**3. Challenges of embedded software design**

Embedded system development tools have traditionally lagged behind tools for the development of general systems (ChristopherChristopher, 2000). Unlike general systems, the design space for embedded systems is extremely large, so it is difficult to contain all of the facilities to specify, design, and test embedded systems. The number of embedded systems increased rapidly year by year and then the designers of the embedded system face ever-increasing challenges in the design stage. Some of these challenges are listed below:

Potential of Grid Technology for Embedded Systems and Applications 329

MATLAB is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numeric computation. The MATLAB infrastructure design is based on the gird computing technology .MATLAB is used to solve problems in several application areas such as signal and image processing, communications, control design, test and measurement, financial modeling and analysis, and computational biology. Add-on toolboxes extend the MATLAB environment to solve

Simulink is a companion product to MATLAB that offers an environment for multidomain simulation and Model-Based Design for dynamic and embedded systems. It provides an interactive graphical environment and a customizable set of block libraries that allows users

In this chapter we used the Model Based Design method to eliminate some of the embedded system challenges. Model Based Design is a simulation based method so, if the embedded system becomes large and more complicated, its simulation time will be increased. To accelerate the simulation time of such embedded systems, some parallel and distributed

Currently, many researches are focused on determining a good way to eliminate the challenges of the embedded systems design. Embedded systems have particularly tight performance, time to market and cost constraint. To meet these constraints, researchers try to find solutions to efficiently design the systems with required performances. Recently, the MBD method is considered to be one of the chief techniques in this field. The Model Based Design method is considered one of the leading techniques as a solution of those challenges. In this method, the model can be used to verify the plant design and the control algorithm. MBD method puts a system model at the center of the development process, from requirement development through design implementation (Woodward and Mosterman,

The system specifications phase is started by the analysis and the documentation of the system requirements. In the traditional method, this step is accomplished using the paperbased method which results in poor communication in the design process, errors in the design as well as limited traceability between the design and the requirements. In the MBD method, the model can provide an excellent virtual environment for high level descriptions of the embedded system, as shown in Figure 2. This figure illustrates the main four elements of the MBD method. The description for elements of Model Based Design method is

As designs become larger and more complicated, it becomes necessary to first describe them at a high level of abstraction. For example, Simulink (The MathWork web site) can provide specific block-sets such as signal processing, communication, video and image processing block set to help the designer to build an abstraction model. This model provides a

particular classes of problems in different application areas.

systems (grid computing method) are necessary.

**5. Model based design**

2007).

presented below.

**5.1 Executable specifications**

to design, simulate, implement, and test a variety of time-varying systems.

should be executed is unavailable. Therefore, a simulator of the embedded hardware is very useful for the development of the embedded software but it becomes a difficult matter because of the length of time required to build a simulator (Woodward and Mosterman, 2007 & Madhukar and Lee, 2008).

However, nowadays, embedded systems have garnered more interests in the research community, as well as there being an increased need for those embedded systems. The increase of the embedded system challenges opens a wide range of research in the development tools. Most of researchers try to find a design tool that can solve some of the challenges of embedded system design. Model Based Design method is one of the techniques for developing embedded software and it puts a system model at the center of the developing processes. For example, the environment supplied by MathWorks, Inc. allows engineers to mathematically model the behaviors of the physical system and re-use the program components in the library. This approach meets with significant success in some applications. This chapter will investigate the development of the inverter power supply as an example of the embedded system. The embedded software of the inverter power supply is optimized and tested using the Model Based Design (MBD) method. Moreover, the superiority of this method to the traditional design method is verified.


**4.3 Types of tests**

In what follows, three classes of testing useful during analysis of step-like change-points have been identified. The first two involve testing the segment of data within which a change-point is found. The third asks if a multiple change-point model is adequate.

*Severe Testing and Characterization of Change Points in Climate Time Series DOI: http://dx.doi.org/10.5772/intechopen.98364*

#### *4.3.1 Detection test*

Complex climate time-series data is almost certainly misspecified for *any* change-point detection test – thus the goal is adequate applicability to questions of interest. In testing for multiple change-points, many methods, including the MSBV, examine data only between presumptive lower and upper bounding points and restart estimation of the distribution parameters. The assumptions of the basic detection methods used must be considered.

Issues potentially arising include false detection, timing errors, and false negatives. Timing error includes misplacement and imprecision. The MSBV incorporates a resampling strategy [38] which reduces imprecision. False positives (deterministic and non-deterministic) can be uncovered by post-detection assessments, but false negatives introduce down-stream non-stationarities that interfere with detection of later change-points. Combining tests with differing assumptions and different nulls probes for both non-deterministic and deterministic causes of false results including sub-detection threshold events.

Analysis of covariance (ANCOVA) is used post-detection of a change-point by MSBV (which does not consider trend) to ensure that the presence of the changepoint provides explanatory power in an unconstrained disjoint linear statistical model which allows trend. It does not attempt to locate an alternative change-point – the Zivot-Andrews test however, see below, does this in passing. ANOVA tests for change of trend and change of level are obtained in passing but in R2019, final *p*values for change-points are obtained from only from ANCOVA.

