The traditional blood glucose estimation method requires to take the invasive measurements several times a day. Therefore, it has a high infection risk and the users are suffered from the pain. Moreover, the long term consumable cost is high. Recently, the wearable and non‐invasive blood glucose estimation approach has been proposed. However, due to the unreliability of the acquisition device, the presence of the noise and the variations of the acquisition environments, the obtained features and the reference blood glucose values are highly unreliable. Moreover, different subjects have different responses of the infrared light to the blood glucose. To address this issue, a polynomial fitting approach to smooth the obtained features or the reference blood glucose values has been proposed. In particular, the design of the coefficients in the polynomial is formulated as the various optimisation problems. First, the blood glucose values are estimated based on the individual optimisation approaches. Second, the absolute difference values between the estimated blood glucose values and the actual blood glucose values based on each optimisation approach are computed. Third, these absolute difference values for each optimisation approach are sorted in the ascending order. Fourth, for each sorted blood glucose value, the optimisation method corresponding to the minimum absolute difference value is selected. Fifth, the accumulate probability of each selected optimisation method is computed. If the accumulate probability of any selected optimisation method at a point is greater than a threshold value, then the accumulate probabilities of these three selected optimisation methods at that point are reset to zero. A range of the sorted blood glucose values are defined as that with the corresponding boundaries points being the previous reset point and this reset point. Hence, after performing the above procedures for all the sorted reference blood glucose values in the validation set, the regions of the sorted reference blood glucose values and the corresponding optimisation methods in these regions are determined. It is worth noting that the conventional lowpass denoising method was performed in the signal domain (either in the time domain or in the frequency domain), while the authors’ proposed method is performed in the feature space or the reference blood glucose space. Hence, the authors’ proposed method can further improve the reliability of the obtained feature values or the reference blood glucose values so as to improve the accuracy of the blood glucose estimation. Moreover, the individual modelling regression method has been employed here to suppress the effects of different users having different responses of the infrared light to the blood glucose values. The computer numerical simulation results show that the authors’ proposed method yields the mean absolute relative deviation (MARD) at 0.0930 and the percentage of the test data falling in the zone A of the Clarke error grid at 94.1176%. The PPGs are acquired. After performing the SSA bit plane denoising and extracting various features, the feature smoothing via the fusion of various optimisation approaches is performed. Finally, the random forest is employed for performing the blood glucose estimation. It is a common disease that severely affected the human life and the public health. According to the report issued by the International Diabetes Federation (IDF), an extra of 73.6 millions of people in the worldwide will be suffered from the diabetes at 2045 , 2. As tTo monitor the blood glucose values, the traditional method is to have the measurements via the finger prickle approach several times a day. However, this approach has the infection risk  and the In many practical data acquisition applications, the regression based smoothing techniques including the linear regression method, the polynomial regression method, the radial basis function regression method and the Fourier basis regression method are used for performing the data pre‐processing to eliminate the acquisition errors. Since the order of the polynomial can be changed easily to meet the required specification on the accuracy, this method has a great flexibility. Therefore, the polynomial regression method was widely used in the image processing community, the data processing community and the parameter estimation community. Besides, some parameter design methods were proposed recently. For examples, the full vector based finite element method with an anisotropic perfect matched layer added to the designed model as a boundary condition was employed , 14, 15.L1 norm of a vector is the sum of the absolute values of its elements. By minimising the L1 norm of an error vector, the majorities of the error points are with the small values. As the error vector is sparse, it yields a good estimation for the majority of the data points. Besides, the L∞ norm of a vector is the maximum absolute value of its elements. By minimising the L∞ norm of an error vector, the data points with the large errors are reduced. Recently, the sparse optimisation approach and the risk optimisation approach were used for performing the data smoothing [L2 norm of a vector is the square root of the sum of the squares of its elements. The L2 norm error values are between the L1 norm error values and the L∞ norm error values. Moreover, as the L2 norm error function is differentiable, the conventional gradient descent approach can be used to find the solution of the optimisation