cssi/SciSciGPT-SciSciNet huggingface dataset:
The art of community detection

Networks in nature possess a remarkable amount of structure. Via a series of data-driven discoveries, the cutting edge of network science has recently progressed from positing that the random graphs of mathematical graph theory might accurately describe real networks to the current viewpoint that networks in nature are highly complex and structured entities. The identification of high order structures in networks unveils insights into their functional organization. Recently, Clauset, Moore, and Newman, introduced a new algorithm that identifies such heterogeneities in complex networks by utilizing the hierarchy that necessarily organizes the many levels of structure. Here, we anchor their algorithm in a general community detection framework and discuss the future of community detection.
Matricial Wasserstein-1 Distance

We propose an extension of the Wasserstein 1-metric ( $ {W_{{1}}}$ ) for density matrices, matrix-valued density measures, and an unbalanced interpretation of mass transport. We use duality theory and, in particular, a “dual of the dual” formulation of $ {W_{{1}}}$ . This matrix analog of the Earth Mover’s Distance has several attractive features including ease of computation.
Statics and dynamics of a one-dimensional quantum many-body system

The macroscopic zero-temperature behavior of weakly incommensurate systems in one dimension is described in terms of solitons. The soliton density n obeys equations displaying several types of singular interfacelike solutions: (i) equilibrium or moving boundary between the $n=0$ and finite n regions, and (ii) stationary or moving annihilation front separating solitons from antisolitons.
Learning to detect and mitigate cross-layer attacks in wireless networks: Framework and applications

Security threats such as jamming and route manipulation can have significant consequences on the performance of modern wireless networks. To increase the efficacy and stealthiness of such threats, a number of extremely challenging, next-generation cross-layer attacks have been recently unveiled. Although existing research has thoroughly addressed many single-layer attacks, the problem of detecting and mitigating cross-layer attacks still remains unsolved. For this reason, in this paper we propose a novel framework to analyze and address cross-layer attacks in wireless networks. Specifically, our framework consists of a detection and a mitigation component. The attack detection component is based on a Bayesian learning detection scheme that constructs a model of observed evidence to identify stealthy attack activities. The mitigation component comprises a scheme that achieves the desired trade-off between security and performance. We specialize and evaluate the proposed framework by considering a specific cross-layer attack that uses jamming as an auxiliary tool to achieve route manipulation. Simulations and experimental results obtained with a testbed made up by USRP software-defined radios demonstrate the effectiveness of the proposed methodology.
Pathological Pulmonary Lobe Segmentation from CT Images Using Progressive Holistically Nested Neural Networks and Random Walker

Automatic pathological pulmonary lobe segmentation(PPLS) enables regional analyses of lung disease, a clinically important capability. Due to often incomplete lobe boundaries, PPLS is difficult even for experts, and most prior art requires inference from contextual information. To address this, we propose a novel PPLS method that couples deep learning with the random walker (RW) algorithm. We first employ the recent progressive holistically-nested network (P-HNN) model to identify potential lobar boundaries, then generate final segmentations using a RW that is seeded and weighted by the P-HNN output. We are the first to apply deep learning to PPLS. The advantages are independence from prior airway/vessel segmentations, increased robustness in diseased lungs, and methodological simplicity that does not sacrifice accuracy. Our method posts a high mean Jaccard score of \(0.888\pm 0.164\) on a held-out set of 154 CT scans from lung-disease patients, while also significantly (\(p < 0.001\)) outperforming a state-of-the-art method.
Exploring Speech Enhancement with Generative Adversarial Networks for Robust Speech Recognition

We investigate the effectiveness of generative adversarial networks (GANs) for speech enhancement, in the context of improving noise robustness of automatic speech recognition (ASR) systems. Prior work [1] demonstrates that GANs can effectively suppress additive noise in raw waveform speech signals, improving perceptual quality metrics; however this technique was not justified in the context of ASR. In this work, we conduct a detailed study to measure the effectiveness of GANs in enhancing speech contaminated by both additive and reverberant noise. Motivated by recent advances in image processing [2], we propose operating GANs on log-Mel filterbank spectra instead of waveforms, which requires less computation and is more robust to reverberant noise. While GAN enhancement improves the performance of a clean-trained ASR system on noisy speech, it falls short of the performance achieved by conventional multi-style training (MTR). By appending the GAN-enhanced features to the noisy inputs and retraining, we achieve a 7% WER improvement relative to the MTR system.
Layer Trajectory LSTM.