### *4.3.2 Tests for heteroskedasticity for segmentation of data with change-points*

The full set of change-points in an entire sequence is tested here by the studentized Breusch-Pagan test (hereafter SBP test) for homoskedasticity of the residuals of the disjoint multi-segment model (JR2017 utilised the equivalent White's test [39]). An adequate model explanation of a time series, under the assumption of i.i.d. error, should have a featureless residual. This test has a null of homoskedasticity, rejected in favour of heteroskedasticity at low probabilities.

#### *4.3.3 Tests for stationarity in a segment*

Our detection test and the subsequent probability assignments by ANCOVA or ANOVA, and the further misspecification testing all assume serial independence either in the null or contrast hypothesis.

In these tests the segment containing a provisional change-point is tested for features that may deceive tests for shifts and trends. The MY test, ANCOVA, and where used ANOVA tests, have ruling assumptions of serial independence. The MSBV, and other multiple break tests assume some form of censorship between provisional data segments (determination of change-points within provisional bounds includes only the data within the bounds); but tests of the overall model assume homogeneity of error, thus of variance (e.g. the Akaike Information Criterion or AIC). The SBP also assumes this. All of these above tests are formalised as null hypothesis statistical tests (NHST) and as such they each are subject to their own ruling assumptions. The ruling assumptions are incorporated in the interpretation of the tests.

Autocorrelation in climate time-series is variously treated; some propose its estimation and removal [40], some warn against this idea [41]. Some treat it as a short term process and a cause of deception in change-point analyses [42], others have treated it as a persistent signal [43]. In climate signals, autocorrelation often appears to be time varying. Therefore we apply the MSBV without adjustment for autocorrelation and perform post-detection analysis to determine whether the detection test is likely to have been interfered with. In general, regression based statistical tests assume the absence of deterministic step-like changes and of unitroot, or red-noise progression.

Because multiple UR tests are performed, and because they each have differing ruling assumptions, the tests are interpreted in terms of evidence for and against stationarity in the underlying processes. In the econometric literature an exogenous change is one imposed upon a model from outside the model. We elected to retain this word where concepts were derived from economic papers as meaning an

Transient unit root behaviour, if it occurred, could indicate some sort of regime change, temporarily decoupled from normal forcings. If, in addition, measured noise was not persistent this would show I(0) behaviour; or, if it were fully persistent, as I(1) behaviour. In regional signals in which this occurs, the region may also have become coupled to other sub-systems [46]. This could indicate that the underlying physical model is incomplete and that a missing variable misspecification has resulted. On the other hand, persistent unit root behaviour means that a

The Earth system is constrained so that the overall temperature cannot solely follow a pure random walk – at worst it would follow a Brownian bridge (i.e. sequences where the end-points are meaningful and accepted as deterministic but the path is apparently a random walk [47]). However the composition of summary deterministic signals, such as the GMST, involves manipulations that can produce data that existing unit root tests will identify as containing unit roots, and furthermore deceive deterministic tests in much the same way as random walk data. This

Random walk progression may be present in climate data because of transient physical conditions, or because the data is unrelated to the physical processes assumed (M-S due to irrelevant variables). Additionally there may be features in the data that do not correspond to any of a shift, a trend change, or unit root behaviour (M-S due to missing variables), and UR tests are potentially sensitive to this. This source of deception must also be dealt with. Other features may be present in the data but not detected. For instance, a step-like shift well above a detectability threshold may be present together with a number of small, deterministic shifts below detectability, and this latter may be taken to be evidence of stochastic drift by

The unit root based tests used here all inherit in one form or another the Dickey

*ρ* represents the portion of the signal (*Yt*�1) carried forward by autocorrelation, *β* represents the (deterministic) linear trend, *μ* represents the intercept, and *et* is the i.i.d. error with zero mean and a constant variance *σ*2. If *ρ* ¼ 0 this describes a deterministic trend with no autocorrelation, if 0>*ρ* <1 there is a deterministic trend with a degree of autocorrelation, and if *ρ* ¼ 1, regardless of other parameters it contains a unit root. If all other parameters are zero and *ρ* equals one, then there is no deterministic trend, no offset, and *Yi* is a random walk. This formulation is modified and sometimes rearranged in different ways by the three UR tests used

*Yt* ¼ *μ* þ *βt* þ *ρYt*�1 þ *et* (6)

abrupt and deterministic change in a deterministic time-series.

*Severe Testing and Characterization of Change Points in Climate Time Series*

issue was extensively examined in R2019 and is addressed later.

*4.3.7 Unit roots, non-stationarity, and climate*

*DOI: http://dx.doi.org/10.5772/intechopen.98364*

deterministic change-point analysis is suspect.

*4.3.8 Detecting unit root presence*

a UR test.

here.

**219**

Fuller (DF) model [48].

The term unit-root refers to processes with a characteristic equation that has a value of one. If a unit characteristic is moving average, the error is integrated order zero or I(0), if it is auto-regressive, it is integrated order one, I(1). I(0) processes tend to revert to a mean, I(1) processes follow a martingale [44], and is dominated by red-noise. The integration order defines the number of successive differencing operations required to produce a trend-stationary series.