problem. Because of this reason, the L2 norm error function is widely used for finding the coefficients of the polynomial for performing the smoothing operation. This is also known as the least squares approach. By applying different approaches with different error norm functions for performing the smoothing operation, different smoothed features are yielded. However, no individual approach is appropriate for estimating all the data points. Hence, the fusion of these three approaches is required. Nevertheless, there is no simple rule for performing the fusion. Hence, this paper is to address this issue.On the other hand, the moothing . Apart fThis paper is to address the unreliability of both the extracted features and the reference blood glucose values. First, this paper employs the individual modelling approach to train the regression system. This can eliminate the effects of different subjects having different responses of the infrared light to the blood glucose values. Second, this paper proposes a method to fuse the various optimisation approaches together for performing the polynomial fitting to smooth the features. This can improve the reliability of the extracted features and the reference blood glucose values. Compared to the commonly used data smoothing methods such as the moving averaging method, the Gaussian filtering method, the median filtering method, the locally weighted regression method and the Savitzky Golay (SG) filtering method, the computer numerical simulation results show that our proposed method outperforms the existing methods.A feature domain based smoothing method is proposed to improve the reliability of the obtained features and the reference blood glucose values.A method is proposed for fusing the various optimisation approaches for performing the polynomial fitting to smooth the obtained features and the reference blood glucose values.An individual data modelling approach is proposed for performing the blood glucose estimation. This can effectively eliminate the effects of different individuals having different responses of the infrared light to the blood glucose values so as to improve the reliability of the obtained features and the reference blood glucose values.The main contributions of this paper are as follows:The outline of this paper is as follows. Section 22.1The near infrared spectroscopy is a study of the electromagnetic wave. When a beam of photons is hit on the substances in the human tissue , 8, the It is worth noting that the autonomic nerves play a vital role in regulating the various physiological activities of the body . HoweverBesides using the absorption of the near infrared light and the HRV to estimate the blood glucose levels, the transit time of the PPG was also used to estimate the blood glucose values . In part2.2Eight volunteers are recruited for performing the data acquisition. In particular, the subjects take the ketogenic diet during the first 4 days, the normal diet between the fifth day and the eighth day as well as drinking cola after lunch and dinner during the last 4 days. Figure 2.3The block diagram of our proposed algorithm is shown in Figure 2.3.1There are two sets of acquisition devices for acquiring the PPGs. Figure The Bene Check blood glucose metre and the Yuwell sphygmomanometer are employed to take the reference blood glucose value and the reference blood pressure values, respectively. Both devices have the FDA certification. Here, three measurements are taken every time and every measurement only takes one reference blood glucose value as well as one systolic blood pressure (SBP) value and one diastolic blood pressure (DBP) value. Then, the average of these three reference blood glucose values as well as the average of these three SBP values and the average of these three DBP values are employed as the final reference values.In order to obtain the reference blood glucose values and the reference blood pressure values, the Bene Check blood glucose metre and the Yuwell sphygmomanometer are employed for the acquisitions, respectively. It is worth noting that both the devices have the corresponding FDA certifications. In this paper, three measurements are taken every time and every measurement only takes one reference blood glucose value as well as one SBP value and one diastolic blood pressure (DBP) value. Then, the average of these three reference blood glucose values as well as the average of these three SBP values and the average of these three DBP values are employed as the corresponding final reference values.2.3.2To perform the training, all the PPGs acquired from an individual subject are mixed together. Then, the individual dataset is randomly divided into two non‐overlapped subsets. They are the training set and the test set. In particular, approximately 75% of the individual dataset is defined as the training set and the rest approximately 25% of the individual dataset is defined as the test set. Figure 2.3.3Since the HRs of different subjects are different, the frequency bands of different PPGs acquired from different subjects are different. Hence, an adaptive based denoising method is required to address this problem. Among them, the singular spectrum analysis (SSA) based denoising method is the most common adaptive denoising method. However, the conventional SSA based denoising method is to discard the whole SSA component. In this case, some signal information is lost. To address this issue, an SSA based bit plane method is employed for denoising the