The Dixmier trace and the Wodzicki residue for global pseudo-differential operators on compact manifolds

In this note, we announce the results of our investigation on the Dixmier trace and the Wodzicki residue for pseudo-differential operators on compact manifolds. We give formulae for the Dixmier trace and the non-commutative residue (also called Wodzicki’s residue) of invariant pseudo-differential operators on compact manifolds with or without boundary. For every closed manifold, the notion of global symbol for invariant pseudo-differential operators will be based on the Fourier analysis associated to every elliptic and positive operator (developed by M. Ruzhansky, V. Turunen and J. Delgado). In particular, for each compact Lie group we will use its representation theory. For the analysis of operators on compact manifolds with boundary, we will use the non-harmonic analysis associated with boundary valued problems (developed by M. Ruzhansky, N. Tokmagambetov, and J. Delgado).En esta nota se anuncian los resultados de nuestra investigación sobre la traza de Dixmier y el residuo de Wodzicki para operadores pseudodiferenciales sobre variedades compactas. Se calcula la traza de Dixmier y el residuo no conmutativo (residuo de Wodzicki) de operadores pseudodiferenciales invariantes sobre variedades compactas con o sin borde. Para cada variedad cerrada (suave, compacta y sin borde), se emplea la noción de símbolo global que viene dada por el análisis de Fourier asociado a cada operador elíptico y positivo (desarrollado por M. Ruzhansky and V. Turunen para para grupos de Lie y por M. Ruzhansky, N. Tokmagambetov y J. Delgado para variedades cerradas). En particular, para cada grupo de Lie compacto, se usa su teoría de representación. Respecto al análisis de operadores sobre variedades con borde, se usa el análisis no armónico asociado a problemas con valores de frontera (introducido por M. Ruzhansky, N. Tokmagambetov, y J. Delgado)

Modelling and Test of an Integrated Magnetic Spring-Eddy Current Damper for Space Applications

This article belongs to the Special Issue Actuators and Dampers for Vibration Control: Damping and Isolation Applications.We present the design, manufacturing, and dynamical characterization of a mechanical suspension made by a passive magnetic spring and an eddy current damper integrated into a single device. Three configurations with 2, 3, and 4 permanent magnets axially distributed with opposite polarizations are designed, simulated, manufactured, and tested. Stiffness of 2410, 2050, 2090 N/m and damping coefficient of 5.45, 10.52 and 17.25 Ns/m are measured for the 2-, 3-, and 4-magnets configurations, respectively. The magnetic suspension provides good mechanical properties combined with excellent cleanness and high reliability, which is very desirable in mechanical systems for space applications.The research leading to these results has received funding from the Spanish Ministerio de Economía y Competitividad under the Plan Estatal de I+D+I 2013-2016, grant agreement no ESP2015-72458-EXP

Factor H-related protein 1 neutralizes anti-factor H autoantibodies in autoimmune hemolytic uremic syndrome.

The autoimmune form of atypical hemolytic uremic syndrome (HUS) is characterized by circulating autoantibodies against the complement regulator factor H, and is often associated with deficiency of the factor H-related proteins CFHR1 and CFHR3. Here we studied whether anti-factor H autoantibodies crossreact with CFHR1, and determined functional consequences of this. In ELISA, anti-factor H immunoglobulin G (IgG) autoantibodies from 24 atypical HUS patients bound to the short consensus repeat 20 domain of factor H, 21 antibodies also recognized CFHR1, but none CFHR3. Three patients also had anti-factor H IgA autoantibodies crossreacting with CFHR1. Analysis of the IgG fractions in CFHR1-deficient patients found that CFHR1-IgG complexes were formed during plasma exchange treatment, indicating that autoantibodies recognize CFHR1 in vivo. Recombinant CFHR1 prevented hemolysis of sheep erythrocytes caused by patient plasma containing anti-factor H IgG, but it did not inhibit red cell lysis caused by a factor H mutation (W1183 L) in the short consensus repeat 20 domain. Thus, exogenous CFHR1 provided during plasma exchange therapy may neutralize anti-factor H autoantibodies and help in the treatment of autoimmune atypical HUS

Autoantibodies to complement components in C3 glomerulopathy and atypical hemolytic uremic syndrome.