#### *4.3.4 Residuals compared to initial data*

In our work, both the raw data, and the residuals after removal of internal steps and trends, are tested. The rationale for testing both derives from the formulation of the tests themselves, since in these tests, the deterministic and non-deterministic components are separately parameterised. The set of tests chosen are from the econometric literature, and each is framed as a null hypothesis significance test (NHST) with its own specific assumptions. Each test poses either *H0* or *H1* as presence of an assumed non-deterministic unit root progression (see Chapter 2) in data, and the alternatives are chosen from a small range of deterministic features. Crucially, each must be interpreted in the light of its own ruling assumptions.

### *4.3.5 The full process applied to a single time-series*

The program of tests thus sharpens the error-statistical reasoning component of the TM/SI framework.

#### *4.3.6 Deceptive features detectable with unit root tests*

The application of deterministic methods such as OLS to non-deterministic data progression such as a random walk is a misspecification; the results may be deceptive with meaningless shifts and/or trends. Unit root (UR) tests probe the data for features that can superficially imitate deterministic structural changes by cumulative random walks, a red or near red progression. It has been shown by Monte Carlo methods that a test for deterministic trends will find deterministic trends in about 85% of realizations that contain only a stochastic (UR) trend [45]. However combinations of UR tests may also be used to detect both stochastic and deterministic non-stationary sequences, due their varied ruling assumptions and constructions.

Because multiple UR tests are performed, and because they each have differing ruling assumptions, the tests are interpreted in terms of evidence for and against stationarity in the underlying processes. In the econometric literature an exogenous change is one imposed upon a model from outside the model. We elected to retain this word where concepts were derived from economic papers as meaning an abrupt and deterministic change in a deterministic time-series.

## *4.3.7 Unit roots, non-stationarity, and climate*

Transient unit root behaviour, if it occurred, could indicate some sort of regime change, temporarily decoupled from normal forcings. If, in addition, measured noise was not persistent this would show I(0) behaviour; or, if it were fully persistent, as I(1) behaviour. In regional signals in which this occurs, the region may also have become coupled to other sub-systems [46]. This could indicate that the underlying physical model is incomplete and that a missing variable misspecification has resulted. On the other hand, persistent unit root behaviour means that a deterministic change-point analysis is suspect.

The Earth system is constrained so that the overall temperature cannot solely follow a pure random walk – at worst it would follow a Brownian bridge (i.e. sequences where the end-points are meaningful and accepted as deterministic but the path is apparently a random walk [47]). However the composition of summary deterministic signals, such as the GMST, involves manipulations that can produce data that existing unit root tests will identify as containing unit roots, and furthermore deceive deterministic tests in much the same way as random walk data. This issue was extensively examined in R2019 and is addressed later.

#### *4.3.8 Detecting unit root presence*

Random walk progression may be present in climate data because of transient physical conditions, or because the data is unrelated to the physical processes assumed (M-S due to irrelevant variables). Additionally there may be features in the data that do not correspond to any of a shift, a trend change, or unit root behaviour (M-S due to missing variables), and UR tests are potentially sensitive to this. This source of deception must also be dealt with. Other features may be present in the data but not detected. For instance, a step-like shift well above a detectability threshold may be present together with a number of small, deterministic shifts below detectability, and this latter may be taken to be evidence of stochastic drift by a UR test.

The unit root based tests used here all inherit in one form or another the Dickey Fuller (DF) model [48].

$$Y\_t = \mu + \beta t + \rho Y\_{t-1} + \mathbf{e}\_t \tag{6}$$

*ρ* represents the portion of the signal (*Yt*�1) carried forward by autocorrelation, *β* represents the (deterministic) linear trend, *μ* represents the intercept, and *et* is the i.i.d. error with zero mean and a constant variance *σ*2. If *ρ* ¼ 0 this describes a deterministic trend with no autocorrelation, if 0>*ρ* <1 there is a deterministic trend with a degree of autocorrelation, and if *ρ* ¼ 1, regardless of other parameters it contains a unit root. If all other parameters are zero and *ρ* equals one, then there is no deterministic trend, no offset, and *Yi* is a random walk. This formulation is modified and sometimes rearranged in different ways by the three UR tests used here.

It is important to note that time-series of successive differences of a step-change in an otherwise stationary time series will contain only one out of range difference. Hence the DF model is intrinsically insensitive to deterministic step changes. Another important property of a unit root process is that the variance of the process increases over time, whereas the variance of a stationary process is constant. This gives a second strategy for determining unit root like behaviour – testing for diverging variance. The Kwiatkowski-Phillips-Schmidt-Shin test (KPSS), [49] examines the properties of the variance rather than the fitted parameters, and it primarily focussed on determination of stationarity. As a result it is more sensitive to exogenous changes.

Eq. (6) is expanded to allow for multiple lags in the case of the Augmented Dickey Fuller (ADF) test, taking advantage of the recursive nature of the formula.