PPGs. First, the SSA is applied to all the PPGs in both the training set and the test set. Here, the SSA decomposes each PPG into 32 components. Second, for each value in each SSA component, it is represented using a finite number of bits. In this paper, the word length of each value is 13 bits. Third, the noise level of each SSA component is estimated. Fourth, the total number of bits corresponding to the noise contaminated to each SSA component is set as the logarithm (based two) of its estimated noise level. Fifth, these noise bits are set to zero. Sixth, each value in each SSA component is reconstructed using the retained bits. Seventh, each PPG is reconstructed by summing up all the processed SSA components together. Eighth, the SSA is performed again on each reconstructed PPG. Ninth, only the first SSA component is retained and it is taken as the denoised PPG. Figure 2.3.4103 features are extracted in each denoised PPG in both the training set and the test set. These 103 features are classified into five categories.Category 1 : First, each meal time and each data acquisition time are recorded in each measurement. Here, all the times are defined as the total number of hours after the midnight of that day. Then, the difference between the data acquisition time and the previous meal time is computed. This difference is taken as the feature. Therefore, there is only one feature for each feature vector in this category.Category 2 (Features related to the blood pressure): Both the SBP value and the DBP value are employed as the features. Therefore, there are two features for this category.Category 3 (Features related to the absorption of the infrared light by the blood glucose): There are two LEDs emitting the light with the wavelength being equal to 1450 nm and another two LEDs emitting the light with the wavelength being equal to 1650 nm. Therefore, there are four PPGs acquired at each time. Since the AC component and the DC component of the acquired PPGs are related to the absorption of the infrared light by the blood glucose, the mean and the variance of each PPG are computed and they are used as the features. As a result, there are eight features for each feature vector in this category.Category 4 (Features related to the HRV): There is a LED emitting the light with the wavelength being equal to 880 nm. Here, there are four finger cots covering the LED. Hence, there are also four PPGs acquired at each measurement. For each PPG, there are 13 features related to the HRV with six features extracted from the time domain and seven features extracted from the frequency domain. For those six features extracted from the time domain, they are the average and the standard deviation (SD) of the PP intervals, the root mean squares and the SD of the differences between two consecutive PP intervals as well as the total number and the percentage of the total number of the differences between two consecutive PP intervals with the differences being greater than 50 ms. For those seven features extracted from the frequency domain, they are the total power of the PPG in the whole frequency spectrum, that in the frequency band between 0 and 0.04 Hz (VLF), that in the frequency band between 0.04 and 0.15 Hz (LF) and that in the frequency band between 0.15 and 0.4 Hz (HF), as well as the ratio of the LF to the HF, the normalised LF and the normalised HF. Overall, there are 52 features for each feature vector in this category.Category 5 (Features related to the HR): The same four PPGs defined in Category 4 are employed for extracting the HR features. First, the HRs are estimated based on the PP intervals of each PPG. Then, the mean, the median, the mode, the variance, the SD, the range, the interquartile range, the skewness, the kurtosis and the median absolute deviation of the HRs are computed. They are used as the features. Here, there are ten features for each PPG. As there are four PPGs for each measurement, there are 40 features for each feature vector in this category.2.3.5yˆi be the vector containing the ith feature extracted from all the PPGs in the training set. Then, yˆi is normalised to the unit energy vector. Let gi=1yˆiTyˆi be the normalised gain. Let yi be the normalised vector. That is, yi=giyˆi. Likewise, for the ith feature extracted from a PPG in the test set, the feature value is multiplied to gi to obtain the normalised feature value.To smooth the feature values or the reference blood glucose values, first they are normalised. In particular, let L2 norm optimisation method, the L1 norm optimisation method and the L∞ norm optimisation method. Let N be the total number of the measurements in the training set. For each normalised feature, the normalised feature values and the reference blood glucose values are first sorted according to the ascending order of the reference blood glucose values. Let xi,yi be the ith sorted pair of the normalised feature value and the corresponding reference blood glucose value. Let ai be the coefficients of the polynomial.Second, a polynomial fitting approach is employed for smoothing the features or the reference blood glucose values in the training set. It is worth noting that a large value of the polynomial order does not achieve the smoothing purpose. On the other hand, a small value of the polynomial order results to the over smoothing. Hence, this paper sets the order of the polynomial equal to 3. Moreover, three different formulations are employed for finding the coefficients of the polynomial. They are based on the