It is popular to stack LSTM layers to get better modeling power, especially when large amount of training data is available. However, an LSTM-RNN with too many vanilla LSTM layers is very hard to train and there still exists the gradient vanishing issue if the network goes too deep. This issue can be partially solved by adding skip connections between layers, such as residual LSTM. In this paper, we propose a layer trajectory LSTM (ltLSTM) which builds a layer-LSTM using all the layer outputs from a standard multi-layer time-LSTM. This layer-LSTM scans the outputs from time-LSTMs, and uses the summarized layer trajectory information for final senone classification. The forward-propagation of time-LSTM and layer-LSTM can be handled in two separate threads in parallel so that the network computation time is the same as the standard time-LSTM. With a layer-LSTM running through layers, a gated path is provided from the output layer to the bottom layer, alleviating the gradient vanishing issue. Trained with 30 thousand hours of EN-US Microsoft internal data, the proposed ltLSTM performed significantly better than the standard multi-layer LSTM and residual LSTM, with up to 9.0% relative word error rate reduction across different tasks.
Generalized Multiplicities of Edge Ideals

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show that the j-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the j-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert–Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs.
Addressing integration error for polygonal finite elements through polynomial projections: A patch test connection

Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead to a deterioration of convergence of the finite element solutions. We propose a general remedy, inspired by techniques in the recent literature of mimetic finite differences, for restoring consistency and thereby ensuring the satisfaction of the patch test and recovering optimal rates of convergence. The proposed approach, based on polynomial projections of the basis functions, allows for the use of moderate number of integration points and brings the computational cost of polygonal finite elements closer to that of the commonly used linear triangles and bilinear quadrilaterals. Numerical studies of a two-dimensional scalar diffusion problem accompany the theoretical considerations.
Scalable Coordinated Exploration in Concurrent Reinforcement Learning

We consider a team of reinforcement learning agents that concurrently operate in a common environment, and we develop an approach to efficient coordinated exploration that is suitable for problems of practical scale. Our approach builds on the seed sampling concept introduced in Dimakopoulou and Van Roy (2018) and on a randomized value function learning algorithm from Osband et al. (2016). We demonstrate that, for simple tabular contexts, the approach is competitive with those previously proposed in Dimakopoulou and Van Roy (2018) and with a higher-dimensional problem and a neural network value function representation, the approach learns quickly with far fewer agents than alternative exploration schemes.
On the performance of random block codes over finite-state fading channels

As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This article seeks to characterize the performance of block codes over finite-state channels with memory. In particular, classical results from information theory are revisited in the context of channels with rare transitions, and bounds on the probabilities of decoding failure are derived for random codes. This creates an analysis framework where channel dependencies within and across codewords are preserved. Such results can subsequently be integrated into a queueing problem formulation. Overall, this study offers new insights about the potential impact of channel correlation on the performance of delay-aware, point-to-point communication links.
Asymptotically flat three-manifolds contain minimal planes

Abstract Let ( M , g ) be an asymptotically flat 3-manifold containing no closed embedded minimal surfaces. We prove that for every point p ∈ M there exists a complete properly embedded minimal plane in M containing p .
Regularized Gradient Descent: A Nonconvex Recipe for Fast Joint Blind Deconvolution and Demixing

Author(s): Ling, Shuyang; Thomas, Strohmer | Abstract: We study the question of extracting a sequence of functions {fi,gi}si=1 from observing only the sum of their convolutions, i.e., from y=∑si=1fi∗gi. While convex optimization techniques are able to solve this joint blind deconvolution-demixing problem provably and robustly under certain conditions, for medium-size or large-size problems we need computationally faster methods without sacrificing the benefits of mathematical rigor that come with convex methods. In this paper we present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. Our two-step algorithm converges to the global minimum linearly and is also robust in the presence of additive noise. While the derived performance bounds are suboptimal in terms of the information-theoretic limit, numerical simulations show remarkable performance even if the number of measurements is close to the number of degrees of freedom. We discuss an application of the proposed framework in wireless communications in connection with the Internet-of-Things.
The defocusing energy-supercritical cubic nonlinear wave equation in dimension five

