Gene expression relationship between prostate cancer cells of Gleason 3, 4 and normal epithelial cells as revealed by cell type-specific transcriptomes

Background: Prostate cancer cells in primary tumors have been typed CD10(-)/CD13(-)/CD24(hi)/CD26(+)/CD38(lo)/CD44(-)/CD104(-). This CD phenotype suggests a lineage relationship between cancer cells and luminal cells. The Gleason grade of tumors is a descriptive of tumor glandular differentiation. Higher Gleason scores are associated with treatment failure. Methods: CD26(+) cancer cells were isolated from Gleason 3+3 (G3) and Gleason 4+4 (G4) tumors by cell sorting, and their gene expression or transcriptome was determined by Affymetrix DNA array analysis. Dataset analysis was used to determine gene expression similarities and differences between G3 and G4 as well as to prostate cancer cell lines and histologically normal prostate luminal cells. Results: The G3 and G4 transcriptomes were compared to those of prostatic cell types of non-cancer, which included luminal, basal, stromal fibromuscular, and endothelial. A principal components analysis of the various transcriptome datasets indicated a closer relationship between luminal and G3 than luminal and G4. Dataset comparison also showed that the cancer transcriptomes differed substantially from those of prostate cancer cell lines. Conclusions: Genes differentially expressed in cancer are potential biomarkers for cancer detection, and those differentially expressed between G3 and G4 are potential biomarkers for disease stratification given that G4 cancer is associated with poor outcomes. Differentially expressed genes likely contribute to the prostate cancer phenotype and constitute the signatures of these particular cancer cell types.

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

UPGRADING THE GLEASON SCORE IN EXTENDED PROSTATE BIOPSY: IMPLICATIONS FOR TREATMENT CHOICE

Purpose: To determine the incidence of overestimation of Gleason score (GS) in extended prostate biopsy, and consequently circumventing unnecessary aggressive treatment. Methods and Materials: This is a retrospective study of 464 patients who underwent prostate biopsy and radical prostatectomy between January 2001 and November 2007. The GS from biopsy and radical prostatectomy were compared. The incidence of overestimation of GS in biopsies and tumor volume were studied. Multivariate analysis was applied to find parameters that predict upgrading the GS in prostate biopsy. Results: The exact agreement of GS between prostate biopsy and radical prostatectomy occurred in 56.9% of cases. In 29.1% cases it was underestimated, and it was overestimated in 14%. One hundred and six (22.8%) patients received a diagnosis of high GS (8, 9, or 10) in a prostate biopsy. In 29.2% of cases, the definitive Gleason Score was 7 or lower. In cases in which GS was overestimated in the biopsy, tumors were significantly smaller. In multivariate analysis, the total percentage of tumor was the only independent factor in overestimation of GS. Tumors occupying less than 33% of cores had a 5.6-fold greater chance of being overestimated. Conclusion: In the extended biopsy era and after the International Society of Urological Pathology consensus on G, almost one third of tumors considered to have high GS at the biopsy may be intermediate-risk cancers. In that condition, tumors are smaller in biopsy. This should be remembered by professionals involved with prostate cancer to avoid overtreatment and undesirable side effects. (c) 2009 Elsevier Inc.

The effect of the number of biopsy cores on the concordance between prostate biopsy and prostatectomy Gleason score - A prostate volume-controlled study

Context.-Studies analyzing the concordance of biopsy and radical prostatectomy (RP) Gleason scores have limitations. Some included 2 or more centers, used historical controls from the early prostate specific antigen era or lacked a clear definition of the biopsy schemes. Furthermore, most did not control the results for prostate volume. Objective.-To confirm whether prediction of RP Gleason score can be optimized by taking more biopsy cores in a contemporary series of patients, with pathologic samples analyzed by the same pathologist, and controlling these results for prostate volume. Design.-The study comprised a retrospective case-control analysis of 393 patients with prostate cancer treated with RP. Patients were divided into 3 groups: those in group 1 underwent a 6-core biopsy; group 2, an 8-core biopsy; and group 3, a 10 or more-core biopsy. Concordance rates between biopsy and RP Gleason scores, as well as the rates of undergrading and overgrading, were determined for each biopsy scheme. Results.-Concordance rates were 60.9%, 58.3%, and 64.6% for patients from groups 1, 2, and 3, respectively (P = .18). When we analyzed patients with prostate volumes of less than 50 cm(3), concordance rates were 58.3%, 58.3%, and 65.1% for each group, respectively (P = .03). Among patients with prostate volumes of 50 cm3 or more, concordance rates were 70%, 58.1%, and 63.6%, respectively (P = .66). Conclusions.-Taking 10 or more cores can improve the prediction of RP Gleason score in patients with prostate volumes of less than 50 cm3. For patients with prostate volumes of 50 cm3 or more, increasing the biopsy cores to 10 or more did not improve prediction of RP Gleason score.

THE POINCARE-BENDIXSON THEOREM ON THE KLEIN BOTTLE FOR CONTINUOUS VECTOR FIELDS

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent injective trajectory.

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

THE IMPLICIT FUNCTION THEOREM FOR CONTINUOUS FUNCTIONS

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence. some versions of these classic theorems are proved when we consider differenciable (not necessarily C-1) maps.

On the Hartman-Grobman Theorem with Parameters

The Hartman-Grobman Theorem of linearization is extended to families of dynamical systems in a Banach space X, depending continuously on parameters. We prove that the conjugacy also changes continuously. The cases of nonlinear maps and flows are considered, and both in global and local versions, but global in the parameters. To use a special version of the Banach-Caccioppoli Theorem we introduce equivalent norms on X depending on the parameters. The functional setting is suitable for applications to some nonlinear evolution partial differential equations like the nonlinear beam equation.

Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.

Friedel oscillations in one-dimensional metals: From Luttinger`s theorem to the Luttinger liquid

Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations. (C) 2008 Elsevier B.V. All rights reserved.

Sylow`s theorem for Moufang loops

For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion for the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops. (c) 2009 Elsevier Inc. All rights reserved.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.