Search results for "Matrix"
showing 10 items of 3205 documents
On delocalization of eigenvectors of random non-Hermitian matrices
2019
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-\log^{2} n}$ $$ \min\limits_{I\subset[n],\,|I|= m}\|{\bf v}_I\| \geq \frac{m^{3/2}}{n^{3/2}\log^Cn}\|{\bf v}\| $$ for any real eigenvector ${\bf v}$ and any $m\in[\log^C n,n]$, where ${\bf v}_I$ denotes the restriction of ${\bf v}$ to $I$. Further, when the entries of $A$ are complex, with i.i.d real and imaginary parts, we show that with probability at least $1-e^{-\log^{2} n}$ all eigenvectors of $A$ are delocalized in the sense that $$ \min\l…
Fourth Moments and Independent Component Analysis
2015
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
3-D shape reconstruction in an active stereo vision system using genetic algorithms
2003
Abstract The recovery of 3-D shape information (depth) using stereo vision analysis is one of the major areas in computer vision and has given rise to a great deal of literature in the recent past. The widely known stereo vision methods are the passive stereo vision approaches that use two cameras. Obtaining 3-D information involves the identification of the corresponding 2-D points between left and right images. Most existing methods tackle this matching task from singular points, i.e. finding points in both image planes with more or less the same neighborhood characteristics. One key problem we have to solve is that we are on the first instance unable to know a priori whether a point in t…
Matrix isolation studies on the co-condensation reactions of molecular SiO and GeO: the characterisation of the novel cyclic species SiGeO(2), Si(2)G…
2010
Matrix isolation IR studies, together with DFT calculations, have established that the co-condensation of molecular SiO and GeO in low temperature (12 K) nitrogen matrices leads to the formation of the novel silicon germanium oxide species SiGeO(2), Si(2)GeO(3) and SiGe(2)O(3) analogous to the known dimer and trimer species M(2)O(2) and M(3)O(3) (M = Si, Ge). Controlled diffusion studies in the temperature range 20-34 K result in a significant increase in trimer formation, which implies a very low activation energy for this oligomerisation step. Characteristic IR modes are assigned for all three novel mixed oxide molecules, and the DFT calculations establish that these species have cyclic C…
Rotational Isomerism in Acetic Acid: The First Experimental Observation of the High-Energy Conformer
2003
The high-energy conformer of acetic acid (cis-AA) is produced in an Ar matrix by vibrational excitation of the OH stretching overtone of the ground conformational state (trans-AA). IR-absorption spectroscopy provides a clear identification of the reaction product. cis-AA converts back to trans-AA in a time scale of minutes at 8 K by tunneling. http://dx.doi.org/10.1021/ja038341a
Cytotoxicity and modes of action of four naturally occuring benzophenones: 2,2′,5,6′-Tetrahydroxybenzophenone, guttiferone E, isogarcinol and isoxant…
2012
Abstract Introduction The emergence of drug-resistant cancer cells drastically reduces the efficacy of many antineoplasic agents and, consequently, increases the frequency of therapeutic failure. Benzophenones are known to display many pharmacological properties including cytotoxic activities. The present study was aimed at investigating the cytotoxicity and the modes of action of four naturally occurring benzophenones 2,2′,5,6′-tetrahydroxybenzophenone ( 1 ), isogarcinol ( 2 ), isoxanthochymol ( 3 ) and guttiferone E ( 4 ) on a panel of eleven cancer cell lines including various sensitive and drug-resistant phenotypes. Methods The cytotoxicity of the compounds was determined using a resazu…
Exploring the Potential of Short-Baseline Physics at Fermilab
2018
We study the capabilities of the short baseline neutrino program at Fermilab to probe the unitarity of the lepton mixing matrix. We find the sensitivity to be slightly better than the current one. Motivated by the future DUNE experiment, we have also analyzed the potential of an extra liquid Argon near detector in the LBNF beamline. Adding such a near detector to the DUNE setup will substantially improve the current sensitivity on non-unitarity. This would help to remove CP degeneracies due to the new complex phase present in the neutrino mixing matrix. We also study the sensitivity of our proposed setup to light sterile neutrinos for various configurations.
Stochastic Control Problems
2003
The general theory of stochastic processes originated in the fundamental works of A. N. Kolmogorov and A. Ya. Khincin at the beginning of the 1930s. Kolmogorov, 1938 gave a systematic and rigorous construction of the theory of stochastic processes without aftereffects or, as it is customary to say nowadays, Markov processes. In a number of works, Khincin created the principles of the theory of so-called stationary processes.
Higher order matrix differential equations with singular coefficient matrices
2015
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.