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

Ex vivo characterization of allo-MHC-restricted T cells specific for a single MHC-peptide complex.

Alloreactive T cells are thought to be a potentially rich source of high-avidity T cells with therapeutic potential since tolerance to self-Ags is restricted to self-MHC recognition. Given the particularly high frequency of alloreactive T cells in the peripheral immune system, we used numerous MHC class I multimers to directly visualize and isolate viral and tumor Ag-specific alloreactive CD8 T cells. In fact, all but one specificities screened were undetectable in ex vivo labeling. In this study, we report the occurrence of CD8 T cells specifically labeled with allo-HLA-A*0201/Melan-A/MART-1(26-35) multimers at frequencies that are in the range of 10(-4) CD8 T cells and are thus detectable ex vivo by flow cytometry. We report the thymic generation and shaping of tumor Ag-specific, alloreactive T cells as well as their fate once seeded in the periphery. We show that these cells resemble their counterparts in HLA-A*0201-positive individuals, based on their structural and functional attributes.

Monosomal karyotype in acute myeloid leukemia: a better indicator of poor prognosis than a complex karyotype.

PURPOSE: To investigate the prognostic value of various cytogenetic components of a complex karyotype in acute myeloid leukemia (AML). PATIENTS AND METHODS: Cytogenetics and overall survival (OS) were analyzed in 1,975 AML patients age 15 to 60 years. RESULTS: Besides AML with normal cytogenetics (CN) and core binding factor (CBF) abnormalities, we distinguished 733 patients with cytogenetic abnormalities. Among the latter subgroup, loss of a single chromosome (n = 109) conferred negative prognostic impact (4-year OS, 12%; poor outcome). Loss of chromosome 7 was most common, but outcome of AML patients with single monosomy -7 (n = 63; 4-year OS, 13%) and other single autosomal monosomies (n = 46; 4-year OS, 12%) did not differ. Structural chromosomal abnormalities influenced prognosis only in association with a single autosomal monosomy (4-year OS, 4% for very poor v 24% for poor). We derived a monosomal karyotype (MK) as a predictor for very poor prognosis of AML that refers to two or more distinct autosomal chromosome monosomies (n = 116; 4-year OS, 3%) or one single autosomal monosomy in the presence of structural abnormalities (n = 68; 4-year OS, 4%). In direct comparisons, MK provides significantly better prognostic prediction than the traditionally defined complex karyotype, which considers any three or more or five or more clonal cytogenetic abnormalities, and also than various individual specific cytogenetic abnormalities (eg, del[5q], inv[3]/t[3;3]) associated with very poor outcome. CONCLUSION: MK enables (in addition to CN and CBF) the prognostic classification of two new aggregates of cytogenetically abnormal AML, the unfavorable risk MK-negative category (4-year OS, 26% +/- 2%) and the highly unfavorable risk MK-positive category (4-year OS, 4% +/- 1%).

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

[Doublon: 10.1007/s00428-009-0853-4] Soft tissue sarcomas with complex genomic profiles.

Soft tissue sarcomas (STS) with complex genomic profiles (50% of all STS) are predominantly composed of spindle cell/pleomorphic sarcomas, including leiomyosarcoma, myxofibrosarcoma, pleomorphic liposarcoma, pleomorphic rhabdomyosarcoma, malignant peripheral nerve sheath tumor, angiosarcoma, extraskeletal osteosarcoma, and spindle cell/pleomorphic unclassified sarcoma (previously called spindle cell/pleomorphic malignant fibrous histiocytoma). These neoplasms show, characteristically, gains and losses of numerous chromosomes or chromosome regions, as well as amplifications. Many of them share recurrent aberrations (e.g., gain of 5p13-p15) that seem to play a significant role in tumor progression and/or metastatic dissemination. In this paper, we review the cytogenetic, molecular genetic, and clinicopathologic characteristics of the most common STS displaying complex genomic profiles. Features of diagnostic or prognostic relevance will be discussed when needed.

A-Kinase Anchoring Protein Lbc Coordinates a p38 Activating Signaling Complex Controlling Compensatory Cardiac Hypertrophy.

