Index statistical properties of sparse random graphs.

Using the replica method, we develop an analytical approach to compute the characteristic function for the probability P(N)(K,λ) that a large N×N adjacency matrix of sparse random graphs has K eigenvalues below a threshold λ. The method allows to determine, in principle, all moments of P(N)(K,λ), from which the typical sample-to-sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with N≫1 for |λ|>0, with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a nonmonotonic behavior as a function of λ. These results contrast with rotationally invariant random matrices, where the index variance scales only as lnN, with an universal prefactor that is independent of λ. Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.

Finite-size corrections to the spectrum of regular random graphs: An analytical solution.

We develop a thorough analytical study of the O(1/N) correction to the spectrum of regular random graphs with N→∞ nodes. The finite-size fluctuations of the resolvent are given in terms of a weighted series over the contributions coming from loops of all possible lengths, from which we obtain the isolated eigenvalue as well as an analytical expression for the O(1/N) correction to the continuous part of the spectrum. The comparison between this analytical formula and direct diagonalization results exhibits an excellent agreement, confirming the correctness of our expression.

Spectra of sparse non-hermitian random matrices: an analytical solution.

We present the exact analytical expression for the spectrum of a sparse non-hermitian random matrix ensemble, generalizing two standard results in random-matrix theory: this analytical expression constitutes a non-hermitian version of the Kesten-McKay measure as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs, which are locally treelike. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends in a nonmonotonic way upon the degree of symmetry of the graph edges.

Spectra of sparse regular graphs with loops.

We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary lengths. The implications of our results for the structural and dynamical properties of network models are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization. Analytical formulas for the spectrum are obtained for specific lengths of the loops.

Localization transition in symmetric random matrices.

We study the behavior of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown.

Milk, rather than other foods, is associated with vertebral bone mass and circulating IGF-1 in female adolescents.

SUMMARY: Low calcium intake hampers bone mineral acquisition in adolescent girls. This study explores dietary calcium sources and nutrients possibly associated with vertebral mass. Milk intake is not influenced by genetic variants of the lactase gene and is positively associated with serum IGF-1 and with lumbar vertebrae mineral content and density. INTRODUCTION: Low calcium intake hampers bone mineral acquisition during adolescence. We identified calcium sources and nutrients possibly associated with lumbar bone mineralization and calcium metabolism in adolescent girls and evaluated the possible influence of a genetic polymorphic trait associated with adult-type hypolactasia. METHODS: Lumbar bone mineral content (BMC), bone mineral density (BMD), and area, circulating IGF-1, markers of bone metabolism, and -13910 LCT (lactase gene) polymorphism; and intakes of milk, dairy products, calcium, phosphorus, magnesium, proteins, and energy were evaluated in 192 healthy adolescent girls. RESULTS: After menarche, BMC, BMD, serum IGF-1, and serum PTH were tightly associated with milk consumption, but not with other calcium sources. All four parameters were also associated with phosphorus, magnesium, protein, and energy from milk, but not from other sources. Girls with milk intakes below 55 mL/day have significantly lower BMD, BMC, and IGF-1 and higher PTH compared to girls consuming over 260 mL/day. Neither BMC, BMD, calcium intakes, nor milk consumption were associated with -13910 LCT polymorphism. CONCLUSIONS: Milk consumption, preferably to other calcium sources, is associated with lumbar BMC and BMD in postmenarcheal girls. Aside from being a major source of calcium, milk provides phosphates, magnesium, proteins, and as yet unidentified nutrients likely to favor bone health.

Period-two cycles in a feedforward layered neural network model with symmetric sequence processing.

The effects of dominant sequential interactions are investigated in an exactly solvable feedforward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns c.

Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation.

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. Earlier work by Coolen and Sherrington on a parallel dynamics far from saturation is extended here to account for finite stochastic noise due to a Hebbian and a sequential learning rule. Phase diagrams are obtained with stationary states and quasiperiodic nonstationary solutions. The relevant dependence of these diagrams and of the quasiperiodic solutions on the stochastic noise and on initial inputs for the overlaps is explicitly discussed.

Establishment of plasma membrane polarity in mammary epithelial cells correlates with changes in prolactin trafficking and in annexin VI recruitment to membranes.

