Dynamics and spectrum of the Cesàro operator on C-infinity(R+)

[EN] The spectrum and point spectrum of the Cesaro averaging operator C acting on the Frechet space C-infinity(R+) of all C-infinity functions on the interval [0, infinity) are determined. We employ an approach via C-0-semigroup theory for linear operators. A spectral mapping theorem for the resolvent of a closed operator acting on a locally convex space is established; it constitutes a useful tool needed to establish the main result. The dynamical behaviour of C is also investigated.The research of the first two authors was partially supported by the projects MTM2013-43540-P, GVA Prometeo II/2013/013 and GVA ACOMP/2015/186 (Spain).Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2016). Dynamics and spectrum of the Cesàro operator on C-infinity(R+). Monatshefte für Mathematik. 181:267-283. https://doi.org/10.1007/s00605-015-0863-zS267283181Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic semigroups of operators. Rev. R. Acad. Cien. Serie A Mat. RACSAM 106, 299–319 (2012)Albanese, A.A., Bonet, J., Ricker, W.J.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: Uniform mean ergodicity of $$C_0$$ C 0 -semigroups in a class of in Fréchet spaces. Funct. Approx. Comment. Math. 50, 307–349 (2014)Albanese, A.A., Bonet, J., Ricker, W.J.: On the continuous Cesàro operator in certain function spaces. Positivity 19, 659–679 (2015)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces $$\ell ^{p+}$$ ℓ p + and $$L^{p-}$$ L p - . Glasgow Math. J. (accepted)Arendt, W.: Gaussian estimates and interpolation of the spectrum in $$L^p$$ L p . Diff. Int. Equ. 7, 1153–1168 (1994)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Grosse-Erdmann, K.G., Manguillot, A.P.: Linear chaos. Universitext, Springer Verlag, London (2011)Hille, E.: Remarks on ergodic theorems. Trans. Am. Math. Soc. 57, 246–269 (1945)Jarchow, H.: Locally convex spaces. Teubner, Stuttgart (1981)Komura, T.: Semigroups of operators in locally convex spaces. J. Funct. Anal. 2, 258–296 (1968)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Malgrange, B.: Idéaux de fonctions différentiables et division des distributions. Distributions, Editions École Polytechnique, Palaiseau, pp. 1–21 (2003)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press. Oxford University Press, New York (1997)Seeley, R.T.: Extension of $$C^\infty$$ C ∞ functions defined in a half space. Proc. Am. Math. Soc. 15, 625–626 (1964)Siskakis, A.G.: Composition semigroups and the Cesàro operator. J. London Math. Soc. (2) 36, 153–164 (1987)Yosida, K.: Functional analysis. Springer, New York, Berlin, Heidelberg (1980)Valdivia, M.: Topics in locally convex spaces. North-Holland Math. Stud. 67, North-Holland, Amsterdam (1982

New ophthalmosaurid ichthyosaurs from the European lower cretaceous demonstrate extensive ichthyosaur survival across the Jurassic–Cretaceous boundary

Background Ichthyosauria is a diverse clade of marine amniotes that spanned most of the Mesozoic. Until recently, most authors interpreted the fossil record as showing that three major extinction events affected this group during its history: one during the latest Triassic, one at the Jurassic–Cretaceous boundary (JCB), and one (resulting in total extinction) at the Cenomanian-Turonian boundary. The JCB was believed to eradicate most of the peculiar morphotypes found in the Late Jurassic, in favor of apparently less specialized forms in the Cretaceous. However, the record of ichthyosaurs from the Berriasian–Barremian interval is extremely limited, and the effects of the end-Jurassic extinction event on ichthyosaurs remains poorly understood. Methodology/Principal Findings Based on new material from the Hauterivian of England and Germany and on abundant material from the Cambridge Greensand Formation, we name a new ophthalmosaurid, Acamptonectes densus gen. et sp. nov. This taxon shares numerous features with Ophthalmosaurus, a genus now restricted to the Callovian–Berriasian interval. Our phylogenetic analysis indicates that Ophthalmosauridae diverged early in its history into two markedly distinct clades, Ophthalmosaurinae and Platypterygiinae, both of which cross the JCB and persist to the late Albian at least. To evaluate the effect of the JCB extinction event on ichthyosaurs, we calculated cladogenesis, extinction, and survival rates for each stage of the Oxfordian–Barremian interval, under different scenarios. The extinction rate during the JCB never surpasses the background extinction rate for the Oxfordian–Barremian interval and the JCB records one of the highest survival rates of the interval. Conclusions/Significance There is currently no evidence that ichthyosaurs were affected by the JCB extinction event, in contrast to many other marine groups. Ophthalmosaurid ichthyosaurs remained diverse from their rapid radiation in the Middle Jurassic to their total extinction at the beginning of the Late Cretaceous