LetJ2(a) be the objective function of the optimisation problem. Here, it is defined as the energy of the error between the estimated blood glucose values and the actual blood glucose values. In particular, the optimisation problem is formulated as follows:Let This is equivalent toa and setting its gradient vector to the zero vector, we have the following equation:By computing its gradient vector with respect to a is found, y is replaced by Xa. This is the vector of the smoothed reference blood glucose values. The above procedures are repeated for each feature and the mean of these vectors of the smoothed reference blood glucose values are taken as the final vector of the smoothed reference blood glucose values.Once J1(a) be the objective function of the optimisation problem. Here, it is defined as the sum of the absolute error between the estimated blood glucose values and the actual blood glucose values. In particular, the optimisation problem is defined as follows:Let This is equivalent toz be a dummy vector and let ι be a vector with all its elements being equal to one. The above optimisation problem is equivalent to the following optimisation problem:Xa−y≤z,Let −Xa+y≤z.and IN be the N×N identity matrix. Let a∼=az, f=0ι, X∼=X−IN−X−IN and y∼=y−y. The above optimisation problem becomes the following standard linear programing problem:X∼a∼≤y∼.Let a∼ and multiplying X in front of this extracted vector, the vector of the smoothed reference blood glucose values is obtained. Likewise, y is replaced by this smoothed reference blood glucose values and the above procedures are repeated for each feature. Finally, the mean of these vectors of the smoothed reference blood glucose values are taken as the final vector of the smoothed reference blood glucose values.The solution of this standard linear programing problem can be found via the simplex method. By extracting the first four elements in J∞(a) be the objective function of the optimisation problem. Here, it is defined as the maximum absolute error between the estimated blood glucose values and the actual blood glucose values. In particular, the optimisation problem is defined as follows:Let This is equivalent toε be a dummy scalar. The above optimisation problem is equivalent to the following optimisation problem:Xa−y≤ει,Let −Xa+y≤ει.and aˆ=aε, fˆ=01 and Xˆ=X−ι−X−ι. The above optimisation problem becomes the following standard linear programing problem:Xˆaˆ≤y∼.Let aˆ and multiplying X in front of this extracted vector, the vector of the smoothed reference blood glucose values is obtained. Next, y is replaced by this smoothed reference blood glucose values and the above procedures are repeated for each feature. Finally, the mean of these vectors of the smoothed reference blood glucose values are taken as the final vector of the smoothed reference blood glucose values.Likewise, the solution of this standard linear programing problem can be found via the simplex method. Then, by extracting the first four elements in To smooth the feature values, the above three methods are repeated by swapping the vector of the feature values and the vector of the reference blood glucose values. However, instead of iterating the above procedures for each feature in the above algorithms, now it is only require to perform one iteration in the above algorithms because there is only one vector of the reference blood glucose values.2.3.6In this paper, the random forest (RF) is employed to rank the importance of the features. The features with the highest 25 importance are selected. Hence, the new training set and the new test set with 25 dimensional feature vectors are formed. It is worth noting that the individual modelling approach is employed. Therefore, different features are selected for different subjects.2.3.7To develop the regression models, three models are employed. They are the support vector regression (SVR) model, the Gaussian regression model and the RF regression model. The parameters in these three models are found using the same training set.2.3.8L1 norm optimisation method, the L2 norm optimisation method and the L∞ norm optimisation method are fused together. In particular, 23 of the data in the previous training set is redefined as the new training set and the rest 13 of the data in the previous training set is defined as the validation set. Therefore, 50% of the overall data is used to form the new training set, 25% of the overall data is used to form the validation set and the rest 25% of the overall data is used to form the test set. First, a RF based regression model is built using the feature vectors and the reference blood glucose values in the new training set with their values smoothed by the polynomial found via the L1 norm optimisation method. Then, the built model is applied to the feature vectors in the validation set for performing the blood glucose estimation. Next, the absolute differences between the estimated blood glucose values and the reference blood glucose values in the validation set are computed. After that, these absolute difference values are sorted according to the ascending order of the reference blood glucose values in the validation set. Let e1 be the vector of these sorted absolute difference values. Likewise, the above procedures are repeated for the features or the reference blood glucose values smoothed by the polynomials found via the L2 norm optimisation method and the L∞ norm optimisation method. Let e2 and e∞ be the vectors of these sorted absolute difference values, respectively. Now, for