cssi/SciSciGPT-SciSciNet huggingface dataset:
The Subelliptic Heat Kernels of the Quaternionic Hopf Fibration

The main goal of this work is to study the sub-Laplacian of the unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the quaternionic projective space. We obtain in particular explicit formulas for its heat kernel and deduce an expression for the Green function of the conformal sub-Laplacian and small-time asymptotics. As a byproduct of our study we also obtain several results related to the sub-Laplacian of a projected Hopf fibration.
A Robust solver for a second order mixed finite element method for the Cahn-Hilliard equation

Abstract We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn–Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element splitting scheme for the Cahn–Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spatial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild.
Norm convergence of multiple ergodic averages for commuting transformations

Let T1,…,Tl:X→X be commuting measure-preserving transformations on a probability space . We show that the multiple ergodic averages are convergent in as for all ; this was previously established for l=2 by Conze and Lesigne [J. P. Conze and E. Lesigne. Theoremes ergodique por les mesures diagonales. Bull. Soc. Math. France112 (1984), 143–175] and for general l assuming some additional ergodicity hypotheses on the maps Ti and TiTj−1 by Frantzikinakis and Kra [N. Frantzikinakis and B. Kra. Convergence of multiple ergodic averages for some commuting transformations. Ergod. Th. & Dynam. Sys.25 (2005), 799–809] (with the l=3 case of this result established earlier by Zhang [Q. Zhang. On the convergence of the averages . Mh. Math.122 (1996), 275–300]). Our approach is combinatorial and finitary in nature, inspired by recent developments regarding the hypergraph regularity and removal lemmas, although we will not need the full strength of those lemmas. In particular, the l=2 case of our arguments is a finitary analogue of those by Conze and Lesigne.
Nonlinear Response Functions of Strongly Correlated Boson Fields: Bose-Einstein Condensates and Fractional Quantum Hall Systems

Nonlinear response functions of strongly correlated boson fields subject to an external perturbation are calculated. In particular, the second-order response functions and susceptibilities of finite-temperature Bose-Einstein condensates (BECs) in a one-dimensional harmonic trap driven by an external field coupled to particle density are calculated by solving the time-dependent Hartree-Fock-Bogoliubov equations. These pro- vide additional insight into the BEC dynamics, beyond those of the linear response regime. We further demon- strate that the results directly apply to electron liquids in the fractional quantum Hall effect regime that can be mapped onto an effective boson system coupled to a Chern-Simons gauge field.
Universal hierarchical structure of quasiperiodic eigenfunctions

We determine exact exponential asymptotics of eigenfunctions and of corresponding transfer matrices of the almost Mathieu operators for all frequencies in the localization regime. This uncovers a universal structure in their behavior, governed by the continued fraction expansion of the frequency, explaining some predictions in physics literature. In addition it proves the arithmetic version of the frequency transition conjecture. Finally, it leads to an explicit description of several non-regularity phenomena in the corresponding non-uniformly hyperbolic cocycles, which is also of interest as both the first natural example of some of those phenomena and, more generally, the first non-artificial model where non-regularity can be explicitly studied.
Value function approximation in noisy environments using locally smoothed regularized approximate linear programs

Recently, Petrik et al. demonstrated that I4-Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and value function approximation steps simultaneously. RALP's performance guarantees become looser if sampled next states are used. For very noisy domains, RALP requires an accurate model rather than samples, which can be unrealistic in some practical scenarios. In this paper, we demonstrate this weakness, and then introduce Locally Smoothed L1-Regularized Approximate Linear Programming (LS-RALP). We demonstrate that LS-RALP mitigates inaccuracies stemming from noise even without an accurate model. We show that, given some smoothness assumptions, as the number of samples increases, error from noise approaches zero, and provide experimental examples of LS-RALP's success on common reinforcement learning benchmark problems.
Fast and Accurate Entity Recognition with Iterated Dilated Convolutions

Today when many practitioners run basic NLP on the entire web and large-volume traffic, faster methods are paramount to saving time and energy costs. Recent advances in GPU hardware have led to the emergence of bi-directional LSTMs as a standard method for obtaining per-token vector representations serving as input to labeling tasks such as NER (often followed by prediction in a linear-chain CRF). Though expressive and accurate, these models fail to fully exploit GPU parallelism, limiting their computational efficiency. This paper proposes a faster alternative to Bi-LSTMs for NER: Iterated Dilated Convolutional Neural Networks (ID-CNNs), which have better capacity than traditional CNNs for large context and structured prediction. Unlike LSTMs whose sequential processing on sentences of length N requires O(N) time even in the face of parallelism, ID-CNNs permit fixed-depth convolutions to run in parallel across entire documents. We describe a distinct combination of network structure, parameter sharing and training procedures that enable dramatic 14-20x test-time speedups while retaining accuracy comparable to the Bi-LSTM-CRF. Moreover, ID-CNNs trained to aggregate context from the entire document are more accurate than Bi-LSTM-CRFs while attaining 8x faster test time speeds.
A Family of Tractable Graph Distances.

Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in diverse areas, including, e.g., image processing and social networks. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics and thus come with no guarantees. Classic graph distances such as, e.g., the chemical and the CKS distance are arguably natural and intuitive, and are indeed also metrics, but they are intractable: as such, their computation does not scale to large graphs. We define a broad family of graph distances, that includes both the chemical and the CKS distance, and prove that these are all metrics. Crucially, we show that our family includes metrics that are tractable. Moreover, we extend these distances by incorporating auxiliary node attributes, which is important in practice, while maintaining both the metric property and tractability.
Polynomial interpolation over quaternions

Abstract Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated “on the left” and “on the right”. If the interpolation problem involves interpolation conditions of the same (left or right) type, the results are very much similar to the complex case: a consistent problem has a unique solution of a low degree (less than the number of interpolation conditions imposed), and the solution set of the homogeneous problem is an ideal in the ring H [ z ] . The problem containing both “left” and “right” interpolation conditions is quite different: there may exist infinitely many low-degree solutions and the solution set of the homogeneous problem is a quasi-ideal in H [ z ] .
Spatially-Aware Comparison and Consensus for Clusterings.

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a combination of the representations of their constituent points. We use this representation and the underlying metric to design a spatially-aware consensus clustering procedure. This consensus procedure is implemented via a novel reduction to Euclidean clustering, and is both simple and efficient. All of our results apply to both soft and hard clusterings. We accompany these algorithms with a detailed experimental evaluation that demonstrates the efficiency and quality
Solitary Waves and Their Linear Stability in Nonlinear Lattices

Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr¨ odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, which span a large number of lattice periods. In this limit, the allowed positions of solitary waves relative to the lattice, as well as their linear stability properties, hinge upon a certain recurrence relation which contains information beyond all orders of the usual two-scale perturbation expansion. It follows that only two such positions are permissible, and of those two solitary waves, one is linearly stable and the other unstable. For a cosine lattice, in particular, the two possible solitary waves are centered at a maximum or minimum of the lattice, with the former being stable, and the analytical predictions for the associated linear stability eigenvalues are in excellent agreement with numerical results. Furthermore, a countable set of multi-solitary-wave bound states are constructed analytically. In spite of rather different physical settings, the exponential asymptotics approach followed here is strikingly similar to that taken in earlier studies of solitary wavepackets involving a periodic carrier and a slowly varying envelope, which underscores the general value of this procedure for treating multiscale solitary-wave problems.
On the critical group of the missing Moore graph

We consider the critical group of a hypothetical Moore graph of diameter 2 and valency 57. Determining this group is equivalent to finding the Smith normal form of the Laplacian matrix of such a graph. We show that all of the Sylow p-subgroups of the critical group must be elementary abelian with the exception of p=5. We prove that the 5-rank of the Laplacian matrix determines the critical group up to two possibilities.
Existence of strong and nontrivial solutions to strongly coupled elliptic systems

Abstract We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of nontrivial and non-constant solutions (or pattern formations) will also be studied.
Questions and remarks on discrete and dense subgroups of Diff(I)

In recent decades, many remarkable papers have appeared which are devoted to the study of finitely generated subgroups of Diff+([0, 1]) (see [8, 15, 16, 19–23, 29, 30, 39, 40] only for some of the most recent developments). In contrast, discrete subgroups of the group Diff+([0, 1]) are much less studied. Very little is known in this area especially in comparison with the very rich theory of discrete subgroups of Lie groups which has started in the works of F. Klein and H. Poincare in the 19th century, and has experienced enormous growth in the works of A. Selberg, A. Borel, G. Mostow, G. Margulis and many others in the 20th century. Many questions which are either very easy or have been studied a long time ago for (discrete) subgroups of Lie groups remain open in the context of the infinite-dimensional group Diff+([0, 1]) and its relatives.
Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter-dependent shocks

