Reduced neutron widths in the nuclear data ensemble: Experiment andtheory do not agree by Koehler P.E.

“…I have analyzed reduced neutron widths (Γ0n) for the subset of 1245 resonances in the nuclear data ensemble (NDE) for which they have been reported. Random matrix theory (RMT) predicts for the Gaussian orthogonal ensemble (GOE) that these widths should follow a χ2 distribution having one degree of freedom (ν = 1) - the Porter Thomas (PT) distribution. …”
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The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices by Wang Feng, Sun Deshu

“…The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. …”
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Distributed Averaging Problems of Agriculture Picking Multi-Robot Systems via Sampled Control by Fengying Ma, Hui Yao, Mingjun Du, Peng Ji, Xiaoan Si

“…With the algebraic graph theory concepts and the matrix theory, a distributed protocol is proposed based on the nearest sampled neighbor information. …”
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Analyticity constraints bound the decay of the spectral form factor by Pablo Martinez-Azcona, Aurélia Chenu

“…The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.…”
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Ranking and synchronization from pairwise measurements via SVD by d'Aspremont, A, Cucuringu, M, Tyagi, H

“…We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods.…”

Reactivity of complex communities can be more important than stability by Yang, Y, Coyte, KZ, Foster, KR, Li, A

“…Here, we challenge this focus, showing that short-term dynamics can be a better predictor of outcomes for complex ecosystems. Using random matrix theory, we study how complex ecosystems behave immediately after small perturbations. …”

SPONGE: A generalized eigenproblem for clustering signed networks by Cucuringu, M, Davies, P, Glielmo, A, Tyagi, H

“…We provide theoretical guarantees for our approach in the setting of a signed stochastic block model, by leveraging tools from matrix perturbation theory and random matrix theory. An extensive set of numerical experiments on both synthetic and real data shows that our approach compares favorably with state-of-the-art methods for signed clustering, especially for large number of clusters and sparse measurement graphs.…”

Emergence of world-stock-market network by Saeedian, M, Jamali, T, Kamali, M, Bayani, H, Yasseri, T, Jafari, G

“…Towards this end, we analyze the cross-correlation matrix of the indices of these forty markets using Random Matrix Theory (RMT). We find the degree of collective behavior among the markets and the share of each market in their structural formation. …”

The loss surfaces of neural networks with general activation functions by Baskerville, N, Keating, J, Mezzadri, F, Najnudel, J

“…In doing so, we chart a new path through the spin glass complexity calculations using supersymmetric methods in random matrix theory which may prove useful in other contexts. …”

On the moments of characteristic polynomials by Jonnadula, B, Keating, J, Mezzadri, F

“…We calculate the moments of the characteristic polynomials of N × N matrices drawn from the Hermitian ensembles of Random Matrix Theory, at a position t in the bulk of the spectrum, as a series expansion in powers of t. …”

Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they? by Mur-Petit, J, Molina, R

“…We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. …”

May's instability in large economies by Moran, J, Bouchaud, J-P

“…Relying on results from random matrix theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong, or when substitutability of their production inputs is reduced. …”

Dynamics of NYSE correlation structure during global crisis in 2008: evidence from complex network analysis by Djauhari, M. A., Lee, G. S.

“…To understand its behavior, random matrix theory and/or graph theory are/is usually used. …”

Electrodynamics of planar reflecting structures with chiral layers based on thin-wire helix by O.V. Osipov, A.O. Pocheptsov, T.A. Antipova

“…The possibility of incident microwave energy discrete multi-frequency concentration at a number of resonant frequencies is proved. The matrix theory for describing a multilayer chiral metamaterial and the obtained relations for the transfer matrices of the chiral layer based on helices are considered. …”
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The fundamentals for craniofacial morphogenesis -A review with emphasis on the decisive dynamics by Gaurav Agnihotri

“…In accordance with functional matrix theory, the major determinant of growth of maxilla and mandible is enlargement of nasal and oral cavities, which grow in response to functional needs. …”
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Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model by Eduardo Jonathan Torres-Herrera, Lea F. Santos

“…By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. …”
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Finite-time dissipative filter design for discrete-time stochastic interval systems with time-varying delays by Guici Chen, Xin Zhou, Qing Zhang

“…Taking a representative subsystem from a stochastic convex hull system, based on convex analysis and matrix theory, a new interval matrix method is proposed to study the finite-time dissipative filter problem, which can deduct the conservativeness. …”
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Normalized Sombor Indices as Complexity Measures of Random Networks by R. Aguilar-Sánchez, J. A. Méndez-Bermúdez, José M. Rodríguez, José M. Sigarreta

“…Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. …”
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A two-grid mixed finite volume element method for nonlinear time fractional reaction-diffusion equations by Zhichao Fang, Ruixia Du, Hong Li, Yang Liu

“…By using the Browder fixed point theorem and the matrix theory, the existence and uniqueness for the nonlinear and linearized MFVE schemes are obtained, respectively. …”
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Asynchronous Consensus Dynamics for Group of High-Order Agents Under Switching Topologies and Time-Varying Delays by Shi Li, Jianping Chen

“…The related knowledge of nonnegative matrix theory is used to solve this convergence problem, and further establish a sufficient algebraic condition of achieving high-order consensus. …”
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