In response to stress, the heart undergoes a remodeling process associated with cardiac hypertrophy that eventually leads to heart failure. A-kinase anchoring proteins (AKAPs) have been shown to coordinate numerous prohypertrophic signaling pathways in cultured cardiomyocytes. However, it remains to be established whether AKAP-based signaling complexes control cardiac hypertrophy and remodeling in vivo. In the current study, we show that AKAP-Lbc assembles a signaling complex composed of the kinases PKN, MLTK, MKK3, and p38α that mediates the activation of p38 in cardiomyocytes in response to stress signals. To address the role of this complex in cardiac remodeling, we generated transgenic mice displaying cardiomyocyte-specific overexpression of a molecular inhibitor of the interaction between AKAP-Lbc and the p38-activating module. Our results indicate that disruption of the AKAP-Lbc/p38 signaling complex inhibits compensatory cardiomyocyte hypertrophy in response to aortic banding-induced pressure overload and promotes early cardiac dysfunction associated with increased myocardial apoptosis, stress gene activation, and ventricular dilation. Attenuation of hypertrophy results from a reduced protein synthesis capacity, as indicated by decreased phosphorylation of 4E-binding protein 1 and ribosomal protein S6. These results indicate that AKAP-Lbc enhances p38-mediated hypertrophic signaling in the heart in response to abrupt increases in the afterload.

Exported oscillator competition: A concept to analyse complex rhytms

We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such as a particular class of heart arrhythmia.

Pain and beliefs after musuloskeletal trauma: Complex relationships during the first year of rehabilitation

Introduction.- Pain and beliefs have an influence on the patient's course in rehabilitation and their relationships are complex. The aim of this study was to understand the relationships between pain at admission and the evolution of beliefs during rehabilitation as well as the relationships between pain and beliefs one year after rehabilitation.Patients and methods.- Six hundred and thirty-one consecutive patients admitted in rehabilitation after musculoskeletal trauma, were included and assessed at admission, at discharge and one year after discharge. Pain was measured by VAS (Visual Analogical Scale) and beliefs by judgement on Lickert scales. Four kinds of beliefs were evaluated: fear of a severe origin of pain, fear of movement, fear of pain and feeling of distress (loss of control). The association between pain and beliefs was assessed by logistic regressions, adjusted for gender, age, native language, education and bio-psycho-social complexity.Results.- At discharge, 44% of patients felt less distressed by pain, 34% are reinsured with regard to their fear of a severe origin of pain, 38% have less fear of pain and 33% have less fear of movement. The higher the pain at admission, the higher the probability that the distress diminished, this being true up to a threshold (70 mm/100) beyond which there was a plateau. At one year, the higher the pain, the more dysfunctional the fears.Discussion.- The relationships between pain and beliefs are complex and may change all along rehabilitation. During hospitalization, one could hope that the patient would be reinsured and would gain self-control again, if pain does not exceed a certain threshold. After one year, high pain increases the risk of dysfunctional beliefs. For clinical practice, these data suggest to think in terms of the more accessible "entrance door", act against pain and/or against beliefs, adpated to each patient.

Comparison between detailed digital and conventional soil maps of an area with complex geology

Since different pedologists will draw different soil maps of a same area, it is important to compare the differences between mapping by specialists and mapping techniques, as for example currently intensively discussed Digital Soil Mapping. Four detailed soil maps (scale 1:10.000) of a 182-ha sugarcane farm in the county of Rafard, São Paulo State, Brazil, were compared. The area has a large variation of soil formation factors. The maps were drawn independently by four soil scientists and compared with a fifth map obtained by a digital soil mapping technique. All pedologists were given the same set of information. As many field expeditions and soil pits as required by each surveyor were provided to define the mapping units (MUs). For the Digital Soil Map (DSM), spectral data were extracted from Landsat 5 Thematic Mapper (TM) imagery as well as six terrain attributes from the topographic map of the area. These data were summarized by principal component analysis to generate the map designs of groups through Fuzzy K-means clustering. Field observations were made to identify the soils in the MUs and classify them according to the Brazilian Soil Classification System (BSCS). To compare the conventional and digital (DSM) soil maps, they were crossed pairwise to generate confusion matrices that were mapped. The categorical analysis at each classification level of the BSCS showed that the agreement between the maps decreased towards the lower levels of classification and the great influence of the surveyor on both the mapping and definition of MUs in the soil map. The average correspondence between the conventional and DSM maps was similar. Therefore, the method used to obtain the DSM yielded similar results to those obtained by the conventional technique, while providing additional information about the landscape of each soil, useful for applications in future surveys of similar areas.

The major histocompatibility complex and perfumers' descriptions of human body odors

The MHC (major histocompatibility complex) is a group of genes that play a crucial role in immune recognition and in tolerance of tissue grafting. The MHC has also been found to influence body odors, body odor preferences, and mate choice in mice and humans. Here we test whether verbal descriptions of human body odors can be linked to the MHC. We asked 45 male students to live as odor neutral as possible for two consecutive days and to wear a T-shirt during the nights. The odors of these T-shirts were then described by five evaluators: two professional perfumers and three laymen. One of the perfumers was able to describe the T-shirt odors in such a way that some of the allelic specificity of the MHC was significantly revealed (after Bonferroni correction for multiple testing). This shows that, although difficult, some people are able to describe MHCcorrelated body odor components.