An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

This paper deals with singular systems of index k ≥ 1. Our main goal is to find a state-feedback such that the closed-loop system satis- fies the regularity condition and it is nonnegative and stable. In order to do that, the core-nilpotent decomposition of a square matrix is applied to the singular matrix of the system. Moreover, if the Drazin projector of this matrix is nonnegative then the previous decomposition allows us to write the core-part of the matrix in a specific block form. In addition, an algorithm to study this kind of systems via a state-feedback is designed.This paper has been partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228].Herrero Debón, A.; Francisco J. Ramírez; Thome, N. (2014). An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index. Linear and Multilinear Algebra. 1-11. https://doi.org/10.1080/03081087.2014.904559S11

Further properties on the core partial order and other matrix partial orders

This paper carries further the study of core partial order initiated by Baksalary and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:681-697]. We have extensively studied the core partial order, and some new characterizations are obtained in this paper. In addition, simple expressions for the already known characterizations of the minus, the star (and one-sided star), the sharp (and one-sided sharp) and the diamond partial orders are also obtained by using a Hartwig-Spindelbck decomposition.This author was partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228] and by Universidad Nacional de La Pampa, Argentina, Facultad de Ingenieria [grant number Resol. No 049/11].Malik, SB.; Rueda, LC.; Thome, N. (2014). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra. 62(12):1629-1648. https://doi.org/10.1080/03081087.2013.839676S162916486212Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8Groβ, J., Hauke, J., & Markiewicz, A. (1999). Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and its Applications, 289(1-3), 161-168. doi:10.1016/s0024-3795(98)10108-8Mosić, D., & Djordjević, D. S. (2012). Reverse order law for the group inverse in rings. Applied Mathematics and Computation, 219(5), 2526-2534. doi:10.1016/j.amc.2012.08.088Patrício, P., & Costa, A. (2009). On the Drazin index of regular elements. Open Mathematics, 7(2). doi:10.2478/s11533-009-0015-6Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052Hartwig, R. E., & Spindelböck, K. (1983). Matrices for whichA∗andA†commute. Linear and Multilinear Algebra, 14(3), 241-256. doi:10.1080/03081088308817561Baksalary, O. M., Styan, G. P. H., & Trenkler, G. (2009). On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications, 430(10), 2798-2812. doi:10.1016/j.laa.2009.01.015Mielniczuk, J. (2011). Note on the core matrix partial ordering. Discussiones Mathematicae Probability and Statistics, 31(1-2), 71. doi:10.7151/dmps.1134Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.978089871951

Modular and predictable assembly of porous organic molecular crystals

Nanoporous molecular frameworks are important in applications such as separation, storage and catalysis. Empirical rules exist for their assembly but it is still challenging to place and segregate functionality in three-dimensional porous solids in a predictable way. Indeed, recent studies of mixed crystalline frameworks suggest a preference for the statistical distribution of functionalities throughout the pores rather than, for example, the functional group localization found in the reactive sites of enzymes. This is a potential limitation for 'one-pot' chemical syntheses of porous frameworks from simple starting materials. An alternative strategy is to prepare porous solids from synthetically preorganized molecular pores. In principle, functional organic pore modules could be covalently prefabricated and then assembled to produce materials with specific properties. However, this vision of mix-and-match assembly is far from being realized, not least because of the challenge in reliably predicting three-dimensional structures for molecular crystals, which lack the strong directional bonding found in networks. Here we show that highly porous crystalline solids can be produced by mixing different organic cage modules that self-assemble by means of chiral recognition. The structures of the resulting materials can be predicted computationally, allowing in silico materials design strategies. The constituent pore modules are synthesized in high yields on gram scales in a one-step reaction. Assembly of the porous co-crystals is as simple as combining the modules in solution and removing the solvent. In some cases, the chiral recognition between modules can be exploited to produce porous organic nanoparticles. We show that the method is valid for four different cage modules and can in principle be generalized in a computationally predictable manner based on a lock-and-key assembly between modules

Insights into GABA receptor signalling in TM3 Leydig cells

gamma-Aminobutyric acid (GABA) is an emerging signalling molecule in endocrine organs, since it is produced by endocrine cells and acts via GABA(A) receptors in a paracrine/autocrine fashion. Testicular Leydig cells are producers and targets for GABA. These cells express GABA(A) receptor subunits and in the murine Leydig cell line TM3 pharmacological activation leads to increased proliferation. The signalling pathway of GABA in these cells is not known in this study. We therefore attempted to elucidate details of GABA(A) signalling in TM3 and adult mouse Leydig cells using several experimental approaches. TM3 cells not only express GABA(A) receptor subunits, but also bind the GABA agonist {[}H-3] muscimol with a binding affinity in the range reported for other endocrine cells (K-d = 2.740 +/- 0.721 nM). However, they exhibit a low B-max value of 28.08 fmol/mg protein. Typical GABA(A) receptor-associated events, including Cl- currents, changes in resting membrane potential, intracellular Ca2+ or cAMP, were not measurable with the methods employed in TM3 cells, or, as studied in part, in primary mouse Leydig cells. GABA or GABA(A) agonist isoguvacine treatment resulted in increased or decreased levels of several mRNAs, including transcription factors (c-fos, hsf-1, egr-1) and cell cycle-associated genes (Cdk2, cyclin D1). In an attempt to verify the cDNA array results and because egr-1 was recently implied in Leydig cell development, we further studied this factor. RT-PCR and Western blotting confirmed a time-dependent regulation of egr-1 in TM3. In the postnatal testis egr-1 was seen in cytoplasmic and nuclear locations of developing Leydig cells, which bear GABA(A) receptors and correspond well to TM3 cells. Thus, GABA acts via an untypical novel signalling pathway in TM3 cells. Further details of this pathway remain to be elucidated. Copyright (c) 2005 S. Karger AG, Base

