A remark on totally smooth renormings

[EN] E. Oja, T. Viil, andD. Werner showed, in Totally smooth renormings, Archiv der Mathematik, 112, 3, (2019), 269-281, that a weakly compactly generated Banach space ( X, center dot) with the property that every linear functional on X has a unique Hahn-Banach extension to the bidual X ** (the so-called Phelps' property U in X **, also known as the Hahn-Banach smoothness property) can be renormed to have the stronger property that for every subspace Y of X, every linear functional on Y has a unique Hahn-Banach extension to X ** (the so-called total smoothness property of the space). We mention here that this result holds in full generality -without any restriction on the space- and in a stronger form, thanks to a result ofM. Raja, On dual locally uniformly rotund norms, Israel Journal of Mathematics 129 (2002), 77-91.Supported by AEI/FEDER (project MTM2017-83262-C2-2-P of Ministerio de Economia y Competitividad), by Fundacion Seneca, Region de Murcia (Grant 19368/PI/14), and Universitat Politecnica de Valencia (A. J. Guirao). Supported by AEI/FEDER (project MTM2017-83262-C2-1-P of Ministerio de Economia y Competitividad) and Universitat Politecnica de Valencia (V. Montesinos). We thank the referees for their work, that neatly improved the original version of this note to its final form.Cobollo, C.; Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2020). A remark on totally smooth renormings. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-4. https://doi.org/10.1007/s13398-020-00831-5S141142Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach space theory: the basis of linear and nonlinear analysis. Springer, New York (2011)Fabian, M., Montesinos, V., Zizler, V.: Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Ser. A. Mat. RACSAM. 100(1–2), 101–125 (2006)Ferrari, S., Orihuela, J., Raja, M.: Generalized metric properties of spheres and renorming of Banach spaces. Rev. R. Acad. Cienc. Exactas Fis. Natl. Ser. A Math. RACSAM. 113, 2655–2663 (2019)Foguel, S.R.: On a theorem by A. E. Taylor. Proc. Amer. Math. Soc. 9, 325 (1958)Godefroy, G.: Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité. Israel J. Math. 38, 209–220 (1981)Guirao, A.J., Montesinos, V., Zizler, V.: Open Problems in the geometry and analysis of Banach spaces. Springer International Pub, Switzerland (2016)Harmand, P., Werner, D., Werner, W.: M-ideals in Banach spaces and Banach algebras. Lecture notes in math, vol. 1547. Springer, Berlin (1993)Haydon, R.: Locally uniformly rotund norms in Banach spaces and their duals. J. Funct. Anal. 254, 2023–2039 (2008)Oja, E., Viil, T., Werner, D.: Totally smooth renormings. Archiv. der. Mathematik. 112(3), 269–281 (2019)Phelps, R.R.: Uniqueness of Hahn–Banach extensions and unique best approximation. Trans. Amer. Math. Soc. 95, 238–255 (1960)Raja, M.: On dual locally uniformly rotund norms. Israel J. Math. 129, 77–91 (2002)Smith, R.J., Troyanski, S.L.: Renormings of $$C(K)$$ spaces. Rev. R. Acad. Cienc. Exactas Fís. Natl. Ser. A Math. RACSAM 104(2), 375–412 (2010)Sullivan, F.: Geometrical properties determined by the higher duals of a Banach space. Illinois J. Math. 21, 315–331 (1977)Taylor, A.E.: The extension of linear functionals. Duke Math. J. 5, 538–547 (1939

Quantitative imaging of coronary blood flow

Positron emission tomography (PET) is a nuclear medicine imaging modality based on the administration of a positron-emitting radiotracer, the imaging of the distribution and kinetics of the tracer, and the interpretation of the physiological events and their meaning with respect to health and disease. PET imaging was introduced in the 1970s and numerous advances in radiotracers and detection systems have enabled this modality to address a wide variety of clinical tasks, such as the detection of cancer, staging of Alzheimer's disease, and assessment of coronary artery disease (CAD). This review provides a description of the logic and the logistics of the processes required for PET imaging and a discussion of its use in guiding the treatment of CAD. Finally, we outline prospects and limitations of nanoparticles as agents for PET imaging

Living biointerfaces based on non-pathogenic bacteria to direct cell differentiation

