Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from nondestructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem.We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential illposedness, the stability estimate obtained is optimal

Exponential instability for inverse elliptic problems with unknown boundaries

We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed

Optimal Placement of Water Quality Monitoring Stations in Sewer Systems: An Information Theory Approach

A core problem associated with the water quality monitoring in the sewer system is the optimal placement of a limited number of monitoring sites. A methodology is provided for optimally design water quality monitoring stations in sewer networks. The methodology is based on information theory, formulated as a multi-objective optimization problem and solved using NSGA-II. Computer code is written to estimate two entropy quantities, namely Joint Entropy, a measure of information content, and Total Correlation, a measure of redundancy, which are maximized and minimized, respectively. The test on a real sewer network suggests the effectiveness of the proposed methodology

Tubulin nitration in human gliomas

Immunohistochem. and biochem. investigations showed that significant protein nitration occurs in human gliomas, esp. in grade IV glioblastomas at the level of astrocytes and oligodendrocytes and neurons. Enhanced alpha-tubulin immunoreactivity was co-present in the same elements in the glioblastomas. Proteomic methodologies were employed to identify a nitrated protein band at 55 kDa as alpha-tubulin. Peptide mass fingerprinting procedures demonstrated that tubulin is nitrated at Tyr224 in grade IV tumor samples but is unmodified in grade I samples and in non-cancerous brain tissue. These results provide the first characterization of endogenously nitrated tubulin from human tumor samples

Exponential instability in the fractional Calder\'on problem

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on problem and the truncated Hilbert transform.Comment: 17 page

Sensory Experience Differentially Modulates the mRNA Expression of the Polysialyltransferases ST8SiaII and ST8SiaIV in Postnatal Mouse Visual Cortex

Polysialic acid (PSA) is a unique carbohydrate composed of a linear homopolymer of α-2,8 linked sialic acid, and is mainly attached to the fifth immunoglobulin-like domain of the neural cell adhesion molecule (NCAM) in vertebrate neural system. In the brain, PSA is exclusively synthesized by the two polysialyltransferases ST8SiaII (also known as STX) and ST8SiaIV (also known as PST). By modulating adhesive property of NCAM, PSA plays a critical role in several neural development processes such as cell migration, neurite outgrowth, axon pathfinding, synaptogenesis and activity-dependent plasticity. The expression of PSA is temporally and spatially regulated during neural development and a tight regulation of PSA expression is essential to its biological function. In mouse visual cortex, PSA is downregulated following eye opening and its decrease allows the maturation of GABAergic synapses and the opening of the critical period for ocular dominance plasticity. Relatively little is known about how PSA levels are regulated by sensory experience and neuronal activity. Here, we demonstrate that while both ST8SiaII and ST8SiaIV mRNA levels decrease around the time of eye opening in mouse visual cortex, only ST8SiaII mRNA level reduction is regulated by sensory experience. Using an organotypic culture system from mouse visual cortex, we further show that ST8SiaII gene expression is regulated by spiking activity and NMDA-mediated excitation. Further, we show that both ST8SiaII and ST8SiaIV mRNA levels are positively regulated by PKC-mediated signaling. Therefore, sensory experience-dependent ST8SiaII gene expression regulates PSA levels in postnatal visual cortex, thus acting as molecular link between visual activity and PSA expression