A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

GTP and Ca2+ Modulate the Inositol 1,4,5-Trisphosphate-Dependent Ca2+ Release in Streptolysin O-Permeabilized Bovine Adrenal Chromaffin Cells

The inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ release was studied using streptolysin O-permeabilized bovine adrenal chromaffin cells. The IP3-induced Ca2+ release was followed by Ca2+ reuptake into intracellular compartments. The IP3-induced Ca2+ release diminished after sequential applications of the same amount of IP3. Addition of 20 μM GTP fully restored the sensitivity to IP3. Guanosine 5'-O-(3-thio)triphosphate (GTPγS) could not replace GTP but prevented the action of GTP. The effects of GTP and GTPγS were reversible. Neither GTP nor GTPγS induced release of Ca2+ in the absence of IP3. The amount of Ca2+ whose release was induced by IP3 depended on the free Ca2+ concentration of the medium. At 0.3 μM free Ca2+, a half-maximal Ca2+ release was elicited with ∼0.1 μM IP3. At 1 μM free Ca2+, no Ca2+ release was observed with 0.1 μM IP3; at this Ca2+ concentration, higher concentrations of IP3 (0.25 μM) were required to evoke Ca2+ release. At 8 μM free Ca2+, even 0.25 μM IP3 failed to induce release of Ca2+ from the store. The IP3-induced Ca2+ release at constant low (0.2 μM) free Ca2+ concentrations correlated directly with the amount of stored Ca2+. Depending on the filling state of the intracellular compartment, 1 mol of IP3 induced release of between 5 and 30 mol of Ca2+

The changing patterns of group politics in Britain

Two interpretations of ways in which group politics in Britain have presented challenges to democracy are reviewed: neo-corporatism or pluralistic stagnation and the rise of single issue interest groups. The disappearance of the first paradigm created a political space for the second to emerge. A three-phase model of group activity is developed: a phase centred around production interests, followed by the development of broadly based 'other regarding' groups, succeeded by fragmented, inner directed groups focusing on particular interests. Explanations of the decay of corporatism are reviewed. Single issue group activity has increased as party membership has declined and is facilitated by changes in traditional media and the development of the internet. Such groups can overload the policy-making process and frustrate depoliticisation. Debates about the constitution and governance have largely ignored these issues and there is need for a debate

Sequence Dependence of Self-Interacting Random Chains

We study the thermodynamic behavior of the random chain model proposed by Iori, Marinari and Parisi, and how this depends on the actual sequence of interactions along the chain. The properties of randomly chosen sequences are compared to those of designed ones, obtained through a simulated annealing procedure in sequence space. We show that the transition to the folded phase takes place at a smaller strength of the quenched disorder for designed sequences. As a result, folding can be relatively fast for these sequences.Comment: 14 pages, uuencoded compressed postscript fil

The Social Climbing Game

The structure of a society depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society's hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a "disordered" society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult.Comment: 14 pages, 9 figure

Lines, Circles, Planes and Spheres

Let $S$ be a set of $n$ points in $\mathbb{R}^3$, no three collinear and not all coplanar. If at most $n-k$ are coplanar and $n$ is sufficiently large, the total number of planes determined is at least $1 + k \binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2})$. For similar conditions and sufficiently large $n$, (inspired by the work of P. D. T. A. Elliott in \cite{Ell67}) we also show that the number of spheres determined by $n$ points is at least $1+\binom{n-1}{3}-t_3^{orchard}(n-1)$, and this bound is best possible under its hypothesis. (By $t_3^{orchard}(n)$, we are denoting the maximum number of three-point lines attainable by a configuration of $n$ points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.Comment: 37 page

Strong Pinning and Plastic Deformations of the Vortex Lattice

We investigate numerically the dynamically generated plastic deformations of a 3D vortex lattice (VL) driven through a disorder potential with isolated, strong pinning centers (point-like or extended along the field direction). We find that the VL exhibits a very peculiar dynamical behavior in the plastic flow regime, in particular, topological excitations consisting of three or four entangled vortices are formed. We determine the critical current density $j_c$ and the activation energy for depinning $U_c$ in the presence of a finite density of strong pinning centers.Comment: 12 pages, TeX type, Postscript figure

Markerless Vision-Based Skeleton Tracking in Therapy of Gross Motor Skill Disorders in Children

This chapter presents a research towards implementation of a computer vision system for markerless skeleton tracking in therapy of gross motor skill disorders in children suffering from mild cognitive impairment. The proposed system is based on a low-cost 3D sensor and a skeleton tracking software. The envisioned architecture is scalable in the sense that the system may be used as a stand-alone assistive tool for tracking the effects of therapy or it may be integrated with an advanced autonomous conversational agent to maintain the spatial attention of the child and to increase her motivation to undergo a long-term therapy