Uniqueness and stability of time and space-dependent conductivity in a hyperbolic cylindrical domain

This paper is devoted to the reconstruction of the time and space-dependent coefficient in an infinite cylindrical hyperbolic domain. Using a local Carleman estimate we prove the uniqueness and a H\"older stability in the determining of the conductivity by a single measurement on the lateral boundary. Our numerical examples show good reconstruction of the location and contrast of the conductivity function in three dimensions.Comment: arXiv admin note: text overlap with arXiv:1501.0138

Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensures unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data

AN INVERSE SOURCE PROBLEM FOR THE DIFFUSION EQUATION WITH FINAL OBSERVATION

We investigate the inverse problem involving recovery of source temperature from the information of final temperature profile. We prove that we can uniquely recover the source of a n-dimensional heat equation from the measurement of the temperature at fixed time provided that the source is known in an arbitrary subdomain. The algorithm is based on the Carleman estimate. By using a Bukhgeim-Klibanov method, as a first step, we determine the source term by two measurements. A compacity and analyticity arguments procedure help to reduce the number of measurements

Numerical studies of the Lagrangian approach for reconstruction of the conductivity in a waveguide

We consider an inverse problem of reconstructing the conductivity function in a hyperbolic equation using single space-time domain noisy observations of the solution on the backscattering boundary of the computational domain. We formulate our inverse problem as an optimization problem and use Lagrangian approach to minimize the corresponding Tikhonov functional. We present a theorem of a local strong convexity of our functional and derive error estimates between computed and regularized as well as exact solutions of this functional, correspondingly. In numerical simulations we apply domain decomposition finite element-finite difference method for minimization of the Lagrangian. Our computational study shows efficiency of the proposed method in the reconstruction of the conductivity function in three dimensions

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

PINK1 Defect Causes Mitochondrial Dysfunction, Proteasomal Deficit and α-Synuclein Aggregation in Cell Culture Models of Parkinson's Disease

Mutations in PTEN induced kinase 1 (PINK1), a mitochondrial Ser/Thr kinase, cause an autosomal recessive form of Parkinson's disease (PD), PARK6. Here, we report that PINK1 exists as a dimer in mitochondrial protein complexes that co-migrate with respiratory chain complexes in sucrose gradients. PARK6 related mutations do not affect this dimerization and its associated complexes. Using in vitro cell culture systems, we found that mutant PINK1 or PINK1 knock-down caused deficits in mitochondrial respiration and ATP synthesis. Furthermore, proteasome function is impaired with a loss of PINK1. Importantly, these deficits are accompanied by increased α-synclein aggregation. Our results indicate that it will be important to delineate the relationship between mitochondrial functional deficits, proteasome dysfunction and α-synclein aggregation

Stroke genetics informs drug discovery and risk prediction across ancestries

Previous genome-wide association studies (GWASs) of stroke — the second leading cause of death worldwide — were conducted predominantly in populations of European ancestry1,2. Here, in cross-ancestry GWAS meta-analyses of 110,182 patients who have had a stroke (five ancestries, 33% non-European) and 1,503,898 control individuals, we identify association signals for stroke and its subtypes at 89 (61 new) independent loci: 60 in primary inverse-variance-weighted analyses and 29 in secondary meta-regression and multitrait analyses. On the basis of internal cross-ancestry validation and an independent follow-up in 89,084 additional cases of stroke (30% non-European) and 1,013,843 control individuals, 87% of the primary stroke risk loci and 60% of the secondary stroke risk loci were replicated (P < 0.05). Effect sizes were highly correlated across ancestries. Cross-ancestry fine-mapping, in silico mutagenesis analysis3, and transcriptome-wide and proteome-wide association analyses revealed putative causal genes (such as SH3PXD2A and FURIN) and variants (such as at GRK5 and NOS3). Using a three-pronged approach4, we provide genetic evidence for putative drug effects, highlighting F11, KLKB1, PROC, GP1BA, LAMC2 and VCAM1 as possible targets, with drugs already under investigation for stroke for F11 and PROC. A polygenic score integrating cross-ancestry and ancestry-specific stroke GWASs with vascular-risk factor GWASs (integrative polygenic scores) strongly predicted ischaemic stroke in populations of European, East Asian and African ancestry5. Stroke genetic risk scores were predictive of ischaemic stroke independent of clinical risk factors in 52,600 clinical-trial participants with cardiometabolic disease. Our results provide insights to inform biology, reveal potential drug targets and derive genetic risk prediction tools across ancestries

Simultaneous reconstruction of Maxwell’s coefficients from backscattering data

We use the conjugade gradient method for the solution of an inverse problem for simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D using backscattering data. We show stability of our inverse problem using the Carleman estimates. Our numerical experiments show reliable reconstruction of both parameters using the optimization approach