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On study for change point regression problems using a difference-based regression model

Jong Suk Parka, Chun Gun Park1,b, Kyeong Eun Leea

aDepartment of Statistics, Kyungpook National University, Korea;
bDepartment of Mathematics, Kyonggi University, Korea
Correspondence to: 1Department of Mathematics, Kyonggi University, 154-42, Gwanggyosan-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do 16227, Korea. E-mail: cgpark@kgu.ac.kr
Received May 9, 2019; Revised September 26, 2019; Accepted October 11, 2019.
Abstract
This paper derive a method to solve change point regression problems via a process for obtaining consequential results using properties of a difference-based intercept estimator first introduced by Park and Kim (Communications in Statistics - Theory Methods, 2019) for outlier detection in multiple linear regression models. We describe the statistical properties of the difference-based regression model in a piecewise simple linear regression model and then propose an efficient algorithm for change point detection. We illustrate the merits of our proposed method in the light of comparison with several existing methods under simulation studies and real data analysis. This methodology is quite valuable, “no matter what regression lines” and “no matter what the number of change points”.
Keywords : change point, difference-based intercept estimator, difference-based regression model, piecewise linear regression
1. Introduction

A piecewise linear regression model is a special type of relationship between a dependent variable and one (or more) explanatory variables that consists of piecewise lines. In this model, the matter of interest is the boundary points of the adjacent lines called break points, change points or jointpoints (Muggeo, 2008). Change point problems occur in fields such as molecular biology, machine learning, and econometrics. The results derived from statistical inference could be misleading if there exist change points; consequently, it is important to ascertain the threshold values where the effect of the independent variable changes (Ulm, 1991; Betts et al., 2007; Muggeo, 2008).

Significant literature has been developed in many fields related to the change point regression problems since the 1950’s (Quandt, 1958). Many studies have focused on testing for change points rather than estimates since then (Kim and Siegmund, 1989; Andrews, 1993; Andrews and Ploberger, 1994). However, later statisticians have focused on estimates (Loader, 1996; Bai, 1997; Julious, 2001; Muggeo, 2003; Zhou and Liang, 2008). Subsequently, related software programs on detecting change points have been developed. Some R packages related to these problems include strucchange (Zeileis et al., 2002), segmented (Muggeo, 2008), and chngpt (Fong et al., 2017), which have worked only under certain conditions of a continuous or discontinuous type, a single covariate or multiple covariates, and no change point, one change point or multiple change points. For example, the R package segmented (Muggeo, 2003, 2008) supports the continuous type of a mean function that is a connected line at the change point, and allows multiple change points. The chngpt package proposed by Fong et al. (2017) also supports both continuous and discontinuous types in logistic regression models as well as linear regression models and allows two-phase regression models. Most of all R packages for change point detection support only one covariate, except for the segmented package which is available for several covariates under strong conditions (https://cran.r-project.org/web/packages/segmented/segmented.pdf).

Park and Kim (2019) first introduced a difference-based regression model (DBRM) which is useful for outlier detection in multiple linear regression models. The proposed outlier detection approach uses a difference-based intercept estimator that is influenced by anomalous data. Based on the DBRM we can apply properties of this estimator to the piecewise regression model. In particular, we propose an efficient algorithm for change point detection in a piecewise simple linear regression model (PSLR). Compared to the previously mentioned methods, our proposed method has advantages that can be applied to various circumstances: continuous or discontinuous types, single covariate or multiple covariates, and no change point, one change point or multiple change points.

The remainder of this paper is organized as follows. In Section 2, we briefly describe piecewise linear regression models. In Section 3, we utilize the process of the DBRM (Park and Kim, 2019) and derive the statistical properties of the difference-based coefficient estimator in the PSLR. An algorithm to detect change points will then be given in Section 4. In Section 5 and Section 6, we illustrate the merits of our proposed method in comparison with several existing methods by simulation studies and real data analysis. The article concludes with a discussion in Section 7.

2. Piecewise linear regression model

In this section, we consider a piecewise regression model. To do this, we use a multiple change point regression model described by Chen et al. (2011). Assume that the number of regimes is r + 1 with r change points, response variable is the y = (y1, y2, …, yN)′, and the number of regressors is p, where change points are defined in terms of only one of the regressors, x. Other regressors are expressed as z1, …, zp−1. Then general piecewise linear regression model is:

$y i = { α 1 , 1 + β 1 , 1 x i + ∑ l = 2 p β l z i , l - 1 + ϵ i , if i ≤ n 1 , α 1 , 2 + β 1 , 2 x i + ∑ l = 2 p β l z i , l - 1 + ϵ i , if n 1 < i ≤ n 1 + n 2 , ⋮ ⋮ α 1 , m + β 1 , m x i + ∑ l = 2 p β l z i , l - 1 + ϵ i , if ∑ l = 1 m - 1 n l < i ≤ ∑ l = 1 m n l , ⋮ ⋮ α 1 , r + 1 + β 1 , r + 1 x i + ∑ l = 2 p β l z i , l - 1 + ϵ i , if ∑ l = 1 r n l < i ≤ N .$

Here, N is the total number of observations. As for δ = (δ1, δ2, …, δr)′ is the r × 1 vector, and its parameters are change point parameters which satisfy δ1 < δ2 < · · · < δr. n1 is the number of observations in the first regime (xiδ1), nm is the number of observations in the mth regime (δm−1 < xiδm) for m = 2, …, r, and $n r + 1 = N - ∑ m = 1 r n m$.

A piecewise linear regression model is classified by Hawkins (1980) as continuous and discontinuous. Continuous type here means that the regression function is a connected line at the change point, δm that satisfies the following equation: α1,m + β1,mδm = α1,m+1 + β1,m+1δm for m = 1, 2, …, r. If this is not satisfied, the model is discontinuous.

Below, we use Equation (2.1) with r = 1 and p = 1, assuming that change point location, δ is unknown and this model has two regimes. Without loss of generality, assume that n = #(xiδ) (i.e., x1 ≤ · · · ≤ xn < δxn+1 ≤ · · · ≤ xN). Then the formula can be expressed as:

$y i = { α 1 + β 1 x i + ϵ i , if i ≤ n , α 2 + β 2 x i + ϵ i , if i > n ,$

where α1, α2, β1, and β2 are unknown parameters and $ϵ i ∼ iid N ( 0 , σ 2 )$. For these two phase linear models, Fong et al. (2017) distinguished them into step, hinge, segmented, and stegmented. We now address change point problems using the Model (2.2), and use the four types to illustrate.

3. Difference-based regression model for PSLR

### 3.1. Fitting PSLR using difference-based regression model

In this section, after introducing the DBRM (Park and Kim, 2019), we explain how to apply the process of the DBRM to the PSLR. Park and Kim (2019) proposed an outlier-detection approach using the properties of an intercept estimator in the DBRM. This method uses only the estimator of the intercept: it does not require estimating the other parameters in the DBRM. In this paper, we first use the DBRM process to detect change points and explain how to apply DBRM to the PSLR.

First, we describe the DBRM without change points. Then, the simple linear regression can be expressed as: yi = α + βxi + ϵi, i = 1, …, N. Let y(k)i be the difference between yi and yk and x(k)i be the difference between xi and xk, where k = u, …, N. Here, u is the minimum number of observations to estimate parameters, and we set u = 5. Also, we assume that i = 1, …, k − 1 due to the effect of the change point. The DBRM for the kth observation is written as

$y ( k ) i ∣ ϵ k = - ϵ k + β x ( k ) i + ϵ i , ϵ i ∼ iid N ( 0 , σ 2 ) ,$

where β is the slope of regression line.

Second, we describe the DBRM with change point using Equation (2.2). This model is divided into two parts according to the value of k affected by the location of the change point. For the first part (kn), the DBRM for the kth observation is

$y ( k ) i ∣ ϵ k = - ϵ k + β 1 x ( k ) i + ϵ i , ϵ i ∼ iid N ( 0 , σ 2 ) ,$

where β1 is the slope of the first regression line. For the second part (k > n), the DBRM for the kth observation is

$y ( k ) i ∣ ϵ k = - ϵ k + α 1 - α 2 + ( β 1 - β 2 ) x k + β 1 x ( k ) i + ϵ i , ϵ i ∼ iid N ( 0 , σ 2 ) ,$

where α1, α2, β1, and β2 are the coefficients of each regression line in Equation (2.2). For k = u, …, N, Model (3.1), (3.2), and (3.3) can be expressed as a simple linear regression model:

$y ( k ) i ∣ ϵ k = α ( k ) + β ( k ) x ( k ) i + ϵ i , ϵ i ∼ iid N ( 0 , σ 2 ) ,$

where i = 1, …, k − 1, and α(k) and β(k) are regression coefficients of these models for the kth observation. In simple notation, the matrix form is as follows.

$( y 1 - y k y 2 - y k ⋮ y k - 1 - y k ) = ( 1 ( x 1 - x k ) 1 ( x 2 - x k ) ⋮ ⋮ 1 ( x k - 1 - x k ) ) ( α ( k ) β ( k ) ) + ( ϵ 1 ϵ 2 ⋮ ϵ k - 1 ) .$

Then we estimate the kth coefficients, α(k) and β(k) in the DBRM (3.4) using the least square estimators. The result of the DBRM without change point leads to the estimators as the following two parts: intercept estimator $α^(k)|ϵk$ and slope estimator $β^(k)|ϵk$.

$α ^ ( k ) ∣ ϵ k = - ( y k - y ¯ ( k ) ) + ( x k - x ¯ ( k ) ) ( β ^ ( k ) ∣ ϵ k ) ,$ $β ^ ( k ) ∣ ϵ k = ∑ j = 1 k - 1 ( x j - x ¯ ( k ) ) ( y j - y ¯ ( k ) ) ∑ j = 1 k - 1 ( x j - x ¯ ( k ) ) 2 ,$

where $x ¯ ( k ) = ∑ j = 1 k - 1 x j / ( k - 1 )$ and $y ¯ ( k ) = ∑ j = 1 k - 1 y j / ( k - 1 )$. The result of the DBRM with change point is divided into two parts based on where k is located: when k = n, n is the number of observations in the first regime. In this case, $α^(n)|ϵn$ and $β^(n)|ϵn$ are expressed as

$α ^ ( n ) ∣ ϵ n = - ( y n - y ¯ ( n ) ) + ( x n - x ¯ ( n ) ) ( β ^ ( n ) ∣ ϵ n ) ,$ $β ^ ( n ) ∣ ϵ n = ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) ( y j - y ¯ ( n ) ) ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 ,$

where $x ¯ ( n ) = ∑ j = 1 n - 1 x j / ( n - 1 )$ and $y ¯ ( n ) = ∑ j = 1 n - 1 y j / ( n - 1 )$. In the case of k = n + 1, the expression of α̂(n+1)|ϵn+1 and β̂(n+1)|ϵn+1 using Equation (3.6) is noted as

$α ^ ( n + 1 ) ∣ ϵ n + 1 = ( n - 1 ) R n + 1 ( α ^ ( n ) ∣ ϵ n ) - ( y n + 1 - y n ) + ( x n + 1 - x n ) ( β ^ ( n ) ∣ ϵ n ) ,$ $β ^ ( n + 1 ) ∣ ϵ n + 1 = P n + 1 ( β ^ ( n ) ∣ ϵ n ) + Q n + 1 ( y n - y ¯ ( n ) ) ,$

where

$R n + 1 = ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 - ( x n + 1 - x n ) ( x n - x ¯ ( n ) ) n ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 + ( n - 1 ) ( x n - x ¯ ( n ) ) 2 , P n + 1 = n ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 n ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 + ( n - 1 ) ( x n - x ¯ ( n ) ) 2 , Q n + 1 = ( n - 1 ) ( x n - x ¯ ( n ) ) n ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 + ( n - 1 ) ( x n - x ¯ ( n ) ) 2 .$

### 3.2. Statistical properties of coefficient estimators

For k = u, …, N, we provide mean and variance of the kth coefficient estimators, $α^(k)|ϵk$ and $β^(k)|ϵk$ in the following two parts: no change point and one change point.

