Bounds on changes in Ritz values for a perturbed invariant subspace of a Hermitian matrix

The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix $X$ with columns that form an orthonormal basis for a subspace \X, and a Hermitian matrix $A$, the eigenvalues of $X^HAX$ are called Ritz values of $A$ with respect to \X. If the subspace \X is $A$-invariant then the Ritz values are some of the eigenvalues of $A$. If the $A$-invariant subspace \X is perturbed to give rise to another subspace \Y, then the vector of absolute values of changes in Ritz values of $A$ represents the absolute eigenvalue approximation error using \Y. We bound the error in terms of principal angles between \X and \Y. We capitalize on ideas from a recent paper [DOI: 10.1137/060649070] by A. Knyazev and M. Argentati, where the vector of absolute values of differences between Ritz values for subspaces \X and \Y was weakly (sub-)majorized by a constant times the sine of the vector of principal angles between \X and \Y, the constant being the spread of the spectrum of $A$. In that result no assumption was made on either subspace being $A$-invariant. It was conjectured there that if one of the trial subspaces is $A$-invariant then an analogous weak majorization bound should only involve terms of the order of sine squared. Here we confirm this conjecture. Specifically we prove that the absolute eigenvalue error is weakly majorized by a constant times the sine squared of the vector of principal angles between the subspaces \X and \Y, where the constant is proportional to the spread of the spectrum of $A$. For many practical cases we show that the proportionality factor is simply one, and that this bound is sharp. For the general case we can only prove the result with a slightly larger constant, which we believe is artificial.Comment: 12 pages. Accepted to SIAM Journal on Matrix Analysis and Applications (SIMAX

Homage to George E. Palade Cell Protein Secretion in Vascular Biology: Overview and Updates

Abstract This short overview and updates expresses our brain-and-heart homage to George Emil Palade, "the most influential cell biologist ever". In his 1971 paper Palade wrote for Albert Claude, the founder of biological electron microscopic method: "Seldom has a field owed so much to a single man". Herein, we articulate the same words for George Palade, the Teacher of many generations in cell biology research and education. Accordingly, we focus on two paradigm shifts in the cell biology, namely (i) the transition from light to transmission electron microscopy in studying cell protein secretion made by George Palade, and (ii) the transition from contractile to secretory phenotype of vascular smooth muscle cells made by Maria Daria Haust followed and developed by our research group. Altogether, we argue that one of the present challenges in vascular biology is to cultivate secreto-centric thinking and thus further focusing on how we could make the vascular muscle's secretory pathways work for the benefit of human's cardiovascular health

Basal pseudoaneurysm of the lateral wall of the left ventricle – case report

Left ventricle pseudoaneurysm is a rare but serious complication, most often secondary to myocardial infarction. It is associated with high mortality due to a significant risk of rupture. We present a case of a patient with a large basal pseudoaneurysm of the lateral wall of the left ventricle. The pseudoaneurysm is discovered from a chest radiography performed after a COVID-19 infection. The diagnosis is confirmed by echocardiography and ventriculography. The patient underwent surgical treatment by endoventricular patch plasty – Dor procedure. The patient in our case lacked the typical symptoms and ECG features, furthermore he had no history of myocardial infarction, cardiac surgery, trauma or endocarditis

NGF-ome: its metabotrophic expression. Homage to Rita Levi-Montalcini

Nowadays, in the postgenome time, many "-ome" studies have emerged including proteome, transcriptome, interactome, metabolome, adipokinome, connectome. In this vein, the catchall term NGF-ome embodies all the actions of NGF in health and disease. Accordingly, the present Festschrift, also tabula gratulatoria, is to honor and acknowledge the contributions of the distinguished neuroscientist and magistra Rita Levi-Montalcini, the Nobel Prize winner-1986 for the discoverer of NGF. Today, NGF and another neurotrophin, brain-derived neuroptrophic factor (BDNF), are well recognized to mediate multiple biological phenomena, ranging from the neurotrophic through immunotrophic and epitheliotrophic to metabotrophic effects. These latter effects are involved in the maintenance of cardiometabolic homeostasis (glucose and lipid metabolism as well as energy balance, and cardioprotection). Circulating and/or tissue levels of NGF and BDNF are altered in cardiometabolic diseases (atherosclerosis, obesity, type 2 diabetes, metabolic syndrome, and type 3 diabetes/Alzheimer's disease). A hypothesis thus emerged that a metabotrophic deficit due to the reduction of NGF/BDNF availability and/or utilization may be implicated in the pathogenesis of cariometabolic and neurodegenerative diseases. The present challenge is therefore to cultivate a metabotrophic thinking about how we can modulate NGF/BDNF secretion and signaling for the benefit of human cardiometabolic and mood health.Biomedical Reviews 2010; 21: 25-29

Upper Limit of D0 Production in Central Pb-Pb Collisions at 158A GeV

Results are presented from a search for the decays D0 -> Kmin piplus and D0bar -> Kplus pimin in a sample of 3.8x10^6 central Pb-Pb events collected with a beam energy of 158A GeV by NA49 at the CERN SPS. No signal is observed. An upper limit on D0 production is derived and compared to predictions from several models.Comment: REVTEX 5 pages, 4 figure

Bose-Einstein correlations of pion pairs in central Pb+Pb collisions at CERN SPS energies

Measurements of Bose-Einstein correlations of pion pairs in central Pb+Pb collisions were performed with the NA49 detector at the CERN SPS for beam energies of 20A, 30A, 40A, 80A, and 158A GeV. Correlation functions were measured in the longitudinally co-moving ``out-side-long'' reference frame as a function of rapidity and transverse momentum in the forward hemisphere of the reaction. Radius and correlation strength parameters were obtained from fits of a Gaussian parametrization. The results show a decrease of the radius parameters with increasing transverse momentum characteristic of strong radial flow in the pion source. No striking dependence on pion-pair rapidity or beam energy is observed. Static and dynamic properties of the pion source are obtained from simultaneous fits with a blast-wave model to radius parameters and midrapidity transverse momentum spectra. Predictions of hydrodynamic and microscopic models of Pb+Pb collisions are discussed.Comment: 22 pages, 23 figure

Multiplicity fluctuations in nuclear collisions at 158 A GeV

System size dependence of multiplicity fluctuations of charged particles produced in nuclear collisions at 158 A GeV was studied in the NA49 CERN experiment. Results indicate a non-monotonic dependence of the scaled variance of the multiplicity distribution with a maximum for semi-peripheral Pb+Pb interactions with number of projectile participants of about 35. This effect is not observed in a string-hadronic model of nuclear collision HIJING.Comment: Presented at "Focus on Multiplicity", 17-19 of June, Bari, Ital

Transverse Momentum Fluctuations in Nuclear Collisions at 158 AGeV

Results are presented on event-by-event fluctuations in transverse momentum of charged particles, produced at forward rapidities in p+p, C+C, Si+Si and Pb+Pb collisions at 158 AGeV. Three different characteristics are discussed: the average transverse momentum of the event, the Phi_pT fluctuation measure and two-particle transverse momentum correlations. In the kinematic region explored, the dynamical fluctuations are found to be small. However, a significant system size dependence of Phi_pT is observed, with the largest value measured in peripheral Pb+Pb interactions. The data are compared with predictions of several models.Comment: will be submitted to Phys. Rev.