115,260 research outputs found
Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations
Binding and unbinding of ligands to specific sites of a macromolecule are one
of the most elementary molecular interactions inside the cell that embody the
computational processes of biological regulations. The interaction between
transcription factors and the operators of genes and that between ligands and
binding sites of allosteric enzymes are typical examples of such molecular
interactions. In order to obtain the general mathematical framework of
biological regulations, we formulate these interactions as finite Markov
processes and establish a computational theory of regulatory activities of
macromolecules based mainly on graphical analysis of their state transition
diagrams. The contribution is summarized as follows: (1) Stochastic
interpretation of Michaelis-Menten equation is given. (2) Notion of
\textit{probability flow} is introduced in relation to detailed balance. (3) A
stochastic analogy of \textit{Wegscheider condition} is given in relation to
loops in the state transition diagram. (4) A simple graphical method of
computing the regulatory activity in terms of ligands' concentrations is
obtained for Wegscheider cases.Comment: 20 pages, 13 figure
Finite elements and the discrete variable representation in nonequilibrium Green's function calculations. Atomic and molecular models
In this contribution, we discuss the finite-element discrete variable
representation (FE-DVR) of the nonequilibrium Green's function and its
implications on the description of strongly inhomogeneous quantum systems. In
detail, we show that the complementary features of FEs and the DVR allows for a
notably more efficient solution of the two-time Schwinger/Keldysh/Kadanoff-Baym
equations compared to a general basis approach. Particularly, the use of the
FE-DVR leads to an essential speedup in computing the self-energies.
As atomic and molecular examples we consider the He atom and the linear
version of H in one spatial dimension. For these closed-shell models we,
in Hartree-Fock and second Born approximation, compute the ground-state
properties and compare with the exact findings obtained from the solution of
the few-particle time-dependent Schr\"odinger equation.Comment: 12 pages, 3 figures, submitted as proceedings of conference "PNGF IV
Quantum Algorithm for Molecular Properties and Geometry Optimization
It is known that quantum computers, if available, would allow an exponential
decrease in the computational cost of quantum simulations. We extend this
result to show that the computation of molecular properties (energy
derivatives) could also be sped up using quantum computers. We provide a
quantum algorithm for the numerical evaluation of molecular properties, whose
time cost is a constant multiple of the time needed to compute the molecular
energy, regardless of the size of the system. Molecular properties computed
with the proposed approach could also be used for the optimization of molecular
geometries or other properties. For that purpose, we discuss the benefits of
quantum techniques for Newton's method and Householder methods. Finally, global
minima for the proposed optimizations can be found using the quantum basin
hopper algorithm, which offers an additional quadratic reduction in cost over
classical multi-start techniques.Comment: 6 page
Two-qubit Quantum Logic Gate in Molecular Magnets
We proposed a scheme to realize a controlled-NOT quantum logic gate in a
dimer of exchange coupled single-molecule magnets, . We
chosen the ground state and the three low-lying excited states of a dimer in a
finite longitudinal magnetic field as the quantum computing bases and
introduced a pulsed transverse magnetic field with a special frequency. The
pulsed transverse magnetic field induces the transitions between the quantum
computing bases so as to realize a controlled-NOT quantum logic gate. The
transition rates between the quantum computing bases and between the quantum
computing bases and other excited states are evaluated and analyzed.Comment: 7 pages, 2 figure
The Coupled Electronic-Ionic Monte Carlo Simulation Method
Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion
Monte Carlo or Path Integral Monte Carlo are the most accurate and general
methods for computing total electronic energies. We will review methods we have
developed to perform QMC for the electrons coupled to a classical Monte Carlo
simulation of the ions. In this method, one estimates the Born-Oppenheimer
energy E(Z) where Z represents the ionic degrees of freedom. That estimate of
the energy is used in a Metropolis simulation of the ionic degrees of freedom.
Important aspects of this method are how to deal with the noise, which QMC
method and which trial function to use, how to deal with generalized boundary
conditions on the wave function so as to reduce the finite size effects. We
discuss some advantages of the CEIMC method concerning how the quantum effects
of the ionic degrees of freedom can be included and how the boundary conditions
can be integrated over. Using these methods, we have performed simulations of
liquid H2 and metallic H on a parallel computer.Comment: 27 pages, 10 figure
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