Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Forecasting volatility using a continuous time model

This paper evaluates the forecasting performance of a continuous stochastic volatility model with two factors of volatility (SV2F) and compares it to those of GARCH and ARFIMA models. The empirical results show that the volatility forecasting ability of the SV2F model is better than that of the GARCH and ARFIMA models, especially when volatility seems to change pattern. We use ex-post volatility as a proxy of the realized volatility obtained from intraday data and the forecasts from the SV2F are calculated using the reprojection technique proposed by Gallant and Tauchen (1998).

The possibility for continuous growth with exhaustible resources: unknowingly an agreement has been reached, but it may not be correct

It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that , unnoticed by the pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarises some preliminary work by the author that indicates that this common position may not be correct

Nuclear factor I-C links platelet-derived growth factor and transforming growth factor beta1 signaling to skin wound healing progression.

Transforming growth factor beta (TGF-beta) and platelet-derived growth factor A (PDGFAlpha) play a central role in tissue morphogenesis and repair, but their interplay remain poorly understood. The nuclear factor I C (NFI-C) transcription factor has been implicated in TGF-beta signaling, extracellular matrix deposition, and skin appendage pathologies, but a potential role in skin morphogenesis or healing had not been assessed. To evaluate this possibility, we performed a global gene expression analysis in NFI-C(-/-) and wild-type embryonic primary murine fibroblasts. This indicated that NFI-C acts mostly to repress gene expression in response to TGF-beta1. Misregulated genes were prominently overrepresented by regulators of connective tissue inflammation and repair. In vivo skin healing revealed a faster inflammatory stage and wound closure in NFI-C(-/-) mice. Expression of PDGFA and PDGF-receptor alpha were increased in wounds of NFI-C(-/-) mice, explaining the early recruitment of macrophages and fibroblasts. Differentiation of fibroblasts to contractile myofibroblasts was also elevated, providing a rationale for faster wound closure. Taken together with the role of TGF-beta in myofibroblast differentiation, our results imply a central role of NFI-C in the interplay of the two signaling pathways and in regulation of the progression of tissue regeneration.

Long-term outcome after cognitive and behavioral regression in nonlesional epilepsy with continuous spike-waves during slow-wave sleep.

PURPOSE: To present the long-term follow-up of 10 adolescents and young adults with documented cognitive and behavioral regression as children due to nonlesional focal, mainly frontal, epilepsy with continuous spike-waves during slow wave sleep (CSWS). METHODS: Past medical and electroencephalography (EEG) data were reviewed and neuropsychological tests exploring main cognitive functions were administered. KEY FINDINGS: After a mean duration of follow-up of 15.6 years (range, 8-23 years), none of the 10 patients had recovered fully, but four regained borderline to normal intelligence and were almost independent. Patients with prolonged global intellectual regression had the worst outcome, whereas those with more specific and short-lived deficits recovered best. The marked behavioral disorders resolved in all but one patient. Executive functions were neither severely nor homogenously affected. Three patients with a frontal syndrome during the active phase (AP) disclosed only mild residual executive and social cognition deficits. The main cognitive gains occurred shortly after the AP, but qualitative improvements continued to occur. Long-term outcome correlated best with duration of CSWS. SIGNIFICANCE: Our findings emphasize that cognitive recovery after cessation of CSWS depends on the severity and duration of the initial regression. None of our patients had major executive and social cognition deficits with preserved intelligence, as reported in adults with early destructive lesions of the frontal lobes. Early recognition of epilepsy with CSWS and rapid introduction of effective therapy are crucial for a best possible outcome.

