scholarly journals Eigenstate Thermalization Hypothesis for Wigner Matrices

2021 ◽  
Author(s):  
Giorgio Cipolloni ◽  
László Erdős ◽  
Dominik Schröder
Keyword(s):  
High Probability ◽  
Square Root ◽  
Commun Math Phys ◽  
Optimal Convergence Rate ◽  
Optimal Error ◽  
Wigner Matrix ◽  
Appl Math ◽  
Very High ◽  
Deterministic Matrix ◽  
Math Phys

AbstractWe prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).

Costs and Benefits of the Transition to Low-carbon Economyin Russia: Perspectives up to 2050

2014 ◽  
pp. 70-91 ◽  
Author(s):  
I. Bashmakov ◽  
A. Myshak
Keyword(s):  
Emission Reduction ◽  
High Probability ◽  
Ghg Emissions ◽  
Mitigation Measures ◽  
Low Carbon ◽  
Costs And Benefits ◽  
Ghg Emission ◽  
Research Groups ◽  
Emissions Mitigation ◽  
Very High

This paper investigates costs and benefits associated with low-carbon economic development pathways realization to the mid XXI century. 30 scenarios covering practically all “visions of the future” were developed by several research groups based on scenario assumptions agreed upon in advance. It is shown that with a very high probability Russian energy-related GHG emissions will reach the peak before 2050, which will be at least 11% below the 1990 emission level. The height of the peak depends on portfolio of GHG emissions mitigation measures. Efforts to keep 2050 GHG emissions 25-30% below the 1990 level bring no GDP losses. GDP impact of deep GHG emission reduction - by 50% of the 1990 level - varies from plus 4% to minus 9%. Finally, very deep GHG emission reduction - by 80% - may bring GDP losses of over 10%.

scholarly journals Spectral gap in random bipartite biregular graphs and applications

2021 ◽  
pp. 1-39
Author(s):  
Gerandy Brito ◽  
Ioana Dumitriu ◽  
Kameron Decker Harris
Keyword(s):  
Community Detection ◽  
Adjacency Matrix ◽  
Moment Method ◽  
Coding Theory ◽  
High Probability ◽  
Spectral Gap ◽  
Matrix Completion ◽  
Full Rank ◽  
The Moment ◽  
Deterministic Matrix

Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

scholarly journals Antibiotic-associated diarrhea in children: how to identify, what to do and how to treat?

2016 ◽  
Vol 1 (1) ◽  
pp. 78-89
Author(s):  
I. N. Zakharova ◽  
I. V. Berezhnaya ◽  
E. B. Mumladze
Keyword(s):  
High Risk ◽  
Antibiotic Therapy ◽  
Intestinal Microbiota ◽  
High Probability ◽  
Pseudomembranous Colitis ◽  
Inflammatory Diseases ◽  
Pediatric Practice ◽  
Antibiotic Associated Diarrhea ◽  
New Generation ◽  
Very High

Rational antibiotic therapy is one of the most important components in the treatment of children with various infectious and inflammatory diseases. However, wide and sometimes unjustified use of AB in pediatric practice often leads to the development of a variety of complications. Children receiveing AB, especially during the first 5 years of life, are at a very high risk of developing antibiotic-associated diarrhea (AAD) which manifests itself in three or more episodes of unformed stools for two or more consecutive days or for 8 weeks after withdrawal. The most relevant pathogen of AAD is C. difficile which, according to various data, causes from 10 to 25% of AAD cases and 90 to 100% of all cases of pseudomembranous colitis (PMC). Given the high probability of developing dangerous complications such as PMC, special attention should be paid to the prevention of the infection associated with C. difficile by reducing the frequency of uncontrolled and unjustified use of AB. A new generation of eco-antibiotics can be recommended which allow to maintain diversity of the intestinal microbiota and are less likely to cause complications.

scholarly journals Alternative proofs of some formulas for two tridiagonal determinants

2018 ◽  
Vol 10 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Feng Qi ◽  
Ai-Qi Liu
Keyword(s):  
Chebyshev Polynomials ◽  
Tridiagonal Matrix ◽  
Fibonacci Polynomials ◽  
Detailed Proof ◽  
Delannoy Numbers ◽  
Appl Math ◽  
Math Phys

Abstract In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant. This is a companion of the paper [F. Qi, V. Čerňanová,and Y. S. Semenov, Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), in press.

