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

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

Variety and the evolution of refinery processing

Evolutionary theories of economic development stress the role of variety as both a determinant and a result of growth. In this paper we develop a measure of variety, based on Weitzman's maximum likelihood procedure. This measure is based on the distance between products, and indicates the degree of differentiation of a product population. We propose a generic method, which permits to regroup the products with very similar characteristics values before choosing randomly the product models to be used to calculate Weitzman's measure. We apply the variety measure to process characteristics of oil refining. The results obtained for this technology show classic evolutionary specialization patterns that can be understood on the basis of niche theory. Here the changes in variety are related to changes in the range of the services the technology considered can deliver, range which plays a role similar to that of the size of the habitat of a biological species.TECHNOLOGICAL EVOLUTION; REFINERY PROCESSES; NICHE THEORY; WEITZMAN MEASURE

‘Habituated to Drunkenness’: Opinions of New Orleanians about Prohibition as Revealed through Letters to the Editor of The Times-Picayune, 1918-1922

Both popular and scholarly observers have portrayed New Orleans as a city both supported and burdened by its image as a diverse cultural other within the American South, historically tolerant of certain sins of the flesh. This image has been used by proponents and critics alike in order to push their respective agenda regarding the Crescent City. This thesis will not seek to discredit this image that is based largely on fact. However, using Prohibition as a case study, this thesis will use letters to the editor to uncover attitudes of New Orleanians in opposition to this reputation to reveal alternative and historically silenced voices of New Orleans, since for instance people of a certain age, gender, or ethnicity were silenced in the halls of government. This paper will reveal the opinions of New Orleanians regarding Prohibition and what these opinions can tell us about New Orleans’s image

The "exterior approach" applied to the inverse obstacle problem for the heat equation

International audienceIn this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple level set method is used to characterize the obstacle. We present several mixed formulations of quasi-reversibility that enable us to use some classical conforming finite elements. Among these, an iterated formulation that takes the noisy Cauchy data into account in a weak way is selected to serve in some numerical experiments and show the feasibility of our strategy of identification. 1. Introduction. This paper deals with the inverse obstacle problem for the heat equation, which can be described as follows. We consider a bounded domain D ⊂ R d , d ≥ 2, which contains an inclusion O. The temperature in the complementary domain Ω = D \ O satisfies the heat equation while the inclusion is characterized by a zero temperature. The inverse problem consists, from the knowledge of the lateral Cauchy data (that is both the temperature and the heat flux) on a subpart of the boundary ∂D during a certain interval of time (0, T) such that the temperature at time t = 0 is 0 in Ω, to identify the inclusion O. Such kind of inverse problem arises in thermal imaging, as briefly described in the introduction of [9]. The first attempts to solve such kind of problem numerically go back to the late 80's, as illustrated by [1], in which a least square method based on a shape derivative technique is used and numerical applications in 2D are presented. A shape derivative technique is also used in [11] in a 2D case as well, but the least square method is replaced by a Newton type method. Lastly, the shape derivative together with the least square method have recently been used in 3D cases [18]. The main feature of all these contributions is that they rely on the computation of forward problems in the domain Ω × (0, T): this computation obliges the authors to know one of the two lateral Cauchy data (either the temperature or the heat flux) on the whole boundary ∂D of D. In [20], the authors introduce the so-called " enclosure method " , which enables them to recover an approximation of the convex hull of the inclusion without computing any forward problem. Note however that the lateral Cauchy data has to be known on the whole boundary ∂D. The present paper concerns the " exterior approach " , which is an alternative method to solve the inverse obstacle problem. Like in [20], it does not need to compute the solution of the forward problem and in addition, it is applicable even if the lateral Cauchy data are known only on a subpart of ∂D, while no data are given on the complementary part. The " exterior approach " consists in defining a sequence of domains that converges in a certain sense to the inclusion we are looking for. More precisely, the nth step consists, 1. for a given inclusion O n , in approximating the temperature in Ω n × (0, T) (Ω n := D \ O n) with the help of a quasi-reversibility method, 2. for a given temperature in Ω n × (0, T), in computing an updated inclusion O n+1 with the help of a level set method. Such " exterior approach " has already been successfully used to solve inverse obstacle problems for the Laplace equation [5, 4, 15] and for the Stokes system [6]. It has also been used for the heat equation in the 1D case [2]: the problem in this simple case might be considered as a toy problem since the inclusion reduces to a point in some bounded interval. The objective of the present paper is to extend the " exterior approach " for the heat equation to any dimension of space, with numerical applications in the 2D case. Let us shed some light on the two steps o

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed