Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems

Undergraduate teaching assistant impact on student academic achievement.

This study evaluated the impact that trained and supported undergraduate teaching assistants (UTAs) may have had on the academic achievement of students in the first semester of an introductory chemistry course for science and engineering majors. Framed by the concepts of Lave and Wenger’s Community of Practice and Wheeler, Martin and Suls’ Proxy Model of Social Comparison , the study used an untreated control group with dependent post-test only design. Covariates related to student academic achievement and contextual variables were also collected and used to build models for the final exam core outcome variable. Hierarchical linear models indicated that having a UTA gave students with above-average college GPA a statistically significant boost on final exam score. More importantly, having a UTA was associated with persistence into the next course in the two-semester introductory chemistry sequence, regardless of academic achievement

Development of undergraduate teaching assistants as effective instructors in STEM courses.

This study examined the development of peer mentoring skills and deepening of content knowledge by trained and supported undergraduate teaching assistants (UTAs) working with students in entry-level STEM courses across nine departments at a large research intensive U.S. university. Data were collected from two sources: a survey with 10 items requesting 5-point Likert-type responses and an open-ended reflection written by each UTA to process their experiences. The survey responses were analyzed by comparing rates of agreement across the 10 items. Statements from the reflections were categorized by research question and descriptively labeled to capture the essence of implied or explicit meaning. UTAs reported developing stronger pedagogical skills and fostering metacognitive approaches to learning, as well as benefitting personally from improved communication skills. UTAs also indicated they have deepened their own knowledge of content in their discipline and learned to use more strategies for becoming a better learner

Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with non-Hermitian potential $V$ lie in the disjoint union of two disks in the right and left half plane, respectively, provided that the $L^1-norm$ of $V$ is bounded from above by the speed of light times the reduced Planck constant. An analogous result for the Schr\"odinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on $V$ implies the absence of nonreal eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials

Enhanced hydrogen peroxide generation accompanies the beneficial bioenergetic effects of methylene blue in isolated brain mitochondria

The redox dye methylene blue (MB) is proven to have beneficial effects in various models of neurodegenerative diseases. Here we investigated the effects of MB (100 nM, 300 nM, and 1 μM) on key bioenergetic parameters and on H2O2 production/elimination in isolated guinea pig brain mitochondria under normal as well as respiration-impaired conditions. As measured by high-resolution Oxygraph the rate of resting oxygen consumption was increased, but the ADP-stimulated respiration was unaffected by MB with any of the substrates (glutamate malate, succinate, or α-glycerophosphate) used for supporting mitochondrial respiration. In mitochondria treated with inhibitors of complex I or complex III MB moderately but significantly increased the rate of ATP production, restored ΔΨm, and increased the rate of Ca2+ uptake. The effects of MB are consistent with transferring electrons from upstream components of the electron transport chain to cytochrome c, which is energetically favorable when the flow of electrons in the respiratory chain is compromised. On the other hand, MB significantly increased the production of H2O2 measured by Amplex UltraRed fluorimetry under all conditions, in resting, ATP-synthesizing, and respiration-impaired mitochondria, with each substrate combination supporting respiration. Furthermore, it also decreased the elimination of H2O2. Generation of H2O2 without superoxide formation, observed in the presence of MB, is interpreted as a result of reduction of molecular oxygen to H2O2 by the reduced MB. The elevated generation and impaired elimination of H2O2 should be considered for the overall oxidative state of mitochondria treated with MB

Stability and Convergence of Product Formulas for Operator Matrices

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.Comment: to appear in Integral Equations and Operator Theory (ISSN: 1420-8989

Novel mitochondrial transition pore inhibitor N‐methyl‐4‐isoleucine cyclosporin is a new therapeutic option in acute pancreatitis

Bile acids, ethanol and fatty acids affect pancreatic ductal fluid and bicarbonate secretion via mitochondrial damage, ATP depletion and calcium overload. •Pancreatitis-inducing factors open the membrane transition pore (mPTP) channel via cyclophilin D activation in acinar cells, causing calcium overload and cell death; genetic or pharmacological inhibition of mPTP improves the outcome of acute pancreatitis in animal models. •Here we show that genetic and pharmacological inhibition of mPTP protects mitochondrial homeostasis and cell function evoked by pancreatitis-inducing factors in pancreatic ductal cells. •The results also show that the novel cyclosporin A derivative NIM811 protects mitochondrial function in acinar and ductal cells, and it preserves bicarbonate transport mechanisms in pancreatic ductal cells. •We found that NIM811 is highly effective in different experimental pancreatitis models and has no side-effects. NIM811 is a highly suitable compound to be tested in clinical trials

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144