cssi/SciSciGPT-SciSciNet huggingface dataset:
Adaptive Pilot Patterns for CA-OFDM Systems in Nonstationary Wireless Channels

In this paper, we investigate the performance gains of adapting pilot spacing and power for carrier aggregation orthogonal frequency-division multiplexing (CA-OFDM) systems in nonstationary wireless channels. In current multiband CA-OFDM wireless networks, all component carriers use the same pilot density, which is designed for poor channel environments. This leads to unnecessary pilot overhead in good channel conditions and performance degradation in the worst channel conditions. We propose adaptation of pilot spacing and power using a codebook-based approach, where the transmitter and the receiver exchange information about the fading characteristics of the channel over a short period of time, which are stored as entries in a channel profile codebook. We present a heuristic algorithm that maximizes the achievable rate by finding the optimal pilot spacing and power from a set of candidate pilot configurations. We also analyze the computational complexity of our proposed algorithm and the feedback overhead. We describe methods to minimize the computation and feedback requirements for our algorithm in multiband CA scenarios and present simulation results in typical terrestrial and air-to-ground/air-to-air nonstationary channels. Our results show that significant performance gains can be achieved when adopting adaptive pilot spacing and power allocation in nonstationary channels. We also discuss important practical considerations and provide guidelines to implement adaptive pilot spacing in CA-OFDM systems.
A primal-dual convergence analysis of boosting

Boosting combines weak learners into a predictor with low empirical risk. Its dual constructs a high entropy distribution upon which weak learners and training labels are uncorrelated. This manuscript studies this primal-dual relationship under a broad family of losses, including the exponential loss of AdaBoost and the logistic loss, revealing: • Weak learnability aids the whole loss family: for any e > 0, O(ln(1/e)) iterations suffice to produce a predictor with empirical risk e-close to the infimum; • The circumstances granting the existence of an empirical risk minimizer may be characterized in terms of the primal and dual problems, yielding a new proof of the known rate O(ln(1/e)); • Arbitrary instances may be decomposed into the above two, granting rate O(1/e), with a matching lower bound provided for the logistic loss.
A parameterized activation function for learning fuzzy logic operations in deep neural networks

We present a deep learning architecture for learning fuzzy logic expressions. Our model uses an innovative, parameterized, differentiable activation function that can learn a number of logical operations by gradient descent. This activation function allows a neural network to determine the relationships between its input variables and provides insight into the logical significance of learned network parameters. We provide a theoretical basis for this parameterization and demonstrate its effectiveness and utility by successfully applying our model to five classification problems from the UCI Machine Learning Repository.
ISTRICT: An Interdependent Strategic Trust Mechanism for the Cloud-Enabled Internet of Controlled Things

The cloud-enabled Internet of controlled things (IoCT) envisions a network of sensors, controllers, and actuators connected through a local cloud in order to intelligently control physical devices. Because cloud services are vulnerable to advanced persistent threats (APTs), each device in the IoCT must strategically decide whether to trust cloud services that may be compromised. In this paper, we present iSTRICT, an interdependent strategic trust mechanism for the cloud-enabled IoCT. iSTRICT is composed of three interdependent layers. In the cloud layer, iSTRICT uses FlipIt games to conceptualize APTs. In the communication layer, it captures the interaction between devices and the cloud using signaling games. In the physical layer, iSTRICT uses optimal control to quantify the utilities in the higher level games. Best response dynamics link the three layers in an overall “game-of-games,” for which the outcome is captured by a concept called Gestalt Nash equilibrium (GNE). We prove the existence of a GNE under a set of natural assumptions and develop an adaptive algorithm to iteratively compute the equilibrium. Finally, we apply iSTRICT to trust management for autonomous vehicles that rely on measurements from remote sources. We show that strategic trust in the communication layer achieves a worst-case probability of compromise for any attack and defense costs in the cyber layer.
A note on exact forms on almost complex manifolds

Reformulations of Donaldson’s “tamed to compatible” question are obtained in terms of spaces of exact forms on a compact almost complex manifold (M, J). In dimension 4, we show that J admits a compatible symplectic form if and only if J admits tamed symplectic forms with arbitrarily given J-anti-invariant parts. Some observations about the cohomology of J-modified de Rham complexes are also made.
A function approximation approach to estimation of policy gradient for POMDP with structured policies

