The Homogeneous Broadcast Problem in Narrow and Wide Strips

Let $P$ be a set of nodes in a wireless network, where each node is modeled as a point in the plane, and let $s\in P$ be a given source node. Each node $p$ can transmit information to all other nodes within unit distance, provided $p$ is activated. The (homogeneous) broadcast problem is to activate a minimum number of nodes such that in the resulting directed communication graph, the source $s$ can reach any other node. We study the complexity of the regular and the hop-bounded version of the problem (in the latter, $s$ must be able to reach every node within a specified number of hops), with the restriction that all points lie inside a strip of width $w$. We almost completely characterize the complexity of both the regular and the hop-bounded versions as a function of the strip width $w$.Comment: 50 pages, WADS 2017 submissio

An ETH-Tight Exact Algorithm for Euclidean TSP

We study exact algorithms for {\sc Euclidean TSP} in $\mathbb{R}^d$. In the early 1990s algorithms with $n^{O(\sqrt{n})}$ running time were presented for the planar case, and some years later an algorithm with $n^{O(n^{1-1/d})}$ running time was presented for any $d\geq 2$. Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on {\sc Euclidean TSP}, except for a lower bound stating that the problem admits no $2^{O(n^{1-1/d-\epsilon})}$ algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of {\sc Euclidean TSP} by giving a $2^{O(n^{1-1/d})}$ algorithm and by showing that a $2^{o(n^{1-1/d})}$ algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201

Kinetics and mechanism of the reaction of acetonyl radical, CH3(CO)CH2, with Br2

The low pressure fast discharge flow method with laser induced fluorescence detection of CH3C(O)CH2 was employed to study the kinetics of the reaction CH3C(O)CH2 + Br2 → CH3C(O)CH2Br + Br (1) at 298, 323 and 365 K. The rate coefficient at room temperature is k1 = (2.33 ± 0.04 (2σ)) 10–12 cm3 molecule–1 s–1, which increases slightly with increasing temperature. Quantum chemistry (G2) and theoretical rate theory (conventional TST) computations have supplied results in qualitative agreement with experiment. The relatively slow rate of reaction (1) can be due to the resonance stabilization of the acetonyl radical. Keywords: reaction kinetics, acetonyl radical, Br2 molecule, resonance stabilizatio

The compact radio structure of the high-redshift blazar J1430+4204 before and after a major outburst

The high-redshift (z=4.72) blazar J1430+4204 produced an exceptional radio outburst in 2006. We analyzed 15-GHz radio interferometric images obtained with the Very Long Baseline Array (VLBA) before and after the outburst, to search for possible structural changes on milli-arcsecond angular scales and to determine physical parameters of the source.Comment: Proceedings of the 5th Workshop of Young Researchers in Astronomy and Astrophysics, Budapest, 2009; to be published in J. Phys.: Conf. Series (JPCS); 4 pages, 3 figure

Páronként érintkező hengerek

Littlewood több mint ötven évig nyitott diszkrét geometriai kérdését válaszoljuk meg: létezik a térben hét páronként érintkező, végtelen hosszú, azonos átmérőjű körhenger

Folding Polyominoes into (Poly)Cubes

We study the problem of folding a polyomino $P$ into a polycube $Q$, allowing faces of $Q$ to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of $P$ or can divide squares in half (diagonally and/or orthogonally), (b) must be mountain or can be both mountain and valley, (c) can remain flat (forming an angle of $180^\circ$), and (d) must lie on just the polycube surface or can have interior faces as well. Second, we give all the inclusion relations among all models that fold on the grid lines of $P$. Third, we characterize all polyominoes that can fold into a unit cube, in some models. Fourth, we give a linear-time dynamic programming algorithm to fold a tree-shaped polyomino into a constant-size polycube, in some models. Finally, we consider the triangular version of the problem, characterizing which polyiamonds fold into a regular tetrahedron.Comment: 30 pages, 19 figures, full version of extended abstract that appeared in CCCG 2015. (Change over previous version: Fixed a missing reference.

Characteristics of ferroelectric-ferroelastic domains in N{\'e}el-type skyrmion host GaV4_4S8_8

GaV$_4$S$_8$ is a multiferroic semiconductor hosting N{\'e}el-type magnetic skyrmions dressed with electric polarization. At T$_s$ = 42K, the compound undergoes a structural phase transition of weakly first-order, from a non-centrosymmetric cubic phase at high temperatures to a polar rhombohedral structure at low temperatures. Below T$_s$, ferroelectric domains are formed with the electric polarization pointing along any of the four $\left< 111 \right>$ axes. Although in this material the size and the shape of the ferroelectric-ferroelastic domains may act as important limiting factors in the formation of the N{\'e}el-type skyrmion lattice emerging below T$_C$=13\:K, the characteristics of polar domains in GaV$_4$S$_8$ have not been studied yet. Here, we report on the inspection of the local-scale ferroelectric domain distribution in rhombohedral GaV$_4$S$_8$ using low-temperature piezoresponse force microscopy. We observed mechanically and electrically compatible lamellar domain patterns, where the lamellae are aligned parallel to the (100)-type planes with a typical spacing between 100 nm-1.2 $\mu$m. We expect that the control of ferroelectric domain size in polar skyrmion hosts can be exploited for the spatial confinement and manupulation of N{\'e}el-type skyrmions