Search

Significance Prostate cancer is the most common cancer among men. An accurate diagnosis of its severity at detection plays a major role in improving their survival. Recently, machine learning models using biomarkers identified from Raman micro-spectroscopy discriminated intraductal carcinoma of the prostate (IDC-P) from cancer tissue with a ≥85 % detection accuracy and differentiated high-grade prostatic intraepithelial neoplasia (HGPIN) from IDC-P with a ≥97.8 % accuracy. Aim To improve the classification performance of machine learning models identifying different types of prostate cancer tissue using a new dimensional reduction technique. Approach A radial basis function (RBF) kernel support vector machine (SVM) model was trained on Raman spectra of prostate tissue from a 272-patient cohort (Centre hospitalier de l'Universite de Montreal, CHUM) and tested on two independent cohorts of 76 patients [University Health Network (UHN)] and 135 patients (Centre hospitalier universitaire de Quebec-Universite Laval, CHUQc-UL). Two types of engineered features were used. Individual intensity features, i.e., Raman signal intensity measured at particular wavelengths and novel Raman spectra fitted peak features consisting of peak heights and widths. Results Combining engineered features improved classification performance for the three aforementioned classification tasks. The improvements for IDC-P/cancer classification for the UHN and CHUQc-UL testing sets in accuracy, sensitivity, specificity, and area under the curve (AUC) are (numbers in parenthesis are associated with the CHUQc-UL testing set): +4 % (+8 % ), +7 % (+9 % ), +2 % (6%), +9 (+9) with respect to the current best models. Discrimination between HGPIN and IDC-P was also improved in both testing cohorts: +2.2 % (+1.7 % ), +4.5 % (+3.6 % ), +0 % (+0 % ), +2.3 (+0). While no global improvements were obtained for the normal versus cancer classification task [+0 % (-2 % ), +0 % (-3 % ), +2 % (-2 % ), +4 (+3)], the AUC was improved in both testing sets. Conclusions Combining individual intensity features and novel Raman fitted peak features, improved the classification performance on two independent and multicenter testing sets in comparison to using only individual intensity features.

Author(s): Kapre, Rohan; Zhou, Junhan; Li, Xinzhe; Beckett, Laurel; Louie, Angelique Y | Abstract: PurposeTo demonstrate that constant coefficient of variation (CV), but nonconstant absolute variance in MRI relaxometry (T1 , T2 , R1 , R2 ) data leads to erroneous conclusions based on standard linear models such as ordinary least squares (OLS). We propose a gamma generalized linear model identity link (GGLM-ID) framework that factors the inherent CV into parameter estimates. We first examined the effects on calculations of contrast agent relaxivity before broadening to other applications such as analysis of variance (ANOVA) and liver iron content (LIC).MethodsEightnmodels including OLS and GGLM-ID were initially fit to data obtained on sulfated dextran iron oxide (SDIO) nanoparticles. Both a resampling simulation on the data as well as two separate Monte Carlo simulations (with and without concentration error) were performed to determine mean square error (MSE) and type I error rate. We then evaluated the performance of OLS/GGLM-ID on R1 repeatability and LIC data sets.ResultsOLS had an MSE of 4-5× that of GGLM-ID as well as a type I error rate of 20-30%, whereas GGLM-ID was near the nominal 5% level in the relaxivity study. Only OLS found statistically significant effects of MRI facility on relaxivity in an R1 repeatability study, but no significant differences were found in a resampling, whereas GGLM was more consistent. GGLM-ID was also superior to OLS for modeling LIC.ConclusionsOLS leads to erroneous conclusions when analyzing MRI relaxometry data. GGLM-ID factors in the inherent CV of an MRI experiment, leading to more reproducible conclusions.

The brew temperature is widely considered a key parameter affecting the final quality of coffee, with a temperature near 93 °C often described as optimal. In particular, drip brewers that do not achieve a minimum brew temperature of 92 °C within a prescribed time period fail their certification. There is little empirical evidence in terms of rigorous sensory descriptive analysis or consumer preference testing, however, to support any particular range of brew temperatures. In this study, we drip-brewed coffee to specific brew strengths, as measured by total dissolved solids (TDS), and extraction yields, as measured by percent extraction (PE), spanning the range of the classic Coffee Brewing Control Chart. Three separate brew temperatures of 87 °C, 90 °C, or 93 °C were tested, adjusting the grind size and overall brew time as necessary to achieve the target TDS and PE. Although the TDS and PE both significantly affected the sensory profile of the coffee, surprisingly the brew temperature had no appreciable impact. We conclude that brew temperature should be considered as only one of several parameters that affect the extraction dynamics, and that ultimately the sensory profile is governed by differences in TDS and PE rather than the brew temperature, at least over the range of temperatures tested.