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter dependent basis. The sought after parametric reduced-basis are obtained by transporting the snapshots in a spatially and parametrically dependent transport field. Key to the proposed approach is the observation that the transport fields are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The proposed approach is also integrated with well-known hyper-reduction strategies to obtain significant computational speed-ups. The method is successfully applied to the reduction of a parametric 1-D flow in a converging-diverging nozzle, a parametric 2-D supersonic flow over a forward facing step and a parametric 2-D jet diffusion flame in a combustor.
Learned perceptual image enhancement

Learning a typical image enhancement pipeline involves minimization of a loss function between enhanced and reference images. While L 1 and L 2 losses are perhaps the most widely used functions for this purpose, they do not necessarily lead to perceptually compelling results. In this paper, we show that adding a learned no-reference image quality metric to the loss can significantly improve enhancement operators. This metric is implemented using a CNN (convolutional neural network) trained on a large-scale dataset labelled with aesthetic preferences ofhuman raters. This loss allows us to conveniently perform back-propagation in our learning framework to simultaneously optimize for similarity to a given ground truth reference and perceptual quality. This perceptual loss is only used to train parameters of image processing operators, and does not impose any extra complexity at inference time. Our experiments demonstrate that this loss can be effective for tuning a variety of operators such as local tone mapping and dehazing.
On the achievable rates of decentralized equalization in massive MU-MIMO systems

Massive multi-user (MU) multiple-input multiple-output (MIMO) promises significant gains in spectral efficiency compared to traditional, small-scale MIMO technology. Linear equalization algorithms, such as zero forcing (ZF) or minimum mean-square error (MMSE)-based methods, typically rely on centralized processing at the base station (BS), which results in (i) excessively high interconnect and chip input/output data rates, and (ii) high computational complexity. In this paper, we investigate the achievable rates of decentralized equalization that mitigates both of these issues. We consider two distinct BS architectures that partition the antenna array into clusters, each associated with independent radio-frequency chains and signal processing hardware, and the results of each cluster are fused in a feed forward network. For both architectures, we consider ZF, MMSE, and a novel, non-linear equalization algorithm that builds upon approximate message passing (AMP), and we theoretically analyze the achievable rates of these methods. Our results demonstrate that decentralized equalization with our AMP-based methods incurs no or only a negligible loss in terms of achievable rates compared to that of centralized solutions.
Extreme Compressive Sampling for Covariance Estimation

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms. Through information-theoretic techniques, lower bounds showing that this estimator is minimax-optimal for both infinity and spectral norm estimation problems are established. These results are also specialized to give matching upper and lower bounds for estimating the population covariance of a collection of Gaussian vectors, again in the compressive measurement model. The analysis conducted in this paper shows that the effective sample complexity for this problem is scaled by a factor of $m^{2}/d^{2}$ , where $m$ is the compression dimension and $d$ is the ambient dimension. Applications to subspace learning (principal components analysis) and learning over distributed sensor networks are also discussed.
Learning from Comparisons and Choices

When tracking user-specific online activities, each user's preference is revealed in the form of choices and comparisons. For example, a user's purchase history is a record of her choices, i.e. which item was chosen among a subset of offerings. A user's preferences can be observed either explicitly as in movie ratings or implicitly as in viewing times of news articles. Given such individualized ordinal data in the form of comparisons and choices, we address the problem of collaboratively learning representations of the users and the items. The learned features can be used to predict a user's preference of an unseen item to be used in recommendation systems. This also allows one to compute similarities among users and items to be used for categorization and search. Motivated by the empirical successes of the MultiNomial Logit (MNL) model in marketing and transportation, and also more recent successes in word embedding and crowdsourced image embedding, we pose this problem as learning the MNL model parameters that best explain the data. We propose a convex relaxation for learning the MNL model, and show that it is minimax optimal up to a logarithmic factor by comparing its performance to a fundamental lower bound. This characterizes the minimax sample complexity of the problem, and proves that the proposed estimator cannot be improved upon other than by a logarithmic factor. Further, the analysis identifies how the accuracy depends on the topology of sampling via the spectrum of the sampling graph. This provides a guideline for designing surveys when one can choose which items are to be compared. This is accompanied by numerical simulations on synthetic and real data sets, confirming our theoretical predictions.
Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon

We present a new efficient way to perform hybrid density functional theory (DFT)-based electronic structure calculations. The new method uses an interpolative separable density fitting (ISDF) procedure to construct a set of numerical auxiliary basis vectors and a compact approximation of the matrix consisting of products of occupied orbitals represented in a large basis set such as the planewave basis. Such an approximation allows us to reduce the number of Poisson solves from O(Ne2) to O(Ne) when we apply the exchange operator to occupied orbitals in an iterative method for solving the Kohn–Sham equations, where Ne is the number of electrons in the system to be studied. We show that the ISDF procedure can be carried out in O(Ne3) operations, with a much smaller preconstant compared to methods used in existing approaches. When combined with the recently developed adaptively compressed exchange (ACE) operator formalism, which reduces the number of times the exchange operator needs to be updated, the result...
Knowledge Aided Consistency for Weakly Supervised Phrase Grounding

Given a natural language query, a phrase grounding system aims to localize mentioned objects in an image. In weakly supevised scenario, mapping between image regions (i.e., proposals) and language is not available in the training set. Previous methods address this deficiency by training a grounding system via learning to reconstruct language information contained in input queries from predicted proposals. However, the optimization is solely guided by the reconstruction loss from the language modality, and ignores rich visual information contained in proposals and useful cues from external knowledge. In this paper, we explore the consistency contained in both visual and language modalities, and leverage complementary external knowledge to facilitate weakly supervised grounding. We propose a novel Knowledge Aided Consistency Network (KAC Net) which is optimized by reconstructing input query and proposal's information. To leverage complementary knowledge contained in the visual features, we introduce a Knowledge Based Pooling (KBP) gate to focus on query-related proposals. Experiments show that KAC Net provides a significant improvement on two popular datasets.
Global bifurcation theory for periodic traveling interfacial gravity–capillary waves

Abstract We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity–capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can be positive, negative, or zero, and the surface tension parameter is positive. Thus, included in the parameter set are the cases of pure capillary water waves and gravity–capillary water waves. Our choice of coordinates allows for the possibility that the fluid interface is not a graph over the horizontal. We use a technical reformulation which converts the traveling wave equations into a system of the form “identity plus compact.” Rabinowitz' global bifurcation theorem is applied and the final conclusion is the existence of either a closed loop of solutions, or an unbounded set of nontrivial traveling wave solutions which contains waves which may move arbitrarily fast, become arbitrarily long, form singularities in the vorticity or curvature, or whose interfaces self-intersect.
Scale-invariant structures of spiral waves.

Abstract Background Spiral waves are considered to be one of the potential mechanisms that maintain complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. Method We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. Results Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. Conclusions Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.
Zagier duality for level p weakly holomorphic modular forms

We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level p with $$11 \le p \le 37$$ with poles only at the cusp at $$\infty $$ , and special cases of duality for an infinite class of prime levels. We derive generating functions for the bases for genus 1 levels.
How Will the Internet of Things Enable Augmented Personalized Health

The Internet of Things refers to network-enabled technologies, including mobile and wearable devices, which are capable of sensing and actuation as well as interaction and communication with other similar devices over the Internet. The IoT is profoundly redefining the way we create, consume, and share information. Ordinary citizens increasingly use these technologies to track their sleep, food intake, activity, vital signs, and other physiological statuses. This activity is complemented by IoT systems that continuously collect and process environment-related data that has a bearing on human health. This synergy has created an opportunity for a new generation of healthcare solutions.
On the u-invariant of function fields of curves over complete discretely valued fields

Abstract Let K be a complete discretely valued field with residue field κ. If char ( K ) = 0 , char ( κ ) = 2 and [ κ : κ 2 ] = d , we prove that there exists an integer N depending on d such that the u-invariant of any function field in one variable over K is bounded by N. The method of proof is via introducing the notion of uniform boundedness for the p-torsion of the Brauer group of a field and relating the uniform boundedness of the 2-torsion of the Brauer group to the finiteness of the u-invariant. We prove that the 2-torsion of the Brauer group of function fields in one variable over K is uniformly bounded.
Spatio-Temporal Interference Correlation and Joint Coverage in Cellular Networks