Erratum: Commun. Math. Phys. 217, 127-163 (2001)

2002 ◽  
Vol 225 (1) ◽  
pp. 219-221 ◽  
Author(s):  
Not Available Not Available
Keyword(s):  
Commun Math Phys ◽  
Math Phys

scholarly journals Low-cost infrared sensor for wildlife detection in vegetation

2017 ◽  
Vol 63 (Special Issue) ◽  
pp. S13-S17
Author(s):  
Lev Jakub ◽  
Shapoval Vadym ◽  
Bartoška Jan ◽  
Kumhála František
Keyword(s):  
High Speed ◽  
High Probability ◽  
Low Cost ◽  
Low Noise ◽  
Infrared Sensor ◽  
Direct Sunlight ◽  
Infrared Technology ◽  
Wildlife Detection ◽  
Infrared Array ◽  
Very High

The protection of wild animals from mutilation or being killed during haymaking is still a serious problem connected with high working speeds and widths of modern harvesting machines. That is why the main aim of this study was to test low-cost, high-speed and low-noise infrared array sensor Melexis MLX90621 for the application of wildlife detection with the potential to be used in front of the mower equipment. The tests with two different crops with or without a hidden dog were made. Results showed that the sensor is able to detect an animal hidden in the crop with very high probability. Nevertheless, direct sunlight conditions can cause the problems when using infrared technology. A simultaneous use of other sensors working on different principle than infrared technology can be thus recommended.

scholarly journals Surjectivity of near-square random matrices

2019 ◽  
Vol 29 (2) ◽  
pp. 267-292
Author(s):  
Hoi. H. Nguyen ◽  
Elliot Paquette
Keyword(s):  
Random Matrices ◽  
High Probability ◽  
Sparse Matrices ◽  
Integral Lattice ◽  
Integral Matrix ◽  
Random Integral ◽  
Very High ◽  
Dependent Entries ◽  
Independent And Identically Distributed

AbstractWe show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.

Resonance broadening in high density gases

1977 ◽  
Vol 55 (14) ◽  
pp. 1243-1251 ◽  
Author(s):  
H.R. Zaidi
Keyword(s):  
Experimental Data ◽  
Excited States ◽  
High Density ◽  
Square Root ◽  
Many Body ◽  
Extended Range ◽  
Line Widths ◽  
Very High ◽  
Peak Value ◽  
Resonance Broadening

The resonance broadening of a transition between two excited states of a radiator in a high density gas is investigated. The important many body shielding contributions are included to all orders, and the two body correlations for the close collisions are approximately taken into account. Corrections to the line width and shift at moderately high densities are calculated. The results agree with the experimental data for krypton. The density dependence of the width parameter is examined at very high densities also. It is found that this parameter, after reaching a peak value, decreases with further increase in the density. Moreover, the square root dependence of the line widths on the density is not valid over any extended range of gas densities.

scholarly journals Thrombophilia in obstetric practice

2021 ◽  
Vol 99 (1) ◽  
pp. 15-20
Author(s):  
A. P. Melnikov ◽  
M. G. Kashchuk ◽  
K. N. Ahvlediani ◽  
I. N. Bokarev
Keyword(s):  
High Risk ◽  
Pregnant Women ◽  
High Probability ◽  
Risk Group ◽  
High Risk Group ◽  
Thromboembolic Complications ◽  
Spontaneous Thrombosis ◽  
Obstetric Practice ◽  
Very High

The rate of thromboembolic complications associated with thrombophilia is very high; therefore the detection of thrombophilia mutations in the high-risk group of patients is important for the prevention of morbidity, mortality and obstetric losses. The problem of thrombophilia is dealt with by doctors of various specialties: laboratory stuff, geneticists, vascular surgeons, hematologists, neurologists, cardiologists and obstetricians-gynecologists. At the same time, patients with spontaneous thrombosis are followed-up for years without proper examination for thrombophilia. Considering that pregnancy is a condition associated with a high probability of re-thrombosis, it is advisable to determine the cause and tactics of management and treatment of pregnant women as early as possible during the period of pregnancy.

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