Mammary epithelial cells (MEC) of lactating animals ferry large amounts of milk constituents in vesicular structures which have mostly been characterized by morphological approaches (Ollivier-Bousquet, 1998). Recently, we have shown that under conditions of lipid deprivation, perturbed prolactin traffic paralleled changes in the membrane phospholipid composition and in the cytosol versus membrane distribution of annexin VI (Ollivier-Bousquet et al., 1997). To obtain additional information on the membrane events involved in the vesicular transport of the hormone to the apical pole of the cell, we conducted a biochemical study on prolactin-containing vesicles in MEC at two different stages of differentiation. We first showed that MEC of pregnant and lactating rabbits exhibited membrane characteristics of non-polarized and polarized cells respectively, using annexin IV and the alpha-6 subunit of integrin as membrane markers. Incubation of both cell types with biotinylated prolactin for 1 h at 15 degrees C, followed by a 10-min chase at 37 degrees C revealed that prolactin transport was activated upon MEC membrane polarization. This was confirmed by subcellular fractionation of prolactin-containing vesicles on discontinuous density gradients. In non-polarized MEC, (125)I-prolactin was mainly recovered in gradient fractions enriched with endocytotic vesicles either after incubation at 15 degrees C or after a 10-min chase at 37 degrees C. In contrast, in polarized MEC, the hormone switched from endocytotic compartments to a fraction enriched in exocytotic clathrin-coated vesicles during the 10-min chase at 37 degrees C. Association of annexin VI to prolactin carriers was next studied in both non-polarized and polarized cells. Membrane compartments collected at each gradient interface were solubilized under mild conditions by Triton X-100 (TX100) and the distribution of annexin VI in TX100-insoluble and TX100-soluble fractions was analyzed by Western blotting. Upon MEC polarization, the amount of annexin VI recovered in TX100-insoluble fractions changed. Quite interestingly, it increased in a membrane fraction enriched with endocytotic clathrin-coated vesicles, suggesting that annexin VI may act as a sorting signal in prolactin transport.

Speciation and kinetics related to catalytic carbonylation in the presence of cis-[Ir(CO)2I2]P(C6H5)4 under CO and H2 pressures.

The differences in the reactivities of the square-planar complexes cis-[Rh(CO)2I2]- (1) and cis-[Ir(CO)2I2]- (2), involved in the catalytic carbonylation of olefins, are investigated, with P(C6H5)4+ as the counterion, by ambient- and high-pressure NMR and IR spectroscopy. Under an elevated pressure of CO, 1 and 2 form the [M(CO)3I] complexes with the equilibrium constants KIr approximately 1.8 x 10(-3) and KRh approximately 4 x 10(-5). The ratio KIr/KRh close to 50 shows that, under catalytic conditions (a few megapascals), only complex 1 remains in the anionic form, while a major amount of the iridium analogue 2 is converted to a neutral species. The oxidative addition reactions of HI with 1 and 2 give two monohydrides of different geometries, mer,trans-[HRh(CO)2I3]- (3) and fac,cis-[HIr(CO)2I3]- (4), respectively. Both hydrides are unstable at ambient temperature and form, within minutes for Rh and within hours for Ir, the corresponding cis-[M(CO)2I2]- (1 or 2) and [M(CO)2I4]- (5 or 6) species and H2. When an H2 pressure of 5.5 MPa is applied to a nitromethane solution of complex 2, ca. 50% of 2 is transformed to cis-dihydride complexes. The formation of cis,cis,cis-[IrH2(CO)2I2]- (8a) is followed by intermolecular rearrangements to form cis,trans,cis-[IrH2(CO)2I2]- (8b) and cis,cis,trans-[IrH2(CO)2I2]- (8c). A small amount of a dinuclear species, [Ir2H(CO)4I4]x- (9), is also observed. The formation rate constants for 8a and 8b at 262 K are k1(262) = (4.42 +/- 0.18) x 10(-4) M-1 s-1, k-1(262) = (1.49 +/- 0.07) x 10(-4) s-1, k2(262) = (2.81 +/- 0.04) x 10(-5) s-1, and k-2(262) = (5.47 +/- 0.16) x 10(-6) s-1. The two equilibrium constants K1(262) = [8a]/([2][H2]) = 2.97 +/- 0.03 M-1 and K2(262) = [8b]/[8a] = 5.13 +/- 0.10 show that complex 8b is the thermodynamically stable addition product. However, no similar H2 addition products of the rhodium analogue 1 are observed. The pressurization with H2 of a solution containing 2 and 6 give the monohydride 4, the dihydrides 8a and 8b, the dinuclear complex 9, and the two new complexes [Ir(CO)2I3] (10) and [HIr(CO)2I2] (11). The reactions of the iridium complexes with H2 and HI are summarized in a single scheme.

