There are no multiply-perfect Fibonacci numbers

Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors

Electrical stimulation alleviates depressive-like behaviors of rats: investigation of brain targets and potential mechanisms

Deep brain stimulation (DBS) is a promising therapy for patients with refractory depression. However, key questions remain with regard to which brain target(s) should be used for stimulation, and which mechanisms underlie the therapeutic effects. Here, we investigated the effect of DBS, with low- and high-frequency stimulation (LFS, HFS), in different brain regions (ventromedial prefrontal cortex, vmPFC; cingulate cortex, Cg; nucleus accumbens (NAc) core or shell; lateral habenula, LHb; and ventral tegmental area) on a variety of depressive-like behaviors using rat models. In the naive animal study, we found that HFS of the Cg, vmPFC, NAc core and LHb reduced anxiety levels and increased motivation for food. In the chronic unpredictable stress model, there was a robust depressive-like behavioral phenotype. Moreover, vmPFC HFS, in a comparison of all stimulated targets, produced the most profound antidepressant effects with enhanced hedonia, reduced anxiety and decreased forced-swim immobility. In the following set of electrophysiological and histochemical experiments designed to unravel some of the underlying mechanisms, we found that vmPFC HFS evoked a specific modulation of the serotonergic neurons in the dorsal raphe nucleus (DRN), which have long been linked to mood. Finally, using a neuronal mapping approach by means of c-Fos expression, we found that vmPFC HFS modulated a brain circuit linked to the DRN and known to be involved in affect. In conclusion, HFS of the vmPFC produced the most potent antidepressant effects in naive rats and rats subjected to stress by mechanisms also including the DRN.postprin

De Sitter Waves and the Zero Curvature Limit

We show that a particular set of global modes for the massive de Sitter scalar field (the de Sitter waves) allows to manage the group representations and the Fourier transform in the flat (Minkowskian) limit. This is in opposition to the usual acceptance based on a previous result, suggesting the appearance of negative energy in the limit process. This method also confirms that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far as one wishes to recover ordinary QFT in the flat limit.Comment: 9 pages, latex no figure, to appear in Phys. Rev.