• No change point: In the case of Model (3.1) without change point, the mean and variance of coefficient estimators, $α^(k)|ϵk$ and $β^(k)|ϵk$ for the kth observation are expressed as

$E ( α ^ ( k ) ) = E ( E ( α ^ ( k ) ∣ ϵ k ) ) = E ( - ϵ k ) = 0 ,$ $Var ( α ^ ( k ) ) = E ( V ( α ^ ( k ) ∣ ϵ k ) ) + V ( E ( α ^ ( k ) ∣ ϵ k ) ) = ∑ j = 1 k - 1 ( x j - x k ) 2 ( k - 1 ) ∑ j = 1 k - 1 ( x j - x ¯ ( k ) ) 2 σ 2 + σ 2 ,$ $E ( β ^ ( k ) ) = E ( E ( β ^ ( k ) ∣ ϵ k ) ) = β ,$ $Var ( β ^ ( k ) ) = E ( V ( β ^ ( k ) ∣ ϵ k ) ) + V ( E ( β ^ ( k ) ∣ ϵ k ) ) = σ 2 ∑ j = 1 k - 1 ( x j - x ¯ ( k ) ) 2 ,$

where $x ¯ ( k ) = ∑ j = 1 k - 1 x j / ( k - 1 )$ and β is the coefficient of regression line.

• One change point: When k = n of Model (3.2) and k = n + 1 of Model (3.3), respectively, the mean and variance are expressed as following two parts. If k = n, there are

$E ( α ^ ( n ) ) = E ( E ( α ^ ( n ) ∣ ϵ n ) ) = E ( - ϵ n ) = 0 ,$ $Var ( α ^ ( n ) ) = E ( V ( α ^ ( n ) ∣ ϵ n ) ) + V ( E ( α ^ ( n ) ∣ ϵ n ) ) = ∑ j = 1 n - 1 ( x j - x n ) 2 ( n - 1 ) ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 σ 2 + σ 2 ,$ $E ( β ^ ( n ) ) = E ( E ( β ^ ( n ) ∣ ϵ n ) ) = β 1 ,$ $Var ( β ^ ( n ) ) = E ( V ( β ^ ( n ) ∣ ϵ n ) ) + V ( E ( β ^ ( n ) ∣ ϵ n ) ) = σ 2 ∑ j = 1 n - 1 ( x j - x ¯ ( n ) ) 2 ,$

where $x ¯ ( n ) = ∑ j = 1 n - 1 x j / ( n - 1 )$ and β1 is the coefficient of the first regression line in Equation (3.2). If k = n + 1, there are

$E ( α ^ ( n + 1 ) ) = E ( E ( α ^ ( n + 1 ) ∣ ϵ n + 1 ) ) = E ( λ n + 1 - ϵ n + 1 ) = λ n + 1 ,$ $Var ( α ^ ( n + 1 ) ) = E ( V ( β ^ ( n + 1 ) ∣ ϵ n + 1 ) ) + V ( E ( β ^ ( n + 1 ) ∣ ϵ n + 1 ) ) = ∑ j = 1 n ( x j - x n + 1 ) 2 n ∑ j = 1 n ( x j - x ¯ ( n + 1 ) ) 2 σ 2 + σ 2 ,$ $E ( β ^ ( n + 1 ) ) = E ( E ( β ^ ( n + 1 ) ∣ ϵ n + 1 ) ) = β 1 ,$ $Var ( β ^ ( n + 1 ) ) = E ( V ( β ^ ( n + 1 ) ∣ ϵ n + 1 ) ) + V ( E ( β ^ ( n + 1 ) ∣ ϵ n + 1 ) ) = σ 2 ∑ j = 1 n ( x j - x ¯ ( n + 1 ) ) 2 ,$

where λn+1 = α1α2 + (β1β2)xn+1. For k = n + 2, n + 3, …, N, the difference based observations aren’t of the linear relationship between x(k)i and y(k)i, i = 1, 2, …, k − 1 with the first regime, (xj, yj), j = 1, 2, …, n, so $E(α^(n+2))≠λn+2-ϵn+2$.

In accordance with Equation (3.8), the mean of the intercept estimator is zero. If kn, results are also similar to the previous result. However, in accordance with Equation (3.10), the mean of the intercept estimator is non-zero value, λn+1. Prior to the change point, the mean of the intercept estimator is zero, but beyond the change point, the mean of the intercept estimator is non-zero. The estimated intercept is highly influenced by which observation is removed and then by whether the removed observation is the change point (or not). Hence, we use the difference-based intercept estimator for change point detection.

4. Hypothesis testing for change point detection

In this section, we explain characteristics of an intercept estimator, $α^(k)|ϵk$, k = u, …, N, and propose a testing method for change point detection using properties of the intercept estimator. In order to detect locations of change points, we also further develop algorithm using the properties of $α^(k)|ϵk$.

### 4.1. Characteristics of intercept estimator

The difference-based intercept estimator is highly affected by the change point. We now explain the characteristics of the intercept estimator in three cases: no change point, one change point, and two change points.

• No change point: Assume a simple linear regression model (y = −4x + 5) without change point. In Figure 1(b), we display the scatter plot of the kth observation and the intercept estimate without the kth observation with k = u, …, N. As a result, estimated $α^(k)|ϵk$’s are random at zero.

• One change point: Assume a piecewise linear regression model with one change point. This model also has two types of continuous or discontinuous. If the model is a continuous type, $α^(k)|ϵk$’s appear randomly at zero prior to the true change point. But, $α^(k)|ϵk$’s have the same sign values and tend to increase or decrease beyond the true change point in Figure 2(b). However, if the model is discontinuous type, the estimated intercepts have the highest or lowest point beyond the true change point in

• Two change points: Assume a continuous piecewise linear regression model with two change points. As shown above, $α^(k)|ϵk$’s appear randomly at zero prior to the first change point. But passing each change point, the intercept estimates have different patterns in

### 4.2. A testing method for change point detection

In most cases, a simple graphical analysis is able to detect a change point, but in other cases a hypothesis test is required. In accordance with Section 3.2, if there is no change point, intercept estimators, $α^(k)|ϵk$’s are random at zero. However, if there are change points, intercept estimators have patterns beyond the change point. Accordingly, we detect change points using these characteristics. In order to do so, we consider rank test (Bartels, 1982) which perform better than an ordinary run test in our simulation.

Bartels (1982) considered the rank version of the von Neumann’s ratio statistic and obtained the critical values of this statistic under the randomness hypothesis. Suppose Rt is the rank of the tth observation in T observations. The null hypothesis H0 of randomness is rejected at large in absolute value of the test statistic

$Bar * = Bar - E [ Bar ] D [ Bar ] = Bar - 2 2 5 / ( 5 T + 7 ) ,$

where $Bar = ∑ t = 1 T - 1 ( R t - R t + 1 ) 2 / ∑ t = 1 T ( R t - R ¯ ) 2$. It is known that Bar* is asymptotically standard normal distributed under H0. In this paper, we use the rank, the corresponding sequential number of {α̂(u), α̂(u+1), …, α̂(s)} with s = u + v − 1, …, N. Here, v is the minimum number of observations for the test, and we set v = 5. For this test, we use R package randtests (Mateus and Caeiro, 2015).

Let us revisit the simulation data described in Section 4.1 and apply the randomness test proposed by Bartels (1982). Here, the indices for ascending and descending data are same as the indices and s of algorithm in Section 4.3. As a result, Figures 58 show the corresponding plots for this rank test. In Figures 5(a) and (b), the test results show that all points are random if there is no change point. However, if there are change points, the test results indicate that all points are not random, regardless of the type of piecewise regression (Figures 68).

### 4.3. Algorithm

In accordance with Section 4.2, the result of randomness test is highly affected by which observation is a change point or not. Therefore, we propose a computing algorithm consisting of the following four steps in order to detect change point.

• Step 1. For k = u, …, N, fit the Model (3.4):

$y ( k ) i ∣ ϵ k = α ( k ) + β ( k ) x ( k ) i + ϵ i , i = 1 , … , k - 1 ;$

• Step 2. Estimate the difference-based intercept estimators:

• - Do k = u : N{

* Estimate intercepts, $α^(k)|ϵk$;

* Estimate intercepts $α^(N-k+1)|ϵN-k+1$; }

• - Lets $α ^ asc = ( α ^ asc ( u ) , α ^ asc ( u + 1 ) , … , α ^ asc ( N ) )$ and $α ^ des = ( α ^ des N - u + 1 , … , α ^ des ( 2 ) , α ^ des ( 1 ) )$;

• Step 3. Perform the rank test (Bartels, 1982):

• - Do s = (u + v − 1) : N{

* Put $α ^ asc , s = ( α ^ asc ( u ) , α ^ asc ( u + 1 ) , … , α ^ asc ( s ) )$ and $α ^ des , s = ( α ^ des ( N - u + 1 ) , … , α ^ des ( N - s + 1 ) )$;

* Perform the randomness test for sequence $α^asc,s$ and $α^des,s$;

* Compute the p-value of each test and put pasc,s and pdes,s; }

• - Rewrite pasc = (pasc,u+v−1, …, pasc,N) and pdes = (pdes,Nuv+2, …, pdes,2, pdes,1);

• Step 4. Decide if change points exist:

• - Using the results of Step 3, the hypothesis, H0: there is no change point, H0 is rejected if pasc,N > 0.05 and pdes,1 > 0.05;

• - If H0 is rejected, i.e., there are change points, then the number of change points is determined by the following procedures:

* Let maxasc be arg min{s : pasc,s < 0.05, s = (u+v−1), …, N} and mindes be arg max{s : pdes,s < 0.05, s = 1, …, (Nuv + 2)};

* If maxasc ≥ mindes, there is one change point;

* Otherwise, there are two or more change points;

• Step 5. Detect the location of first change points:

• - If there is one change point between maxasc and mindes, assume that the number of observations in the first regime, $n^$ is the median between maxasc and mindes;

• - If there are two or more change points, repeat the following loop until maxasc ≥ mindes {

* Put N = mindes −1;

* Perform Steps 1–4; }

• - Then there is first change point between maxasc and mindes. Here, assume that the number of observations in the first regime, $n^$ is the median between maxasc and mindes.

The other change points can be detected with the remaining data except for the first regime corresponding to $n^$ detected using the above algorithm.

5. Simulation studies

We conduct simulations to evaluate the performance of our approach compared to other existing approaches: R packages chngpt (Fong et al., 2017; Fong and He, 2018) and segmented (Muggeo, 2008, 2017). First, chngpt provides both estimation and hypothesis testing functionalities for four types of piecewise regression models. Second, segmented package offers a module to estimate the parameters in a GLM with segmented relationships. This package supports the continuous model.

### 5.1. Simulation setting

In order to assess and compare the performance of the proposed difference-based intercept estimators, simulations have been conducted under different conditions: sample sizes (N = 50, 100), the number of change points (r = 0, 1, 2), types of piecewise regression, and the number of independent variables. We generated 100 data sets for each model. The model is divided as follows.

• Model 1. This model for comparison is yi = 5 − 4xi + ϵi, with i = 1, …, N, where $ϵ i ∼ iid N ( 0 , 1.5 )$ and N = 50. The covariate xi is generated with U(0, 10).

