Random Sampling Monte-Carlo Approach to Studying Entropic Elasticity Properties of Cell Proteins and Lipids

2010 ◽  
Author(s):  
Eduard Karpov
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Cell Protein ◽  
Specific Load ◽  
Linear Elastic ◽  
Entropic Elasticity ◽  
Energy Profiles ◽  
Lipid Chain ◽  
Entropic Contribution ◽  
Potential Energy Profiles

An efficient numerical Monte-Carlo method is proposed for the estimation of the entropic contribution to the elastic properties of cell protein and lipid chain biomolecules. Specific load-extension curves are obtained numerically for a group of molecules with degenerate potential energy profiles. Spread of the linear elastic regimes and dependence on the molecular weight and geometric parameters of the molecules are discussed.

scholarly journals Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 580
Author(s):  
Pavel Shcherbakov ◽  
Mingyue Ding ◽  
Ming Yuchi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computational Mathematics ◽  
Closed Form Solutions ◽  
Monte Carlo Techniques ◽  
Control Optimization ◽  
Point Representation ◽  
Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

scholarly journals Why simple quadrature is just as good as Monte Carlo

2020 ◽  
Vol 26 (1) ◽  
pp. 1-16
Author(s):  
Kevin Vanslette ◽  
Abdullatif Al Alsheikh ◽  
Kamal Youcef-Toumi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Bayesian Probability ◽  
Independent Factor ◽  
Worst Case ◽  
Statistical Equivalence ◽  
Deterministic Sampling ◽  
Quadrature Methods ◽  
Quadrature Sampling ◽  
Simple Quadrature

AbstractWe motive and calculate Newton–Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that MC random sampling is statistically indistinguishable from a method that uses deterministic sampling on a randomly shuffled (permuted) function. We use this statistical equivalence to regularize the form of permissible Bayesian quadrature integration priors such that they are guaranteed to be objectively comparable with MC. This leads to the proof that simple quadrature methods have expected variances that are less than or equal to their corresponding theoretical MC integration variances. Separately, using Bayesian probability theory, we find that the theoretical standard deviations of the unbiased errors of simple Newton–Cotes composite quadrature integrations improve over their worst case errors by an extra dimension independent factor {\propto N^{-\frac{1}{2}}}. This dimension independent factor is validated in our simulations.

Potential energy profiles for unimolecular reactions of organic ions: [C3H8N]+ and [C3H7O]+

1978 ◽  
Vol 13 (12) ◽  
pp. 721-728 ◽  
Author(s):  
Richard D. Bowen ◽  
Dudley H. Williams ◽  
G. Hvistendahl ◽  
John R. Kalman
Keyword(s):  
Potential Energy ◽  
Unimolecular Reactions ◽  
Organic Ions ◽  
Energy Profiles ◽  
Potential Energy Profiles

ChemInform Abstract: Potential Energy Profiles of Proton Transfer Processes in Cationic Clusters

ChemInform ◽  
2010 ◽  
Vol 31 (13) ◽  
pp. no-no
Author(s):  
J. Bertran ◽  
A. Oliva ◽  
L. Rodriguez-Santiago ◽  
M. Sodupe
Keyword(s):  
Potential Energy ◽  
Proton Transfer ◽  
Transfer Processes ◽  
Energy Profiles ◽  
Potential Energy Profiles

scholarly journals Photon Enhanced Interaction and Entanglement in Semiconductor Position-Based Qubits

2019 ◽  
Vol 9 (21) ◽  
pp. 4534 ◽  
Author(s):  
Panagiotis Giounanlis ◽  
Elena Blokhina ◽  
Dirk Leipold ◽  
Robert Staszewski
Keyword(s):  
Potential Energy ◽  
Entanglement Entropy ◽  
Electrostatic Actuation ◽  
Quantum States ◽  
Quantum Trajectory ◽  
Energy Profiles ◽  
Si Quantum Dot ◽  
And Control ◽  
Potential Energy Profiles ◽  
External Driving

CMOS technologies facilitate the possibility of implementing quantum logic in silicon. In this work, we discuss a minimalistic modelling of entangled photon communication in semiconductor qubits. We demonstrate that electrostatic actuation is sufficient to construct and control desired potential energy profiles along a Si quantum dot (QD) structure allowing the formation of position-based qubits. We further discuss a basic mathematical formalism to define the position-based qubits and their evolution under the presence of external driving fields. Then, based on Jaynes–Cummings–Hubbard formalism, we expand the model to include the description of the position-based qubits involving four energy states coupled with a cavity. We proceed with showing an anti-correlation between the various quantum states. Moreover, we simulate an example of a quantum trajectory as a result of transitions between the quantum states and we plot the emitted/absorbed photos in the system with time. Lastly, we examine the system of two coupled position-based qubits via a waveguide. We demonstrate a mechanism to achieve a dynamic interchange of information between these qubits over larger distances, exploiting both an electrostatic actuation/control of qubits and their photon communication. We define the entanglement entropy between two qubits and we find that their quantum states are in principle entangled.

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