title: Repetitive Transcranial Magnetic Stimulation: A Call for Better Data

authors: Wilson, Marcus T.

subjects: Science & Technology

abstract: Repetitive Transcranial Magnetic Stimulation (rTMS) is increasingly used to treat stroke, Parkinson's disease and depression (Fregni et al., 2005; Loo and Mitchell, 2005; Hallet, 2007; O'Reardon et al., 2007; Ridding and Rothwell, 2007). rTMS uses bursts of magnetic pulses to change the excitability and connection strengths of cortical neurons. However, the evidence to inform clinical application is highly inconsistent (Thut and Pascual-Leone, 2010; Hamada et al., 2013) and substantially based on trial and error. Systematic theory is lacking. Typically, in rTMS research, measurements of motor-evoked potential (MEP) are made, often in terms of the strength of the MEP and the length of the cortical silent period that follows. However, the MEP is probably a poor and certainly an indirect measure of changes in the brain (Nicolo et al., 2015), clouding our understanding of rTMS mechanisms. In practice, therefore, particular amplitudes and timing of pulses in an rTMS sequence are selected because they show promise in small subsets of people. However, even basics such as the sign of any change in the outcome measure (e.g., does the MEP increase or decrease?) is debated. Many results show a wide spread in responses. It has become common to talk about “responders” and “non-responders” although evidence for a binary distinction in these two groups is lacking—in reality there is usually a continuum of response often including potentiation in some and depression in others (Nettekoven et al., 2015). Moreover, Héroux et al. (2015) provide evidence that the irreproducibility of results may be due to small sample sizes, unscientific screening of subjects and data, and selective reporting of results.

text: Repetitive Transcranial Magnetic Stimulation: A Call for Better Data Repetitive Transcranial Magnetic Stimulation (rTMS) is increasingly used to treat stroke, Parkinson's disease and depression (Fregni et al., 2005; Loo and Mitchell, 2005; Hallet, 2007; O'Reardon et al., 2007; Ridding and Rothwell, 2007). rTMS uses bursts of magnetic pulses to change the excitability and connection strengths of cortical neurons. However, the evidence to inform clinical application is highly inconsistent (Thut and Pascual-Leone, 2010; Hamada et al., 2013) and substantially based on trial and error. Systematic theory is lacking. Typically, in rTMS research, measurements of motor-evoked potential (MEP) are made, often in terms of the strength of the MEP and the length of the cortical silent period that follows. However, the MEP is probably a poor and certainly an indirect measure of changes in the brain (Nicolo et al., 2015), clouding our understanding of rTMS mechanisms. In practice, therefore, particular amplitudes and timing of pulses in an rTMS sequence are selected because they show promise in small subsets of people. However, even basics such as the sign of any change in the outcome measure (e.g., does the MEP increase or decrease?) is debated. Many results show a wide spread in responses. It has become common to talk about “responders” and “non-responders” although evidence for a binary distinction in these two groups is lacking—in reality there is usually a continuum of response often including potentiation in some and depression in others (Nettekoven et al., 2015). Moreover, Héroux et al. (2015) provide evidence that the irreproducibility of results may be due to small sample sizes, unscientific screening of subjects and data, and selective reporting of results.

year: 2016

title: Construction of lattice rules for multiple integration based on a weighted discrepancy

authors: Sinescu, Vasile

subjects: Lattice rules

abstract: High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications.
In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain
weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature
points required for reasonable accuracy would be astronomical because of the large number of variables.
The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a  low weighted discrepancy . In simple terms, the  discrepancy  is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called  product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are  general . In the weighted
settings mentioned above, the quality of the lattice rules is assessed by the  weighted discrepancy  mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges 
from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.

text: Construction of lattice rules for multiple integration based on a weighted discrepancy High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications.
In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain
weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature
points required for reasonable accuracy would be astronomical because of the large number of variables.
The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a  low weighted discrepancy . In simple terms, the  discrepancy  is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called  product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are  general . In the weighted
settings mentioned above, the quality of the lattice rules is assessed by the  weighted discrepancy  mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges 
from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.

year: 2008

title: Indigenous fertility in Aotearoa New Zealand: How does ethnic identity affect birth spacing and timing?

authors: Rarere, Moana

abstract: The survival of Indigenous peoples in the CANZUS states of Canada, Australia, Aotearoa New Zealand, and the United States is nothing short of remarkable. Not only have Indigenous peoples thwarted colonial tropes of the vanishing native but, for decades, Indigenous population growth rates have significantly outpaced those of the dominant settler populations. The future survival of Indigenous peoples fundamentally rests on continued natural increase, and understanding the causes and consequences of fertility behaviour is critical. While total fertility rates for Indigenous women in CANZUS countries are relatively low, childbearing tends to be concentrated at younger ages in contrast to the dominant white populations. The fertility transitions of both settler and Indigenous populations in the CANZUS states are well documented, however, a significant gap remains: how cultural factors shape contemporary Indigenous fertility behaviours. Using Aotearoa as a case study, we explore the relationship between Māori cultural identity, birth timing, and the duration of birth intervals. We use the 1995 New Zealand Women: Family, Employment and Education survey data to further test the impact of cultural identity on birth transition rates using the piecewise exponential model and Kaplan-Meier estimates. We find that women who identify Mainly Māori (exclusively or primarily) are at greater risk of bearing much earlier to first birth but not necessarily subsequent births. However, because of the earlier start, Māori have a longer reproductive window to bear more children, and at higher birth orders still bear earlier than non-Māori. The empirical evidence strengthens our case to suggest that cultural orientation has some influence on Indigenous fertility and contributes to the development of Indigenous-centred theories of fertility and demography more broadly.

text: Indigenous fertility in Aotearoa New Zealand: How does ethnic identity affect birth spacing and timing? The survival of Indigenous peoples in the CANZUS states of Canada, Australia, Aotearoa New Zealand, and the United States is nothing short of remarkable. Not only have Indigenous peoples thwarted colonial tropes of the vanishing native but, for decades, Indigenous population growth rates have significantly outpaced those of the dominant settler populations. The future survival of Indigenous peoples fundamentally rests on continued natural increase, and understanding the causes and consequences of fertility behaviour is critical. While total fertility rates for Indigenous women in CANZUS countries are relatively low, childbearing tends to be concentrated at younger ages in contrast to the dominant white populations. The fertility transitions of both settler and Indigenous populations in the CANZUS states are well documented, however, a significant gap remains: how cultural factors shape contemporary Indigenous fertility behaviours. Using Aotearoa as a case study, we explore the relationship between Māori cultural identity, birth timing, and the duration of birth intervals. We use the 1995 New Zealand Women: Family, Employment and Education survey data to further test the impact of cultural identity on birth transition rates using the piecewise exponential model and Kaplan-Meier estimates. We find that women who identify Mainly Māori (exclusively or primarily) are at greater risk of bearing much earlier to first birth but not necessarily subsequent births. However, because of the earlier start, Māori have a longer reproductive window to bear more children, and at higher birth orders still bear earlier than non-Māori. The empirical evidence strengthens our case to suggest that cultural orientation has some influence on Indigenous fertility and contributes to the development of Indigenous-centred theories of fertility and demography more broadly.

year: 2023