Search results for "Haar"
showing 10 items of 44 documents
The probability that $x$ and $y$ commute in a compact group
2010
We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…
The probability that $x^m$ and $y^n$ commute in a compact group
2013
In a recent article [K.H. Hofmann and F.G. Russo, The probability that $x$ and $y$ commute in a compact group, Math. Proc. Cambridge Phil. Soc., to appear] we calculated for a compact group $G$ the probability $d(G)$ that two randomly picked elements $x, y\in G$ satisfy $xy=yx$, and we discussed the remarkable consequences on the structure of $G$ which follow from the assumption that $d(G)$ is positive. In this note we consider two natural numbers $m$ and $n$ and the probabilty $d_{m,n}(G)$ that for two randomly selected elements $x, y\in G$ the relation $x^my^n=y^nx^m$ holds. The situation is more complicated whenever $n,m>1$. If $G$ is a compact Lie group and if its identity component $G_…
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis
2008
In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces.
From Rome to Constantinople. Studies in honour of Averil Cameron. By Hagit Amirav and Bas Ter Haar Romeny. (Late Antique History and Religion.) Pp. x…
2010
A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series
2020
We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for…
Recent acquired STD and the use of HAART in the Italian Cohort of Naive for Antiretrovirals (I.Co.N.A): analysis of the incidence of newly acquired h…
2008
Objective: To estimate the incidence of newly acquired syphilis (n-syphilis) and hepatitis B infection (n-hepatitis B) in I.Co.N.A. and to evaluate the impact of HAART, calendar date and risk group. Methods: Cohort study: Incidence was calculated by person-years analyses. Poisson regression was used for the multivariate model. Results: The rate of n-syphilis was 23.4/1,000 PYFU and it increased over time; HIV transmission risk was the most important predictor: men who have sex with men (MSM) had a considerable higher risk (RR 5.92, 95% CI 2.95-12.13 vs IDU/exIDU, p < 0.0001). The rate of n-hepatitis B was 12.2/1,000 PYFU; it declined in recent years and halved per 10 years age. Patients wit…
Firmas zīmju atpazīšana un marķēšana attēlos un to tālāks pielietojums
2016
Maģistra darbs apraksta objektu atpazīšanas iespējas izmantojot video un attēlus. Darba ietvaros pirmajā nodaļā tika apskatītas pielietotās tehnoloģijas un populāri uzdevumi, kurus ar šīm tehnoloģijām iespējams risināt, kā arī attīstībā novērojamās tendences. Darba otrajā nodaļā apskatīti populāri jau esoši risinājumi ar kuru palīdzību no attēliem vai video jau tiek izgūta informācija, šie uzdevumi tie jau sen tiek pielietoti praksē. Aprakstīts to lietojuma princips un nepieciešamība. Darba trešajā nodaļā apskatīti dažādi interesanti sarežģītāki uzdevumi, kuros ir iespējams pielietot iepriekš apskatīto objektu atpazīšanas tehnoloģiju. Starp šiem uzdevumiem ir gan tādi, kuri jau tiek lietoti…
Entanglement dynamics and relaxation in a few-qubit system interacting with random collisions
2008
The dynamics of a single qubit interacting by a sequence of pairwise collisions with an environment consisting of just two more qubits is analyzed. Each collision is modeled in terms of a random unitary operator with a uniform probability distribution described by the uniform Haar measure. We show that the purity of the system qubit as well as the bipartite and the tripartite entanglement reach time averaged equilibrium values characterized by large instantaneous fluctuations.These equilibrium values are independent of the order of collision among the qubits. The relaxation to equilibrium is analyzed also in terms of an ensemble average of random collision histories. Such average allows for…
Object Recognition and Modeling Using SIFT Features
2013
In this paper we present a technique for object recognition and modelling based on local image features matching. Given a complete set of views of an object the goal of our technique is the recognition of the same object in an image of a cluttered environment containing the object and an estimate of its pose. The method is based on visual modeling of objects from a multi-view representation of the object to recognize. The first step consists of creating object model, selecting a subset of the available views using SIFT descriptors to evaluate image similarity and relevance. The selected views are then assumed as the model of the object and we show that they can effectively be used to visual…
Long Time Behaviour on a Path Group of the Heat Semi-group Associated to a Bilaplacian
2011
We show that in long-time the heat semi-group on a path group associated to a Bilaplacian on the group tends to the Haar distribution on a path group.