This paper provides an analytical framework with foundations in stochastic geometry to characterize the spatio-temporal interference correlation as well as the joint coverage probability at two spatial locations in a cellular network. In particular, modeling the locations of cellular base stations (BSs) as a Poisson point process, we study interference correlation at two spatial locations $\ell _{1}$ and $\ell _{2}$ separated by a distance $v$ , when the user follows the closest BS association policy at both spatial locations and moves from $\ell _{1}$ to $\ell _{2}$ . With this user displacement, two scenarios can occur: i) the user is handed off to a new serving BS at $\ell _{2}$ , or ii) no handoff occurs and the user is served by the same BS at both locations. After providing intermediate results, such as probability of handoff and distance distributions of the serving BS at the two user locations, we use them to derive exact expressions for spatio-temporal interference correlation coefficient and joint coverage probability for any distance separation $v$ . We also study two different handoff strategies: i) handoff skipping , and ii) conventional handoffs , and derive the expressions of joint coverage probability for both strategies. The exact analysis is not straightforward and involves a careful treatment of the neighborhood of the two spatial locations and the resulting handoff scenarios. To provide analytical insights, we also provide easy-to-use expressions for two special cases: i) static user ( $v =0$ ) and ii) highly mobile user ( $v \rightarrow \infty )$ . As expected, our analysis shows that the interference correlation and joint coverage probability decrease with increasing $v$ , with $v \rightarrow \infty $ corresponding to a completely uncorrelated scenario. Further design insights are also provided by studying the effect of few network/channel parameters, such as BS density and path loss on the interference correlation.
Multilingual Constituency Parsing with Self-Attention and Pre-Training.

We show that constituency parsing benefits from unsupervised pre-training across a variety of languages and a range of pre-training conditions. We first compare the benefits of no pre-training, fastText, ELMo, and BERT for English and find that BERT outperforms ELMo, in large part due to increased model capacity, whereas ELMo in turn outperforms the non-contextual fastText embeddings. We also find that pre-training is beneficial across all 11 languages tested; however, large model sizes (more than 100 million parameters) make it computationally expensive to train separate models for each language. To address this shortcoming, we show that joint multilingual pre-training and fine-tuning allows sharing all but a small number of parameters between ten languages in the final model. The 10x reduction in model size compared to fine-tuning one model per language causes only a 3.2% relative error increase in aggregate. We further explore the idea of joint fine-tuning and show that it gives low-resource languages a way to benefit from the larger datasets of other languages. Finally, we demonstrate new state-of-the-art results for 11 languages, including English (95.8 F1) and Chinese (91.8 F1).
Scalar conservation laws with multiple rough fluxes

We study pathwise entropy solutions for scalar conservation laws with inhomogeneous fluxes and quasilinear multiplicative rough path dependence. This extends the previous work of Lions, Perthame and Souganidis who considered spatially independent and inhomogeneous fluxes with multiple paths and a single driving singular path respectively. The approach is motivated by the theory of stochastic viscosity solutions which relies on special test functions constructed by inverting locally the flow of the stochastic characteristics. For conservation laws this is best implemented at the level of the kinetic formulation which we follow here.
Hierarchical Symbolic Dynamic Filtering of Streaming Non-stationary Time Series Data

Abstract This paper proposes a hierarchical feature extractor for non-stationary streaming time series based on the concept of switching observable Markov chain models. The slow time-scale non-stationary behaviors are considered to be a mixture of quasi-stationary fast time-scale segments that are exhibited by complex dynamical systems. The key idea is to model each unique stationary characteristics without apriori knowledge (e.g., number of possible unique characteristics) at a lower logical level, and capture the transitions from one low-level model to another at a higher level. In this context, the concepts in the recently developed Symbolic Dynamic Filtering is extended, to build an online algorithm suited for handling quasi-stationary data at a lower level and a non-stationary behavior at a higher level without apriori knowledge. A key observation made in this study is that the rate of change of data likelihood seems to be a better indicator of change in data characteristics compared to the traditional methods that mostly consider data likelihood for change detection. Thus, an adaptive Chinese Restaurant Process (CRP) distribution is formulated to accommodate the rate of change of data likelihood in the learning algorithm. The algorithm also aims to minimize model complexity while capturing data characteristics (likelihood). Efficacy demonstration and comparative evaluation of the proposed algorithm are performed using time series data both from a simulated system that exhibit nonlinear dynamics as well as a real residential electrical energy disaggregation case study using the publicly available reference energy disaggregation dataset (REDD). We discuss results that show that the proposed hierarchical symbolic dynamic filtering (HSDF) algorithm can identify underlying features with significantly high degree of accuracy, even under very noisy conditions. Based on our validation experiments, we demonstrate better performance of the proposed fast algorithm compared to the baseline Hierarchical Dirichlet Process-Hidden Markov Models (HDP-HMM). The proposed algorithm’s low computational complexity also makes it suitable for on-board, real time operations.
The dual Radon–Nikodym property for finitely generated Banach C ( K )-modules

