;aepsi;) for random, oblivious, and computationally bounded channels, or if parties have shared randomness unknown to the channel. Surprisingly, these rates exceed the 1 -- a#x03A9;(a#x221A;H(aepsi;)) = 1 -- a#x03A9;(a#x221A;aepsi; log 1/aepsi;) interactive channel capacity bound which [Kol and Raz, STOC'13] recently proved for random errors. We conjecture 1 -- a#x0398;(a#x221A;aepsi; log log 1/aepsi;) and 1 -- a#x0398;(a#x221A;aepsi;) to be the optimal rates for their respective settings and therefore to capture the interactive channel capacity for random and adversarial errors. In addition to being very communication efficient, our randomized coding schemes have multiple other advantages. They are computationally efficient, extremely natural, and significantly simpler than prior (non-capacity approaching) schemes. In particular, our protocols do not employ any coding but allow the original protocol to be performed as-is, interspersed only by short exchanges of hash values. When hash values do not match, the parties backtrack. Our approach is, as we feel, by far the simplest and most natural explanation for why and how robust interactive communication in a noisy environment is possible.
Stretching Convex Domains to Capture Many Lattice Points

We consider an optimal stretching problem for strictly convex domains in $\mathbb{R}^d$ that are symmetric with respect to each coordinate hyperplane, where stretching refers to transformation by a diagonal matrix of determinant 1. Specifically, we prove that the stretched convex domain which captures the most positive lattice points in the large volume limit is balanced: the (d − 1)-dimensional measures of the intersections of the domain with each coordinate hyperplane are equal. Our results extend those of Antunes and Freitas, van den Berg, Bucur and Gittins, Ariturk and Laugesen, van den Berg and Gittins, and Gittins and Larson. The approach is motivated by the Fourier analysis techniques used to prove the classical $\#\{(i,j) \in \mathbb{Z}^2 : i^2 +j^2 \le r^2 \} =\pi r^2 + \mathcal{O}(r^{2/3})$ result for the Gauss circle problem.
AutoPrognosis: Automated Clinical Prognostic Modeling via Bayesian Optimization with Structured Kernel Learning

Clinical prognostic models derived from largescale healthcare data can inform critical diagnostic and therapeutic decisions. To enable off-theshelf usage of machine learning (ML) in prognostic research, we developed AUTOPROGNOSIS: a system for automating the design of predictive modeling pipelines tailored for clinical prognosis. AUTOPROGNOSIS optimizes ensembles of pipeline configurations efficiently using a novel batched Bayesian optimization (BO) algorithm that learns a low-dimensional decomposition of the pipelines high-dimensional hyperparameter space in concurrence with the BO procedure. This is achieved by modeling the pipelines performances as a black-box function with a Gaussian process prior, and modeling the similarities between the pipelines baseline algorithms via a sparse additive kernel with a Dirichlet prior. Meta-learning is used to warmstart BO with external data from similar patient cohorts by calibrating the priors using an algorithm that mimics the empirical Bayes method. The system automatically explains its predictions by presenting the clinicians with logical association rules that link patients features to predicted risk strata. We demonstrate the utility of AUTOPROGNOSIS using 10 major patient cohorts representing various aspects of cardiovascular patient care.
Multipodal Structure and Phase Transitions in Large Constrained Graphs

We study the asymptotics of large, simple, labeled graphs constrained by the densities of two subgraphs. It was recently conjectured that for all feasible values of the densities most such graphs have a simple structure. Here we prove this in the special case where the densities are those of edges and of k-star subgraphs, $$k\ge 2$$ fixed. We prove that under such constraints graphs are “multipodal”: asymptotically in the number of vertices there is a partition of the vertices into $$M < \infty $$ subsets $$V_1, V_2, \ldots , V_M$$ , and a set of well-defined probabilities $$g_{ij}$$ of an edge between any $$v_i \in V_i$$ and $$v_j \in V_j$$ . For $$2\le k\le 30$$ we determine the phase space: the combinations of edge and k-star densities achievable asymptotically. For these models there are special points on the boundary of the phase space with nonunique asymptotic (graphon) structure; for the 2-star model we prove that the nonuniqueness extends to entropy maximizers in the interior of the phase space.
Multiple Instance Curriculum Learning for Weakly Supervised Object Detection.

