E. Jordão Neves

Critical droplets and metastability for a Glauber dynamics at very low temperatures

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability.

Behavior of droplets for a class of Glauber dynamics at very low temperature

SummaryWe consider a class of Glauber dynamics for the two-dimensional nearest neighbor ferromagnetic Ising model in which the rate with which each spin flips depends only on the increment in energy caused by its flip in a monotonic non-increasing fashion.We extend to this class results previously shown for the particular case of Metropolis dynamics [NS]. We show that for fixed volume and external field 0<h<1, at very low temperature small rectangular droplets of sping +1 in a sea of spins −1 tend to shrink, while large droplets tend to grow and cover the whole system. The threshold between the two behaviors is sharply defined, the critical length being 2/h.An example is given which shows that without the assumption of monotonicity of the rates this result may be false.We use the result on critical droplets to show that starting from the configuration with all spins down, the systems in the class that we consider evolve in a metastable fashion until the configuration with all spins up is reached.For similar systems in higher dimensions we show that under analogous conditions on the rates, small enough droplets are likely to shrink, while large enough droplets are likely to grow.

Molecular classifiers for gastric cancer and nonmalignant diseases of the gastric mucosa

High incidence of gastric cancer-related death is mainly due to diagnosis at an advanced stage in addition to the lack of adequate neoadjuvant therapy. Hence, new tools aimed at early diagnosis would have a positive impact in the outcome of the disease. Using cDNA arrays having 376 genes either identified previously as altered in gastric tumors or known to be altered in human cancer, we determined expression signature of 99 tissue fragments representing normal gastric mucosa, gastritis, intestinal metaplasia, and adenocarcinomas. We first validated the array by identifying molecular markers that are associated with intestinal metaplasia, considered as a transition stage of gastric adenocarcinomas of the intestinal type as well as markers that are associated with diffuse type of gastric adenocarcinomas. Next, we applied Fisher’s linear discriminant analysis in an exhaustive search of trios of genes that could be used to build classifiers for class distinction. Many classifiers could distinguish between normal and tumor samples, whereas, for the distinction of gastritis from tumor and for metaplasia from tumor, fewer classifiers were identified. Statistical validations showed that trios that discriminate between normal and tumor samples are powerful classifiers to distinguish between tumor and nontumor samples. More relevant, it was possible to identify samples of intestinal metaplasia that have expression signature resembling that of an adenocarcinoma and can now be used for follow-up of patients to determine their potential as a prognostic test for malignant transformation.

Long Range Order in the Ground State of Two-Dimensional Antiferromagnets

Abstract We show the existence of long range order in the ground state of the two-dimensional isotropic Heisenberg antiferromagnet for S⩾ 3 2 . The method yields also long range order in the ground state for the larger class of anisotropic quantum antiferromagnetic spin systems with or without transverse magnetic fields.

Early Changes in Gene Expression Induced by Tobacco Smoke: Evidence for the Importance of Estrogen within Lung Tissue

Lung cancer is the leading cause of cancer deaths in the United States, surpassing breast cancer as the primary cause of cancer-related mortality in women. The goal of the present study was to identify early molecular changes in the lung induced by exposure to tobacco smoke and thus identify potential targets for chemoprevention. Female A/J mice were exposed to either tobacco smoke or HEPA-filtered air via a whole-body exposure chamber (6 h/d, 5 d/wk for 3, 8, and 20 weeks). Gene expression profiles of lung tissue from control and smoke-exposed animals were established using a 15K cDNA microarray. Cytochrome P450 1b1, a phase I enzyme involved in both the metabolism of xenobiotics and the 4-hydroxylation of 17β-estradiol (E2), was modulated to the greatest extent following smoke exposure. A panel of 10 genes were found to be differentially expressed in control and smoke-exposed lung tissues at 3, 8, and 20 weeks (P < 0.001). The interaction network of these differentially expressed genes revealed new pathways modulated by short-term smoke exposure, including estrogen metabolism. In addition, E2 was detected within murine lung tissue by gas chromatography-coupled mass spectrometry and immunohistochemistry. Identification of the early molecular events that contribute to lung tumor formation is anticipated to lead to the development of promising targeted chemopreventive therapies. In conclusion, the presence of E2 within lung tissue when combined with the modulation of cytochrome P450 1b1 and other estrogen metabolism genes by tobacco smoke provides novel insight into a possible role for estrogens in lung cancer. Cancer Prev Res; 3(6); 707–17. ©2010 AACR.