Motivation We introduce PRINCESS, a privacy-preserving international collaboration framework for analyzing rare disease genetic data that are distributed across different continents. PRINCESS leverages Software Guard Extensions (SGX) and hardware for trustworthy computation. Unlike a traditional international collaboration model, where individual-level patient DNA are physically centralized at a single site, PRINCESS performs a secure and distributed computation over encrypted data, fulfilling institutional policies and regulations for protected health information. Results To demonstrate PRINCESS’ performance and feasibility, we conducted a family-based allelic association study for Kawasaki Disease, with data hosted in three different continents. The experimental results show that PRINCESS provides secure and accurate analyses much faster than alternative solutions, such as homomorphic encryption and garbled circuits (over 40 000× faster). Availability and Implementation https://github.com/achenfengb/PRINCESS_opensource Supplementary information Supplementary data are available at Bioinformatics online.

Algorithms for evaluating and optimizing the useful anomalous correlation and the anomalous signal in a SAD data set are described., A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. Here, algorithms and tools for evaluating and optimizing the useful anomalous correlation and the anomalous signal in a SAD experiment are described. A simple theoretical framework [Terwilliger et al. (2016 ▸), Acta Cryst. D72, 346–358] is used to develop methods for planning a SAD experiment, scaling SAD data sets and estimating the useful anomalous correlation and anomalous signal in a SAD data set. The phenix.plan_sad_experiment tool uses a database of solved and unsolved SAD data sets and the expected characteristics of a SAD data set to estimate the probability that the anomalous substructure will be found in the SAD experiment and the expected map quality that would be obtained if the substructure were found. The phenix.scale_and_merge tool scales unmerged SAD data from one or more crystals using local scaling and optimizes the anomalous signal by identifying the systematic differences among data sets, and the phenix.anomalous_signal tool estimates the useful anomalous correlation and anomalous signal after collecting SAD data and estimates the probability that the data set can be solved and the likely figure of merit of phasing.

In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known results. This includes a 1999 example of Faltings from his Baker’s Garden article. We also extend the theory of these Nevanlinna constants to what we call “multidivisor Nevanlinna constants,” which allow the proximity function to involve the maximum of Weil functions for finitely many divisors.

Author(s): Oh, Sung-Jin; Tataru, Daniel | Abstract: This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical $4+1$ dimensional hyperbolic Yang--Mills equation. The Threshold Theorem asserts that topologically trivial solutions with energy below twice the ground state energy are global and scatter. The Dichotomy Theorem applies to solutions in arbitrary topological class with large energy, and provides two exclusive alternatives: Either the solution is global and scatters, or it bubbles off a soliton in either finite time or infinite time. Using the caloric gauge developed in the first paper, the continuation/scattering criteria established in the second paper, and the large data analysis in an arbitrary topological class at optimal regularity in the third paper, here we perform a blow-up analysis which shows that the failure of global well-posedness and scattering implies either the existence of a soliton with at most the same energy bubbling off, or the existence existence of a nontrivial self-similar solution. The proof is completed by showing that the latter solutions do not exist.

This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. Our results determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. We also show that the ultimate bound on the maximum achievable rate of convergence via time delay is e (Euler's number) times the delay free rate. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. The final contribution of this paper is to show the application of our results in analyzing the use of a delayed feedback to increase the rate of convergence of an agreement algorithm for networked systems.

This paper forms the first part of a series by the authors [GMV2,GMV3] concerning the structure theory of nilspaces of Antol\'in Camarena and Szegedy. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$ satisfying some natural axioms. Antol\'in Camarena and Szegedy proved that from these axioms it follows that (certain) nilspaces are isomorphic (in a strong sense) to an inverse limit of nilmanifolds. The aim of our project is to provide a new self-contained treatment of this theory and give new applications to topological dynamics. This paper provides an introduction to the project from the point of view of applications to higher order Fourier analysis. We define and explain the basic definitions and constructions related to cubespaces and nilspaces and develop the weak structure theory, which is the first stage of the proof of the main structure theorem for nilspaces. Vaguely speaking, this asserts that a nilspace can be built as a finite tower of extensions where each of the successive fibers is a compact abelian group. We also make some modest innovations and extensions to this theory. In particular, we consider a class of maps that we term fibrations, which are essentially equivalent to what are termed fiber-surjective morphisms by Anatol\'in Camarena and Szegedy, and we formulate and prove a relative analogue of the weak structure theory alluded to above for these maps. These results find applications elsewhere in the project., Comment: 64 pages, minor revision based on referee's report, results and proofs have not been changed, this version is accepted for publication in J. Anal. Math

Quantile and quantile effect functions are important tools for descriptive and causal analyses due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This paper offers a simple, practical construction of simultaneous confidence bands for quantile and quantile effect functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling methods for observed and counterfactual distributions, and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. We find that universal insurance coverage increases the number of doctor visits across the entire distribution, and that the racial test score gap is small at early ages but grows with age due to socio economic factors affecting child development especially at the top of the distribution. These are new, interesting empirical findings that complement previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering existing inference methods invalid for obtaining uniform confidence bands for observed and counterfactual quantile functions and for their difference -- the quantile effects functions., Comment: 38 pages, 6 figures, 4 tables

