An Integral Kernel for Weakly Pseudoconvex Domains

A new explicit construction of Cauchy-Fantappi\'e kernels is introduced for an arbitrary weakly pseudoconvex domain with smooth boundary. While not holomorphic in the parameter, the new kernel reflects the complex geometry and the Levi form of the boundary. Some estimates are obtained for the corresponding integral operator, which provide evidence that this kernel and related constructions give useful new tools for complex analysis on this general class of domains

Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.Comment: 20 page

Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions

[EN] We develop a theory of pseudodifferential operators of infinite order for the global classes S. of ultradifferentiable functions in the sense of Bjorck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.The first author was partially supported by the project GV Prometeo 2017/102, and the second author by the project MTM2016-76647-P. This article is part of the PhD. Thesis of V. Asensio. The authors are very grateful to the two referees for the careful reading and their suggestions and comments, which improved the paper.Asensio, V.; Jornet Casanova, D. (2019). Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3477-3512. https://doi.org/10.1007/s13398-019-00710-8S347735121134Albanese, A.A., Jornet, D., Oliaro, A.: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Math. Nachr. 285(4), 411–425 (2012)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6, 351–407 (1966)Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446(1), 920–944 (2017)Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Results Math. 17(3–4), 206–237 (1990)Braun, R.W.: An extension of Komatsu’s second structure theorem for ultradistributions. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40(2), 411–417 (1993)Cappiello, M.: Fourier integral operators of infinite order and applications to SG-hyperbolic equations. Tsukuba J. Math. 28(2), 311–361 (2004)Cappiello, M., Pilipović, S., Prangoski, B.: Parametrices and hypoellipticity for pseudodifferential operators on spaces of tempered ultradistributions. J. Pseudo-Differ. Oper. Appl. 5(4), 491–506 (2014)Fernández, C., Galbis, A., Jornet, D.: $$\omega$$-hypoelliptic differential operators of constant strength. J. Math. Anal. Appl. 297(2), 561–576 (2004). Special issue dedicated to John HorváthFernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Math. 167(2), 99–131 (2005)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)Hashimoto, S., Morimoto, Y., Matsuzawa, T.: Opérateurs pseudodifférentiels et classes de Gevrey. Commun. Partial Differ. Equ. 8(12), 1277–1289 (1983)Hörmander, L.: Pseudo-differential operators. Commun. Pure Appl. Math. 18, 501–517 (1965)Kohn, J.J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. Pure Appl. Math. 18, 269–305 (1965)Komatsu, H.: Ultradistributions. I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20, 25–105 (1973)Langenbruch, M.: Continuation of Gevrey regularity for solutions of partial differential operators. In Functional analysis (Trier, 1994), pages 249–280. de Gruyter, Berlin (1996)Nicola, F.: Rodino, Luigi: Global pseudo-differential calculus on Euclidean spaces, volume 4 of Pseudo-Differential Operators. Theory and Applications. Birkhäuser Verlag, Basel (2010)Prangoski, B.: Pseudodifferential operators of infinite order in spaces of tempered ultradistributions. J. Pseudo-Differ. Oper. Appl. 4(4), 495–549 (2013)Rodino, L.: Linear partial differential operators in Gevrey spaces. World Scientific Publishing Co., Inc., River Edge (1993)Shubin, M.A.: Pseudodifferential operators and spectral theory. Springer-Verlag, Berlin, second edition. Translated from the 1978 Russian original by Stig I. Andersson (2001)Zanghirati, L.: Pseudodifferential operators of infinite order and Gevrey classes. Ann. Univ. Ferrara Sez. VII (N.S.) 31, 197–219, 1985 (1986

Adaptive Filtering Enhances Information Transmission in Visual Cortex

Sensory neuroscience seeks to understand how the brain encodes natural environments. However, neural coding has largely been studied using simplified stimuli. In order to assess whether the brain's coding strategy depend on the stimulus ensemble, we apply a new information-theoretic method that allows unbiased calculation of neural filters (receptive fields) from responses to natural scenes or other complex signals with strong multipoint correlations. In the cat primary visual cortex we compare responses to natural inputs with those to noise inputs matched for luminance and contrast. We find that neural filters adaptively change with the input ensemble so as to increase the information carried by the neural response about the filtered stimulus. Adaptation affects the spatial frequency composition of the filter, enhancing sensitivity to under-represented frequencies in agreement with optimal encoding arguments. Adaptation occurs over 40 s to many minutes, longer than most previously reported forms of adaptation.Comment: 20 pages, 11 figures, includes supplementary informatio

Structure of hadron resonances with a nearby zero of the amplitude

We discuss the relation between the analytic structure of the scattering amplitude and the origin of an eigenstate represented by a pole of the amplitude.If the eigenstate is not dynamically generated by the interaction in the channel of interest, the residue of the pole vanishes in the zero coupling limit. Based on the topological nature of the phase of the scattering amplitude, we show that the pole must encounter with the Castillejo-Dalitz-Dyson (CDD) zero in this limit. It is concluded that the dynamical component of the eigenstate is small if a CDD zero exists near the eigenstate pole. We show that the line shape of the resonance is distorted from the Breit-Wigner form as an observable consequence of the nearby CDD zero. Finally, studying the positions of poles and CDD zeros of the KbarN-piSigma amplitude, we discuss the origin of the eigenstates in the Lambda(1405) region.Comment: 7 pages, 3 figures, v2: published versio

Mindergie: A pervasive learning game for pro-environmental behaviour at the workplace

This chapter reports about a pervasive learning game to increase the environmental awareness and pro-environmental behaviour at the workplace. Based on a discussion of the theoretical background and related work we introduce the game design and game elements. Results of a formative evaluation study are presented and discussed. Results show that incentive mechanisms are less important than challenging game components that involve employees in proposing solutions for energy conservation at the workplace. Conclusions are drawn for future games and energy conservation activities at the workplace.This project has been partially funded by a SURFnet innovation grant for sustainable ICT solutions and partially by the Welten Institute – Research Centre for Learning, Teaching and Technology of the Open University of the Netherlands

Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments.

