Derivations on symmetric quasi-Banach ideals of compact operators

Let $\mathcal{I,J}$ be symmetric quasi-Banach ideals of compact operators on an infinite-dimensional complex Hilbert space $H$, let $\mathcal{J:I}$ be a space of multipliers from $\mathcal{I}$ to $\mathcal{J}$. Obviously, ideals $\mathcal{I}$ and $\mathcal{J}$ are quasi-Banach algebras and it is clear that ideal $\mathcal{J}$ is a bimodule for $\mathcal{I}$. We study the set of all derivations from $\mathcal{I}$ into $\mathcal{J}$. We show that any such derivation is automatically continuous and there exists an operator $a\in\mathcal{J:I}$ such that $\delta(\cdot)=[a,\cdot]$, moreover $\|a\|_{\mathcal{B}(H)}\leq\|\delta\|_\mathcal{I\to J}\leq 2C\|a\|_\mathcal{J:I}$, where $C$ is the modulus of concavity of the quasi-norm $\|\cdot\|_\mathcal{J}$. In the special case, when $\mathcal{I=J=K}(H)$ is a symmetric Banach ideal of compact operators on $H$ our result yields the classical fact that any derivation $\delta$ on $\mathcal{K}(H)$ may be written as $\delta(\cdot)=[a,\cdot]$, where $a$ is some bounded operator on $H$ and $\|a\|_{\mathcal{B}(H)}\leq\|\delta\|_\mathcal{I\to I}\leq 2\|a\|_{\mathcal{B}(H)}$.Comment: 21 page

Precise measurement of Γ(H⟶γγ)\Gamma (H \longrightarrow \gamma \gamma) at a PLC and theoretical consequences

With the LEP II Higgs search approaching exclusion limits on low values of $\tan \beta \sim 2$ it becomes increasingly important to investigate physical quantities sensitive to large masses of a pseudoscalar Higgs mass. This regime is difficult and over a large range of $\tan \beta$ impossible to cover at the LHC proton proton collider. In this paper we focus on the achievable statistical precision of the Higgs decay into two photons at a future $\gamma \gamma$ collider (PLC) in the MSSM mass range below 130 GeV. The MSSM and SM predictions for $\Gamma (H \longrightarrow \gamma \gamma)$ can differ by up to 10 % even in the decoupling limit of large $m_A$. We summarize recent progress in both the theoretical understanding of the background process $\gamma \gamma \longrightarrow q \bar{q}$, $q=\{b,c\}$, and in the expected detector performance allow for a high accuracy of the lightest MSSM or SM Higgs boson decay into a $b \bar{b}$ pair. We find that for optimized but still realistic detector and accelerator assumptions, statistically a 1.4% accuracy is feasible after about four years of collecting data for a Higgs boson mass which excludes $\tan \beta <2$.Comment: 14 pages, 7 figures, contributed to LP99 at Stanford, C

Investigation the structure and properties of deformed semi-finished products produced from chips of Al–Mg alloys system alloyed with scandium

The article presents the results of studies that make it possible to solve the problem of processing secondary waste from expensive aluminum alloys without irretrievable loss of metal. For this purpose, tasks were set and solved for the development of technological schemes for obtaining longish deformed semi-finished products from chip waste of Al–Mg alloys 01570 and 1580 alloyed with scandium using methods of powder metallurgy and metal forming. For their experimental verification, the operations of chip briquetting, combined rolling-extrusion (continuous extrusion), sectional rolling, hot extrusion and drawing in combination with heat treatment were applied. According to these schemes, semi-finished products in the form of rods and wires were obtained. Structure and mechanical properties were investigated. It has been revealed that when hot-extruded rods are obtained from chip briquettes of alloy 01570 on a vertical hydraulic press, even with significant degrees of deformation during extrusion, the margin of plastic properties is small and makes it possible to obtain a wire with a diameter of only 4.2 mm after drawing. The processing of briquettes from 1580 alloy chips using the combined rolling-extrusion method makes it possible to obtain after cold deformation a wire with a diameter of up to 3 mm. At the same time, the influence of the annealing process on the structure and properties of deformed semi-finished products from the investigated alloys was studied. It is shown that due to the low plasticity of the investigated material cold working of the rods must be carried out with small degrees of deformation, alternating it with intermediate annealing according to the proposed regime. An analysis of the physical and mechanical properties of the wire obtained using combined processing showed that its strength and plastic properties are comparable to the properties of the wire obtained from a cast billet, and the structure is characterized by a high degree of elaboration and compactness. Thus, as a result of the research, technological schemes have been developed and processing parameters have been determined for the production of rods and wire from graded chip waste of alloys 01570 and 1580 using compaction, discrete and continuous extrusion, as well as cold drawing. © 2022 The AuthorsMinistry of Education and Science of the Russian Federation, Minobrnauka: FSRZ-2020-0013The research was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (scientific theme code FSRZ-2020-0013)

SLITRK2, an X-linked modifier of the age at onset in C9orf72 frontotemporal lobar degeneration

The G4C2-repeat expansion in C9orf72 is the most common cause of frontotemporal dementia and of amyotrophic lateral sclerosis. The variability of age at onset and phenotypic presentations is a hallmark of C9orf72 disease. In this study, we aimed to identify modifying factors of disease onset in C9orf72 carriers using a family-based approach, in pairs of C9orf72 carrier relatives with concordant or discordant age at onset. Linkage and association analyses provided converging evidence for a locus on chromosome Xq27.3. The minor allele A of rs1009776 was associated with an earlier onset (P = 1 × 10-5). The association with onset of dementia was replicated in an independent cohort of unrelated C9orf72 patients (P = 0.009). The protective major allele delayed the onset of dementia from 5 to 13 years on average depending on the cohort considered. The same trend was observed in an independent cohort of C9orf72 patients with extreme deviation of the age at onset (P = 0.055). No association of rs1009776 was detected in GRN patients, suggesting that the effect of rs1009776 was restricted to the onset of dementia due to C9orf72. The minor allele A is associated with a higher SLITRK2 expression based on both expression quantitative trait loci (eQTL) databases and in-house expression studies performed on C9orf72 brain tissues. SLITRK2 encodes for a post-synaptic adhesion protein. We further show that synaptic vesicle glycoprotein 2 and synaptophysin, two synaptic vesicle proteins, were decreased in frontal cortex of C9orf72 patients carrying the minor allele. Upregulation of SLITRK2 might be associated with synaptic dysfunctions and drives adverse effects in C9orf72 patients that could be modulated in those carrying the protective allele. How the modulation of SLITRK2 expression affects synaptic functions and influences the disease onset of dementia in C9orf72 carriers will require further investigations. In summary, this study describes an original approach to detect modifier genes in rare diseases and reinforces rising links between C9orf72 and synaptic dysfunctions that might directly influence the occurrence of first symptoms

Dedifferentiation of Foetal CNS Stem Cells to Mesendoderm-Like Cells through an EMT Process

Tissue-specific stem cells are considered to have a limited differentiation potential. Recently, this notion was challenged by reports that showed a broader differentiation potential of neural stem cells, in vitro and in vivo, although the molecular mechanisms that regulate plasticity of neural stem cells are unknown. Here, we report that neural stem cells derived from mouse embryonic cortex respond to Lif and serum in vitro and undergo epithelial to mesenchymal transition (EMT)-mediated dedifferentiation process within 48 h, together with transient upregulation of pluripotency markers and, more notably, upregulation of mesendoderm genes, Brachyury (T) and Sox17. These induced putative mesendoderm cells were injected into early gastrulating chick embryos, which revealed that they integrated more efficiently into mesoderm and endoderm lineages compared to non-induced cells. We also found that TGFβ and Jak/Stat pathways are necessary but not sufficient for the induction of mesendodermal phenotype in neural stem cells. These results provide insights into the regulation of plasticity of neural stem cells through EMT. Dissecting the regulatory pathways involved in these processes may help to gain control over cell fate decisions

Comparison of clinical rating scales in genetic frontotemporal dementia within the GENFI cohort

BACKGROUND: Therapeutic trials are now underway in genetic forms of frontotemporal dementia (FTD) but clinical outcome measures are limited. The two most commonly used measures, the Clinical Dementia Rating (CDR)+National Alzheimer’s Disease Coordinating Center (NACC) Frontotemporal Lobar Degeneration (FTLD) and the FTD Rating Scale (FRS), have yet to be compared in detail in the genetic forms of FTD. METHODS: The CDR+NACC FTLD and FRS were assessed cross-sectionally in 725 consecutively recruited participants from the Genetic FTD Initiative: 457 mutation carriers (77 microtubule-associated protein tau (MAPT), 187 GRN, 193 C9orf72) and 268 family members without mutations (non-carrier control group). 231 mutation carriers (51 MAPT, 92 GRN, 88 C9orf72) and 145 non-carriers had available longitudinal data at a follow-up time point. RESULTS: Cross-sectionally, the mean FRS score was lower in all genetic groups compared with controls: GRN mutation carriers mean 83.4 (SD 27.0), MAPT mutation carriers 78.2 (28.8), C9orf72 mutation carriers 71.0 (34.0), controls 96.2 (7.7), p<0.001 for all comparisons, while the mean CDR+NACC FTLD Sum of Boxes was significantly higher in all genetic groups: GRN mutation carriers mean 2.6 (5.2), MAPT mutation carriers 3.2 (5.6), C9orf72 mutation carriers 4.2 (6.2), controls 0.2 (0.6), p<0.001 for all comparisons. Mean FRS score decreased and CDR+NACC FTLD Sum of Boxes increased with increasing disease severity within each individual genetic group. FRS and CDR+NACC FTLD Sum of Boxes scores were strongly negatively correlated across all mutation carriers (r_{s} =−0.77, p<0.001) and within each genetic group (r_{s} =−0.67 to −0.81, p<0.001 in each group). Nonetheless, discrepancies in disease staging were seen between the scales, and with each scale and clinician-judged symptomatic status. Longitudinally, annualised change in both FRS and CDR+NACC FTLD Sum of Boxes scores initially increased with disease severity level before decreasing in those with the most severe disease: controls −0.1 (6.0) for FRS, −0.1 (0.4) for CDR+NACC FTLD Sum of Boxes, asymptomatic mutation carriers −0.5 (8.2), 0.2 (0.9), prodromal disease −2.3 (9.9), 0.6 (2.7), mild disease −10.2 (18.6), 3.0 (4.1), moderate disease −9.6 (16.6), 4.4 (4.0), severe disease −2.7 (8.3), 1.7 (3.3). Sample sizes were calculated for a trial of prodromal mutation carriers: over 180 participants per arm would be needed to detect a moderate sized effect (30%) for both outcome measures, with sample sizes lower for the FRS. CONCLUSIONS: Both the FRS and CDR+NACC FTLD measure disease severity in genetic FTD mutation carriers throughout the timeline of their disease, although the FRS may be preferable as an outcome measure. However, neither address a number of key symptoms in the FTD spectrum, for example, motor and neuropsychiatric deficits, which future scales will need to incorporate