901 research outputs found
Explicitly Invertible Approximations of the Gaussian Q-Function: A Survey
Communications and information theory use the Gaussian -function, a positive and decreasing function, across the literature. Its approximations were created to simplify mathematical study of the Gaussian -function expressions. This is important since the -function cannot be represented in closed-form terms of elementary functions. In a noise model with the Gaussian distribution function and various digital modulation schemes, closed-form approximations of the Gaussian -function are used to predict a digital communications system's symbol error probability (SEP) or bit error probability (BEP). Another significant scenario pertains to fading channels, whereby it is important to accurately determine, through a closed-form expression, the precise evaluations of complex integrals involved in the computations of SEP or BEP. In addition to the aforementioned scenarios, it is imperative for a communications system designer to ascertain the requisite operational signal-to-noise ratio for the specific application, based on the target SEP (or BEP). In this scenario, the crucial role of the explicit invertibility of the Gaussian -function approximation is of significant importance in achieving this objective. In this paper we propose a survey of the approximations of the Gaussian -function found in the literature, reviewing also the approximations originally given for the 4 classical special functions related to it, restricting the analysis to the explicitly invertible ones, and classifying them on the basis of their accuracy (on the significant range), simplicity, and easiness of inversion, also distinguishing the bounds from approximations. We also list the inverses of some of them, already published or newly found in this research
A new accurate approximation of the Gaussian Q-function with relative error less than 1 thousandth in a significant domain
The approximations of the Gaussian Q-function found in the literature have been often developed with the goal of obtaining high estimation accuracies in deriving the error probability for digital modulation schemes. Unfortunately, the obtained mathematical expressions are often too complex, even difficultly tractable. A new approximation for the Gaussian Q-function is presented in the form of the standard normal density multiplied by a rational function. The rational function is simply a linear combination of the first 5 integer negative powers of the same term, linear in x, using only 4 decimal constants. In this paper we make some considerations about the significant interval where to consider the Q-function in telecommunication theory. The relative error in absolute value of the given approximation is less than 0.06% in the considered significant interval
Performance Study of a Class of Irregular Near Capacity Achieving LDPC Codes
This paper investigates the performance of a class of irregular low-density parity-check (LDPC) codes through a recently published low complexity upper bound on their beliefpropagation decoding thresholds. Moreover, their performance analysis is carried out through a recently published algorithmic method, presented in Babich et al. 2017 paper. In particular, the class considered is characterized by variable node degree distributions λ(x) of minimum degree i1 > 2: being, in this case, λ0(0) = λ2 = 0, this is useful to design LDPC codes presenting a linear minimum distance growth with the block length with probability 1, as shown in Di et al.'s 2006 paper. These codes unfortunately cannot reach capacity under iterative decoding, since the achievement of capacity requires λ2 ≠ 0. However, in this latter case, the block error probability might converge to a constant, as shown in the aforementioned paper
Understanding the evolution of native pinewoods in Scotland will benefit their future management and conservation
Scots pine (Pinus sylvestris L.) is a foundation species in Scottish highland forests and a national icon. Due to heavy exploitation, the current native pinewood coverage represents a small fraction of the postglacial maximum. To reverse this decline, various schemes have been initiated to promote planting of new and expansion of old pinewoods. This includes the designation of seed zones for control of the remaining genetic resources. The zoning was based mainly on biochemical similarity among pinewoods but, by definition, neutral molecular markers do not reflect local phenotypic adaptation. Environmental variation within Scotland is substantial and it is not yet clear to what extent this has shaped patterns of adaptive differentiation among Scottish populations. Systematic, rangewide common-environment trials can provide insights into the evolution of the native pinewoods, indicating how environment has influenced phenotypic variation and how variation is maintained. Careful design of such experiments can also provide data on the history and connectivity among populations, by molecular marker analysis. Together, phenotypic and molecular datasets from such trials can provide a robust basis for refining seed transfer guidelines for Scots pine in Scotland and should form the scientific basis for conservation action on this nationally important habitat
The critical dimension for a 4th order problem with singular nonlinearity
We study the regularity of the extremal solution of the semilinear biharmonic
equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple
Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under
Dirichlet boundary conditions on . We complete
here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the
identification of a "pull-in voltage" \la^*>0 such that a stable classical
solution u_\la with 0 exists for \la\in (0,\la^*), while there is
none of any kind when \la>\la^*. Our main result asserts that the extremal
solution is regular provided while is singular () for , in which case
on the unit ball, where
and .Comment: 19 pages. This paper completes and replaces a paper (with a similar
title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this
author's papers can be downloaded at this http://www.birs.ca/~nassif
MLP: a MATLAB toolbox for rapid and reliable auditory threshold estimation
In this paper, we present MLP, a MATLAB toolbox enabling auditory
thresholds estimation via the adaptive Maximum Likelihood procedure proposed
by David Green (1990, 1993). This adaptive procedure is particularly appealing for
those psychologists that need to estimate thresholds with a good degree of accuracy
and in a short time. Together with a description of the toolbox, the current text
provides an introduction to the threshold estimation theory and a theoretical
explanation of the maximum likelihood adaptive procedure. MLP comes with a
graphical interface and it is provided with several built-in, classic psychoacoustics
experiments ready to use at a mouse click
Results of the IGEC-2 search for gravitational wave bursts during 2005
The network of resonant bar detectors of gravitational waves resumed
coordinated observations within the International Gravitational Event
Collaboration (IGEC-2). Four detectors are taking part in this collaboration:
ALLEGRO, AURIGA, EXPLORER and NAUTILUS. We present here the results of the
search for gravitational wave bursts over 6 months during 2005, when IGEC-2 was
the only gravitational wave observatory in operation. The network data analysis
implemented is based on a time coincidence search among AURIGA, EXPLORER and
NAUTILUS, keeping the data from ALLEGRO for follow-up studies. With respect to
the previous IGEC 1997-2000 observations, the amplitude sensitivity of the
detectors to bursts improved by a factor about 3 and the sensitivity bandwidths
are wider, so that the data analysis was tuned considering a larger class of
detectable waveforms. Thanks to the higher duty cycles of the single detectors,
we decided to focus the analysis on three-fold observation, so to ensure the
identification of any single candidate of gravitational waves (gw) with high
statistical confidence. The achieved false detection rate is as low as 1 per
century. No candidates were found.Comment: 10 pages, to be submitted to Phys. Rev.
Genetic Determinants of Variability in Glycated Hemoglobin (HbA1c) in Humans: Review of Recent Progress and Prospects for Use in Diabetes Care
Glycated hemoglobin A1c (HbA1c) indicates the percentage of total hemoglobin that is bound by glucose, produced from the nonenzymatic chemical modification by glucose of hemoglobin molecules carried in erythrocytes. HbA1c represents a surrogate marker of average blood glucose concentration over the previous 8 to 12 weeks, or the average lifespan of the erythrocyte, and thus represents a more stable indicator of glycemic status compared with fasting glucose. HbA1c levels are genetically determined, with heritability of 47% to 59%. Over the past few years, inroads into understanding genetic predisposition by glycemic and nonglycemic factors have been achieved through genome-wide analyses. Here I review current research aimed at discovering genetic determinants of HbA1c levels, discussing insights into biologic factors influencing variability in the general and diabetic population, and across different ethnicities. Furthermore, I discuss briefly the relevance of findings for diabetes monitoring and diagnosis
- …