We consider the energy-supercritical nonlinear wave equation $u_{tt}-\Delta u+|u|^2u=0$ with defocusing cubic nonlinearity in dimension $d=5$ with no radial assumption on the initial data. We prove that a uniform-in-time {\it a priori} bound on the critical norm implies that solutions exist globally in time and scatter at infinity in both time directions. Together with our earlier works in dimensions $d\geq 6$ with general data and dimension $d=5$ with radial data, the present work completes the study of global well-posedness and scattering in the energy-supercritical regime for the cubic nonlinearity under the assumption of uniform-in-time control over the critical norm.
Butterfly Counting in Bipartite Networks

We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete 2x2 biclique, the simplest cohesive higher-order structure in a bipartite graph. Our main contribution is a suite of randomized algorithms that can quickly approximate the number of butterflies in a graph with a provable guarantee on accuracy. An experimental evaluation on large real-world networks shows that our algorithms return accurate estimates within a few seconds, even for networks with trillions of butterflies and hundreds of millions of edges.
Towards Robust Deep Neural Networks with BANG

Machine learning models, including state-of-the-art deep neural networks, are vulnerable to small perturbations that cause unexpected classification errors. This unexpected lack of robustness raises fundamental questions about their generalization properties and poses a serious concern for practical deployments. As such perturbations can remain imperceptible – the formed adversarial examples demonstrate an inherent inconsistency between vulnerable machine learning models and human perception – some prior work casts this problem as a security issue. Despite the significance of the discovered instabilities and ensuing research, their cause is not well understood and no effective method has been developed to address the problem. In this paper, we present a novel theory to explain why this unpleasant phenomenon exists in deep neural networks. Based on that theory, we introduce a simple, efficient, and effective training approach, Batch Adjusted Network Gradients (BANG), which significantly improves the robustness of machine learning models. While the BANG technique does not rely on any form of data augmentation or the utilization of adversarial images for training, the resultant classifiers are more resistant to adversarial perturbations while maintaining or even enhancing the overall classification performance.
Chiral Polarization Scale at Finite Temperature

We study the chiral polarization properties of low-lying Dirac eigenmodes at finite temperature using the overlap operator. Results for pure gauge theory on both sides of deconfinement phase transition are presented. We find that the polarization scale decreases as we increase the temperature, but it remains non-zero as we cross in the deconfined phase and vanishes only when T 1:4Tc. This is caused by the presence of near-zero modes which, we find, are chirally polarized.
Limit theorems for monochromatic stars

Let $T(K_{1, r}, G_n)$ be the number of monochromatic copies of the $r$-star $K_{1, r}$ in a uniformly random coloring of the vertices of the graph $G_n$. In this paper we provide a complete characterization of the limiting distribution of $T(K_{1, r}, G_n)$, in the regime where $\mathbb E(T(K_{1, r}, G_n))$ is bounded, for any growing sequence of graphs $G_n$. The asymptotic distribution is a sum of mutually independent components, each term of which is a polynomial of a single Poisson random variable of degree at most $r$. Conversely, any limiting distribution of $T(K_{1, r}, G_n)$ has a representation of this form. Examples and connections to the birthday problem are discussed.
Finiteness Properties of Local Cohomology for F-Pure Local Rings

In this paper, we show that for an $F$-pure local ring $(R,\m)$, all local cohomology modules $H_{\m}^i(R)$ have finitely many Frobenius compatible submodules. This answers positively an open question raised by F.Enescu and M.Hochster. We also prove that if $(R,\m)$ is excellent and is $F$-pure on the punctured spectrum, then all local cohomology modules have finite length in the category of $R$-modules with Frobenius action. Finally, we show that the property that all $H_{\m}^(R)$ have finitely many Frobenius compatible submodules passes to localizations.
EMIT: An Efficient MAC Paradigm for the Internet of Things

The future Internet of Things (IoT) networks are expected to be composed of a large population of low-cost devices communicating dynamically with access points or neighboring devices to communicate small bundles of delay-sensitive data. To support the high-intensity and short-lived demands of these emerging networks, we propose an efficient MAC paradigm for IoT (EMIT). Our paradigm bypasses the high overhead and coordination costs of existing MAC solutions by employing an interference-averaging strategy that allows users to share their resources simultaneously. In contrast to the predominant interference-suppressing approaches, EMIT exploits the dense and dynamic nature of IoT networks to reduce the spatio-temporal variability of interference to achieve low-delay and high-reliability in service. This paper introduces foundational ideas of EMIT by characterizing the global interference statistics in terms of single-device operation and develops power-rate allocation strategies to guarantee low-delay high-reliability performance. A significant portion of our work is aimed at validating these theoretical principles in experimental test beds and simulations, where we compare the performance of EMIT with a CSMA-based MAC protocol. Our comparisons confirm the beneficial characteristics of EMIT and reveal significant gains over CSMA strategies in the case of IoT traffic.
Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

