Cutoff Scheme Research Articles

Molecular level approaches for investigation of electron transfer in nonpolar solvents

The authors extend their previous work published in Leontyev and TachiyaJ. Chem. Phys. 123, 224502 (2005) and study not only forward but also reverse electron transfer between pyrene and dimethylaniline in a nonpolar solvent, n-hexane. The distribution function methodology and molecular dynamics technique adopted in their previous work are used. Two algorithms (I and II) are formulated for obtaining the reorganization energy and the solvation free energy difference in the linear response approximation. The two algorithms are combined with different cutoff schemes and tested for polarizable and nonpolarizable solvent models. Agreement between the results obtained by the two algorithms was achieved only for simulations employing the particle mesh Ewald treatment. It is concluded that algorithm I provides a reliable scheme for evaluation of the reorganization energy and the solvation free energy difference. Moreover, a new algorithm referred to as the G-function algorithm is formulated which does not assume the linear response approximation, and is tested on evaluation of the solvation free energy difference. Agreement between the results from the G-function algorithm and those from algorithms I and II is fairly good, although it depends on the degree of statistical consistency of the simulations. In the case of nonpolar solvents the G-function method has practical importance because, unlike the conventional thermodynamic integration approach, it requires equilibrium molecular configuration ensembles only for the initial and final states of the system.

QCD factorization for deep-inelastic scattering at large Bjorken [formula omitted

We study deep-inelastic scattering factorization on a nucleon in the end-point regime x B ∼ 1 − O ( Λ QCD / Q ) where the traditional operator product expansion is supposed to fail. We argue, nevertheless, that the standard result holds to leading order in 1 − x B due to the absence of dependence on the scale Q 2 ( 1 − x B ) 2 . Refactorization at the scale Q 2 ( 1 − x B ) in the coefficient function can be made in the soft-collinear effective theory and remains valid in the end-point regime. On the other hand, the traditional refactorization approach that relies on gauge dependent quantities, introduces the spurious scale Q 2 ( 1 − x B ) 2 in various factors, which drives them nonperturbative in the region of our interest. We show how to improve the situation by introducing a rapidity cutoff scheme, and how to recover the effective theory refactorization by choosing appropriately the cutoff parameter. Through a one-loop calculation, we demonstrate explicitly that the proper soft subtractions must be made in the collinear matrix elements to avoid double counting of soft contributions.

Spectral calibration of exponential Lévy models

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation.

Assessing the influence of electrostatic schemes on molecular dynamics simulations ofsecondary structure forming peptides

Electrostatic interactions play a fundamental role in determining the structure anddynamics of biomolecules in solution. However the accurate representation of electrostaticsin classical mechanics based simulation approaches such as molecular dynamics (MD) is achallenging task. Given the growing importance that MD simulation methods are taking onin the study of protein folding, protein stability and dynamics, and in structure predictionand design projects, it is important to evaluate the influence that different electrostaticschemes have on the results of MD simulations. In this paper we performed longtimescale simulations (500 ns) of two peptides, beta3 and RN24 forming differentsecondary structures, using for each peptide four different electrostatic schemes(namely PME, reaction field correction, and cut-off schemes with and withoutneutralizing counterions) for a total of eight 500 ns long MD runs. The structural andconformational features of each peptide under the different conditions were evaluated interms of the time dependence of the flexibility, secondary structure evolution,hydrogen-bonding patterns, and several other structural parameters. The degreeof sampling for each simulation as a function of the electrostatic scheme wasalso critically evaluated. Our results suggest that, while in the case of the shortpeptide RN24 the performances of the four methods are comparable, PME and RFschemes perform better in maintaining the structure close to the native one for theβ-sheet peptide beta3, in which long range contacts are mostly responsible for the definitionof the native structure.

On the Ewald Artifacts in Computer Simulations. The Test-Case of the Octaalanine Peptide With Charged Termini

The treatment of electrostatic interactions in molecular simulations is of fundamental importance. Ewald and related methods are being increasingly used to the detriment of cutoff schemes, which are known to produce several artifacts. A potential drawback of the Ewald method is the spatial periodicity that is imposed to the system, which could produce artifacts when applied in the simulation of liquids. In this work we analyze the octaalanine peptide with charged termini in explicit solvent, for which severe effects due to the use of Ewald sums were predicted using continuum electrostatics. Molecular Dynamics simulations for a total of 158 nanoseconds were performed in cells of different sizes. From the comparison of the results of different system sizes, no significant periodicity-induced artifacts were observed. It is argued that in current biomolecular simulations, the incomplete sampling is likely to affect the results to a larger extent than the artifacts induced by the use of Ewald sums.

