scholarly journals Eigenvectors of a matrix under random perturbation

2020 ◽  
pp. 2150023
Author(s):  
Florent Benaych-Georges ◽  
Nathanaël Enriquez ◽  
Alkéos Michaïl
Keyword(s):  
Random Matrix ◽  
Hermitian Matrix ◽  
Random Perturbation ◽  
Perturbative Expansion ◽  
The State ◽  
Operator Norm ◽  
Spectral Measures ◽  
Large Size ◽  
Variance Profile

In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent, centered, with a variance profile. This is done through a perturbative expansion of spectral measures associated to the state defined by a given vector.

scholarly journals Recent Developments in Coatings, Gratings, and Reflective Components

1984 ◽  
Vol 79 ◽  
pp. 607-616
Author(s):  
R. R. Shannon
Keyword(s):  
State Of The Art ◽  
New Technology ◽  
The State ◽  
Current Technology ◽  
Large Size ◽  
Incoming Radiation ◽  
Recent Developments ◽  
Electronic Sensors ◽  
Large Primary ◽  
Telescope System

The requirements on gratings and coatings for astronomical use differ from the general industrial requirements primarily in the scale of the components to be fabricated. Telescopes have large primary mirrors which require large coating plants to handle the components. Dispersive elements are driven by the requirement to be efficient in the presence of large working apertures, and usually optimize to large size in order to efficiently use the incoming radiation. Beyond this, there is a “new” technology of direct electronic sensors that places specific limits upon the image scale that can be used at the output of a telescope system, whether direct imagery or spectrally divided imagery is to be examined. This paper will examine the state of the art in these areas and suggest some actions and decisions that will be required in order to apply current technology to the predicted range of large new telescopes.

The crystalline waters of the Bodoquena Plateau revealed Hypostomus froehlichi (Siluriformes: Loricariidae), a new armored catfish from the rio Paraguay basin in Brazil

Zootaxa ◽  
2021 ◽  
Vol 4933 (1) ◽  
pp. 98-112
Author(s):  
CLÁUDIO H. ZAWADZKI ◽  
GABRIELA NARDI ◽  
LUIZ FERNANDO CASERTA TENCATT
Keyword(s):  
New Species ◽  
The State ◽  
Flagship Species ◽  
Mato Grosso ◽  
Diagnostic Characters ◽  
Large Size ◽  
Numerical Variation ◽  
Mato Grosso Do Sul ◽  
Continuous Range

The menaced and poorly-known waters of the Bodoquena Plateau revealed a new resident, the stunning Hypostomus froehlichi sp. n., a large-sized armored catfish, which is finally described after more than twenty years since its discovery. The Bodoquena Plateau is drained by the rio Paraguay basin, and is located in the state of Mato Grosso do Sul, Brazil. The new species differs from its congeners on the Bodoquena crystalline waters by having teeth with morphological and numerical variation in adult specimens. There is a continuous range of specimens having about 20 thick and worn teeth to specimens having about 50 thin teeth with intact crowns and lanceolate main cusps. Additional diagnostic characters are: dentaries angled more than 90 degrees, dark blotches, one plate bordering supraoccipital, moderate keel along dorsal series of plates, usually two rows of blotches per interradial membrane on dorsal, pectoral and ventral fins, and by attaining comparatively large size. Hypostomus froehlichi seems to be endemic to the area of the Bodoquena Plateau, in rivers draining to the rio Miranda. The description of the new species reveals a potential conservation flagship species as it is one of the most seen and documented fish by visitors and divers in the clear waters from the touristic, though menaced, Bonito region in Brazil. 

Building Boundaries

2017 ◽  
Author(s):  
Shuang Chen
Keyword(s):  
Land Ownership ◽  
The State ◽  
Land Allocation ◽  
Half Century ◽  
Large Size ◽  
Initial Settlement

This chapter examines the ways the state built new boundaries among immigrants. It analyzes the four population categories recorded on state household registers—metropolitan, rural, and floating bannermen, and civilian commoners—as well as the unregistered population. Through land allocation, the state assigned these population categories differentiated entitlements. Each metropolitan banner household received twice as much land as a rural banner household did. Floating bannermen and civilian commoners had no entitlement to land and could only work as tenants and laborers. Moreover, the state purposefully used population registration to manipulate the entitlements of its subject population, as it intentionally left a large size of unregistered population outside of the system. The chapter concludes with an assessment of the distribution of registered land ownership among the four population categories a half century after the initial settlement, showing the enduring inequality created by state land allocation.

scholarly journals The Expected Norm of Random Matrices

2000 ◽  
Vol 9 (2) ◽  
pp. 149-166 ◽  
Author(s):  
YOAV SEGINER
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Operator Norm ◽  
Euclidean Norm ◽  
Constant Independent ◽  
Multiplicative Constant ◽  
The Matrix

We compare the Euclidean operator norm of a random matrix with the Euclidean norm of its rows and columns. In the first part of this paper, we show that if A is a random matrix with i.i.d. zero mean entries, then E∥A∥h [les ] Kh (E maxi ∥ai[bull ] ∥h + E maxj ∥aj[bull ] ∥h), where K is a constant which does not depend on the dimensions or distribution of A (h, however, does depend on the dimensions). In the second part we drop the assumption that the entries of A are i.i.d. We therefore consider the Euclidean operator norm of a random matrix, A, obtained from a (non-random) matrix by randomizing the signs of the matrix's entries. We show that in this case, the best inequality possible (up to a multiplicative constant) is E∥A∥h [les ] (c log1/4 min {m, n})h (E maxi ∥ai[bull ] ∥h + E maxj ∥aj[bull ] ∥h) (m, n the dimensions of the matrix and c a constant independent of m, n).

