Finite-size versus Surface effects in nanoparticles

We study the finite-size and surface effects on the thermal and spatial behaviors of the magnetisation of a small magnetic particle. We consider two systems: 1) A box-shaped isotropic particle of simple cubic structure with either periodic or free boundary conditions. This case is treated analytically using the isotropic model of D-component spin vectors in the limit $D\to \infty$, including the magnetic field. 2) A more realistic particle ($\gamma$-Fe$_{2}$O$_{3}$) of ellipsoidal (or spherical) shape with open boundaries. The magnetic state in this particle is described by the anisotropic classical Dirac-Heisenberg model including exchange and dipolar interactions, and bulk and surface anisotropy. This case is dealt with by the classical Monte Carlo technique. It is shown that in both systems finite-size effects yield a positive contribution to the magnetisation while surface effects render a larger and negative contribution, leading to a net decrease of the magnetisation of the small particle with respect to the bulk system. In the system 2) the difference between the two contributions is enhanced by surface anisotropy. The latter also leads to non saturation of the magnetisation at low temperatures, showing that the magnetic order in the core of the particle is perturbed by the magnetic disorder on the surface. This is confirmed by the profile of the magnetisation.Comment: 6 pages of RevTex including 4 Figures, invited paper to 3rd EuroConference on Magnetic Properties of Fine Nanoparticles, Barcelona, October 9

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Overexpression of stathmin in breast carcinomas points out to highly proliferative tumours

We recently discovered that stathmin was overexpressed in a subgroup of human breast carcinomas. Stathmin is a cytosolic phosphoprotein proposed to act as a relay integrating diverse cell signalling pathways, notably during the control of cell growth and differentiation. It may also be considered as one of the key regulators of cell division for its ability to destabilize microtubules in a phosphorylation-dependent manner. To assess the significance of stathmin overexpression in breast cancer, we evaluated the correlation of stathmin expression, quantified by reverse transcription polymerase chain reaction, with several disease parameters in a large series of human primary breast cancer (n = 133), obtained in strictly followed up women, whose clinico-pathological data were fully available. In agreement with our preliminary survey, stathmin was found overexpressed in a subgroup of tumours (22%). In addition, overexpression was correlated to the loss of steroid receptors (oestrogen, P = 0.0006; progesterone, P = 0.008), and to the Scarff–Bloom–Richardson histopathological grade III (P = 0.002), this latter being ascribable to the mitotic index component (P = 0.02). Furthermore studies at the DNA level indicated that stathmin is overexpressed irrespective of its genomic status. Our findings raise important questions concerning the causes and consequences of stathmin overexpression, and the reasons of its inability to counteract cell proliferation in the overexpression group. © 2000 Cancer Research Campaig

Field dependence of the temperature at the peak of the ZFC magnetization

The effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization, $M_{ZFC}$, is studied using the recently obtained analytic results of Coffey et al. (Phys. Rev. Lett. {\bf 80}(1998) 5655) for the prefactor of the N\'{e}el relaxation time which allow one to precisely calculate the prefactor in the N\'{e}el-Brown model and thus the blocking temperature as a function of the coefficients of the Taylor series expansion of the magnetocrystalline anisotropy. The present calculations indicate that even a precise determination of the prefactor in the N\'{e}el-Brown theory, which always predicts a monotonic decrease of the relaxation time with increasing field, is insufficient to explain the effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization. On the other hand, we find that the non linear field-dependence of the magnetization along with the magnetocrystalline anisotropy appears to be of crucial importance to the existence of this maximum.Comment: 14 LaTex209 pages, 6 EPS figures. To appear in J. Phys.: Condensed Matte

On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v

On the Milnor formula in arbitrary characteristic

The Milnor formula $\mu=2\delta-r+1$ relates the Milnor number $\mu$, the double point number $\delta$ and the number $r$ of branches of a plane curve singularity. It holds over the fields of characteristic zero. Melle and Wall based on a result by Deligne proved the inequality $\mu\geq 2\delta-r+1$ in arbitrary characteristic and showed that the equality $\mu=2\delta-r+1$ characterizes the singularities with no wild vanishing cycles. In this note we give an account of results on the Milnor formula in characteristic $p$. It holds if the plane singularity is Newton non-degenerate (Boubakri et al. Rev. Mat. Complut. (2010) 25) or if $p$ is greater than the intersection number of the singularity with its generic polar (Nguyen H.D., Annales de l'Institut Fourier, Tome 66 (5) (2016)). Then we improve our result on the Milnor number of irreducible singularities (Bull. London Math. Soc. 48 (2016)). Our considerations are based on the properties of polars of plane singularities in characteristic $p$.Comment: 18 page

The combinatorics of plane curve singularities. How Newton polygons blossom into lotuses