Role of Lipid Charge in Organization of Water/Lipid Bilayer Interface: Insights via Computer Simulations

Anionic unsaturated lipid bilayers represent suitable model systems that mimic real cell membranes: they are fluid and possess a negative surface charge. Understanding of detailed molecular organization of water-lipid interfaces in such systems may provide an important insight into the mechanisms of proteins' binding to membranes. Molecular dynamics (MD) of full-atom hydrated lipid bilayers is one of the most powerful tools to address this problem in silico. Unfortunately, wide application of computational methods for such systems is limited by serious technical problems. They are mainly related to correct treatment of long-range electrostatic effects. In this study a physically reliable model of an anionic unsaturated bilayer of 1,2-dioleoyl-sn-glycero-3-phosphoserine (DOPS) was elaborated and subjected to long-term MD simulations. Electrostatic interactions were treated with two different algorithms: spherical cutoff function and particle-mesh Ewald summation (PME). To understand the role of lipid charge in the system behavior, similar calculations were also carried out for zwitterionic bilayer composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). It was shown that, for the charged DOPS bilayer, the PME protocol performs much better than the cutoff scheme. In the last case a number of artifacts in the structural organization of the bilayer were observed. All of them were attributed to inadequate treatment of electrostatic interactions of lipid headgroups with counterions. Electrostatic properties, along with structural and dynamic parameters, of both lipid bilayers were investigated. Comparative analysis of the MD data reveals that the water-lipid interface of the DOPC bilayer is looser than that for DOPS. This makes possible deeper penetration of water molecules inside the zwitterionic (DOPC) bilayer, where they strongly interact with carbonyls of lipids. This can lead to thickening of the membrane interface in zwitterionic as compared to negatively charged bilayers.

Absolute free energies of binding of peptide analogs to the HIV‐1 protease from molecular dynamics simulations

The constants of binding of five peptide analogs to the active site of the HIV-1 aspartic-protease are calculated based on a novel sampling scheme that is efficient and does not introduce any approximations in addition to the energy function used to describe the system. The results agree with experiments. The squared correlation coefficient of the calculated vs. the measured values is 0.79. The sampling scheme consists of a series of molecular dynamics integrations with biases. The biases are selected based on an estimate of the probability density function of the system in a way to explore the conformational space and to reduce the statistical error in the calculated binding constants. The molecular dynamics integrations are done with a vacuum potential using a short cutoff scheme. To estimate the probability density of the simulated system, the results of the molecular dynamics integrations are combined using an extension of the weighted histogram analysis method (C. Bartels, Chem. Phys. Letters 331 (2000) 446-454). The probability density of the solvated ligand-protein system is obtained by applying a correction for the use of the short cutoffs in the simulations and by taking into account solvation with an electrostatic term and a hydrophobic term. The electrostatic part of the solvation is determined by finite difference Poisson-Boltzmann calculations; the hydrophobic part of the solvation is set proportional to the solvent accessible surface area. Setting the hydrophobic surface tension parameter equal to 8 mol(-1) K(-1) A(-2), absolute binding constants are in the muM to nM range. This is in agreement with experiments. The standard errors determined from eight repeated binding constant determinations are a factor of 14 to 411. A single determination of a binding constant is done with 499700 steps of molecular dynamics integration and 4500 finite difference Poisson-Boltzmann calculations. The simulations can be analyzed with respect to conformational changes of the active site of the HIV-1 protease or the ligands upon binding and provide information that complements experiments and can be used in the drug development process.

Tree Expansion of the Wilson Effective Action and Reduction of the Polchinski Flow Equations

In a tree expansion of the Wilson effective action, reduction of the Polchinski flow equations to their 1PI part is performed. We extract a certain subset of the connected cutoff Green functions that determines the renormalization group flow of the 1PI part of the Wilson effective action. 1. Introduction In the exact renormalization group (RG) approach to continuum field theories, there are two types of flow equations for the effective actions: the Polchinski flow equations (PFE) 1) for the Wilson effective action Seff ,a nd the fl ow equations 2), 3) for the Legendre effective actions Γeff . We call the latter “Legendre flow equations” (LFE). Although these two types of the flow equations are formally equivalent for exact effective actions Seff and Γeff, there is a clear distinction in their structure when used with some approximation method, such as truncation in a field polynomial expansion of the effective actions. Consider, for example, a NambuJona-Lasinio type model. In LFE, 4-fermi flow equations are not affected by higherdimensional multi-fermi operators. By contrast, the PFE requires the contribution of 6-fermi operators in order to determine the RG flow of 4-fermi operators. This difference originates from the fact that the action is 1PI in one case but not in the other. Furthermore, the Wilson effective action is known to have a strong cutoff scheme dependence, as pointed out in Ref. 4). In spite of these disadvantages, the Wilson effective action plays an important role in symmetry considerations. In particular, even if the standard realization of a symmetry is incompatible with the RG regularization, an effective but exact symmetry may be realized along the RG flow. The regularization-dependent symmetry which has attracted interest in recent years is characterized by the quantum master equation for the Wilson effective action. 5) It is not at all obvious if the realization of this symmetry is preserved under the Legendre transformation. Therefore, it is worth considering the RG approach based upon the Wilson effective action to which the PFE applies. The purpose of this note is to investigate the structure of Seff and the PFE in detail. Using a tree expansion, we extract a certain subset of the connected cutoff Green functions that determines the RG flow of the 1PI part of Seff , precisely in the same manner as the LFE. This is the 1PI reduction of the PFE. The entire set of PFE is shown to be decomposed into infinitely many sets of equations generated by the reduced PFE we have obtained. As an application of our formalism, we obtain the 6-fermi operators needed to describe the 4-fermi flow equations.

