Breaking the exponential wall in classical simulations of fidelity

We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom for almost all initial states. Then we present an algorithm whose cost is independent of the system's dimensionality and show that, within a continuous family of algorithms, our algorithm is the only one with this property. Simultaneously we propose a general analytical approach to estimate efficiency of trajectory-based methods.Comment: 5 pages, 3 figure

Beating the efficiency of both quantum and classical simulations with semiclassics

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods, and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of quantum fidelity in up to 100 dimensions with 2^1700-dimensional Hilbert space.Comment: 5 pages, 4 figure

Efficient evaluation of accuracy of molecular quantum dynamics using dephasing representation

Ab initio methods for electronic structure of molecules have reached a satisfactory accuracy for calculation of static properties, but remain too expensive for quantum dynamical calculations. We propose an efficient semiclassical method for evaluating the accuracy of a lower level quantum dynamics, as compared to a higher level quantum dynamics, without having to perform any quantum dynamics. The method is based on dephasing representation of quantum fidelity and its feasibility is demonstrated on the photodissociation dynamics of CO2. We suggest how to implement the method in existing molecular dynamics codes and describe a simple test of its applicability.Comment: 5 pages, 2 figure

On the Efficiency of Semiclassical and Classical Approximations of Quantum Fidelity in Many-Dimensional Systems

This thesis is focused on classical and semiclassical approximations of a specific quantum time correlation function, the “quantum fidelity.” Namely, we rigorously study the efficiency of a continuous class of algorithms for the evaluation of its classical limit and both the cost and the error of a particular semiclassical approximation of it. In the physics domain, quantum fidelity can be used to study the cross section of inelastic neutron scattering and phenomena like decoherence and irreversibility in NMR experiments. In chemical physics, quantum fidelity can be employed to compute the spectrum of a quantum state, to evaluate the accuracy of quantum dynamics on an approximate potential energy surface, and to verify the importance of nonadiabatic electronic transitions in molecules. Unfortunately, as for any numerical simulation of a quantum dynamical object, many-dimensional calculations of quantum fidelity are extremely expensive computationally. Classical methods, not including any quantum effect, are generally believed to be efficient approximations for the numerical evaluation of large systems’ properties when quantum effects are not important. We prove that, previous to this research, the computational costs of available algorithms for the simulation of classical fidelity increased exponentially with the number of degrees of freedom and we single out, within a continuous family of algorithms, the only one for which the number of trajectories needed for convergence is independent of the system’s dimensionality. Recently a semiclassical method, called “dephasing representation” (DR), has been proposed to approximate quantum fidelity accurately and efficiently. Although semiclassical methods, approximately including all types of quantum effects, are generally more accurate but much less efficient than classical methods, we prove that for the semiclassical DR there exists at least one algorithm for which the number of trajectories needed for convergence is independent of dimensionality and also that this semiclassical algorithm is even faster than the most efficient classical fidelity algorithm previously singled out. Encouraged by the surprising efficiency of the specific semiclassical method, we investigate the error of the DR compared to the quantum benchmark

Evaluation of Load Distribution in a Mandibular Model with Four Implants Depending on the Number of Prosthetic Screws Used for OT-Bridge System: A Finite Element Analysis (FEA)

In full-arch implant rehabilitations, when the anterior screw abutment channel compromises the aesthetic of the patient, the OT-Bridge system used with its Seeger rings may provide the necessary retention of the prosthesis. However, no studies have evaluated the forces generated at the Seeger level during loading. This Finite Element Analysis aims to investigate the mechanical behavior of Seeger rings in a mandibular model with four implants and an OT-Bridge system, used without one or two anterior prosthetic screws. A 400 N unilateral load was virtually applied on a 7 mm distal cantilever. Two different variables were considered: the constraint conditions using two or three screws instead of four and the three different framework materials (fiberglass reinforced resin, cobalt-chrome, TiAl6V4). The FEA analysis exhibited tensile and compressive forces on the Seeger closest to the loading point. With the resin framework, a tension force on abutment 3.3 generates a displacement from 5 to 10 times greater than that respectively expressed in metal framework materials. In a full-arch rehabilitation with four implants, the case with three prosthetic screws seems to be a safer and more predictable configuration instead of two. Considering the stress value exhibited and the mechanical properties of the Seeger, the presence of only two prosthetic screws could lead to permanent deformation of the Seeger in the screwless abutment closest to the loading point