We extend the well-known criterion of Lotz for the dual Radon–Nikodym property (RNP) of Banach lattices to finitely generated Banach C(K)-modules and Banach C(K)-modules of finite multiplicity. Namely, we prove that if X is a Banach space from one of these classes then its Banach dual $$X^\star $$ has the RNP iff X does not contain a closed subspace isomorphic to $$\ell ^1$$ .
Secure distributed membership tests via secret sharing: How to hide your hostile hosts: Harnessing shamir secret sharing

Data security and availability for operational use are frequently seen as conflicting goals. Research on searchable encryption and homomorphic encryption are a start, but they typically build from encryption methods that, at best, provide protections based on problems assumed to be computationally hard. By contrast, data encoding methods such as secret sharing provide information-theoretic data protections. Archives that distribute data using secret sharing can provide data protections that are resilient to malicious insiders, compromised systems, and untrusted components. In this paper, we create the Serial Interpolation Filter, a method for storing and interacting with sets of data that are secured and distributed using secret sharing. We provide the ability to operate over set-oriented data distributed across multiple repositories without exposing the original data. Furthermore, we demonstrate the security of our method under various attacker models and provide protocol extensions to handle colluding attackers. The Serial Interpolation Filter provides information-theoretic protections from a single attacker and computationally hard protections from colluding attackers.
Software-defined Radios: Architecture, state-of-the-art, and challenges

Abstract Software-defined Radio (SDR) is a programmable transceiver with the capability of operating various wireless communication protocols without the need to change or update the hardware. Progress in the SDR field has led to the escalation of protocol development and a wide spectrum of applications, with a greater emphasis on programmability, flexibility, portability, and energy efficiency in cellular, WiFi, and M2M communication. Consequently, SDR has earned a lot of attention and is of great significance to both academia and industry. SDR designers intend to simplify the realization of communication protocols while enabling researchers to experiment with prototypes on deployed networks. This paper is a survey of the state-of-the-art SDR platforms in the context of wireless communication protocols. We offer an overview of SDR architecture and its basic components, and then discuss the significant design trends and development tools. In addition, we highlight key contrasts between SDR architectures with regards to energy, computing power, and area, based on a set of metrics. We also review existing SDR platforms and present an analytical comparison as a guide to developers. Finally, we recognize a few of the related research topics and summarize potential solutions.
Back to Mechanisms of Superconductivity in Low-Doped Strontium Titanate

We have analyzed two mechanisms proposed recently for superconductivity in doped SrTiO3 - the plasmon-mediated pairing and the potential of an instantaneous attraction between two electrons that owes its origin to the exchange by high-frequency optical phonons. The first approach seems to be self-consistent, but in a limited range of the dielectric constant. As to the direct instantaneous interaction between two electrons,it was hypothesized as due to the exchange by the band LO phonons. The latter supposition was incorrect. In the current paper, it shows that the contributions into the pairing matrix element possessing the structure of a net attraction come about only as the result of disorder. Indeed, the experiment revealed the mobility edge in doped SrTiO3. Doped electrons occupying states with the energy below the mobility edge are localized on dopants thereby become strongly coupled with the lattice vibrations. The emergence of the localized phonon modes attached to defect is one of the results of such electron-lattice coupling. For two electrons in the conduction band the virtual exchange by the quantum of such local mode manifests itself as the effective attraction. The total contribution into the pairing matrix element from these processes, increasing with concentration can overwhelm the Coulomb repulsion screened by the band LO phonons. That is, the role previously ascribed to the band LO phonons actually belongs to the localized phonons.
Some power series involving involutions in Coxeter groups

