The impact of organ motion and the appliance of mitigation strategies on the effectiveness of hypoxia-guided proton therapy for non-small cell lung cancer.

BACKGROUND AND PURPOSE To investigate the impact of organ motion on hypoxia-guided proton therapy treatments for non-small cell lung cancer (NSCLC) patients. MATERIALS AND METHODS Hypoxia PET and 4D imaging data of six NSCLC patients were used to simulate hypoxia-guided proton therapy with different motion mitigation strategies including rescanning, breath-hold, respiratory gating and tumour tracking. Motion-induced dose degradation was estimated for treatment plans with dose painting of hypoxic tumour sub-volumes at escalated dose levels. Tumour control probability (TCP) and dosimetry indices were assessed to weigh the clinical benefit of dose escalation and motion mitigation. In addition, the difference in normal tissue complication probability (NTCP) between escalated proton and photon VMAT treatments have been assessed. RESULTS Motion-induced dose degradation was found for target coverage (CTV V95% up to -4%) and quality of the dose-escalation-by-contour (QRMS up to 6%) as a function of motion amplitude and amount of dose escalation. The TCP benefit coming from dose escalation (+4-13%) outweighs the motion-induced losses (<2%). Significant average NTCP reductions of dose-escalated proton plans were found for lungs (-14%), oesophagus (-10%) and heart (-16%) compared to conventional VMAT plans. The best plan dosimetry was obtained with breath hold and respiratory gating with rescanning. CONCLUSION NSCLC affected by hypoxia appears to be a prime target for proton therapy which, by dose-escalation, allows to mitigate hypoxia-induced radio-resistance despite the sensitivity to organ motion. Furthermore, substantial reduction in normal tissue toxicity can be expected compared to conventional VMAT. Accessibility and standardization of hypoxia imaging and clinical trials are necessary to confirm these findings in a clinical setting

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Convergence of arithmetic means of operators in Fréchet spaces

Every Köthe echelon Fréchet space XX that is Montel and not isomorphic to a countable product of copies of the scalar field admits a power bounded continuous linear operator TT such that I−TI−T does not have closed range, but the sequence of arithmetic means of the iterates of TT converges to 0 uniformly on the bounded sets in XX. On the other hand, if XX is a Fréchet space which does not have a quotient isomorphic to a nuclear Köthe echelon space with a continuous norm, then the sequence of arithmetic means of the iterates of any continuous linear operator TT (for which (1/n)Tn(1/n)Tn converges to 0 on the bounded sets) converges uniformly on the bounded subsets of XX, i.e., TT is uniformly mean ergodic, if and only if the range of I−TI−T is closed. This result extends a theorem due to Lin for such operators on Banach spaces. The connection of Browder’s equality for power bounded operators on Fréchet spaces to their uniform mean ergodicity is exposed. An analysis of the mean ergodic properties of the classical Cesàro operator on Banach sequence spaces is also given. © 2012 Elsevier Ltd. All rights reserved.The research of Jose Bonet was partially supported by MEC and FEDER Project MTM 2007-62643, GV Project Prometeo/2008/101 (Spain) and ACOMP/2012/090.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2013). Convergence of arithmetic means of operators in Fréchet spaces. Journal of Mathematical Analysis and Applications. 401(1):160-173. https://doi.org/10.1016/j.jmaa.2012.11.060S160173401

