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

阿爾泰哈巴河群的沉積時代及其構造背景

Habahe Group mainly consists of elastic sediments, which widely distribute in the Chinese Altai and can provide important constraints on the tectonic evolution of the Central Asian Orogenic Belt (CAOB). However, there are different opinions about its deposition time and tectonic background. Previous studies suggested that the Habahe Group formed in Sinian to Mid-Ordovician or Mid- to Late Ordovician in a passive continental margin. On the other hand, recent geological investigations reveal a long lasting subduction-related setting in the Chinese Altai at least since Cambrian. The current geochronological study for detrital zircons from the Habahe Group reveals that the detrital zircons of individual samples, irrespective of their lithological and metamorphic differences, all show similar age patterns, with the early Paleozoic ( 206Pb/ 238U age = 463 ± 542Ma) grains predominating. The youngest detrital zircons from different samples display similar ages (ca. 470Ma), which may reflect the maximum deposition time of the Habahe Group. Dating of growth rim of detrital zircons from migmatite yielded a Mid-Devonian age (384 ± 6Ma), which was coeval with intrusion of Early to Mid-Devonian granitic plutons in the area and clearly indicates the minimum deposition time of the Hababe Group. Therefore, the deposition time of the Habahe Group can be constrained to be Mid-Ordovician to Early Devonian. Zircon U Pb dating results indicate that the detrital zircons of the Habahe Group are dominated by early Paleozoic grains, with small proportion formed in Precambrian. The early Paleozoic detrital zircons are mostly magmatic in origin, and their less rounded shapes indicate a limited transportation. The age and morphological characteristics of the detrital zircons are consistent with those of detrital zircons in active tectonic settings and indicate that the Chinese Altai was under an active continental margin environment during the Early Paleozoic. 北疆阿爾泰造山帶的哈巴河群變質碎屑巖分布廣泛,其沉積時代和構造環境對于認識中亞造山帶的演化歷史有重要意義。早期研究認為哈巴河群沉積于震旦紀—中奧陶世時期,形成于被動大陸邊緣構造環境。而最近有學者根據中亞造山帶的地質演化背景提出,阿爾泰形成于活動陸緣構造環境。對哈巴河群中碎屑鋯石的年代學研究表明,不同巖性或變質程度不同的樣品碎屑鋯石主要類群具有相似的年齡分布特征,其206Pb/238U 年齡主要介于463～542Ma 之間。在這些樣品中, 最年輕的碎屑鋯石年齡均集中于470Ma 左右,代表了碎屑沉積的時代下限。而哈巴河群混合巖樣品中碎屑鋯石增生邊形成于中泥盆世晚期（384±6Ma）,與侵入該群的早古生代花崗巖的年齡十分接近,大致反映了哈巴河群碎屑巖沉積時代的上限,因此哈巴河群的沉積時代應在早泥盆世—中奧陶世之間。鋯石的形態和內部結構特征顯示哈巴河群的年輕碎屑鋯石類群（463～542Ma）主要為巖漿鋯石,其磨圓度較差,而且在比例上遠高于前寒武紀碎屑鋯石。上述特點與活動大陸邊緣碎屑鋯石類群分布特征完全一致,反映阿爾泰在中奧陶世至早泥盆世可能處于活動大陸邊緣構造環境。postprin

Multiplexed, High Density Electrophysiology with Nanofabricated Neural Probes

Extracellular electrode arrays can reveal the neuronal network correlates of behavior with single-cell, single-spike, and sub-millisecond resolution. However, implantable electrodes are inherently invasive, and efforts to scale up the number and density of recording sites must compromise on device size in order to connect the electrodes. Here, we report on silicon-based neural probes employing nanofabricated, high-density electrical leads. Furthermore, we address the challenge of reading out multichannel data with an application-specific integrated circuit (ASIC) performing signal amplification, band-pass filtering, and multiplexing functions. We demonstrate high spatial resolution extracellular measurements with a fully integrated, low noise 64-channel system weighing just 330 mg. The on-chip multiplexers make possible recordings with substantially fewer external wires than the number of input channels. By combining nanofabricated probes with ASICs we have implemented a system for performing large-scale, high-density electrophysiology in small, freely behaving animals that is both minimally invasive and highly scalable