Cranial Growth and Variation in Edmontosaurs (Dinosauria: Hadrosauridae): Implications for Latest Cretaceous Megaherbivore Diversity in North America

The well-sampled Late Cretaceous fossil record of North America remains the only high-resolution dataset for evaluating patterns of dinosaur diversity leading up to the terminal Cretaceous extinction event. Hadrosaurine hadrosaurids (Dinosauria: Ornithopoda) closely related to Edmontosaurus are among the most common megaherbivores in latest Campanian and Maastrichtian deposits of western North America. However, interpretations of edmontosaur species richness and biostratigraphy have been in constant flux for almost three decades, although the clade is generally thought to have undergone a radiation in the late Maastrichtian. We address the issue of edmontosaur diversity for the first time using rigorous morphometric analyses of virtually all known complete edmontosaur skulls. Results suggest only two valid species, Edmontosaurus regalis from the late Campanian, and E. annectens from the late Maastrichtian, with previously named taxa, including the controversial Anatotitan copei, erected on hypothesized transitional morphologies associated with ontogenetic size increase and allometric growth. A revision of North American hadrosaurid taxa suggests a decrease in both hadrosaurid diversity and disparity from the early to late Maastrichtian, a pattern likely also present in ceratopsid dinosaurs. A decline in the disparity of dominant megaherbivores in the latest Maastrichtian interval supports the hypothesis that dinosaur diversity decreased immediately preceding the end Cretaceous extinction event

Cranial Pathologies in a Specimen of Pachycephalosaurus

. The specimen features two large oval depressions on the dorsal surface, accompanied by numerous circular pits on the margin and inner surface of the larger depressions.In order to identify the origin of these structures, computed tomography (CT) data and morphological characteristics of the specimen are analyzed and compared with similar osteological structures in fossil and extant archosaurs caused by taphonomic processes, non-pathologic bone resorption, and traumatic infection/inflammatory origins. The results of these analyses suggest that the structures are pathologic lesions likely resulting from a traumatic injury and followed by secondary infection at the site.The presence of lesions on a frontoparietal dome, and the exclusivity of their distribution along the dorsal dome surface, offers further insight into frontoparietal dome function and supports previously hypothesized agonistic behavior in pachycephalosaurids

Cranial Ontogeny in Stegoceras validum (Dinosauria: Pachycephalosauria): A Quantitative Model of Pachycephalosaur Dome Growth and Variation

Historically, studies of pachycephalosaurs have recognized plesiomorphically flat-headed taxa and apomorphically domed taxa. More recently, it has been suggested that the expression of the frontoparietal dome is ontogenetic and derived from a flat-headed juvenile morphology. However, strong evidence to support this hypothesis has been lacking. Here we test this hypothesis in a large, stratigraphically constrained sample of specimens assigned to Stegoceras validum, the best known pachycephalosaur, using multiple independent lines of evidence including conserved morphology of ornamentation, landmark-based allometric analyses of frontoparietal shape, and cranial bone histology. New specimens show that the diagnostic ornamentation of the parietosquamosal bar is conserved throughout the size range of the sample, which links flat-headed specimens to domed S. validum. High-resolution CT scans of three frontoparietals reveal that vascularity decreases with size and document a pattern that is consistent with previously proposed histological changes during growth. Furthermore, aspects of dome shape and size are strongly correlated and indicative of ontogenetic growth. These results are complementary and strongly support the hypothesis that the sample represents a growth series of a single taxon. Cranial dome growth is positively allometric, proceeds from a flat-headed to a domed state, and confirms the synonymy of Ornatotholus browni as a juvenile Stegoceras. This dataset serves as the first detailed model of growth and variation in a pachycephalosaur. Flat-headed juveniles possess three characters (externally open cranial sutures, tuberculate dorsal surface texture, and open supratemporal fenestrae) that are reduced or eliminated during ontogeny. These characters also occur in putative flat-headed taxa, suggesting that they may also represent juveniles of domed taxa. However, open cranial sutures and supratemporal fenestrae are plesiomorphic within Ornithischia, and thus should be expected in the adult stage of a primitive pachycephalosaur. Additional lines of evidence will be needed to resolve the taxonomic validity of flat-headed pachycephalosaur taxa

