An invariant of scale-free graphs

In many applications (including biology and the study of computer networks) graphs are found to be scale-free. It has been argued that this property alone does not tell us much about the structure of the graph. In this paper, we introduce a numerical characteristic of a graph, which we call the astral index, and which can be calculated efficiently. We demonstrate that the Barab�si-Albert algorithm for generating scale-free graphs produces not just scale-free graphs, but only scale-free graphs with a constant astral index. On some examples of biological graphs, we see that they not only are scale-free, but also share the value of the astral index with Barab�si-Albert graphs. For comparison, we demonstrate that the Erd?s?R�nyi model for generating random graphs also generates only graphs with a constant astral index, whose value significantly differs from that of graphs generated by the Barab�si-Albert algorithm

A simple technique for choosing and managing secure passwords: passwords with a random on-paper part

Recently I proposed a novel way of choosing and managing passwords in a secure way, especially suitable for the typical situation of a modern user with multiple accounts and frequent password changes on some of the accounts. The name I suggested for it is ?passwords with a random on-paper part?, shortened as PROPP. The PROPP method is also suitable for scenarios in which the user needs to log in on a wide and unpredictable range of devices, although in the description below I concentrate on a one-computer scenario

Efficient adaptive implementation of the serial schedule generation scheme using preprocessing and bloom filters

The majority of scheduling metaheuristics use indirect representation of solutions as a way to efficiently explore the search space. Thus, a crucial part of such metaheuristics is a “schedule generation scheme” – procedure translating the indirect solution representation into a schedule. Schedule generation scheme is used every time a new candidate solution needs to be evaluated. Being relatively slow, it eats up most of the running time of the metaheuristic and, thus, its speed plays significant role in performance of the metaheuristic. Despite its importance, little attention has been paid in the literature to efficient implementation of schedule generation schemes. We give detailed description of serial schedule generation scheme, including new improvements, and propose a new approach for speeding it up, by using Bloom filters. The results are further strengthened by automated control of parameters. Finally, we employ online algorithm selection to dynamically choose which of the two implementations to use. This hybrid approach significantly outperforms conventional implementation on a wide range of instances

Authentication grid

A new challenge-and-response user authentication method is described, whose aims are: - Reuse the standard password-based authentication as much as possible - Reduce the danger of shoulder-surfing - Keep the authentication process usable - Use modern touch-screen technolog

Towards human readability of automated unknottedness proofs

© 2018 CEUR-WS. All rights reserved. When is a knot actually unknotted? How does one convince a human reader of the correctness of an answer to this question for a given knot diagram? For knots with a small number of crossings, humans can be efficient in spotting a sequence of untangling moves. However, for knot diagrams with hundreds of crossings, computer assistance is necessary. There have been recent developments in algorithms for both (indirectly) (i) detecting unknotedness and (directly) (ii) producing such sequences of untangling moves. Automated reasoning can be applied to (i) and, to some extent, (ii), but the computer output is not necessarily human-readable. We report on work in progress towards bridging the gap between the computer output and human readability, via generating human-readable visual proofs of unknottedness

Ranks of ideals in inverse semigroups of difunctional binary relations

The set Dn of all difunctional relations on an n element set is an inverse semigroup under a variation of the usual composition operation. We solve an open problem of Kudryavtseva and Maltcev (Publ Math Debrecen 78(2):253–282, 2011), which asks: What is the rank (smallest size of a generating set) of Dn? Specifically, we show that the rank of Dn is B(n)+n, where B(n) is the nth Bell number. We also give the rank of an arbitrary ideal of Dn. Although Dn bears many similarities with families such as the full transformation semigroups and symmetric inverse semigroups (all contain the symmetric group and have a chain of J-classes), we note that the fast growth of rank(Dn) as a function of n is a property not shared with these other families

Visual Algebraic proofs for Unknot Detection

A knot diagram looks like a two-dimensional drawing of aknotted rubberband. Proving that a given knot diagram can be untangled(that is, is a trivial knot, called an unknot) is one of the most famousproblems of knot theory. For a small knot diagram, one can try to finda sequence of untangling moves explicitly, but for a larger knot diagramproducing such a proof is difficult, and the produced proofs are hardto inspect and understand. Advanced approaches use algebra, with anadvantage that since the proofs are algebraic, a computer can be usedto produce the proofs, and, therefore, a proof can be produced evenfor large knot diagrams. However, such produced proofs are not easy toread and, for larger diagrams, not likely to be human readable at all.We propose a new approach combining advantages of these: the proofsare algebraic and can be produced by a computer, whilst each part ofthe proof can be represented as a reasonably small knot-like diagram(a new representation as a labeled tangle diagram), which can be easilyinspected by a human for the purposes of checking the proof and findingout interesting facts about the knot diagram

Dihedral semigroups, their defining relations and an application to describing knot semigroups of rational links

It is known that a knot (link) is rational if and only if its π-orbifold group is dihedral. A semigroup version of this result has been formulated as a conjecture. Working towards proving the conjecture, we describe certain semigroups associated with twist links, clarify how these semigroups are related to dihedral groups and find defining relations of these semigroups