We study two basic problems regarding edit errors (insertions and deletions). The first one is document exchange, where two parties Alice and Bob hold two strings x and y with a bounded edit distance k. The goal is to have Alice send a short sketch to Bob, so that Bob can recover x based on y and the sketch. The second one is the fundamental problem of designing error correcting codes for edit errors, where the goal is to construct an explicit code to transmit a message x through a channel that can add at most k worst case insertions and deletions, so that the original message x can be successfully recovered at the other end of the channel. Both problems have been extensively studied for decades, and in this paper we focus on deterministic document exchange protocols and binary codes for insertions and deletions (insdel codes). If the length of x is n, then it is known that for small k (e.g., k ≤ n/4), in both problems the optimal sketch size or the optimal number of redundant bits is Θ(k log n/k). In particular, this implies the existence of binary codes that can correct e fraction of insertions and deletions with rate 1-Θ(e log (1/e). However, known constructions are far from achieving these bounds. In this paper we significantly improve previous results on both problems. For document exchange, we give an efficient deterministic protocol with sketch size O(k log^2 n/k). This significantly improves the previous best known deterministic protocol, which has sketch size O(k^2 + k log^2 n) [2]. For binary insdel codes, we obtain the following results: 1) An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log^2 n/k). In particular this implies an explicit family of binary insdel codes that can correct e fraction of insertions and deletions with rate 1-O(e log^2 1/(1-e))=1-O(e). This significantly improves the previous best known result which only achieves rate 1-O(√e) [11], [10], and is optimal up to a log (1/e) factor. 1) An explicit binary insdel code which encodes an n-bit message x against k errors with redundancy O(k log n). This significantly improves the previous best known result of [4], which only works for constant k and has redundancy O(k^2 log k log n); and that of [2], which has redundancy O(k^2 + k log^2 n). Our code has optimal redundancy for k ≤ n^1-α, any constant 0 < α < 1. This is the first explicit construction of binary insdel codes that has optimal redundancy for a wide range of error parameters k, and this brings our understanding of binary insdel codes much closer to that of standard binary error correcting codes. In obtaining our results we introduce several new techniques. Most notably, we introduce the notion of e-self matching hash functions and e-synchronization hash functions. We believe our techniques can have further applications in the literature.
Collective Influence Algorithm to find influencers via optimal percolation in massively large social media.

We elaborate on a linear-time implementation of Collective-Influence (CI) algorithm introduced by Morone, Makse, Nature 524, 65 (2015) to find the minimal set of influencers in networks via optimal percolation. The computational complexity of CI is O(N log N) when removing nodes one-by-one, made possible through an appropriate data structure to process CI. We introduce two Belief-Propagation (BP) variants of CI that consider global optimization via message-passing: CI propagation (CIP) and Collective-Immunization-Belief-Propagation algorithm (CIBP) based on optimal immunization. Both identify a slightly smaller fraction of influencers than CI and, remarkably, reproduce the exact analytical optimal percolation threshold obtained in Random Struct. Alg. 21, 397 (2002) for cubic random regular graphs, leaving little room for improvement for random graphs. However, the small augmented performance comes at the expense of increasing running time to O(N2), rendering BP prohibitive for modern-day big-data. For instance, for big-data social networks of 200 million users (e.g., Twitter users sending 500 million tweets/day), CI finds influencers in 2.5 hours on a single CPU, while all BP algorithms (CIP, CIBP and BDP) would take more than 3,000 years to accomplish the same task.
Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits

The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially critical to include time-varying parameters that impact viral epidemic-like propagation. We connect the control of such stochastic processes with time-varying behavior to the stochastic shortest path problem and obtain solutions for various cost functions. Then, under a mean-field scaling, this general class of stochastic processes is shown to converge to a corresponding dynamical system. We further establish that the optimal control of this class of processes converges to the optimal control of the limiting dynamical system. Our comparative study of the optimal control of both systems renders various important mathematical properties of interest.
Survey propagation revisited

Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding the success of SP, it was recently shown that SP can be viewed as a form of belief propagation, computing marginal probabilities over certain objects called covers of a formula. This explanation was, however, shortly dismissed by experiments suggesting that non-trivial covers simply do not exist for large formulas. In this paper, we show that these experiments were misleading: not only do covers exist for large hard random formulas, SP is surprisingly accurate at computing marginals over these covers despite the existence of many cycles in the formulas. This re-opens a potentially simpler line of reasoning for understanding SP, in contrast to some alternative lines of explanation that have been proposed assuming covers do not exist.
An algorithmic blend of LPs and ring equations for promise CSPs

Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well known problems can be cast as promise CSPs including approximate graph and hypergraph coloring, discrepancy minimization, and interesting variants of satisfiability. Similar to CSPs, the tractability of promise CSPs can be tied to the structure of associated operations on the solution space called (weak) polymorphisms. However, compared to CSPs whose polymorphisms are well-structured algebraic objects called clones, polymorphisms in the promise world are much less constrained --- essentially any infinite family of functions obeying mild conditions can arise as polymorphisms. Under the thesis that non-trivial polymorphisms govern tractability, promise CSPs therefore provide a fertile ground for the discovery of novel algorithms.In previous work, we classified all tractable cases of Boolean promise CSPs when the constraint predicates are symmetric. The algorithms were governed by three kinds of polymorphism families: (i) parity functions, (ii) majority functions, or (iii) a non-symmetric (albeit block-symmetric) family we called alternating threshold. In this work, we provide a vast generalization of these algorithmic results. Specifically, we show that promise CSPs that admit a family of "regional-periodic" polymorphisms are solvable in polynomial time, assuming that determining which region a point is in can be computed in polynomial time. Such polymorphisms are quite general and are obtained by gluing together several functions that are periodic in the Hamming weights in different blocks of the input. For example, we can have functions that equal parity for relative Hamming weights up to 1/2, and Majority (so identically 1) for weights above 1/2.Our algorithm is based on a novel combination of linear programming and solving linear systems over rings. We also abstract a framework based on reducing a promise CSP to a CSP over an infinite domain, solving it there (via the said combination of LPs and ring equations), and then rounding the solution to an assignment for the promise CSP instance. The rounding step is intimately tied to the family of polymorphisms, and clarifies the connection between polymorphisms and algorithms in this context. As a key ingredient, we introduce the technique of finding a solution to a linear program with integer coefficients that lies in a different ring (such as [MATH HERE]) to bypass ad-hoc adjustments for lying on a rounding boundary.
On Equivalence of Martingale Tail Bounds and Deterministic Regret Inequalities

We study an equivalence of (i) deterministic pathwise statements appearing in the online learning literature (termed regret bounds), (ii) high-probability tail bounds for the supremum of a collection of martingales (of a specific form arising from uniform laws of large numbers for martingales), and (iii) in-expectation bounds for the supremum. By virtue of the equivalence, we prove exponential tail bounds for norms of Banach space valued martingales via deterministic regret bounds for the online mirror descent algorithm with an adaptive step size. We extend these results beyond the linear structure of the Banach space: we define a notion of martingale type for general classes of real-valued functions and show its equivalence (up to a logarithmic factor) to various sequential complexities of the class (in particular, the sequential Rademacher complexity and its offset version). For classes with the general martingale type 2, we exhibit a finer notion of variation that allows partial adaptation to the function indexing the martingale. Our proof technique rests on sequential symmetrization and on certifying the existence of regret minimization strategies for certain online prediction problems.
Learning Latent Super-Events to Detect Multiple Activities in Videos

In this paper, we introduce the concept of learning latent super-events from activity videos, and present how it benefits activity detection in continuous videos. We define a super-event as a set of multiple events occurring together in videos with a particular temporal organization; it is the opposite concept of sub-events. Real-world videos contain multiple activities and are rarely segmented (e.g., surveillance videos), and learning latent super-events allows the model to capture how the events are temporally related in videos. We design temporal structure filters that enable the model to focus on particular sub-intervals of the videos, and use them together with a soft attention mechanism to learn representations of latent super-events. Super-event representations are combined with per-frame or per-segment CNNs to provide frame-level annotations. Our approach is designed to be fully differentiable, enabling end-to-end learning of latent super-event representations jointly with the activity detector using them. Our experiments with multiple public video datasets confirm that the proposed concept of latent super-event learning significantly benefits activity detection, advancing the state-of-the-arts.
Consistent map-based 3D localization on mobile devices

