In this paper, we prove that there exists a function ρk = (4 + o(1))k such that G(n, ρ/n) contains a k-regular graph with high probability whenever ρ > ρk. In the case of k = 3, it is also shown that G(n, ρ/n) contains a 3-regular graph with high probability whenever ρ > λ ≈ 5.1494. These are the first constant bounds on the average degree in G(n, p) for the existence of a k-regular subgraph. W...

We study the diameter of a family of random graphs on the torus that can be used to model wireless networks. In the random connection model two points x and y are connected with probability g(y − x) where g is a given function. We prove that the diameter of the graph is bounded by a constant, that only depends on ‖g‖1, with high probability as the number of vertices in the graph tends to infinity.

For any class of binary functions on [n] = {1, . . . , n} a classical result by Sauer states a sufficient condition for its VC-dimension to be at least d: its cardinality should be at least O(n). A necessary condition is that its cardinality be at least 2 (which is O(1) with respect to n). How does the size of a ‘typical’ class of VC-dimension d compare to these two extreme thresholds ? To answ...

Suppose we want to compute a Boolean function f, but instead of receiving the input, we only get l -faulty copies of each input bit. A typical solution in this case is to take the majority value of the faulty bits for each individual input bit and apply f on the majority values. We call this the trivial construction. We show that if f : {0; 1}n → {0; 1} and are known, the best function construc...

We propose a scheme for privacy-preserving escrow of financial transactions. The objective of the scheme is to preserve privacy and anonymity of the individual user engaging in financial transactions until the cumulative amount of all transactions in a certain category, for example all transactions with a particular counterparty in any single month, reaches a pre-specified threshold. When the t...

Sorting and balanced routing problems for synchronous mesh-like processor networks with reconfigurable buses are considered. Induced by the argument that broadcasting along buses of arbitrary length withinunit time seems rather non-realistic, we consider basic problems on reconfigurable meshes that can be solved efficiently even with restricted bus length. It is shown that on r-dimensional reco...

We show that in multi-sender communication games where senders imperfectly observe the state, if the state space is large enough, then there can exist equilibria arbitrarily close to full revelation of the state as the noise in the senders’observations gets small. In the case of replacement noise, where the senders observe the true state with high probability, we show this under mild assumption...

We consider three range-free localization protocols for sensor networks and analyze their accuracy in terms of the expected area of uncertainty of position per sensor. Assuming a small set of anchor nodes that know their position and broadcast it, we consider at first the simple Intersection protocol. In this protocol a sensor assumes its position is within the part of the plane that is covered...

Say Hwa Tan 1 ID , Heng-Dong Xi 2 and Weihua Li 3,* 1 Queensland Microand Nanotechnology Centre, Griffith University, 170 Kessels Road, Brisbane, QLD 4111, Australia; [email protected] 2 School of Aeronautics, Northwestern Polytechnical University, 127 West Youyi Rd., Xi’an 710072, China; [email protected] 3 School of Mechanical, Materials and Mechatronic Engineering, University o...

In this work we present a comparison of the quantum efficiencies (QE) of the 411312+ 411512 transition of Er3+ in ZBLAN (58 ZrF4-18 BaF2-5.5 LaF3-3 A1F3-15 NaF), BIGaZYT (30 Be2-18 InF3-20 ZnF2-10 YF3-10 ThF4-12 GaF3), and silica (67.7 Si02-16.2 SiO-11.1 Ca0-5 A1203) glasses obtained by photoacoustic spectroscopy. In the case of ZBLAN and BIGaZYT glasses, the method takes into account the 4111,...