Stochastic Schroedinger equation from optimal observable evolution

In this article, we consider a set of trial wave-functions denoted by | Q \right> and an associated set of operators $A_\alpha$ which generate transformations connecting those trial states. Using variational principles, we show that we can always obtain a quantum Monte-Carlo method where the quantum evolution of a system is replaced by jumps between density matrices of the form $D = |Q_a> <Q_b|$, and where the average evolutions of the moments of $A_\alpha$ up to a given order $k$, i.e. , $< A_{\alpha_1} A_{\alpha_2} >$,..., , are constrained to follow the exact Ehrenfest evolution at each time step along each stochastic trajectory. Then, a set of more and more elaborated stochastic approximations of a quantum problem is obtained which approach the exact solution when more and more constraints are imposed, i.e. when $k$ increases. The Monte-Carlo process might even become exact if the Hamiltonian $H$ applied on the trial state can be written as a polynomial of $A_\alpha$. The formalism makes a natural connection between quantum jumps in Hilbert space and phase-space dynamics. We show that the derivation of stochastic Schroedinger equations can be greatly simplified by taking advantage of the existence of this hierarchy of approximations and its connection to the Ehrenfest theorem. Several examples are illustrated: the free wave-packet expansion, the Kerr oscillator, a generalized version of the Kerr oscillator, as well as interacting bosons or fermions.Comment: 13 pages, 1 figur

Metastable liquid lamellar structures in binary and ternary mixtures of Lennard-Jones fluids

We have carried out extensive equilibrium molecular dynamics (MD) simulations to investigate the Liquid-Vapor coexistence in partially miscible binary and ternary mixtures of Lennard-Jones (LJ) fluids. We have studied in detail the time evolution of the density profiles and the interfacial properties in a temperature region of the phase diagram where the condensed phase is demixed. The composition of the mixtures are fixed, 50% for the binary mixture and 33.33% for the ternary mixture. The results of the simulations clearly indicate that in the range of temperatures $78 < T < 102 ^{\rm o}$K, --in the scale of argon-- the system evolves towards a metastable alternated liquid-liquid lamellar state in coexistence with its vapor phase. These states can be achieved if the initial configuration is fully disordered, that is, when the particles of the fluids are randomly placed on the sites of an FCC crystal or the system is completely mixed. As temperature decreases these states become very well defined and more stables in time. We find that below $90 ^{\rm o}$K, the alternated liquid-liquid lamellar state remains alive for 80 ns, in the scale of argon, the longest simulation we have carried out. Nonetheless, we believe that in this temperature region these states will be alive for even much longer times.Comment: 18 Latex-RevTex pages including 12 encapsulated postscript figures. Figures with better resolution available upon request. Accepted for publication in Phys. Rev. E Dec. 1st issu

Pro-inflammatory cytokines predict relapse-free survival after one month of interferon-α but not observation in intermediate risk melanoma patients

Background: E1697 was a phase III trial of adjuvant interferon (IFN)-α2b for one month (Arm B) versus observation (Arm A) in patients with resected melanoma at intermediate risk. We evaluated the levels of candidate serum cytokines, the HLA genotype, polymorphisms of CTLA4 and FOXP3 genes and the development of autoantibodies for their association with relapse free survival (RFS) in Arm A and Arm B among 268 patients with banked biospecimens. Methods: ELISA was used to test 5 autoantibodies. Luminex/One Lambda LABTypeRSSO was used for HLA Genotyping. Selected CTLA4 and FOXP3 Single nucleotide polymorphisms (SNPs) and microsatellites were tested for by polymerase chain reaction (PCR). Sixteen serum cytokines were tested at baseline and one month by Luminex xMAP multiplex technology. Cox Proportional Hazards model was applied and the Wald test was used to test the marginal association of each individual marker and RFS. We used the Lasso approach to select the markers to be included in a multi-marker Cox Proportional Hazards model. The ability of the resulting models to predict one year RFS was evaluated by the time-dependent ROC curve. The leave-one-out method of cross validation (LOOCV) was used to avoid over-fitting of the data. Results: In the multi-marker modeling analysis conducted in Arm B, one month serum IL2Rα, IL- 12p40 and IFNα levels predicted one year RFS with LOOCV AUC = 82%. Among the three markers selected, IL2Rα and IFNα were the most stable (selected in all the cross validation cycles). The risk score (linear combination of the 3 markers) separated the RFS curves of low and high risk groups well (p = 0.05). This model did not hold for Arm A, indicating a differential marker profile in Arm B linked to the intervention (adjuvant therapy). Conclusions: Early on-treatment proinflammatory serum markers (IL2Rα, IL-12p40, IFNα) significantly predict RFS in our cohort of patients treated with adjuvant IFN-α2b and warrant further study

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011

Landsat Thematic Mapper imagery for mapping disturbed and rehabilitated vegetation, North Stradbroke Island, Queensland

The vegetation of North Stradbroke Island is inadequately represented on current maps. This is particularly the case for successional communities resulting from sand mining rehabilitation. A classification of vegetation and the extent of succession in a mined area and its surrounds was produced from Landsat Thematic Mapper imagery using micro-BRIAN image processing software. Results indicated 20 distinct spectral classes which, with the aid of secondary data sources, were identified as major vegetation formations. Seven of these classes related to different stages of revegetation. From groundtruthing, each of these classes was separable in terms of different structure, canopy coverage, and proportion of dead vegetation. -Author