Genetically modified Lactococcus lactis, non-pathogenic bacteria expressing the FNIII7-10 fibronectin fragment as a protein membrane have been used to create a living biointerface between synthetic materials and mammalian cells. This FNIII7-10 fragment comprises the RGD and PHSRN sequences of fibronectin to bind α5β1 integrins and triggers signalling for cell adhesion, spreading and differentiation. We used L. lactis strain to colonize material surfaces and produce stable biofilms presenting the FNIII7-10 fragment readily available to cells. Biofilm density is easily tunable and remains stable for several days. Murine C2C12 myoblasts seeded over mature biofilms undergo bipolar alignment and form differentiated myotubes, a process triggered by the FNIII7-10 fragment. This biointerface based on living bacteria can be further modified to express any desired biochemical signal, establishing a new paradigm in biomaterial surface functionalisation for biomedical applications

Emotion Modulation of Visual Attention: Categorical and Temporal Characteristics

Background: Experimental research has shown that emotional stimuli can either enhance or impair attentional performance. However, the relative effects of specific emotional stimuli and the specific time course of these differential effects are unclear. Methodology/Principal Findings: In the present study, participants (n = 50) searched for a single target within a rapid serial visual presentation of images. Irrelevant fear, disgust, erotic or neutral images preceded the target by two, four, six, or eight items. At lag 2, erotic images induced the greatest deficits in subsequent target processing compared to other images, consistent with a large emotional attentional blink. Fear and disgust images also produced a larger attentional blinks at lag 2 than neutral images. Erotic, fear, and disgust images continued to induce greater deficits than neutral images at lag 4 and 6. However, target processing deficits induced by erotic, fear, and disgust images at intermediate lags (lag 4 and 6) did not consistently differ from each other. In contrast to performance at lag 2, 4, and 6, enhancement in target processing for emotional stimuli was observed in comparison to neutral stimuli at lag 8. Conclusions/Significance: These findings suggest that task-irrelevant emotion information, particularly erotica, impairs intentional allocation of attention at early temporal stages, but at later temporal stages, emotional stimuli can have an enhancing effect on directed attention. These data suggest that the effects of emotional stimuli on attention can be bot

Breast imaging technology: Recent advances in imaging endogenous or transferred gene expression utilizing radionuclide technologies in living subjects - applications to breast cancer

A variety of imaging technologies is being investigated as tools for studying gene expression in living subjects. Two technologies that use radiolabeled isotopes are single photon emission computed tomography (SPECT) and positron emission tomography (PET). A relatively high sensitivity, a full quantitative tomographic capability, and the ability to extend small animal imaging assays directly into human applications characterize radionuclide approaches. Various radiolabeled probes (tracers) can be synthesized to target specific molecules present in breast cancer cells. These include antibodies or ligands to target cell surface receptors, substrates for intracellular enzymes, antisense oligodeoxynucleotide probes for targeting mRNA, probes for targeting intracellular receptors, and probes for genes transferred into the cell. We briefly discuss each of these imaging approaches and focus in detail on imaging reporter genes. In a PET reporter gene system for in vivo reporter gene imaging, the protein products of the reporter genes sequester positron emitting reporter probes. PET subsequently measures the PET reporter gene dependent sequestration of the PET reporter probe in living animals. We describe and review reporter gene approaches using the herpes simplex type 1 virus thymidine kinase and the dopamine type 2 receptor genes. Application of the reporter gene approach to animal models for breast cancer is discussed. Prospects for future applications of the transgene imaging technology in human gene therapy are also discussed. Both SPECT and PET provide unique opportunities to study animal models of breast cancer with direct application to human imaging. Continued development of new technology, probes and assays should help in the better understanding of basic breast cancer biology and in the improved management of breast cancer patients

Decision or No Decision: How Do Patient–Physician Interactions End and What Matters?

BACKGROUND: A clearly stated clinical decision can induce a cognitive closure in patients and is an important investment in the end of patient–physician communications. Little is known about how often explicit decisions are made in primary care visits. OBJECTIVE: To use an innovative videotape analysis approach to assess physicians’ propensity to state decisions explicitly, and to examine the factors influencing decision patterns. DESIGN: We coded topics discussed in 395 videotapes of primary care visits, noting the number of instances and the length of discussions on each topic, and how discussions ended. A regression analysis tested the relationship between explicit decisions and visit factors such as the nature of topics under discussion, instances of discussion, the amount of time the patient spoke, and competing demands from other topics. RESULTS: About 77% of topics ended with explicit decisions. Patients spoke for an average of 58 seconds total per topic. Patients spoke more during topics that ended with an explicit decision, (67 seconds), compared with 36 seconds otherwise. The number of instances of a topic was associated with higher odds of having an explicit decision (OR = 1.73, p < 0.01). Increases in the number of topics discussed in visits (OR = 0.95, p < .05), and topics on lifestyle and habits (OR = 0.60, p < .01) were associated with lower odds of explicit decisions. CONCLUSIONS: Although discussions often ended with explicit decisions, there were variations related to the content and dynamics of interactions. We recommend strengthening patients’ voice and developing clinical tools, e.g., an “exit prescription,” to improving decision making

