Numerical Calibration of Steiner trees

In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided

From the Mendeleev periodic table to particle physics and back to the periodic table

We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry (special issue to commemorate the one hundredth anniversary of the death of Mendeleev who died in 1907); version 2: 16 pages; some sentences added; acknowledgment and references added; misprints correcte

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

Detection of K-Ras mutations in tumour samples of patients with non-small cell lung cancer using PNA-mediated PCR clamping

Non-small cell lung cancers (NSCLC), in particular adenocarcinoma, are often mixed with normal cells. Therefore, low sensitivity of direct sequencing used for K-Ras mutation analysis could be inadequate in some cases. Our study focused on the possibility to increase the detection of K-Ras mutations in cases of low tumour cellularity. Besides direct sequencing, we used wild-type hybridisation probes and peptide-nucleic-acid (PNA)-mediated PCR clamping to detect mutations at codons 12 and 13, in 114 routine consecutive NSCLC frozen surgical tumours untreated by targeted drugs. The sensitivity of the analysis without or with PNA was 10 and 1% of tumour DNA, respectively. Direct sequencing revealed K-Ras mutations in 11 out of 114 tumours (10%). Using PNA-mediated PCR clamping, 10 additional cases of K-Ras mutations were detected (21 out of 114, 18%, P<0.005), among which five in samples with low tumour cellularity. In adenocarcinoma, K-Ras mutation frequency increased from 7 out of 55 (13%) by direct sequencing to 15 out of 55 (27%) by clamped-PCR (P<0.005). K-Ras mutations detected by these sensitive techniques lost its prognostic value. In conclusion, a rapid and sensitive PCR-clamping test avoiding macro or micro dissection could be proposed in routine analysis especially for NSCLC samples with low percentage of tumour cells such as bronchial biopsies or after neoadjuvant chemotherapy

Apoptotic HPV Positive Cancer Cells Exhibit Transforming Properties

Previous studies have shown that DNA can be transferred from dying engineered cells to neighboring cells through the phagocytosis of apoptotic bodies, which leads to cellular transformation. Here, we provide evidence of an uptake of apoptotic-derived cervical cancer cells by human mesenchymal cells. Interestingly, HeLa (HPV 18+) or Ca Ski (HPV16+) cells, harboring integrated high-risk HPV DNA but not C-33 A cells (HPV-), were able to transform the recipient cells. Human primary fibroblasts engulfed the apoptotic bodies effectively within 30 minutes after co-cultivation. This mechanism is active and involves the actin cytoskeleton. In situ hybridization of transformed fibroblasts revealed the presence of HPV DNA in the nucleus of a subset of phagocytosing cells. These cells expressed the HPV16/18 E6 gene, which contributes to the disruption of the p53/p21 pathway, and the cells exhibited a tumorigenic phenotype, including an increased proliferation rate, polyploidy and anchorage independence growth. Such horizontal transfer of viral oncogenes to surrounding cells that lack receptors for HPV could facilitate the persistence of the virus, the main risk factor for cervical cancer development. This process might contribute to HPV-associated disease progression in vivo

In Vivo Chromatin Organization of Mouse Rod Photoreceptors Correlates with Histone Modifications

BACKGROUND: The folding of genetic information into chromatin plays important regulatory roles in many nuclear processes and particularly in gene transcription. Post translational histone modifications are associated with specific chromatin condensation states and with distinct transcriptional activities. The peculiar chromatin organization of rod photoreceptor nuclei, with a large central domain of condensed chromatin surrounded by a thin border of extended chromatin was used as a model to correlate in vivo chromatin structure, histone modifications and transcriptional activity. METHODOLOGY: We investigated the functional relationships between chromatin compaction, distribution of histone modifications and location of RNA polymerase II in intact murine rod photoreceptors using cryo-preparation methods, electron tomography and immunogold labeling. Our results show that the characteristic central heterochromatin of rod nuclei is organized into concentric domains characterized by a progressive loosening of the chromatin architecture from inside towards outside and by specific combinations of silencing histone marks. The peripheral heterochromatin is formed by closely packed 30 nm fibers as revealed by a characteristic optical diffraction signal. Unexpectedly, the still highly condensed most external heterochromatin domain contains acetylated histones, which are usually associated with active transcription and decondensed chromatin. Histone acetylation is thus not sufficient in vivo for complete chromatin decondensation. The euchromatin domain contains several degrees of chromatin compaction and the histone tails are hyperacetylated, enriched in H3K4 monomethylation and hypo trimethylated on H3K9, H3K27 and H4K20. The transcriptionally active RNA polymerases II molecules are confined in the euchromatin domain and are preferentially located at the vicinity of the interface with heterochromatin. CONCLUSIONS: Our results show that transcription is located in the most decondensed and highly acetylated chromatin regions, but since acetylation is found associated with compact chromatin it is not sufficient to decondense chromatin in vivo. We also show that a combination of histone marks defines distinct concentric heterochromatin domains