Entwined Pairs and Schroedinger 's Equation

We show that a point particle moving in space-time on entwined-pair paths generates Schroedinger's equation in a static potential in the appropriate continuum linit. This provides a new realist context for the Schroedinger equation within the domain of classical stochastic processes. It also suggests that self-quantizing systems may provide considerable insight into conventional quantum mechanics.Comment: 16 pg. 1 fi

Entwined Paths, Difference Equations and the Dirac Equation

Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are `self-quantizing'. We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process in the same sense that the Diffusion and Telegraph equations are phenomenological descriptions of stochastic processes.Comment: 15 pages, 5 figures Replacement 11/02 contains minor editorial change

The Dirac Equation in Classical Statistical Mechanics

The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model `self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics.Comment: Condensed version of a talk given at the MRST conference, 05/02, Waterloo, Ont. 7 page

Pubertal presentation in seven patients with congenital adrenal hyperplasia due to P450 Oxidoreductase deficiency

Context: P450 oxidoreductase (POR) is a crucial electron donor to all microsomal P450 cytochrome (CYP) enzymes including 17α-hydroxylase (CYP17A1), 21-hydroxylase (CYP21A2) and P450 aromatase. Mutant POR causes congenital adrenal hyperplasia with combined glucocorticoid and sex steroid deficiency. P450 oxidoreductase deficiency (ORD) commonly presents neonatally, with disordered sex development in both sexes, skeletal malformations, and glucocorticoid deficiency. \ud \ud Objective: The aim of the study was to describe the clinical and biochemical characteristics of ORD during puberty. \ud \ud Design: Clinical, biochemical, and genetic assessment of seven ORD patients (five females, two males) presenting during puberty was conducted. \ud \ud Results: Predominant findings in females were incomplete pubertal development (four of five) and large ovarian cysts (five of five) prone to spontaneous rupture, in some only resolving after combined treatment with estrogen/progestin, GnRH superagonists, and glucocorticoids. Pubertal development in the two boys was more mildly affected, with some spontaneous progression. Urinary steroid profiling revealed combined CYP17A1 and CYP21A2 deficiencies indicative of ORD in all patients; all but one failed to mount an appropriate cortisol response to ACTH stimulation indicative of adrenal insufficiency. Diagnosis of ORD was confirmed by direct sequencing, demonstrating disease-causing POR mutations. \ud \ud Conclusion: Delayed and disordered puberty can be the first sign leading to a diagnosis of ORD. Appropriate testosterone production during puberty in affected boys but manifest primary hypogonadism in girls with ORD may indicate that testicular steroidogenesis is less dependent on POR than adrenal and ovarian steroidogenesis. Ovarian cysts in pubertal girls may be driven not only by high gonadotropins but possibly also by impaired CYP51A1-mediated production of meiosis-activating sterols due to mutant POR

Kinematics and uncertainty relations of a quantum test particle in a curved space-time

A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic multiplication of space-time points. In the case of the Minkowski space-time, left and right translations of the geodesic multiplication coincide and amount to a rigid shift of the space-time x->x+a. In a curved space-time infinitesimal geodesic right translations can be used to define the (geodesic) momentum operators. The commutation relations of position and momentum operators are taken as the quantum kinematic algebra. As an example, detailed calculations are performed for the space-time of a weak plane gravitational wave. The uncertainty relations following from the commutation rules are derived and their physical meaning is discussed.Comment: 6 pages, LaTeX, talk given in the session ``Quantum Fields in Curved Space'' at the VIII Marcel Grossmann Conference in Jerusalem, Israel, June 199

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2<mu <3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord, is given by ord=3-mu . A brand new system is characterized by the degree ord=mu -2. If the system is prepared at time -ta<0$ and the observation begins at time t=0, we derive the following scenario. For times 0<t<<ta the system is satisfactorily described by the fractional derivative with ord=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.Comment: 11 pages, 4 figure

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control