EGFR Gene Overexpression Retained in an Invasive Xenograft Model by Solid Orthotopic Transplantation of Human Glioblastoma Multiforme Into Nude Mice

Orthotopic xenograft animal model from human glioblastoma multiforme (GBM) cell lines often do not recapitulate an extremely important aspect of invasive growth and epidermal growth factor receptor (EGFR) gene overexpression of human GBM. We developed an orthotopic xenograft model by solid transplantation of human GBM into the brain of nude mouse. The orthotopic xenografts sharing the same histopathological features with their original human GBMs were highly invasive and retained the overexpression of EGFR gene. The murine orthotopic GBM models constitute a valuable in vivo system for preclinical studies to test novel therapies for human GBM

CHARGE syndrome

CHARGE syndrome was initially defined as a non-random association of anomalies (Coloboma, Heart defect, Atresia choanae, Retarded growth and development, Genital hypoplasia, Ear anomalies/deafness). In 1998, an expert group defined the major (the classical 4C's: Choanal atresia, Coloboma, Characteristic ears and Cranial nerve anomalies) and minor criteria of CHARGE syndrome. Individuals with all four major characteristics or three major and three minor characteristics are highly likely to have CHARGE syndrome. However, there have been individuals genetically identified with CHARGE syndrome without the classical choanal atresia and coloboma. The reported incidence of CHARGE syndrome ranges from 0.1–1.2/10,000 and depends on professional recognition. Coloboma mainly affects the retina. Major and minor congenital heart defects (the commonest cyanotic heart defect is tetralogy of Fallot) occur in 75–80% of patients. Choanal atresia may be membranous or bony; bilateral or unilateral. Mental retardation is variable with intelligence quotients (IQ) ranging from normal to profound retardation. Under-development of the external genitalia is a common finding in males but it is less apparent in females. Ear abnormalities include a classical finding of unusually shaped ears and hearing loss (conductive and/or nerve deafness that ranges from mild to severe deafness). Multiple cranial nerve dysfunctions are common. A behavioral phenotype for CHARGE syndrome is emerging. Mutations in the CHD7 gene (member of the chromodomain helicase DNA protein family) are detected in over 75% of patients with CHARGE syndrome. Children with CHARGE syndrome require intensive medical management as well as numerous surgical interventions. They also need multidisciplinary follow up. Some of the hidden issues of CHARGE syndrome are often forgotten, one being the feeding adaptation of these children, which needs an early aggressive approach from a feeding team. As the child develops, challenging behaviors become more common and require adaptation of educational and therapeutic services, including behavioral and pharmacological interventions

RNA polymerase II stalling promotes nucleosome occlusion and pTEFb recruitment to drive immortalization by Epstein-Barr virus

Epstein-Barr virus (EBV) immortalizes resting B-cells and is a key etiologic agent in the development of numerous cancers. The essential EBV-encoded protein EBNA 2 activates the viral C promoter (Cp) producing a message of ~120 kb that is differentially spliced to encode all EBNAs required for immortalization. We have previously shown that EBNA 2-activated transcription is dependent on the activity of the RNA polymerase II (pol II) C-terminal domain (CTD) kinase pTEFb (CDK9/cyclin T1). We now demonstrate that Cp, in contrast to two shorter EBNA 2-activated viral genes (LMP 1 and 2A), displays high levels of promoter-proximally stalled pol II despite being constitutively active. Consistent with pol II stalling, we detect considerable pausing complex (NELF/DSIF) association with Cp. Significantly, we observe substantial Cp-specific pTEFb recruitment that stimulates high-level pol II CTD serine 2 phosphorylation at distal regions (up to +75 kb), promoting elongation. We reveal that Cp-specific pol II accumulation is directed by DNA sequences unfavourable for nucleosome assembly that increase TBP access and pol II recruitment. Stalled pol II then maintains Cp nucleosome depletion. Our data indicate that pTEFb is recruited to Cp by the bromodomain protein Brd4, with polymerase stalling facilitating stable association of pTEFb. The Brd4 inhibitor JQ1 and the pTEFb inhibitors DRB and Flavopiridol significantly reduce Cp, but not LMP1 transcript production indicating that Brd4 and pTEFb are required for Cp transcription. Taken together our data indicate that pol II stalling at Cp promotes transcription of essential immortalizing genes during EBV infection by (i) preventing promoter-proximal nucleosome assembly and ii) necessitating the recruitment of pTEFb thereby maintaining serine 2 CTD phosphorylation at distal regions