Mechanism of CO exchange on cis-[M(CO)2X2]- complexes (M=Rh,Ir;X=Cl, Br, or I).

The CO exchange on cis-[M(CO)2X2]- with M = Ir (X = Cl, la; X = Br, 1b; X = I, 1c) and M = Rh (X = Cl, 2a; X = Br, 2b; X = I, 2c) was studied in dichloromethane. The exchange reaction [cis-[M(CO)2X2]- + 2*CO is in equilibrium cis-[M(*CO)2X2]- + 2CO (exchange rate constant: kobs)] was followed as a function of temperature and carbon monoxide concentration (up to 6 MPa) using homemade high gas pressure NMR sapphire tubes. The reaction is first order for both CO and cis-[M(CO)2X2]- concentrations. The second-order rate constant, k2(298) (=kobs)[CO]), the enthalpy, deltaH*, and the entropy of activation, deltaS*, obtained for the six complexes are respectively as follows: la, (1.08 +/- 0.01) x 10(3) L mol(-1) s(-1), 15.37 +/- 0.3 kJ mol(-1), -135.3 +/- 1 J mol(-1) K(-1); 1b, (12.7 +/- 0.2) x 10(3) L mol(-1) s(-1), 13.26 +/- 0.5 kJ mol(-1), -121.9 +/- 2 J mol(-1) K(-1); 1c, (98.9 +/- 1.4) x 10(3) L mol(-1) s(-1), 12.50 +/- 0.6 kJ mol(-1), -107.4 +/- 2 J mol(-1) K(-1); 2a, (1.62 +/- 0.02) x 10(3) L mol(-1) s(-1), 17.47 +/- 0.4 kJ mol(-1), -124.9 +/- 1 J mol(-1) K(-1); 2b, (24.8 +/- 0.2) x 10(3) L mol(-1) s(-1), 11.35 +/- 0.4 kJ mol(-1), -122.7 +/- 1 J mol(-1) K(-1); 2c, (850 +/- 120) x 10(3) L mol(-1), s(-1), 9.87 +/- 0.8 kJ mol(-1), -98.3 +/- 4 J mol(-1) K(-1). For complexes la and 2a, the volumes of activation were measured and are -20.9 +/- 1.2 cm3 mol(-1) (332.0 K) and -17.2 +/- 1.0 cm3 mol(-1) (330.8 K), respectively. The second-order kinetics and the large negative values of the entropies and volumes of activation point to a limiting associative, A, exchange mechanism. The reactivity of CO exchange follows the increasing trans effect of the halogens (Cl < Br << I), and this is observed on both metal centers. For the same halogen, the rhodium complex is more reactive than the iridium complex. This reactivity difference between rhodium and iridium is less marked for chloride (1.5: 1) than for iodide (8.6:1) at 298 K.

Added benfluorex in obese insulin-requiring type 2 diabetes.