In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked coupling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID-19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to $18-m$ March, 2020 where $m$ is equal to the number of prediction days. Compared with integer-order system ($\alpha=0$), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case without network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number $R_0$ is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when $R_0\le 1$, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future., Comment: 11 pages, 10 figures, ND Special Issue paper submitted

This paper describes the development of a new uncertainty estimator for slitting method residual stress measurements. The new uncertainty estimator accounts for uncertainty in the regularization-based smoothing included in the residual stress calculation procedure, which is called regularization uncertainty. The work describes a means to quantify regularization uncertainty and then, in the context of a numerical experiment, compares estimated uncertainty to known errors. The paper further compares a first-order uncertainty estimate, established by a repeatability experiment, to the new uncertainty estimator and finds good correlation between the two estimates of precision. Furthermore, the work establishes a procedure for automated determination of the regularization parameter value that minimizes total uncertainty. In summary, the work shows that uncertainty in the regularization parameter is a significant contributor to the total uncertainty in slitting method measurements and that the new uncertainty estimator provides a reasonable estimate of single measurement uncertainty.

Laser ultrasonic techniques (LUTs) are becoming widely used for damage detection based on full-field ultrasonic data. In general, LUTs provide threedimensional (3-D) ultrasonic signals from which significant informative features may be extracted about the health condition of a structure. In this paper, statistical convariance method is proposed to investigate 3-D ultrasonic features. A laser ultrasonic interrogation method based on a Q-switched laser scanning system was used to interrogate 3-D ultrasonic signals in to a 2 mm aluminum plate. The ultrasonic signals in three-dimensional (3-D) space were generated, indexed by spatial N (xdirection), spatial M (y-direction), and temporal K (t-direction) samples, respectively. Then, two sets of covariance matrices were obtained based on the vector variables in x-direction and y-direction respectively for all k time samples respectively. The covariance imaging and the corresponding variance map were obtained. The wavelength and group velocity of S0 and A0 modes were able estimated from the variance map. The wavelength of the S0 and A0 modes were estimated with the deviation error of 2.3% and 11% respectively. The group velocities of S0 and A0 modes were estimated with the deviation error of 1.8% and 0.9%. The analysis will be further performed to develop group velocity curves for a range of frequency in metal and composite plates.

Our very eloquent charge from Jan van Mill was to “draw a line to Brouwer from descriptive set theory, but this proved elusive: in fact there are few references to Brouwer, in Lusin (1928) [36] and Lusin (1930), none of them substantial; and even though Brouwer refers to Borel, Lebesgue and Hadamard in his early papers, it does not appear that he was influenced by their work in any substantive way. 1 We have not found any references by him to more developed work in descriptive set theory, after the critical Lebesgue (1905). So instead of looking for historical connections or direct influences (in either direction), we decided to identify and analyze some basic themes, problems and results which are common to these two fields; and, as it turns out, the most significant connections are between intuitionistic analysis and effective descriptive set theory, hence the title. ⇒ We will outline our approach and (limited) aims in Section 1 , marking with an arrow (like this one) those paragraphs which point to specific parts of the article. Suffice it to say here that our main aim is to identify a few, basic results of descriptive set theory which can be formulated and justified using principles that are both intuitionistically and classically acceptable; that we will concentrate on the mathematics of the matter rather than on history or philosophy; and that we will use standard, classical terminology and notation. This is an elementary, mostly expository paper, broadly aimed at students of logic and set theory who also know the basic facts about recursive functions but need not know a lot about either intuitionism or descriptive set theory. The only (possibly) new result is Theorem 6.1 , which justifies simple definitions and proofs by induction in Kleene’s Basic System of intuitionistic analysis, and is then used in Theorem 7.1 , Theorem 7.2 to give in the same system a rigorous definition of the Borel sets and prove that they are analytic; the formulation and proof of this last result is one example where methods from effective descriptive set theory are used in an essential way.

Frequent inventory data of container nurseries is needed by growers to ensure proper management and marketing strategies. In this paper, inventory data are estimated from aerial images. Since there are thousands of nursery species, it is difficult to find a generic classification algorithm for all cases. In this paper, the development of classification methods was confined to three representative categories: green foliage, yellow foliage, and flowering plants. Vegetation index thresholding and the support vector machine (SVM) were used for classification. Classification accuracies greater than 97% were obtained for each case. Based on the classification results, an algorithm based on canopy area mapping was built for counting. The effects of flight altitude, container spacing, and ground cover type were evaluated. Results showed that container spacing and interaction of container spacing with ground cover type have a significant effect on counting accuracy. To mimic the practical shipping and moving process, incomplete blocks with different voids were created. Results showed that the more plants removed from the block, the higher the accuracy. The developed algorithm was tested on irregular- or regular-shaped plants and plants with and without flowers to test the stability of the algorithm, and accuracies greater than 94% were obtained. Published version

Recent advances in clustering have included continuous relaxations of the Cheeger cut problem and those which address its linear approximation using the graph Laplacian. In this paper, we show how to use the graph Laplacian to solve the fully nonlinear Cheeger cut problem, as well as the ratio cut optimization task. Both problems are connected to total variation minimization, and the related Ginzburg-Landau functional is used in the derivation of the methods. The graph framework discussed in this paper is undirected. The resulting algorithms are efficient ways to cluster thedata into two classes, and they can be easily extended to case of multiple classes, or used on a multiclass data set via recursive bipartitioning. In addition to showing results on benchmark data sets, we also show an application of the algorithm to hyperspectral video data.