• Model 2. Consider the Model (2.2) with one change point. We also divide this model using four types separated by Fong et al. (2017). The data generating processes for the covariate variable x is the same as in Model 1 and $ϵ i ∼ iid N ( 0 , 1 )$. Also, n = 25 and N = 50. We set four type models according to the values of the parameters α1, α2, β1, and β2 as follows.

• - hinge: This model is zero slope prior to the change point and continuous at the change point. We set parameters β1 = 0, α1 = 2, β2 = 5, and α2 = α1 +(β1β2)δ with change point location δ = xn.

• - segmented: This model generalizes the hinge model by allowing non-zero slope prior to the change point. Accordingly, put the parameter of the model be β1 = −4, α1 = 5, β2 = 2, and α2 = α1 + (β1β2)δ with change point location δ = xn.

• - step: In this model, both regression lines have a slope of 0, and are discontinuous at the change point. We set parameters β1 = 0, α1 = 12, β2 = 0, and α2 = 3.

• - stegmented: According to Fong et al. (2017), stegmented model is viewed as the fusion of the segmented and step models. Both regression liens have different slopes and intercepts. We set parameters β1 = −4, α1 = 10, β2 = 2, and α2 = 2.

• Model 3. Consider the model with two change points. We assume that the model is continuous at the change points:

$y i = { α 1 + β 1 x i + ɛ i , if i ≤ n , α 2 + β 2 x i + ɛ i , if n < i ≤ n + n 2 , α 3 + β 3 x i + ɛ i , if i > n + n 2 ,$

where $ϵ i ∼ iid N ( 0 , 1 )$ and N = 100. We set β1 = −2, α1 = 5, β2 = 1, α2 = α1 + (β1β2)δ1, β3 = −2, and α3 = α2 + (β2β3)δ2 with change point locations δ1 = xn and δ2 = xn+n2 with n = 25 and n + n2 = 60. The covariate xi is generated with U(0, 20).

• Model 4. We assume a multiple linear regression model with two explanatory variables and one change point:

$y i = { α 1 + β 1 x i + γ 1 z i + ɛ i , if i ≤ n , α 2 + β 2 x i + γ 2 z i + ɛ i , if i < n ,$

where $ϵ i ∼ iid N ( 0 , 1 )$ and N = 50. The change point is defined in terms of only one of the regressors, x. The location of the change point, δ is x25. The covariate xi and zi are generated with U(0, 1), respectively. We set two types models according to the values of the parameters as follows.

• - Continuous type: This model consists of a connected line at the change point. We set parameters θ1 = (α1, β1, γ1 = (5, −3, 2) and θ2 = (α2, β2, γ2 = (α1 + (β1β2)δ, 2, 2).

• - Discontinuous type: This model consists of a disconnected line at the change point. We set parameters θ1 = (α1, β1, γ1 = (5, −3, 2) and θ2 = (0, 2, 2).

Here, u = 5 and v = 5 for estimation and testing of the difference-based intercept estimator. To compare the performance of our difference-based change point detection method and R packages, segmented and chngpt, we consider the following setting of these packages. In segmented, we use “davies.test” and “pscore.test” of these functions for testing and “segmented” function for detection of change points. In chngpt, we use testing function, “chngpt.test” that tests each of the four types, respectively. The significance level for the rank test of Bartels (1982) is 0.05.

### 5.2. Simulation results

In this section, performances of our proposed procedure are evaluated by results of 100 replicates for each model. The results are summarized in Table 1, where we report the proportions of false detections among 100 replications.

We evaluate the ratio of falsely detecting a change point when there is no change point (Model 1). As a result, in our method (DCD), the ratio of false detections among 100 replications is 0.01, and is remarkably accurate. This implies that our approach can identify the existence of change points under various circumstances. However, in SEG, the ratio is 0.03 and in CHN, it is close to one. CHN tends to find the most appropriate change point for the model.

We evaluate the ratio of not detecting change points when there are change points (Models 2–4). First, our method (DCD) and CHN produce negligible percentages of false detection of change points for all types of model. However, results of SEG show a high ratio in the continuous model, but not in the discontinuous model. This is because this package is intended to be suitable for a continuous model. Second, for Model 3, all three methods show accurate results. Finally, in simulation of Model 4, our method shows accurate results regardless of the type of model, but SEG and CHN perform worse than our method.

In the following, we evaluate the accuracy of change point estimation when there are change points. The performance of the change point estimator has been evaluated, through mean and standard deviation (SD). The performance of the three methods is also evaluated via the absolute relative bias (ARB) (Chen et al., 2011) that represents the percentage error of the estimate $n^$ compared to the true value $n(|(n^-n)/n|×100)$). Table 2, Figure 9, and Figure 10 show the results.

We first discuss Model 2 with only one change point. Our method and CHN estimate the location of change point with reasonable accuracy (Table 2). However, results of SEG estimate the location of change point accurately in the continuous model, but not accurately in the discontinuous model. In the simulation of Model 3 and Model 4, our method (DCD) works better than the other two methods. The results in Figure 9 and Figure 10 indicate that our method is more accurate than the other two methods. It is shown that our method is superior in the case of one change point and in the case of two change points in the simple linear regression model as well as superior in the case of one change point in the multiple regression model.

Figure 11 and Figure 12 display scatter plots of the intercept estimates and the results of the rank test for Model 4. The intercept estimate is influenced by the change point effect. This means that the difference-based intercept estimators that correspond to the observations including the change point effect, are large values.

6. Real data analysis

In this section, we apply our difference-based change point detection method to Down syndrome (DS) data (Davison and Hinkley, 1997). This data set is used by Muggeo (2008) to evaluate his method. There are three explanatory variables: the number of babies with DS (cases), the number of total births (births) and the mother’s mean age (age). DS risk generally increases with mother’s age, but evaluation is needed to show at what point a risk change occurs.

We apply our method (DCD) to this data and show the estimated intercepts in Figure 13. These estimates show a distinct trend between the 13th observation and the 17th observation. Even though a clear stopping rule is not provided, we can check for existence of change points using a trend of difference-based intercept estimates. Randomness tests are performed on the intercepts added one by one; in addition, we also show the scatter plot and the estimated $n^$ for each method. As a result, $n^$s of the three methods are slightly different in Figure 14. For our method, the number of observations in the first regime determined by the median of the interval between min and max, is 16. For SEG method, under a null left slope constraint, the number of the first regime observations is 14 (Muggeo, 2008). For CHN method, under the hinge type, the number of the first regime observations is 15.

7. Discussion

In this paper, we derive a way to solve change point regression problems via a process for getting the consequential results using the properties of a difference-based intercept estimator (Park and Kim, 2019) as well as describe the statistical properties of the DBRM in a PSLR. We also propose an algorithm for change point detection.

We compare the proposed methodology with other methods available in the recent literatures, SEG and CHN. The simulation results indicate that the performance of the proposed method is good in various circumstances. First, our method can successfully identify the existence of change points under various circumstances: continuous and discontinuous types, single covariate and multiple covariates, one change point and multiple change points. We can check for existence of change points using a trend of the difference-based intercept estimators despite not providing a clear stopping rule. We also determine the change point location as an interval and point estimation using our proposed algorithm. Our method is also more accurate than the other two methods, SEG and CHN: our method is superior in the case of one change point and in the case of two change points in the simple linear regression model, and our method is superior in the case one change point in the multiple regression model. Our method is affected by the number of samples in each regime and must have at least 15 samples. Therefore, we need to develop our method to make robust estimates regardless of the sample size in each regime as well as develop an algorithm that automatically searches for change point detection.

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2018R1D1A1B070).

Figures
Fig. 1.

Intercept estimates in the DBRM without change point: (a) scatter plot of x and y; (b) estimated intercepts in the DBRM without the kth observation, k = 5, …, N. DBRM = difference-based regression model.

Fig. 2.

Intercept estimates in the DBRM with one change point (continuous type) with true number of observations in the first regime (n) = 25: (a) scatter plot of x and y; (b) estimated intercepts in the DBRM without the kth observation, k = 5, …, N. DBRM = difference-based regression model.

Fig. 3.

Intercept estimates in the DBRM with one change point (discontinuous type) with true number of observations in the first regime (n) = 25: (a) scatter plot of x and y; (b) estimated intercepts in the DBRM without the kth observation, k = 5, …, N. DBRM = difference-based regression model.

Fig. 4.

Intercept estimates in the DBRM with two change points with true number of observations in the first regime (n) = 25, and in the second regime (n2) = 35: (a) scatter plot of x and y; (b) estimated intercepts in the DBRM without the kth observation, k = 5, …, N. DBRM = difference-based regression model.

Fig. 5.

Bartels test of intercept estimators without change point.

Fig. 6.

Bartels test of intercept estimators with one change point (continuous type) with true number of observations in the first regime (n) = 25 (estimated $n^$ is 24).

Fig. 7.

Bartels test of intercept estimators with one change point (discontinuous type) with true number of observations in the first regime (n) = 25 (estimated $n^$ is 25).

Fig. 8.

Bartels test of intercept estimators with two change points with true number of observations in the first regime (n) = 25, and in the second regime (n2) = 35 (estimated $n^$ is 28).

Fig. 9.

Boxplots of n estimated by each method on simulated data for Model 2 with N = 50 and true number of observations in the first regime (n) = 25.

Fig. 10.

Boxplots of the first n estimated by each method on simulated data for Model 3 and Model 4: (a) Model 3: N = 100, true number of observations in the first regime (n) = 25, and in the second regime (n2) = 35. (b) and (c) Model 4: N = 50, true number of observations in the first regime (n) = 25.

Fig. 11.

Intercept estimators and result of Bartels test on simulated data for Model 4 (continuous type), true number of observations in the first regime (n) = 25 (estimated $n^$ is 25).

Fig. 12.

Intercept estimators and result of Bartels test on simulated data for Model 4 (discontinuous type), true number of observations in the first regime (n) = 25 (estimated $n^$ is 25.).

Fig. 13.

Estimated intercepts in the DBRM without the kth observation in our example data. DBRM = difference-based regression model.

Fig. 14.

Scatter plot and regimes obtained each method in our example data. DCD = our difference-based change point detection method; SEG = R package segmented proposed by Muggeo (2008, 2017); CHN = R package chngpt proposed by Fong et al. (2017), Fong and He (2018).

TABLES

### Table 1

Comparison among three methods: DCD, SEG, and CHN

Model r DCD SEG CHN
Model 1 No 0.02 0.03 1.00

Model 2 hinge One 0.00 0.00 0.00
segmented 0.00 0.00 0.00
step 0.00 0.86 0.00
stegmented 0.00 0.00 0.00

Model 3 One 0.00 0.00 0.00

Model 4 Connected Two 0.00 0.00 0.03
Disconnected 0.00 0.06 0.04

DCD = our difference-based change point detection method; SEG = R package segmented proposed by Muggeo (2008, 2017); CHN = R package chngpt proposed by Fong et al. (2017), Fong and He (2018); r = the number of true change points.

### Table 2

Performances of DCD: mean, SD, and ARB of estimated $n^$ when repeated 100 times; true number of observation in the first regime (n) = 25

Model DCD SEG CHN

Mean SD ARB Mean SD ARB Mean SD ARB
Model 1 - - - - - - 6.01 0.00 75.96

Model 2 hinge 24.78 1.84 0.88 24.59 4.64 1.64 24.99 0.10 0.04
segmented 24.24 2.73 3.04 24.26 1.17 2.96 24.76 0.83 0.96
step 24.87 3.37 0.52 3.63 1.09 85.48 26.00 0.92 4.00
stegmented 24.44 2.79 2.24 17.41 9.95 30.36 26.00 0.00 4.00

Model 3 24.80 3.29 0.80 67.24 1.66 168.96 18.02 0.00 27.92

Model 4 Connected 24.91 1.49 0.36 24.39 3.34 2.44 24.77 1.52 0.92
Disconnected 25.75 1.74 3.00 31.46 8.14 25.84 34.21 3.67 36.84

DCD = our difference-based change point detection method; SEG = R package segmented proposed by Muggeo (2008, 2017); CHN = R package chngpt proposed by Fong et al. (2017), Fong and He (2018); SD = standard deviation; ARB = absolute relative bias.