A unit root exists if *ρ*1 ¼ 1. The number of lags can be specified by the user or, as

The ADF test implementation used is programmed in R, available in the package 'urca' [57], and estimate and removes auto-correlation then applies a DF test. The code allows for three variants, are available, (a) a unit root, (b) a unit root with drift, and (c) a unit root with drift and a deterministic time trend – which corresponds to the model of Eq. (7) (above) and which we use. We select suitable autocorrelation lags on the basis of an information criterion, using the call "ur.df (ys, type = "trend", lags = 7, selectlags = "AIC")" following Hacker [58]. The resulting possible reduction in power in the test (inability to distinguish unit root from near unit root) is compensated by other tests in the suite. The test assumes no exogenous change, and *H0* may be accepted in the presence of one

There are two variant of the KPSS test used here to test for level and trend stationarity. These tests invert the sense of the testing with respect to the ADF test, rejecting an *H0* of stationarity in favour of *H1*, a presumption of a unit root. In this case a regime shift may well appear as *H1*, with a step change being non level stationary and a trend change being non trend stationary. We use the R package 'tseries' [60] and invoke the two tests as kpss.test(ys), to test for level stationarity (henceforth KPSS-L) and kpss.test(ys,null = "Trend") to test for trend stationarity

KPSS tests are designed to give weight to stationarity. Assuming that the timeseries can be decomposed into the sum of a deterministic trend, a random walk and a stationary error, the model of Eq. (6) is re-parameterised as follows with *rt*

*Yt* ¼ *rt* þ *βt* þ *u*1*t*

*rt* ¼ *rt*�1 þ *u*2*t*

Where *u*1*t* is a stationary process, and *u*2*t* is an i.i.d. process with zero mean and a

If *σ*2 ¼ 0 then *rt* is constant and the stationary process*u*1*t* dominates. If not, then a unit root enters via *u*2*t* and *rt* is a random walk. Under a random walk, variance increases with time. Therefore this expectation is tested by estimating the variance

series (f g *e*1*::en* ) is given by residuals of an OLS linear regression (f g *e*1*::en* ).). To test for level stationarity the residual series is replaced by *et* ¼ *yt* � *y*. Then for both

2 . To test for trend stationarity, a residual

*i*¼1*ei* and for *T* samples, the test

*k*

*j*¼2

*j*¼2*ρ j*

*ρ j*Δ*yt*�*j*þ1 þ *et* (7)

Δ*yt*�*j*þ1.

(8)

This is more explicit below where *k* multiple lags are included as P*k*

*Severe Testing and Characterization of Change Points in Climate Time Series*

Δ*Yi* ¼ *b*0 þ *b*1*t* þ ð Þ *ρ*1 � 1 *Yi*�1 þX

The difference series is then computed,

*DOI: http://dx.doi.org/10.5772/intechopen.98364*

([59], page 76).

(henceforth KPSS-T).

variance *σ*2.

statistic is given as

**221**

representing the random walk

using the Newey-West estimator [61] *s*

cases, partial sums of residuals are defined as *St* ¼ P*i*

**5.2 KPSS**

here, selected by using an information criterion.

## **5. Proposed tests and strategies**

The unit root methods used are all coded in R and are, (a) a development of the DF test, the Augmented Dickey-Fuller test (ADF), which takes *H0* of a I(1) unit root against an alternative *H1* of a presumption of no unit root (in this implementation trend and multiply lagged autocorrelation is allowed for), (b) two variants of the KPSS, which takes a *H0* of stationarity (or trend-stationarity) rejecting it in favour of an alternative *H1* of a presumption of unit root, and (c) the Zivot-Andrews test (ZA) [50], which takes a *H0* of I(1) unit root behaviour with a possible endogenous drift against an alternative *H1* of trend-stationarity with exogenous structural change. A trend change or a step change would constitute an exogenous structural change.

Use of a combination of UR tests is not new. The combination of ADF and of KPSS testing has been used before in order to add precision to an analysis of monthly inflation expectations (e.g. [51] Appendix B).

The tests are being applied to data within which a single presumptive deterministic, exogenous, step-like changes was detected. No such change is allowed for in the KPSS and ADF tests, the presumption of unit-root in *H0* or *H1* of the above tests is reinterpreted as evidence of non-stationarity. Evidence of unit-root like behaviour is then sought by examination of the residuals after the removal of the deterministic internal trends and shifts detected in the data.

In general, where evidence of a unit-root is detected, it may be due to undetected deterministic features, and hence will be initially treated as evidence of either deterministic non-stationarity or stochastic non-stationarity.

For all of the above tests, the R implementations take published critical values of the test statistic at the 0.01, 0.05, and 0.1 levels. The KPSS implementation interpolates the test statistic against these values to give probabilities between 0.01 and 0.1, the ADF and ZA implementations simply give the critical values and the test statistic.

None of the tests proposed consider unit root presence or absence when possible structural breaks (such as shifts or trend changes) exist under both the null and alternate hypotheses. The problem is under active consideration [52–54].

#### **5.1 ADF**

The ADF test is a variation of the Dickey Fuller test for trend stationarity in the possible presence of unit root. It has a null hypothesis of unit root against an alternative of stationarity after compensation for auto-correlation [48, 55]. The ADF test has relatively low power, and in this type of application a finding of a UR may be because of a single deterministic permanent shift or trend-change [56], as noted above.

*Severe Testing and Characterization of Change Points in Climate Time Series DOI: http://dx.doi.org/10.5772/intechopen.98364*

Eq. (6) is expanded to allow for multiple lags in the case of the Augmented Dickey Fuller (ADF) test, taking advantage of the recursive nature of the formula. This is more explicit below where *k* multiple lags are included as P*k j*¼2*ρ j* Δ*yt*�*j*þ1. The difference series is then computed,

$$
\Delta Y\_i = b\_0 + b\_1 t + (\rho\_1 - 1)Y\_{i-1} + \sum\_{j=2}^k \rho\_j \Delta y\_{t-j+1} + \mathbf{e}\_t \tag{7}
$$

A unit root exists if *ρ*1 ¼ 1. The number of lags can be specified by the user or, as here, selected by using an information criterion.

