The weak core inverse

[EN] In this paper, we introduce a new generalized inverse, called weak core inverse (or, in short, WC inverse) of a complex square matrix. This new inverse extends the notion of the core inverse defined by Baksalary and Trenkler (Linear Multilinear Algebra 58(6):681-697, 2010). We investigate characterizations, representations, and properties for this generalized inverse. In addition, we introduce weak core matrices (or, in short, WC matrices) and we show that these matrices form a more general class than that given by the known weak group matrices, recently investigated by H. Wang and X. Liu.In what follows, we detail the acknowledgements. D.E. Ferreyra, F.E. Levis, A.N. Priori - Partially supported by Universidad Nacional de Rio Cuarto (Grant PPI 18/C559) and CONICET (Grant PIP 112-201501-00433CO). D.E. Ferreyra F.E. Levis - Partially supported by ANPCyT (Grant PICT 201803492). D.E. Ferreyra, N. Thome -Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (Grant Resol. Nro. 135/19). N. Thome -Partially supported by Ministerio de Economia, Industria y Competitividad of Spain (Grant Red de Excelencia MTM2017-90682-REDT) and by Universidad Nacional del Sur of Argentina (Grant 24/L108). We would like to thank the Referees for their valuable comments and suggestions which helped us to considerably improve the presentation of the paperFerreyra, DE.; Levis, FE.; Priori, AN.; Thome, N. (2021). The weak core inverse. Aequationes Mathematicae. 95(2):351-373. https://doi.org/10.1007/s00010-020-00752-zS351373952Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications, 2nd edn. Springer, New York (2003)Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)Baksalary, O.M., Trenkler, G.: On a generalized core inverse. Appl. Math. 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CLOCK Genes and Circadian Rhythmicity in Alzheimer Disease

Disturbed circadian rhythms with sleep problems and disrupted diurnal activity are often seen in patients suffering from Alzheimer disease (AD). Both endogenous CLOCK genes and external Zeitgeber are responsible for the maintenance of circadian rhythmicity in humans. Therefore, modifications of the internal CLOCK system and its interactions with exogenous factors might constitute the neurobiological basis for clinically observed disruptions in rhythmicity, which often have grave consequences for the quality of life of patients and their caregivers. Presently, more and more data are emerging demonstrating how alterations of the CLOCK gene system might contribute to the pathophysiology of AD and other forms of dementia. At the same time, the impact of neuropsychiatric medication on CLOCK gene expression is under investigation

Characterizations of k-commutative equalities for some outer generalized inverses

[EN] In this paper, we present necessary and sufficient conditions for the k-commutative equality , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.D. E. Ferreyra F. E. Levis Partially supported by a Consejo Nacional de Investigaciones Científicas y Técnicas CONICET s Posdoctoral Research Fellowship, UNRC [grant number PPI 18/C472] and CONICET [grant number PIP 112-201501-00433CO], respectively. N. Thome Partially supported by Secretaría de Estado de Investigación, Desarrollo e Innovación Ministerio de Economía, Industria y Competitividad of Spain [grant number DGI MTM2013-43678-P and Grant Red de Excelen- cia PMTM2017-90682-REDT]. D. E. Ferreyra and N. Thome Partially supported Universidad Nacional de La Pampa (UNLPam), Facultad de Ingeniería [grant Resol. No 155/14].Ferreyra, DE.; Levis, F.; Thome, N. (2018). Characterizations of k-commutative equalities for some outer generalized inverses. Linear and Multilinear Algebra. 1-16. https://doi.org/10.1080/03081087.2018.1500994S116Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Manjunatha Prasad, K., & Mohana, K. S. (2013). Core–EP inverse. Linear and Multilinear Algebra, 62(6), 792-802. doi:10.1080/03081087.2013.791690Malik, S. B., & Thome, N. (2014). On a new generalized inverse for matrices of an arbitrary index. Applied Mathematics and Computation, 226, 575-580. doi:10.1016/j.amc.2013.10.060Mehdipour, M., & Salemi, A. (2017). On a new generalized inverse of matrices. Linear and Multilinear Algebra, 66(5), 1046-1053. doi:10.1080/03081087.2017.1336200Malik, S. B., Rueda, L., & Thome, N. (2016). The class ofm-EPandm-normal matrices. Linear and Multilinear Algebra, 64(11), 2119-2132. doi:10.1080/03081087.2016.1139037Wang, H. (2016). Core-EP decomposition and its applications. Linear Algebra and its Applications, 508, 289-300. doi:10.1016/j.laa.2016.08.008Wang H, Chen J. Weak group inverse. Available from: http://arxiv.org/abs/1704.08403v1Wei, Y. (1998). A characterization and representation of the generalized inverse A(2)T,S and its applications. Linear Algebra and its Applications, 280(2-3), 87-96. doi:10.1016/s0024-3795(98)00008-1Rakić, D. S., Dinčić, N. Č., & Djordjević, D. S. (2014). Core inverse and core partial order of Hilbert space operators. Applied Mathematics and Computation, 244, 283-302. doi:10.1016/j.amc.2014.06.112Stanimirović, P. S., Katsikis, V. N., & Ma, H. (2016). Representations and properties of theW-Weighted Drazin inverse. Linear and Multilinear Algebra, 65(6), 1080-1096. doi:10.1080/03081087.2016.1228810Ferreyra, D. E., Levis, F. E., & Thome, N. (2017). Revisiting the core EP inverse and its extension to rectangular matrices. Quaestiones Mathematicae, 41(2), 265-281. doi:10.2989/16073606.2017.1377779Deng, C. Y., & Du, H. K. (2009). REPRESENTATIONS OF THE MOORE-PENROSE INVERSE OF 2×2 BLOCK OPERATOR VALUED MATRICES. Journal of the Korean Mathematical Society, 46(6), 1139-1150. doi:10.4134/jkms.2009.46.6.1139Wang, H., & Liu, X. (2014). Characterizations of the core inverse and the core partial ordering. Linear and Multilinear Algebra, 63(9), 1829-1836. doi:10.1080/03081087.2014.97570

