Kernel Ellipsoidal Trimming

Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods

Covariant three-body equations in phi^3 field theory

We derive four-dimensional relativistic three-body equations for the case of a field theory with a three-point interaction vertex. These equations describe the coupled 2->2, 2->3, and 3->3 processes, and provide the means of calculating the kernel of the 2->2 Bethe-Salpeter equation. Our equations differ from all previous formulations in two essential ways. Firstly, we have overcome the overcounting problems inherent in earlier works. Secondly, we have retained all possible two-body forces when one particle is a spectator. In this respect, we show how it is necessary to also retain certain three-body forces as these can give rise to (previously overlooked) two-body forces when used in a 2->3 process. The revealing of such hidden two-body forces gives rise to a further novel feature of our equations, namely, to the appearance of a number of subtraction terms. In the case of the piNN system, for example, the NN potential involves a subtraction term where two pions, exchanged between the nucleons, interact with each other through the pi-pi t-matrix. The necessity of an input pi-pi interaction is surprising and contrasts markedly with the corresponding three-dimensional description of the piNN system where no such interaction explicitly appears. This illustrates the somewhat unexpected result that the four-dimensional equations differ from the three-dimensional ones even at the operator level.Comment: 33, FIAS-R-22

Turbulent luminance in impassioned van Gogh paintings

We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation

Integrability and Conformal Symmetry in the BCS model

The exactly solvable BCS Hamiltonian of superconductivity is considered from several viewpoints: Richardson's ansatz, conformal field theory, integrable inhomogenous vertex models and Chern-Simons theory.Comment: Latex with macros included, 12 pages, Proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 2001. Editors: Andrea Cappelli and Giuseppe Mussardo. to be published by Kluwer, Academic Publishers. Corrected some typos and further acknowledgment

Evaluating the impact of incentives on clinical trial participation: Protocol for a mixed methods, community-engaged study

Background: Monetary incentives in research are frequently used to support participant recruitment and retention. However, there are scant empirical data regarding how researchers decide upon the type and amount of incentives offered. Likewise, there is little guidance to assist study investigators and institutional review boards (IRBs) in their decision-making on incentives. Monetary incentives, in addition to other factors such as the risk of harm or other intangible benefits, guide individuals' decisions to enroll in research studies. These factors emphasize the need for evidence-informed guidance for study investigators and IRBs when determining the type and amount of incentives to provide to research participants. Objective: The specific aims of our research project are to (1) characterize key stakeholders' views on and assessments of incentives in biomedical HIV research; (2) reach consensus among stakeholders on the factors that are considered when choosing research incentives, including consensus on the relative importance of such factors; and (3) pilot-test the use of the guidance developed via aims 1 and 2 by presenting stakeholders with vignettes of hypothetical research studies for which they will choose corresponding incentive types. Methods: Our 2-year study will involve monthly, active engagement with a stakeholder advisory board of people living with HIV, researchers, and IRB members. For aim 1, we will conduct a nationwide survey (N=300) among people living with HIV to understand their views regarding the incentives used in HIV research. For aim 2, we will collect qualitative data by conducting focus groups with people living with HIV (n=60) and key informant interviews with stakeholders involved in HIV research (people living with HIV, IRB members, and biomedical HIV researchers: n=36) to extend and deepen our understanding of how incentives in HIV research are perceived. These participants will also complete a conjoint analysis experiment to gain an understanding of the relative importance of key HIV research study attributes and the impact that these attributes have on study participation. The data from the nationwide survey (aim 1) will be triangulated with the qualitative and conjoint analysis data (aim 2) to create 25 vignettes that describe hypothetical HIV research studies. Finally, individuals from each stakeholder group will select the most appropriate incentive that they feel should be used in each of the 25 vignettes (aim 3). Results: The stakeholder advisory board began monthly meetings in March 2021. All study aims are expected to be completed by December 2022. Conclusions: By studying the role of incentives in HIV clinical trial participation, we will establish a decision-making paradigm to guide the choice of incentives for HIV research and, eventually, other types of similar research and facilitate the ethical recruitment of clinical research participants

Strong Universality in Forced and Decaying Turbulence

The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte

Entangled Quantum Clocks for Measuring Proper-Time Difference

We report that entangled pairs of quantum clocks (non-degenerate quantum bits) can be used as a specialized detector for precisely measuring difference of proper-times that each constituent quantum clock experiences. We describe why the proposed scheme would be more precise in the measurement of proper-time difference than a scheme of two-separate-quantum-clocks. We consider possibilities that the proposed scheme can be used in precision test of the relativity theory.Comment: no correction, 4 pages, RevTe

Can a Lattice String Have a Vanishing Cosmological Constant?

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.Comment: 14 page

Path lengths in turbulence

By tracking tracer particles at high speeds and for long times, we study the geometric statistics of Lagrangian trajectories in an intensely turbulent laboratory flow. In particular, we consider the distinction between the displacement of particles from their initial positions and the total distance they travel. The difference of these two quantities shows power-law scaling in the inertial range. By comparing them with simulations of a chaotic but non-turbulent flow and a Lagrangian Stochastic model, we suggest that our results are a signature of turbulence.Comment: accepted for publication in Journal of Statistical Physic