Variation-norm and fluctuation estimates for ergodic bilinear averages

For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of Lacey and Bourgain where almost surely convergence of the sequence was proved (which is equivalent to the qualitative statement that the number of fluctuations is finite at each scale). Via transference, the proof reduces to establishing new bilinear Lp bounds for variation-norms of truncated bilinear operators on R, and the main ingredient of the proof of these bounds is a variation-norm extension of maximal Bessel inequalities of Lacey and Demeter--Tao--Thiele.Comment: 37 pages, new version fixed some references not displaying correctl

IPv6 Network Mobility

Network Authentication, Authorization, and Accounting has been used since before the days of the Internet as we know it today. Authentication asks the question, “Who or what are you?” Authorization asks, “What are you allowed to do?” And fi nally, accounting wants to know, “What did you do?” These fundamental security building blocks are being used in expanded ways today. The fi rst part of this two-part series focused on the overall concepts of AAA, the elements involved in AAA communications, and highlevel approaches to achieving specifi c AAA goals. It was published in IPJ Volume 10, No. 1[0]. This second part of the series discusses the protocols involved, specifi c applications of AAA, and considerations for the future of AAA

Simulating Cellular Communications in Vehicular Networks: Making SimuLTE Interoperable with Veins

The evolution of cellular technologies toward 5G progressively enables efficient and ubiquitous communications in an increasing number of fields. Among these, vehicular networks are being considered as one of the most promising and challenging applications, requiring support for communications in high-speed mobility and delay-constrained information exchange in proximity. In this context, simulation frameworks under the OMNeT++ umbrella are already available: SimuLTE and Veins for cellular and vehicular systems, respectively. In this paper, we describe the modifications that make SimuLTE interoperable with Veins and INET, which leverage the OMNeT++ paradigm, and allow us to achieve our goal without any modification to either of the latter two. We discuss the limitations of the previous solution, namely VeinsLTE, which integrates all three in a single framework, thus preventing independent evolution and upgrades of each building block.Comment: Published in: A. Foerster, A. Udugama, A. Koensgen, A. Virdis, M. Kirsche (Eds.), Proc. of the 4th OMNeT++ Community Summit, University of Bremen - Germany - September 7-8, 201

Localization in tame and wild coalgebras

We apply the theory of localization for tame and wild coalgebras in order to prove the following theorem: "Let Q be an acyclic quiver. Then any tame admissible subcoalgebra of KQ is the path coalgebra of a quiver with relations".Comment: 23 pages, to appear in Journal of Pure and Applied Algebr

3D Gravity and Gauge Theories

I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes weighted with the Turaev-Viro invariant. Then, I discuss how this invariant can be included in the general framework of lattice gauge theory (qQCD$_3$). To make sense of it, one needs a quantum analog of the Peter-Weyl theorem and an invariant measure, which are introduced explicitly. The consideration here is limited to the simplest and most interesting case of $SL_q(2)$, $q=e^{i\frac{2\pi}{k+2}}$. At the end, I dwell on 3D generalizations of matrix models.Comment: 20 pp., NBI-HE-93-67 (Contribution to Proceedings of 1993 Cargese workshop

Filtering Network Traffic Based on Protocol Encapsulation Rules

Packet filtering is a technology at the foundation of many traffic analysis tasks. While languages and tools for packet filtering have been available for many years, none of them supports filters operating on the encapsulation relationships found in each packet. This represents a problem as the number of possible encapsulations used to transport traffic is steadily increasing and we cannot define exactly which packets have to be captured. This paper presents our early work on an algorithm that models protocol filtering patterns (including encapsulation constraints) as Finite State Automata and supports the composition of multiple expressions within the same filter. The resulting, optimized filter is then translated into executable code. The above filtering algorithms are available in the NetBee open source library, which provides some basic tools for handling network packets (e.g., a tcpdump-like program) and APIs to build more advanced tool

An Analisys of Business VPN Case Studies

A VPN (Virtual Private Network) simulates a secure private network through a shared public insecure infrastructure like the Internet. The VPN protocol provides a secure and reliable access from home/office on any networking technology transporting IP packets. In this article we study the standards for VPN implementation and analyze two case studies regarding a VPN between two routers and two firewalls.VPN; Network; Protocol.

Oracles Are Subtle But Not Malicious

Theoretical computer scientists have been debating the role of oracles since the 1970's. This paper illustrates both that oracles can give us nontrivial insights about the barrier problems in circuit complexity, and that they need not prevent us from trying to solve those problems. First, we give an oracle relative to which PP has linear-sized circuits, by proving a new lower bound for perceptrons and low- degree threshold polynomials. This oracle settles a longstanding open question, and generalizes earlier results due to Beigel and to Buhrman, Fortnow, and Thierauf. More importantly, it implies the first nonrelativizing separation of "traditional" complexity classes, as opposed to interactive proof classes such as MIP and MA-EXP. For Vinodchandran showed, by a nonrelativizing argument, that PP does not have circuits of size n^k for any fixed k. We present an alternative proof of this fact, which shows that PP does not even have quantum circuits of size n^k with quantum advice. To our knowledge, this is the first nontrivial lower bound on quantum circuit size. Second, we study a beautiful algorithm of Bshouty et al. for learning Boolean circuits in ZPP^NP. We show that the NP queries in this algorithm cannot be parallelized by any relativizing technique, by giving an oracle relative to which ZPP^||NP and even BPP^||NP have linear-size circuits. On the other hand, we also show that the NP queries could be parallelized if P=NP. Thus, classes such as ZPP^||NP inhabit a "twilight zone," where we need to distinguish between relativizing and black-box techniques. Our results on this subject have implications for computational learning theory as well as for the circuit minimization problem.Comment: 20 pages, 1 figur