Analytic approximation of matrix functions in Lp

"Vegeu el resum a l'inici del document del fitxer adjunt."

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Sentinel lymph node involvement and a high Breslow index are independent factors of risk for early relapse of melanoma.

AIM: The clinical relevance of sentinel lymph node (SLN) analysis was evaluated prospectively and compared with other known risk factors of relapse in early stage melanoma. METHODS: Surgery was guided by lymphoscintigraphy, blue dye and gamma probe detection. SLN were analysed by haematoxylin eosin (HE) histochemistry and multimarker immunohistochemistry (IHC). Disease free survival (DFS) was evaluated with Kaplan-Meier plots according to different parameters and Cox analyses of variance. RESULTS: From 210 patients a total of 381 SLN were excised. Lymphoscintigraphy identified all excised SLN with only 2 false positive lymphatic lakes. Fifty patients (24%) had tumour positive SLN. With a mean follow-up of 31.3 months, 29 tumour recurrences were observed, 19 (38%) in 50 SLN positive and 10 (6%) in 160 SLN negative patients. Strong predictive factors for early relapse (p < 0.0005) were SLN positivity and a high Breslow index. CONCLUSION: SLN tumour positivity is an independent factor of high risk for early relapse with a higher power of discrimination than the Breslow index.

An approximation algorithm for #k-SAT

"Vegeu el resum a l'inici del document del fitxer adjunt"

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

La régression tumorale n'est pas un facteur de risque d'atteinte du ganglion sentinelle dans les mélanomes fins (indice de Breslow < or = 1 mm) [Tumour regression is not predictive for higher risk of sentinel node involvement in thin melanomas (Breslow thickness < or = 1 mm)]

Background: Thin melanomas (Breslow thickness <= 1 mm) are considered highly curable. The aim of this study was to evaluate the correlation between histological tumour regression and sentinel lymph node (SLN) involvement in thin melanomas. Patients and methods: This was a retrospective single-centre study of 34 patients with thin melanomas undergoing SLN biopsy between April 1998 and January 2005. Results: The study included 14 women and 20 men of mean age 56.3 years. Melanomas were located on the neck (n = 3), soles (n = 4), trunk (n = 13) and extremities (n = 14). Pathological examination showed 25 SSM, four acral lentiginous melanomas, three in situ melanomas, one nodular melanoma and one unclassified melanoma with a mean Breslow thickness of 0.57 mm. Histological tumour regression was observed in 26 over 34 cases and ulceration was found in one case. Clark levels were as follows: I (n = 3), II (n = 20), III (n = 9), IV (n = 2). Growth phase was available in 15 cases (seven radial and eight vertical). Mitotic rates, available in 24 cases, were: 0 (n = 9), 1 (n = 11), 2 (n = 2), 3 (n = 1), 6 (n = 1). One patient with histological tumour regression (2.9% of cases and 3.8% of cases with regressing tumours) had a metastatic SLN. One patient negative for SLN had a lung relapse and died of the disease. Mean follow-up was 26.2 months. Conclusion: The results of the present study and the analysis of the literature show that histological regression of the primary tumour does not seem predictive of higher risk of SLN involvement in thin melanomas. This suggests that screening for SLN is not indicated in thin melanomas, even those with histological regression.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

The robustness of the weak selection approximation for the evolution of altruism against strong selection.

The weak selection approximation of population genetics has made possible the analysis of social evolution under a considerable variety of biological scenarios. Despite its extensive usage, the accuracy of weak selection in predicting the emergence of altruism under limited dispersal when selection intensity increases remains unclear. Here, we derive the condition for the spread of an altruistic mutant in the infinite island model of dispersal under a Moran reproductive process and arbitrary strength of selection. The simplicity of the model allows us to compare weak and strong selection regimes analytically. Our results demonstrate that the weak selection approximation is robust to moderate increases in selection intensity and therefore provides a good approximation to understand the invasion of altruism in spatially structured population. In particular, we find that the weak selection approximation is excellent even if selection is very strong, when either migration is much stronger than selection or when patches are large. Importantly, we emphasize that the weak selection approximation provides the ideal condition for the invasion of altruism, and increasing selection intensity will impede the emergence of altruism. We discuss that this should also hold for more complicated life cycles and for culturally transmitted altruism. Using the weak selection approximation is therefore unlikely to miss out on any demographic scenario that lead to the evolution of altruism under limited dispersal.

A First approximation to the realism/idealism debate about the external world

El text intenta fer una primera aproximació al debat contemporani entre realistes i anti-realistes sobre el món empíric, centrant-se en les posicions de Putnam i Nagel. El seu objectiu principal és el d'entendre les motivacions de les posicions i l'estructura actual del debat, i el d'establir les característiques que hauria de tenir qualsevol posició satisfactòria

Appropriation of technology in "non-western" societies: an approximation to the case of Bulgaria

The principal focus of the PhD thesis lies in the Social Software area and the appropriation of technology in "non-Western" societies taking the example of Bulgaria. The term "non-Western" is used to explain places considered technologically underdeveloped. The aims have been to capture how Bulgarian users creatively interpret and appropriate Internet identifying the sociocultural, political and subjective conditions in which that appropriation occurs, to identify emerging practices based on the interpretation and use of Internet and the impact they had on society and what conditions could influence the technological interpretation and the meaning these practices had for both users and social configuration of Internet as media in Bulgaria. An ethnographic approach has been used simultaneously in different online and offline contexts. On the one hand, this study is based on exploration of the Bulgarian Internet Space through online participant observation in forums and websites reviews and on the other hand, on semi-structured interviews with different types of users of the virtual platforms found, made both face to face and online and finally online participant observation at the same platforms. It is based on some contributions of the ethnographic work of Christine Hine in virtual environments and the notions of time and space of Barbara Czarniawska contextualized in the modern form of organization that occurs in a network of multiple and fragmented contexts across many movements.

On spectral approximation, Folner sequences and crossed products

In this article we review first some of the possibilities in which the notions of Fo lner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Fo lner sequence for the crossed product of a concrete C* -algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C* -algebra generated by bounded Jacobi operators.

Bernstein's problem on weighted polynomial approximation

We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis].

On concentrators and related approximation constants

Pippenger [Pi77] showed the existence of (6m,4m,3m,6)-concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m,4m,3m,5.05)-concentrator (which is no longer regular, but has fewer edges). We apply this result to improve the constant of approximation of almost additive set functions by additive set functions from 44.5 (established by Kalton and Roberts in [KaRo83] to 39. We show a more direct connection of the latter problem to the Whitney type estimate for approximation of continuous functions on a cube in &b&R&/b&&sup&d&/sup& by linear functions, and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in [BrKa00] to 73.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small