Expression Profile of Malignant and Nonmalignant Lesions of Esophagus and Stomach: Differential Activity of Functional Modules Related to Inflammation and Lipid Metabolism

Adenocarcinomas of stomach and esophagus are frequently associated with preceding inflammatory alterations of the normal mucosa. Whereas intestinal metaplasia of the gastric mucosa is associated with higher risk of malignization, Barretts disease is a risk factor for adenocarcinoma of the esophagus. Barretts disease is characterized by the substitution of the squamous mucosa of the esophagus by a columnar tissue classified histopathologically as intestinal metaplasia. Using cDNA microarrays, we determined the expression profile of normal gastric and esophageal mucosa as well as intestinal metaplasia and adenocarcinomas from both organs. Data were explored to define functional alterations related to the transformation from squamous to columnar epithelium and the malignant transformation from intestinal metaplasia to adenocarcinomas. Based on their expression profile, adenocarcinomas of the esophagus showed stronger correlation with intestinal metaplasia of the stomach than with Barretts mucosa. Second, we identified two functional modules, lipid metabolism and cytokine, as being altered with higher statistical significance. Whereas the lipid metabolism module is active in samples representing intestinal metaplasia and inactive in adenocarcinomas, the cytokine module is inactive in samples representing normal esophagus and esophagitis. Using the concept of relevance networks, we determined the changes in linear correlation of genes pertaining to these two functional modules. Exploitation of the data presented herein will help in the precise molecular characterization of adenocarcinoma from the distal esophagus, avoiding the topographical and descriptive classification that is currently adopted, and help with the proper management of patients with Barretts disease.

Differentially expressed genes in gastric tumors identified by cDNA array

Using cDNA fragments from the FAPESP/lICR Cancer Genome Project, we constructed a cDNA array having 4512 elements and determined gene expression in six normal and six tumor gastric tissues. Using t-statistics, we identified 80 cDNAs whose expression in normal and tumor samples differed more than 3.5 sample standard deviations. Using Self-Organizing Map, the expression profile of these cDNAs allowed perfect separation of malignant and non-malignant samples. Using the supervised learning procedure Support Vector Machine, we identified trios of cDNAs that could be used to classify samples as normal or tumor, based on single-array analysis. Finally, we identified genes with altered linear correlation when their expression in normal and tumor samples were compared. Further investigation concerning the function of these genes could contribute to the understanding of gastric carcinogenesis and may prove useful in molecular diagnostics.

Characterization of global transcription profile of normal and HPV-immortalized keratinocytes and their response to TNF treatment

BackgroundPersistent infection by high risk HPV types (e.g. HPV-16, -18, -31, and -45) is the main risk factor for development of cervical intraepithelial neoplasia and cervical cancer. Tumor necrosis factor (TNF) is a key mediator of epithelial cell inflammatory response and exerts a potent cytostatic effect on normal or HPV16, but not on HPV18 immortalized keratinocytes. Moreover, several cervical carcinoma-derived cell lines are resistant to TNF anti-proliferative effect suggesting that the acquisition of TNF-resistance may constitute an important step in HPV-mediated carcinogenesis. In the present study, we compared the gene expression profiles of normal and HPV16 or 18 immortalized human keratinocytes before and after treatment with TNF for 3 or 60 hours.MethodsIn this study, we determined the transcriptional changes 3 and 60 hours after TNF treatment of normal, HPV16 and HPV18 immortalized keratinocytes by microarray analysis. The expression pattern of two genes observed by microarray was confirmed by Northern Blot. NF-κB activation was also determined by electrophoretic mobility shift assay (EMSA) using specific oligonucleotides and nuclear protein extracts.ResultsWe observed the differential expression of a common set of genes in two TNF-sensitive cell lines that differs from those modulated in TNF-resistant ones. This information was used to define genes whose differential expression could be associated with the differential response to TNF, such as: KLK7 (kallikrein 7), SOD2 (superoxide dismutase 2), 100P (S100 calcium binding protein P), PI3 (protease inhibitor 3, skin-derived), CSTA (cystatin A), RARRES1 (retinoic acid receptor responder 1), and LXN (latexin). The differential expression of the KLK7 and SOD2 transcripts was confirmed by Northern blot. Moreover, we observed that SOD2 expression correlates with the differential NF-κB activation exhibited by TNF-sensitive and TNF-resistant cells.ConclusionThis is the first in depth analysis of the differential effect of TNF on normal and HPV16 or HPV18 immortalized keratinocytes. Our findings may be useful for the identification of genes involved in TNF resistance acquisition and candidate genes which deregulated expression may be associated with cervical disease establishment and/or progression.

A DISCRETE VARIATIONAL PROBLEM RELATED TO ISING DROPLETS AT LOW TEMPERATURES

We consider a variational problem on thed-dimensional latticeZd which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZd can have restricted to three classes of subsets ofZd. If ϕ is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZd which are neighbors and such that only one of them belongs to ϕ.

Reconstruction of Gray-Scale Images

We present an algorithm to reconstruct gray scale images corrupted by noise. We use a Bayesian approach. The unknown original image is assumed to be a realization of a Markov random field on a finite two dimensional region Λ ⊂ Z2. This image is degraded by some noise, which is assumed to act independently in each site of Λ and to have the same distribution on all sites. For the estimator we use the mode of the posterior distribution: the so called maximum a posteriori (MAP) estimator. The algorithm, that can be used for both gray-scale and multicolor images, uses the binary decomposition of the intensity of each color and recovers each level of this decomposition using the identification of the problem of finding the two color MAP estimator with the min-cut max-flow problem in a binary graph, discovered by Greig et al. (1989). Experimental results and a detailed example are given in the text. We also provide a web page where additional information and examples can be found.