Spectral projections and resolvent bounds for partially elliptic quadratic differential operators

We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers-Fokker-Planck operators with quadratic potentials. For the norms of spectral projections for these operators, we obtain complete asymptotic expansions in dimension one, and for arbitrary dimension, we obtain exponential upper bounds and the rate of exponential growth in a generic situation. We furthermore obtain a complete characterization of those operators with orthogonal spectral projections onto the ground state.Comment: 60 pages, 3 figures. J. Pseudo-Differ. Oper. Appl., to appear. Revised according to referee report, including minor changes to Corollary 1.8. The final publication will be available at link.springer.co

Baryon Washout, Electroweak Phase Transition, and Perturbation Theory

We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-by-order in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.Comment: 25 pages, 9 figures; v2 minor typos correcte

Nekrasov Functions and Exact Bohr-Sommerfeld Integrals

In the case of SU(2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon model. If the same construction is literally applied to monodromies of exact wave functions, the prepotential turns into the one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a problem of describing the full Nekrasov function as a seemingly straightforward double-parametric quantization of sine-Gordon model. This also provides a new link between the Liouville and sine-Gordon theories.Comment: 10 page

Optimal free descriptions of many-body theories

Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. Although these systems are promising for technological applications, they also present conceptual challenges, as they require approaches beyond mean-field and perturbation theory. Here we develop a general framework for identifying the free theory that is closest to a given interacting model in terms of their ground-state correlations. Moreover, we quantify the distance between them using the entanglement spectrum. When this interaction distance is small, the optimal free theory provides an effective description of the low-energy physics of the interacting model. Our construction of the optimal free model is non-perturbative in nature; thus, it offers a theoretical framework for investigating strongly correlated systems

Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Long-term therapy of interferon-alpha induced pulmonary arterial hypertension with different PDE-5 inhibitors: a case report

BACKGROUND: Interferon alpha2 is widely used in hepatitis and high-risk melanoma. Interferon-induced pulmonary arterial hypertension as a side effect is rare. CASE PRESENTATION: We describe a melanoma patient who developed severe pulmonary arterial hypertension 30 months after initiation of adjuvant interferon alpha2b therapy. Discontinuation of interferon did not improve pulmonary arterial hypertension. This patient could be treated successfully with phosphodiesterase-5 inhibitor therapy. CONCLUSION: This is only the 5th case of interferon-induced pulmonary arterial hypertension and the first documented case where pulmonary arterial hypertension was not reversible after termination of interferon alpha2 therapy. If interferon alpha2 treated patients develop respiratory symptoms, pulmonary arterial hypertension should be considered in the differential diagnosis. For these patients phosphodiesterase-5 inhibitors, e.g. sildenafil or vardenafil, could be an effective therapeutic approach

A framework for resolving motivational conflict via attractor dynamics

Motivation modulates behaviour depending upon contextual and internal cues. Like animals, successful artificial agents must implement different behavioural strategies in order to satisfy dynamical needs. Such causal factors emerge from internal homeostatic or allostatic processes, as well as from external stimuli or threats. However, when two or more needs coalesce, a situation of motivational conflict ensues. In this work we present a four-stage dynamical framework for the resolution of motivational conflict based upon principles from dynamical systems and statistical mechanics. As a central mechanism for the resolution of conflict we propose the use of potentials with multiple wells or minima. This model leads to behavioural switching either by means of a bifurcation or by the stochastic escape from one of the wells. We present analytical and simulation results that reproduce known motivational conflict phenomena observed in the study of animal behaviour, in the case of two conflicting motivations

Particle simulation approach for subcellular dynamics and interactions of biological molecules

BACKGROUND: Spatio-temporal dynamics within cells can now be visualized at appropriate resolution, due to the advances in molecular imaging technologies. Even single-particle tracking (SPT) and single fluorophore video imaging (SFVI) are now being applied to observation of molecular-level dynamics. However, little is known concerning how molecular-level dynamics affect properties at the cellular level. RESULTS: We propose an algorithm designed for three-dimensional simulation of the reaction-diffusion dynamics of molecules, based on a particle model. Chemical reactions proceed through the interactions of particles in space, with activation energies determining the rates of these chemical reactions at each interaction. This energy-based model can include the cellular membrane, membranes of other organelles, and cytoskeleton. The simulation algorithm was tested for a reversible enzyme reaction model and its validity was confirmed. Snapshot images taken from simulated molecular interactions on the cell-surface revealed clustering domains (size ~0.2 μm) associated with rafts. Sample trajectories of raft constructs exhibited "hop diffusion". These domains corralled the diffusive motion of membrane proteins. CONCLUSION: These findings demonstrate that our approach is promising for modelling the localization properties of biological phenomena

Linear-time protein 3-D structure searching with insertions and deletions

<p>Abstract</p> <p>Background</p> <p>Two biomolecular 3-D structures are said to be similar if the RMSD (root mean square deviation) between the two molecules' sequences of 3-D coordinates is less than or equal to some given constant bound. Tools for searching for similar structures in biomolecular 3-D structure databases are becoming increasingly important in the structural biology of the post-genomic era.</p> <p>Results</p> <p>We consider an important, fundamental problem of reporting all substructures in a 3-D structure database of chain molecules (such as proteins) which are similar to a given query 3-D structure, with consideration of indels (<it>i.e.</it>, insertions and deletions). This problem has been believed to be very difficult but its exact computational complexity has not been known. In this paper, we first prove that the problem in unbounded dimensions is NP-hard. We then propose a new algorithm that dramatically improves the average-case time complexity of the problem in 3-D in case the number of indels <it>k </it>is bounded by a constant. Our algorithm solves the above problem for a query of size <it>m </it>and a database of size <it>N </it>in average-case <it>O</it>(<it>N</it>) time, whereas the time complexity of the previously best algorithm was <it>O</it>(<it>Nm</it>^<it>k</it>+1).</p> <p>Conclusions</p> <p>Our results show that although the problem of searching for similar structures in a database based on the RMSD measure with indels is NP-hard in the case of unbounded dimensions, it can be solved in 3-D by a simple average-case linear time algorithm when the number of indels is bounded by a constant.</p

Fission Hindrance in Hot Nuclei

The role of dynamics in fission has attracted much interest since the discovery of this process over fifty years ago. However, the study of the dynamical aspects of fission was for many years hampered by the lack of suitable experimental observables against which theoretical calculations could be tested. For example, it was found that the total kinetic energy release in fission can be described equally well by very different dissipation mechanisms, namely the wall formula, that is based on the collisions of the nucleons with the moving wall of the system, as well as a bulk viscosity of the nuclear matter. Although early theoretical work suggested that the fission process may be described as a diffusion process over the fission barrier, this was largely forgotten because of the success of a purely statistical model which instead of enumerating the ultimate final states of the process argues that the fission rate is determined at the {open_quote}transition state{close_quote} as the system traverses the fission saddle point. It was therefore significant when Gavron showed that the transition state model was unable to describe the number of neutrons emitted prior to scission at high excitation energy in reactions of {sup 16}O+{sup 142}Nd. Subsequent experimental work using different methods to measure the fission dissipation/viscosity has confirmed these initial observations. It was therefore very surprising when Moretto in recent publications concluded that their analysis of fission excitation functions obtained with a and {alpha} and {sup 3}He induced projectiles was perfectly in accord with the transition state model and left no room for fission viscosity. In this paper we`ll show that Moretto`s analysis is flawed by assuming first chance fission only (in direct contradiction to the experimental observation of pre-scission neutron emission in heavy-ion induced fission), and reveal why the systematics presented by Moretto looked so convincing despite these flaws