Eterodimero apoA-IM-apoA-II: proposta di un modello strutturale a supporto della sua particolare sensibilità alla proteolisi

In this study, we propose a structure for the heterodimer between apolipoprotein A-IMilano and apolipoprotein A-II (apoA-IM–apoA-II) in a synthetic high-density lipoprotein (HDL) containing L--palmitoyloleoyl phosphatidylcholine. We applied bioinformatics/computational tools and procedures, such as molecular docking, molecular and essential dynamics, starting from published crystal structures for apolipoprotein A-I and apolipoprotein A-II. Structural and energetic analyses onto the simulated system showed that the molecular dynamics produced a stabilized synthetic HDL. The essential dynamic analysis showed a deviation from the starting belt structure. Our structural results were validated by limited proteolysis experiments on HDL from apoA-IM carriers in comparison with control HDL. The high sensitivity of apoA-IM–apoA-II to proteases was in agreement with the high root mean-square fluctuation values and the reduction in secondary structure content from molecular dynamics data. Circular dichroism on synthetic HDL containing apoA-IM–apoA-II was consistent with the -helix content computed on the proposed model

Twisted nanoribbons from a RGD-bearing cholic acid derivative

In light of the biomedical interest for self-assembling amphiphiles bearing the tripeptide Arg-Gly-Gly (RGD), a cholic acid derivative was synthesized by introducing an aromatic moiety on the steroidal skeleton and the RGD sequence on the carboxylic function of its chain 17–24, thus forming a peptide amphiphile with the unconventional rigid amphiphilic structure of bile salts. In aqueous solution, the compound self-assembled into long twisted ribbons characterized by a very low degree of polydispersity in terms of width (≈25 nm), thickness (≈4.5 nm) and pitch (≈145 nm). It was proposed that in the ribbon the molecules are arranged in a bilayer structure with the aromatic moieties in the interior, strongly involved in the intermolecular interaction, whereas the RGD residues are located at the bilayer-water interface. The nanostructure is significantly different from those generally provided by RGD-containing amphiphiles with the conventional peptide-tail structure, for which fibers with a circular cross-section were observed, and successfully tested as scaffolds for tissue regeneration. From previous work on the use of this kind of nanostructures, it is known that features like morphology, rigidity, epitope spacing and periodicity are important factors that dramatically affect cell adhesion and signaling. Within this context, the reported results demonstrate that bile salt-based peptide surfactants are promising building blocks in the preparation of non-trivial RGD-decorated nanoaggregates with well-defined morphologies and epitope distributions

Synthesis and activity of endomorphin-2 and morphiceptin analogues with proline surrogates in position 2

The opioid agonists endomorphins (Tyr-Pro-Trp-Phe-NH(2); EM1 and Tyr-Pro-Phe-Phe-NH(2); EM2) and morphiceptin (Tyr-Pro-Phe-Pro-NH(2)) exhibit an extremely high selectivity for mu-opioid receptor. Here a series of novel EM2 and morphiceptin analogues containing in place of the proline at position 2 the S and R residues of beta-homologues of proline (HPro), of 2-pyrrolidinemethanesulphonic acid (HPrs) and of 3-pyrrolidinesulphonic acid (beta Prs) have been synthesized and their binding affinity and functional activity have been investigated. The highest p-receptor affinity is shown by [(S)beta Prs(2)]EM2 analogue (6e) which represents the first example of a beta-sulphonamido analogue in the field of mold peptides. (C) 2010 Elsevier Masson SAS. All rights reserved