Cycles of length three and four in tournaments

Linial and Morgenstern conjectured that, among all $n$-vertex tournaments with $d\binom{n}{3}$ cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for $d\ge 1/36$ by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate that the family of extremal examples is broader than expected and give its full description for $d\ge 1/16$

Optical Holonomic Quantum Computer

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity and scalability are addressed and several steps are taken towards the physical implementation of this model.Comment: 16 pages, 3 figures, REVTE

Visually targeted reaching in horse-head grasshoppers

Visually targeted reaching to a specific object is a demanding neuronal task requiring the translation of the location of the object from a two-dimensionsal set of retinotopic coordinates to a motor pattern that guides a limb to that point in three-dimensional space. This sensorimotor transformation has been intensively studied in mammals, but was not previously thought to occur in animals with smaller nervous systems such as insects. We studied horse-head grasshoppers (Orthoptera: Proscopididae) crossing gaps and found that visual inputs are sufficient for them to target their forelimbs to a foothold on the opposite side of the gap. High-speed video analysis showed that these reaches were targeted accurately and directly to footholds at different locations within the visual field through changes in forelimb trajectory and body position, and did not involve stereotyped searching movements. The proscopids estimated distant locations using peering to generate motion parallax, a monocular distance cue, but appeared to use binocular visual cues to estimate the distance of nearby footholds. Following occlusion of regions of binocular overlap, the proscopids resorted to peering to target reaches even to nearby locations. Monocular cues were sufficient for accurate targeting of the ipsilateral but not the contralateral forelimb. Thus, proscopids are capable not only of the sensorimotor transformations necessary for visually targeted reaching with their forelimbs but also of flexibly using different visual cues to target reaches. © 2012 The Royal Society

Перспективи використання тонкодисперсних вуглецевих матеріалів

У останні десятиліття особливу увагу вчених привертає дослідження різних алотропних видозмін вуглецю, зокрема природних: алмазу, графіту, лонсдейліту, фулерену, вуглецевих нанотрубок (у тому числі шунгіту – природного нанотехн-логічного матеріалу) і штучних: карбіну, графену, аморфного вуглецю (кокс, вугілля, технічний вуглець, сажа, активоване вугілля). Водночас у техніці все більше розповсюдження отримують тонкодисперсні вуглецеві матеріали, зокрема тонкодисперсне вугілля та технічний вуглець, тонкоподрібнений аморфний вуглець, активоване вугілля, дослідженню яких присвячено ряд окремих досліджень, у т.ч. і авторів статті