The alternative pathway of complement is implicated in the pathogenesis of several renal diseases, such as atypical hemolytic uremic syndrome, dense deposit disease and other forms of C3 glomerulopathy. The underlying complement defects include genetic and/or acquired factors, the latter in the form of autoantibodies. Because the autoimmune forms require a specific treatment, in part different from that of the genetic forms, it is important to detect the autoantibodies as soon as possible and understand their characteristics. In this overview, we summarize the types of anti-complement autoantibodies detected in such diseases, i.e. autoantibodies to factor H, factor I, C3b, factor B and those against the C3 convertases (C3 nephritic factor and C4 nephritic factor). We draw attention to newly described autoantibodies and their characteristics, and highlight similarities and differences in the autoimmune forms of these diseases

Accelerometer-Measured Physical Activity, Inactivity, and Related Factors in Family Caregivers of Patients with Terminal Cancer

The physical activity (PA) and inactivity of family caregivers of cancer patients were investigated and related to burden and quality of life through a cross-sectional multicentre study. A total of 75 caregivers were recruited from June 2020 to March 2021. The levels of PA and inactivity were estimated with a wrist accelerometer, 24 h a day, for 7 consecutive days. The Quality of Life Family Version, the Caregiver Strain Index, the total duration of care, the average number of hours spent in care, and the assistance received were registered. Our results showed that moderate-to-vigorous PA was 96.40 ± 46.93 min/day, with 90.7% of participants performing more than 150 min/week of physical activity, and this was significantly associated with age (r = −0.237). Daily inactivity was 665.78 ± 94.92 min, and inactivity for 20–30 min was significantly associated with caregiver burden (r = 0.232) and quality of life (r = −0.322). Compliance with the World Health Organization recommendations was significantly associated with a lower quality of life (r = −0.269). The strength of these associations was limited (r ~0.2). In conclusion, the PA performed by most caregivers met the established recommendations, although older caregivers (>65 years old) performed lower moderate-to-vigorous PA than younger ones. In addition, the mean inactive time was high (11 h/day), showing slight relationships with the burden and quality of life of caregiversExternal funding for this study involving research, development, and innovation (R + D + I) in biomedical and health sciences in Andalusia was obtained from the Regional Health Ministry of “Junta de Andalucia”, under Project AP-0225-2019. This work was partially funded by Junta de Andalucia and ERDF with the project “UMA20-FEDERJA-154” of financial support for R + D + I projects in the ERDF-Andalusia Operational Programme 2014–2020 (Programa Operativo FEDER Andalucía 2014-2020). J.C.-P. is supported by a predoctoral grant from the Spanish Ministry of Education (Ministerio de Educación), grant number FPU19/02326. Partial funding for open access charge: Universidad de Málag

Metal Knitting: A New Strategy for Cold Gas Spray Additive Manufacturing

Cold Spray Additive Manufacturing (CSAM) is an emergent technique to produce parts by the additive method, and, like other technologies, it has pros and cons. Some advantages are using oxygen-sensitive materials to make parts, such as Ti alloys, with fast production due to the high deposition rate, and lower harmful residual stress levels. However, the limitation in the range of the parts' geometries is a huge CSAM con. This work presents a new conceptual strategy for CSAM spraying. The controlled manipulation of the robot arm combined with the proper spraying parameters aims to optimize the deposition efficiency and the adhesion of particles on the part sidewalls, resulting in geometries from thin straight walls, less than 5 mm thick, up to large bulks. This new strategy, Metal Knitting, is presented regarding its fundamentals and by comparing the parts' geometries produced by Metal Knitting with the traditional strategy. The Metal Knitting described here made parts with vertical sidewalls, in contrast to the 40 degrees of inclination obtained by the traditional strategy. Their mechanical properties, microstructures, hardness, and porosity are also compared for Cu, Ti, Ti6Al4V, 316L stainless steel, and Al

Heterogeneity but individual constancy of epitopes, isotypes and avidity of factor H autoantibodies in atypical hemolytic uremic syndrome

