Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Non-random autosome segregation: a stepping stone for the evolution of sex chromosome complexes?

A new study in Caenorhabditis elegans shows that homologous autosomes segregate non-randomly with the sex chromosome in the heterogametic sex. Segregation occurs according to size, small autosomes segregating with, and large autosomes segregating away from the X-chromosome. Such sex-biased transmission of autosomes could facilitate the spread of sexually antagonistic alleles whose effects favor the fitness of one sex at the expense of the other. This may provide a first step toward the evolution of new sex determination systems.

Morphological changes in convection-diffusion-limited deposition

The effect of hydrodynamic flow upon diffusion-limited deposition on a line is investigated using a Monte Carlo model. The growth process is governed by the convection and diffusion field. The convective diffusion field is simulated by the biased-random walker resulting from a superimposed drift that represents the convective flow. The development of distinct morphologies is found with varying direction and strength of drift. By introducing a horizontal drift parallel to the deposition plate, the diffusion-limited deposit changes into a single needle inclined to the plate. The width of the needle decreases with increasing strength of drift. The angle between the needle and the plate is about 45° at high flow rate. In the presence of an inclined drift to the plate, the convection-diffusion-limited deposit leads to the formation of a characteristic columnar morphology. In the limiting case where the convection dominates, the deposition process is equivalent to ballistic deposition onto an inclined surface.

Ex-Vivo Ultransonographic Control Of Resection Margin During Partial Nephrectomy

Introduction & Objectives: Surgery remains the treatment of choice for localized renal cell neoplasia. While radical nephrectomy was long considered as gold standard, partial nephrectomy (PN) has widened its indications over the past twodecades and has shown oncological results equivalent to radical nephrectomy for small tumors. Moreover, it is considered superior to radical nephrectomy in terms of non-cancer related mortality. The role of negative surgical margin has been widely debated. Intraoperative frozen section analysis has been shown to be unreliable, expensive, time-consuming and not well correlated to final pathology. The goal of the present study was to assess the correlation of intraoperative exvivo ultrasonographic (US) evaluation of resection margin to definitive pathology in patients undergoing PN.Materials & Methods: An observational study was carried out in ours 2 institutions from February 2008 to October 2010. Patients undergoing PN for T1-T2 renal tumors were included. Ex vivo US evaluation was performed. Considering availability of US engine, not all consecutive eligible patients were included. PN was undertaken either by open surgery or laparoscopic access in a standardized technique. The "minimal healthy tissue margin" technique was applied. Once resected, the specimen was kept in a saline solution and US determination of tumor margins was performed. Sequential images were captured in order to evaluate the whole capsule.Results: Twenty-two patients (9 women, age 63±11 years[46-78]) were included in the present analysis. Open or laparoscopic PN was performed in 19 and 3 patients, respectively. Intraoperative ex-vivo US showed negative surgical margin in all cases except one, needing a complementary renal parenchyma resection. US duration ranged from 1 to 4 minutes, with a median time of 1 minute. Definitive histological analysis confirmed the presence of 3 angiomyolipoma, 15 clear cell carcinoma (11 pT1a,3 pT1b,1 pT2), 3 chromophobe carcinoma (1 pT1a,1 pT1b,1 pT2) and 1 pT1a type II papillary tumor. Mean tumor size was 3,4±2.1 cm [0,6-7,2]. Final pathology revealed R0 margins in all cases.Conclusions: Intraoperative ex-vivo US evaluation of resection margin in patients undergoing PN is feasible, time-efficient, well correlated to definitive pathological examination, and should be evaluated in further prospective trials.

Analysis of bioavailable arsenic in rice with whole cell living bioreporter bacteria.

A multiwell plate bioassay was developed using genetically modified bacteria (bioreporter cells) to detect inorganic arsenic extracted from rice. The bacterial cells expressed luciferase upon exposure to arsenite, the activity of which was detected by measurement of cellular bioluminescence. The bioreporter cells detected arsenic in all rice varieties tested, with averages of 0.02-0.15 microg of arsenite equivalent per gram of dry weight and a method detection limit of 6 ng of arsenite per gram of dry rice. This amounted to between approximately 20 and 90% of the total As content reported by chemical methods for the same sample and suggested that a major proportion of arsenic in rice is in the inorganic form. Calibrations of the bioassay with pure inorganic and organic arsenic forms showed that the bacterial cells react to arsenite with highest affinity, followed by arsenate (with 25% response relative to an equivalent arsenite concentration) and trimethylarsine oxide (at 10% relative response). A method for biocompatible arsenic extraction was elaborated, which most optimally consisted of (i) grinding rice to powder, (ii) mixing with an aqueous solution containing pancreatic enzymes, (iii) mechanical shearing, (iv) extraction in mild acid conditions and moderate heat, and (v) centrifugation and pH neutralization. Detection of mainly inorganic arsenic by the bacterial cells may have important advantages for toxicity assessment of rice consumption and would form a good complement to total chemical arsenic determination.