each reference blood glucose value in the validation set, there are three absolute difference values based on the polynomials found by the L1 norm optimisation method, the L2 norm optimisation method and the L∞ norm optimisation method. The optimisation method corresponding to the minimum value among these three values is selected. It is found that the selected optimisation methods can be partitioned into several regions according to the sorted reference blood glucose values. To determine the regions of the sorted reference blood glucose values and the corresponding selected optimisation method, the accumulate probability approach is proposed. That is, the accumulate probability of each selected optimisation method is computed. Let ε be a threshold value. In this paper, ε is set at 0.6. If the accumulate probability of any selected optimisation method at a point is greater than ε, then the accumulate probabilities of these three selected optimisation methods at that point are reset to zero and a range of the sorted blood glucose values are defined as that with the corresponding boundaries points being the previous reset point and this reset point. Hence, after performing the above procedures for all the reference blood glucose values in the validation set, the regions of the sorted reference blood glucose values and the corresponding optimisation methods in these regions are determined. Finally, after applying the RF models formulated using these three optimisation methods to a feature vector in the test set, there are three estimated blood glucose values. Then, the mean of these three estimated blood glucose values is computed. Next, according to the model developed in the validation set, the corresponding blood glucose value is selected as the final estimated blood glucose value.To yield a more accurate blood glucose estimation, the features or the reference blood glucose values smoothed by the polynomials with their coefficients found via the 33.1L1 norm optimisation method (denoted as O_f1), only smoothing the feature values via the L2 norm optimisation method (denoted as O_f2), only smoothing the feature values via the L∞ norm optimisation method (denoted as O_f∞), only smoothing the reference blood glucose values via the L1 norm optimisation method (denoted as B1_O), only smoothing the reference blood glucose values via the L2 norm optimisation method (denoted as B2_O), only smoothing the reference blood glucose values via the L∞ norm optimisation method (denoted as B∞_O), smoothing both the feature values and the reference blood glucose values via the L1 norm optimisation method (denoted as B1_f1), smoothing both the feature values and the reference blood glucose values via the L2 norm optimisation method (denoted as B2_f2), smoothing both the feature values and the reference blood glucose values via the L∞ norm optimisation method (denoted as B∞_f∞), and neither smoothing the feature values nor the reference blood glucose values (denoted as O_O).As discussed in Section In this paper, three different criteria are employed for evaluating the blood glucose estimation performances. They are the value of R, the mean absolute error (MAE) and the root mean squares error (RMSE). Here, the SD of the estimated blood glucose values is also presented. Table In order to demonstrate the effectiveness of fusing the various methods and the effectiveness of using the individual modelling approach, Table FIGURE 8The order pairs of the estimated blood glucose values and the actual blood glucose values falling in the various regions in the Clarke error grid yielded by the various methods. (a) The fusion method using the PPGs based on the individuals. (b) The O_f1 method using the PPGs based on the individuals. (c) The O_f2 method using the PPGs based on the individuals. (d) The O_f∞ method using the PPGs based on the individuals. (e) The O_O method using the PPGs based on the individuals. (f) The O_O method using the PPGs based on all the subjects.3.2In order to have a fair comparison, the results yielded by all the methods are based on the same dataset established in this paper. Moreover, in order to verify the effectiveness of our proposed method, the results yielded by our proposed method are compared to those yielded by the current state of art method. In particular, since the SG filtering based method can effectively extract the underlying trend of the data and it is also based on the polynomial fitting approach, it is widely used for smoothing the features. Hence, this method is employed for performing the comparison. Here, the SG filtering with the following models including the RF model, the back propagation neural network (BPNN) model and the gradient boosting decision tree (GBDT) model is compared. It computes the total error within the window and the weights of the polynomial are obtained by minimising the total error via the least squares approach. Here, the window length is set at 5 and the order of the polynomial is set at 3. Table 4For the non‐invasive blood glucose estimation, the LEDs emit the near infrared light and the near infrared light is received by the sensors for generating the PPGs. At the same time, the reference blood glucose values are taken. Then, the features are extracted from the PPGs. Next, the regression model is built based on the extracted features and the reference blood glucose values. Finally, for a given test data, the blood glucose value is estimated using the built model. However, due to the uncertainty