Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations

We give the exact expressions of the partial susceptibilities $\chi^{(3)}_d$ and $\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\, [1,1];\, z)$ and $_4F_3([1/2,1/2,1/2,1/2],\, [1,1,1]; \, z)$ hypergeometric functions. By solving the connection problems we analytically compute the behavior at all finite singular points for $\chi^{(3)}_d$ and $\chi^{(4)}_d$. We also give new results for $\chi^{(5)}_d$. We see in particular, the emergence of a remarkable order-six operator, which is such that its symmetric square has a rational solution. These new exact results indicate that the linear differential operators occurring in the $n$-fold integrals of the Ising model are not only "Derived from Geometry" (globally nilpotent), but actually correspond to "Special Geometry" (homomorphic to their formal adjoint). This raises the question of seeing if these "special geometry" Ising-operators, are "special" ones, reducing, in fact systematically, to (selected, k-balanced, ...) $_{q+1}F_q$ hypergeometric functions, or correspond to the more general solutions of Calabi-Yau equations.Comment: 35 page

Diagonals of rational functions and selected differential Galois groups

International audienceWe recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. In all the examples emerging from physics, the minimal linear differential operators annihilating these diagonals of rational functions have been shown to actually possess orthogonal or symplectic differential Galois groups. In order to understand the emergence of such orthogonal or symplectic groups, we analyze exhaustively three sets of diagonals of rational functions, corresponding respectively to rational functions of three variables, four variables and six variables. We impose the constraints that the degree of the denominators in each variable is at most one, and the coefficients of the monomials are 0 or $\;\pm 1,$ so that the analysis can be exhaustive. We find the minimal linear differential operators annihilating the diagonals of these rational functions of three, four, five and six variables. We find that, even for these sets of examples which, at first sight, have no relation with physics, their differential Galois groups are always orthogonal or symplectic groups. We discuss the conditions on the rational functions such that the operators annihilating their diagonals do not correspond to orthogonal or symplectic differential Galois groups, but rather to generic special linear groups

Le retour des grands mammifères sauvages dans la région méditerranéenne française.

Cet article consacré au retour des grands mammifères sauvages dans la région méditerranéenne française, parle du passé des extinctions, de la pénurie à l'abondance des grands mammifères, de l'historique de l'évolution des ongulés (sanglier, chevreuil, cerf, mouflon, chamois et bouquetin), des évolutions probables, et des connaissances prévisibles

Reduction of brain metastases in plasminogen activator inhibitor-1-deficient mice with transgenic ocular tumors

Plasminogen activator inhibitor-1 is known to play a paradoxical positive role in tumor angiogenesis, but its contribution to metastatic spread remains unclear. We studied the impact of plasminogen activator inhibitor (PAI)-1 deficiency in a transgenic mouse model of ocular tumors originating from retinal epithelial cells and leading to brain metastasis (TRP-1/SV40 Tag mice). PAI-1 deficiency did not affect primary tumor growth or vascularization, but was associated with a smaller number of brain metastases. Brain metastases were found to be differentially distributed between the two genotypes. PAI-1-deficient mice displayed mostly secondary foci expanding from local optic nerve infiltration, whereas wild-type animals displayed more disseminated nodules in the scissura and meningeal spaces. SuperArray GEarray analyses aimed at detecting molecules potentially compensating for PAI-1 deficiency demonstrated an increase in fibroblast growth factor-1 (FGF-1) gene expression in primary tumors, which was confirmed by reverse transcription-polymerase chain reaction and western blotting. Our data provide the first evidence of a key role for PAI-1 in a spontaneous model of metastasis and suggest that angiogenic factors, such as FGF-1, may be important for primary tumor growth and may compensate for the absence of PAI-1. They identify PAI-1 and FGF-1 as important targets for combined antitumor strategie

Copper-deficiency in Brassica napus induces copper remobilization, molybdenum accumulation and modification of the expression of chloroplastic proteins