References
1. Andrews DWK (1993). Tests for parameter instability and structural change with unknown change point, Econometrica, 61, 821-856.
2. Andrews DWK and Ploberger W (1994). Optimal tests when a nuisance parameter is present only under the alternative, Econometrica, 62, 1383-1414.
3. Bai J (1997). Estimation of a change point in multiple regressions models, Review of Economics and Statistics, 79, 551-563.
4. Bartels R (1982). The rank version of von Neumann’s ratio test for randomness, Journal of the American Statistical Association, 77, 40-46.
5. Betts M, Forbes G, and Diamond A (2007). Thresholds in songbird occurrence in relation to landscape structure, Conservation Biology, 21, 1046-1058.
6. Chen CWS, Chan JSK, Gerlach R, and Hsieh WYL (2011). A comparison of estimators for regression models with change points, Statistics and Computing, 21, 395-414.
7. Davison A and Hinkley D (1997). Bootstrap Methods and Their Application, Cambridge University Press,.
8. Fong Y and He Z. Package ’chngpt’: Estimation and Hypothesis Testing for Threshold Regression, R package version 2018.7-25.
9. Fong Y, Huang Y, Gilbert PB, and Permar SR (2017). chngpt: threshold regression model estimation and inference, BMC Bioinformatics, 18,.
10. Hawkins DM (1980). A note on continuous and discontinuous segmented regressions, Technometrics, 22, 443-444.
11. Julious SA (2001). Inference and estimation in a changepoint regression problem, The Statistician, 50, 51-61.
12. Kim HJ and Siegmund D (1989). The likelihood ratio test for a changepoint in simple linear regression, Biometrika, 76, 409-423.
13. Loader CR (1996). Change point estimation using nonparametric regression, The Annals of Statistics, 24, 1667-1678.
14. Mateus A and Caeiro F. Package ‘randtests’: Testing randomness in R, R package version 1.0.
15. Muggeo VMR (2003). Estimating regression models with unknown break-points, Statistics in Medicine, 22, 3055-3071.
16. Muggeo VMR (2008). Segmented: An R package to fit regression models with broken-line relationships, R News, 8(1), 20-25.
17. Muggeo VMR. Package ‘segmented’: Regression Models with Break-Points/Change-Points Estimation, R package version 0.5-3.0.
18. Park CG and Kim I (2019). Robust difference-based outlier detection, Communications in Statistics - Theory Methods, Published online.
19. Quandt RE (1958). The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association, 53, 873-880.
20. Ulm K (1991). A statistical methods for assessing a threshold in epidemiological studies, Statistics in Medicine, 10, 341-349.
21. Zeileis A, Kleiber C, Krämer W, and Hornik K (2002). Testing and Dating Structural Changes in Exchange Rate Regimes, Computational Statistics and Data Analysis, 54, 1696-1706.
22. Zhou HL and Liang KY (2008). On estimating the change point in generalized linear models, IMS Collections Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 1, 305-320.


text:
Hardcover | $40.00 Short | £27.95 | ISBN: 9780262017671 | 322 pp. | 6 x 9 in | 56 figures, 80 tables| September 2012 ebook |$28.00 Short | ISBN: 9780262306133 | 322 pp. | 6 x 9 in | 56 figures, 80 tables| September 2012

Immigration and Labor Market Mobility in Israel, 1990 to 2009

Overview

After the collapse of the Soviet Union in 1989, Soviet Jews emigrated in large numbers to Israel. Over the next ten years, Israel absorbed approximately 900,000 immigrants from the former Soviet Union, an influx that equaled about twenty percent of the Israeli population. Most of these new immigrants of working age were college-educated and highly skilled. Once in Israel, they were eligible for a generous package of benefits, including housing subsidies, Hebrew language training, and vocational education. This episode provides a natural experiment for testing the consequences of a large immigration inflow of skilled workers. This book provides a detailed analysis of the gradual process of occupational upgrading of immigrants and the associated rise in their wages.

Based on their analysis, the authors conclude that even a very large and unanticipated wave of immigration can be integrated within the local labor market without any significant long-term adverse economic effect on natives. The small effect on wages and employment of natives is explained by the capital inflows into Israel and the gradual entry of immigrants into high-skill jobs as they invest in local human capital. An important contribution of the book to the immigration literature is the formulation and estimation of stochastic dynamic models that combine job search with investment in human capital and the analysis of alternative government policies within this framework.

Sarit Cohen Goldner is Lecturer in the Department of Economics at Bar-Ilan University.

Zvi Eckstein is Dean of the School of Economics in the Interdisciplinary Center Herzliya and served as Deputy Governor of the Bank of Israel from 2006 to 2011.

Yoram Weiss is Professor of Economics at Tel-Aviv University.

• Immigration and Labor Market Mobility in Israel, 1990 to 2009
• Immigration and Labor Market Mobility in Israel, 1990 to 2009
• Sarit Cohen Goldner, Zvi Eckstein, and Yoram Weiss
• The MIT Press
• Cambridge, Massachusetts
• London, England
• 2012
• Massachusetts Institute of Technology
• All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
• MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email special_sales@mitpress.mit.edu or write to Special Sales Department, The MIT Press, 55 Hayward Street, Cambridge, MA 02142.
• Related material for this book, including tables, figures, data, and programs, can be found at http://www.tau.ac.il/~eckstein/immigrants.html.
• This book was set in Times Roman by Toppan Best-set Premedia Limited. Printed and bound in the United States of America.
• Library of Congress Cataloging-in-Publication Data
• Cohen Goldner, Sarit.
• Immigration and labor market mobility in Israel, 1990 to 2009 / Sarit Cohen Goldner, Zvi Eckstein, and Yoram Weiss.
•  p. cm.
• Includes bibliographical references and index.
• ISBN 978-0-262-01767-1 (hardcover : alk. paper)
• 1. Labor market—Israel. 2. Foreign workers, Russian—Israel. 3. Israel—Emigration and immigration—Economic conditions. 4. Immigrants—Israel—Economic conditions. I. Eckstein, Zvi. II. Weiss, Yoram. III. Title.
• HD5812.2.A6C64 2012
• 331.12′909569409049—dc23
• 2011048965
• 10 9 8 7 6 5 4 3 2 1
• Contents
• List of Tables
•  ix
• List of Figures
•  xiii
• Acknowledgments
•  xv
• 1 Introduction 1
• 1.1 Introduction 1
• 1.2 Background 2
• 1.3 Description of the Chapters 3
• 1.4 Lessons 11
• 2 The Aggregate Macroeconomic Impact of a Large Inflow of Immigrants 15
• 2.1 Introduction 15
• 2.2 Natives and Immigrants in the Labor Market 19
• 2.3 The Capital–Labor Ratio—Trends and Adjustment 26
• 2.4 An Open-Economy Equilibrium Model with Adjustment Costs 27
• 2.4.1 Model Specification
•  31
• 2.4.2 Calibration
•  32
• 2.4.3 Simulations
•  33
• 2.4.4 Related Literature
•  35
• 2.5 Immigration and GNP Growth: A Puzzle?
•  35
• 2.6 Summary
•  36
• Appendix: Quality-Adjusted Labor
•  37
• 3 On the Wage Growth of Immigrants
•  41
• 3.1 Introduction
•  41
• 3.2 A Model for Immigrant Earning Equations 46
• 3.3 The Empirical Earning Function
•  50
• 3.4 Data
•  54
• 3.5 Estimation Results
•  56
• 3.5.1 Results for Natives
•  56
• 3.5.2 Results for Immigrants
• 57
• 3.6 Decomposition of Wage Growth 59
• 3.7 Occupational Transitions
•  62
• 3.8 Convergence of Wages
•  63
• 3.8.1 Convergence of Residual Distributions
•  64
• 3.8.2 Convergence of Average Wages
•  65
• 3.9 Summary
•  69
• 4 Immigrants’ Choice of Employment, Occupation, and Human Capital: Dynamic Stochastic Empirical Models
•  73
• 4.1 Introduction
•  73
• 4.2 The Data
•  76
• 4.2.1 (A) Females
•  78
• 4.2.2 (B) Males
•  84
• 4.3 Model Specifications
•  89
• 4.3.1 (A) Females
•  89
• 4.3.2 (B) Males
•  93
• 4.4 Solution and Estimation Methods
•  97
• 4.4.1 Solution
•  98
• 4.4.2 Estimation Method
•  100
• 4.4.3 Identification
•  101
• 4.5 Results
•  102
• 4.5.1 The Model’s Fit
•  103
• 4.5.2 Estimated Parameters
•  112
• 4.6 Policy Analysis: Training
•  131
• 4.6.1 (A) Females
•  133
• 4.6.2 (B) Males
•  142
• 4.6.3 Summary
•  147
• 4.7 Verification of the Model: Out-of-Sample Predictions
•  150
• 4.7.1 Out-of-Sample Predictions
•  152
• 4.7.2 Aggregate Trends
•  153
• 4.7.3 High-Skilled Immigrants
•  155
• 4.7.4 Summary 155
• 4.8 The Value of Immigrating to Israel
•  157
• 4.9 Concluding Remarks
•  160
• 5 Job Search and Loss of Skills
•  163
• 5.1 Introduction
•  163
• 5.2 Data
•  165
• 5.3 The Model
•  168
• 5.4 Implementation of the Model
•  172
• 5.5 Results
•  176
• 5.5.1 Wages
•  176
• 5.5.2 Nonmonetary Returns
•  177
• 5.2.3 Job-Offer and Job-Termination Probabilities
•  177
• 5.2.4 Choice Probabilities and Types
•  179
• 5.6 The Model’s Fit
•  182
• 5.7 Loss of Human Capital
•  188
• 5.8 Summary
• 195
• Appendix: Supplementary Tables 198
• 6 The Joint Choice of Residential Location and Employment by Immigrants
•  205
• 6.1 Introduction
•  205
• 6.2 The Theoretical Model
•  207
• 6.2.1 The Housing Market
•  207
• 6.2.2 Production Technology
•  207
• 6.2.3 The Labor Market
•  208
• 6.2.4 Wages
•  208
• 6.2.5 Job-Offer Probabilities
•  209
• 6.2.6 Job Search
•  209
• 6.2.7 Utility
•  209
• 6.2.8 The Immigrant’s Problem
•  210
• 6.2.9 The Model’s Predictions
•  210
• 6.3 Model Specification
•  211
• 6.3.1 The Value Function
•  211
• 6.3.2 The Wage Function
•  212
• 6.3.3 Areas of Residence, Occupations, and Job Search
•  213
• 6.3.4 Job-Offer Probabilities
•  214
• 6.3.5 The Immigrant’s Choice on Arrival in Israel
•  215
• 6.4 Estimation and Identification
•  217
• 6.5 Data
•  219
• 6.6 Results
•  222
• 6.6.1 Wage Parameters
•  222
• 6.6.2 Job-Offer Probability Parameters
•  223
• 6.6.3 Weight of the Monetary Component in Immigrants’ Choices
•  226
• 6.6.4 The Probability of Search on Each Path
•  226
• 6.6.5 Nonemployment
•  227
• 6.6.6 Distribution of Immigrants by Area of Residence and Occupation
•  229
• 6.6.7 The Probability of Moving between Areas of Residence and Occupations
•  229
• 6.6.8 Utilization of the Immigrants’ Human Capital in Israel
•  234
• 6.7 Comparison of the Model’s Prediction to Other Data Sources
•  237
• 6.8 Conclusions
•  238
• Appendix A: Supplementary Model for Estimating the Wage Premium and Rate of Promotion
•  240
• Appendix B: Supplementary Tables
•  241
• 7 Immigrants from the FSU after Twenty Years in Israel: Evidence and Interpretation
•  245
• 7.1 Introduction
•  245
• 7.2 Employment, Occupations, and Wages
•  246
• 7.3 Social Indicators
•  260
• 7.3.1 Housing
•  260
• 7.3.2 Marriage Patterns
•  263
• 7.4 Return Migration and Out-Migration
•  267
• 7.5 Concluding Remarks
•  269
• Notes
•  273
• References
•  293
• Index
•  299
• Related material for this book, including tables, figures, data, and programs, can be found at http://www.tau.ac.il/~eckstein/immigrants.html.

