A note on complex plane curve singularities up to diffeomorphism and their rigidity

We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by Ephraim for irreducible hypersurfaces before, but his proof is not constructive. Indeed, we show that the complex isomorphism is given by the Taylor series of the diffeomorphism. We also prove an analogous result for the case of non-irreducible hypersurfaces containing an irreducible component of zero-dimensional isosingular locus. Moreover, we provide a general overview of the different classifications of plane curve singularities

Chaos for the Hyperbolic Bioheat Equation

The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that this chaotic behaviour still appears when we add a source term to this equation, i.e. in the Hyperbolic Bioheat Equation. These results can also be applied for the Wave Equation and for a higher order version of the Hyperbolic Bioheat Equation.The authors are supported in part by MEC and FEDER, Projects MTM2010-14909 and MTM2013-47093-P.Conejero, JA.; Ródenas Escribá, FDA.; Trujillo Guillen, M. (2015). Chaos for the Hyperbolic Bioheat Equation. Discrete and Continuous Dynamical Systems - Series A. 35(2):653-668. doi:10.3934/dcds.2015.35.653S65366835

Monitoring dynamics of human adenovirus disassembly induced by mechanical fatigue

The standard pathway for virus infection of eukaryotic cells requires disassembly of the viral shell to facilitate release of the viral genome into the host cell. Here we use mechanical fatigue, well below rupture strength, to induce stepwise disruption of individual human adenovirus particles under physiological conditions, and simultaneously monitor disassembly in real time. Our data show the sequence of dismantling events in individual mature (infectious) and immature (noninfectious) virions, starting with consecutive release of vertex structures followed by capsid cracking and core exposure. Further, our experiments demonstrate that vertex resilience depends inextricably on maturation, and establish the relevance of penton vacancies as seeding loci for virus shell disruption. The mechanical fatigue disruption route recapitulates the adenovirus disassembly pathway in vivo, as well as the stability differences between mature and immature virionsWe acknowledge funding by grants from the Ministry of Science and Innovation of Spain, PIB2010US-00233, FIS2011-29493, Consolider CSD2010-00024 and CAM project and the Comunidad de Madrid No. S2009/MAT-1467 to P. J. P.; BFU2010-16382/BMC to C.S.M.; and FIS2011-16090-E to C.S.M. and P.J.P. S.J.F acknowledges funding from the National Institutes of Health, USA (GM037705 and AI1058172). A.J.P.-B. holds a Juan de la Cierva postdoctoral contract from the Ministry of Science and Innovation of Spain; A.O.-E. and R.M.-C. are recipients of predoctoral fellowships from the Ministry of Education and the Instituto de Salud Carlos III of Spain, respectivel

Generation of ultra-short light pulses by a rapidly ionizing thin foil

A thin and dense plasma layer is created when a sufficiently strong laser pulse impinges on a solid target. The nonlinearity introduced by the time-dependent electron density leads to the generation of harmonics. The pulse duration of the harmonic radiation is related to the risetime of the electron density and thus can be affected by the shape of the incident pulse and its peak field strength. Results are presented from numerical particle-in-cell-simulations of an intense laser pulse interacting with a thin foil target. An analytical model which shows how the harmonics are created is introduced. The proposed scheme might be a promising way towards the generation of attosecond pulses. PACS number(s): 52.40.Nk, 52.50.Jm, 52.65.RrComment: Second Revised Version, 13 pages (REVTeX), 3 figures in ps-format, submitted for publication to Physical Review E, WWW: http://www.physik.tu-darmstadt.de/tqe

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915

Qualitative and Quantitative Performance of 18 F-FDG-PET/MRI versus 18 F-FDG-PET/CT in Patients with Head and Neck Cancer

ABSTRACT BACKGROUND AND PURPOSE: MR imaging and PET/CT are integrated in the work-up of head and neck cancer patients. The hybrid imaging technology 18 F-FDG-PET/MR imaging combining morphological and functional information might be attractive in this patien

miR-146a rs2431697 identifies myeloproliferative neoplasm patients with higher secondary myelofibrosis progression risk

Myelofibrosis (MF) occurs as part of the natural history of polycythemia vera (PV) and essential thrombocythemia (ET), and remarkably shortens survival. Although JAK2V617F and CALR allele burden are the main transformation risk factors, inflammation plays a critical role by driving clonal expansion toward end-stage disease. NF-κB is a key mediator of inflammation-induced carcinogenesis. Here, we explored the involvement of miR-146a, a brake in NF-κB signaling, in MPN susceptibility and progression. rs2910164 and rs2431697, that affect miR-146a expression, were analyzed in 967 MPN (320 PV/333 ET/314 MF) patients and 600 controls. We found that rs2431697 TT genotype was associated with MF, particularly with post-PV/ET MF (HR = 1.5; p < 0.05). Among 232 PV/ET patients (follow-up time=8.5 years), 18 (7.8%) progressed to MF, being MF-free-survival shorter for rs2431697 TT than CC + CT patients (p = 0.01). Multivariate analysis identified TT genotype as independent predictor of MF progression. In addition, TT (vs. CC + CT) patients showed increased plasma inflammatory cytokines. Finally, miR-146a−/− mice showed significantly higher Stat3 activity with aging, parallel to the development of the MF-like phenotype. In conclusion, we demonstrated that rs2431697 TT genotype is an early predictor of MF progression independent of the JAK2V617F allele burden. Low levels of miR-146a contribute to the MF phenotype by increasing Stat3 signaling

Energy Prediction for Cloud Workload Patterns

The excessive use of energy consumption in Cloud infrastructures has become one of the major cost factors for Cloud providers to maintain. In order to enhance the energy efficiency of Cloud resources, proactive and reactive management tools are used. However, these tools need to be supported with energy-awareness not only at the physical machine (PM) level but also at virtual machine (VM) level in order to enhance decision-making. This paper introduces an energy-aware profiling model to identify energy consumption for heterogeneous and homogeneous VMs running on the same PM and presents an energy-aware prediction framework to forecast future VMs energy consumption. This framework first predicts the VMs’ workload based on historical workload patterns using Autoregressive Integrated Moving Average (ARIMA) model. The predicted VM workload is then correlated to the physical resources within this framework in order to get the predicted VM energy consumption. Compared with actual results obtained in a real Cloud testbed, the predicted results show that this energy-aware prediction framework can get up to 2.58 Mean Percentage Error (MPE) for the VM workload prediction, and up to −4.47 MPE for the VM energy prediction based on periodic workload pattern

Well-posedness for degenerate third order equations with delay and applications to inverse problems

[EN] In this paper, we study well-posedness for the following third-order in time equation with delay <disp-formula idoperators defined on a Banach space X with domains D(A) and D(B) such that t)is the state function taking values in X and u(t): (-, 0] X defined as u(t)() = u(t+) for < 0 belongs to an appropriate phase space where F and G are bounded linear operators. Using operator-valued Fourier multiplier techniques we provide optimal conditions for well-posedness of equation (0.1) in periodic Lebesgue-Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel-Lizorkin spaces Fp,qs(T,X). A novel application to an inverse problem is given.The first, second and third authors have been supported by MEC, grant MTM2016-75963-P. The second author has been supported by AICO/2016/30. The fourth author has been supported by MEC, grant MTM2015-65825-P.Conejero, JA.; Lizama, C.; Murillo-Arcila, M.; Seoane Sepúlveda, JB. (2019). 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