Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

Reply to "Comment on 'Solutions of the telegrapher's equation in the presence of traps'"

This reply adds a number of details to remarks by Foong and Kanno [preceding Comment, Phys. Rev. A 46, 5296 (1992)] on our paper [Phys. Rev. A 45, 2222 (1992)] regarding the discontinuities observed in the curves generated in that paper.

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Identification of different heart tissues from MRI C-SENC images using an unsupervised multi-stage fuzzy clustering technique.

PURPOSE: To objectively characterize different heart tissues from functional and viability images provided by composite-strain-encoding (C-SENC) MRI. MATERIALS AND METHODS: C-SENC is a new MRI technique for simultaneously acquiring cardiac functional and viability images. In this work, an unsupervised multi-stage fuzzy clustering method is proposed to identify different heart tissues in the C-SENC images. The method is based on sequential application of the fuzzy c-means (FCM) and iterative self-organizing data (ISODATA) clustering algorithms. The proposed method is tested on simulated heart images and on images from nine patients with and without myocardial infarction (MI). The resulting clustered images are compared with MRI delayed-enhancement (DE) viability images for determining MI. Also, Bland-Altman analysis is conducted between the two methods. RESULTS: Normal myocardium, infarcted myocardium, and blood are correctly identified using the proposed method. The clustered images correctly identified 90 +/- 4% of the pixels defined as infarct in the DE images. In addition, 89 +/- 5% of the pixels defined as infarct in the clustered images were also defined as infarct in DE images. The Bland-Altman results show no bias between the two methods in identifying MI. CONCLUSION: The proposed technique allows for objectively identifying divergent heart tissues, which would be potentially important for clinical decision-making in patients with MI.

The membrane-associated transient receptor potential vanilloid channel is the central heat shock receptor controlling the cellular heat shock response in epithelial cells.

The heat shock response (HSR) is a highly conserved molecular response to various types of stresses, including heat shock, during which heat-shock proteins (Hsps) are produced to prevent and repair damages in labile proteins and membranes. In cells, protein unfolding in the cytoplasm is thought to directly enable the activation of the heat shock factor 1 (HSF-1), however, recent work supports the activation of the HSR via an increase in the fluidity of specific membrane domains, leading to activation of heat-shock genes. Our findings support the existence of a plasma membrane-dependent mechanism of HSF-1 activation in animal cells, which is initiated by a membrane-associated transient receptor potential vanilloid receptor (TRPV). We found in various non-cancerous and cancerous mammalian epithelial cells that the TRPV1 agonists, capsaicin and resiniferatoxin (RTX), upregulated the accumulation of Hsp70, Hsp90 and Hsp27 and Hsp70 and Hsp90 respectively, while the TRPV1 antagonists, capsazepine and AMG-9810, attenuated the accumulation of Hsp70, Hsp90 and Hsp27 and Hsp70, Hsp90, respectively. Capsaicin was also shown to activate HSF-1. These findings suggest that heat-sensing and signaling in mammalian cells is dependent on TRPV channels in the plasma membrane. Thus, TRPV channels may be important drug targets to inhibit or restore the cellular stress response in diseases with defective cellular proteins, such as cancer, inflammation and aging.

Subgroup-specific structural variation across 1,000 medulloblastoma genomes.

Medulloblastoma, the most common malignant paediatric brain tumour, is currently treated with nonspecific cytotoxic therapies including surgery, whole-brain radiation, and aggressive chemotherapy. As medulloblastoma exhibits marked intertumoural heterogeneity, with at least four distinct molecular variants, previous attempts to identify targets for therapy have been underpowered because of small samples sizes. Here we report somatic copy number aberrations (SCNAs) in 1,087 unique medulloblastomas. SCNAs are common in medulloblastoma, and are predominantly subgroup-enriched. The most common region of focal copy number gain is a tandem duplication of SNCAIP, a gene associated with Parkinson's disease, which is exquisitely restricted to Group 4α. Recurrent translocations of PVT1, including PVT1-MYC and PVT1-NDRG1, that arise through chromothripsis are restricted to Group 3. Numerous targetable SCNAs, including recurrent events targeting TGF-β signalling in Group 3, and NF-κB signalling in Group 4, suggest future avenues for rational, targeted therapy.

Five essays on bankruptcy

Chapter 2 Bankruptcy Initiation In The New Era of Chapter 11 2.1 Abstract The bankruptcy act of 1978 placed corporate managers (as debtor in possession) in control of the bankruptcy process. Between 2000 and 2001 managers apparently lost this control to secured creditors. This study examines financial ratios of firms filing for bankruptcy between 1993 and 2004 and tests the hypothesis that the change from manager to creditor control created or exacerbated the managerial (and dominant creditor) incentive to delay bankruptcy filing. We find a clear deterioration in the financial conditions of firms filing after 2001. This is consistent with managers (or creditors who control them) delaying filing for bankruptcy. We also observe patterns of operating losses and liquidations that suggest adverse economic consequences from such delay. Chapter 3 Bankruptcy Resolution: Priority of Claims with the Secured Creditor in Control 3.1 Abstract We present new evidence on the violation of priority of claims in bankruptcy using a sample of 222 firms that tiled for Chapter 11 bankruptcy over the 1993-2004 period. Our study reveals a dramatic reduction in the violations of priority of claims compared to research on prior periods. These results are consistent with changes in both court practices and laws transferring power to the secured creditors over our sample period. We also find an increase in the time from the date of a bankruptcy filing to reaching plan confirmation where priority is not violated. Chapter 4 Bankruptcy Resolution: Speed, APR Violations and Delaware 4.1 Abstract We analyze speed of bankruptcy resolution on a sample of 294 US firms filing for bankruptcy in the 1993-2004 period. We find strong association between type of Chapter II filing and speed of bankruptcy resolution. We also find that violations to the absolute priority rule reduce the time from bankruptcy filing to plan confirmation. This is consistent with the hypothesis that creditors are willing to grant concessions in exchange for faster bankruptcy resolution. Furthermore, after controlling for the type of filing and violations to the absolute priority rule, we do not find any difference in the duration of the bankruptcy process for firms filing in Delaware, New York, or other bankruptcy districts. Chapter 5 Financial Distress and Corporate Control 5.1 Abstract We examine the replacement rates of directors and executives in 63 firms filing for bank ruptcy during the 1995-2002 period. We find that over 76% of directors and executives are replaced in the four year period from the year prior to the bankruptcy filing through three years after. These rates are higher than those found in prior research and is consistent with changes in bankruptcy procedures and practice (i.e. the increased secured creditors control over the process due to both DIP financing and changes in the Uniform Commercial Code) having a significant impact on the corporate governance of firms in financial distress. Chapter 6 Financial Statement Restatements: Decision to File for Bankruptcy 6.1 Abstract On a sample of 201 firms that restated their financial statements we analyze the process of regaining investor trust in a two year period after the restatement. We find that 20% of firms that restate their financial statements tile for bankruptcy or restructure out of court. Our results also indicate that the decisions to change auditor or management is correlated with a higher probability of failure. Increased media attention appears to partly explain the decision of firms to restructure their debt or tile for bankruptcy.