Residual-based localization and quantification of peaks in x-ray diffractograms

We consider data consisting of photon counts of diffracted x-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the power of the peaks is to be measured from a baseline which itself must be identified. Most methods of de-noising data of this kind do not explicitly take into account the modality of the final estimate. The residual-based procedure we propose uses the so-called taut string method, which minimizes the number of peaks subject to a tube constraint on the integrated data. The baseline is identified by combining the result of the taut string with an estimate of the first derivative of the baseline obtained using a weighted smoothing spline. Finally, each individual peak is expressed as the finite sum of kernels chosen from a parametric family.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS181 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Some results about diagonal operators on Köthe echelon spaces

[EN] Several questions about diagonal operators between Köthe echelon spaces are investigated: (1) The spectrum is characterized in terms of the Köthe matrices defining the spaces, (2) It is characterized when these operators are power bounded, mean ergodic or uniformly mean ergodic, and (3) A description of the topology in the space of diagonal operators induced by the strong topology on the space of all operators is given.This research was partially supported by MINECO Project MTM2016-76647-P and the grant PAID-01-16 of the Universitat Politècnica de València.Rodríguez-Arenas, A. (2019). Some results about diagonal operators on Köthe echelon spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):2959-2968. https://doi.org/10.1007/s13398-019-00663-yS295929681134Agathen, S., Bierstedt, K.D., Bonet, J.: Projective limits of weighted (LB)-spaces of continuous functions. Arch. Math. 92, 384–398 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34(2), 401–436 (2009)Bennett, G.: Some elementary inequalities. Quart. J. Math. 38, 401–425 (1987)Bennett, G.: Factorizing the classical inequalities. Mem. Am. Math. Soc. (1996). https://doi.org/10.1090/memo/0576Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces, Functional Analysis, Holomorphy and Approximation Theory. North-Holland Math. Studies 71, 27–91 (1982)Bonet, J., Jordá, E., Rodríguez-Arenas, A.: Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterr. J. Math 15, 108 (2018)Crofts, G.: Concerning perfect Fréchet spaces and transformations. Math. Ann. 182, 67–76 (1969)Kellogg, C.N.: An extension of the Hausdorff–Young theorem. Michig. Math. J. 18, 121–127 (1971)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, New York (1997)Vasilescu, F.H.: Analytic Functional Calculus and Spectral Decompositions. D. Reidel Publ. Co., Dordrecht (1982)Wengenroth, J.: Derived Functors in Functional Analysis. Springer, Berlin (2003)Yosida, K.: Functional Analysis. Springer, Berlin (1980

