Performance guarantees for greedy maximization of non-submodular controllability metrics

A key problem in emerging complex cyber-physical networks is the design of information and control topologies, including sensor and actuator selection and communication network design. These problems can be posed as combinatorial set function optimization problems to maximize a dynamic performance metric for the network. Some systems and control metrics feature a property called submodularity, which allows simple greedy algorithms to obtain provably near-optimal topology designs. However, many important metrics lack submodularity and therefore lack provable guarantees for using a greedy optimization approach. Here we show that performance guarantees can be obtained for greedy maximization of certain non-submodular functions of the controllability and observability Gramians. Our results are based on two key quantities: the submodularity ratio, which quantifies how far a set function is from being submodular, and the curvature, which quantifies how far a set function is from being supermodular

Minerals of Indiana

Indiana Geological Survey Bulletin 18Undisturbed Paleozoic sediments form the bedrock surface of Indiana. The most common minerals in these sediments are calcite, clay minerals, dolomite, glauconite, goethite, gypsum, hematite, limonite (hydrous iron oxides), quartz, and siderite. Found less abundantly are anhydrite, apatite, aragonite, barite, celestite, copiapite, epsomite, fluorite, marcasite, melanterite, millerite, pyrite, pyrrhotite, smythite, sphalerite, strontianite, sulfur, and wad. These minerals occur in veins and cavities; along bedding, joint, and fracture surfaces and stylolite seams; and in geodes in limestones. Reported and observed locations and modes of occurrence are presented for each of the minerals except most clay and minerals. The more unusual minerals that occur in glacial materials of Indiana, native copper, diamond, galena, native gold, and native silver, are described in full. A literature study was the basis for a brief discussion of the history of Indiana minerals. The present report questions the reported occurrences in Indiana of native bismuth, graphite, malachite, moissanite, nitromagnesite, and stibnite.Indiana Department of Conservatio

Emotional Strategies as Catalysts for Cooperation in Signed Networks

The evolution of unconditional cooperation is one of the fundamental problems in science. A new solution is proposed to solve this puzzle. We treat this issue with an evolutionary model in which agents play the Prisoner's Dilemma on signed networks. The topology is allowed to co-evolve with relational signs as well as with agent strategies. We introduce a strategy that is conditional on the emotional content embedded in network signs. We show that this strategy acts as a catalyst and creates favorable conditions for the spread of unconditional cooperation. In line with the literature, we found evidence that the evolution of cooperation most likely occurs in networks with relatively high chances of rewiring and with low likelihood of strategy adoption. While a low likelihood of rewiring enhances cooperation, a very high likelihood seems to limit its diffusion. Furthermore, unlike in non-signed networks, cooperation becomes more prevalent in denser topologies.Comment: 24 pages, Accepted for publication in Advances in Complex System

High-Resolution spectroscopy of the low-mass X-ray binary EXO 0748-67

We present initial results from observations of the low-mass X-ray binary EXO 0748-67 with the Reflection Grating Spectrometer on board the XMM-Newton Observatory. The spectra exhibit discrete structure due to absorption and emission from ionized neon, oxygen, and nitrogen. We use the quantitative constraints imposed by the spectral features to develop an empirical model of the circumsource material. This consists of a thickened accretion disk with emission and absorption in the plasma orbiting high above the binary plane. This model presents challenges to current theories of accretion in X-ray binary systems.Comment: 5 pages, 4 figures, accepted by A&A letters, XMM special issu

First Passage Properties of the Erdos-Renyi Random Graph

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma

On large deviation properties of Erdos-Renyi random graphs

We show that large deviation properties of Erd\"os-R\'enyi random graphs can be derived from the free energy of the $q$-state Potts model of statistical mechanics. More precisely the Legendre transform of the Potts free energy with respect to $\ln q$ is related to the component generating function of the graph ensemble. This generalizes the well-known mapping between typical properties of random graphs and the $q\to 1$ limit of the Potts free energy. For exponentially rare graphs we explicitly calculate the number of components, the size of the giant component, the degree distributions inside and outside the giant component, and the distribution of small component sizes. We also perform numerical simulations which are in very good agreement with our analytical work. Finally we demonstrate how the same results can be derived by studying the evolution of random graphs under the insertion of new vertices and edges, without recourse to the thermodynamics of the Potts model.Comment: 38 pages, 9 figures, Latex2e, corrected and extended version including numerical simulation result