A further remark on dynamic programming for partially observed markov processes

In (Stochastic Process. Appl. 103 (2003) 293), a pair of dynamic programming inequalities were derived for the 'separated'ergodic control problem for partially observed Markov processes, using the 'vanishing discount'argument. In this note, we strengthen these results to derive a single dynamic programming equation for the same

A further remark on dynamic programming for partially observed Markov processes

In (Stochastic Process. Appl. 103 (2003) 293), a pair of dynamic programming inequalities were derived for the 'separated' ergodic control problem for partially observed Markov processes, using the 'vanishing discount' argument. In this note, we strengthen these results to derive a single dynamic programming equation for the same

A further remark on dynamic programming for partially observed Markov processes

In (Stochastic Process. Appl. 103 (2003) 293), a pair of dynamic programming inequalities were derived for the 'separated' ergodic control problem for partially observed Markov processes, using the 'vanishing discount' argument. In this note, we strengthen these results to derive a single dynamic programming equation for the same

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti

Advancing the case for microbial conservation

The majority of the biomass and biodiversity of life on the Earth is accounted for by microbes. They play pivotal roles in biogeochemical cycles and harbour novel metabolites that have industrial uses. For these reasons the conservation of microbial ecosystems, communities and even specific taxa should be a high priority. We review the reasons for including microorganisms in conservation agenda. We discuss some of the complications in this endeavour, including the unresolved argument about whether microorganisms have intrinsic value, which influences some of the non-instrumental motivations for their conservation and, from a more pragmatic perspective, exactly what it is that we seek to conserve (microorganisms, their habitats or their gene pools). Despite complications, priorities can be defined for microbial conservation and we provide practical examples of such priorities

On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise

We consider the family of stochastic partial differential equations indexed by a parameter \eps\in(0,1], \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} (t,x)\in(0,T]\times\Rd with suitable initial conditions. In this equation, $L$ is a second-order partial differential operator with constant coefficients, $\sigma$ and $b$ are smooth functions and $\dot{F}$ is a Gaussian noise, white in time and with a stationary correlation in space. Let p^\eps_{t,x} denote the density of the law of u^\eps(t,x) at a fixed point (t,x)\in(0,T]\times\Rd. We study the existence of \lim_{\eps\downarrow 0} \eps^2\log p^\eps_{t,x}(y) for a fixed $y\in\R$. The results apply to a class of stochastic wave equations with $d\in\{1,2,3\}$ and to a class of stochastic heat equations with $d\ge1$.Comment: 39 pages. Will be published in the book " Stochastic Analysis and Applications 2014. A volume in honour of Terry Lyons". Springer Verla

A report of a rare congenital malformation in a Nepalese child with congenital pouch colon: a case report

Congenital pouch colon is one of rare congenital anomalies. We report a 3-day-old male child with congenital pouch colon who underwent a window colostomy but died because of overwhelming sepsis. Due to its rarity, many surgeons in our part of the world may not be aware of it, hence increasing the potential to its mismanagement. However, with simple keen observations, we can safely come to its diagnosis. The aim of this report is to bring attention to congenital pouch colon associated with anorectal malformation in our country, with a brief emphasis on an approach to its diagnosis and initial management

Ribonucleotide reductase regulatory subunit M2 drives glioblastoma TMZ resistance through modulation of dNTP production

During therapy, adaptations driven by cellular plasticity are partly responsible for driving the inevitable recurrence of glioblastoma (GBM). To investigate plasticity-induced adaptation during standard-of-care chemotherapy temozolomide (TMZ), we performed in vivo single-cell RNA sequencing in patient-derived xenograft (PDX) tumors of GBM before, during, and after therapy. Comparing single-cell transcriptomic patterns identified distinct cellular populations present during TMZ therapy. Of interest was the increased expression of ribonucleotide reductase regulatory subunit M2 (RRM2), which we found to regulate dGTP and dCTP production vital for DNA damage response during TMZ therapy. Furthermore, multidimensional modeling of spatially resolved transcriptomic and metabolomic analysis in patients’ tissues revealed strong correlations between RRM2 and dGTP. This supports our data that RRM2 regulates the demand for specific dNTPs during therapy. In addition, treatment with the RRM2 inhibitor 3-AP (Triapine) enhances the efficacy of TMZ therapy in PDX models. We present a previously unidentified understanding of chemoresistance through critical RRM2-mediated nucleotide production