The ADF test implementation used is programmed in R, available in the package 'urca' [57], and estimate and removes auto-correlation then applies a DF test. The code allows for three variants, are available, (a) a unit root, (b) a unit root with drift, and (c) a unit root with drift and a deterministic time trend – which corresponds to the model of Eq. (7) (above) and which we use. We select suitable autocorrelation lags on the basis of an information criterion, using the call "ur.df (ys, type = "trend", lags = 7, selectlags = "AIC")" following Hacker [58]. The resulting possible reduction in power in the test (inability to distinguish unit root from near unit root) is compensated by other tests in the suite. The test assumes no exogenous change, and *H0* may be accepted in the presence of one ([59], page 76).

#### **5.2 KPSS**

There are two variant of the KPSS test used here to test for level and trend stationarity. These tests invert the sense of the testing with respect to the ADF test, rejecting an *H0* of stationarity in favour of *H1*, a presumption of a unit root. In this case a regime shift may well appear as *H1*, with a step change being non level stationary and a trend change being non trend stationary. We use the R package 'tseries' [60] and invoke the two tests as kpss.test(ys), to test for level stationarity (henceforth KPSS-L) and kpss.test(ys,null = "Trend") to test for trend stationarity (henceforth KPSS-T).

KPSS tests are designed to give weight to stationarity. Assuming that the timeseries can be decomposed into the sum of a deterministic trend, a random walk and a stationary error, the model of Eq. (6) is re-parameterised as follows with *rt* representing the random walk

$$\begin{aligned} Y\_t &= r\_t + \beta t + u\_{1t} \\\\ r\_t &= r\_{t-1} + u\_{2t} \end{aligned} \tag{8}$$

Where *u*1*t* is a stationary process, and *u*2*t* is an i.i.d. process with zero mean and a variance *σ*2.

If *σ*2 ¼ 0 then *rt* is constant and the stationary process*u*1*t* dominates. If not, then a unit root enters via *u*2*t* and *rt* is a random walk. Under a random walk, variance increases with time. Therefore this expectation is tested by estimating the variance using the Newey-West estimator [61] *s* 2 . To test for trend stationarity, a residual series (f g *e*1*::en* ) is given by residuals of an OLS linear regression (f g *e*1*::en* ).). To test for level stationarity the residual series is replaced by *et* ¼ *yt* � *y*. Then for both cases, partial sums of residuals are defined as *St* ¼ P*i i*¼1*ei* and for *T* samples, the test statistic is given as

$$LM = \frac{\sum\_{i=1}^{T} \mathbb{S}\_i^2}{s^2 T^2} \tag{9}$$

**5.4 Empirical quantification of false determination rates**

*Severe Testing and Characterization of Change Points in Climate Time Series*

both UR and non-UR separately, for each test.

*DOI: http://dx.doi.org/10.5772/intechopen.98364*

method hold for the segment of data and to what extent?

tional deterministic change-points below detection thresholds.

discontinuous trend stationary data fitted appropriately.

the residuals supports the existence of a change-point.

Monte Carlo method.

**5.5 Applying these UR tests**

low *p*-values by ANCOVA.

*5.5.1 Level stationarity*

*5.5.2 Trend stationarity*

showing non-stationarity.

**223**

All of these tests are posed as null hypothesis tests. As such they only reject the null hypothesis at a particular level once sufficient evidence is found against it, and when the data size is limited, the power (the probability of correctly rejecting the null hypothesis) is similarly reduced. Therefore, in R2019 (page 100) the four tests were each tested separately for their false positive and false negative rates using a

This aids interpretation since data segments vary in length. Before proceeding further, one may ask how meaningful the nominal *p-*values are, or as in R2019, one can determine the minimum data length required to allow acceptance of a finding of

Assuming an objective change-point method has been used bounded between two objectively determined change-points. Do the assumptions of the detection

These tests are all applied to the segments of data within which a single changepoint has already been provisionally identified. The change-point itself is not otherwise considered. However, since the climate data being tested provisionally contains a deterministic change and only the ZA test is formulated with this as a ruling assumption, findings of non-stationarity may be caused by the presence of addi-

Level stationarity is not simply a zero trend, since data with zero trend may be either deterministically or stochastically level, and even if deterministic may not be linear. A deterministic change-point detection method may return indeterminate change-points given non-linear trend. The residuals around stochastic trend will retain a UR characteristic. Trend stationary data has level stationary residuals, as do

A segment of data with a valid change point should not be found to be level stationary, it should not be in a segment with unit root behaviour, and if it shows trending behaviour this should not be due to a drifting unit root. It should also have

The KPSS-L test is used here with an expectation that segments of climate data in which a change-point occurs contain a step-like shift but may also contain a change of trend. Hence it is used as a cross check. Further, once the deterministic internal shift and trend components are removed the residual should be both level and trend stationary. Level non-stationarity in the segment and level stationarity in

Data with a provisional change of trend is expected to be non-trend-stationary.

