Biased statistics for traces of cyclic p-fold covers over finite fields

In this paper, we discuss in more detail some of the results on the statistics of the trace of the Frobenius endomorphism associated to cyclic p-fold covers of the projective line that were presented in [1]. We also show new findings regarding statistics associated to such curves where we fix the number of zeros in some of the factors of the equation in the affine model

Multiphase shape optimization problems

This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min (Formula presented.) where D ⊆ ℝd is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi, and m is a positive constant. For a large class of such functionals, we analyze qualitative properties of the cells and the interaction between them. Each cell is itself a subsolution for a (single-phase) shape optimization problem, from which we deduce properties like finite perimeter, inner density, separation by open sets, absence of triple junction points, etc. As main examples we consider functionals involving the eigenvalues of the Dirichlet Laplacian of each cell, i.e., Fi = λki

Some remarks on the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians

We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of the ($p$-)Laplacian with Robin boundary conditions with respect to all domains in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the disjoint union of two balls of equal volume, and that this is the unique domain with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a minimiser cannot be independent of the value of the constant $\alpha$ in the boundary condition, or equivalently of the volume $M$. We obtain similar results for the Laplacian with generalised Wentzell boundary conditions $\Delta u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.Comment: 16 page

KillerFLIP: A Novel Lytic Peptide Specifically Inducing Cancer Cell Death

One of the objectives in the development of effective cancer therapy is induction of tumor-selective cell death. Toward this end, we have identified a small peptide that, when introduced into cells via a TAT cell-delivery system, shows a remarkably potent cytoxicity in a variety of cancer cell lines and inhibits tumor growth in vivo, whereas sparing normal cells and tissues. This fusion peptide was named killer FLIP as its sequence was derived from the C-terminal domain of c-FLIP, an anti-apoptotic protein. Using structure activity analysis, we determined the minimal bioactive core of killerFLIP, namely killerFLIP-E. Structural analysis of cells using electron microscopy demonstrated that killerFLIP-E triggers cell death accompanied by rapid (within minutes) plasma membrane permeabilization. Studies of the structure of the active core of killer FLIP (-E) indicated that it possesses amphiphilic properties and self-assembles into micellar structures in aqueous solution. The biochemical properties of killerFLIP are comparable to those of cationic lytic peptides, which participate in defense against pathogens and have also demonstrated anticancer properties. We show that the pro-cell death effects of killer FLIP are independent of its sequence similarity with c-FLIP L as killer FLIP-induced cell death was largely apoptosis and necroptosis independent. A killer FLIP-E variant containing a scrambled c-FLIP L motif indeed induced similar cell death, suggesting the importance of the c-FLIP L residues but not of their sequence. Thus, we report the discovery of a promising synthetic peptide with novel anticancer activity in vitro and in vivo.

Clypeina tibanai, sp. nov. (Polyphysaceae, Dasycladales, Chlorophyta), a mid-Cretaceous green alga from the Potiguar Basin, Brazilian margin of the young South Atlantic Ocean

The fossil genus Clypeina (Michelin, 1845) comprises some 40 species. We describe Clypeina tibanai, a new spe-cies from ? upper Albian–Cenomanian strata of the Potiguar Basin, Brazil, characterised by closely set verticils of tubular, bended laterals. It is compared with Clypeina hanabataensis Yabe & Toyama, 1949, a Late Jurassic species, and with Pseudoactinoporella fragilis (Conrad, 1970), an Early Cretaceous taxon. The new species be-longs to a short list of green algae found in the young South Atlantic oceanic corridor, an assemblage defining a phycological paleobioprovince discrete from that of the Tethyan realm

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

On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions

Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic eigenfunctions of quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains $\nu_n$ of the $n$-th eigenfunction satisfies $n\ge \nu_n$. Here, we provide a new interpretation for the Courant nodal deficiency $d_n = n-\nu_n$ in the case of quantum graphs. It equals the Morse index --- at a critical point --- of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning --- it is the number of unstable directions in the vicinity of the critical point corresponding to the $n$-th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.Comment: 22 pages, 6 figure

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

killerFLIP: a novel lytic peptide specifically inducing cancer cell death

One of the objectives in the development of effective cancer therapy is induction of tumor-selective cell death. Toward this end, we have identified a small peptide that, when introduced into cells via a TAT cell-delivery system, shows a remarkably potent cytoxicity in a variety of cancer cell lines and inhibits tumor growth in vivo, whereas sparing normal cells and tissues. This fusion peptide was named killerFLIP as its sequence was derived from the C-terminal domain of c-FLIP, an anti-apoptotic protein. Using structure activity analysis, we determined the minimal bioactive core of killerFLIP, namely killerFLIP-E. Structural analysis of cells using electron microscopy demonstrated that killerFLIP-E triggers cell death accompanied by rapid (within minutes) plasma membrane permeabilization. Studies of the structure of the active core of killerFLIP (-E) indicated that it possesses amphiphilic properties and self-assembles into micellar structures in aqueous solution. The biochemical properties of killerFLIP are comparable to those of cationic lytic peptides, which participate in defense against pathogens and have also demonstrated anticancer properties. We show that the pro-cell death effects of killerFLIP are independent of its sequence similarity with c-FLIPL as killerFLIP-induced cell death was largely apoptosis and necroptosis independent. A killerFLIP-E variant containing a scrambled c-FLIPL motif indeed induced similar cell death, suggesting the importance of the c-FLIPL residues but not of their sequence. Thus, we report the discovery of a promising synthetic peptide with novel anticancer activity in vitro and in vivo