During the last 40 years, crop breeding has strongly increased yields but has had adverse effects on the content of micronutrients, such as Fe, Mg, Zn and Cu, in edible products despite their sufficient supply in most soils. This suggests that micronutrient remobilization to edible tissues has been negatively selected. As a consequence, the aim of this work was to quantify the remobilization of Cu in leaves of Brassica napus L. during Cu deficiency and to identify the main metabolic processes that were affected so that improvements can be achieved in the future. While Cu deficiency reduced oilseed rape growth by less than 19% compared to control plants, Cu content in old leaves decreased by 61.4%, thus demonstrating a remobilization process between leaves. Cu deficiency also triggered an increase in Cu transporter expression in roots (COPT2) and leaves (HMA1), and more surprisingly, the induction of the MOT1 gene encoding a molybdenum transporter associated with a strong increase in molybdenum (Mo) uptake. Proteomic analysis of leaves revealed 33 proteins differentially regulated by Cu deficiency, among which more than half were located in chloroplasts. Eleven differentially expressed proteins are known to require Cu for their synthesis and/or activity. Enzymes that were located directly upstream or downstream of Cu-dependent enzymes were also differentially expressed

The Meta VCI Map consortium for meta-analyses on strategic lesion locations for vascular cognitive impairment using lesion-symptom mapping: design and multicenter pilot study

Introduction: The Meta VCI Map consortium performs meta-analyses on strategic lesion locations for vascular cognitive impairment using lesion-symptom mapping. Integration of data from different cohorts will increase sample sizes, to improve brain lesion coverage and support comprehensive lesion-symptom mapping studies. Methods: Cohorts with available imaging on white matter hyperintensities or infarcts and cognitive testing were invited. We performed a pilot study to test the feasibility of multicenter data processing and analysis and determine the benefits to lesion coverage. Results: Forty-seven groups have joined Meta VCI Map (stroke n = 7800 patients; memory clinic n = 4900; population-based n = 14,400). The pilot study (six ischemic stroke cohorts, n = 878) demonstrated feasibility of multicenter data integration (computed tomography/magnetic resonance imaging) and achieved marked improvement of lesion coverage. Discussion: Meta VCI Map will provide new insights into the relevance of vascular lesion location for cognitive dysfunction. After the successful pilot study, further projects are being prepared. Other investigators are welcome to join

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics: 1. The formation and the evolution of very massive stars (with a mass >120 Mo) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collison of 10-20 most massive stars of the cluster (the process is known as runaway merging). The further evolution is governed by stellar wind mass loss during core hydrogen burning and during core helium burning (the WR phase of very massive stars). Our simulations reveal that as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed but with a maximum mass of 70 Mo. In small metallicity clusters however, it cannot be excluded that the runaway merging process is responsible for pair instability supernovae or for the formation of intermediate mass black holes with a mass of several 100 Mo. 2. Massive runaways can be formed via the supernova explosion of one of the components in a binary (the Blaauw scenario) or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g., zeta Pup, lambda Cep, BD+433654) are the product of the collision and merger of 2 or 3 massive stars.Comment: Updated and final versio

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

We consider the random-bond +- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*= 0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T=0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents nu=1.50(4) and eta=0.128(8), and beta = 0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2 = 0.Comment: 32 pages, added refs and a discussion on hyperscalin

Antiretroviral-naive and -treated HIV-1 patients can harbour more resistant viruses in CSF than in plasma

Objectives The neurological disorders in HIV-1-infected patients remain prevalent. The HIV-1 resistance in plasma and CSF was compared in patients with neurological disorders in a multicentre study. Methods Blood and CSF samples were collected at time of neurological disorders for 244 patients. The viral loads were >50 copies/mL in both compartments and bulk genotypic tests were realized. Results On 244 patients, 89 and 155 were antiretroviral (ARV) naive and ARV treated, respectively. In ARV-naive patients, detection of mutations in CSF and not in plasma were reported for the reverse transcriptase (RT) gene in 2/89 patients (2.2%) and for the protease gene in 1/89 patients (1.1%). In ARV-treated patients, 19/152 (12.5%) patients had HIV-1 mutations only in the CSF for the RT gene and 30/151 (19.8%) for the protease gene. Two mutations appeared statistically more prevalent in the CSF than in plasma: M41L (P = 0.0455) and T215Y (P = 0.0455). Conclusions In most cases, resistance mutations were present and similar in both studied compartments. However, in 3.4% of ARV-naive and 8.8% of ARV-treated patients, the virus was more resistant in CSF than in plasma. These results support the need for genotypic resistance testing when lumbar puncture is performe