Flux-Across-Surfaces Theorem for a Dirac Particle

We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime

Naive Realism about Operators

A source of much difficulty and confusion in the interpretation of quantum mechanics is a ``naive realism about operators.'' By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about ``measuring operators'' that occurs when the subject is quantum mechanics. Without a specification of what should be meant by ``measuring'' a quantum observable, such an expression can have no clear meaning. A definite specification is provided by Bohmian mechanics, a theory that emerges from Sch\"rodinger's equation for a system of particles when we merely insist that ``particles'' means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm---for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators!Comment: 18 pages, LaTex2e with AMS-LaTeX, to appear in Erkenntnis, 1996 (the proceedings of the international conference ``Probability, Dynamics and Causality,'' Luino, Italy, 15-17 June 1995, a special issue edited by D. Costantini and M.C. Gallavotti and dedicated to Prof. R. Jeffrey

On the quantum probability flux through surfaces

We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a given region, which may be simply expressed in terms of the current. This simple formula for these statistics does not appear as such in the literature. It is proposed that the formula, which is very different from the usual quantum mechanical measurement formulas, be verified experimentally. A full understanding of the quantum current and the associated formula is provided by Bohmian mechanics.Comment: 15 pages, 3 figures, revised and more detailed version, to be published in Journal of Statistical Physics, August 9

Time of Arrival from Bohmian Flow

We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalises earlier proposals by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wave packet.Comment: 18 pages, 8 figures, to appear in Journ. Phys. A; representation of ref. 5 improved (thanks to Rick Leavens

A Review on Joint Models in Biometrical Research

In some fields of biometrical research joint modelling of longitudinal measures and event time data has become very popular. This article reviews the work in that area of recent fruitful research by classifying approaches on joint models in three categories: approaches with focus on serial trends, approaches with focus on event time data and approaches with equal focus on both outcomes. Typically longitudinal measures and event time data are modelled jointly by introducing shared random effects or by considering conditional distributions together with marginal distributions. We present the approaches in an uniform nomenclature, comment on sub-models applied to longitudinal measures and event time data outcomes individually and exemplify applications in biometrical research

Scattering theory from microscopic first principles

We sketch a derivation of abstract scattering theory from the microscopic first principles defined by Bohmian mechanics. We emphasize the importance of the flux-across-surfaces theorem for the derivation, and of randomness in the impact parameter of the initial wave function---even for an, inevitably inadequate, orthodox derivation.Comment: To appear in Physica A, May 200

Proposed mechanism of action of saxitoxin in aquatic systems based on expression profiling in lower eukaryotes

Saxitoxin is a secondary metabolite produced by several species of dinoflagellates and cyanobacteria. The molecular target in mammals and higher eukaryotes is the sodium channel protein in nerve and muscle cells, where it binds with high affinity and effectively blocks the inward flow of sodium ions. The molecular target of saxitoxin in lower eukaryotes, such as those inhabiting the same ecosystems as the toxin-producing algae, is not known. The role of the toxin in the ecology of the algae is also a mystery. This dissertation sought to determine the molecular effects and possible target of saxitoxin on lower eukaryotes as a means to gain insights on the function of the toxin within the ecosystem. Global expression profiling with the yeast Saccharomyces cerevisiae using the Affymetrix GeneChip identified a set of genes commonly associated with copper homeostasis as being significantly differentially expressed upon short-term exposure to saxitoxin.The pattern of regulation of these genes was then compared to the patterns generated upon exposure to excess copper and excess iron using quantitative reverse-transcriptase PCR. The repression of two genes, FET3 and CTR1, suggested intracellular copper levels may be compromised when cells were in the presence of saxitoxin. To further explore the hypothesis of saxitoxin altering internal copper levels, a comparative transcriptomics study was performed with the green alga Chlamydomonas reinhardtii. Expression profiles of a pre-defined set of genes were compared following exposure to saxitoxin and excess copper, with results indicating that saxitoxin was also altering copper homeostasis in C. reinhardtii. The established model of copper transport in S. cerevisiae coupled with the known structural design of the Ctr1 protein suggests that saxitoxin is binding to plasma membrane copper transporters, in a manner analogous to that of sodium channel binding.The final section of this dissertation examined the phylogenetic relationship between two varieties of the dinoflagellate Pyrodinium bahamense. While var. compressum is an established saxitoxin producer, it has been determined that var. bahamense was the source of recent saxitoxin outbreaks in the western Atlantic. Based on small subunit ribosomal RNA gene sequences, the two are 99% identical, suggesting a reclassification based on genetic rather than morphological features

Optimization of struvite precipitation in synthetic biologically treated swine wastewater - Determination of the optimal process parameters

A sustainable way to recover phosphorus (P) in swine wastewater involves a preliminary step of P dissolution followed by the separation of particulate organic matter. The next two steps are firstly the precipitation of struvite crystals done by adding a crystallization reagent (magnesia) and secondly the filtration of the crystals. A design of experiments with five process parameters was set up to optimize the size of the struvite crystals in a synthetic swine wastewater. More than 90% of P was recovered as large crystals of struvite in optimal conditions which were: low Mg:Ca ratio (2.25:1), the leading parameter, high N:P ratio (3:1), moderate stirring rate (between 45 and 90 rpm) and low temperature (below 20°C). These results were obtained despite the presence of a large amount of calcium and using a cheap reactant (MgO). The composition of the precipitates was identified by Raman analysis and solid dissolution. Results showed that amorphous calcium phosphate (ACP) co-precipitated with struvite and that carbonates were incorporated with solid fractions

Multiple sclerosis, the measurement of disability and access to clinical trial data

Background: Inferences about long-term effects of therapies in multiple sclerosis (MS) have been based on surrogate markers studied in short-term trials. Nevertheless, MS trials have been getting steadily shorter despite the lack of a consensus definition for the most important clinical outcome - unremitting progression of disability. Methods: We have examined widely used surrogate markers of disability progression in MS within a unique database of individual patient data from the placebo arms of 31 randomised clinical trials. Findings: Definitions of treatment failure used in secondary progressive MS trials include much change unrelated to the target of unremitting disability. In relapsing-remitting MS, disability progression by treatment failure definitions was no more likely than similarly defined improvement for these disability surrogates. Existing definitions of disease progression in relapsing-remitting trials encompass random variation, measurement error and remitting relapses and appear not to measure unremitting disability. Interpretation: Clinical surrogates of unremitting disability used in relapsing -remitting trials cannot be validated. Trials have been too short and/or degrees of disability change too small to evaluate unremitting disability outcomes. Important implications for trial design and reinterpretation of existing trial results have emerged long after regulatory approval and widespread use of therapies in MS, highlighting the necessity of having primary trial data in the public domain