A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions

[EN] We give a simple proof of a general theorem of Kotake-Narasimhan for elliptic operators in the setting of ultradifferentiable functions in the sense of Braun, Meise and Taylor. We follow the ideas of Komatsu. Based on an example of Metivier, we also show that the ellipticity is a necessary condition for the theorem to be true.C. Boiti and D. Jornet were partially supported by the INdAM-GNAMPA Projects 2014 and 2015. D. Jornet was partially supported by MINECO, Project MTM2013-43540-PBoiti, C.; Jornet Casanova, D. (2017). A simple proof of Kotake-Narasimhan theorem in some classes of ultradifferentiable functions. Journal of Pseudo-Differential Operators and Applications. 8(2):297-317. https://doi.org/10.1007/s11868-016-0163-yS29731782Boiti, C., Jornet, D.: The problem of iterates in some classes of ultradifferentiable functions. Oper. Theory Adv. Appl. Birkhauser Basel 245, 21–33 (2015)Boiti, C., Jornet, D.: A characterization of the wave front set defined by the iterates of an operator with constant coefficients. arXiv:1412.4954Boiti, C., Jornet, D., Juan-Huguet, J.: Wave front set with respect to the iterates of an operator with constant coefficients. Abstr. Appl. Anal. 2014, 1–17 Article ID 438716 (2014). doi: 10.1155/2014/438716Bolley, P., Camus, J., Mattera, C.: Analyticité microlocale et itérés d’operateurs hypoelliptiques. Séminaire Goulaouic-Schwartz, 1978–1979, Exp No. 13, École Polytech, PalaiseauBonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways of define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14, 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.: Superposition in classes of ultradifferentiable functions. Publ. Res. I Math. Sci. 42(2), 399–419 (2006)Jornet Casanova, D.: Operadores Pseudodiferenciales en Clases no Casianalíticas de Tipo Beurling. Universitat Politècnica de València (2004). doi: 10.4995/Thesis/10251/54953Juan-Huguet, J.: Iterates and hypoellipticity of partial differential operators on non-quasianalytic classes. Integr. Equ. Oper. Theory 68, 263–286 (2010)Juan-Huguet, J.: A Paley–Wiener type theorem for generalized non-quasianalytic classes. Stud. Math. 208(1), 31–46 (2012)Komatsu, H.: A characterization of real analytic functions. Proc. Jpn Acad. 36, 90–93 (1960)Komatsu, H.: On interior regularities of the solutions of principally elliptic systems of linear partial differential equations. J. Fac. Sci. Univ. Tokyo Sect. 1, 9, 141–164 (1961)Komatsu, H.: A proof of Kotaké and Narasimhan’s theorem. Proc. Jpn Acad. 38(9), 615–618 (1962)Kotake, T., Narasimhan, M.S.: Regularity theorems for fractional powers of a linear elliptic operator. Bull. Soc. Math. Fr. 90, 449–471 (1962)Kumano-Go, H.: Pseudo-Differential Operators. The MIT Press, Cambridge, London (1982)Langenbruch, M.: P-Funktionale und Randwerte zu hypoelliptischen Differentialoperatoren. Math. Ann. 239(1), 55–74 (1979)Langenbruch, M.: Fortsetzung von Randwerten zu hypoelliptischen Differentialoperatoren und partielle Differentialgleichungen. J. Reine Angew. Math. 311/312, 57–79 (1979)Langenbruch, M.: On the functional dimension of solution spaces of hypoelliptic partial differential operators. Math. Ann. 272, 217–229 (1985)Langenbruch, M.: Bases in solution sheaves of systems of partial differential equations. J. Reine Angew. Math. 373, 1–36 (1987)Lions, J.L., Magenes, E.: Problèmes aux limites non homogènes et applications, vol. 3. Dunod, Paris (1970)Métivier, G.: Propriété des itérés et ellipticité. Commun. Part. Differ. Eq. 3(9), 827–876 (1978)Nelson, E.: Analytic vectors. Ann. Math. 70, 572–615 (1959)Newberger, E., Zielezny, Z.: The growth of hypoelliptic polynomials and Gevrey classes. Proc. Am. Math. Soc. 39(3), 547–552 (1973)Oldrich, J.: Sulla regolarità delle soluzioni delle equazioni lineari ellittiche nelle classi di Beurling. (Italian) Boll. Un. Mat. Ital. (4) 2, 183–195 (1969)Petzsche, H.-J., Vogt, D.: Almost analytic extension of ultradifferentiable functions and the boundary values of holomorphic functions. Math. Ann. 267(1), 17–35 (1984

Pairing in high-density neutron matter including short- and long-range correlations

Pairing gaps in neutron matter need to be computed in a wide range of densities to address open questions in neutron-star phenomenology. Traditionally, the Bardeen-Cooper-Schrieffer approach has been used to compute gaps from bare nucleon-nucleon interactions. Here we incorporate the influence of short-and long-range correlations in the pairing gaps. Short-range correlations are treated, including the appropriate fragmentation of single-particle states, and substantially suppress the gaps. Long-range correlations dress the pairing interaction via density and spin modes and provide a relatively small correction. We use different interactions, some with three-body forces, as a starting point to control for any systematic effects. Results are relevant for neutron-star cooling scenarios, in particular in view of the recent observational data on Cassiopeia A

A century of limnological evolution and interactive threats in the Panama Canal: Long-term assessments from a shallow basin