Data with constant trend and a step-like change may show as trend stationary depending on the assumptions of the specific test. The KPSS-T test and the ADF test as formulated here may return different results in the presence of a step-like shift and no trend change, with the ADF test showing trend stationarity and the KPSS

Both the ADF test and the ZA test below, perform by estimating an autoregression parameter by OLS, whereas the KPSS tests examine the properties of the variance of the time series (KPSS-L) or of the difference series (KPSS-T).

#### **5.3 Zivot-Andrews test**

The previous tests are confounded by deterministic/exogenous change (steps or shifts), and additionally a combination non-deterministic and deterministic change must be detected.

The Zivot-Andrews test (ZA) [50] tests for the presence of a unit root (with a possible deterministic/exogenous change) against an alternative of stationarity with at most one exogenous change. An advantage is that the test also returns a time of a possible exogenous change [62] – but note that an exogenous change can be any of step, transient or trend change.

The code is in the R package "urca", called as "ur.za(ys, model = "both")", which allows for changes in trend or steps. *H0* is UR without exogenous change. *H1* is trend-stationary with a possible exogenous change at an unknown time.

The ruling assumptions are (a) that there is at most one exogenous structural change (b) in a multivariable model, that only one exhibits unit root. In either of these cases other tests are preferred [54]. Here, we are testing a single variable with intervals bounded by breaks within which we have already detected exactly one break, whilst others may be below a detectability threshold. It has been previously shown that rejection of the null of a unit root could be due to a structural break even in the presence of unit root [63], whilst the presence of more than one break in the absence of a unit root may lead to the acceptance of the *H0* of UR [64].

Acceptance of *H0* does not imply merely UR, but rather, UR without exactly one deterministic break, [56], and thus *H1* means not UR or not a single break. Given we know there is a break (detected by MSBV, confirmed by ANCOVA), *H1* is reinterpreted as not UR, or more than one break.

The model used here is that documented by Zivot and Andrews (50) as Model (C). The model follows the ADF approach and its equation contains more complex parameters for: intercept and change of intercept (a step-like change), *μ*^ þ *θDUt* ^*λ* � �; and trend and change of trend, *β*^*t* þ ^*γDT*∗ *t* ^*λ* � �. The remaining parameters are similar to the ADF; autocorrelation with lags, *α*^*yt*�1 þ P*k j*¼1^*cj*Δ*yt*�*j* and the presumed i.i.d. error …

$$\mathcal{Y}\_t = \hat{\mu} + \theta \mathcal{D} U\_t(\hat{\lambda}) + \hat{\beta}t + \hat{\gamma} \mathcal{D} T\_t^\* \left(\hat{\lambda}\right) + \hat{\alpha} \mathcal{Y}\_{t-1} + \sum\_{j=1}^k \hat{c}\_j \Delta \mathcal{Y}\_{t-j} + \mathcal{e}\_t \tag{10}$$

Circumflexes above represent estimates of parameters. ^*λ* is a value that is minimised during the search for the most likely time of a break, *DUt* ^*λ* � � ¼ 1 if *t*> *Tλ*, the time of change, 0 otherwise, and *DT*∗ *t* ^*λ* � � ¼ *t* � *Tλ* if *t*>*Tλ*, 0 otherwise. Parameters estimated include the time of change and each of the parameters of the above model. ^*λ* is estimated so as to minimise the one side t-statistic for *α* ¼ 1, which in turn leads to rejection of the null. One should note that in the absence of any deterministic change-point the test functioned as a stationarity test when empirically assessed.


**Author details**

**4. Chapter summary**

118 Contemporary Gynecologic Practice

logic corticosteroid dosages.

treating CAH.

vitamin D3.

PCOS.

**5. Nomenclature**

CAH-congenital adrenal hyperplasia

17-OHP-17-hydroxyprogesterone

eGFR estimated glomerular filtration rate

NCAH-non-classic congenital adrenal hyperplasia

PCOS-polycystic ovarian (Stein-Leventhal) syndrome

linemia.

**•** Insulin resistance/hyperinsulinemia is a constant feature of both classical and non-classic

**•** In vitro studies suggest that 2 mechanisms for the above observation are gain of 17-αhydroxylase activity and decrease of 21-hydroxylase activity in the presence of hyperinsu‐

**•** Interventions which reduce insulin resistance/hyperinsulinemia dependably ameliorate the phenotypic/biochemical course of CAH and acquired/unmasked adrenal hyperplasia as they do in PCOS. In the case of NCAH insulin sensitizing interventions eliminate the need for corticosteroids and their attendant side effects, while in classical CAH insulin sensitiza‐ tion shows at least an ability to ameliorate the condition without resorting to supraphysio‐

**•** Other drugs and herbals with insulin sensitizing properties may ultimately prove useful in

**•** Cysticercosis is able to evoke a 4 part endocrine disrupting effect in the human host: insulin resistance, hyperandrogenism, feminization, and enhance 1-α-hydroxylation of 25-OH-

**•** Modifying the cysticercosis-evoked hormonal milieu with the insulin sensitizer, metformin and the SERM, raloxifene is capable of effectively treating cysticercosis induced PCOS, reducing the parasite burden, and reversing the overexpression of 1-α-hydroxylase.