Angiotensin II favors progression to heart failure in diabetic hearts: role of myocardial fatty acid oxidation downregulation

Purpose: Diabetic myocardium is particularly vulnerable to develop heart failure in response to chronic stress conditions including hypertension or myocardial infarction. We have recently observed that angiotensin II (Ang II)-mediated downregulation of the fatty acid oxidation pathway favors occurrence of heart failure by myocardial accumulation of lipids (lipotoxicity). Because diabetic heart is exposed to high levels of circulating fatty acid, we determined whether insulin resistance favors development of heart failure in mice with Ang II-mediated myocardial remodeling.Methods: To study the combined effect of diabetes and Ang II-induced heart remodeling, we generated leptin-deficient/insulin resistant (Lepob/ob) mice with cardiac targeted overexpression of angiotensinogen (TGAOGN). Left ventricular (LV) failure was indicated by pulmonary congestion (lung weight/tibial length>+2SD of wild-type mice). Myocardial metabolism and function were assessed during in vitro isolated working heart perfusion.Results: Forty-eight percent of TGAOGN mice without insulin resistance exhibited pulmonary congestion at the age of 6 months associated with increased myocardial BNP expression (+375% compared with WT) and reduced LV power (developed pressure x cardiac output; -15%). The proportion of mice presenting heart failure was markedly increased to 71% in TGAOGN mice with insulin resistance (TGAOGN/Lepob/ob). TGAOGN/Lepob/ob mice with heart failure exhibited further increase of BNP compared with failing non-diabetic TGAOGN mice (+146%) and further reduction of cardiac power (-59%). Mice with insulin resistance alone (Lepob/ob) did not exhibit signs of heart failure or LV dysfunction. Myocardial fatty acid oxidation measured during in vitro perfusion was markedly increased in non-failing hearts from Lepob/ob mice (+380% compared with WT) and glucose oxidation decreased (-72%). In contrast, fatty acid and glucose oxidation did not differ from Lepob/ob mice in hearts from TGAOGN/Lepob/ob mice without heart failure. However, both fatty acid and glucose oxidation were markedly decreased (-47% and -48%, respectively, compared with WT/Lepob/+) in failing hearts from TGAOGN/Lepob/ob mice. Reduction of fatty acid oxidation was associated with marked reduction of protein expression of a number of regulatory enzymes implied in fatty acid oxidation.Conclusions: Insulin resistance favors the progression to heart failure during chronic exposure of the myocardium to Ang II. Our results are compatible with a role of Ang II-mediated downregulation of fatty acid oxidation, potentially promoting lipotoxicity.

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).

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Identification and characterization of novel molecular mechanisms involved in initiation and progression of myelination