Let W be a Coxeter group. We show that a certain power series involving a sum over all involutions in W can be expressed in terms of the Poincare series of W . (The case where W is finite has been known earlier.) Introduction 0.1. Let V ′ be an n-dimensional vector space over the finite field Fq and let V = Fq2⊗FqV ′, an n-dimensional vector space over Fq2 . Let F : V → V be the Fq-linear isomorphism λ ⊗ v → λ ⊗ v where λ ∈ Fq2 , v ∈ V ′. Let F be the set of all flags V∗ = (V1 ⊂ V2 ⊂ Vn) in V where for i = 1, . . . , n, Vi there exists an i-dimensional Fq2-subspace of V ; let F ′ be the analogous set defined in terms of V ,Fq instead of V,Fq2 . Note that F induces a bijection F → F , V∗ = (V1 ⊂ V2 ⊂ Vn) → F (V∗) = (F (V1)F (V2)F (Vn)). The standard way to count the number |F| elements in F is to fix V 0 ∗ ∈ F and to partition F into pieces indexed by the symmetric group Sn; the piece corresponding to w ∈ Sn is the set of all V∗ ∈ F such that V 0 ∗ , V∗ are in relative position (this piece contains exactly q elements where l : Sn → N is the standard length function). This yields the expression |F| = ∑ w∈Sn q . Similarly we have |F ′| = ∑ w∈Sn q . Another way to compute |F| without a choice of V 0 ∗ is to partition F into pieces indexed by the set I of involutions in Sn; the piece corresponding to z ∈ I is the set of all V∗ ∈ F such that V∗, F (V∗) are in relative position z (this piece contains exactly |F ′|ql(z)( q−1 q+1 ) where φ(z) is the number of (−1)-eigenvalues of z in the reflection representation of Sn). (If we had taken a z in Sn − I we would have got an empty piece.) This yields the expression |F| = |F ′| ∑ z∈I q ( q−1 q+1 ) . We deduce that the sum ∑ z∈I q( q − 1 q + 1 ) (a kind of weighted Poincare polynomial based on involutions) is equal to a quotient of two ordinary Poincare polynomials: ∑
A Fast and Scalable Joint Estimator for Integrating Additional Knowledge in Learning Multiple Related Sparse Gaussian Graphical Models

We consider the problem of including additional knowledge in estimating sparse Gaussian graphical models (sGGMs) from aggregated samples, arising often in bioinformatics and neuroimaging applications. Previous joint sGGM estimators either fail to use existing knowledge or cannot scale-up to many tasks (large $K$) under a high-dimensional (large $p$) situation. In this paper, we propose a novel \underline{J}oint \underline{E}lementary \underline{E}stimator incorporating additional \underline{K}nowledge (JEEK) to infer multiple related sparse Gaussian Graphical models from large-scale heterogeneous data. Using domain knowledge as weights, we design a novel hybrid norm as the minimization objective to enforce the superposition of two weighted sparsity constraints, one on the shared interactions and the other on the task-specific structural patterns. This enables JEEK to elegantly consider various forms of existing knowledge based on the domain at hand and avoid the need to design knowledge-specific optimization. JEEK is solved through a fast and entry-wise parallelizable solution that largely improves the computational efficiency of the state-of-the-art $O(p^5K^4)$ to $O(p^2K^4)$. We conduct a rigorous statistical analysis showing that JEEK achieves the same convergence rate $O(\log(Kp)/n_{tot})$ as the state-of-the-art estimators that are much harder to compute. Empirically, on multiple synthetic datasets and two real-world data, JEEK outperforms the speed of the state-of-arts significantly while achieving the same level of prediction accuracy. Available as R tool @ this http URL
ON THE LEGENDRIAN AND TRANSVERSE CLASSIFICATION OF CABLINGS

In this note we study Legendrian and transverse knots in the knot type of a (p, q)-cable of a knot K in S. We give two structural theorems that describe when the (p, q)cable of a Legendrian simple knot type K is also Legendrian simple.
C is not Equivalent to C− in its Jacobian: A Tropical Point of View

We show that the Abel-Jacobi image of a tropical curve $C$ in its Jacobian $J(C)$ is not algebraically equivalent to its reflection by using a simple calculation in tropical homology.
Topological bounds for Fourier coefficients and applications to torsion