This survey may be seen as an introduction to the use of toric and tropical geometry in the analysis of plane curve singularities, which are germs $(C,o)$ of complex analytic curves contained in a smooth complex analytic surface $S$. The embedded topological type of such a pair $(S, C)$ is usually defined to be that of the oriented link obtained by intersecting $C$ with a sufficiently small oriented Euclidean sphere centered at the point $o$, defined once a system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one works more generally over an arbitrary algebraically closed field of characteristic zero, one speaks instead of the combinatorial type of $(S, C)$. One may define it by looking either at the Newton-Puiseux series associated to $C$ relative to a generic local coordinate system $(x,y)$, or at the set of infinitely near points which have to be blown up in order to get the minimal embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this germ by the resolution. Each point of view leads to a different encoding of the combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques diagram, or a weighted dual graph. The three trees contain the same information, which in the complex setting is equivalent to the knowledge of the embedded topological type. There are known algorithms for transforming one tree into another. In this paper we explain how a special type of two-dimensional simplicial complex called a lotus allows to think geometrically about the relations between the three types of trees. Namely, all of them embed in a natural lotus, their numerical decorations appearing as invariants of it. This lotus is constructed from the finite set of Newton polygons created during any process of resolution of $(C,o)$ by successive toric modifications.Comment: 104 pages, 58 figures. Compared to the previous version, section 2 is new. The historical information, contained before in subsection 6.2, is distributed now throughout the paper in the subsections called "Historical comments''. More details are also added at various places of the paper. To appear in the Handbook of Geometry and Topology of Singularities I, Springer, 202

Cancer risk management strategies and perceptions of unaffected women 5 years after predictive genetic testing for BRCA1/2 mutations

In a French national cohort of unaffected females carriers/non-carriers of a BRCA1/2 mutation, long-term preventive strategies and breast/ovarian cancer risk perceptions were followed up to 5 years after test result disclosure, using self-administered questionnaires. Response rate was 74%. Carriers (N=101) were younger (average age±SD=37±10) than non-carriers (N=145; 42±12). There were four management strategies that comprised 88% of the decisions made by the unaffected carriers: 50% opted for breast surveillance alone, based on either magnetic resonance imaging (MRI) and other imaging (31%) or mammography alone (19%); 38% opted for either risk reducing salpingo-oophorectomy (RRSO) and breast surveillance, based on MRI and other imaging (28%) or mammography alone (10%). The other three strategies were: risk reducing mastectomy (RRM) and RRSO (5%), RRM alone (2%) and neither RRM/RRSO nor surveillance (6%). The results obtained for various age groups are presented here. Non-carriers often opted for screening despite their low cancer risk. Result disclosure increased carriers' short-term high breast/ovarian cancer risk perceptions (P⩽0.02) and decreased non-carriers' short- and long-term perceptions (P<0.001). During follow-up, high breast cancer risk perceptions increased with time among those who had no RRM and decreased in the opposite case; high ovarian cancer risk perceptions increased further with time among those who had no RRSO and decreased in the opposite case; RRSO did not affect breast cancer risk perceptions. Informed decision-making involves letting women know whether opting for RRSO and breast MRI surveillance is as effective in terms of survival as RRM and RRSO

Prognostic value of CCND1 gene status in sporadic breast tumours, as determined by real-time quantitative PCR assays

The CCND1 gene, a key cell-cycle regulator, is often altered in breast cancer, but the mechanisms underlying CCND1 dysregulation and the clinical significance of CCND1 status are unclear. We used real-time quantitative PCR and RT–PCR assays based on fluorescent TaqMan methodology to quantify CCND1 gene amplification and expression in a large series of breast tumours. CCND1 overexpression was observed in 44 (32.8%) of 134 breast tumour RNAs, ranging from 3.3 to 43.7 times the level in normal breast tissues, and correlated significantly with positive oestrogen receptor status (P=0.0003). CCND1 overexpression requires oestrogen receptor integrity and is exacerbated by amplification at 11q13 (the site of the CCND1 gene), owing to an additional gene dosage effect. Our results challenge CCND1 gene as the main 11q13 amplicon selector. The relapse-free survival time of patients with CCND1-amplified tumours was shorter than that of patients without CCND1 alterations, while that of patients with CCND1-unamplified-overexpressed tumours was longer (P=0.011). Only the good prognostic significance of CCND1-unamplified-overexpression status persisted in Cox multivariate regression analysis. This study confirms that CCND1 is an ER-responsive or ER-coactivator gene in breast cancer, and points to the CCND1 gene as a putative molecular marker predictive of hormone responsiveness in breast cancer. Moreover, CCND1 amplification status dichotomizes the CCND1-overexpressing tumors into two groups with opposite outcomes