**•** Serial measurement of vitamin D metabolites may prove to be a fairly economical way of

**•** Cysticercosis may ultimately prove to be a fairly common cause of insulin resistance and

following parasite burden and treatment response compared to serial MRI.

adrenal hyperplasia as well medication induced/unmasked adrenal hyperplasia.

Alan Sacerdote1,2,3,4 and Gül Bahtiyar1,2,3,4

1 Division of Endocrinology, Woodhull Medical and Mental Health Center, Brooklyn, NY, USA


*3.6. Validation of RNA-Seq Gene Expression Levels Using RT-qPCR*

To validate the accuracy of RNA-Seq results, ten genes in HL60 and KG1a were also detected by RT-qPCR. As a result, the RNA-Seq-detected expression regulation of 20 genes were verified by RT-qPCR detection (Figure 7A,B). Additionally, the qPCR-detected CD38 expression (Figure 1E) was also in agreement with that detected by RNA-Seq (Figure 3B). These data indicated that the RNA-Seq results were reliable.

**Figure 7.** Validation of RNA-Seq DEGs using RT-qPCR: (**A**,**B**) the expression levels of 10 selected DEGs in the iron nanoparticle-treated HL60 (**A**) and KG1a (**B**) cells. All values are mean ± SD with *n* = 3. ns, no significance; \*, *p* < 0.05; \*\*, *p* < 0.01, \*\*\*, *p* < 0.001, \*\*\*\*, and *p* < 0.0001. (**C**,**D**) The comparison of fold change detected by RT-qPCR and RNA-Seq in the iron nanoparticle-treated HL60 and (**C**,**D**) KG1a cells.


*2.2. Building Description*

The case study of this work is the Rectorate building of the University of the Basque Country (Spain) constructed in the 1970s. It is a large building divided in three blocks (west, central and east), as shown in Figure 1. For the purpose of this work, only the west block was considered, which is an office building that includes a nursery. Four storeys form the block: floor 0 (Ground Floor) and Floor 2 (2F) consist of rooms and offices while Floor 1 (1F) and Floor 3 (3F) are mainly open spaces (see Figure 2). As the building use is office work, the occupation takes place only during weekdays, being reduced during summer. There is lighting consumption from 7 a.m. to 8 p.m., except on the second floor, where lighting consumption ends at 6 p.m. The building has a centralised heating system with hot water radiators powered by a campus district heating. The heating works the whole year following a control program according to a schedule from 6 a.m. to 7 p.m. except in July and August, when the heating remains off. A refurbishment of the building was made in the summer of 2016 on the ground floor and in the summer of 2017 in the rest of the building to reduce its energy consumption.

**Figure 1.** (**a**) View of the whole rectorate building that is formed by three blocks (west, central and east). This work focussed in the study of the retrofitting measures carried out in the west block. (**b**) West block before retrofitting. (**c**) West block after retrofitting.

### 2.2.1. Building Description before Retrofitting

Before the retrofitting, the building did not have any insulation. Most of the façade was built with precast reinforced concrete panels with non-ventilated air gap. Regarding the windows, some were single-glazed with wooden frame, and others were double-glazed but with aluminium frame without thermal break. Before retrofitting, there was no air conditioning or mechanical ventilation system.

### 2.2.2. Building Description after Retrofitting

The refurbishment consisted in several measures to improve the building's envelope and energy system. The façade was insulated with vacuum insulated panels (VIPs) to reduce heat losses through the envelope. Some windows were replaced by high-performance windows. To improve the lighting consumption of the building, LED lighting was installed. A ventilation system with heat recovery was added on each floor. Furthermore, thermostatic valves were installed to improve the control of the hot water radiators. A detailed description of the refurbishment and an assessment of the heat loss coefficient of the building is provided in [20].

**Figure 2.** Plans of the four floors in the west block of the building with their space distribution and dimensions. The use of each space is represented with colours: offices (brown), nursery (green), storage rooms (grey), corridors (pink) and server room (blue). In addition, the distribution of the sensors is also displayed: circles, illuminance, temperature and relative humidity; triangles, calorimeters; and square, lighting consumption.

### 2.2.3. Monitoring Description of the Building

The monitoring started before the refurbishment to investigate the necessary energy conservation measures. Thus, monitored data before and after retrofitting from sensors located all around the building are available. Monitored data before retrofitting correspond to 2016 and 2017, and data after retrofitting correspond to s 2018 and 2019; all data are minute-by-minute values. In particular, on the ground floor, the renovation started a year earlier with the insulation of a false ceiling and the installation of LED lighting. In this case, the years considered before retrofitting are 2015 and 2016. The monitored variables include outdoors conditions, indoors conditions and building heating and lighting consumption. Table 1 presents all the monitored variables in the building used to assess the impact that the retrofitting had on the building's energy performance, comfort and lighting. Indoor condition sensors are located in several points at each floor, as shown in Figure 2. The electrical consumption and the heating demand is provided per floor. Further information about the monitoring of the building can be found in the work carried out by Erkoreka et al. [69].


