Fast and reliable handoff for vehicular networks

A layer-3 mobility management scheme for an all-IP Wireless Access Network (WAN), and in particular for vehicular networks, is developed in this paper. The proposed method enables fast and reliable handoff. This feature is extremely important for high speed vehicular networks. Since vehicles are characterized by likely-predictable path, as well as very high speed, handoff events can and should be predicted in order to achieve fast and reliable handoff. As it is shown in this study, the proposed scheme can significantly reduce the packet loss ratio caused by frequent handoff events experienced by high speed vehicles. This scheme is topology-independent in the sense that it does not assume any network topology. The key idea is to use a topology-learning algorithm that enables to perform localized mobility management, by efficiently re-selecting a Mobility Anchor Point (MAP) node. The goal of the proposed scheme is to maintain a continues connection subject to user-dependent delay constraints, while minimizing the signaling cost and packet loss ratio associated with handoff events. This scheme is consistent with the existing mobility management schemes currently used in Mobile IP (MIP) and cellular networks, and it fits into the Hierarchical Mobile IPv6 (HMIPv6) scheme defined in Mobile IPv6 (MIPv6) for integrating mobile terminals with the Internet wired backbone.     

Efficient IP-Based TV Service Over UMTS Networks

The problem of providing an efficient and low-cost video streaming service over wireless access networks is considered in this work. In order to tackle the ??last mile?? bottleneck for video delivery to the home, we propose a content-aware architecture, that incorporates popularity-dependent video patching with application-enabled multicast content delivery. The key idea is to exploit the Broadcast/Multicast Service Center (BM-SC) in Universal Mobile Telecommunications System (UMTS) networks, by forwarding individual requests for popular data to the BM-SC, and then to serve these requests efficiently by multicast content distribution. The proposed method offers a tremendous bandwidth saving, in comparison with the MAC-enabled multicasting currently exists in wireless networks. We analyze the conditions under which multicast content delivery offers a better QoS, in terms of service delay, over the individual service currently used for video streaming.     

Triple-hybrid sub-micron particles: Ag@polymer@silica

Journal of Sol-Gel Science and Technology - Methods for the synthesis of triple-hybrid (metal, organic polymer, ceramic component) submicron particles of silver@(polymer@silica) spheres were...     

Application of the Finite Cell Method to patient-specific femur simulations

Standard methods for predicting the mechanical response of a human femur bone from quantitative computer-tomography (qCT) scans are classically based on the h-version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high-order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high-order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient-specific femur is presented. The femur model is determined based on qCT-scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p-FE analysis and validated by results from an in-vitro test of the modeled femur. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Johnson–Lindenstrauss Lemma Almost Characterizes Hilbert Space, But Not Quite

Let X be a normed space that satisfies the Johnson–Lindenstrauss lemma (J–L lemma, in short) in the sense that for any integer n and any x ₁,…,x _n ∈X, there exists a linear mapping L:X→F, where F⊆X is a linear subspace of dimension O(log n), such that ‖x _i −x _j ‖≤‖L(x _i )−L(x _j )‖≤O(1)⋅‖x _i −x _j ‖ for all i,j∈{1,…,n}. We show that this implies that X is almost Euclidean in the following sense: Every n-dimensional subspace of X embeds into Hilbert space with distortion 2^2O(log*n)2^{2^{O(\log^{*}n)}} . On the other hand, we show that there exists a normed space Y which satisfies the J–L lemma, but for every n, there exists an n-dimensional subspace E _n ⊆Y whose Euclidean distortion is at least 2^Ω(α(n)), where α is the inverse Ackermann function.     

The Euclidean Distortion of the Lamplighter Group

We show that the cyclic lamplighter group C ₂ ? C _n embeds into Hilbert space with distortion $\mathrm{O}(\sqrt{\log n})We show that the cyclic lamplighter group C ₂ ≀ C _n embeds into Hilbert space with distortion O(?{logn})\mathrm{O}(\sqrt{\log n}) . This matches the lower bound proved by Lee et al. (Geom. Funct. Anal., 2009), answering a question posed in that paper. Thus, the Euclidean distortion of C ₂ ≀ C _n is \varTheta(?{logn})\varTheta(\sqrt{\log n}) . Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni et al. (Isr. J. Math. 52(3):251–265, 1985) and by Gromov (see de Cornulier et. al. in Geom. Funct. Anal., 2009), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings of finite groups.     

Maximum gradient embeddings and monotone clustering

Let (X,d _X ) be an n-point metric space. We show that there exists a distribution over non-contractive embeddings into trees f: X → T such that for every x ∈ X, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.     

Random martingales and localization of maximal inequalities

Let (X,d,μ) be a metric measure space. For ∅≠R⊆(0,∞) consider the Hardy-Littlewood maximal operator

     

A symmetry principle for topological quantum order

We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The major guiding principle behind our approach is that of symmetries and entanglement. These symmetries may be actual symmetries of the Hamiltonian characterizing the system, or emergent symmetries. To this end, we introduce the concept of low-dimensional Gauge-like symmetries (GLSs), and the physical conservation laws (including topological terms, fractionalization, and the absence of quasi-particle excitations) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The physical engine for TQO are topological defects associated with the restoration of GLSs. These defects propagate freely through the system and enforce TQO. Our results are strongest for gapped systems with continuous GLSs. At zero temperature, selection rules associated with the GLSs enable us to systematically construct general states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. Indices associated with these symmetries correspond to different topological sectors. All currently known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin-exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. The symmetry based framework discussed herein allows us to go beyond standard topological field theories and systematically engineer new physical models with finite temperature TQO (both Abelian and non-Abelian). Furthermore, we analyze the insufficiency of entanglement entropy (we introduce SU(N) Klein models on small world networks to make the argument even sharper), spectral structures, maximal string correlators, and fractionalization in establishing TQO. We show that Kitaev’s Toric code model and Wen’s plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain, demonstrating that despite the spectral gap in these systems the toric operator expectation values may vanish once thermal fluctuations are present. This illustrates the fact that the quantum states themselves in a particular (operator language) representation encode TQO and that the duality mappings, being non-local in the original representation, disentangle the order. We present a general algorithm for the construction of long-range string and brane orders in general systems with entangled ground states; this algorithm relies on general ground states selection rules and becomes of the broadest applicability in gapped systems in arbitrary dimensions. We exactly recast some known non-local string correlators in terms of local correlation functions. We discuss relations to problems in graph theory.     

Hyperplane projections of the unit ball of ℓ p n

Let B _p ⁿ ={x∈\R ⁿ ;\; \sum _i=1 ⁿ |x _i | ^p ≤ 1} , 1≤ p\le+∈fty . We study the extreme values of the volume of the orthogonal projection of B _p ⁿ onto hyperplanes H\subset \R ⁿ . For a fixed H , we prove that the ratio vol(P _H B _p ⁿ )/ vol(B _p ^n-1 ) is non-decreasing in p∈[1,+∈fty] . Received May 21, 2001, and in revised form September 2, 2001. Online publication December 17, 2001.