Search results for "Matrix"
showing 10 items of 3205 documents
Economic Sector Identification in a Set of Stocks Traded at the New York Stock Exchange: A Comparative Analysis
2006
We review some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a set of stocks traded at the New York Stock Exchange. The investigated time series are recorded at a daily time horizon. All the considered methods are able to detect economic information and the presence of clusters characterized by the economic sector of stocks. However, different methodologies provide different information about the considered set. Our comparative analysis suggests that th…
Emergence of time-horizon invariant correlation structure in financial returns by subtraction of the market mode
2007
We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. Result crucially depends on whether the data is restricted to the ``internal'' dynamics of the market, where the ``center of mass'' motion (the market mode) is removed or not. If the market mode is not removed, we find that the structure emerges, as the time-horizon increases, from splitting a single large cluster. In NYSE we find that when the market mode is removed, the structure of correlation at t…
Shrinkage and spectral filtering of correlation matrices: A comparison via the Kullback-Leibler distance
2007
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a multivariate Gaussian distribution. Here we use the Kullback-Leibler distance to investigate the performance of filtering methods based on Random Matrix Theory and on the shrinkage technique. We also present some results on the application of the Kullback-Leibler distance to multivariate data which are non Gaussian distributed.
On the equivalence between the Scheduled Relaxation Jacobi method and Richardson's non-stationary method
2017
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations ($Au=b$) associated with elliptic problems. It inherits its robustness and accelerates its convergence rate computing a set of $P$ relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of $M$ consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method. …
Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
2017
This article reports world averages of measurements of $b$-hadron, $c$-hadron, and $\tau$-lepton properties obtained by the Heavy Flavor Averaging Group using results available through summer 2016. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, \CP~violation parameters, parameters of semileptonic decays and CKM matrix elements.
Measurement of matter-antimatter differences in beauty baryon decays
2017
Differences in the behaviour of matter and antimatter have been observed in $K$ and $B$ meson decays, but not yet in any baryon decay. Such differences are associated with the non-invariance of fundamental interactions under the combined charge-conjugation and parity transformations, known as $C\!P$ violation. Using data from the LHCb experiment at the Large Hadron Collider, a search is made for $C\!P$-violating asymmetries in the decay angle distributions of $\Lambda^0_b$ baryons decaying to $p\pi^-\pi^+\pi^-$ and $p\pi^-K^+K^-$ final states. These four-body hadronic decays are a promising place to search for sources of $C\!P$ violation both within and beyond the Standard Model of particle…
Transition-Dipole Moments for Electronic Excitations in Strong Magnetic Fields Using Equation-of-Motion and Linear Response Coupled-Cluster Theory
2019
An implementation of transition-dipole moments at the equation-of-motion coupled-cluster singles-doubles (EOM-CCSD) and CCSD linear response (LR) levels of theory for the treatment of atoms and molecules in strong magnetic fields is presented. The presence of a finite magnetic field leads, in general, to a complex wave function and a gauge-origin dependence, necessitating a complex computer code together with the use of gauge-including atomic orbitals. As in the field-free case, for EOM-CC, the evaluation of transition-dipole moments consists of setting up the one-electron transition-density matrix (TDM) which is then contracted with dipole-moment integrals. In the case of CC-LR, the evalua…
Extension of the Launay Quantum Reactive Scattering Code and Direct Computation of Time Delays.
2019
Scattering computations, particularly within the realm of molecular physics, have seen an increase in study since the development of powerful quantum methods. These dynamical processes can be analyzed via (among other quantities) the duration of the collision process and the lifetime of the intermediate complex. We use the Smith matrix Q = -iℏS†dS/dE calculated from the scattering matrix S and its derivative with respect to the total energy. Its real part contains the state-to-state time delays, and its eigenvalues give the lifetimes of the metastable states [ Smith Phys. Rev. 1960 , 118 , 349 - 356 ]. We propose an extension of the Launay HYP3D code [ Launay and Le Dourneuf Chem. Phys. Let…
Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory
2019
We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from st…
A Wigner molecule at extremely low densities: a numerically exact study
2019
In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state an…