Endorsements

“This book brings together years of careful and insightful scholarship on one of the largest migration episodes for which good data are available: the migration of Jews from the ex-Soviet Union to Israel. I recommend it to anyone interested in the economic assimilation or impact of immigrants.”
--Jennifer Hunt, Department of Economics, Rutgers University"—

“This book provides a comprehensive and rigorous analysis, conducted over a fifteen year period, of the unanticipated large influx of Russian immigrants to Israel that occurred after the collapse of the Soviet Union. The authors consider both how these immigrants were assimilated into the labor market and the economy-wide adjustments that ensued. The book is a major contribution that is a must-read for both researchers and policy makers.”
--Kenneth Wolpin, Walter H. and Leonore C. Annenberg Professor in the Social Sciences, University of Pennsylvania"—

Immigration and Labor Market Mobility in Israel, 1990-2009 constitutes a major contribution to our understanding of the adjustment and impact of immigrants on the destination country. One advantage of this study of Israel is the unique experience of a large (relative to the host economy) exogenous immigration. Another is that it is not on an English-speaking developed economy of overseas settlement, which are the source of so much of the immigration literature. As a result, this book helps put into perspective the research findings on immigration among the English-speaking developed countries.”
--Barry Chiswick, Chair of the Economics Department, George Washington University"—

"Immigration and Labor Market Mobility in Israel, 1990 to 2009 is a splendid book on an important topic. Following the collapse of the Soviet Union immigrants from its member countries poured into Israel, increasing its population by 20 percent. The book studies their absorption in the Israeli economy and their impact on local workers, using detailed data sets that have been assembled for this purpose. The topic is fascinating and the analysis exemplary both in depth and breadth."
--Elhanan Helpman, Galen L. Stone Professor of International Trade, Harvard University"—

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text:
This function allows you to make arbitrary changes to how mizer works by allowing you to replace any mizer function with your own version. You should do this only as a last resort, when you find that you can not use the standard mizer extension mechanism to achieve your goal.

customFunction(name, fun)

## Arguments

name Name of mizer function to replace The custom function to use as replacement

## Details

If the function you need to overwrite is one of the mizer rate functions, then you should use setRateFunction() instead of this function. Similarly you should use setResource() to change the resource dynamics and setReproduction() to change the density-dependence in reproduction.

If you find that your goal really does require you to overwrite a mizer function, please also create an issue on the mizer issue tracker at https://github.com/sizespectrum/mizer/issues to describe your goal, because it will be interesting to the mizer community and may motivate future improvements to the mizer functionality.

Note that customFunction() only overwrites the function used by the mizer code. It does not overwrite the function that is exported by mizer. This is clarified when you run the code in the Examples section.

## Examples

if (FALSE) {
fake_project <- function(...) "Fake"
customFunction("project", fake_project)
mizer::project(NS_params) # This will print "Fake"
project(NS_params) # This will still use the old project() function
# To undo the effect:
customFunction("project", project)
mizer::project(NS_params) # This will again use the old project()
}


text:
# Speed of light

dantenewton

## Homework Statement

Question

Given that the speed of light in a vacuum is 3.0 x 10^8 ms^-1, calculate the speed of light in a diamond of refractive index 2.4.

## Homework Equations

-
3. Attempt

So if the refractive index is 2.4, which means 2.4 = sin i / sin r, how can I solve this question? Can anyone give me a helping hand?

Mentor
You're thinking of Snell's law, but all you need is the definition of index of refraction.

dantenewton
You're thinking of Snell's law, but all you need is the definition of index of refraction.

Thank you but, doesn't the refractive index involves Snell's law?

Mentor
Thank you but, doesn't the refractive index involves Snell's law?

The other way around, actually. :tongue: Snell's law involves the refractive indexes of the materials.

Look up the definition of refractive index!

Mentor
Last edited by a moderator:


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 International Book Series of Mathematical Texts 2001; 172 pp; hardcover ISBN-10: 973-99097-7-9 ISBN-13: 978-973-99097-7-8 List Price: US$28 Member Price: US$22.40 Order Code: THETA/2 This book delivers a swift, yet concise, introduction to some aspects of rotation $$C^*$$-algebras and almost Mathieu operators. The two topics come from different areas of analysis: operator algebras and the spectral theory of Schrödinger operators, but can be approached in a unified way. The book does not try to be the definitive treatise on the subject, but rather presents a survey highlighting the important results and demonstrating this unified approach. For each real number $$\alpha$$, the rotation $$C^*$$-algebra $$A_\alpha$$ can be abstractly defined as the universal $$C^*$$-algebra generated by two elements $$U$$ and $$V$$ subject to the relation $$UV = e^{2\pi i \alpha} VU$$. When $$\alpha$$ is an integer, $$A_\alpha$$ is isomorphic to the commutative $$C^*$$-algebra of continuous functions on a two-dimensional torus. When $$\alpha$$ is not an integer, the algebra is sometimes called a non-commutative 2-torus. In this respect, some of the methods you will find here can be regarded as a sort of non-commutative Fourier analysis. An almost Mathieu operator is a type of self-adjoint operator on the Hilbert space $$\ell^2 = \ell^2(\mathbf{Z})$$. The exposition is geared toward a wide audience of mathematicians: researchers and advanced students interested in operator algebras, operator theory and mathematical physics. Readers are assumed to be acquainted with some functional analysis, such as definitions and basic properties of $$C^*$$-algebras and von Neumann algebras, some general results from ergodic theory, as well as the Fourier transform (harmonic analysis) on elementary abelian locally compact groups of the form $$\mathbf{R}^d \times \mathbf{Z}^k \times \mathbf{T}^1 \times F$$, where $$F$$ is a finite group. Much progress has been made on these topics in the last twenty years. The present book will introduce you to the subjects and to the significant results. A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS. Readership Graduate students and research mathematicians interested in functional analysis, quantum theory, and operator theory. Table of Contents Prerequisites on rotation $$C^*$$-algebras Almost Mathieu operators and automorphisms of $$A_\alpha$$ Perturbations of the spectrum of $$H_{\alpha, \lambda}$$ The spectrum of almost Mathieu operators for rational $$\alpha$$ The absence of isolated points in the spectrum of $$H_{\alpha, \lambda}$$ Lyapunov exponents and pure point spectrum The Lebesgue measure of $$\mathrm{spec}_{(p/q,\lambda)}$$ Some estimates for the Lebesgue measure of $$\mathrm{spec}(H_{(p/q,\lambda)})$$ Spectral computations for certain non-self-adjoint operators Projections in rotation $$C^*$$-algebras The approximation of irrational rotation $$C^*$$-algebras The approximation of irrational non-commutative spheres Subject index Notation


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# zbMATH — the first resource for mathematics

A weak version of the Lipman-Zariski conjecture. (English) Zbl 1327.32016
Summary: The complex-analytic version of the Lipman-Zariski conjecture says that a complex space is smooth if its tangent sheaf is locally free. We prove the following weak version of the conjecture:
A normal complex space is smooth if its tangent sheaf is locally free and locally admits a basis consisting of pairwise commuting vector fields.
The main tool used in the proof of our result is a new extension theorem for reflexive differential forms on a normal complex space. It says that a closed holomorphic differential form of degree one defined on the smooth locus of a normal complex space can be extended to a holomorphic differential form on any resolution of singularities of the complex space.
##### MSC:
 32C15 Complex spaces 32C20 Normal analytic spaces 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32S05 Local complex singularities
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##### References:
 [1] Birkar, C; Cascini, P; Hacon, CD; McKernan, J, Existence of minimal models for varieties of log general type, J. Am. Math. Soc., 23, 405-468, (2010) · Zbl 1210.14019 [2] Druel, S.: The Zariski-Lipman conjecture for log canonical spaces. arXiv:1301.5910 (math.AG) (2013) · Zbl 1357.14009 [3] Flenner, H, Extendability of differential forms on nonisolated singularities, Invent. Math., 94, 317-326, (1988) · Zbl 0658.14009 [4] Graf, P.: An optimal extension theorem for 1-forms and the Lipman-Zariski conjecture. arXiv:1301.7315 (math.AG) (2013) · Zbl 0641.32020 [5] Grauert, H.: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Inst. Hautes Études Sci. Publ. Math. (5), 64 (1960) · Zbl 0158.32901 [6] Grauert, H, Über modifikationen und exzeptionelle analytische mengen, Math. Ann., 146, 331-368, (1962) · Zbl 0173.33004 [7] Greb, D; Kebekus, S; Kovács, SJ; Peternell, T, Differential forms on log canonical spaces, Publ. Math. Inst. Hautes Études Sci., 114, 87-169, (2011) · Zbl 1258.14021 [8] Greb, D., Kebekus, S., Peternell, T.: Reflexive differential forms on singular spaces - Geometry and Cohomology. Journal für die Reine und Angewandte Mathematik (Crelle’s Journal), published electronically (2013). doi:10.1515/crelle-2012-0097 · Zbl 1314.32014 [9] Greuel, GM, Dualität in der lokalen kohomologie isolierter singularitäten, Math. Ann., 250, 157-173, (1980) · Zbl 0417.14003 [10] Hochster, M, The Zariski-lipman conjecture in the graded case, J. Algebra, 47, 411-424, (1977) · Zbl 0401.13006 [11] Källström, R, The Zariski-lipman conjecture for complete intersections, J. Algebra, 337, 169-180, (2011) · Zbl 1250.14003 [12] Kaup, L., Kaup, B.: Holomorphic functions of several variables, de Gruyter Studies in Mathematics, vol. 3. Walter de Gruyter & Co., Berlin (1983). doi:10.1515/9783110838350. An introduction to the fundamental theory, With the assistance of Gottfried Barthel, Translated from the German by Michael Bridgland · Zbl 0528.32001 [13] Kollár, J.: Lectures on resolution of singularities, Annals of Mathematics Studies, vol. 166. Princeton University Press, Princeton, NJ (2007) · Zbl 1113.14013 [14] Lipman, J, Free derivation modules on algebraic varieties, Am. J. Math., 87, 874-898, (1965) · Zbl 0146.17301 [15] Manaresi, M, Sard and Bertini type theorems for complex spaces, Ann. Mat. Pura Appl. 4, 131, 265-279, (1982) · Zbl 0498.32013 [16] Oeljeklaus, K; Richthofer, W, Linearization of holomorphic vector fields and a characterization of cone singularities, Abh. Math. Sem. Univ. Hamburg, 58, 63-87, (1988) · Zbl 0641.32020 [17] Reiffen, HJ, Das lemma von Poincaré für holomorphe differential-formen auf komplexen Räumen, Math. Z., 101, 269-284, (1967) · Zbl 0164.09401 [18] Steenbrink, J; Straten, D, Extendability of holomorphic differential forms near isolated hypersurface singularities, Abh. Math. Sem. Univ. Hamburg, 55, 97-110, (1985) · Zbl 0584.32018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