In this paper we analyze the long-time behavior of 3-dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by C t - 1 $t^{-1}$ for large t. This proves a conjecture of Perelman for this class of initial topologies. The proof of this fact illustrates the fundamental ideas that are used in the subsequent papers of the author.

In this paper we develop the basic tools for a classification of Killing vector fields of constant length on pseudo-Riemannian homogeneous spaces. This extends a recent paper of M. Xu and J. A. Wolf, which classified the pairs $(M,\xi)$ where $M = G/H$ is a Riemannian normal homogeneous space, G is a compact simple Lie group, and $\xi \in \mathfrak{g}$ defines a nonzero Killing vector field of constant length on $M$. The method there was direct computation. Here we make use of the moment map $M \to \mathfrak{g}^{*}$ and the flag manifold structure of $\mathrm{Ad} (G) \xi$ to give a shorter, more geometric proof which does not require compactness and which is valid in the pseudo-Riemannian setting. In that context we break the classification problem into three parts. The first is easily settled. The second concerns the cases where $\xi$ is elliptic and $G$ is simple (but not necessarily compact); that case is our main result here. The third, which remains open, is a more combinatorial problem involving elements of the first two.

Consider a finite two-player game with one round of communication. Restrict players to a subset of “monotonic” strategies. The paper justifies this restriction. The paper provides sufficient conditions under which the strategies of the restricted game that survive iterative deletion of weakly dominated strategies favor the agent who can communicate.

The problem of high-speed traversal of sharp toolpath corners, within a prescribed geometrical tolerance 𝜖, is addressed. Each sharp corner is replaced by a quintic Pythagorean–hodograph (PH) curve that meets the incoming/outgoing path segments with G 2 continuity, and deviates from the exact corner by no more than the prescribed tolerance 𝜖. The deviation and extremum curvature admit closed-form expressions in terms of the corner angle 𝜃 and side-length L, allowing precise control over these quantities. The PH curves also permit a smooth modulation of feedrate around the corner by analytic reduction of the interpolation integral. To demonstrate this, real-time interpolator algorithms are developed for three model feedrate functions. Specifying the feedrate as a quintic polynomial in the curve parameter accommodates precise acceleration continuity, but has no obvious geometrical interpretation. An inverse linear dependence on curvature offers a purely geometrical specification, but incurs slight initial and final tangential acceleration discontinuities. As an alternative, a hybrid form that incorporates the main advantages of these two approaches is proposed. In each case, the ratio $f=V_{\min }/V_{0}$ of the minimum and nominal feedrates is a free parameter, and the improved cornering time is analyzed. This paper develops the basic cornering algorithms—their implementation and performance analysis are described in detail in a companion paper.

This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist, we complete the proof., 64 pages

In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidity of bounded domains in hyperbolic spaces. We also obtain the global scalar curvature rigidity for conformal deformations of metrics in the domains, where the lapse functions are positive, on vacuum static spaces with positive scalar curvature, and show such domains are maximal, which generalizes the work in [15]., Comment: 14 pages, new references added, a few typo fixed

This paper introduces notions and tools for finite time stability of closed sets for a class of hybrid systems. The proposed finite time stability notion consists of both Lyapunov stability and finite time convergence. Several sufficient conditions for a closed set to have such a property for a hybrid system are established. Robustness of finite time stability to small perturbations is studied by the regularity of the system data. Relationships between finite time stability and asymptotic stability of sets are also investigated. Examples illustrating the results are discussed throughout the paper.

This paper is the first part of a trilogy [22, 23] dedicated to a proof of global well-posedness and scattering of the \((4+1)\)-dimensional mass-less Maxwell–Klein–Gordon equation (MKG) for any finite energy initial data. The main result of the present paper is a large energy local well-posedness theorem for MKG in the global Coulomb gauge, where the lifespan is bounded from below by the energy concentration scale of the data. Hence the proof of global well-posedness is reduced to establishing non-concentration of energy. To deal with non-local features of MKG we develop initial data excision and gluing techniques at critical regularity, which might be of independent interest.

Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. Many studies have analyzed how population structure influences statistics of genetic variants and developed several statistical approaches to correct for population structure. However, the impact of population structure on GEI statistics in GWASs has not been extensively studied and nor have there been methods designed to correct for population structure on GEI statistics. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models to account for population structure on GEI statistics. We find that our approach effectively controls population structure on statistics for GEIs as well as for genetic variants., Author Summary Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models that can effectively correct for population structure when searching for GEIs.