Opportunities to Intercalibrate Radiometric Sensors From International Space Station

Highly accurate measurements of Earth's thermal infrared and reflected solar radiation are required for detecting and predicting long-term climate change. We consider the concept of using the International Space Station to test instruments and techniques that would eventually be used on a dedicated mission such as the Climate Absolute Radiance and Refractivity Observatory. In particular, a quantitative investigation is performed to determine whether it is possible to use measurements obtained with a highly accurate reflected solar radiation spectrometer to calibrate similar, less accurate instruments in other low Earth orbits. Estimates of numbers of samples useful for intercalibration are made with the aid of year-long simulations of orbital motion. We conclude that the International Space Station orbit is ideally suited for the purpose of intercalibration

CLARREO Approach for Reference Intercalibration of Reflected Solar Sensors: On-Orbit Data Matching and Sampling

The implementation of the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission was recommended by the National Research Council in 2007 to provide an on-orbit intercalibration standard with accuracy of 0.3% (k = 2) for relevant Earth observing sensors. The goal of reference intercalibration, as established in the Decadal Survey, is to enable rigorous high-accuracy observations of critical climate change parameters, including reflected broadband radiation [Clouds and Earth's Radiant Energy System (CERES)], cloud properties [Visible Infrared Imaging Radiometer Suite (VIIRS)], and changes in surface albedo, including snow and ice albedo feedback. In this paper, we describe the CLARREO approach for performing intercalibration on orbit in the reflected solar (RS) wavelength domain. It is based on providing highly accurate spectral reflectance and reflected radiance measurements from the CLARREO Reflected Solar Spectrometer (RSS) to establish an on-orbit reference for existing sensors, namely, CERES and VIIRS on Joint Polar Satellite System satellites, Advanced Very High Resolution Radiometer and follow-on imagers on MetOp, Landsat imagers, and imagers on geostationary platforms. One of two fundamental CLARREO mission goals is to provide sufficient sampling of high-accuracy observations that are matched in time, space, and viewing angles with measurements made by existing instruments, to a degree that overcomes the random error sources from imperfect data matching and instrument noise. The data matching is achieved through CLARREO RSS pointing operations on orbit that align its line of sight with the intercalibrated sensor. These operations must be planned in advance; therefore, intercalibration events must be predicted by orbital modeling. If two competing opportunities are identified, one target sensor must be given priority over the other. The intercalibration method is to monitor changes in targeted sensor response function parameters: effective offset, gain, nonlinearity, optics spectral response, and sensitivity to polarization. In this paper, we use existing satellite data and orbital simulationmethods to determinemission requirements for CLARREO, its instrument pointing ability, methodology, and needed intercalibration sampling and data matching for accurate intercalibration of RS radiation sensors on orbit

The EOS Prototype Validation Exercise (PROVE) at Jornada: Overview and Lessons Learned

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W+jets Matrix Elements and the Dipole Cascade

We extend the algorithm for matching fixed-order tree-level matrix element generators with the Dipole Cascade Model in Ariadne to apply to processes with incoming hadrons. We test the algoritm on for the process W+n jets at the Tevatron, and find that the results are fairly insensitive to the cutoff used to regularize the soft and collinear divergencies in the tree-level matrix elements. We also investigate a few observables to check the sensitivity to the matrix element correction

Robust avoidance of edge-localized modes alongside gradient formation in the negative triangularity tokamak edge

In a series of high performance diverted discharges on DIII-D, we demonstrate that strong negative triangularity (NT) shaping robustly suppresses all edge-localized mode (ELM) activity over a wide range of plasma conditions: $\langle n\rangle=0.1-1.5\times10^{20}$m$^{-3}$, $P_\mathrm{aux}=0-15$MW and $|B_\mathrm{t}|=1-2.2$T, corresponding to $P_\mathrm{loss}/P_\mathrm{LH08}\sim8$. The full dataset is consistent with the theoretical prediction that magnetic shear in the NT edge inhibits access to ELMing H-mode regimes; all experimental pressure profiles are found to be at or below the infinite-$n$ ballooning stability limit. Importantly, we also report enhanced edge pressure gradients at strong NT that are significantly steeper than in traditional ELM-free L-mode plasmas and provide significant promise for NT reactor integration.Comment: 5 pages, 5 figure

Malt1 protease inactivation efficiently dampens immune responses but causes spontaneous autoimmunity.

The protease activity of the paracaspase Malt1 has recently gained interest as a drug target for immunomodulation and the treatment of diffuse large B-cell lymphomas. To address the consequences of Malt1 protease inactivation on the immune response in vivo, we generated knock-in mice expressing a catalytically inactive C472A mutant of Malt1 that conserves its scaffold function. Like Malt1-deficient mice, knock-in mice had strong defects in the activation of lymphocytes, NK and dendritic cells, and the development of B1 and marginal zone B cells and were completely protected against the induction of autoimmune encephalomyelitis. Malt1 inactivation also protected the mice from experimental induction of colitis. However, Malt1 knock-in mice but not Malt1-deficient mice spontaneously developed signs of autoimmune gastritis that correlated with an absence of Treg cells, an accumulation of T cells with an activated phenotype and high serum levels of IgE and IgG1. Thus, removal of the enzymatic activity of Malt1 efficiently dampens the immune response, but favors autoimmunity through impaired Treg development, which could be relevant for therapeutic Malt1-targeting strategies