Optimisation of stochastic networks with blocking: a functional-form approach

This paper introduces a class of stochastic networks with blocking, motivated by applications arising in cellular network planning, mobile cloud computing, and spare parts supply chains. Blocking results in lost revenue due to customers or jobs being permanently removed from the system. We are interested in striking a balance between mitigating blocking by increasing service capacity, and maintaining low costs for service capacity. This problem is further complicated by the stochastic nature of the system. Owing to the complexity of the system there are no analytical results available that formulate and solve the relevant optimization problem in closed form. Traditional simulation-based methods may work well for small instances, but the associated computational costs are prohibitive for networks of realistic size. We propose a hybrid functional-form based approach for finding the optimal resource allocation, combining the speed of an analytical approach with the accuracy of simulation-based optimisation. The key insight is to replace the computationally expensive gradient estimation in simulation optimisation with a closed-form analytical approximation that is calibrated using a single simulation run. We develop two implementations of this approach and conduct extensive computational experiments on complex examples to show that it is capable of substantially improving system performance. We also provide evidence that our approach has substantially lower computational costs compared to stochastic approximation

Hot ion plasma heating experiments in SUMMA

Initial results are presented for the hot-ion plasma heating experiments conducted in the new SUMMA (superconducting magnetic mirror apparatus) at NASA Lewis Research Center. A discharge is formed by applying a radially inward dc electric field between cylindrical anodes and hallow cathodes located at the peak of the mirrors. Data were obtained at midplane magnetic field strengths from 1.0 to 3.5 tesla. Charge-exchange neutral particle energy analyzer data were reduced to ion temperatures using a plasma model that included a Maxwellian energy distribution superimposed on an azimuthal drift, finite ion orbits, and radial variations in density and electric field. The best ion temperatures in a helium plasma were 5 keV and in hydrogen the H2(+) and H(+) ions were 1.2 keV and 1 keV respectively. Optical spectroscopy line broadening measurements yielded ion temperatures about 50 percent higher than the charge-exchange neutral particle analyzer results. Spectroscopically obtained electron temperature ranged from 3 to 30 eV. Ion temperature was found to scale roughly linearly with the ratio of power input-to-magnetic field strength, P/B

Quantitative Photo-acoustic Tomography with Partial Data

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and improve an earlier result of Bal and Uhlmann to the partial date case. We show that the reconstruction can be uniquely determined by the knowledge of 4 internal data based on well-chosen partial boundary conditions. Stability of this reconstruction is ensured if a convexity condition is satisfied. Similar stability result is obtained without this geometric constraint if 4n well-chosen partial boundary conditions are available, where $n$ is the spatial dimension. The set of well-chosen boundary measurements is characterized by some complex geometric optics (CGO) solutions vanishing on a part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250

Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double layer potentials for the wave equation, for the domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure

Inverse Transport Theory of Photoacoustics

We consider the reconstruction of optical parameters in a domain of interest from photoacoustic data. Photoacoustic tomography (PAT) radiates high frequency electromagnetic waves into the domain and measures acoustic signals emitted by the resulting thermal expansion. Acoustic signals are then used to construct the deposited thermal energy map. The latter depends on the constitutive optical parameters in a nontrivial manner. In this paper, we develop and use an inverse transport theory with internal measurements to extract information on the optical coefficients from knowledge of the deposited thermal energy map. We consider the multi-measurement setting in which many electromagnetic radiation patterns are used to probe the domain of interest. By developing an expansion of the measurement operator into singular components, we show that the spatial variations of the intrinsic attenuation and the scattering coefficients may be reconstructed. We also reconstruct coefficients describing anisotropic scattering of photons, such as the anisotropy coefficient $g(x)$ in a Henyey-Greenstein phase function model. Finally, we derive stability estimates for the reconstructions

A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)

Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force or Hall effect tomography, is a novel hybrid modality designed to be a high-resolution alternative to the unstable Electrical Impedance Tomography. In the present paper we analyze existing mathematical models of this method, and propose a general procedure for solving the inverse problem associated with MAET. It consists in applying to the data one of the algorithms of Thermo-Acoustic tomography, followed by solving the Neumann problem for the Laplace equation and the Poisson equation. For the particular case when the region of interest is a cube, we present an explicit series solution resulting in a fast reconstruction algorithm. As we show, both analytically and numerically, MAET is a stable technique yilelding high-resolution images even in the presence of significant noise in the data

The SOD2 C47T polymorphism influences NAFLD fibrosis severity: evidence from case-control and intra-familial allele association studies.

AIMS: Non-alcoholic fatty liver disease (NAFLD) is a complex disease trait where genetic variations and environment interact to determine disease progression. The association of PNPLA3 with advanced disease has been consistently demonstrated but many other modifier genes remain unidentified. In NAFLD, increased fatty acid oxidation produces high levels of reactive oxygen species. Manganese-dependent superoxide dismutase (MnSOD), encoded by the SOD2 gene, plays an important role in protecting cells from oxidative stress. A common non-synonymous polymorphism in SOD2 (C47T; rs4880) is associated with decreased MnSOD mitochondrial targeting and activity making it a good candidate modifier of NAFLD severity. METHODS: The relevance of the SOD2 C47T polymorphism to fibrotic NAFLD was assessed by two complementary approaches: we sought preferential transmission of alleles from parents to affected children in 71 family trios and adopted a case-control approach to compare genotype frequencies in a cohort of 502 European NAFLD patients. RESULTS: In the family study, 55 families were informative. The T allele was transmitted on 47/76 (62%) possible occasions whereas the C allele was transmitted on only 29/76 (38%) occasions, p=0.038. In the case control study, the presence of advanced fibrosis (stage>1) increased with the number of T alleles, p=0.008 for trend. Multivariate analysis showed susceptibility to advanced fibrotic disease was determined by SOD2 genotype (OR 1.56 (95% CI 1.09-2.25), p=0.014), PNPLA3 genotype (p=0.041), type 2 diabetes mellitus (p=0.009) and histological severity of NASH (p=2.0×10(-16)). CONCLUSIONS: Carriage of the SOD2 C47T polymorphism is associated with more advanced fibrosis in NASH

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.Comment: To appear in Inverse Problem

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page

Genomic catastrophes frequently arise in esophageal adenocarcinoma and drive tumorigenesis

Oesophageal adenocarcinoma (EAC) incidence is rapidly increasing in Western countries. A better understanding of EAC underpins efforts to improve early detection and treatment outcomes. While large EAC exome sequencing efforts to date have found recurrent loss-offunction mutations, oncogenic driving events have been underrepresented. Here we use a combination of whole-genome sequencing (WGS) and single-nucleotide polymorphism-array profiling to show that genomic catastrophes are frequent in EAC, with almost a third (32%, n¼40/123) undergoing chromothriptic events. WGS of 22 EAC cases show that catastrophes may lead to oncogene amplification through chromothripsis-derived double-minute chromosome formation (MYC and MDM2) or breakage-fusion-bridge (KRAS, MDM2 and RFC3). Telomere shortening is more prominent in EACs bearing localized complex rearrangements. Mutational signature analysis also confirms that extreme genomic instability in EAC can be driven by somatic BRCA2 mutations. These findings suggest that genomic catastrophes have a significant role in the malignant transformation of EAC