22 papers · ranked by Valyu relevance
Juerg Froehlich, Alessandro Pizzo
We study quantum chains whose Hamiltonians are perturbations by bounded interactions of short range of a Hamiltonian that does not couple the degrees of freedom located at different sites of the chain and has a strictly positive energy gap above its ground-state energy. We prove that, for small values of a coupling…
Erna Begovic, Ana Perkovic
Convergence of this method was studied in [14, 9, 13, 4]. For different pivot strategies, it was shown that the iterations (1.1) converge in the sense that the sequence (B(k) , k ≥ 0) converges to a diagonal matrix, while (A(k) , k ≥ 0) converges to a normal matrix Λ. If all the eigenvalues of A have different real…
Ingolf Bischer, C. Döring, Andreas Trautner
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we give an efficient algorithm to explicitly compute a transfer matrix which…
Ahmad Y. Al‐Dweik, Ryad Ghanam, Gerard Thompson, M. T. Mustafa
In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form simultaneously. Based on common invariant subspaces, two algorithms for simultaneous block…
Mengmeng Zheng, Guyan Ni
With the great success of the T-product based real tensor methods in the color image and gray video processing, the establishment of T-product based quaternion tensor methods in the color video processing has encountered a challenge, which is the block diagonalization of block circulant quaternion matrices. In this…
AMIRHOSSEIN NAZERIAN, KSHITIJ BHATTA, FRANCESCO SORRENTINO
In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is ‘exact’ in the sense that it preserves all the information…
John C. Baker, Marilyn F. Bishop, Tom McMullen, Hong Qian
Biological processes often involve the attachment and detachment of extended molecules to substrates. Here, the classical dimer model is used to investigate these geometric effects on the free energy, which governs both the equilibrium state and the reaction dynamics. We present a simplified version of Fisher’s…
Marine De Clerck, Oleg Evnin
Gérard and Grellier proposed, under the name of the cubic Szegő equation, a remarkable classical field theory on a circle with a quartic Hamiltonian. The Lax integrability structure that emerges from their definition is so constraining that it allows for writing down an explicit general solution for prescribed initial…
Toru Shiozaki
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N > 10000 is now routine on a single computer node. Such matrices appear…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Marco Congedo, Bijan Afsari, Alexandre Barachant, Maher Moakher + 1 more
'Jesus Malo'] We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest…
Florian Privé
A few algorithms have been developed for splitting the genome in nearly independent blocks of linkage disequilibrium. Due to the complexity of this problem, these algorithms rely on heuristics, which makes them sub-optimal. Here we develop an optimal solution for this problem using dynamic programming. This is now…
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…
Alexre Urzhumtsev, Pavel V. Afonine, Andrew H. Van Benschoten, James S. Fraser + 1 more
The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three…
Daniel Miller, Laurin E. Fischer, Kyano Levi, Eric J. Kuehnke + 4 more
A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum…
Ragnar Groot Koerkamp
We introduce APA2, an exact global pairwise aligner with respect to edit distance. The goal of APA2 is to unify the near-linear runtime of APA on similar sequences with the efficiency of dynamic programming (DP) based methods. Like Edlib, APA2 uses Ukkonen’s band doubling in combination with Myers’ bitpacking. APA2 1)…
Authors not listed
One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short…
Authors not listed
Molecular polaritons are hybrid states formed by the quantum mechanical interaction between light and matter. Recent experiments have shown the ability to drastically modify chemical reactions in both the ground and excited states through the hybridization of the electronic and photonic degrees of freedom. Ab initio…
Wei Pan, Jing Wang, Deyan Sun
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling relationship between the eigenvector and matrix elements exists. Namely, each…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Ardalan Naseri, Ahsan Sanaullah, Shaojie Zhang, Degui Zhi
With the increasing availability of high-quality phased haplotype data, researchers can more effectively identify detailed patterns of haplotype sharing and investigate the population genetic processes that shape them. In this work, we define block cores as genomic segments where multiple haplotype blocks overlap. We…
Leonard Bohnenkämper, Luca Parmigiani, Cedric Chauve, Jens Stoye
Genomic rearrangements are major drivers of evolution and genetic disease. However, studying rearrangements requires segmenting the genomes of interest into conserved regions, called synteny blocks, that highlight structural differences between genomes. Synteny blocks are typically defined from annotated genes or…