Mean ergodic multiplication operators on weighted spaces of continuous functions

[EN] Multiplication operators on weighted Banach spaces and locally convex spaces of continuous functions have been thoroughly studied. In this note, we characterize when continuous multiplication operators on a weighted Banach space and on a weighted inductive limit of Banach spaces of continuous functions are power bounded, mean ergodic or uniformly mean ergodic. The behaviour of the operator on weighted inductive limits depends on the properties of the defining sequence of weights and it differs from the Banach space case.The research of Bonet was partially supported by Project Prometeo/2017/102 of the Generalitat Valenciana. The authors authors were also partially supported by MINECO Project MTM2016-76647-P. Rodriguez also thanks the support of the Grant PAID-01-16 of the Universitat Politecnica de Valencia.Bonet Solves, JA.; Jorda Mora, E.; Rodríguez-Arenas, A. (2018). Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterranean Journal of Mathematics. 15(3):1:108-11:108. https://doi.org/10.1007/s00009-018-1150-8S1:10811:108153Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D.: A survey of some results and open problems in weighted inductive limits and projective description for spaces of holomorphic functions. Bull. Soc. Roy. Sci. Liège 70(4–6), 167–182 (2001)Bierstedt, K.D., Bonet, J.: Some recent results on VC(X). In: Advances in the theory of Fréchet spaces (Istanbul, 1988), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 287, pp. 181–194. Kluwer Acad. Publ., Dordrecht (1989)Bierstedt, K.D., Bonet, J.: Completeness of the (LB)-spaces VC(X). Arch. Math. (Basel) 56(3), 281–285 (1991)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272(1), 107–160 (1982)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces. In: Functional analysis, holomorphy and approximation theory, Rio de Janeiro, pp. 27–91 (1980)Bonet, J., Ricker, W.J.: Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions. Arch. Math. 92, 428–437 (2009)Klilou, M., Oubbi, L.: Multiplication operators on generalized weighted spaces of continuous functions. Mediterr. J. Math. 13(5), 3265–3280 (2016)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 2 (1974)Lotz, H.P.: Uniform convergence of operators on $$L^\infty$$ L ∞ and similar spaces. Math. Z. 190, 207–220 (1985)Manhas, J.S.: Compact multiplication operators on weighted spaces of vector-valued continuous functions. Rocky Mt. J. Math. 34(3), 1047–1057 (2004)Manhas, J.S.: Compact and weakly compact multiplication operators on weighted spaces of vector-valued continuous functions. Acta Sci. Math. (Szeged) 70(1–2), 361–372 (2004)Manhas, J.S., Singh, R.K.: Compact and weakly compact weighted composition operators on weighted spaces of continuous functions. Integral Equ. Oper. Theory 29(1), 63–69 (1997)Meise, R., Vogt, D.: Introduction to Functional Analysis. The Clarendon Press, Oxford University Press, New York (1997)Oubbi, L.: Multiplication operators on weighted spaces of continuous functions. Port. Math. (N.S.) 59(1), 111–124 (2002)Oubbi, L.: Weighted composition operators on non-locally convex weighted spaces. Rocky Mt. J. Math. 35(6), 2065–2087 (2005)Singh, R.K., Manhas, J.S.: Multiplication operators on weighted spaces of vector-valued continuous functions. J. Austral. Math. Soc. Ser. A 50(1), 98–107 (1991)Singh, R.K., Manhas, J.S.: Composition operators on function spaces. North-Holland Publishing Co., Amsterdam (1993)Singh, R.K., Manhas, J.S.: Operators and dynamical systems on weighted function spaces. Math. Nachr. 169, 279–285 (1994)Wilanski, A.: Topology for Analysis. Ginn, Waltham (1970)Yosida, K.: Functional Analysis. Springer, Berlin (1980

Comparative Assessment of Climate Change Scenarios Based on Aquatic Food Web Modeling

In the years 2004 and 2005, we collected samples of phytoplankton, zooplankton, and macroinvertebrates in an artificial small pond in Budapest (Hungary). We set up a simulation model predicting the abundances of the cyclopoids, Eudiaptomus zachariasi, and Ischnura pumilio by considering only temperature and the abundance of population of the previous day. Phytoplankton abundance was simulated by considering not only temperature but the abundances of the three mentioned groups. When we ran the model with the data series of internationally accepted climate change scenarios, the different outcomes were discussed. Comparative assessment of the alternative climate change scenarios was also carried out with statistical methods

Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis

[EN] We use techniques from time-frequency analysis to show that the space S(omega )of rapidly decreasing omega-ultradifferentiable functions is nuclear for every weight function omega(t) = o(t) as t tends to infinity. Moreover, we prove that, for a sequence (M-p)(p) satisfying the classical condition (M1) of Komatsu, the space of Beurling type S-(M)p when defined with L-2 norms is nuclear exactly when condition (M2)' of Komatsu holds.We thank the reviewer very much for the careful reading of our manuscript and the comments to improve the paper. The first three authors were partially supported by the Project FFABR 2017 (MIUR), and by the Projects FIR 2018 and FAR 2018 (University of Ferrara). The first and third authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The research of the second author was partially supported by the project MTM2016-76647-P and the grant BEST/2019/172 from Generalitat Valenciana. The fourth author is supported by FWF-project J 3948-N35.Boiti, C.; Jornet Casanova, D.; Oliaro, A.; Schindl, G. (2021). Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis. Collectanea mathematica. 72(2):423-442. https://doi.org/10.1007/s13348-020-00296-0S423442722Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. London Math. Soc. 2(78), 392–406 (2008)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 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, 920–944 (2017)Boiti, C., Jornet, D., Oliaro, A.: The Gabor wave front set in spaces of ultradifferentiable functions. Monatsh. Math. 188(2), 199–246 (2019)Boiti, C., Jornet, D., Oliaro, A.: About the nuclearity of $$\cal{S}_{(M_{p})}$$ and $$\cal{S}_{\omega }$$. In: Boggiatto, P., et al. (eds.) Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis, pp. 121–129. Birkhäuser, Cham (2020)Boiti, C., Jornet, D., Oliaro, A.: Real Paley-Wiener theorems in spaces of ultradifferentiable functions. J. Funct. Anal. 278(4), 108348 (2020)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. Result. Math. 17, 206–237 (1990)Fernández, 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)Franken, U.: Weight functions for classes of ultradifferentiable functions. Results Math. 25, 50–53 (1994)Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)Gröchenig, K., Leinert, M.: Wiener’s Lemma for twisted convolution and Gabor frames. J. Am. Math. Soc. 17(1), 1–18 (2004)Gröchenig, K., Zimmermann, G.: Spaces of Test Functions via the STFT. J. Funct. Spaces Appl. 2(1), 25–53 (2004)Heinrich, T., Meise, R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364–387 (2007)Hörmander, L.: Notions of Convexity. Progress in Mathematics, vol. 127. Birkhäuser, Boston (1994)Janssen, A.J.E.M.: Duality and Biorthogonality for Weyl-Heisenberg Frames. J. Fourier Anal. Appl. 1(4), 403–436 (1995)Komatsu, H.: Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect IA Math. 20, 25–105 (1973)Langenbruch, M.: Hermite functions and weighted spaces of generalized functions. Manuscripta Math. 119(3), 269–285 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Petzsche, H.J.: Die nuklearität der ultradistributionsräume und der satz vom kern I. Manuscripta Math. 24, 133–171 (1978)Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)Pilipović, S., Prangoski, B., Vindas, J.: On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution. J. Math. Pures Appl. 116, 174–210 (2018)Rodino, L.: Linear Partial Differential Operators in Gevrey Spaces. World Scientific Publishing Co. Inc, River Edge, NJ (1993)Rodino, L., Wahlberg, P.: The Gabor wave front set. Monatsh. Math. 173, 625–655 (2014)Schmets, J., Valdivia, M.: Analytic extension of ultradifferentiable Whitney jets. Collect. Math. 50(1), 73–94 (1999

The Cesàro operator on Korenblum type spaces of analytic functions

[EN] The spectrum of the CesA ro operator , which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fr,chet or (LB) spaces of analytic functions on the open unit disc, is completely determined. It turns out that such spaces are always Schwartz but, with the exception of the Korenblum space, never nuclear. Some consequences concerning the mean ergodicity of are deduced.The research of the first two authors was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2018). The Cesàro operator on Korenblum type spaces of analytic functions. Collectanea mathematica. 69(2):263-281. https://doi.org/10.1007/s13348-017-0205-7S263281692Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. 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Math. 127, 137–168 (1998)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272, 107–160 (1982)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 54, 70–79 (1993)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 64, 101–118 (1998)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge University Press, Cambridge (1995)Domenig, T.: Composition operators on weighted Bergman spaces and Hardy spaces. Atomic Decompositions and Diagonal Operators, Ph.D. Thesis, University of Zürich (1997). [Zbl 0909.47025]Domenig, T.: Composition operators belonging to operator ideals. J. Math. Anal. Appl. 237, 327–349 (1999)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory. 2nd Printing. Wiley Interscience Publ., New York (1964)Edwards, R.E.: Functional Analysis. Theory and Applications. Holt, Rinehart and Winston, New York, Chicago San Francisco (1965)Grothendieck, A.: Topological Vector Spaces. Gordon and Breach, London (1973)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics, vol. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–40 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Melikhov, S.N.: (DFS )-spaces of holomorphic functions invariant under differentiation. J. Math. Anal. Appl. 297, 577–586 (2004)Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal Appl. 340, 1180–1203 (2008)Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)Siskakis, A.: Volterra operators on spaces of analytic functions—a survey. In: Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, pp. 51–68 (2006

