Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Background independent quantum gravity: A Status report

In recent years, free space optical (FSO) communication has gained significant importance owing to its unique features: large bandwidth, license free spectrum, high data rate, easy and quick deployability, less power, and low mass requirements. FSO communication uses optical carrier in the near infrared band to establish either terrestrial links within the Earth’s atmosphere or inter-satellite/deep space links or ground-to-satellite/satellite-to-ground links. It also finds its applications in remote sensing, radio astronomy, military, disaster recovery, last mile access, backhaul for wireless cellular networks, and many more. However, despite of great potential of FSO communication, its performance is limited by the adverse effects (viz., absorption, scattering, and turbulence) of the atmospheric channel. Out of these three effects, the atmospheric turbulence is a major challenge that may lead to serious degradation in the bit error rate performance of the system and make the communication link infeasible. This paper presents a comprehensive survey on various challenges faced by FSO communication system for ground-to-satellite/satellite-to-ground and inter-satellite links. It also provides details of various performance mitigation techniques in order to have high link availability and reliability. The first part of this paper will focus on various types of impairments that pose a serious challenge to the performance of optical communication system for ground-to-satellite/satellite-to-ground and inter-satellite links. The latter part of this paper will provide the reader with an exhaustive review of various techniques both at physical layer as well as at the other layers (link, network, or transport layer) to combat the adverse effects of the atmosphere. It also uniquely presents a recently developed technique using orbital angular momentum for utilizing the high capacity advantage of optical carrier in case of space-based and near-Earth optical communication links. This survey provides the reader with comprehensive details on the use of space-based optical backhaul links in order to provide high capacity and low cost backhaul solutions.

/pdf/optical-communication-in-space-challenges-and-mitigation-41d8by09lh.pdf

Optical Communication in Space: Challenges and Mitigation Techniques

In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett–Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett–Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.

http://inspirehep.net/record/612372/files/arXiv:gr-qc_0301113.pdf

Spin foam models for quantum gravity

Introduction. 1. Mathematical Preliminaries. Submodular Systems and Base Polyhedra. 2. From Matroids to Submodular Systems. Matroids. Polymatroids. Submodular Systems. 3. Submodular Systems and Base Polyhedra. Fundamental Operations on Submodular Systems. Greedy Algorithm. Structures of Base Polyhedra. Intersecting- and Crossing-Submodular Functions. Related Polyhedra. Submodular Systems of Network Type. Neoflows. 4. The Intersection Problem. The Intersection Theorem. The Discrete Separation Theorem. The Common Base Problem. 5. Neoflows. The Equivalence of the Neoflow Problems. Feasibility for Submodular Flows. Optimality for Submodular Flows. Algorithms for Neoflows. Matroid Optimization. Submodular Analysis. 6. Submodular Functions and Convexity. Conjugate Functions and a Fenchel-Type Min-Max Theorem for Submodular and Supermodular Functions. Subgradients of Submodular Functions. The Lovasz Extensions of Submodular Functions. 7. Submodular Programs. Submodular Programs - Unconstrained Optimization. Submodular Programs - Constrained Optimization. Nonlinear Optimization with Submodular Constraints. 8. Separable Convex Optimization. Optimality Conditions. A Decomposition Algorithm. Discrete Optimization. 9. The Lexicographically Optimal Base Problem. Nonlinear Weight Functions. Linear Weight Functions. 10. The Weighted Max-Min and Min-Max Problems. Continuous Variables. Discrete Variables. 11. The Fair Resource Allocation Problem. Continuous Variables. Discrete Variables. 12. The Neoflow Problem with a Separable Convex Cost Function. References. Index.

Submodular functions and optimization

Let G=(U/spl cup/W, E) be a bipartite graph with disjoint vertex sets U and W, edge set E, and girth g. This correspondence presents an algorithm for counting the number of cycles of length g, g+2, and g+4 incident upon every vertex in U/spl cup/W. The proposed cycle counting algorithm consists of integer matrix operations and its complexity grows as O(gn/sup 3/) where n=max(|U|,|W|).

An algorithm for counting short cycles in bipartite graphs

Using numerical calculations, we compare three versions of the Barrett–Crane model of four-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov and Rovelli, we show the partition function diverges very rapidly for many triangulated 4-manifolds. In the version with modified face and edge amplitudes given by Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spin-zero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.

/pdf/spin-foam-models-of-riemannian-quantum-gravity-534m09qiou.pdf

Spin foam models of Riemannian quantum gravity

A receiver-oriented perspective on capacity scaling in mobile ad hoc networks (MANETs) suggests that broadcast and multicast may be more natural traffic models for these systems than the random unicast pairs typically considered. Furthermore, traffic loads for the most promising near-term application for MANET technology — namely, networking at the tactical edge — are largely broadcast. The development of novel MANET approaches targeting broadcast first and foremost, however, has not been reported. Instead, existing system designs largely rely on fundamentally link-based, layered architectures, which are best suited to unicast traffic. In response to the demands of tactical edge communications, TrellisWare Technologies, Inc. developed a MANET system based on Barrage Relay Networks (BRNs). BRNs utilize an autonomous cooperative communication scheme that eliminates the need for link-level collision avoidance. The fundamental physical layer resource in BRNs is not a link, but a portion in space and time of a cooperative, multihop transport fabric. While initial hardware prototypes of BRNs were being refined into products by TrellisWare, a number of concepts similar to those that underlie BRNs were reported independently in the literature. That TrellisWare's tactical edge MANET system design and academic research reconsidering the standard networking approach for MANETs arrived at similar design concepts lends credence to the value of these emerging wireless network approaches.

Barrage Relay Networks

A number of authors have recently considered iterative soft-in soft-out (SISO) decoding algorithms for classical linear block codes that utilize redundant Tanner graphs. Jiang and Narayanan presented a practically realizable algorithm that applies only to cyclic codes while Kothiyal et al. presented an algorithm that, while applicable to arbitrary linear block codes, does not imply a low-complexity implementation. This work first presents the aforementioned algorithms in a common framework and then presents a related algorithm - random redundant iterative decoding - that is both practically realizable and applicable to arbitrary linear block codes. Simulation results illustrate the successful application of the random redundant iterative decoding algorithm to the extended binary Golay code. Additionally, the proposed algorithm is shown to outperform Jiang and Narayanan's algorithm for a number of Bose-Chaudhuri-Hocquenghem (BCH) codes

/pdf/random-redundant-soft-in-soft-out-decoding-of-linear-block-fnuf1jvvpw.pdf

Random Redundant Soft-In Soft-Out Decoding of Linear Block Codes

We consider a coded cooperative data exchange problem with the goal of generating a secret key. In particular, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with the fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in the traditional cooperative data exchange setting can be solved in polynomial time. In doing this, we completely characterize the best possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal. Finally, we extend the single-key results to characterize the minimum number of public transmissions required to generate a desired integer number of statistically independent secret keys.

Thomas R. Halford

Papers

An algorithm for counting short cycles in bipartite graphs

Spin foam models of Riemannian quantum gravity

Barrage Relay Networks

Random Redundant Soft-In Soft-Out Decoding of Linear Block Codes

Coded Cooperative Data Exchange for a Secret Key