Network Lasso: Clustering and Optimization in Large Graphs

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems

Unusual Coupling Between Field-induced Spin Fluctuations and Spin Density Wave in Intermetallic CeAg2Ge2

We report on the experimental evidences for an unusual coupling between the magnetic field- induced fluctuations of correlated Ce-ions coinciding with the discontinuous movement of the underlying spin density wave in the intermetallic rare earth compound CeAg2Ge2. The measurements performed using neutron scattering and magnetic Gruneisen ratio methods suggest that the coupling onsets at H= 2.7 T, T < 3.8 K and persists to the lowest measurement temperature T ~ 0.05 K. These measurements suggest a new mechanism behind the spin fluctuations which can affect the intrinsic properties of the system.Comment: 4 pages, 4 figures, Strongly correlated electrons syste

Computing A Glimpse of Randomness

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted

Grain-boundary grooving and agglomeration of alloy thin films with a slow-diffusing species

We present a general phase-field model for grain-boundary grooving and agglomeration of polycrystalline alloy thin films. In particular, we study the effects of slow-diffusing species on grooving rate. As the groove grows, the slow species becomes concentrated near the groove tip so that further grooving is limited by the rate at which it diffuses away from the tip. At early times the dominant diffusion path is along the boundary, while at late times it is parallel to the substrate. This change in path strongly affects the time-dependence of grain boundary grooving and increases the time to agglomeration. The present model provides a tool for agglomeration-resistant thin film alloy design. keywords: phase-field, thermal grooving, diffusion, kinetics, metal silicidesComment: 4 pages, 6 figure

Capacity market design options: a dynamic capacity investment model and a GB case study

Rising feed-in from renewable energy sources decreases margins, load factors, and thereby profitability of conventional generation in several electricity markets around the world. At the same time, conventional generation is still needed to ensure security of electricity supply. Therefore, capacity markets are currently being widely discussed as a measure to ensure generation adequacy in markets such as France, Germany, and the United States (e.g., Texas), or even implemented for example in Great Britain. We assess the effect of different capacity market design options in three scenarios: 1) no capacity market, 2) a capacity market for new capacity only, and 3) a capacity market for new and existing capacity. We compare the results along the three key dimensions of electricity policy ��� affordability, reliability, and sustainability. In a Great Britain case study we find that a capacity market increases generation adequacy since it provides incentives for new generation investments. Furthermore, our results show that a capacity market can lower the total bill of generation because it can reduce lost load and the potential to exercise market power. Additionally, we find that a capacity market for new capacity only is cheaper than a capacity market for new and existing capacity because it remunerates fewer generators in the first years after its introduction.renewable energy source

Evolution of the bulk properties, structure, magnetic order, and superconductivity with Ni doping in CaFe2-xNixAs2

Magnetization, susceptibility, specific heat, resistivity, neutron and x-ray diffraction have been used to characterize the properties of single crystalline CaFe2-xNixAs2 as a function of Ni doping for x varying from 0 to 0.1. The combined first-order structural and magnetic phase transitions occur together in the undoped system at 172 K, with a small decrease in the area of the a-b plane along with an abrupt increase in the length of the c-axis in the orthorhombic phase. With increasing x the ordered moment and transition temperature decrease, but the transition remains sharp at modest doping while the area of the a-b plane quickly decreases and then saturates. Warming and cooling data in the resistivity and neutron diffraction indicate hysteresis of ~2 K. At larger doping the transition is more rounded, and decreases to zero for x=0.06. The susceptibility is anisotropic for all values of x. Electrical resistivity for x = 0.053 and 0.06 shows a superconducting transition with an onset of nearly 15 K which is further corroborated by substantial diamagnetic susceptibility. For the fully superconducting sample there is no long range magnetic order and the structure remains tetragonal at all temperature, but there is an anomalous increase in the area of the a-b plane in going to low T. Heat capacity data show that the density of states at the Fermi level increases for x > 0.053 as inferred from the value of Sommerfeld coefficient. The regime of superconductivity is quite restrictive, with a maximum TC of 15 K and an upper critical field Hc2=14 T. Superconductivity disappears in the overdoped region.Comment: 14 pages, 12 figures. Submitted to Phys. Rev.