Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations

Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant.Comment: 18 pages, 16 figures, new version with updated abstract and reference

Structure of Demographic Types of Small Towns in Poland Spatial and Temporal Approach

The aim of this paper is to determine changes in the structure of demographic types of small towns in Poland between 2004 and 2013. It is assumed in the paper, following the Central Statistical Office of Poland, that small towns are urban settlements having less than 20,000 inhabitants. The time period covered in this study is the time of Poland’s accession to the EU, which brought reduction of many barriers on the labour market and in migration movement. Demographic types of small towns were determined using Webb’s typology. Natural increase and migration indicators constitute its base. It was found that the share of towns of progressive character decreased and the share of those of regressive character increased in the analyzed period. A negative migration balance had the greatest effect on the number of inhabitants of the analyzed settlement units. The described demographic changes in small towns in Poland were connected with the second stage of demographic transition

TORQUES AND SYNCHRONIZATION OF MUSCLE WORK IN LEG IN THE MARATHON RUN

NI

Efficient MPC with a Mixed Adversary

Over the past 20 years, the efficiency of secure multi-party protocols has been greatly improved. While the seminal protocols from the late 80’s require a communication of Ω(n⁶) field elements per multiplication among n parties, recent protocols offer linear communication complexity. This means that each party needs to communicate a constant number of field elements per multiplication, independent of n. However, these efficient protocols only offer active security, which implies that at most t<n/3 (perfect security), respectively t<n/2 (statistical or computational security) parties may be corrupted. Higher corruption thresholds (i.e., t≥ n/2) can only be achieved with degraded security (unfair abort), where one single corrupted party can prevent honest parties from learning their outputs. The aforementioned upper bounds (t<n/3 and t<n/2) have been circumvented by considering mixed adversaries (Fitzi et al., Crypto' 98), i.e., adversaries that corrupt, at the same time, some parties actively, some parties passively, and some parties in the fail-stop manner. It is possible, for example, to achieve perfect security even if 2/3 of the parties are faulty (three quarters of which may abort in the middle of the protocol, and a quarter may even arbitrarily misbehave). This setting is much better suited to many applications, where the crash of a party is more likely than a coordinated active attack. Surprisingly, since the presentation of the feasibility result for the mixed setting, no progress has been made in terms of efficiency: the state-of-the-art protocol still requires a communication of Ω(n⁶) field elements per multiplication. In this paper, we present a perfectly-secure MPC protocol for the mixed setting with essentially the same efficiency as the best MPC protocols for the active-only setting. For the first time, this allows to tolerate faulty majorities, while still providing optimal efficiency. As a special case, this also results in the first fully-secure MPC protocol secure against any number of crashing parties, with optimal (i.e., linear in n) communication. We provide simulation-based proofs of our construction.ISSN:1868-896

Rule extraction from a neural network by hierarchical multiobjective genetic algorithm

The paper presents a method of rule extraction from the trained neural network by means of a genetic algorithm. The multiobjective approach is used to suit the nature of the problem, since different criteria (accuracy, complexity) may be taken into account during the search for a satisfying solution. The use of a hierarchical algorithm aims at reducing the complexity of the problem and thus enhancing the method performance. The overall structure and details of the algorithm as well as the results of experiments performed on popular benchmark data sets are presented