Schwann cells synthesize a large amount of membrane that form a specialized structure called myelin that surrounds axons and facilitate the transmission of electrical signal along neurons in peripheral nervous system (PNS). Previous studies demonstrated that both Schwann cell differentiation and de-differentiation (in the situation of a nerve injury or demyelinating disease) are regulated by cell-intrinsic regulators including several transcription factors. In particular, the de-differentiation of mature Schwann cells is driven by the activation of multiple negative regulators of myelination including Sox2, c-Jun, Notch and Pax3, all usually expressed in immature Schwann cells and suppressed at the onset of myelination. In order to identify new regulators of myelination involved in the development of the PNS, we analyzed the gene-expression profiling data from developing PNS and from three models of demyelinating neuropathies. This analysis led to the identification of Sox4, a member of the Sox family of transcription factors, as a potential candidate. To characterize the molecular function of Sox4 in PNS, we generated two transgenic lines of mice, which overexpress Sox4 specifically in Schwann cells. Detailed analysis of these mice showed that the overexpression of Sox4 in Schwann cells causes a delay in progression of myelination between post-natal day 2 (P2) and P5. Our in vitro analysis suggested that Sox4 cDNA can be overexpressed while the protein translation is tightly regulated. Interestingly, we observed that Sox4 protein is stabilized in nerves of the CMT4C mouse, a model of the human neuropathy. We therefore crossed Sox4 transgenic mice with CMT4C mice and we observed that Sox4 overexpression exacerbated the neuropathy phenotype in these mice. While recognized as being crucial for the normal function of both neurons and myelinating glial cells, the processes that regulate the beginning of myelination and the nature of the neuro-glial cross-talk remains mostly unknown. In order to gain insight into the molecular pathways involved in the interactions between neurons and associated glial cells, we developed a neuron-glia co-culture system based on microfluidic chambers and successfully induced myelination in this system by ascorbic acid. Importantly, we observed that in addition to acting on Schwann cells, ascorbic acid also modulate neuronal/axonal NRG1/ErbB2-B3 signalling. The experimental setting used in our study thus allowed us to discover a novel phenomena of propagation for myelination in vitro. The further characterization of this event brought us to identify other compounds able to induce myelination: ADAMs secretases inhibitor GM6001 and cyclic-AMP. The results generated during my thesis project are therefore not only important for the advancement of our understanding of how the PNS works, but may also potentially help to develop new therapies aiming at improvement of PNS myelination under disease conditions. - Les cellules de Schwann synthétisent une grande quantité de membrane formant une structure spécialisée appelée myéline qui entoure les axones et facilite la transmission du signal électrique le long des neurones du système nerveux périphérique (SNP). Des études antérieures ont démontré que la différenciation et la dédifférenciation des cellules de Schwann (dans la situation d'une lésion nerveuse ou d'une maladie démyélinisante) sont régulées par des régulateurs cellulaires intrinsèques, incluant plusieurs facteurs de transcription. En particulier, la dédifférenciation des cellules de Schwann matures est contrôlée par l'activation de plusieurs régulateurs négatifs de la myélinisation dont Sox2, c-Jun, Notch et Pax3, tous habituellement exprimés dans des cellules de Schwann immatures et supprimés au début de la myélinisation. Afin d'identifier de nouveaux régulateurs de myélinisation impliqués dans le développement du SNP, nous avons analysé le profil d'expression génique durant le développement du SNP ainsi que dans trois modèles de neuropathies démyélinisantes. Cette analyse a mené à l'identification de Sox4, un membre de la famille des facteurs de transcription Sox, comme étant un candidat potentiel. Dans le but de caractériser la fonction moléculaire de Sox4 dans le SNP, nous avons généré deux lignées transgéniques de souris qui surexpriment Sox4 spécifiquement dans les cellules de Schwann. L'analyse détaillée de ces souris a montré que la surexpression de Sox4 dans les cellules de Schwann provoque un retard dans la progression de la myélinisation entre le jour postnatal 2 (P2) et P5. Notre analyse in vitro a suggéré que l'ADNc de Sox4 peut être surexprimé alors que la traduction des protéines est quand à elle étroitement régulée. De façon intéressante, nous avons observé que la protéine Sox4 est stabilisée dans les nerfs des souris CMT4C, un modèle de neuropathie humaine. Nous avons donc croisé les souris transgéniques Sox4 avec des souris CMT4C et avons observé que la surexpression de Sox4 exacerbe le phénotype de neuropathie chez ces souris. Bien que reconnus comme étant cruciaux pour le fonctionnement normal des neurones et des cellules gliales myélinisantes, les processus qui régulent le début de la myélinisation ainsi que la nature des interactions neurone-glie restent largement méconnus. Afin de mieux comprendre les mécanismes moléculaires impliqués dans les interactions entre les neurones et les cellules gliales leur étant associés, nous avons développé un système de co-culture neurone-glie basé sur des chambres microfluidiques et y avons induit avec succès la myélinisation avec de l'acide ascorbique. Étonnamment, nous avons remarqué que, en plus d'agir sur les cellules de Schwann, l'acide ascorbique module également la voie de signalisation neuronale/axonale NRG1/ErbB2-B3. Le protocole expérimental utilisé dans notre étude a ainsi permis de découvrir un nouveau phénomène de propagation de la myélinisation in vitro. La caractérisation plus poussée de ce phénomène nous a menés à identifier d'autres composés capables d'induire la myélinisation: L'inhibiteur de sécrétases ADAMs GM6001 et l'AMP cyclique. Les résultats obtenus au cours de mon projet de thèse ne sont donc pas seulement importants pour l'avancement de notre compréhension sur la façon dont le SNP fonctionne, mais peuvent aussi potentiellement aider à développer de nouvelles thérapies visant à l'amélioration de la myélinisation du SNP dans des conditions pathologiques.