When supervising an object detector with weakly labeled data, most existing approaches are prone to trapping in the discriminative object parts, e.g., finding the face of a cat instead of the full body, due to lacking the supervision on the extent of full objects. To address this challenge, we incorporate object segmentation into the detector training, which guides the model to correctly localize the full objects. We propose the multiple instance curriculum learning (MICL) method, which injects curriculum learning (CL) into the multiple instance learning (MIL) framework. The MICL method starts by automatically picking the easy training examples, where the extent of the segmentation masks agree with detection bounding boxes. The training set is gradually expanded to include harder examples to train strong detectors that handle complex images. The proposed MICL method with segmentation in the loop outperforms the state-of-the-art weakly supervised object detectors by a substantial margin on the PASCAL VOC datasets.
Spatiotemporal Dynamics of Synthetic Microbial Consortia in Microfluidic Devices

Synthetic microbial consortia consist of two or more engineered strains that grow together and share the same resources. When intercellular signaling pathways are included in the engineered strains, close proximity of the microbes can generate complex dynamic behaviors that are difficult to obtain using a single strain. However, when a consortium is not cultured in a well-mixed environment the constituent strains passively compete for space as they grow and divide, complicating cell-cell signaling. Here, we explore the temporal dynamics of the spatial distribution of consortia cocultured in microfluidic devices. To do this, we grew two different strains of Escherichia coli in microfluidic devices with cell-trapping regions (traps) of several different designs. We found that the size of the traps is a critical determinant of spatiotemporal dynamics. In small traps, cells can easily signal one another, but the relative proportion of each strain within the trap can fluctuate wildly. In large traps, the relative ratio of strains is stabilized, but intercellular signaling can be hindered by distances between cells. This presents a trade-off between the trap size and the effectiveness of intercellular signaling, which can be mitigated by increasing the initial seeding of cells in larger traps. We also built a mathematical model, which suggests that increasing the number of seed cells can also increase the strain ratio variability due to an increased number of strain interfaces in the trap. These results help elucidate the complex behaviors of synthetic microbial consortia in microfluidic traps and provide a means of analysis to help remedy the spatial heterogeneity inherent to different trap types.
Mouth Function Determines the Shape Oscillation Pattern in Regenerating Hydra Tissue Spheres

Hydra is a small freshwater polyp capable of regeneration from small tissue pieces and from aggregates of cells. During regeneration, a hollow bilayered sphere is formed that undergoes osmotically driven shape oscillations of inflation and rupture. These oscillations are necessary for successful regeneration. Eventually, the oscillating sphere breaks rotational symmetry along the future head-foot axis of the animal. Notably, the shape oscillations show an abrupt shift from large-amplitude, long-period oscillations to small-amplitude, short-period oscillations. It has been widely accepted that this shift in oscillation pattern is linked to symmetry breaking and axis formation, and current theoretical models of Hydra symmetry breaking use this assumption as a model constraint. However, a mechanistic explanation for the shift in oscillation pattern is lacking. Using in vivo manipulation and imaging, we quantified the shape oscillation dynamics and dissected the timing and triggers of the pattern shift. Our experiments demonstrate that the shift in the shape oscillation pattern in regenerating Hydra tissue pieces is caused by the formation of a functional mouth and not by shape symmetry breaking as previously assumed. Thus, model assumptions must be revised in light of these new experimental data, which can be used to constrain and validate improved theoretical models of pattern formation in Hydra.
Modeling and Cost Benefit Analysis to Guide Deployment of POC Diagnostics for Non-typhoidal Salmonella Infections with Antimicrobial Resistance