We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that does not depend on the states of POMDP. This function is the conditional mean of the true value function that depends on the states. We show that the critic can be implemented using temporal difference (TD) methods with linear function approximations, and the analytical results on TD and Actor-Critic can be transfered to this case. Although Actor-Critic algorithms have been used extensively in Markov decision processes (MDP), up to now they have not been proposed for POMDP as an alternative to the earlier proposal GPOMDP algorithm, an actor-only method. Furthermore, we show that the same idea applies to semi-Markov problems with a subset of finite-state controllers.
Combinatorial Topic Models using Small-Variance Asymptotics

Topic models have emerged as fundamental tools in unsupervised machine learning. Most modern topic modeling algorithms take a probabilistic view and derive inference algorithms based on Latent Dirichlet Allocation (LDA) or its variants. In contrast, we study topic modeling as a combinatorial optimization problem, and propose a new objective function derived from LDA by passing to the small-variance limit. We minimize the derived objective by using ideas from combinatorial optimization, which results in a new, fast, and high-quality topic modeling algorithm. In particular, we show that our results are competitive with popular LDA-based topic modeling approaches, and also discuss the (dis)similarities between our approach and its probabilistic counterparts.
A doubly associated reference perturbation theory for water

Abstract In this work we develop a new classical perturbation theory for water which incorporates the transition to tetrahedral symmetry in both the dispersion and hydrogen bonding contributions to the free energy. This transition is calculated self-consistently using Wertheim's thermodynamic perturbation theory. However, since the reference fluid structure to the hydrogen bonding theory itself depends on hydrogen bonding, the theory represents an approach which goes beyond perturbation theory. The theory is shown to accurately represent the thermodynamics of pure water. It is demonstrated that the new theory can reproduce the anomalous density maximum as well as minima in the isothermal compressibility and isobaric heat capacity.
Topology of multiple log transforms of 4-manifolds

Given a 4-manifold X and an imbedding T2 × B2 ⊂ X, we describe an algorithm X ↦ Xp,q for drawing the handlebody of the 4-manifold obtained from X by (p, q)-logarithmic transforms along the parallel tori. By using this algorithm for relatively prime (p, q), we obtain a simple handle picture of the Dolgachev surface E(1)p,q, from that we deduce that the exotic copy of differs from the original one by a codimension zero simply connected Stein submanifold Mp,q. This gives examples of infinitely many small Stein manifolds which are exotic copies of each other (rel boundaries). Also by using the description of S2 × S2 as a union of two cusps glued along their boundaries, and by using this algorithm, we show that a pair of log transforms along the tori in these cusps gives back S2 × S2 or .
Phase-Based Alignment and Improved Projection Matching of Parallel Beam Tomography Data

Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of the data values, i.e., the relationship between the data values and the paths of the lines of integration is accurately known. In many applications, e.g., electron and X-ray tomography, it is necessary to establish this relationship using software alignment techniques or image registration due to misalignment when rotating the physical specimen. Unfortunately, highly accurate software alignment is still a challenge to achieve in many cases, and improper alignment results in severe loss in the imaging resolution. In this paper, we develop a new approach that considers the alignment problem through a completely different lens, as a problem of recovering phase shifts in Fourier domain within the reconstruction algorithm. The recovery of these phase shifts serves as the data alignment, which is done by calculating discrepancies between the misaligned data and the current reconstruction. In the development of the approach, we investigate proper selection of parameters, and we show that it is fairly flexible and surprisingly accurate. Finally, the analysis of our approach provides insight into why projection matching alignment by cross correlation can be improved through low pass filtering, which we demonstrate. Our methods are validated in a wide range of examples and settings.
Optimal Control With Noisy Time

This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing Levy process. We provide dynamic programming results for continuous-time finite-horizon control and specialize these results to solve a noisy-time variant of the linear quadratic regulator problem and a portfolio optimization problem with random trade activity rates. For the linear quadratic case, the optimal controller is linear and can be computed from a generalization of the classical Riccati differential equation.
The structure of signals: causal interdependence models for games of incomplete information

Traditional economic models typically treat private information, or signals, as generated from some underlying state. Recent work has explicated alternative models, where signals correspond to interpretations of available information. We show that the difference between these formulations can be sharply cast in terms of causal dependence structure, and employ graphical models to illustrate the distinguishing characteristics. The graphical representation supports inferences about signal patterns in the interpreted framework, and suggests how results based on the generated model can be extended to more general situations. Specific insights about bidding games in classical auction mechanisms derive from qualitative graphical models.
Generalized geometric programming for rate allocation in consensus