To determine the effect of benfluorex on glycaemic control in obese insulin-requiring Type 2 diabetes, 76 patients (aged 53.8 +/- 12.8 years) receiving insulin (> or = 0.5 IU/kg) and an appropriate low-calorie diet were evaluated after a 1-month run-in followed by a 3-month double-blind treatment period (3 tablets daily) with benfluorex (B; n = 37) vs placebo (P; n = 39). At inclusion, the B and P groups respectively did not differ in body weight (80.9 +/- 10.3 vs 77.2 +/- 9.1 kg), body mass index (BMI) (30.1 +/- 4.6 vs 29.0 +/- 2.3 kg/m2) or fasting blood glucose (11.22 +/- 4.33 vs 10.35 +/- 4.42 mmol/l). However, daily insulin dose and HbA1c levels were higher in the B group (59.9 +/- 18.6 vs 50.4 +/- 12.8 IU, p = 0.012; and 7.72 +/- 1.60 vs 6.96 +/- 1.27%, p = 0.025, respectively). After 3 months of treatment, the decrease in daily insulin dose was greater in the B group (8.7 +/- 10.1 vs 2.7 +/- 8.1 IU; p = 0.032), with a decrease in HbA1c (-0.73 +/- 1.74%, p = 0.026), vs no change in the P group (+0.01 +/- 1.65%, NS) and a tendency towards a greater decrease in fasting blood glucose (-1.43 +/- 5.41 vs +0.42 +/- 3.78 mmol/l respectively). Body weight and BMI were also lower in the B group (1.77 ñ 2.27 vs 0.21 ñ 2.68 kg, p = 0.013; and 0.64 +/- 0.84 vs 0.07 +/- 1.07 kg/m2, p = 0.019, respectively) in parallel with the decrease in insulin dose. Triglycerides decreased in the B group vs an increase in the P group (-0.54 +/- 2.04 vs +0.21 +/- 0.70 mmol/l p = 0.06). Total cholesterol decreased within the B group (-0.47 +/- 1.01 mmol/l; p = 0.013) and vs the P group (intergroup p = 0.006). Adverse events were reported in 11 patients in the B group vs 5 in the P group (NS), causing dropout in only one case (intercurrent illness, P group). Addition of benfluorex in obese insulin-requiring Type 2 diabetes thus enhances glycaemic control and lowers both daily insulin requirement and body weight. Benfluorex + insulin is a valid alternative for obese patients who remain poorly controlled despite insulin or who require high doses of insulin.

Bone mineral acquisition during adolescence and early adulthood: a study in 574 healthy females 10-24 years of age.

Low bone mass is known to be associated with an increased risk of fractures. Osteoporosis prevention by maximizing bone mass will be crucial and requires a better knowledge of bone mass acquisition during adolescence. Bone mass was assessed in 574 healthy volunteer females aged 10-24 years. Spine bone mineral density (BMD) in anteroposterior (AP L2-4) and lateral (LAT L3) views was measured using dual-energy X-ray absorptiometry (DXA) and AP bone mineral content (BMC) was calculated. At the same time, spine AP-BMD (L2-4) was evaluated in 333 normal menstruating women, aged 27-47 years. Bone values, osteocalcin and IGF-1 serum concentrations were correlated with chronological age, skeletal age, pubertal stages and time after menarche. In this cross-sectional study, AP- and LAT-BMD and BMC increased dramatically between skeletal ages 10 and 14 or until the first year after menarche. Between 14 and 17 skeletal years of age, AP-BMD and BMC increased moderately, whereas LAT-BMD remained unchanged. After skeletal age 17, or the fourth year after menarche, there was no significant increase in BMD or BMC, and their values did not differ from those of menstruating women. A serum osteocalcin peak was observed at skeletal ages 11-12 or at stage P3, whereas IGF-1 peaked at 13-14 skeletal years of age or at P4 and the first year after menarche. Eighty-six per cent of the adult bone mass of the spine is acquired before skeletal age 14 or the second year after menarche; therefore osteoporosis prevention programs will be particularly effective before that age.

Induction of long-term survival of rat skin allografts by a novel, highly efficient anti-CD4 monoclonal antibody.

The new monoclonal antirat CD4 antibody RIB 5/2, which detects another epitope than those covered by W3/25 and MRC OX35, was tested for its immunosuppressive potency following skin allografting by using strain combinations with different genetic barriers in the MHC and genetic low- or high-responder background. High-dose and long-term therapy of the grafted rats led to a significant delay of the acute rejection (P < 0.01) in the strain combination Wistar Furth-to-BDX as well as in LEW1W-to-LEW1A. No significant prolongation of the mean allograft survival time was obtained for the high-responder rats (LEW1A-to-LEW1W). Cytofluorometric analysis revealed that RIB 5/2 exerts the immunosuppressive activity predominantly by modulation of the CD4 glycoprotein. Furthermore, the dependence of the humoral immune response against the mouse-globulins upon the administered protein quantity could be demonstrated.