Deconstructing the Big Valley Search Space Hypothesis

The big valley hypothesis suggests that, in combinatorial optimisation, local optima of good quality are clustered and surround the global optimum. We show here that the idea of a single valley does not always hold. Instead the big valley seems to de-construct into several valleys, also called ‘funnels’ in theoretical chemistry. We use the local optima networks model and propose an effective procedure for extracting the network data. We conduct a detailed study on four selected TSP instances of moderate size and observe that the big valley decomposes into a number of sub-valleys of different sizes and fitness distributions. Sometimes the global optimum is located in the largest valley, which suggests an easy to search landscape, but this is not generally the case. The global optimum might be located in a small valley, which offers a clear and visual explanation of the increased search difficulty in these cases. Our study opens up new possibilities for analysing and visualising combinatorial landscapes as complex networks

Kayexalate Intake (in Sorbitol) and Jejunal Diverticulitis, a Causative Role or an Innocent Bystander?

Small intestine diverticulosis is a rare entity that is asymptomatic in the majority of cases. However, it may cause serious complications, such as infection, hemorrhage, intestinal obstruction and diverticulitis. Kayexalate (sodium polystyrene sulfonate) in sorbitol has been associated with colonic necrosis and less frequently with upper gastrointestinal injuries in a subset of uremic patients treated for hyperkalemia. We report a case of jejunal diverticulosis with mucosal injury and diverticulitis in a uremic patient treated with Kayexalate and discuss the potential role of Kayexalate in the pathogenesis of diverticulitis

The Snail repressor recruits EZH2 to specific genomic sites through the enrollment of the lncRNA HOTAIR in epithelial-to-mesenchymal transition

The transcription factor Snail is a master regulator of cellular identity and epithelial-to-mesenchymal transition (EMT) directly repressing a broad repertoire of epithelial genes. How chromatin modifiers instrumental to its activity are recruited to Snail-specific binding sites is unclear. Here we report that the long non-coding RNA (lncRNA) HOTAIR (for HOX Transcript Antisense Intergenic RNA) mediates a physical interaction between Snail and enhancer of zeste homolog 2 (EZH2), an enzymatic subunit of the polycomb-repressive complex 2 and the main writer of chromatin-repressive marks. The Snail-repressive activity, here monitored on genes with a pivotal function in epithelial and hepatic morphogenesis, differentiation and cell-type identity, depends on the formation of a tripartite Snail/HOTAIR/EZH2 complex. These results demonstrate an lncRNA-mediated mechanism by which a transcriptional factor conveys a general chromatin modifier to specific genes, thereby allowing the execution of hepatocyte transdifferentiation; moreover, they highlight HOTAIR as a crucial player in the Snail-mediated EMT.Oncogene advance online publication, 25 July 2016; doi:10.1038/onc.2016.260

Complete chloroplast genome sequence of Holoparasite Cistanche Deserticola (Orobanchaceae) reveals gene loss and horizontal gene transfer from Its host Haloxylon Ammodendron (Chenopodiaceae)

The central function of chloroplasts is to carry out photosynthesis, and its gene content and structure are highly conserved across land plants. Parasitic plants, which have reduced photosynthetic ability, suffer gene losses from the chloroplast (cp) genome accompanied by the relaxation of selective constraints. Compared with the rapid rise in the number of cp genome sequences of photosynthetic organisms, there are limited data sets from parasitic plants. The authors report the complete sequence of the cp genome of Cistanche deserticola, a holoparasitic desert species belonging to the family Orobanchaceae