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## Generalized rank weights of reducible codes, optimal cases and related properties. (arXiv:1603.06477v2 [cs.IT] UPDATED)

Reducible codes for the rank metric were introduced for cryptographic purposes. They have fast encoding and decoding algorithms, include maximum rank distance (MRD) codes and can correct many rank err

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Multiple TBI patterns in same patients must be considered Trauma

Multiple TBI patterns in same patients must be considered. Traumas to non-facial areas and hospital mortality 172 (22,8%) patients suffered from 232 total injuries both to cranium and body. Additional body trauma rather than cranium GS-9973 cost occurred in 15, 4% (n = 116) of patients. Of these;

injuries to upper extremity, lower extremity, chest, pelvis and abdomen were seen in 5,8% (n = 44), 4,6% (n = 35), 4% (n = 30), 1, 9% (n = 17) and 1, 6% (n = 12) of patients respectively. In RTA victims the ratios vary, total of 30,7% (n = 63) patients suffered from coexisting trauma and injury of the upper extremity was noticed in 12, 2% (n = 25), followed by injury to lower extremity in 11, 7% (n = 24) chest in 10, 7% (n = 22) MK0683 order pelvis in 4, 9% (n = 10), abdomen in 3, 9% (n = 8). Table 3 illustrates details of injury patterns with co-existing trauma. Table 3 Fractures and injury patterns in patients with coexisting maxillofacial trauma     n of patients % of patients Orthopaedic injuries Hand/wrist 17 9,8 Forearm 16 9,3 Femur 16 9,3 Tibia/Fibula 16 9,3 Humerus 11 6,3 Clavicle/Scapula 10 5,8 Foot/Ankle 9 5,2 Lumber vertebra 3 1,7 Abdominal/Pelvic Pelvis fracture 13 7,5 Spleen hematoma 5 2,9 Liver hematoma

4 2,3 Pelvis hematoma 2 1,1 Gastric perforation 2 1,1 Retroperitoneal hematoma 1 0,5 Torso injuries Clavicle/Scapula fracture 10 5,8 Pnemothorax/Hemothorax 11 6,3 Costa fracture 7 4,0 Pulmonary contusion 2 1,1     n % of patients with TBI TBI’s Subarachnoid haemorrhage 30 44.1 Brain contusion 15 22 Epidural haemorrhage 14 20.5 Pnemocephalus 13 19.1 Subdural haemorrhage 11 16.1 Diffuse axonal injury 4 5.8 A total of 24 patients were intubated during the study period. 17 patients were intubated because of severe traumatic brain injury and 7 from trauma complications such as www.selleckchem.com/HSP-90.html pnemothoraces, hemorrhagic shock etc. Of the 17 severe TBI patients only 2 of them had isolated sagittal maxillary fracture and 1 had soft tissue injury. 3 of the patients had panfacial trauma with Lefort III

type maxillary fracture where as 11 patients had compound midfacial and/or mandibular fracture. 6 of the admitted patients died from TBI, 1 from ICU complication and 2 from internal bleeding. Injury and association with alcohol consumption 158 of the 754 patients had consumed alcohol before trauma. No statistically Elongation factor 2 kinase significant data were revealed between alcohol consumption gender and presence of fracture. Trauma mechanism of facial injury in intoxicated patients was distributed almost evenly, most common cause is violence and compared to other causes, suffering from violence is statistically higher (p < 0.05) furthermore young male group (age between 19-30) is consuming more alcohol compared to other age groups in same gender (p < 0.001). Discussion Trauma is the leading cause of deaths occurred in first 40 years of life and it is well known that MF injuries are frequently seen in polytrauma victims.

1021/ja973744u CrossRef Jeschke G, Matysik J (2003) A reassessm

1021/ja973744u CrossRef Jeschke G, Matysik J (2003) A reassessment of the origin of Stattic order photochemically induced dynamic nuclear polarization effects in solids. Chem Phys 294:239–255. doi:10.1016/S0301-0104(03)00278-7 CrossRef Kaptein R, Oosterhoff JL (1969) Chemically induced dynamic nuclear polarization II (Relation with anomalous ESR spectra). Chem Phys Lett 4:195–197. doi:10.1016/0009-2614(69)80098-9

CrossRef Kondepudi D, Prigogine I (1998) Modern thermodynamics: from heat engines to dissipative structures. Wiley, New York Lendzian F, Huber M, Isaacson RA et al (1993) The electronic structure of the primary donor cation radical in Rhodobacter sphaeroides R-26 Endor and Triple resonance studies in single crystals of reaction centers. Biochim Biophys Acta 1183:139–160. doi:10.1016/0005-2728(93)90013-6 selleck screening library CrossRef Matysik J, Alia A, Gast P et al (2000a) Photochemically induced nuclear spin polarization in reaction centers of photosystem II observed by C-13 solid-state NMR reveals a strongly asymmetric electronic structure of the P680•+ primary donor chlorophyll. Proc Natl Acad Sci USA 97:9865–9870. doi:10.1073/pnas.170138797 click here CrossRefPubMed Matysik J, Alia A, Hollander JG et al (2000b) A set-up to study photochemically induced dynamic nuclear polarization

in photosynthetic reaction centres by solid-state NMR. Indian J Biochem Biophys 37:418–423PubMed McDermott A, Zysmilich MG, Polenova T (1998) Solid state NMR studies of photoinduced polarization in photosynthetic reaction centers: mechanism and simulations. Solid State Nucl Magn Reson 11:21–47. doi:10.1016/S0926-2040(97)00094-5 CrossRefPubMed Polenova T, McDermott AE (1999) A coherent mixing mechanism explains the photoinduced nuclear polarization in Idelalisib mw photosynthetic reaction centers. J Phys Chem B 103:535–548. doi:10.1021/jp9822642

CrossRef Prakash S, Alia A, Gast P et al (2005a) Magnetic field dependence of photo-CIDNP MAS NMR on photosynthetic reaction centers of Rhodobacter sphaeroides WT. J Am Chem Soc 127:14290–14298. doi:10.1021/ja054015e CrossRefPubMed Prakash S, Tong SH, Alia A (2005b) 15N photo-CIDNP MAS NMR on reaction centers of Rhodobacter sphaeroides. In: van der Est A, Bruce D et al (eds) Photosynthesis: fundamental aspects to global perspectives, proceedings of the 13th international congress on photosynthesis. Allen Press, Lawrence, pp 236–237 Prakash S, Alia A, Gast P et al (2006) Photo-CIDNP MAS NMR in intact cells of Rhodobacter sphaeroides R26: molecular and atomic resolution at nanomolar concentration. J Am Chem Soc 128:12794–12799. doi:10.1021/ja0623616 CrossRefPubMed Roth HD (1996) Chemically induced dynamic nuclear polarization. In: Grant DM, Harris RK (eds) Encyclopedia of nuclear magnetic resonance. Wiley, New York Roy E, Diller A, Alia A et al (2006) Magnetic field dependence of 13C photo-CIDNP MAS NMR in plant photosystems I and II.

abies windfalls investigated, (2) assessment of the total density

abies windfalls investigated, (2) assessment of the total density of I. typographus infestation of each of P. abies selected stem and (3) estimation of the mean total infestation density of the stem

in the area investigated. The emphasis should be put on the necessity of use of all three above mentioned stages of estimation. If we use, for example, only the second stage, the evaluation of I. typographus population density can be highly erroneous. In the absence of an adequate number of P. abies windfalls, trap trees can be used. In the large-area method, the selleckchem methods used during sampling rare populations Selleck Saracatinib can be applied to select a representative sample for the windfall population, while remote sensing and aerial photography techniques can be employed to find windthrown gaps (in the PRN1371 surroundings of gaps the windfalls can occur) (e.g. Jackson et al. 2000; Foody et al. 2003). In most studies (e.g. Jakuš 1998; Göthlin et al. 2000; Eriksson et al. 2005, 2008), the I. typographus population density assessment procedures are limited to the second stage and moreover, are not based on statistics which renders the calculation of estimation errors impossible. These procedures consist of counting

I. typographus galleries, maternal galleries or mating chambers in the selected section (sections) of the stem, e.g., on bark strips 15 × 60 cm (Eriksson Etofibrate et al. 2005, 2006, 2008), 20 × 30 cm (Yamaoka et al. 1997), 10 × 10 cm (Erbilgin et al. 2006) in size, or on the bark pieces removed from the entire

stem circumference and of a length not exceeding 0.5 m taken from different stem parts (Jakuš 1998; Grodzki 2004; Kolk 2004). The most important stage in the proposed method is the second stage, allowing quick, accurate and minimally invasive estimation of the total density of infestation of selected windfalls by I. typographus. The I. typographus infestation density on fresh windfalls is strongly dependent on the abundance of such material: (1) in the case of high number of windfalls and low population density, the population is dispersed; (2) in the case of low number of windfalls and high population density, the population is concentrated on accessible windfalls and the attack on standing trees occurs (e.g. Grodzki et al. 2006a). The data collected from windfalls occurring in low population density are not directly comparable with those collected from windfalls occurring in high population density. The proposed method need to be adapted to the local conditions. The analogically developed linear regression functions were also successfully used to evaluate the stem total density of other insect species: Tomicus piniperda occurring on Pinus sylvestris stems as well as Cryphalus piceae and Pityokteines curvidens associated, inter alia, with A.

Measurement of alveolar bone density Dental X-ray films were take

Measurement of alveolar bone density Dental X-ray films were taken and alveolar bone density at the root of the first mandibular premolar measured, as described elsewhere [9], using an originally designed image editing software (No. PCT/jp2004/010815). A line was drawn at the apex of the root, parallel to the boundary of the cement–enamel junction. Another line was drawn halfway between the cement–enamel junction and the apex

of the root. Lines were then drawn perpendicular to those lines at the mesial and distal spaces of the first premolar. The X-ray film density in the area of the resulting rectangles was measured by first dividing the area into pixels with sides 1/1,524 cm

in length. The brightness selleck kinase inhibitor in each pixel was then compared with a scale consisting of 256 steps of brightness (Fig. 1). XAV-939 Fig. 1 Geometry of alveolar bone measurement. a Aluminum step wedge for calibration. b Calibration of density between standard aluminum wedge and maximum/minimum density. c Defining the area of interest for the alveolar bone density In order to align and standardize the brightness and contrast among the X-ray pictures for comparison of the results of measurement among X-ray pictures taken on different occasions, an X-ray picture taken for a normal, healthy person (i.e., a 23-year-old woman having 100% bone mineral density in the example being described) was used as a reference. A histogram

hist[x] of a color bar on the reference picture was normalized according to Eq. 1. Then, the normalized histogram hist[x] is substituted in Eqs. 2 and 3 to thereby calculate the brightness mean value, mean, and the standard deviation, SD, which are referred to as the reference mean value, RefMean, and the reference deviation, RefSD, respectively. Similarly, for each of the pictures to be corrected, the histogram hist[x] of its color bar is normalized and the brightness mean value and the SD for that picture calculated. Mean, the PLEKHM2 mean value of the brightness thus calculated, and SD, standard deviation, RefMean, the reference mean value, and RefSD, the reference deviation, are substituted in Eq. 4 to Z-IETD-FMK price correct the respective pictures with respect to their brightness and contrast and to obtain corrected brightness value Y′(i,j) for each picture. $$\rm hist \left[ x \right] = \frac\rm Num \left[ x \right]\rm TotalNum$$ (1)where x (0 ≤ x ≤ 255) is gradation, Num[x] is the number of pixels for the gradation x in the color bar, and TotalNum is the total number of pixels of the color bar.