This paper is a republication of an MMS paper [A. L. Bertozzi and A. Flenner, Multiscale Model. Simul., 10 (2012), pp. 1090--1118] describing a new class of algorithms for classification of high dimensional data. These methods combine ideas from spectral methods on graphs with nonlinear edge/region detection methods traditionally used in the PDE-based imaging community. The algorithms use the Ginzburg--Landau functional, extended to a graphical framework, which has classical PDE connections to total variation minimization. Convex splitting algorithms allow us to quickly find minimizers of the proposed model and take advantage of fast spectral solvers of linear graph-theoretic problems. We review the diverse computational examples presented in the original paper, involving both basic clustering and semisupervised learning for different applications. Case studies include feature identification in images, segmentation in social networks, and segmentation of shapes in high dimensional datasets. Since the pape...

This paper introduces new incremental stability notions for a class of hybrid dynamical systems given in terms of differential equations and difference equations with state constraints. Incremental stability is defined as the property that the distance between every pair of solutions to the system has stable behavior (incremental stability) and approaches zero asymptotically (incremental attractivity) in terms of graphical convergence. Basic properties of the class of graphically incrementally stable systems are considered as well as those implied by the new notions are revealed. Moreover, several sufficient and necessary conditions for a hybrid system with such a property are established. Examples are presented throughout the paper to illustrate the notions and results.

New and radically reformative thinking about the enactive and embodied basis of cognition holds out the promise of moving forward age-old debates about whether we learn and how we learn. The radical enactive, embodied view of cognition (REC) poses a direct, and unmitigated, challenge to the trademark assumptions of traditional cognitivist theories of mind— those that characterize cognition as always and everywhere grounded in the manipulation of contentful representations of some kind. REC has had some success in understanding how sports skills and expertise are acquired. But, REC approaches appear to encounter a natural obstacle when it comes to understanding skill acquisition in knowledge-rich, conceptually based domains like the hard sciences and mathematics. This paper offers a proof of concept that REC’s reach can be usefully extended into the domain of science, technology, engineering, and mathematics (STEM) learning, especially when it comes to understanding the deep roots of such learning. In making this case, this paper has five main parts. The section “Ancient Intellectualism and the REC Challenge” briefly introduces REC and situates it with respect to rival views about the cognitive basis of learning. The “Learning REConceived: from Sports to STEM?” section outlines the substantive contribution REC makes to understanding skill acquisition in the domain of sports and identifies reasons for doubting that it will be possible to apply the same approach to knowledge-rich STEM domains. The “Mathematics as Embodied Practice” section gives the general layout for how to understand mathematics as an embodied practice. The section “The Importance of Attentional Anchors” introduces the concept “attentional anchor” and establishes why attentional anchors are important to educational design in STEM domains like mathematics. Finally, drawing on some exciting new empirical studies, the section “Seeing Attentional Anchors” demonstrates how REC can contribute to understanding the roots of STEM learning and inform its learning design, focusing on the case of mathematics.

Jim Haglund, Jennifer Morse, and Mike Zabrocki have published papers introducing symmetric function operators, C operator and B operator, and their combinatorial interpretations and identities. Their compositional refinement of the Shuffle Conjecture can be used to represent the image of a schur function under the Bergeron -Garsia nabla operator as a weighted sum of a suitable collection of parking functions. First, we express a schur function under nabla operator with C operator using its definition and fundamental identities about symmetric functions. Then, the compositional Shuffle conjecture can be used as the expression of a family of [Triangle down]Cp₁ ··· Cpk1, with p = (p₁,··· ,pk), composition of n, in terms of a sum of weights of a suitable set of parking functions. Therefore, in this paper, we express the image of a schur function under nable operator as the difference x between two sums of the weights of certain sets of parking functions. Then, we introduce injections between those sets of parking functions for a few cases of schur functions, so that an image of schur functions under nabla operator can be simply expressed using the complementary set of parking functions. The validity of these expressions is still conjectural until the compositional refinement of the Shuffle Conjecture is proved

The article of record as published may be found at http://dx.doi.org/10.1016/j.automatica.2014.10.025 This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions. This work is supported by US Office of Naval Research under Grant N0001412WX21229 Grant N0001412WX21229

© 2014 IEEE. This paper describes an application-specific embedded processor with instruction set extensions (ISEs) for the Dynamic Time Warping (DTW) distance measure, which is widely used in time series similarity search. The ISEs in this paper are implemented using a form of logarithmic arithmetic that offers significant performance and power/energy advantages compared to more traditional floating-point operations.

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are robust in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this papercoincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths. Copyright © Cambridge University Press 2013 A ̂.

We study sequential monitoring procedures that detect instabilities of the regression operator in an underlying (fully) functional regression model allowing for dependence. These open-end and closed-end procedures are built on a functional principal components analysis of both the predictor and response functions, thus giving rise to multivariate detector functions, whose fluctuations are compared against a curved threshold function. The main theoretical result of the paper quantifies the large-sample behavior of the procedures under the null hypothesis of a stable regression operator. To establish these limit results, classical results on functional principal components analysis are generalized to a dependent setting, which may be of interest in its own sake. In an accompanying empirical study we illustrate the finite sample properties, while an application to environmental data highlights practical usefulness. To the best of our knowledge this is the first paper that combines sequential with functional data methodology.

