The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Eigen-Adaptation and Distributed Representation of 2-D Phase, Energy, Scale and Orientation in Spatial Vision

Distributed representations (DR) of cortical channels are pervasive in models of spatio-temporal vision. A central idea that underpins current innovations of DR stems from the extension of 1-D phase into 2-D images. Neurophysiological evidence, however, provides tenuous support for a quadrature representation in the visual cortex, since even phase visual units are associated with broader orientation tuning than odd phase visual units (J.Neurophys.,88,455–463, 2002). We demonstrate that the application of the steering theorems to a 2-D definition of phase afforded by the Riesz Transform (IEEE Trans. Sig. Proc., 49, 3136–3144), to include a Scale Transform, allows one to smoothly interpolate across 2-D phase and pass from circularly symmetric to orientation tuned visual units, and from more narrowly tuned odd symmetric units to even ones. Steering across 2-D phase and scale can be orthogonalized via a linearizing transformation. Using the tiltafter effect as an example, we argue that effects of visual adaptation can be better explained by via an orthogonal rather than channel specific representation of visual units. This is because of the ability to explicitly account for isotropic and cross-orientation adaptation effect from the orthogonal representation from which both direct and indirect tilt after-effects can be explained.

The determinants of R&D investment: A survey of the empirical research

This paper offers an extensive survey and a critical discussion of the empirical literature on the driving factors of R&D. These factors are subsumed under five broad types. The paper first summarises the key predictions from theory regarding each type's R&D effect. It then examines for which factors differences in the theoretical predictions can also be found in empirical studies, and for which factors the empirical evidence is more unanimous. As the focus is on the empirical literature, methodological issues are also highlighted. The major factor types identified in the literature are, individual firm or industry characteristics, particularly internal finance and sales; competition in product markets; R&D tax credits and subsidies; location and resource related factors, such as spillovers from university research within close geographic proximity, membership of a research joint venture and cooperation with research centres, and the human capital embodied in knowledge workers; and spillovers from foreign R&D. Although on balance there is a consensus regarding the R&D effects of most factors, there is also variation in results. Recent work suggests that accounting for non-linearities is one area of research that may explain and encompass contradictory findings.

Collimation of a D-D Neutron Generator for Clinical Implementation of Neutron Stimulated Emission Computed Tomography: a Monte Carlo Study

This work is an investigation into collimator designs for a deuterium-deuterium (DD) neutron generator for an inexpensive and compact neutron imaging system that can be implemented in a hospital. The envisioned application is for a spectroscopic imaging technique called neutron stimulated emission computed tomography (NSECT).

Previous NSECT studies have been performed using a Van-de-Graaff accelerator at the Triangle Universities Nuclear Laboratory (TUNL) in Duke University. This facility has provided invaluable research into the development of NSECT. To transition the current imaging method into a clinically feasible system, there is a need for a high-intensity fast neutron source that can produce collimated beams. The DD neutron generator from Adelphi Technologies Inc. is being explored as a possible candidate to provide the uncollimated neutrons. This DD generator is a compact source that produces 2.5 MeV fast neutrons with intensities of 1012 n/s (4π). The neutron energy is sufficient to excite most isotopes of interest in the body with the exception of carbon and oxygen. However, a special collimator is needed to collimate the 4π neutron emission into a narrow beam. This work describes the development and evaluation of a series of collimator designs to collimate the DD generator for narrow beams suitable for NSECT imaging.

A neutron collimator made of high-density polyethylene (HDPE) and lead was modeled and simulated using the GEANT4 toolkit. The collimator was designed as a 52 x 52 x 52 cm3 HDPE block coupled with 1 cm lead shielding. Non-tapering (cylindrical) and tapering (conical) opening designs were modeled into the collimator to permit passage of neutrons. The shape, size, and geometry of the aperture were varied to assess the effects on the collimated neutron beam. Parameters varied were: inlet diameter (1-5 cm), outlet diameter (1-5 cm), aperture diameter (0.5-1.5 cm), and aperture placement (13-39 cm). For each combination of collimator parameters, the spatial and energy distributions of neutrons and gammas were tracked and analyzed to determine three performance parameters: neutron beam-width, primary neutron flux, and the output quality. To evaluate these parameters, the simulated neutron beams are then regenerated for a NSECT breast scan. Scan involved a realistic breast lesion implanted into an anthropomorphic female phantom.

This work indicates potential for collimating and shielding a DD neutron generator for use in a clinical NSECT system. The proposed collimator designs produced a well-collimated neutron beam that can be used for NSECT breast imaging. The aperture diameter showed a strong correlation to the beam-width, where the collimated neutron beam-width was about 10% larger than the physical aperture diameter. In addition, a collimator opening consisting of a tapering inlet and cylindrical outlet allowed greater neutron throughput when compared to a simple cylindrical opening. The tapering inlet design can allow additional neutron throughput when the neck is placed farther from the source. On the other hand, the tapering designs also decrease output quality (i.e. increase in stray neutrons outside the primary collimated beam). All collimators are cataloged in measures of beam-width, neutron flux, and output quality. For a particular NSECT application, an optimal choice should be based on the collimator specifications listed in this work.

A Randomized Phase II Crossover Study of Imatinib or Rituximab for Cutaneous Sclerosis after Hematopoietic Cell Transplantation.

