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J. Segura

Publications and source records attributed to J. Segura.

At least 37 records · Page 2Linked to original sources
arXiv2016

Computation of the incomplete gamma function for negative values of the argument

An algorithm for computing the incomplete gamma function $γ^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincaré-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $\sim 10^{-13}$ in the parameter region $(a,z) \in [-500,\,500] \times [-500,\,0)$ can be obtained when computing the function $γ^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.

cs.MS↗
arXiv2016

A new type of sharp bounds for ratios of modified Bessel functions

The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.

math.CA↗
arXiv2016

Efficient algorithms for the inversion of the cumulative central beta distribution

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

math.NA↗
arXiv2015

Computing the Kummer function U(a,b,z) for small values of the arguments

We describe methods for computing the Kummer function $U(a,b,z)$ for small values of $z$, with special attention to small values of $b$. For these values of $b$ the connection formula that represents $U(a,b,z)$ as a linear combination of two ${}_1F_1$-functions needs a limiting procedure. We use the power series of the ${}_1F_1$-functions and consider the terms for which this limiting procedure is needed. We give recursion relations for higher terms in the expansion, and we consider the derivative $U^\prime(a,b,z)$ as well. We also discuss the performance for small $\vert z\vert$ of an asymptotic approximation of the Kummer function in terms of modified Bessel functions.

math.CA↗
arXiv2015

GammaCHI: a package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)

A Fortran 90 module (GammaCHI) for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package are the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, cdfgamNC, invcdfgamNC, errorfunction, inverfc, gamma, loggam, gamstar and quotgamm for the computation of the central gamma distribution function (and its complementary function), the inversion of the central gamma distribution function, the computation of the noncentral gamma distribution function (and its complementary function), the inversion of the noncentral gamma distribution function, the computation of the error function and its complementary function, the inversion of the complementary error function, the computation of: the gamma function, the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions, respectively.

cs.MS↗
arXiv2014

Monotonicity properties and bounds for the chi-square and gamma distributions

The generalized Marcum functions $Q_μ(x,y)$ and $P_μ(x,y)$ have as particular cases the non-central $χ^2$ and gamma cumulative distributions, which become central distributions (incomplete gamma function ratios) when the non-centrality parameter $x$ is set to zero. We analyze monotonicity and convexity properties for the generalized Marcum functions and for ratios of Marcum functions of consecutive parameters (differing in one unity) and we obtain upper and lower bounds for the Marcum functions. These bounds are proven to be sharper than previous estimations for a wide range of the parameters. Additionally we show how to build convergent sequences of upper and lower bounds. The particularization to incomplete gamma functions, together with some additional bounds obtained for this particular case, lead to combined bounds which improve previously exiting inequalities.

math.CA↗
arXiv2014

The asymptotic and numerical inversion of the Marcum $Q-$function

The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper we describe a new asymptotic method for inverting the generalized Marcum $Q-$function and for the complementary Marcum $P-$function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations.

math.CA↗
arXiv2014

Computation of a numerically satisfactory pair of solutions of the differential equation for conical functions of non-negative integer orders

We consider the problem of computing satisfactory pairs of solutions of the differential equation for Legendre functions of non-negative integer order $μ$ and degree $-\frac12+iτ$, where $τ$ is a non-negative real parameter. Solutions of this equation are the conical functions ${\rm{P}}^μ_{-\frac12+iτ}(x)$ and ${Q}^μ_{-\frac12+iτ}(x)$, $x>-1$. An algorithm for computing a numerically satisfactory pair of solutions is already available when $-1 1$, the function $\Re\left\{e^{-iπμ} {Q}^μ_{-\frac{1}{2}+iτ}(x) \right\}$. The proposed algorithm allows the computation of the function on a large parameter domain without requiring the use of extended precision arithmetic.

math.CA↗
arXiv2014

Recent software developments for special functions in the Santander-Amsterdam project

We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central chi-square cumulative distributions (also called Marcum Q-functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth-order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions.

math.CA↗
arXiv2013

Computation of the Marcum Q-function

Methods and an algorithm for computing the generalized Marcum $Q-$function ($Q_μ(x,y)$) and the complementary function ($P_μ(x,y)$) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to $10^{-12}$ can be obtained in the parameter region $(x,y,μ) \in [0,\,A]\times [0,\,A]\times [1,\,A]$, $A=200$, while for larger parameters the accuracy decreases (close to $10^{-11}$ for $A=1000$ and close to $5\times 10^{-11}$ for $A=10000$).