All genera of Flaviviridae host a conserved Xrn1-resistant RNA motif

Computer Systems, Imagery and Medi

Completeness in the Mackey topology

Bonet and Cascales [Non-complete Mackey topologies on Banach spaces, Bulletin of the Australian Mathematical Society, 81, 3 (2010), 409-413], answering a question of M. Kunze and W. Arendt, gave an example of a norming norm-closed subspace N of the dual of a Banach space X such that mu(X, N) is not complete,where mu(X, N) denotes the Mackey topology associated with the dual pair aEuroX, NaEuro parts per thousand. We prove in this note that we can decide on the completeness or incompleteness of topologies of this form in a quite general context, thus providing large classes of counterexamples to the aforesaid question. Moreover, our examples use subspaces N of X* that contain a predual P of X (if exists), showing that the phenomenon of noncompleteness that Kunze and Arendt were looking for is not only relatively common but illustrated by "well-located" subspaces of the dual. We discuss also the situation for a typical Banach space without a predual-the space c (0)-and for the James space J.The first author is supported in part by MICINN and FEDER (project no. MTM2008-05396), by Fundacion Seneca (project no. 08848/PI/08), by Generalitat Valenciana (GV/2010/036), and by Universitat Politecnica de Valencia (project no. PAID-06-09-2829). The second author is supported in part by MICINN project no. MTM2011-22417, by Generalitat Valenciana (GV/2010/036), and by Universidad Politecnica de Valencia (project no. PAID-06-09-2829).Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2015). Completeness in the Mackey topology. Functional Analysis and Its Applications. 49(2):97-105. https://doi.org/10.1007/s10688-015-0091-2S97105492J. Bonet and B. Cascales, “Non-complete Mackey topologies on Banach spaces,” Bull. Aust. Math. Soc., 81:3 (2010), 409–413.M. Fabian, P. Habala, P. Hájek, V. Montesinos, and V. Zizler, Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Math., Springer-Verlag, New York, 2011.P. Pérez-Carreras and J. Bonet, Barreled Locally Convex Spaces, North-Holland Mathematical Studies, vol. 131, North-Holland, Amsterdam, 1987.P. Civin and B. Yood, “Quasi-reflexive spaces,” Proc. Amer. Math. Soc., 8:5 (1957), 906–911.J. Diestel, Sequences and Series in Banach Spaces, Graduate Text in Math., vol. 92, Springer-Verlag, New York, 1984.K. Floret, Weakly Compact Sets, Lecture Notes in Math., vol. 801, Springer-Verlag, Berlin, 1980.G. Godefroy, “Boundaries of convex sets and interpolation sets,” Math. Ann., 277:2 (1987), 173–184.R. C. James, “On nonreflexive Banach space isometric with its second conjugate,” Proc. Nat. Acad. Sci. USA, 37 (1951), 174–177.G. Köthe, Topological Vector Spaces I, Springer-Verlag, New York, 1969

Compact convex sets in 2-dimensional asymmetric normed lattices

[EN] In this note, we study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex set with non empty interior in (R-2, q), where q is an asymmetric lattice norm.The first author has been supported by CONACYT (Mexico) under Grant 204028. The second author has been supported by the Ministerio de Economia y Competitividad (Spain) under Grant MTM2012-36740-C02-02.Jonard-Perez, N.; Sánchez Pérez, EA. (2016). Compact convex sets in 2-dimensional asymmetric normed lattices. Quaestiones Mathematicae. 39(1):73-82. https://doi.org/10.2989/16073606.2015.1023864S738239

Improving insect conservation management through insect monitoring and stakeholder involvement

In recent years, the decline of insect biodiversity and the imminent loss of provided ecosystem functions and services has received public attention and raised the demand for political action. The complex, multi-causal contributors to insect decline require a broad interdisciplinary and cross-sectoral approach that addresses ecological and social aspects to find sustainable solutions. The project Diversity of Insects in Nature protected Areas (DINA) assesses insect communities in 21 nature reserves in Germany, and considers interactions with plant diversity, pesticide exposure, spatial and climatic factors. The nature reserves border on agricultural land, to investigate impacts on insect diversity. Part of the project is to obtain scientific data from Malaise traps and their surroundings, while another part involves relevant stakeholders to identify opportunities and obstacles to insect diversity conservation. Our results indicate a positive association between insect richness and biomass. Insect richness was negatively related to the number of stationary pesticides (soil and vegetation), pesticides measured in ethanol, the amount of area in agricultural production, and precipitation. Our qualitative survey along with stakeholder interviews show that there is general support for insect conservation, while at the same time the stakeholders expressed the need for more information and data on insect biodiversity, as well as flexible policy options. We conclude that conservation management for insects in protected areas should consider a wider landscape. Local targets of conservation management will have to integrate different stakeholder perspectives. Scientifically informed stakeholder dialogues can mediate conflicts of interests, knowledge, and values to develop mutual conservation scenarios

Weighted composition operators on Korenblum type spaces of analytic functions

[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ and $$L^{p-}$$. Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces $$ces(p+), 1\le p\le \infty$$. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces $$ces(p-), 1\le p\le \infty$$. Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and $$H^\infty$$ spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form $$uC_{\varphi }$$. Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007

Algebraic entropy in locally linearly compact vector spaces

We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69\u201387, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem