Glassy Random Matrix Models

This paper discusses Random Matrix Models which exhibit the unusual phenomena of having multiple solutions at the same point in phase space. These matrix models have gaps in their spectrum or density of eigenvalues. The free energy and certain correlation functions of these models show differences for the different solutions. Here I present evidence for the presence of multiple solutions both analytically and numerically. As an example I discuss the double well matrix model with potential $V(M)= -{\mu \over 2}M^2+{g \over 4}M^4$ where $M$ is a random $N\times N$ matrix (the $M^4$ matrix model) as well as the Gaussian Penner model with $V(M)={\mu\over 2}M^2-t \ln M$. First I study what these multiple solutions are in the large $N$ limit using the recurrence coefficient of the orthogonal polynomials. Second I discuss these solutions at the non-perturbative level to bring out some differences between the multiple solutions. I also present the two-point density-density correlation functions which further characterizes these models in a new university class. A motivation for this work is that variants of these models have been conjectured to be models of certain structural glasses in the high temperature phase.Comment: 25 pages, Latex, 7 Figures, to appear in PR

Spin glass overlap barriers in three and four dimensions

For the Edwards-Anderson Ising spin-glass model in three and four dimensions (3d and 4d) we have performed high statistics Monte Carlo calculations of those free-energy barriers $F^q_B$ which are visible in the probability density $P_J(q)$ of the Parisi overlap parameter $q$. The calculations rely on the recently introduced multi-overlap algorithm. In both dimensions, within the limits of lattice sizes investigated, these barriers are found to be non-self-averaging and the same is true for the autocorrelation times of our algorithm. Further, we present evidence that barriers hidden in $q$ dominate the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in Phys. Rev.

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.

INTRALUMINAL PENETRATION OF THE BAND IN PATIENTS WITH ADJUSTABLE SILICONE GASTRIC BAMDING: REDIOLOGICAL FINDINGS

The aim of this study was to analyse radiological findings in patients surgically treated for adjustable silicone gastric banding (ASGB) for morbid obesity complicated by band penetration into the gastric lumen. We reviewed the records of four patients with surgically confirmed penetration of gastric band into the gastric lumen; three had preoperative opaque meal, one only a plain abdominal film. Vomiting was the presenting symptom in two cases, whereas others had new weight gain and loss of early satiety. Two patients had normally closed bands: radiography showed that their position had changed from previous controls and the barium meal had passed out of their lumen. Two patients had an open band. One patient had the band at the duodeno-jejunal junction, and the tube connecting the band to the subcutaneous port presented a winding course suggesting the duodenum. In the other case, both plain film and barium studies failed to demonstrate with certainty the intragastric position of the band. As ASGB is becoming widely used, radiologists need to be familiar with its appearances and its complications. Band penetration into the stomach is a serious complication which needs band removal. Patients with this problem, often with non-specific symptoms and even those who are asymptomatic, are encountered during radiographic examinations requested either for gastric problems or follow-up purposes, and have to be properly diagnosed

Pregnancies in an 18-year follow-up after biliopancreatic diversion

Background: 239 pregnancies occurred in 1136 women who had undergone biliopancreatic diversion (BPD). Methods: There were 73 abortions, and 14 pregnancies are presently in their course. The 152 term pregnancies (six twins) occurred in 129 women 2-173 months (mean 42.7) after BPD. Mean age and current excess weight were 31.4 years (20-42) and 29.1% (-6.9-78.2), and mean excess weight loss was 72.9% (30.4-110.5). Results: Mean weight gain during pregnancy was 6.2 kg (-21-25). In 32 patients (21%), parenteral nutritional support was needed. In all the other patients (79%), the usual supplementations were given. Of the newborns, 122 were delivered at term (84.7%) with a mean weight of 2842.4 g (1760-4600 g) and a mean length of 48.5 cm (43-59 cm), while the 22 preterm babies (15.3%) weighed 2151.1 g (1400-3850 g) and had a length of 44.6 cm (33-56 cm). Forty infants (27.8%) were small for gestational age but 17 of them weighed more than 2500 g. Eleven twins (one abortion at 26th week) were also delivered, with a mean weight of 2088.6 g (1200-3100 g) and a mean length of 45.6 cm (35-50 cm). Delivery was spontaneous in 85 instances (56%), while vacuum extractor was used in one, and 66 cesarean sections were performed. There were two birth malformations, one infant died after surgery for meconium obstruction and two died from unknown causes. Of the 129 women, 35 had been infertile before BPD. Conclusions: Disappearance of infertility and decrease of pregnancy risk are to be considered among the beneficial effects of weight reduction following BPD

Biliopancreatic diversion

Biliopancreatic diversion (BPD) has made reacceptable the malabsorptive approach to the surgical treatment of obesity. The procedure, in a series of 2241 patients operated on during a 21-year period, caused a mean permanent reduction of about 75% of the initial excess weight. The indefinite weight maintenance appears to be due to the existence of a threshold absorption capacity for fat and starch, and thus energy, and the weight loss is partly due to increased resting energy expenditure. Beneficial effects other than those consequent to weight loss or reduced nutrient absorption included permanent normalization of serum glucose and cholesterol without any medication and on totally free diet in 100% of cases, both phenomena being due to a specific action of the operation. Operative mortality was less than 0.5%. Specific late complications included anemia, less than 5% with adequate iron or folate supplementation (or both); stomal ulcer, reduced to 3.2% by oral H2-blocker prophylaxis; bone demineralization, increasing up to the fourth year and tending to decrease thereafter, with need of calcium and vitamin D supplementation; neurologic complications, totally avoidable by prompt vitamin B administration to patients at risk; protein malnutrition, which was reduced to a minimum of 3% with 1.3% recurrence, in exchange with a smaller weight loss, by adapting the volume of the gastric remnant and the length of the alimentary limb to the patient's individual characteristics. It is concluded that the correct use of BPD, based on the knowledge of its mechanisms of action, can make the procedure an effective, safe one in all hands

Pregnancy following surgical treatment of morbid obesity. Review of literature and our experience with biliopancreatic diversion [Gravidanza dopo terapia chirurgica dell'obesit\ue0. Revisione bibliografica e nostra esperienza con la diversione biliopancreatica]

Background. An increasing number of women in childbearing age are submitted to surgical treatment of obesity; for this reason pregnancy represents a frequent event in operated patients. Methods. In this sutdy pregnancy in patients with morbid obesity submitted to jejunoileal bypass (JIB) and gastric bypass (GB) are reviewed from the literature and the analysis of our esperience with biliopancreatic diversion (BPD) is reported. Results. In 113 pregnancies after JIB reviewed from the literature, the results seem to be debated either about the course of pregnancy or about maternal and neonatal status. The data of literature concerning the pregnancies following GB are less debated but rather slight. One hundred and fifty-two pregnancies after BPD have a complete documentation concerning maternal conditions, modality of outcome and neonatal situation. Conclusions. Pregnancy occurred in the obese women represents an increased maternal-fetal risk. The excess weight loss, the weight maintenance and the reduced weight changes during pregnancy are an advantage in the operate women who, in any case, need accurate controls of the nutritional status during the whole gestational period. Keeping these cautions pregnancy following surgical treatment of obesity represents an event not only possible but even with less problems than in pregnancy in obese women