Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

Adaptive multibeam antennas for spacelab. Phase A: Feasibility study

The feasibility was studied of using adaptive multibeam multi-frequency antennas on the spacelab, and to define the experiment configuration and program plan needed for a demonstration to prove the concept. Three applications missions were selected, and requirements were defined for an L band communications experiment, an L band radiometer experiment, and a Ku band communications experiment. Reflector, passive lens, and phased array antenna systems were considered, and the Adaptive Multibeam Phased Array (AMPA) was chosen. Array configuration and beamforming network tradeoffs resulted in a single 3m x 3m L band array with 576 elements for high radiometer beam efficiency. Separate 0.4m x 0.4 m arrays are used to transmit and receive at Ku band with either 576 elements or thinned apertures. Each array has two independently steerable 5 deg beams, which are adaptively controlled

Second quantisation for skew convolution products of infinitely divisible measures

Suppose $\lambda_1$ and $\lambda_2$ are infinitely divisible Radon measures on real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1} \rightarrow E_{2}$ be a Borel measurable mapping so that $T(\lambda_1) * \rho = \lambda_2$ for some Radon probability measure $\rho$ on $E_{2}$. Extending previous results for the Gaussian and the Poissonian case, we study the problem of representing the `transition operator' $P_{T}:L^{p}(E_{2}, \lambda_{2}) \rightarrow L^{p}(E_{1}, \lambda_{1})$ given by $$P_{T}f(x) = \int_{E_{2}}f(T(x) + y)d\rho(y) unify notations$$ as the second quantisation of a contraction operator acting between suitably chosen `reproducing kernel Hilbert spaces' associated with $\lambda_1$ and $\lambda_2$.Comment: Some typos have been corrected. To appear in IDAQ

Alleyne on the Ground: Factfinding that Limits Eligibility for Probation or Parole Release

This article addresses the impact of Alleyne v. United States on statutes that restrict an offender’s eligibility for release on parole or probation. Alleyne is the latest of several Supreme Court decisions applying the rule announced in the Court’s 2000 ruling, Apprendi v. New Jersey. To apply Alleyne, courts must for the first time determine what constitutes a minimum sentence and when that minimum is mandatory. These questions have proven particularly challenging in states that authorize indeterminate sentences, when statutes that delay the timing of eligibility for release are keyed to judicial findings at sentencing. The same questions also arise, in both determinate and indeterminate sentencing jurisdictions, under statutes that limit the option of imposing either probation or a suspended sentence upon judicial fact finding. In this Article, we argue that Alleyne invalidates such statutes. We provide analyses that litigants and judges might find useful as these Alleyne challenges make their way through the courts, and offer a menu of options for state lawmakers who would prefer to amend their sentencing law proactively in order to minimize disruption of their criminal justice systems

Anomalous Processes with General Waiting Times: Functionals and Multipoint Structure

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.Comment: Accepted in Phys. Rev. Let

The impact of coping strategies of cancer caregivers on psychophysiological outcomes: an integrative review

A growing number of studies have explored the psychosocial burden experienced by cancer caregivers, but less attention has been given to the psychophysiological impact of caregiving and the impact of caregivers' coping strategies on this association. This paper reviews existing research on the processes underlying distress experienced by cancer caregivers, with a specific focus on the role of coping strategies on psychophysiological correlates of burden

A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise

We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by strictly stable Levy-processes with stability index bigger than one. The limit process turns out to be a strictly stable Levy process with an averaged jump-measure. Unlike in the situation where the diffusion is driven by Brownian motion, there is no drift related enhancement of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit

Metronidazole in the Prophylaxis and treatment of Anaerobic Infection

The influence of prophylactic metronidazole on vaginal carriage rates of anaerobes and the development of postoperative anaerobic infection was studied in 104 women who underwent abdominal hysterectomy. Metronidazole prophylaxis in 54 patients led to a decrease in the anaerobe vaginal carriage rate from 65% pre-operatively to 17% and 28% on the 3rd and 7th postoperative days respectively. In the control group (50 patients) no significant decrease in anaerobe yield was noted, corresponding percentages being 72%, 64%, and 74%. Postoperative infection occurred in 36 patients (28 controls; 8 on prophylactic metronidazole). Wound swabs from all 8 patients in the latter group yielded aerobes, and in 1 patient mixed infection (aerobes/anaerobes) occurred. In 7 of these patients (including the patient with mixed infection), the infection resolved spontaneously, while the 8th patient responded to therapy with metronidazole, kanamycin and ampicillin. In the control patients, 21 cases of postoperative wound infection and 4 of vault infection were seen; wound swabs from patients in the former group yielded aerobes in only 6 cases, and mixed growth of aerobes/ anaerobes in 10 cases. Postoperative wound/vault infections in control patients cleared spontaneously in 18 cases and responded to imidazole therapy, with or without ampicillin and kanamycin, in 7 cases.Web of Scienc

Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces

We find necessary and sufficient conditions for a finite K–bi–invariant measure on a compact Gelfand pair (G, K) to have a square–integrable density. For convolution semigroups, this is equivalent to having a continuous density in positive time. When (G, K) is a compact Riemannian symmetric pair, we study the induced transition density for G–invariant Feller processes on the symmetric space X = G/K. These are obtained as projections of K–bi–invariant L´evy processes on G, whose laws form a convolution semigroup. We obtain a Fourier series expansion for the density, in terms of spherical functions, where the spectrum is described by Gangolli’s L´evy–Khintchine formula. The density of returns to any given point on X is given by the trace of the transition semigroup, and for subordinated Brownian motion, we can calculate the short time asymptotics of this quantity using recent work of Ba˜nuelos and Baudoin. In the case of the sphere, there is an interesting connection with the Funk–Hecke theorem

Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change.Comment: 27 pages; typos correcte