Approximate Euclidean shortest paths in polygonal domains

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input parameter $\epsilon$. We utilize $\Omega$ to compute a $(1+\epsilon)$-approximate geodesic shortest path between the two given points in $O(n + h((\lg{n}) + (\lg{h})^{1+\delta} + (\frac{1}{\epsilon}\lg{\frac{h}{\epsilon}})))$ time. Here, $\epsilon$ is a user parameter, and $\delta$ is a small positive constant (resulting from the time for triangulating the free space of $\cal P$ using the algorithm in \cite{journals/ijcga/Bar-YehudaC94}). Moreover, we devise a $(2+\epsilon)$-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.Comment: a few updates; accepted to ISAAC 201

A Simple Model for Pricing Securities with Equity, Interest-Rate, and Default Risk

We develop a model for pricing derivative and hybrid securities whose value may depend on different sources of risk, namely, equity, interest-rate, and default risks. In addition to valuing such securities the framework is also useful for extracting probabilities of default (PD) functions from market data. Our model is not based on the stochastic process for the value of the firm [which is unobservable], but on the stochastic process for interest rates and the equity price, which are observable. The model comprises a risk-neutral setting in which the joint process of interest rates and equity are modeled together with the default conditions for security payoffs. The model is embedded on a recombining lattice which makes implementation of the pricing scheme feasible with polynomial complexity. We present a simple approach to calibration of the model to market observable data. The framework is shown to nest many familiar models as special cases. The model is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as CDOs. We present several numerical and calibration examples to demonstrate the applicability and implementation of our approach

Polishing diamonds in the rough: the sources of syndicated venture performance

Using an effort-sharing framework for VC syndicates, we assess how syndication impacts investment returns, chances of successful exit, and the time taken to exit. With data from 1980-2003, and applying apposite econometrics for endogeneity to these different performance measures, we are able to ascribe much of the better return to selection, with the value-addition by monitoring role significantly impacting the likelihood and time of exit. While the extant literature on Venture Capital (VC) syndication is divided about the relative importance of the selection and value-add hypotheses, we find that their roles are complementary

A Direct Approach to Arbitrage-Free Pricing of Credit Derivatives

This paper develops a model for the pricing of credit derivatives using observables. The model (i) is arbitrage-free, (ii) accommodates path-dependence, and (iii) handles a range of securities, even with American features. The computer implementation uses a recursive scheme that is convenient and seamlessly processes forward induction and backward recursion, needed to compute more complicated derivative securities.

A Randomized, Controlled Clinical Trial Comparing Efficacy, Safety and Cost Effectiveness of Lornoxicam with Diclofenac Sodium in Patients of Osteoarthritis Knee

Osteoarthritis is a chronic painful condition affecting larger joints; mostcommonly knee joint. Pharmacological control of pain is the mainstay of management of osteoarthritis. Many patientsfail to achieve satisfactory reduction in pain with one of the most commonly prescribed drugs, diclofenac sodium, even after maximum daily allowed doses. Lornoxicam is a newer molecule in the Indian market promising better pain relief incontext of low back pain and post knee replacement surgery pain as compared to standard therapies. As per profile of lornoxicam, if it is better than diclofenac sodium then it will be helpful in managing the patients of osteoarthritis more effectively. Till date no comparative clinical trial has been done to compare these two drugs for the management ofosteoarthritis knee. So, to evaluate the same we carried out this study to compare safety, efficacy and cost effectiveness of lornoxicam and diclofenac sodium in relieving pain in patients of osteoarthritis knee. This study is a randomized, open labeled, controlled clinical trial having 40 newly diagnosed patients with osteoarthritis knee. After random allocationinto two groups i.e. group D and group L (each having 20 patients); group D received diclofenac sodium 50 mg 12 hourly and group L received lornoxicam 4 mg 8 hourly for a period of 3 months. All patients were assessed with visual analogue scale and 100 meter walking test before starting of therapy, at 15 days and at 1, 2 and 3 months of therapy.Adverse drug reactions and cost of therapy was monitored during the study period. Mean decrease in visual analogue scale and time of 100 meter walking test was statistically significant in lornoxicam group as compared to diclofenac sodium. Gastric irritation was reported in one patient from group L and two patients from group D. Lornoxicam significantly relieves pain of osteoarthritis knee than diclofenac sodium without adversely affecting the tolerability to the patients

Evidence of Twisting and Mixed-polarity Solar Photospheric Magnetic Field in Large Penumbral Jets: IRIS and Hinode Observations

A recent study using {\it Hinode} (SOT/FG) data of a sunspot revealed some unusually large penumbral jets that often repeatedly occurred at the same locations in the penumbra, namely at the tail of a penumbral filament or where the tails of multiple penumbral filaments converged. These locations had obvious photospheric mixed-polarity magnetic flux in \NaI\ 5896 Stokes-V images obtained with SOT/FG. Several other recent investigations have found that extreme ultraviolet (EUV)/X-ray coronal jets in quiet Sun regions (QRs), coronal holes (CHs) and near active regions (ARs) have obvious mixed-polarity fluxes at their base, and that magnetic flux cancellation prepares and triggers a minifilament flux-rope eruption that drives the jet. Typical QR, CH, and AR coronal jets are up to a hundred times bigger than large penumbral jets, and in EUV/X-ray images show clear twisting motion in their spires. Here, using IRIS \MgII\ k 2796 \AA\ SJ images and spectra in the penumbrae of two sunspots we characterize large penumbral jets. We find redshift and blueshift next to each other across several large penumbral jets, and interpret these as untwisting of the magnetic field in the jet spire. Using Hinode/SOT (FG and SP) data, we also find mixed-polarity magnetic flux at the base of these jets. Because large penumbral jets have mixed-polarity field at their base and have twisting motion in their spires, they might be driven the same way as QR, CH and AR coronal jets.Comment: 18 pages, 11 figures; to appear in Ap