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.

Fractional hepatic de novo lipogenesis in healthy subjects during near-continuous oral nutrition and bed rest: a comparison with published data in artificially fed, critically ill patients.

BACKGROUND AND AIMS: In critically ill patients, fractional hepatic de novo lipogenesis increases in proportion to carbohydrate administration during isoenergetic nutrition. In this study, we sought to determine whether this increase may be the consequence of continuous enteral nutrition and bed rest. We, therefore, measured fractional hepatic de novo lipogenesis in a group of 12 healthy subjects during near-continuous oral feeding (hourly isoenergetic meals with a liquid formula containing 55% carbohydrate). In eight subjects, near-continuous enteral nutrition and bed rest were applied over a 10 h period. In the other four subjects, it was extended to 34 h. Fractional hepatic de novo lipogenesis was measured by infusing(13) C-labeled acetate and monitoring VLDL-(13)C palmitate enrichment with mass isotopomer distribution analysis. Fractional hepatic de novo lipogenesis was 3.2% (range 1.5-7.5%) in the eight subjects after 10 h of near continuous nutrition and 1.6% (range 1.3-2.0%) in the four subjects after 34 h of near-continuous nutrition and bed rest. This indicates that continuous nutrition and physical inactivity do not increase hepatic de novo lipogenesis. Fractional hepatic de novo lipogenesis previously reported in critically ill patients under similar nutritional conditions (9.3%) (range 5.3-15.8%) was markedly higher than in healthy subjects (P<0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

Genotype 3 is associated with rapid histological progression in chronic HCV infection

While several risk factors for the histological progression of chronic hepatitis C have been identified, the contribution of HCV genotypes to liver fibrosis evolution remains controversial. The aim of the present study was to assess independent predictors for fibrosis progression. Methods: We identified 1540 patients from the Swiss Hepatitis C Cohort database with at least one liver biopsy prior to antiviral treatment. Factors associated with fibrosis stage, steatosis and histological activity were assessed in univariate and multivariate regression models. Fibrosis progression rate per year was calculated in a subgroup of 1263 patients, in whom risk factors were assessed by cumulative incidence curves, logistic and linear regression models. Results: Independent risk factors for rapid fibrosis progression included male sex (OR = 1.66, 95% CI 1.25-2.21, P <0.001), age at infection (OR = 1.08, 95% CI 1.06-1.10, P <0.001), histological activity (OR = 2.14, 95% CI 1.61-2.85, P <0.001) and genotype 3 (OR = 1.97, 95% CI 1.43-2.72, P <0.001). Genotype 2 was associated with slow progression (OR = 0.51, 95% CI 0.30-0.89, P = 0.02), but this observation may be due to the decreased prevalence of genotype 2 over the last decades, leading to an overrepresentation of subjects with genotype 2 with a slow progression rate. Conclusion: This study shows a significant association of genotype 3 with accelerated fibrosis. While assessing risk factors for fibrosis progression, the changing epidemiology of HCV genotypes over time needs to be taken into account.

Plasma Level of Mmp-9 as Predictive Factor for Response and Progression Free Survival in Patients Treated with Bevacizumab (Bev) and Pegylated Liposomal Doxorubicin (Pld): Sakk 24/06