Large tropical river dam projects are expected to accelerate over the forthcoming decades to satisfy growing demand for energy, irrigation and flood control. When tropical rivers are dammed the immediate impacts are relatively well studied, but the long-term (decades-centuries) consequences of impoundment remain poorly known. We combined historical records of water quality, river flow and climate with a multi-proxy (macrofossils, diatoms, biomarkers and trace elements) palaeoecological approach to reconstruct the limnological evolution of a shallow basin in Gatun Lake (Panama Canal, Panama) and assess the effects of multiple linked factors (river damming, forest flooding, deforestation, invasive species, pollution and hydro-climate) on the study area. Results show that a century after dam construction, species invasion, deforestation and salt intrusions have forced a gradual change in the study basin from a swamp-type environment towards a more saline lake-governed system of benthic–littoral production likely associated with the expansion of macrophyte stands. Hydrology still remains the most important long-term (decades) structural factor stimulating salinity intrusions, primary productivity, deposition of minerals, and reduction of water transparency during wet periods. During dry periods, physical-chemical conditions are in turn linked to clear water and aerobic conditions while nutrients shift to available forms for the aquatic biota in the detrital-rich reductive sediments. Our study suggests that to preserve the natural riverine system functioning of this area of the Panama Canal, management activities must address long-term ecosystem structural drivers such as river flow, runoff patterns and physical-chemical conditions

Health Behaviour Changes after Diagnosis of Chronic Illness Among Canadians Aged 50 or Older

Changes in health behaviors (smoking, physical activity, alcohol consumption, and fruit and vegetable consumption) after diagnosis of chronic health conditions (heart disease, cancer, stroke, respiratory disease, and diabetes) were examined among Canadians aged 50 or older. Results from 12 years of longitudinal data from the Canadian National Population Health Survey indicated relatively modest changes in behavior. Although significant decreases in smoking were observed among all groups except those with respiratory disease, at least 75% of smokers did not quit. No significant changes emerged in the percentage meeting physical activity recommendations, except those with diabetes, or in excessive alcohol consumption, except those with diabetes and respiratory disease. The percentage reporting the recommended minimum fruit and vegetable intake did not increase significantly among any group

Genome content and phylogenomics reveal both ancestral and lateral evolutionary pathways in plant-pathogenic Streptomyces species

© 2016, American Society for Microbiology. All Rights Reserved. Streptomyces spp. are highly differentiated actinomycetes with large, linear chromosomes that encode an arsenal of biologically active molecules and catabolic enzymes. Members of this genus are well equipped for life in nutrient-limited environments and are common soil saprophytes. Out of the hundreds of species in the genus Streptomyces, a small group has evolved the ability to infect plants. The recent availability of Streptomyces genome sequences, including four genomes of pathogenic species, provided an opportunity to characterize the gene content specific to these pathogens and to study phylogenetic relationships among them. Genome sequencing, comparative genomics, and phylogenetic analysis enabled us to discriminate pathogenic from saprophytic Streptomyces strains; moreover, we calculated that the pathogen-specific genome contains 4,662 orthologs. Phylogenetic reconstruction suggested that Streptomyces scabies and S. ipomoeae share an ancestor but that their biosynthetic clusters encoding the required virulence factor thaxtomin have diverged. In contrast, S. turgidiscabies and S. acidiscabies, two relatively unrelated pathogens, possess highly similar thaxtomin biosynthesis clusters, which suggests that the acquisition of these genes was through lateral gene transfer

A characterization of the wave front set defined by the iterates of an operator with constant coefficients