Elongation method with cutoff technique for linear SCF scaling

AbstractThe elongation method uses the concept of locality and works in a regionally localized molecular orbital basis set. In this method the system is partitioned into several frozen fragments and an active one. If the coupling between a given frozen fragment and the active space is small enough, one can develop a cutoff scheme for effectively discarding the former in all further calculations. At the Hartree–Fock level many two‐electron integrals are thereby eliminated, leading to a reduction in self‐consistent field computation time. In test calculations on four polyglycine conformers, with an appropriate default threshold for coupling, the cutoff error is very small and/or comparable to that of a normal elongation calculation. On the other hand, the computation time for 20 residues is a factor of 5 less than that of a normal Hartree–Fock treatment and scales linearly (or even sublinearly) with the number of residues. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

The Range and Shielding of Dipole-Dipole Interactions in Phospholipid Bilayers

In molecular dynamics simulations of lipid bilayers, the structure is sensitive to the precise treatment of electrostatics. The dipole-dipole interactions between headgroup dipoles are not long-ranged, but the area per lipid and, through it, other properties of the bilayer are very sensitive to the detailed balance between the perpendicular and in-plane components of the headgroup dipoles. This is affected by the detailed properties of the cutoff scheme or if long-range interactions are included by Ewald or particle-mesh Ewald techniques. Interaction between the in-plane components of the headgroup dipoles is attractive and decays as the inverse sixth power of distance. The interaction is screened by the square of a dielectric permittivity close to the value for water. Interaction between the components perpendicular to the membrane plane is repulsive and decays as the inverse third power of distance. These interactions are screened by a dielectric permittivity of the order 10. Thus, despite the perpendicular components being much smaller in magnitude than the in-plane components, they will dominate the interaction energies at large distances.

Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. We show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone boson masses. We also discuss in detail the price, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization. We also compare the fourth-order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.

Effective potential and vacuum stability within universal extra dimensions

The one-loop effective potential calculated for a generic model that originates from 5-dimensional theory reduced down to 4 dimensions is considered. The cutoff and dimensional regularization schemes are discussed and compared. It is demonstrated that the prescriptions are consistent with each other and lead to the same physical consequences. The stability of the ground state is discussed for a U(1) model that is supposed to mimic the standard model extended to 5 dimensions. It has been shown that fermionic Kaluza-Klein modes can dramatically influence the shape of the effective potential shifting the instability scale even by several orders of magnitude.

Screening for congenital adrenal hyperplasia: adjustment of 17-hydroxyprogesterone cut-off values to both age and birth weight markedly improves the predictive value.

Newborn screening procedures for congenital adrenal hyperplasia (CAH) are still suboptimal because of low specificity, particularly in premature infants. This study evaluated a multitiered strategy for reporting abnormal 17-hydroxyprogesterone screening values that simultaneously takes into account not only birth weight but also age at sampling. A cautious three-tiered cut-off scheme was used during the initial 24 months of CAH screening in Bavaria. Data were then reanalyzed using five birth weight classes to reflect more precisely the markedly higher values in low-birth-weight newborns. Because 17-hydroxyprogesterone values apparently decline with increasing age, these classes were then further subdivided into a total of 21 groups according to the age at sampling. Based on this reanalysis, we defined new multitiered cut-off levels and used them for the next 18 months. A total of 538466 newborns were screened from January 1999 to June 2002; 51 CAH cases were detected. Application of the new threshold values resulted in a 35% reduction of the total recall rate (from 1.13% to 0.74%) and an increase in the positive predictive value from 0.84% to 1.29% without reducing diagnostic sensitivity. This improvement of CAH screening can be achieved by simply using request forms that ask for both age and birth weight at the time of sampling.

Improving the convergence of the chiral expansion for nuclear forces - I: Peripheral phases

We study the two-pion exchange potential at next-to-next-to-leading order in chiral effective field theory. We propose a new cut-off scheme for the pion loop integrals based on spectral function regularization. We show that this method allows for a consistent implementation of constraints from pion-nucleon scattering. It leads to a much improved description of the partial waves with angular momentum l \geq 2 as compared to the calculation utilizing dimensional regularization.

