Fuzzy spaces and new random matrix ensembles

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate that, for any single kind of field (matrix), the distribution of its eigenvalues is still a Wigner semicircle but with a renormalized radius. For observables involving more than one type of matrix we obtain a new distribution corresponding to correlated Wigner semicircles.Comment: 12 pages, 1 figure; version to appear in Phys. Rev.

Spectrum of the Product of Independent Random Gaussian Matrices

We show that the eigenvalue density of a product X=X_1 X_2 ... X_M of M independent NxN Gaussian random matrices in the large-N limit is rotationally symmetric in the complex plane and is given by a simple expression rho(z,\bar{z}) = 1/(M\pi\sigma^2} |z|^{-2+2/M} for |z|<\sigma, and is zero for |z|> \sigma. The parameter \sigma corresponds to the radius of the circular support and is related to the amplitude of the Gaussian fluctuations. This form of the eigenvalue density is highly universal. It is identical for products of Gaussian Hermitian, non-Hermitian, real or complex random matrices. It does not change even if the matrices in the product are taken from different Gaussian ensembles. We present a self-contained derivation of this result using a planar diagrammatic technique for Gaussian matrices. We also give a numerical evidence suggesting that this result applies also to matrices whose elements are independent, centered random variables with a finite variance.Comment: 16 pages, 6 figures, minor changes, some references adde

Large N_c confinement and turbulence

We suggest that the transition that occurs at large $N_c$ in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder. The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in $d=2$ and $d=3$. Our analysis leads us to speculate that the universal behavior observed in these lattice simulations might be a generic feature of confinement, also in $d=4$ Yang-Mills theory.Comment: 4 pages, no figures- Some rewriting - Typos corrected - References completed and some correcte

Asymptotic mean density of sub-unitary ensemble

The large N limit of mean spectral density for the ensemble of NxN sub-unitary matrices derived by Wei and Fyodorov (J. Phys. A: Math. Theor. 41 (2008) 50201) is calculated by a modification of the saddle point method. It is shown that the result coincides with the one obtained within the free probability theory by Haagerup and Larsen (J. Funct. Anal. 176 (2000) 331)

The psychological influence of the diagnosis of breast cancer on therapeutic options selection

The therapeutic management decision-making process for breast cancer is complex, and is influenced by multiple factors including patient age, comorbidities, ethnicity, education, and availability of immediate or delayed reconstruction options. Our study analysed 276 patients diagnosed with breast cancer in the “Colțea” Clinical Hospital between 2014 and 2015. Mean patients age was 61.24, median 62, with a range of 31 to 89 years. Younger age was associated with a less advanced local disease and younger patients were more likely to choose and benefit from conservative surgery. Most patients (61.76%) came from rural areas. Place of origin had a significant influence on the tumor size at the time of diagnosis (3.9 cm vs. 1.8cm) as well as on the choice of surgical procedure. Personalized treatment management plans that include aesthetic satisfaction coupled with oncological safety should be the objectives of contemporary breast surgery. Patient age is so important to the decision making process that it has been proposed as a determinant of educational and counselling strategies. From our experience, young patients from urban areas were more proactive patients. They were diagnosed earlier and more involved in treatment decisions compared with patients from rural areas, who generally did not question the surgeon’s opinion. Factors that influence the decision-making process likely include age, socioeconomic status, availability of radiotherapy, the necessity of periodic follow-up and the concern about recurrence

Multiplication law and S transform for non-hermitian random matrices

We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define the corresponding non-hermitian S transform being a natural generalization of the Voiculescu S transform. In addition we extend the classical hermitian S transform approach to deal with the situation when the random matrix ensemble factors have vanishing mean including the case when both of them are centered. We use planar diagrammatic techniques to derive these results.Comment: 25 pages + 11 figure

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

Conservative surgery of breast cancer in women; psychological benefits

Breast surgery was one of the most dynamic fields of medicine which benefited from significant progress during the last decades. The transition from aggressive and mutilating amputations to conservative, oncoplastic and reconstructive techniques has been constant, offering improved and rewarding results, viewed from both, oncological and aesthetical perspectives. Conservative techniques, especially those which preserve the nipple areola complex, are followed by improved patient’s perception of their body image, confidence and sexuality, with the only drawback of increased anxiety linked to recurrence risk

Real symmetric random matrices and paths counting

Exact evaluation of $$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary probability distribution. These expectations are polynomials in the moments of the matrix entries ; they provide useful information on the spectral density of the ensemble in the large $n$ limit. They also are a straightforward tool to examine a variety of rescalings of the entries in the large $n$ limit.Comment: 23 pages, 10 figures, revised pape

Depression and breast cancer; postoperative short-term implications

Introduction. Pre and postoperative psychological status is an important aspect in patients diagnosed with breast cancer, having a great impact on their quality of life. Considering the high incidence, mortality rate, and the added effect on self-image, breast cancer is considered a major stressor for women worldwide, almost 50% of these experiencing psychological distress. Methods. Our study retrospectively analysed the relationship between preoperative diagnosed depression and the number of medical care days, on patients diagnosed with breast cancer and admitted for surgical treatment in Colțea Clinical Hospital between 2017 and 2018. Results. We had 62 patients scheduled for breast cancer surgery, who had been preoperatively evaluated using psychological tests. Of those patients, 18 had scores indicating significant symptoms of depression (moderate or severe symptoms, HDSR \u3e17). Patients with high HDSR scores needed an 18.4% longer hospitalization than patients without symptoms of depression. They also had 35.4% more ambulatory visits in the month following discharge, and a higher incidence of postoperative complications. Conclusions. There seem to be both physiological and somatic determinants responsible for the need of prolonged medical care, but the mechanisms responsible for these effects remain unclear. Identifying high-risk patients could not only lower the postoperative morbidity, but also increase the therapeutic outcomes