Successful treatment of fusarium solani ecthyma gangrenosum in a patient affected by leukocyte adhesion deficiency type 1 with granulocytes transfusions

<p>Abstract</p> <p>Background</p> <p>Ecthyma gangrenosum (EG) manifests as a skin lesion affecting patients suffering extreme neutropenia and is commonly associated with <it>Pseudomonas aeruginosa </it>in immunocompromised patients. Leukocyte adhesion deficiency I (LAD I) which count among primary immunodeficiency syndromes of the innate immunity, is an autosomal recessive disorder characterized in its severe phenotype by a complete defect in CD18 expression on neutrophils, delayed cord separation, chronic skin ulcers mainly due to recurrent bacterial and fungal infections, leucocytosis with high numbers of circulating neutrophils and an accumulation of abnormally low number of neutrophils at sites of infection.</p> <p>Case Presentation</p> <p>We report at our knowledge the first case of a child affected by LAD-1, who experienced during her disease course a multi-bacterial and fungal EG lesion caused by <it>fusarium solani</it>. Despite targeted antibiotics and anti-fungi therapy, the lesion extended for as long as 18 months and only massive granulocytes pockets transfusions in association with G-CSF had the capacity to cure this lesion.</p> <p>Conclusion</p> <p>We propose that granulocytes pockets transfusions will be beneficial to heal EG especially in severely immunocompromised patients.</p

Probabilistic abstract interpretation: From trace semantics to DTMC’s and linear regression

In order to perform probabilistic program analysis we need to consider probabilistic languages or languages with a probabilistic semantics, as well as a corresponding framework for the analysis which is able to accommodate probabilistic properties and properties of probabilistic computations. To this purpose we investigate the relationship between three different types of probabilistic semantics for a core imperative language, namely Kozen’s Fixpoint Semantics, our Linear Operator Semantics and probabilistic versions of Maximal Trace Semantics. We also discuss the relationship between Probabilistic Abstract Interpretation (PAI) and statistical or linear regression analysis. While classical Abstract Interpretation, based on Galois connection, allows only for worst-case analyses, the use of the Moore-Penrose pseudo inverse in PAI opens the possibility of exploiting statistical and noisy observations in order to analyse and identify various system properties

Vascular disease and vascular risk factors in relation to motor features and cognition in early Parkinson's disease

OBJECTIVE: The purpose of this study was to examine the relationship between vascular disease (and vascular risk factors), cognition and motor phenotype in Parkinson's disease (PD). METHODS: Recently diagnosed PD cases were enrolled in a multicenter prospective observational longitudinal cohort study. Montreal cognitive assessment (normal >23, mild cognitive impairment 22 to 23 or lower but without functional impairment, and dementia 21 or less with functional impairment) and Movement Disorder Society Unified PD Rating Scale part 3 (UPDRS 3) scores were analyzed in relation to a history of vascular events and risk factors. RESULTS: In 1759 PD cases, mean age 67.5 (standard deviation 9.3) years, mean disease duration 1.3 (standard deviation 0.9) years, 65.2% were men, 4.7% had a history of prior stroke or transient ischemic attack, and 12.5% had cardiac disease (angina, myocardial infarction, heart failure). In cases without a history of vascular disease, hypertension was recorded in 30.4%, high cholesterol 27.3%, obesity 20.7%, diabetes 7.2%, and cigarette smoking in 4.6%. Patients with prior stroke or transient ischemic attack were more likely to have cognitive impairment (42% vs 25%) and postural instability gait difficulty (53.5% vs 39.5%), but these findings were not significant after adjustment for age, sex, and disease duration (P = .075). The presence of more than 2 vascular risks was associated with worse UPDRS 3 motor scores (beta coefficient 4.05, 95% confidence interval 1.48, 6.61, p = .002) and with cognitive impairment (ordinal odds ratio 2.24, 95% confidence interval 1.34, 3.74, p = .002). In 842 patients (47.8%) with structural brain imaging, white matter leukoaraiosis, but not lacunar or territorial infarction, was associated with impaired cognition (p = .006) and postural instability gait difficulty (p = .010). CONCLUSION: Vascular comorbidity is significantly associated with cognitive and gait impairment in patients with early PD, which may have prognostic and treatment implications. © 2016 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society

Modeling HIV-1 Drug Resistance as Episodic Directional Selection

The evolution of substitutions conferring drug resistance to HIV-1 is both episodic, occurring when patients are on antiretroviral therapy, and strongly directional, with site-specific resistant residues increasing in frequency over time. While methods exist to detect episodic diversifying selection and continuous directional selection, no evolutionary model combining these two properties has been proposed. We present two models of episodic directional selection (MEDS and EDEPS) which allow the a priori specification of lineages expected to have undergone directional selection. The models infer the sites and target residues that were likely subject to directional selection, using either codon or protein sequences. Compared to its null model of episodic diversifying selection, MEDS provides a superior fit to most sites known to be involved in drug resistance, and neither one test for episodic diversifying selection nor another for constant directional selection are able to detect as many true positives as MEDS and EDEPS while maintaining acceptable levels of false positives. This suggests that episodic directional selection is a better description of the process driving the evolution of drug resistance