In this paper, we seek to provide consistent, real-time 3D localization capabilities to mobile devices navigating within previously mapped areas. To this end, we introduce the Cholesky-Schmidt-Kalman filter (C-SKF), which explicitly considers the uncertainty of the prior map, by employing the sparse Cholesky factor of the map's Hessian, instead of its dense covariance-as is the case for the Schmidt-Kalman filter. By doing so, the C-SKF has memory requirements typically linear in the size of the map, as opposed to quadratic for storing the map's covariance. Moreover, and in order to bound the processing needs of the C-SKF (between linear and quadratic in the size of the map), we introduce two relaxations of the C-SKF algorithm: (i) The sC-SKF, which operates on the Cholesky factors of independent sub-maps resulting from dividing the map into overlapping segments. (ii) We formulate an efficient method for sparsifying the Cholesky factor by selecting and processing a subset of loop-closure measurements based on their temporal distribution. Lastly, we assess the processing and memory requirements of the proposed algorithms, and compare their positioning accuracy against other inconsistent map-based localization approaches that employ measurement-noise-covariance inflation to compensate for the map's uncertainty.
Topological pressure and the variational principle for actions of sofic groups

We introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such spaces. We also establish the variational principle for topological pressure in this sofic context.
Hierarchies of Relaxations for Online Prediction Problems with Evolving Constraints

We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial structure. A key aspect here is that finding the optimal benchmark predictor (even in hindsight, given all the data) might be computationally hard due to the combinatorial nature of the constraints. Despite this, we provide polynomial-time prediction algorithms that achieve low regret against combinatorial benchmark sets. We do so by building improper learning algorithms based on two ideas that work together. The first is to alleviate part of the computational burden through random playout, and the second is to employ Lasserre semidefinite hierarchies to approximate the resulting integer program. Interestingly, for our prediction algorithms, we only need to compute the values of the semidefinite programs and not the rounded solutions. However, the integrality gap for Lasserre hierarchy does enter the generic regret bound in terms of Rademacher complexity of the benchmark set. This establishes a trade-off between the computation time and the regret bound of the algorithm.
Dynamics of KdV Solitons in the Presence of a Slowly Varying Potential

We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation ∂tu = −∂x(∂ xu + 3u − bu), where b(x, t) = b0(hx, ht), h 1 is a slowly varying, but not small, potential. We obtain an explicit description of the trajectory of the soliton parameters of scale and position on the dynamically relevant time scale δh−1 log h−1, together with an estimate on the error of size h. In addition to the Lyapunov analysis commonly applied to these problems, we use a local virial estimate due to Martel-Merle [15]. The results are supported by numerics. The proof does not rely on the inverse scattering machinery and is expected to carry through for the L subcritical gKdV-p equation, 1 < p < 5. The case of p = 3, the modified Korteweg-de Vries (mKdV) equation, is structurally simpler and more precise results can be obtained by the method of Holmer-Zworski [9].
ExaGridPF: A parallel power flow solver for transmission and unbalanced distribution systems

This paper investigates parallelization strategies for solving power flow problems in both transmission and unbalanced, three-phase distribution systems by developing a scalable power flow solver, ExaGridPF, which is compatible with existing high performance computing platforms. Newton-Raphson (NR) and Newton-Krylov (NK) algorithms have been implemented to verify the performance improvement over both standard IEEE test cases and synthesized grid topologies. For three-phase, unbalanced system, we adapt the current injection method (CIM) to model the power flow and utilize SuperLU to parallelize the computing load across multiple threads. The experimental results indicate that more than 5 times speedup ratio can be achieved for synthesized large-scale transmission topologies, and significant efficiency improvements are observed over existing methods for the distribution networks.
A non-traditional view on the modeling of nematic disclination dynamics

Nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. It is well known that the universally accepted Oseen-Frank energy is infinite for configurations that contain disclination line defects. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where, under certain conditions, infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. Equilibria and dynamics (in the absence of flow) of line defects are studied within the proposed model. Using appropriate initial/boundary data, the gradient-flow dynamics of this energy leads to non-singular, line defect equilibrium solutions, including those of half-integer strength. However, we demonstrate that the gradient flow dynamics for this energy is not able to adequately describe defect evolution. Motivated by similarity with dislocation dynamics in solids, a novel 2D-model of disclination dynamics in nematics is proposed. The model is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. We show that the energy function we devise, suitably interpreted, can serve as well for the modeling of equilibria and dynamics of dislocation line defects in solids making the conclusions of this paper relevant to mechanics of both solids and liquid crystals.
A HEREDITARILY INDECOMPOSABLE ASYMPTOTIC $\ell_2$ BANACH SPACE

A famous open problem in functional analysis is whether there exists a Banach space X such that every (bounded linear) operator on X has the form λ+K where λ is a scalar and K denotes a compact operator. This problem is usually called the “scalar-plus-compact” problem [14]. One of the reasons this problem has become so attractive is that by a result of N. Aronszajn and K.T. Smith [7], if a Banach space X is a solution to the scalar-plus-compact problem then every operator on X has a non-trivial invariant subspace and hence X provides a solution to the famous invariant subspace problem. An important advancement in the construction of spaces with “few” operators was made by W.T. Gowers and B. Maurey [16],[17]. The ground breaking work [16] provides a construction of a space without any unconditional basic sequence thus solving, in the negative, the long standing unconditional basic sequence problem. The Banach space constructed in [16] is Hereditarily Indecomposable (HI), which means that no (closed) infinite dimensional subspace can be decomposed into a direct sum of two further infinite dimensional subspaces. It is proved in [16] that if X is a complex HI space then every operator on X can be written as λ + S where λ is a scalar and S is strictly singular (i.e. the restriction of S on any infinite dimensional subspace of X is not an isomorphism). It is also shown in [16] that the same property remains true for the real HI space constructed in [16]. V. Ferenczi [10] proved that if X is a complex HI space and Y is an infinite dimensional subspace of X then every operator from Y to X can be written as λiY + S where iY : Y → X is the inclusion map and S is strictly singular. It was proved in [17] that, roughly speaking, given an algebra of operators satisfying certain conditions, there exists a Banach space X such that for every infinite dimensional subspace Y , every operator from Y to X can be written as a strictly singular perturbation of a restriction to Y of some element of the algebra. The construction of the first HI space prompted researchers to construct HI spaces having additional nice properties. In other words people tried to “marry” the exotic structure of the HI spaces to the nice structure of classical Banach spaces. The reasons behind these efforts were twofold! Firstly, by producing more examples of HI spaces having additional well understood properties we can better understand how the HI property effects other behaviors of the space. Secondly, there is hope that endowing an HI space with additional
Self-reference, biologic and the structure of reproduction.

This paper concentrates on relationships of formal systems with biology. The paper is based on previous papers by the author. We have freely used texts of those papers where the formulations are of use, and we have extended the concepts and discussions herein considerably beyond the earlier work. We concentrate on formal systems not only for the sake of showing how there is a fundamental mathematical structure to biology, but also to consider and reconsider philosophical and phenomenological points of view in relation to natural science and mathematics. The relationship with phenomenology comes about in the questions that arise about the nature of the observer in relation to the observed that arise in philosophy, but also in science in the very act of determining the context and models upon which it shall be based.We examine the schema behind the reproduction of DNA. The DNA molecule consists of two interwound strands, the Watson Strand (W) and the Crick Strand (C). The two strands are bonded to each other via a backbone of base-pairings and these bonds can be broken by certain enzymes present in the cell. In reproduction of DNA the bonds between the two strands are broken and the two strands then acquire the needed complementary base molecules from the cellular environment to reconstitute each a separate copy of the DNA. At this level the situation can be described by a symbolism like this. DNA = -------> --------> = = DNA DNA. Here E stands for the environment of the cell. The first arrow denotes the separation of the DNA into the two strands. The second arrow denotes the action between the bare strands and the environment that leads to the production of the two DNA molecules. The paper considers and compares many formalisms for self-replication, including aspects of quantum formalism and the Temperley-Lieb algebra.
The Number of Edges in k-Quasi-planar Graphs