019 and p = 0 032, respectively) Figure 7 Damage of biofilms of

019 and p = 0.032, respectively). Figure 7 Damage of biofilms of S. mutans wildtype and knock-out mutants for comC , comD and comE Emricasan concentration by carolacton. Biofilms were grown under anaerobic conditions

for 24 h and stained with the LIVE/DEAD BacLight Bacterial Viability staining kit. Green and red fluorescence was determined in triplicate samples, and biofilm damage was calculated as reduction of the fluorescence ratio green/red compared to untreated controls. Standard deviations were calculated from 3 – 5 independent experiments. Thus, the comD knockout mutant was LY2090314 clinical trial slightly less sensitive to carolacton than the wildtype. This could indicate that carolacton interferes with the membrane bound histidine kinase ComD. However, since the comC and comE mutants were

just as sensitive for carolacton as the wildtype, and since there was still considerable activity of carolacton against the comD mutant, other mechanisms must be more important. Influence of carolacton on a pcomX luciferase reporter strain ComX, an alternative sigma-factor, plays a key role in the quorum sensing system of S. mutans which controls not only genetic competence, but also stress tolerance and biofilm formation, leading to the suggestion to call it the “”X-state”" rather than competence this website [39]. ComX is positively induced by CSP through the response regulator ComE, but also by another two component system, CiaRH, and environmental stress [40]. ComX controls the late competence genes, including the machinery for DNA-uptake and processing, but also many other density dependent traits [36, 40–42]. Altogether 240 genes are directly or indirectly controlled by ComX [42]. To investigate the effect of carolacton on the promoter activity of comX a pcomX-luciferase reporter strain was

constructed. For the experiment a concentration of CSP (200 nM) was chosen that induced competence without causing substantial growth inhibition [42]. Figure 8A shows that a severe reduction of CSP-induced comX expression Bupivacaine was caused by addition of carolacton to biofilms grown anaerobically. Furthermore carolacton led to a decrease of growth-dependent, basal comX-reporter activity. Maximum inhibition was seen 60 min post induction at the peak of comX expression. In planktonic culture (Figure 8B) similar results were obtained, but both the CSP induced expression of comX and its inhibition through carolacton occurred over a longer time, e.g. from 45 to 180 min post induction, possibly reflecting the lower cell density in the planktonic culture. Furthermore we found that carolacton reduced the growth-dependent comX-promoter activity of this reporter strain also in the absence of externally added CSP, both in biofilms and in planktonic culture. Figure 8 Effect of carolacton on the comX -promoter activity of S. mutans.

To address this limitation, possible cases were assessed from a r

To address this limitation, possible cases were assessed from a review of the text fields for ON cases with any mention of “jaw.” Another limitation is that prescriptions written by specialists may not have been recorded by the general practitioner. The study design was based on an a priori selection of risk factors that have been previously cited in the literature [1, 4–7, 15] with particular TGF-beta inhibitor focus on those that were highly correlated; therefore, this study may have excluded other potentially important risk factors. In conclusion, using data from the UK GPRD and THIN databases, we found that significant predictors of ON at any skeletal site included

use of systemic corticosteroids in the previous 2 years, hospitalization, referral or specialist

visit, bone fracture, any cancer, osteoporosis, connective tissue disease, and osteoarthritis within the past 5 years. Bisphosphonate use was not a significant predictor of ON. This LY3023414 study aimed to provide a broader perspective on the descriptive epidemiology of ON risk factors than previous published studies. Studies utilizing more recent data may further elucidate the understanding of key predictors of ON. Acknowledgments The authors gratefully acknowledge the following people for their statistical, editorial, and BI2536 clinical expertise in the preparation of this manuscript: Karen Driver, Diane Vonderheide, Emma Hobbs, Andrea Klemes, Coridad Pontes and J. Michael Sprafka. Conflicts of interest Professor Cooper has undertaken consultancy and lecturing commitments for the Alliance for Better Bone Health, Eli Lilly, Novartis, GSK Roche, Servier, MSD, and Amgen. Dr. Steinbuch and Mr. Stevenson are employed by Procter & Gamble. MYO10 Dr. Miday retains stock in Procter & Gamble. Dr. Watts has received honoraria for lectures from Amgen, Novartis, Procter & Gamble, and Sanofi-Aventis; consulting fees from Amgen, Eli Lilly, Novartis,

The third and fourth sets of cells were for PMA-treated live cell

The third and fourth sets of cells were for PMA-treated live cell dilutions and untreated live cell dilutions. Combination of qPCR with PMA treatment PMA treatment was performed as described earlier [21]. Briefly, separate live cells, heat-killed cells, and live/dead

cell mixtures were aliquoted 100 μl in three 1.5-ml microtubes. Two microliters of 10 mM PMA was added to each aliquot to a final concentration of 50 μM. The samples were first incubated at room temperature in the dark for 5 min, with gentle shaking. Then the samples were exposed to a 650-W halogen light source, followed by DNA preparation, and qPCR Citarinostat molecular weight analysis. Detection of live salmonella cells in spiked spinach and beef samples using PMA-qPCR Fresh Emricasan concentration spinach and ground beef purchased from a local retail source, which were confirmed to be free of Salmonella by standard FDA BAM methods [45], was used for the spiking studies. The studies consisted of two parts. In part 1, three Selleck LY2090314 spinach samples (25 g) and three beef samples (25 g) were inoculated with 3 × 101, 3 × 102 and 3 × 103 CFU/g Salmonella strain SARB16. In part 2, three samples three beef samples (25 g) were each inoculated with 3 × 107/g dead cells and with 3 × 101, 3 × 102, and

3 × 103 CFU/g of live cells, respectively. Each spinach or beef sample was mixed with 225 ml of LB medium and homogenized for 2 min using a stomacher (Seward, England). Five milliliters of the enriched cultures was collected at 0, 4, 8, 12 and 24 h after incubation at 37°C with shaking at 180 rpm. The collected samples were centrifuged at 600 × g for 1 min to collect leaf or fat tissues. The supernatants were transferred to 2.0-ml microtubes and centrifuged at 3000 × g for 5 min to collect cells. The cell pellets were suspended in 1.5 ml of LB medium and treated with PMA before DNA extraction and qPCR analysis. Acknowledgments The authors are in debt to Christopher A. Elkins and Ben Tall for critically reviewing this manuscript and providing insightful comments and suggestions.

We thank Huanli Liu for reading this manuscript and giving useful suggestions and Mark Mammel for help in getting Dolichyl-phosphate-mannose-protein mannosyltransferase the background information on bacterial collections in DMB. Additionally, we want to thank the three reviewers who critically reviewed the manuscript and provided useful suggestions for revising the manuscript. Electronic supplementary material Additional file 1: Table S1: Salmonella enterica strains of the SARA and SARB reference collections used in this study. (DOC 59 KB) Additional file 2: Table S2: Selective detecion of live Salmonella cells spiked in beef by PMA-qPCR. (XLS 36 KB) References 1. Alali WQ, Thakur S, Berghaus RD, Martin MP, Gebreyes WA: Prevalence and distribution of Salmonella in organic and conventional broiler poultry farms. Foodborne Pathog Dis 2010, 7:1363–1371.PubMedCrossRef 2.

FEBS Journal 2008, 13:3388–3396 CrossRef 10 Wray S, Wilkie D: Th

FEBS Journal 2008, 13:3388–3396.CrossRef 10. Wray S, Wilkie D: The relationship between plasma urea levels and some muscle trimethylamine levels in Xenopus laevis: a 31P and 14N nuclear magnetic resonance study. J Exp Biol 1995, 198:373–378.PubMed 11. Viennet C, Bride J, Morel B, Bodeau C, HDAC inhibitors list Humbert P: Glycine betaine stimulates human skin fibroblasts growth and collagen production in culture. J Invest Dermatol 2002, 118:1099. 12. Warskulat

U, Reinen A, Grether-Beck S, Krutmann J, Haussinger D: The osmolyte strategy of normal human keratinocytes in maintaining cell homeostasis. J Invest Dermatol 2004, 123:516–521.CrossRefPubMed 13. Coelho-Sampaio T, Ferreira ST, Castro EJ Junior, Vieyra A: Betaine counteracts urea-induced conformational changes signaling pathway and uncoupling of the human erythrocyte Ca2+ pump. Eur J Biochem 1994, 221:1103–1110.CrossRefPubMed 14. Minana M, Hermenegildo C, Llsansola M, Montoliu C, Grisolia S, Felipo V: Carnitine Pitavastatin and choline derivatives containing a trimethylamine group prevent ammonia toxicity in mice and glutamate toxicity in primary cultures of neurons. J Pharmacol Exp Ther 1996, 279:194–199.PubMed 15. Armstrong LE, Casa DJ, Roti MW, Lee EC, Craig SA, Sutherland JW, Fiala KA, Maresh CM: Influence of betaine consumption on strenuous running and sprinting in a hot environment. J Strength Cond Res 2008, 22:851–860.CrossRefPubMed 16. Maresh

Interleukin-2 receptor CM, Farrell MJ, Kraemer WJ, Yamamoto LM, Lee EC, Armstrong LE, Hatfield DL, Sokmen B, Dias JC, Spiering BA, et al.: The Effects of Betaine Supplementation on Strength and Power Performance. Med Sci Sports Exerc 2007, 39:S101. 17. Hoffman J, Ratamess N, Kang J, Rashti S, Faigenbaum A: Effect of Betaine Supplementation on Power Performance and Fatigue. Journal of

the International Society of Sports Nutrition 2009, 6:7–17.CrossRefPubMed 18. Meyer F, Laitano O, Bar-Or O, McDougall D, Heingenhauser GJ: Effect of age and gender on sweat lactate and ammonia concentrations during exercise in the heat. Braz J Med Biol Res 2007, 40:135–143.PubMed 19. Huang CT, Chen ML, Huang LL, Mao IF: Uric acid and urea in human sweat. Chin J Physiol 2002, 45:109–115.PubMed 20. Mickelsen O, Keys A: The composition of sweat, with special reference to the vitamins. J Biol Chem 1943, 149:479–490. 21. Johnson BC, Hamilton TS, Mitchell HH: The effect of choline intake and environmental temperature on the excretion of choline from the human body. J Biol Chem 1945, 159:5–9. 22. Koc H, Mar MH, Ranasinghe A, Swenberg JA, Zeisel SH: Quantitation of choline and its metabolites in tissues and foods by liquid chromatography/electrospray ionization-isotope dilution mass spectrometry. Anal Chem 2002, 74:4734–4740.CrossRefPubMed 23. FNB: Dietary reference intakes for water, potassium, sodium, chloride, and sulfate. Washington DC: The National Acadamies Press; 2004. 24.

rhamnosus A+7-5a; 2, A+28-3b*; 3, E sanguinicola G0-2a*; 4, G0-2

rhamnosus A+7-5a; 2, A+28-3b*; 3, E. sanguinicola G0-2a*; 4, G0-2b; 5, G+21-1a; 6, E. faecalis Q0-1a; 7, Q0-1b; screening assay 8, Q+28-1a, 9, Q+28-1b; 10, L. rhamnosus T0-2a; 11, T+23-1a; 12, T+28-1b (systematic identification for the latter strains shown in Table 2). Molecular size markers are shown in lane M (size in bp indicated) and the figure is a composite of lanes drawn from 8 gels. All the volunteers were colonised with persistent LAB strains (specific to each individual) that represented greater than 1% of their viable faecal growth; at least one of these strains was identified to the species level for each volunteer except J (Table 3). Apart from sharing of the L. salivarius NCIMB

30211 and L. acidophilus NCIMB 30156 strains present within the administered feeding capsule, only one other strain was detected in two volunteers, the L. rhamnosus RAPD type 41 strain (Table 2). This L. rhamnosus strain was shared by individuals P and T (Table 2 and Table 3). Overall, these results demonstrate the ability of the fingerprinting strategy to detect and track the population biology of cultivable faecal

strains representative of a broad range of LAB species. Discussion We successfully developed a rapid, colony-based strain typing strategy that was able to track two Lactobacillus strains from feeding via a capsule through to faecal discharge in human volunteers. The RAPD typing system was capable of genotyping a wide variety of LAB species and its efficacy on single colonies this website provided a means to rapidly discriminate LAB isolates cultivated from human faeces. Evidence for survival and growth of the L. salivarius Belinostat datasheet strain was most convincing as it was not detected in any of volunteers prior to the feeding study (Table 3). In contrast, the L. acidophilus strain used in the capsule represented a very common genotype used in commercial applications (Table 2). Hence the appearance of L. acidophilus

isolates which matched the feeding strain NCIMB 30156 may have been less attributable to consumption of the capsule. However, statistical analysis demonstrated that the distribution of L. acidophilus NCIMB 30156 after the feeding trial was significant in terms of the number of positive volunteers Ribose-5-phosphate isomerase and in the majority of these positive individuals it was the dominant cultivable LAB strain in faeces. As far as we are aware, previous studies evaluating the dynamics of LAB consumption by humans have not examined the cultivable faecal diversity at the strain level. Several studies have used cultivation-independent methods such as real-time PCR to quantify the DNA from probiotic strains present in faeces by extrapolating this amplification data to estimate of the numbers of bacteria. Bartosch et al. [18] used real-time PCR to estimate the total numbers of Bifidobacterium species present in the faeces of elderly people taking a probiotic containing two Bifidobacterium strains and an inulin-based prebiotic.

