Stochastic integration in UMD Banach spaces

In this paper we construct a theory of stochastic integration of processes with values in $\mathcal{L}(H,E)$, where $H$ is a separable Hilbert space and $E$ is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an $H$-cylindrical Brownian motion. Our approach is based on a two-sided $L^p$-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of $\mathcal{L}(H,E)$-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the It\^{o} isometry, the Burkholder--Davis--Gundy inequalities, and the representation theorem for Brownian martingales.Comment: Published at http://dx.doi.org/10.1214/009117906000001006 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic evolution equations in UMD Banach spaces

We discuss existence, uniqueness, and space-time H\"older regularity for solutions of the parabolic stochastic evolution equation dU(t) = (AU(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), t\in [0,\Tend], U(0) = u_0, where $A$ generates an analytic $C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical Brownian motion with values in a Hilbert space $H$. We prove that if the mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$ satisfy suitable Lipschitz conditions and $u_0$ is \F_0-measurable and bounded, then this problem has a unique mild solution, which has trajectories in C^\l([0,T];\D((-A)^\theta) provided $\lambda\ge 0$ and $\theta\ge 0$ satisfy \l+\theta<\frac12. Various extensions of this result are given and the results are applied to parabolic stochastic partial differential equations.Comment: Accepted for publication in Journal of Functional Analysi

Entropy Distance: New Quantum Phenomena

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure

Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation.Comment: Accepted for publication in Journal of Differential Equation

Spin Coherence and 14^{14}N ESEEM Effects of Nitrogen-Vacancy Centers in Diamond with X-band Pulsed ESR

Pulsed ESR experiments are reported for ensembles of negatively-charged nitrogen-vacancy centers (NV$^-$) in diamonds at X-band magnetic fields (280-400 mT) and low temperatures (2-70 K). The NV$^-$ centers in synthetic type IIb diamonds (nitrogen impurity concentration $<1$~ppm) are prepared with bulk concentrations of $2\cdot 10^{13}$ cm$^{-3}$ to $4\cdot 10^{14}$ cm$^{-3}$ by high-energy electron irradiation and subsequent annealing. We find that a proper post-radiation anneal (1000$^\circ$C for 60 mins) is critically important to repair the radiation damage and to recover long electron spin coherence times for NV$^-$s. After the annealing, spin coherence times of T$_2 = 0.74$~ms at 5~K are achieved, being only limited by $^{13}$C nuclear spectral diffusion in natural abundance diamonds. At X-band magnetic fields, strong electron spin echo envelope modulation (ESEEM) is observed originating from the central $^{14}$N nucleus. The ESEEM spectral analysis allows for accurate determination of the $^{14}$N nuclear hypefine and quadrupole tensors. In addition, the ESEEM effects from two proximal $^{13}$C sites (second-nearest neighbor and fourth-nearest neighbor) are resolved and the respective $^{13}$C hyperfine coupling constants are extracted.Comment: 10 pages, 5 figure

Finding a Mate With No Social Skills

Sexual reproductive behavior has a necessary social coordination component as willing and capable partners must both be in the right place at the right time. While there are many known social behavioral adaptations to support solutions to this problem, we explore the possibility and likelihood of solutions that rely only on non-social mechanisms. We find three kinds of social organization that help solve this social coordination problem (herding, assortative mating, and natal philopatry) emerge in populations of simulated agents with no social mechanisms available to support these organizations. We conclude that the non-social origins of these social organizations around sexual reproduction may provide the environment for the development of social solutions to the same and different problems.Comment: 8 pages, 5 figures, GECCO'1

Draft Genome Sequences of Campylobacter jejuni Strains That Cause Abortion in Livestock.

Campylobacter jejuni is an intestinal bacterium that can cause abortion in livestock. This publication announces the public release of 15 Campylobacter jejuni genome sequences from isolates linked to abortion in livestock. These isolates are part of the 100K Pathogen Genome Project and are from clinical cases at the University of California (UC) Davis

Draft Genome Sequence of Multidrug-Resistant Abortive Campylobacter jejuni from Northern California.

Campylobacter jejuni is an enteric bacterium that can cause abortion in livestock. This is the release of a multidrug-resistant Campylobacter jejuni genome from an isolate that caused an abortion in a cow in northern California. This isolate is part of the 100K Pathogen Genome Project