cs.MS↗
arXiv2007

Smart Temperature Sensor for Thermal Testing of Cell-Based ICs

In this paper we present a simple and efficient built-in temperature sensor for thermal monitoring of standard-cell based VLSI circuits. The proposed smart temperature sensor uses a ring-oscillator composed of complex gates instead of inverters to optimize their linearity. Simulation results from a 0.18$μ$m CMOS technology show that the non-linearity error of the sensor can be reduced when an adequate set of standard logic gates is selected.

cs.AR↗
arXiv2007

A Fast Concurrent Power-Thermal Model for Sub-100nm Digital ICs

As technology scales down, the static power is expected to become a significant fraction of the total power. The exponential dependence of static power with the operating temperature makes the thermal profile estimation of high-performance ICs a key issue to compute the total power dissipated in next-generations. In this paper we present accurate and compact analytical models to estimate the static power dissipation and the temperature of operation of CMOS gates. The models are the fundamentals of a performance estimation tool in which numerical procedures are avoided for any computation to set a faster estimation and optimization. The models developed are compared to measurements and SPICE simulations for a 0.12mm technology showing excellent results.

cs.AR↗
arXiv1999

A potential test of the CP properties and Majorana nature of neutrinos

The scattering of solar neutrinos on electrons may reveal their CP properties, which are particularly sensitive to their Majorana nature. The cross section is sensitive to the neutrino dipole moments through an interference of electro-magnetic and weak amplitudes. We show how future solar neutrino experiments with good angular resolution and low energy threshold, such as Hellaz, can be sensitive to the resulting azimuthal asymmetries in event number, and could therefore provide valuable information on the CP properties and the nature of the neutrinos, provided the solar magnetic field direction is fixed.

hep-ph↗
arXiv1999

Probing Neutrino Magnetic Moments at Underground Detectors with Artificial Neutrino Sources

Neutrino-electron scattering can be used to probe neutrino electromagnetic properties at low-threshold underground detectors with good angular and recoil electron energy resolution. We propose to do this using a number of artificial neutrino and anti-neutrino sources such as $^{51}Cr_{24}$ and $^{90}Sr-Y$. The neutrino flux is known to within one percent, in contrast to the reactor case and one can reach lower neutrino energies. For the $^{90}Sr-Y$ source we estimate that the signal expected for a neutrino magnetic moment of $μ_ν=6 \times 10^{-11}μ_{B}$ will be comparable to that expected in the SM and corresponds to a 30% enhancement in the total number of expected events.

hep-ph↗
arXiv1998

Neutrino magnetic moments and low-energy solar neutrino-electron scattering experiments

The scattering of solar neutrinos on electrons is sensitive to the neutrino magnetic moments through an interference of electromagnetic and weak amplitudes in the cross section. We show that future low-energy solar neutrino experiments with good angular resolution can be sensitive to the resulting azimuthal asymmetries in event number and should provide useful information on non-standard neutrino properties such as magnetic moments. We compare asymmetries expected at HELLAZ (mainly pp neutrinos) with those at the Kamiokande and Super-Kamiokande experiments (Boron neutrinos), both for the case of Dirac and Majorana neutrinos and discuss the advantages of low energies. Potentially interesting information on the solar magnetic fields may be accessible.

hep-ph↗
arXiv1997

Neutrino Oscillation and Magnetic Moment from $ν- e^{-}$ Elastic Scattering

We discuss how the measurement of the $\barν_{e}-e^{-}$ elastic cross section at reactor energies can be used to extract new information on the neutrino oscillation parameters. We also consider the magnetic moment contribution and show how both effects tend to cancel each other when the total cross section is measured; to achieve the separation of each of the effects, experiments capable of measuring angular and energy distributions with respect to the outgoing electron become necessary. We study how their different energy and angle dependence enables such a separation; then, the sensitivity to magnetic moments, masses and mixings is discussed. We also show how these experiments can be sensitive to the magnetic moment of $τ$ neutrinos via $\barν_{e}\leftrightarrow \barν_μ$ oscillation.

hep-ph↗
arXiv1994

Neutrino Mass and Magnetic Moment from Neutrino-Electron Scattering

We study both the elastic ($νe \rightarrow νe$) and the radiative process ($νe \rightarrow νe γ$) and discuss how these processes can shed light on some current topics in neutrino physics such as a neutrino magnetic moment and neutrino oscillations. The radiative process allows to reach low values of $Q^2$ without the need to operate at very small energies of recoil electrons, a favourable scenario to search for a neutrino magnetic moment. The elastic cross section contains a dynamical zero at $E_ν=m/(4 sin^2θ_{W})$ and forward electrons for the electron antineutrino channel, which is reachable at reactor facilities and accessible after the convolution with the antineutrino spectrum. The implication for lepton flavour changing transitions in that energy region searched for in neutrino oscillation experiments, which combine disappearance and appearance rates, is discussed.

hep-ph↗