A Simulated Annealing Algorithm for Training Empirical Potential Functions of Protein Folding

In this paper are reported the local minimum problem by means of current greedy algorithm for training the empirical potential function of protein folding on 8623 non-native structures of 31 globular proteins and a solution of the problem based upon the simulated annealing algorithm. This simulated annealing algorithm is indispensable for developing and testing highly refined empirical potential functions.

A Global Minimization Algorithm for Empirical Contact Potential Functions

Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD′s global minimum and refold extended protein structures into ones with root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirical contact potential functions, these results demonstrate that their global minimization problems may be solvable.

A Global Minimization Algorithm for Empirical Contact Potential Functions

Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference （CD） based on pseudo potential function, for simulating empirical contact potential functions and testing global minimization algorithm was proposed. The present article describes a conformational sampiing and global minimization algorithm, which is called WL, based on Monte Carlo simulation and simulated annealing. It can be used to locate CD＇s globe minimum and refold extended protein structures, as small as 0. 03 nm, from the native structures, back to ones with root mean square distance（RMSD）. These results demonstrate that the global minimization problems for empirical contact potential functions may be solvable.

Effects of potential functions on stochastic resonance

In this paper, the effects of a bistable potential function U（x） = -ax2/2＋b｜x＋｜2y/（2y） on stochastic resonance （SR） is discussed. We investigate the effects of index y on the performance of the SR system with fixed parameters a and b, and with fixed potential barriers, respectively. To measure the performance of the SR system in the presence of an aperiodic input, the bit error rate is employed, as is commonly used in binary communications. The numerical simulations strongly support the theoretical results. The goal of this investigation is to explore the effects of the shape of potential functions on SR and give a guidance of nonlinear systems in the application of information processing.

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand.This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand.Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment(i.e.dilatancy rate).Lack of an article that gathers these formulas is clear in the literature.Thus,this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands.Stress-dilatancy relation is usually not the same under compression and extension conditions.Furthermore,it may also be different under loading and unloading conditions.Therefore,the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading.Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship,more weight is allocated to stress-dilatancy relationship in this research.

Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.

Path-Following Control With Obstacle Avoidance of Autonomous Surface Vehicles Subject to Actuator Faults

This paper investigates the path-following control problem with obstacle avoidance of autonomous surface vehicles in the presence of actuator faults,uncertainty and external disturbances.Autonomous surface vehicles inevitably suffer from actuator faults in complex sea environments,which may cause existing obstacle avoidance strategies to fail.To reduce the influence of actuator faults,an improved artificial potential function is constructed by introducing the lower bound of actuator efficiency factors.The nonlinear state observer,which only depends on measurable position information of the autonomous surface vehicle,is used to address uncertainties and external disturbances.By using a backstepping technique and adaptive mechanism,a path-following control strategy with obstacle avoidance and fault tolerance is designed which can ensure that the tracking errors converge to a small neighborhood of zero.Compared with existing results,the proposed control strategy has the capability of obstacle avoidance and fault tolerance simultaneously.Finally,the comparison results through simulations are given to verify the effectiveness of the proposed method.

A Value for Games Defined on Graphs

Given a graph g=( V,A ) , we define a space of subgraphs M with the binary operation of union and the unique decomposition property into blocks. This space allows us to discuss a notion of minimal subgraphs (minimal coalitions) that are of interest for the game. Additionally, a partition of the game is defined in terms of the gain of each block, and subsequently, a solution to the game is defined based on distributing to each player (node and edge) present in each block a payment proportional to their contribution to the coalition.

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Potential-based obstacle avoidance in formation control

Based on the double integrator mathematic model, a new kind of potential function is presented in this paper by referring to the concepts of the electric field; then a new formation control method is proposed, in which the potential functions are used between agent-agent and between agent-obstacle, while state feedback control is applied for the agent and its goal. This strategy makes the whole potential field simpler and helps avoid some local minima. The stability of this combination of potential functions and state feedback control is proven. Some simulations are presented to show the rationality of this control method.