[EN] We characterize the wave front set WF*P (u) with respect to the iterates of a linear partial differential operator with constant coefficients of a classical distribution u is an element of D '(Omega), Omega an open subset in R-n. We use recent Paley-Wiener theorems for generalized ultradifferentiable classes in the sense of Braun, Meise and Taylor. We also give several examples and applications to the regularity of operators with variable coefficients and constant strength. Finally, we construct a distribution with prescribed wave front set of this type.The authors were partially supported by FAR2011 (Universita di Ferrara), "Fondi per le necessita di base della ricerca" 2012 and 2013 (Universita di Ferrara) and the INDAM-GNAMPA Project 2014 "Equazioni Differenziali a Derivate Parziali di Evoluzione e Stocastiche" The research of the second author was partially supported by MINECO of Spain, Project MTM2013-43540-P.Boiti, C.; Jornet Casanova, D. (2017). A characterization of the wave front set defined by the iterates of an operator with constant coefficients. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(3):891-919. https://doi.org/10.1007/s13398-016-0329-8S8919191113Albanese, A.A., Jornet, D., Oliaro, A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. Theory 66, 153–181 (2010)Boiti, C., Jornet, D.: The problem of iterates in some classes of ultradifferentiable functions. In: “Operator Theory: Advances and Applications”. Birkhauser, Basel. 245, 21–32 (2015)Boiti, C., Jornet, D., Juan-Huguet, J.,: Wave front set with respect to the iterates of an operator with constant coefficients. Abstr. Appl. Anal., 1–17 (2014). doi: 10.1155/2014/438716 (Article ID 438716)Bolley, P., Camus, J., Mattera, C.: Analyticité microlocale et itérés d’operateurs hypoelliptiques. In: Séminaire Goulaouic–Schwartz, 1978–79, Exp N.13. École Polytech., PalaiseauBonet, J., Fernández, C., Meise, R.: Characterization of the $$\omega$$ ω -hypoelliptic convolution operators on ultradistributions. Ann. Acad. Sci. Fenn. Math. 25, 261–284 (2000)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, 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.: $$\omega$$ ω -hypoelliptic differential operators of constant strength. J. Math. Anal. Appl. 297, 561–576 (2004)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340, 1153–1170 (2008)Hörmander, L.: On interior regularity of the solutions of partial differential equations. Comm. Pure Appl. Math. XI, 197–218 (1958)Hörmander, L.: Uniqueness theorems and wave front sets for solutions of linear partial differential equations with analytic coefficients. Comm. Pure Appl. Math. 24, 671–704 (1971)Hörmander, L.: The Analysis of Linear Partial Differential Operators I. Springer, Berlin (1990)Hörmander, L.: The Analysis of Linear Partial Differential Operators II. Springer, Berlin (1983)Juan-Huguet, J.: Iterates and hypoellipticity of partial differential operators on non-quasianalytic classes. Integr. Equ. Oper. Theory 68, 263–286 (2010)Juan-Huguet, J.: A Paley–Wiener type theorem for generalized non-quasianalytic classes. Studia Math. 208(1), 31–46 (2012)Komatsu, H.: A characterization of real analytic functions. Proc. Jpn. Acad. 36, 90–93 (1960)Kotake, T., Narasimhan, M.S.: Regularity theorems for fractional powers of a linear elliptic operator. Bull. Soc. Math. France 90, 449–471 (1962)Langenbruch, M.: P-Funktionale und Randwerte zu hypoelliptischen Differentialoperatoren. Math. Ann. 239(1), 55–74 (1979)Langenbruch, M.: Fortsetzung von Randwerten zu hypoelliptischen Differentialoperatoren und partielle Differentialgleichungen. J. Reine Angew. Math. 311/312, 57–79 (1979)Langenbruch, M.: On the functional dimension of solution spaces of hypoelliptic partial differential operators. Math. Ann. 272, 217–229 (1985)Langenbruch, M.: Bases in solution sheaves of systems of partial differential equations. J. Reine Angew. Math. 373, 1–36 (1987)Métivier, G.: Propriété des itérés et ellipticité. Comm. Partial Differ. Equ. 3(9), 827–876 (1978)Newberger, E., Zielezny, Z.: The growth of hypoelliptic polynomials and Gevrey classes. Proc. Amer. Math. Soc. 39(3), 547–552 (1973)Rodino, L.: On the problem of the hypoellipticity of the linear partial differential equations. In: Buttazzo, G. (ed.) Developments in Partial Differential Equations and Applications to Mathematical Physics. Plenum Press, New York (1992)Rodino, L.: Linear partial differential operators in Gevrey spaces. World Scientific, Singapore (1993)Zanghirati, L.: Iterates of a class of hypoelliptic operators and generalized Gevrey classes. Boll. U.M.I. Suppl. 1, 177–195 (1980