Distributed averaging, or distributed average consensus, is a common method for computing the sample mean of the data dispersed among the nodes of a network in a decentralized manner. By iteratively exchanging messages with neighbors, the nodes of the network can converge to an agreement on the sample mean of their initial states. In real-world scenarios, these messages are subject to bandwidth and power constraints, which motivates the design of a lossy compression strategy. Few prior works consider the rate allocation problem from the perspective of constrained optimization, which provides a principled method for the design of lossy compression schemes, allows for the relaxation of certain assumptions, and offers performance guarantees. We show for Gaussian-distributed initial states with entropy-coded scalar quantization and vector quantization that the coding rates for distributed averaging can be optimized through generalized geometric programming. In the absence of side information from past states, this approach finds a rate allocation over nodes and iterations that minimizes the aggregate coding rate required to achieve a target mean square error within a finite run time. Our rate allocation is compared to some of the prior art through numerical simulations. The results motivate the incorporation of side-information through differential or predictive coding to improve rate-distortion performance.
Understanding autoencoders with information theoretic concepts.

Abstract Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the dynamics of learning and the design of autoencoders, a special type of deep learning architectures that resembles a communication channel. By generalizing the information plane to any cost function, and inspecting the roles and dynamics of different layers using layer-wise information quantities, we emphasize the role that mutual information plays in quantifying learning from data. We further suggest and also experimentally validate, for mean square error training, three fundamental properties regarding the layer-wise flow of information and intrinsic dimensionality of the bottleneck layer, using respectively the data processing inequality and the identification of a bifurcation point in the information plane that is controlled by the given data. Our observations have direct impact on the optimal design of autoencoders, the design of alternative feedforward training methods, and even in the problem of generalization.
Tree-structured composition in neural networks without tree-structured architectures

Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models like LSTMs are in fact able to discover and implicitly use recursive compositional structure, at least for tasks with clear cues to that structure in the data. We demonstrate this possibility using an artificial data task for which recursive compositional structure is crucial, and find an LSTM-based sequence model can indeed learn to exploit the underlying tree structure. However, its performance consistently lags behind that of tree models, even on large training sets, suggesting that tree-structured models are more effective at exploiting recursive structure.
The Characteristic Gluing Problem and Conservation Laws for the Wave Equation on Null Hypersurfaces

We obtain necessary and sufficient conditions for the existence of “conservation laws” on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate horizons of extremal black holes. Another (limiting) example of such a conservation law is that which gives rise to the well-known Newman–Penrose constants along the null infinity of asymptotically flat spacetimes. The existence of such conservation laws can be viewed as an obstruction to a certain gluing construction for characteristic initial data for the wave equation. We initiate the general study of the latter gluing problem and show that the existence of conservation laws is in fact the only obstruction. Our method relies on a novel elliptic structure associated to a foliation with 2-spheres of a null hypersurface.
Authorship attribution using a Neural Network Language Model

In practice, training language models for individual authors is often expensive because of limited data resources. In such cases, Neural Network Language Models (NNLMs), generally outperform the traditional non-parametric N-gram models. Here we investigate the performance of a feedforward NNLM on an authorship attribution problem, with moderate author set size and relatively limited data. We also consider how the text topics impact performance. Compared with a well-constructed N-gram baseline method with Kneser-Ney smoothing, the proposed method achieves nearly 2.5% reduction in perplexity and increases author classification accuracy by 3.43% on average, given as few as 5 test sentences. The performance is very competitive with the state of the art in terms of accuracy and demand on test data. The source code, preprocessed datasets, a detailed description of the methodology and results are available at https://github.com/zge/authorship-attribution.
Hydrogen nanobubbles in a water solution of dietary supplement

Using gas chromatography, proton nuclear magnetic resonance and qualitative experiments, we demonstrate that a water solution of dissolved dietary supplement, creating negative redox potential, contains invisible hydrogen nano-bubbles, which remain in the solution for several hours.
Linear bandits in high dimension and recommendation systems

A large number of online services provide automated recommendations to help users to navigate through a large collection of items. New items (products, videos, songs, advertisements) are suggested on the basis of the user's past history and — when available — her demographic profile. Recommendations have to satisfy the dual goal of helping the user to explore the space of available items, while allowing the system to probe the user's preferences. We model this trade-off using linearly parametrized multi-armed bandits and prove upper and lower bounds that coincide up to constants in the data poor (high-dimensional) regime. We test (a variation of) the scheme used for estabilishing achievability on the Netflix dataset, and obtain results in agreement with the theory.
Overlays and group actions

Abstract Overlays were introduced by R.H. Fox [7] as a subclass of covering maps. We offer a different view of overlays: it resembles the definition of paracompact spaces via star refinements of open covers. One introduces covering structures for covering maps and p : X → Y is an overlay if it has a covering structure that has a star refinement. We prove two characterizations of overlays: the first one using existence and uniqueness of lifts of discrete chains, the second one as maps inducing simplicial coverings of nerves of certain covers. We use those characterizations to improve results of Eda–Matijevic concerning topological group structures on domains of overlays whose range is a compact topological group. In case of surjective maps p : X → Y between connected metrizable spaces, we characterize overlays as local isometries: p : X → Y is an overlay if and only if one can metrize X and Y in such a way that p | B ( x , 1 ) : B ( x , 1 ) → B ( p ( x ) , 1 ) is an isometry for each x ∈ X .
Ambient Obstruction Flow

We establish fundamental results for a parabolic flow of Riemannian metrics introduced by Bahuaud-Helliwell in arXiv:1010:4287v1 which is based on the Fefferman-Graham ambient obstruction tensor. First, we obtain local $L^2$ smoothing estimates for the curvature tensor and use them to prove pointwise smoothing estimates for the curvature tensor. We use the pointwise smoothing estimates to show that the curvature must blow up for a finite time singular solution. We also use the pointwise smoothing estimates to prove a compactness theorem for a sequence of solutions with bounded $C^0$ curvature norm and injectivity radius bounded from below at one point. Finally, we use the compactness theorem to obtain a singularity model from a finite time singular solution and to characterize the behavior at infinity of a nonsingular solution.
Power Control and Scheduling under Hard Deadline Constraints for On-Off Fading Channels

We consider the joint scheduling-and-power- allocation problem of a downlink cellular system. The system consists of two groups of users: real- time (RT) and non-real-time (NRT) users. Given some average power constraint on the base station, the problem is to find an algorithm that satisfies the RT and NRT quality-of-service (QoS) constraints. The RT QoS constraints guarantee the portion of RT packets that miss their deadline are no more than a pre-specified threshold. On the other hand, the NRT QoS is only to guarantee the stability of their queues. We propose a sum-rate- maximizing algorithm that satisfy all QoS and average power constraints. The proposed power allocation policy has a closed form expression for the two groups of users. However, the power policy of the RT users differ in structure from the NRT users. The proposed algorithm is optimal for the on-off channel model with a polynomial-time scheduling complexity. Using extensive simulations, the throughput of the proposed algorithm is shown to exceed existing approaches.
Circulation in Blowdown Flows

The blowdown (rapid release) of high pressure gas from a pressure vessel adiabatically cools the gas remaining in the vessel. The gas near the wall is warmed by conduction from the wall, producing radial temperature and density gradients that affect the flow, the mass efflux rate, and the thermodynamic states of both the outflowing and the contained gas. The resulting buoyancy-driven flow circulates the gas through the vessel and reduces, but does not eliminate, these gradients. The purpose of this technical brief is to estimate when blowdown cooling is rapid enough that the gas in the pressure vessel is neither isothermal nor isopycnic, though it remains isobaric. I define a dimensionless number, the buoyancy circulation number, that parametrizes these effects.
q-Binomials and related symmetric unimodal polynomials

The q-binomial coefficients were conjectured to be unimodal as early as the 1850's but it remained unproven until Sylvester's 1878 proof using invariant theory. In 1982, Proctor gave an ‘elementary...
The Information View of Financial Crises

Short-term debt that can serve as a medium of exchange is designed to be information insensitive. No one should be tempted to acquire private information to gain an informational advantage in tradi...
Periodicity of identifying codes in strips

Abstract An identifying code in a graph is a subset of vertices having a nonempty and distinct intersection with the closed neighborhood of every vertex. We prove that the infimum density of any identifying code in S k (an infinite strip of k rows in the square grid) can always be achieved by a periodic identifying code with pattern length at most 2 4 k . Assisted by a compute program implementing Karp's algorithm for minimum cycle mean, we find a periodic identifying code in S 4 with the minimum density 11/28, and a periodic identifying code in S 5 with the minimum density 19/50.
Clustering of Data with Missing Entries