Factor H (FH) autoantibodies are present in 6-10% of atypical hemolytic uremic syndrome (aHUS) patients, most of whom have homozygous deficiency of the FH-related protein FHR-1. Although the pathogenic role of the autoantibodies is established, little is known about their molecular characteristics and changes over time. Here, we describe the specificity and other immunological features of anti-FH autoantibodies in the Spanish and Hungarian aHUS cohorts. A total of 19 patients were included and serial samples of 14 of them were available. FH autoantibodies from FHR-1 deficient patients (n=13) mainly recognized FH, its SCR19-20 fragment and FHR-1, but autoantibody specificity in patients who are homo- or heterozygous for the CFHR1 gene (n=6) was heterogeneous. No significant changes apart from total antibody titer were observed during follow-up in each patient. Fine epitope mapping with recombinant FH SCR19-20 containing single amino acid mutations showed significantly reduced binding in 6 out of 14 patients. In most cases, autoantibody binding to residues 1183-1189 and 1210-1215 was impaired, revealing a major common autoantibody epitope. Avidities showed variations between patients, but in most cases the avidity index did not change upon time. Most autoantibodies were IgG3, and all but three presented only with kappa or with lambda light chains. Although the pathogenic role of anti-FH autoantibodies in aHUS is well established, this study shows autoantibody heterogeneity among patients, but no significant variation in their characteristics over time in each patient. The presence of a single light chain in 16 out of 19 patients and the limited number of recognized epitopes suggest a restricted autoantibody response in most patients

Hβ\beta spectroscopy of the high-inclination black hole transient Swift J1357.2-0933 during quiescence

Swift J1357.2-0933 is a transient low-mass X-ray binary hosting a stellar-mass black hole. The source exhibits optical dips and very broad emission lines during both outburst and quiescence, which are thought to be the result of a high orbital inclination. We present phase-resolved spectroscopy obtained with the 10.4m Gran Telescopio Canarias (GTC). The spectra focus on the $\rm{H}\beta$ spectral region during X-ray quiescence. The emission line is exceptionally broad (full width at half maximum, FWHM > 4000 \AA), in agreement with previous studies focused on $\rm{H}\alpha$. A two-Gaussian fit to the prominent double-peaked profile reveals a periodic variability in the centroid position of the line. We also produced a diagnostic diagram aimed at constraining additional orbital parameters. Together, they allow us to independently confirm the orbital period of the system using a new dataset obtained five years after the previous outburst. However, our estimates for both the systemic velocity and the radial velocity semi-amplitude of the black hole reveal larger values than those found in previous studies. We argue that this could be explained by the precession of the disc and the presence of a hotspot. We found evidence of a narrow inner core in the double-peaked H$\beta$ emission profile. We studied its evolution across the orbit, finding that it is likely to result from the occultation of inner material by the outer rim bulge, further supporting the high orbital inclination hypothesis.Comment: 6 pages, 4 figure

Sex-Specific Relationships of Physical Activity and Sedentary Behaviour with Oxidative Stress and Inflammatory Markers in Young Adults

This study aims to analyse sex-specific associations of physical activity and sedentary behaviour with oxidative stress and inflammatory markers in a young-adult population. Sixty participants (21 women, 22.63 ± 4.62 years old) wore a hip accelerometer for 7 consecutive days to estimate their physical activity and sedentarism. Oxidative stress (catalase, superoxide dismutase, glutathione peroxidase, glutathione, malondialdehyde, and advanced oxidation protein products) and inflammatory (tumour necrosis factor-alpha and interleukin-6) markers were measured. Student t-tests and single linear regressions were applied. The women presented higher catalase activity and glutathione concentrations, and lower levels of advanced protein-oxidation products, tumour necrosis factor-alpha, and interleukin-6 than the men (p < 0.05). In the men, longer sedentary time was associated with lower catalase activity (β = −0.315, p = 0.04), and longer sedentary breaks and higher physical-activity expenditures were associated with malondialdehyde (β = −0.308, p = 0.04). Vigorous physical activity was related to inflammatory markers in the women (tumour necrosis factor-alpha, β = 0.437, p = 0.02) and men (interleukin−6, β = 0.528, p < 0.01). In conclusion, the women presented a better redox and inflammatory status than the men; however, oxidative-stress markers were associated with physical activity and sedentary behaviours only in the men. In light of this, women could have better protection against the deleterious effect of sedentarism but a worse adaptation to daily physical activity.This work was partly supported by Universidad de Cádiz (grant number PR2016-051 and PR2019-054), by Instituto de Investigación e Innovación Biomédica de Cádiz (LI19/21IN-CO09), and by the Spanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovación) (MCIN/AEI/ 10.13039/501100011033), grants PID2019-110063RA-I00 and PID2020-120034RA-I00. J.C.-P. is supported by a predoctoral grant from the Spanish Ministry of Education (Ministerio de Educación) (grant number FPU19/02326). D.V.-D is funded by the Margarita Salas Postdoctoral Program from European Union Next GenerationEU and University of Cádiz. Partial funding for open access charge: Universidad de Málag