Ants in a Labyrinth: A Statistical Mechanics Approach to the Division of Labour

Division of labour (DoL) is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic) interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments

A basal lithostrotian titanosaur (Dinosauria: Sauropoda) with a complete skull: Implications for the evolution and paleobiology of titanosauria

We describe Sarmientosaurus musacchioi gen. et sp. nov., a titanosaurian sauropod dinosaur from the Upper Cretaceous (Cenomanian - Turonian) Lower Member of the Bajo Barreal Formation of southern Chubut Province in central Patagonia, Argentina. The holotypic and only known specimen consists of an articulated, virtually complete skull and part of the cranial and middle cervical series. Sarmientosaurus exhibits the following distinctive features that we interpret as autapomorphies: (1) maximum diameter of orbit nearly 40% rostrocaudal length of cranium; (2) complex maxilla - lacrimal articulation, in which the lacrimal clasps the ascending ramus of the maxilla; (3) medial edge of caudal sector of maxillary ascending ramus bordering bony nasal aperture with low but distinct ridge; (4) ´tongue-like´ ventral process of quadratojugal that overlaps quadrate caudally; (5) separate foramina for all three branches of the trigeminal nerve; (6) absence of median venous canal connecting infundibular region to ventral part of brainstem; (7) subvertical premaxillary, procumbent maxillary, and recumbent dentary teeth; (8) cervical vertebrae with ´strut-like´ centroprezygapophyseal laminae; (9) extremely elongate and slender ossified tendon positioned ventrolateral to cervical vertebrae and ribs. The cranial endocast of Sarmientosaurus preserves some of the most complete information obtained to date regarding the brain and sensory systems of sauropods. Phylogenetic analysis recovers the new taxon as a basal member of Lithostrotia, as the most plesiomorphic titanosaurian to be preserved with a complete skull. Sarmientosaurus provides a wealth of new cranial evidence that reaffirms the close relationship of titanosaurs to Brachiosauridae. Moreover, the presence of the relatively derived lithostrotian Tapuiasaurus in Aptian deposits indicates that the new Patagonian genus represents a ´ghost lineage´ with a comparatively plesiomorphic craniodental form, the evolutionary history of which is missing for at least 13 million years of the Cretaceous. The skull anatomy of Sarmientosaurus suggests that multiple titanosaurian species with dissimilar cranial structures coexisted in the early Late Cretaceous of southern South America. Furthermore, the new taxon possesses a number of distinctive morphologies - such as the ossified cervical tendon, extremely pneumatized cervical vertebrae, and a habitually downward- facing snout - that have rarely, if ever, been documented in other titanosaurs, thus broadening our understanding of the anatomical diversity of this remarkable sauropod clade. The latter two features were convergently acquired by at least one penecontemporaneous diplodocoid, and may represent mutual specializations for consuming low-growing vegetation.Fil: Martínez, Rubén Darío. Universidad Nacional de la Patagonia; ArgentinaFil: Lamanna, Matthew C.. Carnegie Museum Of Natural History; Estados UnidosFil: Novas, Fernando Emilio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "bernardino Rivadavia"; ArgentinaFil: Ridgely, Ryan C.. Ohio University College Of Osteopathic Medicine; Estados UnidosFil: Casal, Gabriel. Universidad Nacional de la Patagonia; ArgentinaFil: Martínez, Javier E.. Hospital Regional de Comodoro Rivadavia; ArgentinaFil: Vita, Javier R.. Resonancia Magnética Borelli; ArgentinaFil: Witmer, Lawrence M.. Ohio University College Of Osteopathic Medicine; Estados Unido

Mourning and melancholia revisited: correspondences between principles of Freudian metapsychology and empirical findings in neuropsychiatry

Freud began his career as a neurologist studying the anatomy and physiology of the nervous system, but it was his later work in psychology that would secure his place in history. This paper draws attention to consistencies between physiological processes identified by modern clinical research and psychological processes described by Freud, with a special emphasis on his famous paper on depression entitled 'Mourning and melancholia'. Inspired by neuroimaging findings in depression and deep brain stimulation for treatment resistant depression, some preliminary physiological correlates are proposed for a number of key psychoanalytic processes. Specifically, activation of the subgenual cingulate is discussed in relation to repression and the default mode network is discussed in relation to the ego. If these correlates are found to be reliable, this may have implications for the manner in which psychoanalysis is viewed by the wider psychological and psychiatric communities