Background: There is currently no identified marker predicting benefit from Bev in patients with breast cancer (pts). We monitored prospectively 6 angiogenesis-related factors in the blood of advanced stage pts treated with a combination of Bev and PLD in a phase II trial of the Swiss Group for Clinical Cancer Research, SAKK.Methods: Pts received PLD (20 mg/m2) and Bev (10 mg/kg) every 2 weeks for a maximum of 12 administrations, followed by Bev monotherapy until progression or severe toxicity. Blood samples were collected at baseline, during treatment and at treatment discontinuation. Enzyme-linked immunosorbent assays (Quantikine, R&DSystems and Reliatech) were used to measure vascular endothelial growth factor (VEGF), placental growth factor (PlGF), matrix metalloproteinase 9 (MMP-9) and soluble VEGF receptors -1, -2 and -3. The natural log-transformed (ln) data for each factor was analyzed by analysis of variance (ANOVA) model to investigate differences between the mean values of the subgroups of interest (where a = 0.05), based on the best tumor response by RECIST.Results: 132 samples were collected in 41 pts. The mean of baseline ln MMP-9 levels was significantly lower in pts with tumor progression than those with tumor response (p=0.0202, log fold change=0.8786) or disease control (p=0.0035, log fold change=0.8427). Higher MMP-9 level was a significant predictor of superior progression free survival (PFS): p=0.0417, hazard ratio=0.574, 95% CI=0.336-0.979. In a multivariate cox proportional hazards model, containing performance status, disease free interval, number of tumor sites, visceral involvement and prior adjuvant chemotherapy, using stepwise regression baseline MMP-9 was still a statistically 117P Table 1. SOLTI-0701* AC01B07* NU07B1* SOR+CAP N=20 PL+CAP N=33 SOR+ GEM/CAP N=23 PL+ GEM/CAP N=27 SOR+PAC N=48 PL+PAC N=46 Baseline characteristics Age, median (range), y 49 (32-72) 53 (30-78 54 (32-69) 57 (31-82) 50 (27-80) 52 (23-74) AJCC stage, n (%) IIIB/IIIC 3 (15) 6 (18) 0 (0) 3 (11) 8 (17) 9 (20) IV 17 (85) 27 (82) 23 (100) 24 (89) 40 (83) 37 (80) Metastatic site, n (%) Non-visceral 3 (15) 6 (18) 7 (30) 6 (22) 9 (19) 17 (37) Visceral 17 (85) 27 (82) 16 (70) 21 (78) 39 (81) 29 (63) Prior metastatic chemo, n (%) 8 (40) 15 (45) 21 (91) 25 (93) - - Efficacy PFS, median, mo 4.3 2.5 3.1 2.6 5.6 5.5 HR (95% CI)_ 0.60 (0.31, 1.14) 0.57 (0.30, 1.09) 0.86 (0.50, 1.45) 1-sided P value_ 0.055 0.044 0.281 Overall survival, median, mo 17.5 16.1 Pending 14.7 18.2 HR (95% CI)_ 0.98 (0.50, 1.89) 1.11 (0.64, 1.94) 1-sided P value_ 0.476 0.352 Safety N=20 N=33 N=22 N=27 N=46 N=46 Tx-emergent Grade 3/4, n (%) 15 (75) 16 (48) 20 (91) 17 (63) 36 (78) 16 (35) Grade 3§ hand-foot skin reaction/ syndrome 8 (40) 5 (15) 8 (36) 0 (0) 14 (30) 2 (4) *Efficacy results based on intent-to-treat population and safety results based on safety population (pts who received study drug[s]); _Cox regression within each subgroup; _log-rank test within each subgroup; §maximum toxicity grade for hand-foot skin reaction/syndrome; AJCC, American Joint Committee on Cancer mittedabstractsª The Author 2011. Published by Oxford University Press on behalf of the European Society for Medical Oncology. All rights reserved. For permissions, please email: journals.permissions@oup.com Downloaded from annonc.oxfordjournals.org at Bibliotheque Cantonale et Universitaire on June 6, 2011 significant factor (p=0.0266). The results of the other measured factors were presented elsewhere.Conclusions: Higher levels of MMP-9 could predict tumor response and superior PFSin pts treated with a combination of Bev and PLD. These exploratory results justify further investigations of MMP-9 in pts treated with Bev combinations in order to assess its role as a prognostic and predictive factor.Disclosure: K. Zaman: Participation in advisory board of Roche; partial sponsoring ofthe study by Roche (the main sponsor was the Swiss Federation against Cancer (Oncosuisse)). B. Thu¨rlimann: stock of Roche; Research grants from Roche. R. vonMoos: Participant of Advisory Board and Speaker honoraria