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Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators
Algorithms complexity linear differential operators common left multiples
2013/9/3
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyse the arithmetic complexity of existing algorithms for LCLMs, as wel...
Linear Coherent Estimation with Spatial Collaboration
Distributed Estimation Wireless Sensor Networks LMMSE Estimators Constrained Optimization
2012/7/9
A power constrained sensor network that consists of multiple sensor nodes and a fusion center (FC) is considered, where the goal is to estimate a random parameter of interest. In contrast to the distr...
Linear independence of time-frequency translates of functions with faster than exponential decay
Gabor system exponential decay HRT conjecture linear independence timefrequency translates analytic zero divisor conjecture
2012/6/29
We establish the linear independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for f...
Linear Programming Relaxations of Quadratically Constrained Quadratic Programs
Quadratic Programming Semidefinite Programming relaxation Linear Programming
2012/6/29
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented,...
Linear Mahler Measures and Double L-values of Modular Forms
Linear Mahler Measures Double L-values of Modular Forms Number Theory
2012/6/27
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
Minimax adaptive tests for the Functional Linear model
Functional linear regression eigenfunction principal com-ponent analysis adaptive testing minimax hypothesis testing
2012/6/21
We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections o...
A Top-Down Account of Linear Canonical Transforms
linear transforms canonical transforms Lie group Sp(2 R) Mathematical Physics
2012/6/21
We contend that what are called Linear Canonical Transforms (LCTs) should be seen as a part of the theory of unitary irreducible representations of the '2+1' Lorentz group. The integral kernel represe...
Estimation in high-dimensional linear models with deterministic design matrices
Identifiability projection ridge regression sparsity thresholding variable selection
2012/6/21
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable sele...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
Weak Markov Processes as Linear Systems
multi-variable system weakMarkov process cascade observability asymptotic completeness
2012/6/15
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter t...
Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles
Asymptotics the critical non-linear wave equation non star-shaped obstacles Analysis of PDEs
2012/6/14
Scattering for the energy critical non-linear wave equation for domains exterior to non trapping obstacles in 3+1 dimension is known for the star-shaped case. In this paper, we extend the scattering f...
Two-component solitons under a spatially modulated linear coupling: Inverted photonic crystals and fused couplers
Two-component solitons spatially modulated linear Inverted photonic crystals fused couplers Optics
2012/5/29
We study two-component solitons and their symmetry-breaking bifurcations (SBBs) in linearly coupled photonic systems with a spatially inhomogeneous strength of the coupling. One system models an inver...
Stability of non-linear integrable accelerator
Stability of non-linear integrable accelerator Accelerator Physics
2012/5/29
The stability of non-linear Integrable Optics Test Accelerator (IOTA) model was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a f...
Solving Linear Differential Equations: A Novel Approach
Linear Differential Equations Novel Approach Mathematical Physics
2012/5/24
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the...
Does Lorentz Force Law Contradict the Principle and Theories of Relativity for Uniform Linear Motion?
Lorentz Force Law Principle and Theories of Relativity Uniform Linear Motion Classical Physics
2012/5/29
I show that no force or torque is generated in cases involving a charge and a magnet with their relative velocity zero, in any inertial frame of reference. A recent suspicion of an anomalous torque an...