Extremal behavior of stochastic integrals driven by regularly varying L\'{e}vy processes

We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving L\'{e}vy process and we determine its limit measure associated with regular variation on the space of c\`{a}dl\`{a}g functions.Comment: Published at http://dx.doi.org/10.1214/009117906000000548 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Functional large deviations for multivariate regularly varying random walks

We extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.--Mat. Nauk 6 (1969) 17--22, Theory Probab. Appl. 14 (1969) 51--64, 193--208] on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of c\`{a}dl\`{a}g functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin probabilities for multivariate random walks and long strange segments. These results make precise the idea of heavy-tailed large deviation heuristics: in an asymptotic sense, only the largest step contributes to the extremal behavior of a multivariate random walk.Comment: Published at http://dx.doi.org/10.1214/105051605000000502 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Abnormal arterial-venous fusions and fate specification in mouse embryos lacking blood flow.

The functions of blood flow in the morphogenesis of mammalian arteries and veins are not well understood. We examined the development of the dorsal aorta (DA) and the cardinal vein (CV) in Ncx1 -/- mutants, which lack blood flow due to a deficiency in a sodium calcium ion exchanger expressed specifically in the heart. The mutant DA and CV were abnormally connected. The endothelium of the Ncx1 -/- mutant DA lacked normal expression of the arterial markers ephrin-B2 and Connexin-40. Notch1 activation, known to promote arterial specification, was decreased in mutant DA endothelial cells (ECs), which ectopically expressed the venous marker Coup-TFII. These findings suggest that flow has essential functions in the DA by promoting arterial and suppressing venous marker expression. In contrast, flow plays a lesser role in the CV, because expression of arterial-venous markers in CV ECs was not as dramatically affected in Ncx1 -/- mutants. We propose a molecular mechanism by which blood flow mediates DA and CV morphogenesis, by regulating arterial-venous specification of DA ECs to ensure proper separation of the developing DA and CV

Extremal behavior of regularly varying stochastic processes

Abstract We study a formulation of regular variation for multivariate stochastic processes on the unit interval with sample paths that are almost surely right-continuous with left limits and we provide necessary and sufficient conditions for such stochastic processes to be regularly varying. A version of the Continuous Mapping Theorem is proved that enables the derivation of the tail behavior of rather general mappings of the regularly varying stochastic process. For a wide class of Markov processes with increments satisfying a condition of weak dependence in the tails we obtain simplified sufficient conditions for regular variation. For such processes we show that the possible regular variation limit measures concentrate on step functions with one step, from which we conclude that the extremal behavior of such processes is due to one big jump or an extreme starting point. By combining this result with the Continuous Mapping Theorem, we are able to give explicit results on the tail behavior of various vectors of functionals acting on such processes. Finally, using the Continuous Mapping Theorem we derive the tail behavior of filtered regularly varying Le´vy processes. r 2004 Elsevier B.V. All rights reserved. MSC: primary 60F17; 60G17; secondary 60G07; 60G7

Assimilation of GNSS ZTD with HARMONIE

Póster presentado en: International Symposium on Data Assimilation 2014 celebrado en Munich, del 24 al 28 de febrero de 201

Interobserver reproducibility of perineural invasion of prostatic adenocarcinoma in needle biopsies

Numerous studies have shown a correlation between perineural invasion (PNI) in prostate biopsies and outcome. The reporting of PNI varies widely in the literature. While the interobserver variability of prostate cancer grading has been studied extensively, less is known regarding the reproducibility of PNI. A total of 212 biopsy cores from a population-based screening trial were included in this study (106 with and 106 without PNI according to the original pathology reports). The glass slides were scanned and circulated among four pathologists with a special interest in urological pathology for assessment of PNI. Discordant cases were stained by immunohistochemistry for S-100 protein. PNI was diagnosed by all four observers in 34.0% of cases, while 41.5% were considered to be negative for PNI. In 24.5% of cases, there was a disagreement between the observers. The kappa for interobserver variability was 0.67-0.75 (mean 0.73). The observations from one participant were compared with data from the original reports, and a kappa for intraobserver variability of 0.87 was achieved. Based on immunohistochemical findings among discordant cases, 88.6% had PNI while 11.4% did not. The most common diagnostic pitfall was the presence of bundles of stroma or smooth muscle. It was noted in a few cases that collagenous micronodules could be mistaken for a nerve. The distance between cancer and nerve was another cause of disagreement. Although the results suggest that the reproducibility of PNI may be greater than that of prostate cancer grading, there is still a need for improvement and standardization

Estimating diagnostic uncertainty in artificial intelligence assisted pathology using conformal prediction

Unreliable predictions can occur when an artificial intelligence (AI) system is presented with data it has not been exposed to during training. We demonstrate the use of conformal prediction to detect unreliable predictions, using histopathological diagnosis and grading of prostate biopsies as example. We digitized 7788 prostate biopsies from 1192 men in the STHLM3 diagnostic study, used for training, and 3059 biopsies from 676 men used for testing. With conformal prediction, 1 in 794 (0.1%) predictions is incorrect for cancer diagnosis (compared to 14 errors [2%] without conformal prediction) while 175 (22%) of the predictions are flagged as unreliable when the AI-system is presented with new data from the same lab and scanner that it was trained on. Conformal prediction could with small samples (N = 49 for external scanner, N = 10 for external lab and scanner, and N = 12 for external lab, scanner and pathology assessment) detect systematic differences in external data leading to worse predictive performance. The AI-system with conformal prediction commits 3 (2%) errors for cancer detection in cases of atypical prostate tissue compared to 44 (25%) without conformal prediction, while the system flags 143 (80%) unreliable predictions. We conclude that conformal prediction can increase patient safety of AI-systems.publishedVersionPeer reviewe

The prognostic impact of the tumour stroma fraction: A machine learning-based analysis in 16 human solid tumour types

Background: The development of a reactive tumour stroma is a hallmark of tumour progression and pronounced tumour stroma is generally considered to be associated with clinical aggressiveness. The variability between tumour types regarding stroma fraction, and its prognosis associations, have not been systematically analysed.Methods: Using an objective machine-learning method we quantified the tumour stroma in 16 solid cancer types from 2732 patients, representing retrospective tissue collections of surgically resected primary tumours. Image analysis performed tissue segmentation into stromal and epithelial compartment based on pan-cytokeratin staining and autofluorescence patterns.Findings: The stroma fraction was highly variable within and across the tumour types, with kidney cancer showing the lowest and pancreato-biliary type periampullary cancer showing the highest stroma proportion (median 19% and 73% respectively). Adjusted Cox regression models revealed both positive (pancreato-biliary type periampullary cancer and oestrogen negative breast cancer, HR(95%CI)=0.56(0.34-0.92) and HR (95%CI)=0.41(0.17-0.98) respectively) and negative (intestinal type periampullary cancer, HR(95%CI)=3.59 (1.49-8.62)) associations of the tumour stroma fraction with survival.Interpretation: Our study provides an objective quantification of the tumour stroma fraction across major types of solid cancer. Findings strongly argue against the commonly promoted view of a general associations between high stroma abundance and poor prognosis. The results also suggest that full exploitation of the prognostic potential of tumour stroma requires analyses that go beyond determination of stroma abundance.</p