Search results for "vector space"

Stochastic Approximation for Multivariate and Functional Median

2010

We propose a very simple algorithm in order to estimate the geometric median, also called spatial median, of multivariate (Small (1990)) or functional data (Gervini (2008)) when the sample size is large. A simple and fast iterative approach based on the Robbins-Monro algorithm (Duflo (1997)) as well as its averaged version (Polyak and Juditsky (1992)) are shown to be effective for large samples of high dimension data. They are very fast and only require O(Nd) elementary operations, where N is the sample size and d is the dimension of data. The averaged approach is shown to be more effective and less sensitive to the tuning parameter. The ability of this new estimator to estimate accurately …

Some experimental issues of AFM tip blind estimation. The effect of noise and resolution

2006

The convolution of tip shape on sample topography can introduce significant inaccuracy in an AFM image, when the tip radius is comparable to the typical dimension of the sample features to be observed. The blind estimation method allows one to obtain information on the AFM tip through an unknown characterizer sample and thus to perform the deconvolution of the tip shape from an image. When applying the blind estimation method to determine the AFM tip shape, some apparently trivial issues relating to the experimental operating parameters must be taken into account. In this paper, the effects of the operating parameters, e.g., sampling intervals (resolution) and instrumental noise, have been …

Real-Time Vector Automata

2013

We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected k×k matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.

The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS

2002

In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth.

NONVANISHING ELEMENTS FOR BRAUER CHARACTERS

2015

Let $G$ be a finite group and $p$ a prime. We say that a $p$-regular element $g$ of $G$ is $p$-nonvanishing if no irreducible $p$-Brauer character of $G$ takes the value $0$ on $g$. The main result of this paper shows that if $G$ is solvable and $g\in G$ is a $p$-regular element which is $p$-nonvanishing, then $g$ lies in a normal subgroup of $G$ whose $p$-length and $p^{\prime }$-length are both at most 2 (with possible exceptions for $p\leq 7$), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for $p>7$) some results in Dolfi and Pacifici [‘Zero…

Limits on entropic uncertainty relations

2010

We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3 MUBs and at least one choice of a larger number of MUBs, the best possible entropic uncertainty relation can be only marginally better than the one that trivially follows from the relation by Maassen and Uffink for 2 bases.

A Flux-Split Algorithm Applied to Relativistic Flows

1998

The equations of RFD can be written as a hyperbolic system of conservation laws by choosing an appropriate vector of unknowns. We give an explicit formulation of the full spectral decomposition of the Jacobian matrices associated with the fluxes in each spatial direction, which is the essential ingredient of the techniques we propose in this paper. These techniques are based on the recently derived flux formula of Marquina, a new way to compute the numerical flux at a cell interface which leads to a conservative, upwind numerical scheme. Using the spectral decompositions in a fundamental way, we construct high order versions of the basic first-order scheme described by R. Donat and A. Marqu…

Individual Differences in Working Memory Capacity Are Unrelated to the Magnitude of Benefits from Object- and Dimension-Based Retro-Cues

2021

Orientation of199mHg by optical pumping detected by ?-radiation anisotropy

1975

199mHg was produced and mass separated at the ISOLDE facility (CERN). Nuclear orientation achieved by optical pumping via the resonance line 6s21S0→6s6p3P1,λ=2537A was monitored by means of the anisotropy of theγ-radiation emitted in the cascade199mHg(I=13/2+) $${}^{199m}Hg(I = 13/2^ + )\xrightarrow[{M4}]{}{}^{199*}Hg(I = 5/2^ - )\xrightarrow[{E2}]{}{}^{199}Hg(I = 1/2^ - ).$$ 199*Hg(I=5/2−)199Hg(I=1/2−).

Subjective Refraction Techniques in the Frame of the Three-Dimensional Dioptric Space

2001

A novel heuristic approach to the well-known representation of the dioptric power in a three-dimensional space is presented. It is shown how this theoretical framework is ideal for discussing the principles of several subjective refraction methods. In particular, this formalism is used to justify the stenopaic slit refraction, the Barnes subjective refraction technique, and the Jackson cross-cylinder procedure. In view of this analysis, some modifications to the traditional procedures are proposed.