Abstract Let Ω ⊂ R 2 be a bounded convex domain in the plane and consider − Δ u = 1 in Ω u = 0 on ∂ Ω . If u assumes its maximum in x 0 ∈ Ω , then the eccentricity of level sets close to the maximum is determined by the Hessian D 2 u ( x 0 ) . We prove that D 2 u ( x 0 ) is negative definite and give a quantitative bound on the spectral gap λ max ( D 2 u ( x 0 ) ) ≤ − c 1 exp ⁡ ( − c 2 diam ( Ω ) inrad ( Ω ) ) for universal c 1 , c 2 > 0 . This is sharp up to constants. The proof is based on a new lower bound for Fourier coefficients whose proof has a topological component: if f : T → R is continuous and has n sign changes, then ∑ k = 0 n / 2 | 〈 f , sin ⁡ k x 〉 | + | 〈 f , cos ⁡ k x 〉 | ≳ n | f ‖ L 1 ( T ) n + 1 ‖ f ‖ L ∞ ( T ) n . This statement immediately implies estimates on higher derivatives of harmonic functions u in the unit ball: if u is very flat in the origin, then the boundary function u ( cos ⁡ t , sin ⁡ t ) : T → R has to have either large amplitude or many roots. It also implies that the solution of the heat equation starting with f : T → R cannot decay faster than ∼ exp ⁡ ( − ( # sign changes ) 2 t / 4 ) .
Conjugacy growth of finitely generated groups

Abstract The conjugacy growth function of a finitely generated group measures the number of conjugacy classes in balls with respect to a word metric. We study the following natural question: Which functions can occur as the conjugacy growth function of finitely generated groups? Our main result answers the question completely. Namely we prove that a function f : N → N can be realized (up to a natural equivalence) as the conjugacy growth function of a finitely generated group if and only if f is non-decreasing and bounded from above by a n for some a ≥ 1 . We also construct a finitely generated group G and a subgroup H ≤ G of index 2 such that H has only 2 conjugacy classes while the conjugacy growth of G is exponential. In particular, conjugacy growth is not a quasi-isometry invariant.
Exploring Hidden Dimensions in Parallelizing Convolutional Neural Networks.

The past few years have witnessed growth in the computational requirements for training deep convolutional neural networks. Current approaches parallelize training onto multiple devices by applying a single parallelization strategy (e.g., data or model parallelism) to all layers in a network. Although easy to reason about, these approaches result in suboptimal runtime performance in large-scale distributed training, since different layers in a network may prefer different parallelization strategies. In this paper, we propose layer-wise parallelism that allows each layer in a network to use an individual parallelization strategy. We jointly optimize how each layer is parallelized by solving a graph search problem. Our evaluation shows that layer-wise parallelism outperforms state-of-the-art approaches by increasing training throughput, reducing communication costs, achieving better scalability to multiple GPUs, while maintaining original network accuracy.
Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications.
Poisson cluster process: Bridging the gap between PPP and 3GPP HetNet models

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach modeling the user and BS locations as independent and homogeneous Poisson point processes (PPPs) has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based model is not rich enough to capture all the spatial configurations that appear in real-world HetNet deployments (on which 3GPP simulation models are based). In this paper, we bridge the gap between the 3GPP simulation models and the popular PPP-based analytical model by developing a new unified HetNet model in which a fraction of users and some BS tiers are modeled as Poisson cluster processes (PCPs). This model captures both non-uniformity and coupling in the BS and user locations. For this setup, we derive exact expression for downlink coverage probability under maximum signal-to-interference ratio (SIR) cell association model. As intermediate results, we define and evaluate sum-product functionals for PPP and PCP. Special instances of the proposed model are shown to closely resemble different configurations considered in 3GPP HetNet models. Our results concretely demonstrate that the performance trends are highly sensitive to the assumptions made on the user and SBS configurations.
Deformations of modules through butterflies and gerbes

Abstract Classifying obstructions to the problem of finding extensions between two fixed modules goes back at least to L. Illusie's thesis. Our approach, following in the footsteps of J. Wise, is to introduce an analogous Grothendieck Topology on the category A-mod of modules over a fixed ring A in a topos E . The problem of finding extensions becomes a banded gerbe and furnishes a cohomology class on the site A-mod. We compare our obstruction and that coming from Illusie's work, giving another construction of the exact sequence Illusie used to obtain his obstruction. Our work circumvents the cotangent complex entirely and answers a question posed by Illusie.
Simplices over finite fields

We prove that, provided $d > k$, every sufficiently large subset of $\mathbf{F}_q^d$ contains an isometric copy of every $k$-simplex that avoids spanning a nontrivial self-orthogonal subspace. We obtain comparable results for simplices exhibiting self-orthogonal behavior.
Equilibrium Analysis of Vertical Mergers

Vertical mergers are known to potentially create an incentive for the merged firm to raise the price of inputs it supplies to its rivals (raising rivals’ cost [RRC]). At the same time, vertical mer...