PURPOSE: Cutaneous sclerosis occurs in 20% of patients with chronic graft-versus-host disease (GVHD) and can compromise mobility and quality of life. EXPERIMENTAL DESIGN: We conducted a prospective, multicenter, randomized, two-arm phase II crossover trial of imatinib (200 mg daily) or rituximab (375 mg/m(2) i.v. weekly × 4 doses, repeatable after 3 months) for treatment of cutaneous sclerosis diagnosed within 18 months (NCT01309997). The primary endpoint was significant clinical response (SCR) at 6 months, defined as quantitative improvement in skin sclerosis or joint range of motion. Treatment success was defined as SCR at 6 months without crossover, recurrent malignancy or death. Secondary endpoints included changes of B-cell profiles in blood (BAFF levels and cellular subsets), patient-reported outcomes, and histopathology between responders and nonresponders with each therapy. RESULTS: SCR was observed in 9 of 35 [26%; 95% confidence interval (CI); 13%-43%] participants randomized to imatinib and 10 of 37 (27%; 95% CI, 14%-44%) randomized to rituximab. Six (17%; 95% CI, 7%-34%) patients in the imatinib arm and 5 (14%; 95% CI, 5%-29%) in the rituximab arm had treatment success. Higher percentages of activated B cells (CD27(+)) were seen at enrollment in rituximab-treated patients who had treatment success (P = 0.01), but not in imatinib-treated patients. CONCLUSIONS: These results support the need for more effective therapies for cutaneous sclerosis and suggest that activated B cells define a subgroup of patients with cutaneous sclerosis who are more likely to respond to rituximab.

Innovation in the pharmaceutical industry: New estimates of R&D costs.

The research and development costs of 106 randomly selected new drugs were obtained from a survey of 10 pharmaceutical firms. These data were used to estimate the average pre-tax cost of new drug and biologics development. The costs of compounds abandoned during testing were linked to the costs of compounds that obtained marketing approval. The estimated average out-of-pocket cost per approved new compound is $1395 million (2013 dollars). Capitalizing out-of-pocket costs to the point of marketing approval at a real discount rate of 10.5% yields a total pre-approval cost estimate of $2558 million (2013 dollars). When compared to the results of the previous study in this series, total capitalized costs were shown to have increased at an annual rate of 8.5% above general price inflation. Adding an estimate of post-approval R&D costs increases the cost estimate to $2870 million (2013 dollars).

The role of vitamin D signalling in the interaction between mesenchymal mammary tumour cells and macrophages

The transition of epithelial-like tumour cells to those exhibiting mesenchymal characteristics (Epithelial-to-mesenchymal Transition; EMT) is an integral process in breast cancer metastasis. EMT can be promoted by Transforming growth factor-beta (TGF-β) which can be found at high levels in the tumour stroma. Tumour-associated macrophages (TAMs) can also induce EMT in breast cancer cells, which is one way that they promote breast cancer metastasis. Vitamin D signalling has been implicated in EMT suppression and plays a role in modulating macrophage differentiation and stimulating their anti-inflammatory functions. This project had two major aims. First, we aimed to create and verify a unique fluorescent reporter gene construct designed to evaluate the dynamics of EMT in real-time and at the single-cell level. While some components of this reporter system were successfully validated, work to complete the final reporter construct is ongoing. The second and main aspect of this project focused on exploring the ability of 1,25-dihydroxyvitamin D3 (1,25D3) to modulate the interaction between mesenchymal mammary tumour cells and TAMs. Unexpectedly, in short-term treatment (48 hours) studies of 4T1 murine mammary tumour cells, we observed that 1,25D3 and TGF-β signalling work together to increase expression of the mesenchymal markers, Snai1, Fn1, and Col1a1. 1,25D3 and TGF-β also synergistically activate transcription of the gene encoding the 1,25D3-catabolizing enzyme, Cyp24a1. The ability of 1,25D3 and TGF-β to enhance expression of these genes was diminished in a long-term treatment (14 days) of 4T1 cells, and this effect was accompanied by a decrease in cell proliferation. 1,25D3 may also cooperate with cytokines produced by normal macrophages and macrophages considered to be TAM-like. Conditioned media experiments revealed that in the presence of factors from normal macrophages, 1,25D3 enhanced expression of Fn1, and in the presence of factors from TAM-like macrophages, 1,25D3 enhanced expression of Fn1 and Cyp24a1. Rather than mitigating the interaction as hypothesized, 1,25D3 may exacerbate the tumour-promoting effects of the EMT-TAM relationship. Also, signalling pathways involved in the EMT-TAM relationship may synergize with 1,25D3 to upregulate Cyp24a1 expression. These findings are important for understanding the potential of vitamin D compounds to be used in the treatment of breast cancer.

VLSI design and implementation of 2-D Inverse Discrete Wavelet Transform

This paper proposes a JPEG-2000 compliant architecture capable of computing the 2 -D Inverse Discrete Wavelet Transform. The proposed architecture uses a single processor and a row-based schedule to minimize control and routing complexity and to ensure that processor utilization is kept at 100%. The design incorporates the handling of borders through the use of symmetric extension. The architecture has been implemented on the Xilinx Virtex2 FPGA.