This paper investigates the cross-linguistic applicability of the concept of frame as developed in the Berkeley FrameNet project. We examine whether the frames created for the annotation of English texts can also function as a tool for the assessment of the accuracy of English-to-Japanese translations. If the semantic structure of a source text is analyzed in terms of the frames evoked by its constituent words and the ways in which the elements of those frames are realized, then those frames, their constituent elements, and their interconnections must somehow be present in the translation. The paper concentrates on passages involving causation, as causal relationships are considered by many to exhibit the most salient differences in rhetorical preference between the two languages.

Here we shall use the same notations of the original paper. The references to equations, lemmas, propositions, theorems are with respect to the paper unless stated otherwise. The argument provided for the proof of Proposition 3.1 is not complete. It overlooks the fact that the solution 2-form η(x, t) of the problem (3.1) may contain non-trivial (2,0) and (0,2) parts. Hence Proposition 3.1 needs a correction. We thank Gilles Carron for pointing out this oversight in the original proof of Proposition 3.1 and his comments. We also thank Luen-Fai Tam for helpful related discussions. We refer interested reader to [5] for an alternate proof of Theorem 1.2. Since the preservation of the positivity for solution 2-forms solving the problem (3.1) in the paper, without knowing that the 2-form being (1,1)-type, seems elusive (even for the (1,1) part projection of the 2-form solutions) we replace (3.1) with the following initial boundary value problem on (1,1)form η. Let Ω be a smooth bounded domain in M . For a given point p ∈ ∂Ω , let ν be the unit outward normal in a small neighborhood near p. We

This paper gives poly-logarithmic-round, distributed δ-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio δ is the maximum number of variables in any constraint. Special cases include Covering Mixed Integer Linear Programs (CMIP), and Weighted Vertex Cover (with δ = 2). Via duality, the paper also gives poly-logarithmic-round, distributed δ-approximation algorithms for Fractional Packing linear programs (where δ is the maximum number of constraints in which any variable occurs), and for Max Weighted c-Matching in hypergraphs (where δ is the maximum size of any of the hyperedges; for graphs δ = 2). The paper also gives parallel (RNC) 2-approximation algorithms for CMIP with two variables per constraint and Weighted Vertex Cover. The algorithms are randomized. All of the approximation ratios exactly match those of comparable centralized algorithms. © 2011 Springer-Verlag.

Various regression methods have been proposed for analyzing recurrent event data. Among them, the semiparametric additive rates model is particularly appealing because the regression coefficients quantify the absolute difference in the occurrence rate of the recurrent events between different groups. Estimation of the additive rates model requires the values of time-dependent covariates being observed throughout the entire follow-up period. In practice, however, the time-dependent covariates are usually only measured at intermittent follow-up visits. In this paper, we propose to kernel smooth functions involving time-dependent covariates across subjects in the estimating function, as opposed to imputing individual covariate trajectories. Simulation studies show that the proposed method outperforms simple imputation methods. The proposed method is illustrated with data from an epidemiologic study of the effect of streptococcal infections on recurrent pharyngitis episodes.

This paper establishes non-asymptotic concentration bound and Bahadur representation for the quantile regression estimator and its multiplier bootstrap counterpart in the random design setting. The non-asymptotic analysis keeps track of the impact of the parameter dimension $d$ and sample size $n$ in the rate of convergence, as well as in normal and bootstrap approximation errors. These results represent a useful complement to the asymptotic results under fixed design and provide theoretical guarantees for the validity of Rademacher multiplier bootstrap in the problems of confidence construction and goodness-of-fit testing. Numerical studies lend strong support to our theory and highlight the effectiveness of Rademacher bootstrap in terms of accuracy, reliability and computational efficiency.

The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analyzing the far tail of observed phenomena. Curiously, important asymptotic properties of likelihood-based estimation under this standard model have yet to be established. In this paper, we formally prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighborhood of the shape parameter., 38 pages, 5 figures

In this paper, we present two new algorithms for computing all Schur functions $$s_\kappa (x_1,\ldots ,x_n)$$ s κ ( x 1 , … , x n ) for partitions $$\kappa $$ κ such that $$|\kappa |\le N$$ | κ | ≤ N . For nonnegative arguments, $$x_1,\ldots ,x_n$$ x 1 , … , x n , both algorithms are subtraction-free and thus each Schur function is computed to high relative accuracy in floating point arithmetic. The cost of each algorithm per Schur function is $$\mathscr {O}(n^2)$$ O ( n 2 ) .

This paper addresses the question of clustering density curves around a unit circle by approximating each such curve by a mixture of an appropriate number of von Mises distributions. This is done first by defining a distance between any two such curves either via $$L^2$$ or a symmetrized Kullback–Leibler divergence. We show that both these measures yield similar results. After demonstrating via simulations that the proposed clustering methods work successfully, they are applied on an illustrative sample of Optical Coherence Tomography data.