Nucleoporin98-96 Function Is Required for Transit Amplification Divisions in the Germ Line of Drosophila melanogaster

Production of specialized cells from precursors depends on a tightly regulated sequence of proliferation and differentiation steps. In the gonad of Drosophila melanogaster, the daughters of germ line stem cells (GSC) go through precisely four rounds of transit amplification divisions to produce clusters of 16 interconnected germ line cells before entering a stereotypic differentiation cascade. Here we show that animals harbouring a transposon insertion in the center of the complex nucleoporin98-96 (nup98-96) locus had severe defects in the early steps of this developmental program, ultimately leading to germ cell loss and sterility. A phenotypic analysis indicated that flies carrying the transposon insertion, designated nup98-962288, had dramatically reduced numbers of germ line cells. In contrast to controls, mutant testes contained many solitary germ line cells that had committed to differentiation as well as abnormally small clusters of two, four or eight differentiating germ line cells. This indicates that mutant GSCs rather differentiated than self-renewed, and that these GSCs and their daughters initiated the differentiation cascade after zero, or less than four rounds of amplification divisions. This phenotype remained unaffected by hyper-activation of signalling pathways that normally result in excessive proliferation of GSCs and their daughters. Expression of wildtype nup98-96 specifically in the germ line cells of mutant animals fully restored development of the GSC lineage, demonstrating that the effect of the mutation is cell-autonomous. Nucleoporins are the structural components of the nucleopore and have also been implicated in transcriptional regulation of specific target genes. The nuclear envelopes of germ cells and general nucleocytoplasmic transport in nup98-96 mutant animals appeared normal, leading us to propose that Drosophila nup98-96 mediates the transport or transcription of targets required for the developmental timing between amplification and differentiation

Context Modulation of Facial Emotion Perception Differed by Individual Difference

Background: Certain facial configurations are believed to be associated with distinct affective meanings (i.e. basic facial expressions), and such associations are common across cultures (i.e. universality of facial expressions). However, recently, many studies suggest that various types of contextual information, rather than facial configuration itself, are important factor for facial emotion perception. Methodology/Principal Findings: To examine systematically how contextual information influences individuals ’ facial emotion perception, the present study estimated direct observers ’ perceptual thresholds for detecting negative facial expressions via a forced-choice psychophysical procedure using faces embedded in various emotional contexts. We additionally measured the individual differences in affective information-processing tendency (BIS/BAS) as a possible factor that may determine the extent to which contextual information on facial emotion perception is used. It was found that contextual information influenced observers ’ perceptual thresholds for facial emotion. Importantly, individuals ’ affectiveinformation tendencies modulated the extent to which they incorporated context information into their facial emotion perceptions. Conclusions/Significance: The findings of this study suggest that facial emotion perception not only depends on facial configuration, but the context in which the face appears as well. This contextual influence appeared differently wit

Sequence-Dependent Fluorescence of Cyanine Dyes on Microarrays

Cy3 and Cy5 are among the most commonly used oligonucleotide labeling molecules. Studies of nucleic acid structure and dynamics use these dyes, and they are ubiquitous in microarray experiments. They are sensitive to their environment and have higher quantum yield when bound to DNA. The fluorescent intensity of terminal cyanine dyes is also known to be significantly dependent on the base sequence of the oligonucleotide. We have developed a very precise and high-throughput method to evaluate the sequence dependence of oligonucleotide labeling dyes using microarrays and have applied the method to Cy3 and Cy5. We used light-directed in-situ synthesis of terminally-labeled microarrays to determine the fluorescence intensity of each dye on all 1024 possible 5′-labeled 5-mers. Their intensity is sensitive to all five bases. Their fluorescence is higher with 5′ guanines, and adenines in subsequent positions. Cytosine suppresses fluorescence. Intensity falls by half over the range of all 5-mers for Cy3, and two-thirds for Cy5. Labeling with 5′-biotin-streptavidin-Cy3/-Cy5 gives a completely different sequence dependence and greatly reduces fluorescence compared with direct terminal labeling