Numerical Evaluation of a Two-Loop Diagram in the Cutoff Regularization**The project supported in part by National Natural Science Foundation of China under Grant Nos. 10075020 and 10205004, the ECUN Renovation Fund for Young Researchers under No. 53200179

The sunset diagram of theory is evaluated numerically in cutoff scheme and a nonzero finite term (in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This finding dramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in our previous work.

Improving the convergence of the chiral expansion for nuclear forces - II: Low phases and the deuteron

Recently we have proposed a new cut-off scheme for pion loop integrals in the two-pion exchange potential. This method allows for a consistent implementation of constraints from pion-nucleon scattering and has been successfully applied to peripheral nucleon-nucleon partial waves. We now consider low partial waves in the non-perturbative regime, where the regularized Lippmann-Schwinger equation has to be solved in order to generate the bound and scattering states. We observe an improved description of most of the phase shifts when going from next-to- to next-to-next-to-leading order in the chiral expansion. We also find a good description of the deuteron properties. In addition, the new cut-off scheme allows to avoid the presence of unphysical deeply bound states. We discuss the cut-off dependence of the four-nucleon low-energy constants and show that their numerical values can be understood in terms of resonance saturation. This connects the effective field theory approach to boson exchange phenomenology.

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E 66, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in the systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the universal character of the Casimir force in the systems with short-ranged interactions. The effects due to dispersion forces are discussed for the systems with periodic or realistic boundary conditions. In contrast to the systems with short-ranged interactions, for L/xi>>1, one observes leading finite-size contributions governed by power laws in L due to the subleading long-ranged character of the interaction, where L is the finite system size and xi is the correlation length.

Solar-neutrino reactions on deuteron in effective field theory

The cross sections for low-energy neutrino–deuteron reactions are calculated within heavy-baryon chiral perturbation theory employing a cut-off regularization scheme. The transition operators are derived up to next-to-next-to-next-to-leading order in the Weinberg counting rules, while the nuclear matrix elements are evaluated using the wave functions generated by a high-quality phenomenological NN potential. With the adoption of the axial-current-four-nucleon coupling constant fixed from the tritium beta decay data, our calculation is free from unknown low-energy constants. Our results exhibit a high degree of stability against different choices of the cutoff parameter, a feature which indicates that, apart from radiative corrections, the uncertainties in the calculated cross sections are less than 1%.

Exact multilocal renormalization group and applications to disordered problems.

We develop a method, the exact multilocal renormalization group (EMRG) which applies to a broad set of theories. It is based on the systematic multilocal expansion of the Polchinski-Wilson exact renormalization group (ERG) equation together with a scheme to compute correlation functions. Integrating out explicitly the nonlocal interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation for a function, its local part. This is done perturbatively around fixed points, but exactly to any given order in the local part. It is thus controlled, at variance with projection methods, e.g., derivative expansions or local potential approximations. Our EMRG method is well-suited to problems such as the pinning of disordered elastic systems, previously described via functional renormalization group (FRG) approach based on a hard cutoff scheme. Since it involves arbitrary cutoff functions, we explicitly verify universality to O(epsilon=4-D), both of the T=0 FRG equation and of correlations. Extension to finite temperature T yields the finite size (L) susceptibility fluctuations characterizing mesoscopic behavior (Deltachi)2 approximately L(straight theta)/T, where straight theta is the energy exponent. Finally, we obtain the universal scaling function to O(epsilon(1/3)) which describes the ground state of a domain wall in a random field confined by a field gradient, compare with exact results and variational method. Explicit two loop exact RG equations are derived and the application to the FRG problem is sketched.

Single channel occupied voice and multi-channel occupied HSCSD over GSM

Random access and traffic channel parts are utilized, respectively, for call establishment and information transmission in the uplink direction, comprising mobile to base station of the Global System for Mobile Communication (GSM) networks. Voice (V) and High Speed Circuit Switched Data (HSCSD) calls use two parallel random access parts and a common traffic channel part where a V call occupies a single traffic channel and a HSCSD call occupies a multiple number of traffic channels. A call is either rejected or blocked if it is unsuccessful either in the random access part or in the traffic channel part. The optimum number of random access slots is directly proportional to the average access arrival rate. According to the specification, four types of retransmission cut-off policies can be executed in the random access part wherein only one type can provide almost zero call rejection probability, pertaining to a limited amount of traffic arrival rate per random access slot. A complete analysis for the traffic channel utilization and call blocking probability for V and HSCSD calls with an exact number of random access slots in collaboration with four different types of retransmission cut-off schemes is introduced. The overall call success probability is devised resorting to call rejection and call blocking probabilities. Results demonstrate that the overall call success probability can be independent of random access part up to a certain call arrival rate if a special type of retransmission cut-off is utilized.