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Xxxx XXXX, Pages 000–000 S 0894-0347(XX)0000-0 arXiv:math/0005308v1 [math.NT] 9 May 2000 RANK ONE CASE OF DWORK’S CONJECTURE DAQING WAN 1. Introduction In the higher rank paper [17], we reduced Dwork’s conjecture from higher rank case over any smooth affine variety X to the rank one case over the simplest affine space A n . In the present paper, we finish our proof by proving the rank one case of Dwork’s conjecture over the affine space A n , which is called the key lemma in [17]. The key lemma had already been proved in [16] in the special case when the Frobenius lifting σ is the simplest q-th power map σ(x) = x q . Thus, the aim of the present paper is to treat the general Frobenius lifting case. Our method here is an improvement of the limiting method in [16]. It allows us to move one step further and obtain some explicit information about the zeros and poles of the unit root L-function. As in [16], to handle the rank one case, we are forced to work in the more difficult infinite rank setting, see section 2 for precise definitions of the various basic infinite rank notions. Let F q denote the finite field of characteristic p > 0. Our main result of this paper is the following theorem. Theorem 1.1. Let φ be a nuclear overconvergent σ-module over the affine n-space A n /F q , ordinary at the slope zero side. Let φ unit be the unit root (slope zero) part of φ. Assume that φ unit has rank one. Let ψ be another nuclear overconvergent σ-module over A n /F q . Then for each integer k, the L-function L(ψ ⊗ φ ⊗k unit , T ) is p-adic meromorphic. Furthermore, the family L(ψ ⊗ φ ⊗k T of L-functions unit parametrized by integers k in each residue class modulo (q − 1) is a strong family of meromorphic functions with respect to the p-adic topology of k. A finite rank σ-module is automatically nuclear. Thus, Theorem 1.1 includes the key lemma of [17] over A n as a special case. The basic ideas of the present paper are the same as the limiting approach in [16]. The details are, however, quite different. In the simplest q-th power Frobenius lifting case, one has the fundamental Dwork trace formula available, which is completely explicit for uniform estimates. This makes it easy to extend the Dwork trace formula to infinite rank setting. It also makes it possible to see the various analytic subtleties involved in a concrete case. As a result, we were able to prove analytically optimal results in [16]. For a general Frobenius lifting (even over the simplest affine n-space A n as we shall work in this paper), one has to use the much more difficult Monsky trace formula which is a generalization of Dwork’s trace formula. Thus, the first task of this paper is to extend the Monsky trace formula to infinite rank setting and to make it sufficiently 1991 Mathematics Subject Classification. Primary 11G40, 11S40; Secondary 11M41, 14G15. Key words and phrases. L-functions, Fredholm determinants, p-adic meromorphic continua- tion, nuclear σ-modules and Banach modules. This work was partially supported by NSF. c American Mathematical Society

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Xxxx XXXX, Pages 000–000 S 0894-0347(XX)0000-0 arXiv:math/0005309v1 [math.NT] 9 May 2000 HIGHER RANK CASE OF DWORK’S CONJECTURE DAQING WAN Dedicated to the memory of Bernard Dwork 1. Introduction In this series of two papers, we prove the p-adic meromorphic continuation of the pure slope L-functions arising from the slope decomposition of an overconvergent F- crystal, as conjectured by Dwork [6]. More precisely, we prove a suitable extension of Dwork’s conjecture in our more general setting of σ-modules, see section 2 for precise definitions of the various notions used in this introduction. Our main result is the following theorem. Theorem 1.1. Let X be a smooth affine variety defined over a finite field F q of characteristic p > 0. Let (M, φ) be a finite rank overconvergent σ-module over X/F q . Then, for each rational number s, the pure slope s L-function L s (φ, T ) attached to φ is p-adic meromorphic everywhere. The proof of this theorem will be completed in two papers. In the present higher rank paper, we introduce a reduction approach which reduces Theorem 1.1 to the special case when the slope s (s = 0) part of φ has rank one and the base space X is the simplest affine space A n . This part is essentially algebraic. It depends on Monsky’s trace formula, Grothendieck’s specialization theorem, the Hodge-Newton decomposition and Katz’s isogeny theorem. In our next paper [23], we will handle the rank one case over the affine space A n . The rank one case is very much analytic in nature and forces us to work in a more difficult infinite rank setting, generalizing and improving the limiting approach introduced in [19]. Dwork’s conjecture grew out of his attempt to understand the p-adic analytic variation of the pure pieces of the zeta function of a variety when the variety moves through an algebraic family. To give an important geometric example, let us con- sider the case that f : Y → X is a smooth and proper morphism over F q with a smooth and proper lifting to characteristic zero. Berthelot’s result [1] says that the relative crystalline cohomology R i f crys,∗ Z p modulo torsion is an overconvergent F-crystal M i over X. Applying Theorem 1.1, we conclude that the pure L-functions arising from these geometric overconvergent F-crystals M i are p-adic meromorphic. In particular, this implies the existence of an exact p-adic formula for geometric p-adic character sums and a suitable p-adic equi-distribution theorem for the roots of zeta functions. For more detailed arithmetic motivations and further open prob- lems, see the expository papers [20][21]. 1991 Mathematics Subject Classification. Primary 11G40, 11S40; Secondary 11M41, 14G15. Key words and phrases. L-functions, p-adic meromorphic continuation, σ-modules. This work was partially supported by NSF. c American Mathematical Society