A Random Matrix Approach to Manipulator Jacobian

2013 ◽  
Author(s):  
Javad Sovizi ◽  
Aliakbar Alamdari ◽  
Venkat N. Krovi
Keyword(s):  
Random Matrix ◽  
Jacobian Matrix ◽  
Random Perturbation ◽  
Random Variable ◽  
System Response ◽  
Kinematic Modeling ◽  
Perturbation Matrix ◽  
Uncertainty Model ◽  
System Information

Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are unable to effectively and efficiently characterize the system response uncertainties. Hence in this paper, we propose a random matrix formulation for the Jacobian matrix of a robotic system. It facilitates characterization of the uncertainty model using limited system information in addition to taking into account the structural inter-dependencies and kinematic complexity of the manipulator. The random Jacobian matrix is modeled such that it adopts a symmetric positive definite random perturbation matrix. The maximum entropy principle permits characterization of this perturbation matrix in the form of a Wishart distribution with specific parameters. Comparing to the random variable/vector based schemes, the benefits now include: incorporating the kinematic configuration and complexity in the probabilistic formulation, achieving the uncertainty model using limited system information (mean and dispersion parameter), and realizing a faster simulation process. A case study of a 6R serial manipulator (PUMA 560) is presented to highlight the critical aspects of the process. A Monte Carlo analysis is performed to capture the deviations of distal path from the desired trajectory and the statistical analysis on the realizations of the end effector position and orientation shows how the uncertainty propagates throughout the system.

Secular strain measurements before and after the CANNIKIN nuclear test

1972 ◽  
Vol 62 (6) ◽  
pp. 1455-1458
Author(s):  
David Butler ◽  
Paul L. Brown
Keyword(s):  
Annual Variation ◽  
High Strain ◽  
Residual Deformation ◽  
Nuclear Test ◽  
The State ◽  
Aleutian Islands ◽  
Strain Measurements ◽  
Large Size ◽  
Before And After ◽  
Made In

abstract Secular earth-strain measurements have been made in the central Aleutian Islands during the years 1970 and 1971. An annual variation of about 3 × 10−6 is evident on all records. A residual deformation of less than 3 × 10−6 per year is detected on most records. The state of strain near Amchitka Island, Alaska, at the time of CANNIKIN, November 6, 1971, differed from the state of strain at the time of the MILROW test, October 2, 1969, by less than 1 × 10−5. The strain records also contain novel episodes of large size (1-3 × 10−6) and high strain rate (1 × 10−7 / hr).

scholarly journals Level crossing in random matrices. II. Random perturbation of a random matrix

2019 ◽  
Vol 52 (21) ◽  
pp. 214001
Author(s):  
Tobias Grøsfjeld ◽  
Boris Shapiro ◽  
Konstantin Zarembo
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Random Perturbation ◽  
Level Crossing

scholarly journals Linear eigenvalue statistics of random matrices with a variance profile

2020 ◽  
pp. 2250004
Author(s):  
Kartick Adhikari ◽  
Indrajit Jana ◽  
Koushik Saha
Keyword(s):  
Random Matrices ◽  
Random Matrix ◽  
Random Variable ◽  
Second Order ◽  
Linear Eigenvalue Statistics ◽  
Eigenvalue Statistics ◽  
Eigenvalue Statistic ◽  
Variation Distance ◽  
Random Matrix Ensembles ◽  
Variance Profile

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centered, of a random matrix with a variance profile and the standard Gaussian random variable. The second-order Poincaré inequality-type result introduced in [S. Chatterjee, Fluctuations of eigenvalues and second order poincaré inequalities, Prob. Theory Rel. Fields 143(1) (2009) 1–40.] is used to establish the bound. Using this bound, we prove central limit theorem for linear eigenvalue statistics of random matrices with different kind of variance profiles. We re-establish some existing results on fluctuations of linear eigenvalue statistics of some well-known random matrix ensembles by choosing appropriate variance profiles.

scholarly journals Concrete minimal 3 × 3 Hermitian matrices and some general cases

2017 ◽  
Vol 50 (1) ◽  
pp. 330-350
Author(s):  
Abel H. Klobouk ◽  
Alejandro Varela
Keyword(s):  
Hermitian Matrix ◽  
Operator Norm ◽  
Hermitian Matrices ◽  
The Real

Abstract Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

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