The Omega Counter, a Frequency Counter Based on the Linear Regression

This article introduces the {\Omega} counter, a frequency counter -- or a frequency-to-digital converter, in a different jargon -- based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the {\Omega} counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a SoC, under test in our laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and {\Lambda} counters. The LR exhibits optimum rejection of white phase noise, superior to that of the {\Pi} and {\Lambda} counters. White noise is the major practical problem of wideband digital electronics, both in the instrument internal circuits and in the fast processes which we may want to measure. The {\Omega} counter finds a natural application in the measurement of the Parabolic Variance, described in the companion article arXiv:1506.00687 [physics.data-an].Comment: 8 pages, 6 figure, 2 table

The Parabolic variance (PVAR), a wavelet variance based on least-square fit

This article introduces the Parabolic Variance (PVAR), a wavelet variance similar to the Allan variance, based on the Linear Regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the $\Omega$ frequency counter, which implements the LR estimate. The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term analysis because the wavelet spans over $2 \tau$, the same of the AVAR wavelet; and good for short-term analysis because the response to white and flicker PM is $1/\tau^3$ and $1/\tau^2$, same as the MVAR. After setting the theoretical framework, we study the degrees of freedom and the confidence interval for the most common noise types. Then, we focus on the detection of a weak noise process at the transition - or corner - where a faster process rolls off. This new perspective raises the question of which variance detects the weak process with the shortest data record. Our simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in all cases, exhibits the best ability to divide between fast noise phenomena (up to flicker FM), and is almost as good as AVAR for the detection of random walk and drift

Lessons From the Field: Community Anti-Drug Coalitions as Catalysts for Change

Analyzes the organization, operation, sustainability, and impact of community anti-drug coalitions. Examines characteristics shared among eight coalitions, including leadership, outcomes, planning, institutionalization, and funding diversification

Epidemic Wave Dynamics Attributable to Urban Community Structure: A Theoretical Characterization of Disease Transmission in a Large Network.

BACKGROUND: Multiple waves of transmission during infectious disease epidemics represent a major public health challenge, but the ecological and behavioral drivers of epidemic resurgence are poorly understood. In theory, community structure—aggregation into highly intraconnected and loosely interconnected social groups—within human populations may lead to punctuated outbreaks as diseases progress from one community to the next. However, this explanation has been largely overlooked in favor of temporal shifts in environmental conditions and human behavior and because of the difficulties associated with estimating large-scale contact patterns. OBJECTIVE: The aim was to characterize naturally arising patterns of human contact that are capable of producing simulated epidemics with multiple wave structures. METHODS: We used an extensive dataset of proximal physical contacts between users of a public Wi-Fi Internet system to evaluate the epidemiological implications of an empirical urban contact network. We characterized the modularity (community structure) of the network and then estimated epidemic dynamics under a percolation-based model of infectious disease spread on the network. We classified simulated epidemics as multiwave using a novel metric and we identified network structures that were critical to the network's ability to produce multiwave epidemics. RESULTS: We identified robust community structure in a large, empirical urban contact network from which multiwave epidemics may emerge naturally. This pattern was fueled by a special kind of insularity in which locally popular individuals were not the ones forging contacts with more distant social groups. CONCLUSIONS: Our results suggest that ordinary contact patterns can produce multiwave epidemics at the scale of a single urban area without the temporal shifts that are usually assumed to be responsible. Understanding the role of community structure in epidemic dynamics allows officials to anticipate epidemic resurgence without having to forecast future changes in hosts, pathogens, or the environment

Modeling, Filtering and Optimization for AFM Arrays

We will present new tools and results developed for Arrays of Microsystems and especially for AFM array design.For modeling,we developed a two-scale model of cantilever arrays in elastodynamics.A robust optimization toolbox is interfaced to aid for design before fabrication.Two real-time computation methods for filtering and control of the coupled cantilevers are studied.One is based on functions of operators and the Cauchy integral formula.It may be realized with PNR.The second one relies to diffusive realization to be implemented in a FPGA.Displacement measurement is done by interferometry