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a clustering algorithm, that will provide good clustering even in the presence of missing data. The proposed technique solves an l o fusion penalty based optimization problem to recover the clusters. We theoretically analyze the conditions needed for the successful recovery of the clusters. We also propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. The method is demonstrated on simulated and real datasets, and is observed to perform well in the presence of large fractions of missing entries.
A simple counterexample to Havil’s “reformulation” of the Riemann Hypothesis

This is an elementary note. It corrects a mistake in the reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant.
Generating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers

An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Such a tableau with precisely $k$ inversion pairs is said to be a $k$-inverted semistandard Young tableau. Building upon earlier work by Fresse and the author, this paper develops generating functions for the numbers of $k$-inverted semistandard Young tableaux of various shapes $\lambda$ and contents $\mu$. An easily-calculable generating function is given for the number of $k$-inverted semistandard Young tableaux that "standardize" to a fixed semistandard Young tableau. For $m$-row shapes $\lambda$ and standard content $\mu$, the total number of $k$-inverted standard Young tableaux of shape $\lambda$ is then enumerated by relating such tableaux to $m$-dimensional generalizations of Dyck paths and counting the numbers of "returns to ground" in those paths. In the rectangular specialization of $\lambda = n^m$ this yields a generating function that involves $m$-dimensional analogues of the famed Ballot numbers. Our various results are then used to directly enumerate all $k$-inverted semistandard Young tableaux with arbitrary content and two-row shape $\lambda = a^1 b^1$, as well as all $k$-inverted standard Young tableaux with two-column shape $\lambda=2^n$.
Simple, locally finite dimensional Lie algebras in positive characteristic

Abstract We prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [ R ( − ) , R ( − ) ] / ( Z ( R ) ∩ [ R ( − ) , R ( − ) ] ) or [ K ( R , ⁎ ) , K ( R , ⁎ ) ] for a simple, locally finite dimensional associative algebra R with involution ⁎. The first proves that a condition we introduce, known as locally nondegenerate, along with the existence of an ad-nilpotent element suffice. The second proves that an ad-integrable Lie algebra is of this type if the characteristic of the ground field is sufficiently large. Lastly we construct a simple, locally finite dimensional associative algebra R with involution ⁎ such that K ( R , ⁎ ) ≠ [ K ( R , ⁎ ) , K ( R , ⁎ ) ] to demonstrate the necessity of considering the commutator in the first two theorems.
Salem Numbers and Automorphisms of Complex Surfaces

For two-dimensional complex tori, we characterize the set of all values of positive entropy that arise from automorphisms. For K3 surfaces, we give suffcient conditions for a positive value to be the entropy of some automorphism.
Effective cycles on blow-ups of Grassmannians

Abstract In this paper we study the pseudoeffective cones of blow-ups of Grassmannians at sets of points. For small numbers of points, the cones are often spanned by proper transforms of Schubert classes. In some special cases, we provide sharp bounds for when the Schubert classes fail to span and we describe the resulting geometry.
Diagonals of Self-adjoint Operators with Finite Spectrum

Summary. Given a finite set X R we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur‐Horn theorem from a finitedimensional setting to an infinite-dimensional Hilbert space analogous to Kadison’s theorem for orthogonal projections (2002) and the second author’s result for operators with three-point spectrum (2013).
Resonance absorption of a broadband laser pulse

Broad bandwidth, infrared light sources have the potential to revolutionize inertial confinement fusion (ICF) by suppressing laser-plasma instabilities. There is, however, a tradeoff: The broad bandwidth precludes high efficiency conversion from the infrared to the ultraviolet, where laser-plasma interactions are weaker. Operation in the infrared could intensify the role of resonance absorption, an effect long suspected to be the shortcoming of early ICF experiments. Here, we present simulations exploring the effect of the bandwidth on resonance absorption. In the linear regime, the bandwidth has little effect on resonance absorption; in the nonlinear regime, the bandwidth suppresses enhanced absorption resulting from the electromagnetic decay instability. These findings evince that, regardless of the bandwidth, an ICF implosion will confront at least linear levels of resonance absorption.
On arithmetical numerical monoids with some generators omitted

