Toward the Rectilinear Crossing Number of KnK_n: New Drawings, Upper Bounds, and Asymptotics

Scheinerman and Wilf (1994) assert that `an important open problem in the study of graph embeddings is to determine the rectilinear crossing number of the complete graph K_n.' A rectilinear drawing of K_n is an arrangement of n vertices in the plane, every pair of which is connected by an edge that is a line segment. We assume that no three vertices are collinear, and that no three edges intersect in a point unless that point is an endpoint of all three. The rectilinear crossing number of K_n is the fewest number of edge crossings attainable over all rectilinear drawings of K_n. For each n we construct a rectilinear drawing of K_n that has the fewest number of edge crossings and the best asymptotics known to date. Moreover, we give some alternative infinite families of drawings of K_n with good asymptotics. Finally, we mention some old and new open problems.Comment: 13 Page

Les Mots et les choses du théâtre. France, Italie, Espagne, XVIe–XVIIe siècles

This volume, consisting of seventeen articles, comprises the proceedings of a conference held in 2015 by the research organization IDT—Les Idées du théâtre, devoted to the study of liminary texts of plays, especially prefaces, dedications, prologues, and critiques

List Distinguishing Parameters of Trees

A coloring of the vertices of a graph G is said to be distinguishing} provided no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing chromatic number of G, chi_D(G), is the minimum number of colors in a distinguishing coloring of G that is also a proper coloring. Recently the notion of a distinguishing coloring was extended to that of a list distinguishing coloring. Given an assignment L= {L(v) : v in V(G)} of lists of available colors to the vertices of G, we say that G is (properly) L-distinguishable if there is a (proper) distinguishing coloring f of G such that f(v) is in L(v) for all v. The list distinguishing number of G, D_l(G), is the minimum integer k such that G is L-distinguishable for any list assignment L with |L(v)| = k for all v. Similarly, the list distinguishing chromatic number of G, denoted chi_{D_l}(G) is the minimum integer k such that G is properly L-distinguishable for any list assignment L with |L(v)| = k for all v. In this paper, we study these distinguishing parameters for trees, and in particular extend an enumerative technique of Cheng to show that for any tree T, D_l(T) = D(T), chi_D(T)=chi_{D_l}(T), and chi_D(T) <= D(T) + 1.Comment: 10 page

Les Mots et les choses du théâtre. France, Italie, Espagne, XVIe–XVIIe siècles

This volume, consisting of seventeen articles, comprises the proceedings of a conference held in 2015 by the research organization IDT—Les Idées du théâtre, devoted to the study of liminary texts of plays, especially prefaces, dedications, prologues, and critiques

HoneyTree: Making Honeywords Sweeter

Cyber deception is an area of cybersecurity based on building detection systems and verification models using decoys or controlled misinformation to confuse or misdirect the adversaries into revealing their presence and/or intentions. In the era of online services where our data is usually protected on the cloud relying on a secret key, even the most secure cyber systems can get compromised, losing highly confidential data to the attackers, including hashed passwords that can be cracked offline. Prior work has been done in carefully placing traps in the systems to detect intrusion activities. The Honeywords project by Juels and Rivest is the most straightforward and successful technique in detecting and deterring offline-password brute force by placing multiple plausible decoy passwords together along with the real password. In this paper, we enhance this approach and combine it with the concept of Merkle tree to build a new model called HoneyTree. Our model achieves twice the level of security as the Honeywords project at the same storage cost. We perform a detailed comparison of our approach to the original Honeywords project and analyze its pros and cons

Subspace hypercyclicity

A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity is interesting, including a nontrivial subspace-hypercyclic operator that is not hypercyclic. There is a Kitai-like criterion that implies subspace-hypercyclicity and although the spectrum of a subspace-hypercyclic operator must intersect the unit circle, not every component of the spectrum will do so. We show that, like hypercyclicity, subspace-hypercyclicity is a strictly infinite-dimensional phenomenon. Additionally, compact or hyponormal operators can never be subspace-hypercyclic.Comment: 15 page

Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.Comment: 26 page

Effect of mild oxidation on the surface chemistry of bituminous coals under different humidity conditions

The influence of humidity conditions on the oxidation of four coals has been studied on the basis of their surface chemistry. A systematic study was carried out in which four coals of different rank were oxidised at 50 °C in two conditions of humidity (20 and 90% moisture levels) and in an air atmosphere. The changes in the surface functional groups were measured by means of diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and X-ray photoelectron spectroscopy (XPS). The lowest rank coals were the most affected by oxidation in all the humidity conditions applied. In the case of the higher rank coals, higher moisture levels promoted the oxidation process. The number of oxygen-containing structures increased after oxidation, the most abundant being the carbonyl and carboxyl groups