Comparing Beliefs, Surveys and Random Walks

Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation, belief propagation and several interesting hybrid methods. We then present numerical experiments which use WSAT (a widely used random-walk based SAT solver) to quantify the complexity of the 3-SAT formulae as a function of their parameters, both as randomly generated and after simplification, guided by survey propagation. Some properties of WSAT which have not previously been reported make it an ideal tool for this purpose -- its mean cost is proportional to the number of variables in the formula (at a fixed ratio of clauses to variables) in the easy-SAT regime and slightly beyond, and its behavior in the hard-SAT regime appears to reflect the underlying structure of the solution space that has been predicted by replica symmetry-breaking arguments. An analysis of the tradeoffs between the various methods of search for satisfying assignments shows WSAT to be far more powerful that has been appreciated, and suggests some interesting new directions for practical algorithm development.Comment: 8 pages, 5 figure

The Price of Fog: a Data-Driven Study on Caching Architectures in Vehicular Networks

Vehicular users are expected to consume large amounts of data, for both entertainment and navigation purposes. This will put a strain on cellular networks, which will be able to cope with such a load only if proper caching is in place, this in turn begs the question of which caching architecture is the best-suited to deal with vehicular content consumption. In this paper, we leverage a large-scale, crowd-collected trace to (i) characterize the vehicular traffic demand, in terms of overall magnitude and content breakup, (ii) assess how different caching approaches perform against such a real-world load, (iii) study the effect of recommendation systems and local contents. We define a price-of-fog metric, expressing the additional caching capacity to deploy when moving from traditional, centralized caching architectures to a "fog computing" approach, where caches are closer to the network edge. We find that for location-specific contents, such as the ones that vehicular users are most likely to request, such a price almost disappears. Vehicular networks thus make a strong case for the adoption of mobile-edge caching, as we are able to reap the benefit thereof -- including a reduction in the distance traveled by data, within the core network -- with little or no of the associated disadvantages.Comment: ACM IoV-VoI 2016 MobiHoc Workshop, The 17th ACM International Symposium on Mobile Ad Hoc Networking and Computing: MobiHoc 2016-IoV-VoI Workshop, Paderborn, German

Static Properties of Dilute Ferri‐ and Antiferromagnets

We report microscopic calculation of the static magnetic and spin‐wave properties of dilute antiferromagnetis (e.g. KMn1−x Zn xF3) and of dilute ferromagnetic garnets. The results are valid at low temperatures but are not restricted to low concentration of dilutents

Theory of the Spin Excitations of Rb\u3csub\u3e2\u3c/sub\u3eMn\u3csub\u3ex\u3c/sub\u3eNi\u3csub\u3e1−x\u3c/sub\u3eF\u3csub\u3e4\u3c/sub\u3e

We give a systematic treatment of the spin excitations of a family of disordered quasi-two-dimensional Heisenberg antiferromagnets, Rb2MnxNi1−xF4, for arbitrary values of x. The density of states, static response functions, and the dynamic susceptibility are calculated numerically. Results at several concentrations are presented graphically. We derive simple analytic theories which give an adequate description of the calculated quantities. The static response functions characterize excitations at low energy and long wave length, and enable us to predict the concentration dependence of the anisotropy gap frequency and the temperature dependence of the magnetization. The dynamic susceptibility is in good agreement with recent neutron-scattering experiments on Rb2Mn0.5Ni0.5F4. The spin-wave density of states for 0.