Harringtonian virtue: Harrington, Machiavelli, and the method of the 'Moment'

This article presents a reinterpretation of James Harrington's writings. It takes issue with J. G. A. Pocock's reading, which treats him as importing into England a Machiavellian ‘language of political thought’. This reading is the basis of Pocock's stress on the republicanism of eighteenth-century opposition values. Harrington's writings were in fact a most implausible channel for such ideas. His outlook owed much to Stoicism. Unlike the Florentine, he admired the contemplative life; was sympathetic to commerce; and was relaxed about the threat of ‘corruption’ (a concept that he did not understand). These views can be associated with his apparent aims: the preservation of a national church with a salaried but politically impotent clergy; and the restoration of the royalist gentry to a leading role in English politics. Pocock's hypothesis is shown to be conditioned by his method; its weaknesses reflect some difficulties inherent in the notion of ‘languages of thought’.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

Differing effects of exogenous and endogenous hydrogen sulphide in carrageenan-induced knee joint synovitis in the rat

Background and purpose: Recent findings suggest that the noxious gas H(2)S is produced endogenously, and that physiological concentrations of H(2)S are able to modulate pain and inflammation in rodents. This study was undertaken to evaluate the ability of endogenous and exogenous H(2)S to modulate carrageenan-induced synovitis in the rat knee. Experimental approach: Synovitis was induced in Wistar rats by intra-articular injection of carrageenan into the knee joint. Sixty minutes prior to carrageenan injection, the rats were pretreated with indomethacin, an inhibitor of H(2)S formation (dl-propargylglycine) or an H(2)S donor [Lawesson`s reagent (LR)]. Key results: Injection of carrageenan evoked knee inflammation, pain as characterized by impaired gait, secondary tactile allodynia of the ipsilateral hindpaw, joint swelling, histological changes, inflammatory cell infiltration, increased synovial myeloperoxidase, protein nitrotyrosine residues, inducible NOS (iNOS) activity and NO production. Pretreatment with LR or indomethacin significantly attenuated the pain responses, and all the inflammatory and biochemical changes, except for the increased iNOS activity, NO production and 3-NT. Propargylglycine pretreatment potentiated synovial iNOS activity (and NO production), and enhanced macrophage infiltration, but had no effect on other inflammatory parameters. Conclusions and implications: Whereas exogenous H(2)S delivered to the knee joint can produce a significant anti-inflammatory and anti-nociceptive effect, locally produced H(2)S exerts little immunomodulatory effect. These data further support the development and use of H(2)S donors as potential alternatives (or complementary therapies) to the available anti-inflammatory compounds used for treatment of joint inflammation or relief of its symptoms.

Effect of neuromuscular electrical stimulation and isotonic exercises in flexor and extensor muscles of knee of hemiplegic patients

Aim. To verify the muscular force and resistance to the movement of the flexor and extensor muscles of the knee of patients with spasticity after treatment with neuromuscular electrical stimulation (NMES) and isotonic exercises. Patients and methods. The patients this study were divided into group I (NMES) and group 2 (isotonic exercises). Their muscular torque and resistance to the movement of the flexor and extensor knee muscles were measured by the isokinetic dynamometer and the degree of spasticity by the modified Ashworth scale before and after ten sessions. Results. Alterations in the scores of the modified Ashworth scale were not observed. An increase in the flexor torque in group 1 (p = 0.041) and in group 2 (p = 0.001) was verified. In the passive mode, group 1 presented a reduction of resistance to the flexion movement (p = 0.026), while in group 2, a reduction of resistance to both the flexion (p = 0,029) and extension movements (p = 0.019) was verified. Conclusions. The two therapeutical resources had their efficiency proven only for the increase of the force of the flexor muscles. The resistance to movement, the isotonic exercises were more effective because they promoted a reduction in the resistance of the flexor and extensor knee muscles.

Coherent states of a particle in a magnetic field and the Stieltjes moment problem

A solution to a version of the Stieltjes moment. problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and resolves the unity. By the help of these coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion. (C) 2009 Elsevier B.V. All rights reserved.

The Apple of His Ire: For monologist Mike Daisey, the death of Steve Jobs was another defining moment in a remarkable career

Monologist Mike Daisey ’96 had been targeting Apple and Steve Jobs for a year. Then Jobs died and Daisey’s show was changed once again.

Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.

Experimental study of the conventional equation to determine a plate's moment of inertia

In this work, we describe an experimental setup in which an electric current is used to determine the angular velocity attained by a plate rotating around a shaft in response to a torque applied for a given period. Based on this information, we show how the moment of inertia of a plate can be determined using a procedure that differs considerably from the ones most commonly used, which generally involve time measurements. Some experimental results are also presented which allow one to determine parameters such as the exponents and constant of the conventional equation of a plate's moment of inertia.

Experimental study of the moment of inertia of a cone - angular variation and inertia ellipsoid

In this paper, an experimental set-up which differs from the traditional ones is established in order to determine the moment of inertia of a right circular cone. Its angular variation and inertia ellipsoid are determined by means of an experimental study. In addition, a system that allows for the evaluation of the angular acceleration and torque through electric current or frequency measurement is utilized.