Neuroprotection against vascular dementia after acupuncture combined with donepezil hydrochloride：P300 event related potential

Acupuncture can be used to treat various nervous system diseases.Here,168 vascular dementia patients were orally administered donepezil hydrochloride alone（5 mg/day,once a day for 56 days）,or combined with acupuncture at Shenting（DU24）,Tianzhu（BL10）,Sishencong（Extra）,Yintang（Extra）,Renzhong（DU26）,Neiguan（PC6）,Shenmen（HT7）,Fengchi（GB20）,Wangu（GB12） and Baihui（DU20）（once a day for 56 days）.Compared with donepezil hydrochloride alone,P300 event related potential latency was shorter with an increased amplitude in patients treated with donepezil hydrochloride and acupuncture.Mini-Mental State Examination score was also higher.Moreover,these differences in P300 latency were identified within different infarcted regions in patients treated with donepezil hydrochloride and acupuncture.These findings indicate that acupuncture combined with donepezil hydrochloride noticeably improves cognitive function in patients with vascular dementia,and exerts neuroprotective effects against vascular dementia.

Structure and analytical potential energy function for the ground state of the BC^x （x=0, -1）

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B^1∏ of ^7LiH

The reasonable dissociation limit of the second excited singlet state B1∏ of ^7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B^∏ state are calculated using a symmetry-adaptedcluster configuration interaction method in full active space. The whole potential energy curve for the B1H state is obtained over the internuclear distance ranging from about 0.10 nm to 0,54 nm, and has a least-square fit to the analytic Murrell-Sorbie function form. The vertical excitation energy is calculated from the ground state to the B^1∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B^1∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.

The Analytical Potential Energy Function of NH Radical Molecule in External Electric Field

The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD （T） method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.

Molecular properties and potential energy function model of BH under external electric field

Using the density functional B3P86/cc-PV5Z method, the geometric structure of BH molecule under different external electric fields is optimized, and the bond lengths, dipole moments, vibration frequencies, and other physical properties parameters are obtained. On the basis of setting appropriate parameters, scanning single point energies are obtained by the same method and the potential energy curves under different external fields are also obtained. These results show that the physical property parameters and potential energy curves may change with external electric field, especially in the case of reverse direction electric field. The potential energy function without external electric field is fitted by Morse potential, and the fitting parameters are obtained which are in good agreement with experimental values. In order to obtain the critical dissociation electric parameter, the dipole approximation is adopted to construct a potential model fitting the corresponding potential energy curve of the external electric field. It is found that the fitted critical dissociation electric parameter is consistent with numerical calculation, so that the constructed model is reliable and accurate. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics, and molecular cooling with Stark effect.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

The theoretical study on the potential energy curves for X^1Σ^+, A^1Π and C^1Σ^- states of SiO molecule

This paper applies the symmetry-aziapted-cluster/symmetry-adapted-cluster configuration-interaction （SAC/SACCI） method to optimize the structures for X^1∑^＋, A^1 Ⅱ and C^1 ∑^- states of SiO molecule with the basis sets D95＋＋, 6-311＋＋G and 6-311＋＋G^＊＊. Comparing the obtained results with the experiments, it gets the conclusion that the basis set 6-311＋＋G^＊＊ is most suitable for the optimal structure calculations of X^1.∑^＋, A^Ⅱ and C^1∑^- states of SiO molecule. The whole potential energy curves for these electronic states are further scanned by using SAC/6-311＋＋G^＊＊ method for the ground state and SAC-CI/6-311＋＋G^＊＊ method for the excited states, then use a least square method to fit Murrell^Sorbie functions, at last the spectroscopic constants and force constants are calculated, which are in good agreement with the experimental data.

The theoretical study on the potential energy curve for X^3△ state of TiO molecule

This paper applies the density functional theory method to optimise the structure for X3A state of TiO molecule with the basis sets 6-31G, 6-31＋＋G and 6-311G^＊＊. Comparing the attained results with the experiments, it obtains the conclusion that the basis set 6-31＋＋G is most suitable for the optimal structure calculations of X3A state of TiO molecule. The whole potential energy curve for the electronic state is further scanned by using B3P86/6-31＋＋G method for the ground state, then it uses a least square fitted to Murrell-Sorbie functions, at last it calculates the spectroscopic constants and force constants, which are in better agreement with the experimental data.