**Power Efficient Data-Aware SRAM Cell for SRAM-Based FPGA Architecture**

Ajay Kumar Singh

[20] S. Keshavarapu, S. Jain and M. Pattanaik. A New Assist Technique to Enhance the Read and Write Margins of Low Voltage SRAM Cell. In: International Symposium on Electronic System Design (ISED); Kolkata. IEEE Computer Society Conference Pub‐

[21] R. Gupta, V. Gadi, H. A. Upendar. Write Assist Scheme to Enhance SRAM Cell Relia‐ bility Using Voltage Sensing Technique. In: International Conference on Embedded

[22] S. Keshavarapu, S. Jain and M. Pattanaik. A New Assist Technique to Enhance the Read and Write Margins of Low Voltage SRAM Cell. In: International Symposium on

lishing Services (CPS); 2012. p. 97–101.

Electronic System Design; 2012. p. 97–101.

Systems; 2016. p. 318–322.

220 Field - Programmable Gate Array

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67257

#### **Abstract**

The design of low‐power SRAM cell becomes a necessity in today's FPGAs, because SRAM is a critical component in FPGA design and consumes a large fraction of the total power. The present chapter provides an overview of various factors responsible for power consumption in FPGA and discusses the design techniques of low‐power SRAM‐ based FPGA at system level, device level, and architecture levels. Finally, the chapter proposes a data‐aware dynamic SRAM cell to control the power consumption in the cell. Stack effect has been adopted in the design to reduce the leakage current. The various peripheral circuits like address decoder circuit, write/read enable circuits, and sense amplifier have been modified to implement a power‐efficient SRAM‐based FPGA.

**Keywords:** FPGA, ASIC, static power, dynamic power, leakage current, SRAM cell, subthreshold cell, data‐aware SRAM cell


*2.4. Pearson Correlation*

This association method's primary goal is to identify two or more correlated variables [45].

The Pearson correlation coefficient measures the degree of correlation between two variables in a linear approach. Let *X* and *Y* be those variables, with measurements given by {*x*1, *x*2, *x*3, ..., *xn*} and {*y*1, *y*2, *y*3, ..., *yn*} and means *x* and *y*. Then, the Pearson coefficient is given by Equation (3) [42].

$$\rho(X,Y) = \frac{\sum\_{i=1}^{n} \left(x\_i - \overline{x}\right) \left(y\_i - \overline{y}\right)}{\left[\sum\_{i=1}^{n} \left(x\_i - \overline{x}\right)^2 \sum\_{i=1}^{n} \left(y\_i - \overline{y}\right)^2\right]^{\frac{1}{2}}} \tag{3}$$

A Pearson coefficient with the range *ρ* = [−1, 1] represents the level of correlation when *ρ* is positive and correlation is direct, and the negative is the inverse [42].

When two variables are highly correlated, one can be redundant. The Pearson correlation works only for linear relations and results in incorrectly measured correlations for nonlinear systems. When classifying with binary outputs, it is possible to identify using Pearson coefficients how an attribute correlates with the target class [42].

Additionally, one can perform a correlation statistical significance test using the *pvalue* coefficient, such as a test of the probability that the correlation coefficient *ρ* is a wrong hypothesis; for example, as a convention from the literature, if *pvalue* > 0.05, it is unreliable. The alternatives for such a determination include statistical tests, such as the *tvalue*, variance analysis (ANOVA), and 1*tailed* or 2*tailed* tests [48].


*Article* **Climatic and Non-Climatic Drivers of Plant Diversity along an Altitudinal Gradient in the Taihang Mountains of Northern China**

**Hongzhu Liang 1,2,3,†, Tonggang Fu 1,†, Hui Gao 1, Min Li 3 and Jintong Liu 1,\***

**Abstract:** Climate is critical for plant altitudinal distribution patterns. Non-climatic factors also have important effects on vegetation altitudinal distribution in mountain regions. The purpose of this study was to explore the current distribution of plant diversity along the altitudinal gradient in the Taihang Mountain range of northern China and to estimate the effects of climatic and non-climatic factors on the elevational pattern. Through a field survey, a total of 480 sampling plots were established in the central Taihang Mountain range. Alpha diversities (the Shannon–Weiner index and Simpson index) and beta diversities (the Jaccard index and Cody index) were measured based on the survey data. Plant community structure change based on the altitudinal gradient was explored by measuring the diversity indices. Canonical correspondence analysis was carried out to determine the factors influencing plant altitudinal distribution. The contributions of climatic and non-climatic factors on plant distribution were determined by partial methods. The results showed that the plant diversity of the elevational gradient complied with a "hump-shaped" pattern, in which communities in the medium altitude area with higher plant diversity had a higher species turnover rate, and non-climatic factors, particularly the anthropogenic factors, had an important influence on the plant altitudinal pattern. In conclusion, climatic and non-climatic factors both had important effects on the plant altitudinal pattern. It is strongly recommended to reduce human interference in mountain vegetation protection and management.

**Keywords:** α- and β-diversity; vascular plants; altitudinal distribution pattern; canonical correspondence analysis; anthropogenic disturbance; Taihang Mountains


**3.11 Emerging treatments in NAFLD/NASH**

Apart from the established treatments, that have been discussed above, there have been also other therapeutic agents that have been shown to be promising in the treatment of NAFLD/NASH (**Figures 11** and **12**). These agents interfere in various stages of the metabolic pathway and may show significant results in improving the radiologic and histologic findings [36].