Searches for electron antineutrino, muon neutrino, and muon antineutrino disappearance driven by sterile neutrino mixing have been carried out by the Daya Bay and MINOS+ collaborations. This Letter presents the combined results of these searches, along with exclusion results from the Bugey-3 reactor experiment, framed in a minimally extended four-neutrino scenario. Significantly improved constraints on the θ_{μe} mixing angle are derived that constitute the most constraining limits to date over five orders of magnitude in the mass-squared splitting Δm_{41}^{2}, excluding the 90% C.L. sterile-neutrino parameter space allowed by the LSND and MiniBooNE observations at 90% CL_{s} for Δm_{41}^{2}<13  eV^{2}. Furthermore, the LSND and MiniBooNE 99% C.L. allowed regions are excluded at 99% CL_{s} for Δm_{41}^{2}<1.6 eV^{2}

What are the consequences of combining nuclear and mitochondrial data for phylogenetic analysis? Lessons from Plethodon salamanders and 13 other vertebrate clades

<p>Abstract</p> <p>Background</p> <p>The use of mitochondrial DNA data in phylogenetics is controversial, yet studies that combine mitochondrial and nuclear DNA data (mtDNA and nucDNA) to estimate phylogeny are common, especially in vertebrates. Surprisingly, the consequences of combining these data types are largely unexplored, and many fundamental questions remain unaddressed in the literature. For example, how much do trees from mtDNA and nucDNA differ? How are topological conflicts between these data types typically resolved in the combined-data tree? What determines whether a node will be resolved in favor of mtDNA or nucDNA, and are there any generalities that can be made regarding resolution of mtDNA-nucDNA conflicts in combined-data trees? Here, we address these and related questions using new and published nucDNA and mtDNA data for <it>Plethodon </it>salamanders and published data from 13 other vertebrate clades (including fish, frogs, lizards, birds, turtles, and mammals).</p> <p>Results</p> <p>We find widespread discordance between trees from mtDNA and nucDNA (30-70% of nodes disagree per clade), but this discordance is typically not strongly supported. Despite often having larger numbers of variable characters, mtDNA data do not typically dominate combined-data analyses, and combined-data trees often share more nodes with trees from nucDNA alone. There is no relationship between the proportion of nodes shared between combined-data and mtDNA trees and relative numbers of variable characters or levels of homoplasy in the mtDNA and nucDNA data sets. Congruence between trees from mtDNA and nucDNA is higher on branches that are longer and deeper in the combined-data tree, but whether a conflicting node will be resolved in favor mtDNA or nucDNA is unrelated to branch length. Conflicts that are resolved in favor of nucDNA tend to occur at deeper nodes in the combined-data tree. In contrast to these overall trends, we find that <it>Plethodon </it>have an unusually large number of strongly supported conflicts between data types, which are generally resolved in favor of mtDNA in the combined-data tree (despite the large number of nuclear loci sampled).</p> <p>Conclusions</p> <p>Overall, our results from 14 vertebrate clades show that combined-data analyses are not necessarily dominated by the more variable mtDNA data sets. However, given cases like <it>Plethodon</it>, there is also the need for routine checking of incongruence between mtDNA and nucDNA data and its impacts on combined-data analyses.</p

Weekly cisplatin and daily oral etoposide is highly effective in platinum pretreated ovarian cancer

We investigated the potential of weekly cisplatin and daily oral etoposide followed by oral etoposide maintenance therapy in patients with platinum-refractory ovarium cancer. One hundred and seven patients were entered on the study, 98 patients completed the induction therapy consisting of cisplatin at either 50 or 70 mg m−2 weekly for six administrations plus oral etoposide at a dose of 50 mg daily. Of these 98 patients, 38 had a platinum treatment-free interval of more than 12 months, 32 had an interval between 4 and 12 months, and 28 had progressed during or within 4 months after last platinum therapy. We assessed response rates and time to progression, and also response duration and survival. Analyses were done on the 98 evaluable patients. All 107 patients were considered evaluable for toxicity. Of the 38 patients with a treatment-free interval of more than 12 months, 92% responded, with 63% complete responses. The median progression-free survival in these patients was 14 months, and the median survival was 26 months. Of the 32 patients with an interval of 4–12 months, 91% responded, with 31% complete responses, a median progression-free interval of 8 and a median overall survival of 16 months. Of the 28 patients with platinum-refractory disease, 46% as yet responded, with 29% complete responses, median progression-free interval of 5 and an overall survival of 13 months. Haematologic and non-haematologic, particularly renal toxicity and neurotoxicity, were notably mild. We conclude that this intensive regimen of weekly cisplatin plus daily etoposide is highly effective and well tolerated in patients with ovarian cancer relapsing after conventional platinum-based combination chemotherapy, including patients who have progressed during or within 4 months after platinum treatment