Numerical monoids (cofinite, additive submonoids of the non-negative integers) arise frequently in additive combinatorics, and have recently been studied in the context of factorization theory. Arithmetical numerical monoids, which are minimally generated by arithmetic sequences, are particularly well-behaved, admitting closed forms for many invariants that are difficult to compute in the general case. In this paper, we answer the question “when does omitting generators from an arithmetical numerical monoid S preserve its (well-understood) set of length sets and/or Frobenius number?” in two extremal cases: (1) we characterize which individual generators can be omitted from S without changing the set of length sets or Frobenius number; and (2) we prove that under certain conditions, nearly every generator of S can be omitted without changing its set of length sets or Frobenius number.
Mission to the Gravitational Focus of the Sun: A Critical Analysis

The gravitational field of the sun will focus light from a distant source to a focal point at a minimal distance of 550 Astronomical Units from the sun. A proposed mission to this gravitational focus could use the sun as a very large lens, allowing (in principle) a large amplification of signal from the target, and a very high magnification. This article discusses some of the difficulties involved in using the sun as such a gravitational telescope for a candidate mission, that of imaging the surface of a previously-detected exoplanet. These difficulties include the pointing and focal length, and associated high magnification; the signal to noise ratio associated with the solar corona, and the focal blur. In addition, a method to calculate the signal gain and magnification is derived using the first-order deflection calculation and classical optics, showing that the gain is finite for an on-axis source of non-zero area. Abstract 1
Sclera Force Control in Robot-assisted Eye Surgery: Adaptive Force Control vs. Auditory Feedback

Surgeon hand tremor limits human capability during microsurgical procedures such as those that treat the eye. In contrast, elimination of hand tremor through the introduction of microsurgical robots diminishes the surgeons tactile perception of useful and familiar tool-to-sclera forces. While the large mass and inertia of eye surgical robot prevents surgeon microtremor, loss of perception of small scleral forces may put the sclera at risk of injury. In this paper, we have applied and compared two different methods to assure the safety of sclera tissue during robot-assisted eye surgery. In the active control method, an adaptive force control strategy is implemented on the Steady-Hand Eye Robot in order to control the magnitude of scleral forces when they exceed safe boundaries. This autonomous force compensation is then compared to a passive force control method in which the surgeon performs manual adjustments in response to the provided audio feedback proportional to the magnitude of sclera force. A pilot study with three users indicate that the active control method is potentially more efficient.
Domain Robust Feature Extraction for Rapid Low Resource ASR Development

Developing a practical speech recognizer for a low resource language is challenging, not only because of the (potentially unknown) properties of the language, but also because test data may not be from the same domain as the available training data.In this paper, we focus on the latter challenge, i.e. domain mismatch, for systems trained using a sequence-based criterion. We demonstrate the effectiveness of using a pre-trained English recognizer, which is robust to such mismatched conditions, as a domain normalizing feature extractor on a low resource language. In our example, we use Turkish Conversational Speech and Broadcast News data.This enables rapid development of speech recognizers for new languages which can easily adapt to any domain. Testing in various cross-domain scenarios, we achieve relative improvements of around 25% in phoneme error rate, with improvements being around 50% for some domains.
A bound for the order of the fundamental group of a complete noncompact Ricci shrinker

For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.
On the GIT quotient space of quintic surfaces

We describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is stable. We also describe the boundary of the GIT quotient, and we discuss the stability of the non-normal surfaces.
Nonlinear elasticity of the phase-field crystal model from the renormalization group

The rotationally covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive. We show that this free energy can be written purely as a function of the strain tensor and thence derive the corresponding equations governing the nonlinear elastic response.
Bifurcation of Soliton Families from Linear Modes in Non-PT-Symmetric Complex Potentials

Continuous families of solitons in the nonlinear Schrodinger equation with non--symmetric complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special form , where is an arbitrary real function. Using this constant of motion, the second-order complex soliton equation is reduced to a new second-order real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous families of solitons bifurcate out from linear discrete modes in these non--symmetric complex potentials. All analytical results are corroborated by numerical examples.
The stability of quantum Markov filters

When are quantum filters asymptotically independent of the initial state? We show that this is the case for absolutely continuous initial states when the quantum stochastic model satisfies an observability condition. When the initial system is finite dimensional, this condition can be verified explicitly in terms of a rank condition on the coefficients of the associated quantum stochastic differential equation.
Sample Efficient Policy Search for Optimal Stopping Domains