Parametric imaging has been shown to provide better quantitation physiologically compared with SUV imaging in PET. With the increased sensitivity from a recently developed total-body PET scanner, whole-body scans with higher temporal resolution become possible for dynamic analysis and parametric imaging. In this paper, we focus on deriving the parameter k1 using compartmental modeling, and on developing a method to acquire whole-body FDG-PET parametric images using only the first 90 seconds of the post-injection scan data with the total-body PET system. Dynamic projections were acquired with a time interval of 1 second for the first 30 seconds and 2 seconds for the following minute. Image-derived input functions were acquired from the reconstructed dynamic sequences in the ascending aorta. The one-tissue compartment model with the total of 4 parameters (k1, k2, blood fraction, delay time) was used. A maximum-likelihood based estimation method was developed with the 1-tissue compartment model solution. The accuracy of the acquired parameters was compared with the ones estimated using a 2-tissue irreversible model with 1-hour long data. All four parametric images were successfully calculated using data from two volunteers. By comparing the time-activity-curves acquired from the volume of interests, it was shown that the parameters estimated using our method were able to predict the time-activity curves of the early dynamics of FDG in different organs. The time delay effects for different organs were also clearly visible in the reconstructed time delay image with delay variations as large as 40 seconds. The estimated parameters using both 90 seconds data and 1-hour long data were in good agreement for k1 and blood fraction, while a large difference of k2 was found between the 90 seconds and 1-hour data, suggesting k2 can’t be reliably estimated from the 90 second scan. We have shown that with the use of total-body PET and the increased sensitivity, it is possible to estimate parametric images based on the very early dynamics following FDG injection. The estimated k1 could potentially be used clinically as an indicator for identifying abnormalities.

Digital fringe projection is a surface-profiling technique used for highly accurate non-contact measurements. As with any measurement technique, a variety of sources degrade to the measurement accuracy of the method. This paper presents an analytically-derived probability density function that explicitly models the surface height measurement error due to inevitable phase measurement error, and it includes the specific case of pixel noise inducing the phase measurement error that ultimately leads to the height estimation error. The accuracy of the model was validated through Monte-Carlo simulations of resultant height distributions subject to arbitrarily correlated pixel intensity noise and experimental digital fringe projection measurements where the pixel-by-pixel height uncertainty estimations were compared to the predictions of the derived model.

This paper investigates the Hamiltonian structure and Poisson bracket formulation of a higher-order, geometrically-exact Cosserat type beam with a deforming cross-section in terms of canonically conjugate variables.

This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample distributional approximation in a unified way, allowing for both boundary and interior evaluation points simultaneously. Using this result, we study the asymptotic efficiency of the estimators, and show that a carefully crafted minimum distance implementation based on “redundant” regressors can lead to efficiency gains. Second, we establish uniform linearizations and strong approximations for the estimators, and employ these results to construct valid confidence bands. Third, we develop extensions to weighted distributions with estimated weights and to local L 2 estimation. Finally, we illustrate our methods with two applications in program evaluation: counterfactual density testing, and IV specification and heterogeneity density analysis. Companion software packages in Stata and R are available.

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems often rely on specific, restrictive problem structures, or are valid only locally around some nominal trajectory. In this paper, we propose a data-driven method to approximate semi-global solutions to HJB equations for general high-dimensional nonlinear systems and compute candidate optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially-trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body, and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time feedback control of these systems., Added section on validation error computation. Updated convergence test formula and associated results

In a prediction tournament, contestants “forecast” by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate forecasters will likely score better. This is true for one-on-one comparisons between contestants. But consider a realistic-size tournament with many contestants, with a range of accuracies. It may seem self-evident that the winner will likely be one of the most accurate forecasters. But, in the setting where the range extends to very accurate forecasters, simulations show this is mathematically false, within a somewhat plausible model. Even outside that setting the winner is less likely than intuition suggests to be one of the handful of best forecasters. Though implicit in recent technical papers, this paradox has apparently not been explicitly pointed out before, though is easily explained. It perhaps has implications for the ongoing IARPA-sponsored research programs involving forecasting.

This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m × n matrix with m ≈ n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of O(log n) sparse factors, each containing O(n) nonzero entries. The factorization can be attained using O(n3/2 log n) computation and O(n log n) memory resources. The proposed algorithm can be implemented in parallel and can apply to matrices with strong or weak admissibility conditions arising from surface integral equation solvers as well as multi-frontal-based finite-difference, finite-element, or finite-volume solvers. A distributed-memory parallel implementation of the algorithm demonstrates excellent scaling behavior.