Effect of two types of biosurfactants on phenanthrene availability to the bacterial bioreporter Burkholderia sartisoli strain RP037.

Biosurfactants are tensio-active agents that have often been proposed as a means to enhance the aqueous solubility of hydrophobic organic contaminants, such as polycyclic aromatic hydrocarbons (PAHs). Biosurfactant-producing bacteria such as those belonging to the genus Pseudomonas might therefore enhance PAH availability to PAH-degrading bacteria. We tested the effects of two types of biosurfactants produced by Pseudomonas sp., cyclic lipopeptides and rhamnolipids, on phenanthrene bioavailability. Bioavailability was judged from growth rates on phenanthrene and from specific induction of a phenanthrene-responsive GFP-reporter in Burkholderia sartisoli strain RP037. Co-culturing of strain RP037 with the lipopeptide-producing bacterium Pseudomonas putida strain PCL1445 enhanced GFP expression compared to a single culture, but this effect was not significantly different when strain RP037 was co-cultivated with a non-lipopeptide-producing mutant of P. putida. The addition of partially purified supernatant extracts from the P. putida lipopeptide producer equally did not unequivocally enhance phenanthrene bioavailability to strain RP037 compared to controls. In contrast, a 0.1% rhamnolipid solution strongly augmented RP037 growth rates on phenanthrene and led to a significantly larger proportion of cells in culture with high GFP expression. Our data therefore suggest that biosurfactant effects may be strongly dependent on the strain and type of biosurfactant.

Expression quantitative trait locus mapping across water availability environments reveals contrasting associations with genomic features in Arabidopsis.

The regulation of gene expression is crucial for an organism's development and response to stress, and an understanding of the evolution of gene expression is of fundamental importance to basic and applied biology. To improve this understanding, we conducted expression quantitative trait locus (eQTL) mapping in the Tsu-1 (Tsushima, Japan) × Kas-1 (Kashmir, India) recombinant inbred line population of Arabidopsis thaliana across soil drying treatments. We then used genome resequencing data to evaluate whether genomic features (promoter polymorphism, recombination rate, gene length, and gene density) are associated with genes responding to the environment (E) or with genes with genetic variation (G) in gene expression in the form of eQTLs. We identified thousands of genes that responded to soil drying and hundreds of main-effect eQTLs. However, we identified very few statistically significant eQTLs that interacted with the soil drying treatment (GxE eQTL). Analysis of genome resequencing data revealed associations of several genomic features with G and E genes. In general, E genes had lower promoter diversity and local recombination rates. By contrast, genes with eQTLs (G) had significantly greater promoter diversity and were located in genomic regions with higher recombination. These results suggest that genomic architecture may play an important a role in the evolution of gene expression.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Climate and vegetation history of western Portugal inferred from Albian near-shore deposits (Gale Formation, Lusitanian Basin)

The late Early Cretaceous greenhouse climate has been studied intensively based on proxy data derived essentially from open marine archives. In contrast, information on continental climatic conditions and on the accompanying response of vegetation is relatively scarce, most notably owing to the stratigraphic uncertainties associated with many Lower Cretaceous terrestrial deposits. Here, we present a palynological record from Albian near-shore deposits of the Lusitanian Basin of W Portugal, which have been independently dated using Sr-isotope signals derived from low-Mg oyster shell calcite. Sr-87/Sr-86 values fluctuate between 0.707373 +/- 0.00002 and 0.707456 +/- 0.00003; absolute values and the overall stratigraphic trend match well with the global open marine seawater signature during Albian times. Based on the new Sr-isotope data, existing biostratigraphic assignments of the succession are corroborated and partly revised. Spore-pollen data provide information on the vegetation community structure and are flanked by sedimentological and clay mineralogical data used to infer the overall climatic conditions prevailing on the adjacent continent. Variations in the distribution of climate-sensitive pollen and spores indicate distinct changes in moisture availability across the studied succession with a pronounced increase in hygrophilous spores in late Early Albian times. Comparison with time-equivalent palynofloras from the Algarve Basin of southern Portugal shows pronounced differences in the xerophyte/hygrophyte ratio, interpreted to reflect the effect of a broad arid climate belt covering southern and southeastern Iberia during Early Albian times.