Optimal stopping problems consider the question of deciding when to stop an observation-generating process in order to maximize a return. We examine the problem of simultaneously learning and planning in such domains, when data is collected directly from the environment. We propose GFSE, a simple and flexible model-free policy search method that reuses data for sample efficiency by leveraging problem structure. We bound the sample complexity of our approach to guarantee uniform convergence of policy value estimates, tightening existing PAC bounds to achieve logarithmic dependence on horizon length for our setting. We also examine the benefit of our method against prevalent model-based and model-free approaches on 3 domains taken from diverse fields.
Metric dimensions and tameness in expansions of the real field

For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.
The algebraic hull of the Kontsevich–Zorich cocycle

We compute the algebraic hull of the Kontsevich-Zorich cocycle over any GL^+_2(R) invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
Dilated Deep Residual Network for Image Denoising

Variations of deep neural networks such as convolutional neural network (CNN) have been successfully applied to image denoising. The goal is to automatically learn a mapping from a noisy image to a clean image given training data consisting of pairs of noisy and clean images. Most existing CNN models for image denoising have many layers. In such cases, the models involve a large amount of parameters and are computationally expensive to train. In this paper, we develop a dilated residual CNN for Gaussian image denoising. Compared with the recently proposed residual denoiser, our method can achieve comparable performance with less computational cost. Specifically, we enlarge receptive field by adopting dilated convolution in residual network, and the dilation factor is set to a certain value. We utilize appropriate zero padding to make the dimension of the output the same as the input. It has been proven that the expansion of receptive field can boost the CNN performance in image classification, and we further demonstrate that it can also lead to competitive performance for denoising problem. Moreover, we present a formula to calculate receptive field size when dilated convolution is incorporated. Thus, the change of receptive field can be interpreted mathematically. To validate the efficacy of our approach, we conduct extensive experiments for both gray and color image denoising with specific or randomized noise levels. Both of the quantitative measurements and the visual results of denoising are promising comparing with state-of-the-art baselines.
Optimally Sorting Evolving Data

We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an output close to the correct output for the current state of the data, repeatedly updating its best estimate of a correct output over time. We show that a simple repeated insertion-sort algorithm can maintain an O(n) Kendall tau distance, with high probability, between a maintained list and an underlying total order of n items in an evolving data model where each comparison is followed by a swap between a random consecutive pair of items in the underlying total order. This result is asymptotically optimal, since there is an Omega(n) lower bound for Kendall tau distance for this problem. Our result closes the gap between this lower bound and the previous best algorithm for this problem, which maintains a Kendall tau distance of O(n log log n) with high probability. It also confirms previous experimental results that suggested that insertion sort tends to perform better than quicksort in practice.
Nanoscale self-templating for oxide epitaxy with large symmetry mismatch.

Direct observations using scanning transmission electron microscopy unveil an intriguing interfacial bi-layer that enables epitaxial growth of a strain-free, monoclinic, bronze-phase VO2(B) thin film on a perovskite SrTiO3 (STO) substrate. We observe an ultrathin (2–3 unit cells) interlayer best described as highly strained VO2(B) nanodomains combined with an extra (Ti,V)O2 layer on the TiO2 terminated STO (001) surface. By forming a fully coherent interface with the STO substrate and a semi-coherent interface with the strain-free epitaxial VO2(B) film above, the interfacial bi-layer enables the epitaxial connection of the two materials despite their large symmetry and lattice mismatch.
Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test

We study a variant of the Miller-Rabin primality test, which only looks at the last (z+1) powers of the base. This test is between Miller-Rabin and Fermat in terms of strength. For (z=1) the test can be thought of as a variant of the Solovay-Strassen test. We show that for every (z ≥ 0) this test has infinitely many "Carmichael" numbers. We also give empirical results on the rate of growth of the test's "Carmichael" numbers, noting that the growth rate decreases geometrically with increasing (z). We provide some heuristic evidence for this pattern. We also extend our existence result to some generalizations of Miller-Rabin that use (b)-th powers instead of squares.
A Large Deviations Analysis of Certain Qualitative Properties of Parallel Tempering and Infinite Swapping Algorithms

Parallel tempering, or replica exchange, is a popular method for simulating complex systems. The idea is to run parallel simulations at different temperatures, and at a given swap rate exchange configurations between the parallel simulations. From the perspective of large deviations it is optimal to let the swap rate tend to infinity and it is possible to construct a corresponding simulation scheme, known as infinite swapping. In this paper we propose a novel use of large deviations for empirical measures for a more detailed analysis of the infinite swapping limit in the setting of continuous time jump Markov processes. Using the large deviations rate function and associated stochastic control problems we consider a diagnostic based on temperature assignments, which can be easily computed during a simulation. We show that the convergence of this diagnostic to its a priori known limit is a necessary condition for the convergence of infinite swapping. The rate function is also used to investigate the impact of asymmetries in the underlying potential landscape, and where in the state space poor sampling is most likely to occur.
Towards a Better Understanding and Regularization of GAN Training Dynamics.

