Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multi-antenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas—and thus the number of rates to be controlled—increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise, the ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate -through this specific derivation— the relevance of some established random CDMA results to the single-user multi-antenna problem.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Evans functions for integral neural field equations with Heaviside firing rate function

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction and stability analysis of front solutions to a scalar neural field model and a limiting case is shown to recover recent results of L. Zhang [On stability of traveling wave solutions in synaptically coupled neuronal networks, Differential and Integral Equations, 16, (2003), pp.513-536.]. Traveling fronts and pulses are considered in more general models possessing either a linear or piecewise constant recovery variable. We establish the stability of coexisting traveling fronts beyond a front bifurcation and consider parameter regimes that support two stable traveling fronts of different speed. Such fronts may be connected and depending on their relative speed the resulting region of activity can widen or contract. The conditions for the contracting case to lead to a pulse solution are established. The stability of pulses is obtained for a variety of examples, in each case confirming a previously conjectured stability result. Finally we show how this theory may be used to describe the dynamic instability of a standing pulse that arises in a model with slow recovery. Numerical simulations show that such an instability can lead to the shedding of a pair of traveling pulses.

Association between mean residual life (MRL) and failure rate functions for continuous and discrete lifetime distributions

The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

n-fold Weibull multiplicative model

In this paper we study the n-fold multiplicative model involving Weibull distributions and examine some properties of the model. These include the shapes for the density and failure rate functions and the WPP plot. These allow one to decide if a given data set can be adequately modelled by the model. We also discuss the estimation of model parameters based on the WPP plot. (C) 2001 Elsevier Science Ltd. All rights reserved.

Development and survival of the diamondback moth (Lepidoptera : Plutellidae) at constant and alternating temperatures

Survival and development time from egg to adult emergence of the diamondback moth, Plutella xylostella (L.), were determined at 19 constant and 14 alternating temperature regimes from 4 to 40degreesC. Plutella xylostella developed successfully front egg to adult emergence at constant temperatures from 8 to 32degreesC. At temperatures from 4 to 6degreesC or from 34 to 40degreesC, partial or complete development of individual stages or instars was possible, with third and fourth instars having the widest temperature limits. The insect developed successfully from egg to adult emergence under alternating regimes including temperatures as low as 4degreesC or as high as 38degreesC. The degree-day model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at both constant and alternating temperatures. The degree-day model described the relationships well from 10 to 30degreesC. The logistic equation and the Wang model fit the data well at temperatures 32degreesC. Under alternating regimes, all three models gave good simulations of development in the mid-temperature range, but only the logistic equation gave close simulations in the low temperature range, and none gave close or consistent simulations in the high temperature range. The distribution of development time was described satisfactorily by a Weibull function. These rate and time distribution functions provide tools for simulating population development of P. xylostella over a wide range of temperature conditions.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

Pattern of recurrence of early breast cancer is different according to intrinsic subtype and proliferation index.

INTRODUCTION Recurrence risk in breast cancer varies throughout the follow-up time. We examined if these changes are related to the level of expression of the proliferation pathway and intrinsic subtypes. METHODS Expression of estrogen and progesterone receptor, Ki-67, human epidermal growth factor receptor 2 (HER2), epidermal growth factor receptor (EGFR) and cytokeratin 5/6 (CK 5/6) was performed on tissue-microarrays constructed from a large and uniformly managed series of early breast cancer patients (N = 1,249). Subtype definitions by four biomarkers were as follows: luminal A (ER + and/or PR+, HER2-, Ki-67 <14), luminal B (ER + and/or PR+, HER2-, Ki-67 ≥14), HER2-enriched (any ER, any PR, HER2+, any Ki-67), triple-negative (ER-, PR-, HER2-, any Ki-67). Subtype definitions by six biomarkers were as follows: luminal A (ER + and/or PR+, HER2-, Ki-67 <14, any CK 5/6, any EGFR), luminal B (ER + and/or PR+, HER2-, Ki-67 ≥14, any CK 5/6, any EGFR), HER2-enriched (ER-, PR-, HER2+, any Ki-67, any CK 5/6, any EGFR), Luminal-HER2 (ER + and/or PR+, HER2+, any Ki-67, any CK 5/6, any EGFR), Basal-like (ER-, PR-, HER2-, any Ki-67, CK5/6+ and/or EGFR+), triple-negative nonbasal (ER-, PR-, HER2-, any Ki-67, CK 5/6-, EGFR-). Each four- or six-marker defined intrinsic subtype was divided in two groups, with Ki-67 <14% or with Ki-67 ≥14%. Recurrence hazard rate function was determined for each intrinsic subtype as a whole and according to Ki-67 value. RESULTS Luminal A displayed a slow risk increase, reaching its maximum after three years and then remained steady. Luminal B presented most of its relapses during the first five years. HER2-enriched tumors show a peak of recurrence nearly twenty months post-surgery, with a greater risk in Ki-67 ≥14%. However a second peak occurred at 72 months but the risk magnitude was greater in Ki-67 <14%. Triple negative tumors with low proliferation rate display a smooth risk curve, but with Ki-67 ≥14% show sharp peak at nearly 18 months. CONCLUSIONS Each intrinsic subtype has a particular pattern of relapses over time which change depending on the level of activation of the proliferation pathway assessed by Ki-67. These findings could have clinical implications both on adjuvant treatment trial design and on the recommendations concerning the surveillance of patients.

On moments and tail behaviors of storage processes

We study the existence of moments and the tail behaviour of the densitiesof storage processes. We give sufficient conditions for existence andnon-existence of moments using the integrability conditions ofsubmultiplicative functions with respect to Lévy measures. Then, we studythe asymptotical behavior of the tails of these processes using the concaveor convex envelope of the release rate function.