MP performed the yeast-two hybrid screening and analysis JMW per

MP performed the yeast-two hybrid screening and analysis. JMW performed the subcellular fractionation and localization assays. JSS and DNM expressed and purified Pictilisib clinical trial wild type His ~ TbLpn. ARK performed the site-directed mutagenesis, expressed, and purified the His ~ DEAD mutant. ASF contributed by performing immunoprecipitation and western hybridization analyses. The in vitro phosphatidic

acid phosphatase assays were performed by MP, DNM, and ARK. MP wrote the manuscript. All authors read and approved the final manuscript.”
“Background Lignocellulosic agricultural byproducts are well known for their use as soil conditioners in the form of compost. According to conservative estimates, around 600–700 million tones (mt) of agricultural waste including 272 mt of crop residues [1]; 40–50 mt of municipal solid waste (MSW) and 500–550 mt of animal dung [2] are available in India every year for bioconversion to compost. Composting is an intense microbial process leading to decomposition

of the most biodegradable materials for further humification [3, 4]. Successful composting depends on a number of factors that have both direct and indirect influence on the activities of the microorganisms. Tiquia et al. [5] included the type of raw material being composted, its nutrient composition and physical characteristics check details such as bulk density, pH, and moisture content etc. as the important factors. Moreover, Fracchia et al. [6] also observed that various other factors influenced the microbial colonization of finished products, i.e., (i) origin and composition of the initial substrates, (ii) previous process conditions and (iii) substrate quality of the finished product. For the composting processes, the importance of microbial communities is well established [7]. Studies on bacterial population, actinobacteria

and fungi during composting have been reported extensively [8]. Liu et al.[9] reported that there were several molecular approaches, which provide powerful adjuncts to the culture-dependent techniques. A known powerful tool, namely PCR has been used for bacterial identification and its Selleck LY2874455 classification at species level [10]. PCR targeting the 16S rRNA gene sequencing is used extensively to study the prokaryote diversity and allows identification of prokaryotes as well as the prediction of phylogenetic Methamphetamine relationships [11]. The analyses of rRNA genes encoding for the small subunit ribosomal RNA (for bacteria, 16S rRNA) [12–14] have recently dramatically increased our knowledge about the contribution of different bacteria to various compost production phases. Molecular approach to characterize and classify microbial communities by cultivation methods has switched to the genetic level, and the analysis of community structure has become possible only with further need to address the cultivation approach for a systematic analysis.


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# Say It With Me: Root-Mean-Square

If you measure a DC voltage, and want to get some idea of how “big” it is over time, it’s pretty easy: just take a number of measurements and take the average. If you’re interested in the average power over the same timeframe, it’s likely to be pretty close (though not identical) to the same answer you’d get if you calculated the power using the average voltage instead of calculating instantaneous power and averaging. DC voltages don’t move around that much.

Try the same trick with an AC voltage, and you get zero, or something nearby. Why? With an AC waveform, the positive voltage excursions cancel out the negative ones. You’d get the same result if the flip were switched off. Clearly, a simple average isn’t capturing what we think of as “size” in an AC waveform; we need a new concept of “size”. Enter root-mean-square (RMS) voltage.

To calculate the RMS voltage, you take a number of voltage readings, square them, add them all together, and then divide by the number of entries in the average before taking the square root: $\sqrt{\frac{1}{n} \left(v_1^2 + v_2^2 +...+ v_n^2\right)}$. The rationale behind this strange averaging procedure is that the resulting number can be used in calculating average power for AC waveforms through simple multiplication as you would for DC voltages. If that answer isn’t entirely satisfying to you, read on. Hopefully we’ll help it make a little more sense.

# Building Transistors with Transistors

Since the 1940s when the first transistor was created, transistors have evolved from ornery blocks of germanium wrangled into basic amplifiers into thousands and thousands of different devices made of all kinds of material that make any number of electrical applications possible, cheap, and reliable. MOSFETs can come in at least four types: P- or N-channel, and enhancement or depletion mode. They also bear different power ratings. And some varieties are more loved than others; for instance, depletion-mode, N-channel power MOSFETs are comparatively scarce. [DeepSOIC] was trying to find one before he decided to make his own by hacking a more readily available enhancement-mode transistor.

For those not intimately familiar with semiconductor physics, the difference between these two modes is essentially the difference between a relay that is normally closed and one that’s normally open. Enhancement-mode transistors are “normally off” and are easy to obtain and (for most of us) useful for almost all applications. On the other hand, if you need a “normally on” transistor, you will need to source a depletion mode transistor. [DeepSOIC] was able to create a depletion mode transistor by “torturing” the transistor to effectively retrain the semiconductor junctions in the device.

If you’re interested in semiconductors and how transistors work on an atomic level, [DeepSOIC]’s project will keep you on the edge of your seat. On the other hand, if you’re new to the field and looking to get a more basic understanding, look no further than these DIY diodes.

# Isolated Voltage Measurements Through Frequency

This one’s not a flashy hack, it’s a great piece of work and a good trick to have up your sleeve. Sometimes you’ve got a voltage difference that you’d like to measure, but either the ground potential is at a different level, or the voltages are too high for your lowly microcontroller.

There are tons of tricks with resistive voltage dividers that you can play. But if you want serious electrical isolation from the target, there’s only one way to go — an optocoupler. But optocouplers only really transmit digital signals, and [Giovanni Carrera] needed to measure an analog voltage.

Enter the voltage-to-frequency IC that does just what it says: produces a square wave with a frequency that’s proportional to the voltage applied. Pass this square wave through an optocoupler, and you can hit one side with voltages approaching lightning strikes without damaging the microcontroller on the other side. And you’re still able to measure the voltage accurately by measuring the frequency on the digital I/O pins of the microcontroller.

[Giovanni] built up and documented a nice circuit. He even tested it for linearity. If you’re ever in the position of needing to measure a voltage in a non-traditional way, you’ll thank him later.

# “Who is John Galt?” Finally Answered

For those who haven’t read [Ayn Rand’s] philosophical tome Atlas Shrugged, there’s a pretty cool piece of engineering stuffed in between the 100-page-long monologues. Although fictional, a character manages to harness atmospheric static electricity and convert it into kinetic energy and (spoilers!) revolutionize the world. Harnessing atmospheric static electricity isn’t just something for fanciful works of fiction, though. It’s a real-world phenomenon and it’s actually possible to build this motor.

As [Richard Feynman] showed, there is an exploitable electrical potential gradient in the atmosphere. By suspending a tall wire in the air, it is possible to obtain voltages in the tens of thousands of volts. In this particular demonstration, a hexacopter is used to suspend a wire with a set of needles on the end. The needles help facilitate the flow of electrons into the atmosphere, driving a current that spins the corona motor at the bottom of the wire.

There’s not much torque or power generated, but the proof of concept is very interesting to see. Of course, the higher you can go the more voltage is available to you, so maybe future devices such as this could exploit atmospheric electricity to go beyond a demonstration and do useful work. We’ve actually featured the motor that was used in this demonstration before, though, so if you’re curious as to how a corona motor works you should head over there.

# Adding a Battery Gauge to a Project With Zero Parts

The typical way of doing a low battery detector is throwing a comparator in the circuit, setting it to measure a certain threshold voltage, and sending that signal off to a microcontroller or other circuit to notify someone the battery is going dead. [Josh] has a simpler way using an 8-bit AVR and zero other parts.

The chip [Josh] is using is the ATtiny84. The ADC in this chip is usually used to measure an unknown voltage against a reference voltage. The trick [Josh] is using is to do this in reverse: The internal 1.1 Volt reference voltage is measured against an unknown scale, namely the input voltage.

The value provided by the ADC on the chip will always be Vin times 1024 over the reference voltage. Since Vin will be 1.1 V in this case, the ADC value is known, it’s only a matter of doing some 6th grade algebra to determine the value of the input voltage.

[Josh] put together a small demonstration where the chip blinks out the number of volts its receiving from a bench power supply. By blinking a LED, it can blink out the current value of VCC as integers, but by using this technique you should be able to get a fairly fine-grained reading of what VCC actually is. Video below.

# Afroman Demonstrates Boost Converters

If you need to regulate your power input down to a reasonable voltage for a project, you reach for a switching regulator, or failing that, an inefficient linear regulator. What if you need to boost the voltage inside a project? It’s boost converter time, and Afrotechmods is here to show you how they work.

In its simplest form, a boost converter can be built from only an inductor, a diode, a capacitor, and a transistor. By switching the transistor on and off with varying duty cycles, energy is stored in the inductor, and then sent straight to the capacitor. Calculating the values for the duty cycle, frequency, inductor, and the other various parts of a boost converter means a whole bunch of math, but following the recommended layout in the datasheets for boost and switching converters is generally good enough.

[Afroman]’s example circuit for this tutorial is a simple boost converter built around an LT1370 switching regulator. In addition to that there’s also a small regulator, diode, a few big caps and resistors, and a pot for the feedback pin. This is all you need to build a simple boost converter, and the pot tied to the feedback pin varies the duty cycle of the regulator, changing the output voltage.

It’s an extremely efficient way to boost voltage, measured by [Afroman] at over 80%. It’s also exceptionally easy to build, with just a handful of parts soldered directly onto a piece of perfboard.

Video below.

# AC vs DC human pain test

Ever wondered just how much being zapped by electricity hurts? Curious if AC is worse than DC? Want to know just how many volts a human body can take? Although many people might cringe at the shear thought of it, [Mehdi Sadaghdar] is an electrical engineer who decided to turn himself into a human guinea pig and find out.

[Mehdi] measured the electrical resistance of his dry skin, his wet skin, and finally his tongue.  He found that his tongue had the least resistance, so it would feel the electricity at much lower levels. Using a bench power supply, he then used his tongue as a testing ground – slowly turning the voltage up and up until he could no longer take the pain. He tested the levels at which: he could first feel the electricity, when it began to get annoying, when it felt like torture, and when he could no longer stand the pain. He tried both AC and DC, and reports that AC is much worse.

Check out the informative, yet admittedly hilarious at times, video after the break. [Mehdi] seems like one awesome engineer! Remember – don’t try this at home.