A graph drawn in the plane is called k-quasi-planar if it does not contain k pair- wise crossing edges. It has been conjectured for a long time that for every fixed k ,t he maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best known upper bound is n(log n) O(log k) . In the present paper, we improve this bound to (nlog n)2 α(n) ck in the special case where the graph is drawn in such a way that every pair of edges meet at most once. Here α(n) denotes the (extremely slowly growing) inverse of the Ackermann function. We also make further progress on the conjecture for k-quasi-planar graphs in which every edge is drawn as an x-monotone curve. Extending some ideas of Valtr, we prove that the maximum number of edges of such graphs is at most 2 ck 6 nlog n.
Universal outlying sequence detection for continuous observations

The following detection problem is studied, in which there are M sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains n independent and identically distributed (i.i.d.) continuous observations from a known distribution π, and the outlier sequence contains n i.i.d. observations from an outlier distribution μ, which is distinct from n, but otherwise unknown. A universal test based on Kullback-Leibler (KL) divergence is built to approximate the maximum likelihood test, with known π and unknown μ. A KL divergence estimator based on data-dependent partitions is employed, and is shown to converge to its true value exponentially fast when the density ratio satisfies 0 < Kl ≤ dμ/dπ ≤ K2, where K1 and K2 are positive constants. The performance of such a KL divergence estimator further implies that the outlier detection test is exponentially consistent. The detection performance of the KL divergence based test is compared with that of a recently introduced test for this problem based on the machine learning approach of maximum mean discrepancy (MMD). Regimes in which the KL divergence based test is better than the MMD based test are identified.
Personalized Pancreatic Tumor Growth Prediction via Group Learning

Tumor growth prediction, a highly challenging task, has long been viewed as a mathematical modeling problem, where the tumor growth pattern is personalized based on imaging and clinical data of a target patient. Though mathematical models yield promising results, their prediction accuracy may be limited by the absence of population trend data and personalized clinical characteristics. In this paper, we propose a statistical group learning approach to predict the tumor growth pattern that incorporates both the population trend and personalized data. In order to discover high-level features from multimodal imaging data, a deep convolutional neural network approach is developed to model the voxel-wise spatio-temporal tumor progression. The deep features are combined with the time intervals and the clinical factors to feed a process of feature selection. Our predictive model is pretrained on a group data set and personalized on the target patient data to estimate the future spatio-temporal progression of the patient’s tumor. Multimodal imaging data at multiple time points are used in the learning, personalization and inference stages. Our method achieves a Dice coefficient of \(86.8\%\,\pm \,3.6\%\) and RVD of \(7.9\%\,\pm \,5.4\%\) on a pancreatic tumor data set, outperforming the DSC of \(84.4\%\,\pm \,4.0\%\) and RVD \(13.9\%\,\pm \,9.8\%\) obtained by a previous state-of-the-art model-based method.
CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training

We propose an adversarial training procedure for learning a causal implicit generative model for a given causal graph. We show that adversarial training can be used to learn a generative model with true observational and interventional distributions if the generator architecture is consistent with the given causal graph. We consider the application of generating faces based on given binary labels where the dependency structure between the labels is preserved with a causal graph. This problem can be seen as learning a causal implicit generative model for the image and labels. We devise a two-stage procedure for this problem. First we train a causal implicit generative model over binary labels using a neural network consistent with a causal graph as the generator. We empirically show that WassersteinGAN can be used to output discrete labels. Later, we propose two new conditional GAN architectures, which we call CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained causal implicit generative model for the labels is then a causal implicit generative model over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset.
Similarity-aware spectral sparsification by edge filtering

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral sparsification methods first extract low-stretch spanning tree from the original graph to form the backbone of the sparsifier, and then recover small portions of spectrally-critical off-tree edges to the spanning tree to significantly improve the approximation quality. However, it is not clear how many off-tree edges should be recovered for achieving a desired spectral similarity level within the sparsifier. Motivated by recent graph signal processing techniques, this paper proposes a similarity-aware spectral graph sparsification framework that leverages efficient spectral off-tree edge embedding and filtering schemes to construct spectral sparsifiers with guaranteed spectral similarity (relative condition number) level. An iterative graph densification scheme is introduced to facilitate efficient and effective filtering of off-tree edges for highly ill-conditioned problems. The proposed method has been validated using various kinds of graphs obtained from public domain sparse matrix collections relevant to VLSI CAD, finite element analysis, as well as social and data networks frequently studied in many machine learning and data mining applications.