Invasive non-typhoidal Salmonella (NTS) is among the leading causes of blood stream infections in sub-Saharan Africa and other developing regions, especially among pediatric populations. Invasive NTS can be difficult to treat and have high case-fatality rates, in part due to emergence of strains resistant to broad-spectrum antibiotics. Furthermore, improper treatment contributes to increased antibiotic resistance and death. Point of care (POC) diagnostic tests that rapidly identify invasive NTS infection, and differentiate between resistant and non-resistant strains, may greatly improve patient outcomes and decrease resistance at the community level. Here we present for the first time a model for NTS dynamics in high risk populations that can analyze the potential advantages and disadvantages of four strategies involving POC diagnostic deployment, and the resulting impact on antimicrobial treatment for patients. Our analysis strongly supports the use of POC diagnostics coupled with targeted antibiotic use for patients upon arrival in the clinic for optimal patient and public health outcomes. We show that even the use of imperfect POC diagnostics can significantly reduce total costs and number of deaths, provided that the diagnostic gives results quickly enough that patients are likely to return or stay to receive targeted treatment.
The Effects of Foreign Multinationals on Workers and Firms in the United States

Governments go to great lengths to attract foreign multinationals because they are thought to raise the wages paid to their employees (direct effects) and to improve outcomes at local domestic firms (indirect effects). We construct the first U.S. employer-employee dataset with foreign ownership information from tax records to measure these direct and indirect effects. We find the average direct effect of a foreign multinational firm on its U.S. workers is a 7 percent increase in wages. This premium is larger for higher skilled workers and for the employees of firms from high GDP per capita countries. We find evidence that it is membership in a multinational production network—instead of foreignness—that generates the foreign firm premium. We leverage the past spatial clustering of foreign-owned firms by country of ownership to identify the indirect effects. An expansion in the foreign multinational share of commuting zone employment substantially increases the employment, value added, and—for higher earning workers—wages at local domestic-owned firms. Per job created by a foreign multinational, our estimates suggest annual gains of 16,000 USD to the aggregate wages of local incumbents, of which about two-thirds is due to indirect effects. Our estimates suggest that—via mega-deals for subsidies from local governments—foreign multinationals are able to extract a sizable fraction of the local surplus they generate.
A robust health equity metric

Abstract Objectives Progress on health equity will require a robust metric. The aim of this article is to propose a new health equity metric that is distinct from existing measures and that allows meaningful comparisons across time and place, is calculable using health data typically available, and measures health equity across all major forms of social exclusion. Study design A cross-sectional study. Methods The new health equity measure was calculated using data included from all 50 states and the District of Columbia in the 2017 Behavioral Risk Factor Surveillance Survey, collected by the US Centers for Disease Control and Prevention. The total sample size was 287,602. State-specific sample sizes ranged from 2269 (Alaska) to 14,685 (Kansas) with a median of 4452. A Healthy Days measure was calculated as the mean number of days that the respondents reported being physically healthy and mentally healthy out of the previous 30 days. The proposed measure defines individual health disutility as the distastefulness associated with one's health falling short of optimal achievable health, instrumentalized as the median health of the most socially privileged category, that of upper-income white men. The value of the health equity metric in a population is the mean value of this distastefulness over the entire population and has a theoretical range of -∞ to 1. Results There is substantial variation across states (mean: 0.13; standard deviation: 0.15), with the District of Columbia (0.48), Minnesota (0.37), and Connecticut (0.30) showing the greatest health equity, and West Virginia (−0.26), Arkansas (−0.18), and Kentucky (−0.13) exhibiting the least. Across states, the value of the health equity metric is not correlated with the size of black-white health disparities. Conclusions It is feasible to use a single health equity metric for consistent and objective measurement of health equity. Doing so may facilitate more rapid progress toward health equity.