Generative adversarial networks (GANs) are notoriously difficult to train and the reasons underlying their (non-)convergence behaviors are still not completely understood. By first considering a simple yet representative GAN example, we mathematically analyze its local convergence behavior in a non-asymptotic way. Furthermore, the analysis is extended to general GANs under certain assumptions. We find that in order to ensure a good convergence rate, two factors of the Jacobian in the GAN training dynamics should be simultaneously avoided, which are (i) the Phase Factor, i.e., the Jacobian has complex eigenvalues with a large imaginary-to-real ratio, and (ii) the Conditioning Factor, i.e., the Jacobian is ill-conditioned. Previous methods of regularizing the Jacobian can only alleviate one of these two factors, while making the other more severe. Thus we propose a new JAcobian REgularization (JARE) for GANs, which simultaneously addresses both factors by construction. Finally, we conduct experiments that confirm our theoretical analysis and demonstrate the advantages of JARE over previous methods in stabilizing GANs.
Strict quotas or tariffs? Implications for product quality and consumer welfare in differentiated product supply chains

Abstract We introduce a supply chain network equilibrium model with differentiated products, in which firms compete on product quantities and quality. We then extend the model to include a strict quota or tariff. We establish the equivalence between the model with a strict quota and that with a tariff, when the quota constraint is tight, and the tariff corresponds to the equilibrium Lagrange multiplier associated with the constraint for the former model. Numerical examples reveal that although firms may benefit from the imposition of a quota or tariff, the welfare of consumers in the country imposing the instrument declines.
Training propulsion: Locomotor adaptation to accelerations of the trailing limb

Many stroke survivors suffer from hemiparesis, a condition that results in impaired walking ability. Walking ability is commonly assessed by walking speed, which is dependent on propulsive force generation both in healthy and stroke populations. Propulsive force generation is determined by two factors: ankle moment and the posture of the trailing limb during push-off. Recent work has used robotic assistance strategies to modulate propulsive force with some success. However, robotic strategies are limited by their high cost and the technical difficulty of fitting and operating robotic devices in a clinical setting. Here we present a new paradigm for goal-oriented gait training that utilizes a split belt treadmill to train both components of propulsive force generation, achieved by accelerating the treadmill belt of the trailing limb during push off. Belt accelerations require subjects to produce greater propulsive force to maintain their position on the treadmill and increase trailing limb angle through increased velocity of the accelerated limb. We hypothesized that locomotor adaptation to belt accelerations would result in measurable after effects in the form of increased propulsive force generation. We tested our protocol on healthy subjects at two acceleration magnitudes. Our results show that 79% of subjects significantly increased propulsive force generation following training, and that larger accelerations translated to larger, more persistent behavioral gains.
D-VAE: A Variational Autoencoder for Directed Acyclic Graphs

Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.
An Entity-Driven Framework for Abstractive Summarization.

Abstractive summarization systems aim to produce more coherent and concise summaries than their extractive counterparts. Popular neural models have achieved impressive results for single-document summarization, yet their outputs are often incoherent and unfaithful to the input. In this paper, we introduce SENECA, a novel System for ENtity-drivEn Coherent Abstractive summarization framework that leverages entity information to generate informative and coherent abstracts. Our framework takes a two-step approach: (1) an entity-aware content selection module first identifies salient sentences from the input, then (2) an abstract generation module conducts cross-sentence information compression and abstraction to generate the final summary, which is trained with rewards to promote coherence, conciseness, and clarity. The two components are further connected using reinforcement learning. Automatic evaluation shows that our model significantly outperforms previous state-of-the-art based on ROUGE and our proposed coherence measures on New York Times and CNN/Daily Mail datasets. Human judges further rate our system summaries as more informative and coherent than those by popular summarization models.