Effects of school-based interventions on mental health stigmatization: a systematic review

Stigmatizing, or discriminatory, perspectives and behaviour, which target individuals on the basis of their mental health, are observed in even the youngest school children. We conducted a systematic review of the published and unpublished, scientific literature concerning the benefits and harms of school-based interventions, which were directed at students 18 years of age or younger to prevent or eliminate such stigmatization. Forty relevant studies were identified, yet only a qualitative synthesis was deemed appropriate. Five limitations within the evidence base constituted barriers to drawing conclusive inferences about the effectiveness and harms of school-based interventions: poor reporting quality, a dearth of randomized controlled trial evidence, poor methods quality for all research designs, considerable clinical heterogeneity, and inconsistent or null results. Nevertheless, certain suggestive evidence derived both from within and beyond our evidence base has allowed us to recommend the development, implementation and evaluation of a curriculum, which fosters the development of empathy and, in turn, an orientation toward social inclusion and inclusiveness. These effects may be achieved largely by bringing especially but not exclusively the youngest children into direct, structured contact with an infant, and likely only the oldest children and youth into direct contact with individuals experiencing mental health difficulties. The possible value of using educational activities, materials and contents to enhance hypothesized benefits accruing to direct contact also requires investigation. Overall, the curriculum might serve as primary prevention for some students and as secondary prevention for others

Discovery and population genomics of structural variation in a songbird genus

Structural variation (SV) constitutes an important type of genetic mutations providing the raw material for evolution. Here, we uncover the genome-wide spectrum of intra- and interspecific SV segregating in natural populations of seven songbird species in the genus Corvus. Combining short-read (N = 127) and long-read re-sequencing (N = 31), as well as optical mapping (N = 16), we apply both assembly- and read mapping approaches to detect SV and characterize a total of 220,452 insertions, deletions and inversions. We exploit sampling across wide phylogenetic timescales to validate SV genotypes and assess the contribution of SV to evolutionary processes in an avian model of incipient speciation. We reveal an evolutionary young (~530,000 years) cis-acting 2.25-kb LTR retrotransposon insertion reducing expression of the NDP gene with consequences for premating isolation. Our results attest to the wealth and evolutionary significance of SV segregating in natural populations and highlight the need for reliable SV genotyping

Optimizing suicide prevention programs and their implementation in Europe (OSPI Europe): an evidence-based multi-level approach

Background Suicide and non-fatal suicidal behaviour are significant public health issues in Europe requiring effective preventive interventions. However, the evidence for effective preventive strategies is scarce. The protocol of a European research project to develop an optimized evidence based program for suicide prevention is presented. Method The groundwork for this research has been established by a regional community based intervention for suicide prevention that focuses on improving awareness and care for depression performed within the European Alliance Against Depression (EAAD). The EAAD intervention consists of (1) training sessions and practice support for primary care physicians,(2) public relations activities and mass media campaigns, (3) training sessions for community facilitators who serve as gatekeepers for depressed and suicidal persons in the community and treatment and (4) outreach and support for high risk and self-help groups (e.g. helplines). The intervention has been shown to be effective in reducing suicidal behaviour in an earlier study, the Nuremberg Alliance Against Depression. In the context of the current research project described in this paper (OSPI-Europe) the EAAD model is enhanced by other evidence based interventions and implemented simultaneously and in standardised way in four regions in Ireland, Portugal, Hungary and Germany. The enhanced intervention will be evaluated using a prospective controlled design with the primary outcomes being composite suicidal acts (fatal and non-fatal), and with intermediate outcomes being the effect of training programs, changes in public attitudes, guideline-consistent media reporting. In addition an analysis of the economic costs and consequences will be undertaken, while a process evaluation will monitor implementation of the interventions within the different regions with varying organisational and healthcare contexts. Discussion This multi-centre research seeks to overcome major challenges of field research in suicide prevention. It pools data from four European regions, considerably increasing the study sample, which will be close to one million. In addition, the study will gather important information concerning the potential to transfer this multilevel program to other health care systems. The results of this research will provide a basis for developing an evidence-based, efficient concept for suicide prevention for EU-member states