of the acquisition device, the presence of the noise, the variations of the acquisition environments and different subjects having different responses of the infrared light to the blood glucose, the obtained features and the reference blood glucose values are highly unreliable. To address this issue, this paper proposes a polynomial fitting approach to smooth the obtained features or the reference blood glucose values to improve their reliability. In particular, the design of the weights in the polynomial is formulated as the various optimisation problems with the objective functions of different optimisation problems being the error function having different the norm criteria. Then, the results yielded by the various methods are fused together. Here, the training sets and the test sets of the regression models are defined based on the individual subjects. The computer numerical simulation results show that our proposed method yields 94.1176% of the data points falling in the region A of the Clarke error grid and the MARD at 0.0930.Since the models are built by the individuals, the limitation of our proposed method is on the change of the physiological properties of the individuals such as the change of the medications taken by the individuals or the change of their meal habits. In this case, the correlation between the training set and the test set will be small. Like most of the machine learning algorithms, the estimation results will be poor. In future, the relationships among the individual models and the transfer from one individual model to another individual model will be investigated. Besides, the method will be developed for other biomedical signal processing applications such as the non‐invasive blood lipid estimation.Yiting Wei is responsible for developing the methodology, implementing the algorithm, acquiring the data and writing the draft of the paper. Bingo Wing‐Kuen Ling is responsible for attracting the funding, managing the project, developing the methodology, supervising the project and revising the paper. Danni Chen, Yuheng Dai and Qing Liu are responsible for validating the results and acquiring the data.There is no conflict of interest.


Approaches like this can produce enhanced exponential growth behavior that is less limited by volume and external surface interference, for an early step toward efficiently building two and three dimensional shapes in logarithmic time. We experimentally demonstrate the division of these polymers via the addition of a single DNA complex that competes with the insertion mechanism and results in the exponential growth of a population of polymers per unit time. In the taxonomically less powerful than a Turing machine. In this sense, a physical Push-Down Automaton can be more powerful than a sequential physical Turing Machine, even though the Turing Machine can compute any computable function. A need for an “extended” computational/physical theory arises, described in the supplementary material section In this paper, we demonstrate a molecular system for the first  A goal in the molecular synthesis field is to build biophysical systems with great complexity and power, with applications to medicine, the environment, and green manufacturing.Molecular programming, nanotechnology and synthetic biology raise the prospect of bottom-up fabrication, the manufacture of complex devices that assemble themselves from simpler components. Biological systems fabricate structures with enormous scale and complex behaviors, defined at atomic-scale resolution, which can grow quickly with small programs relative to their object size and algorithmic complexityIn natural biological systems, periods of programmed exponential growth per unit time is common, and perhaps is almost ubiquitous. Understanding and controlling exponential growth will become key, to obtain acceptable reaction yield and performance for practical applications of bottom-up self-fabrication.10, logic and catalytic circuits13, and triggered assembly of linear15 and dendritic structures8.Over the past several years, new directions in research have been translating computational algorithms into and out of molecular systems using DNA and other molecular substrates. DNA has been used to build autonomous walkersactive synthetic linear polymer system that can grow exponentially quickly in Real Time  there is no instruction for moving or rotating a tile relative to a surface and (b) passive self-assembly is exponentially slower than active self assembly. Several extensions of the aTAM have been proposed, such as staged  assembly27 and signal passing tiles28 have been proposed. These systems are more powerful than the aTAM As we will demonstrate, a sufficiently expressive implementation of an “active” molecular self-assembly approach can achieve these behaviors. We derive a new type of “active” self-assembly system that can be formally defined and easily implemented in molecules.Molecular biology needs a better theoretical framework for understanding the complexity of subsets of molecules that interact with each other to generate behaviors. Computer Science has such a framework but it deals with computational complexity—thus we can say how “hard” a particular mathematical problem is by analyzing how much time and space a computer requires to solve it. On the other hand, in other parts of Biology, we can’t say how computationally “hard” it is to generate behaviors like metamorphosis (the changing of one shape into another) or treadmilling (the growth of a linear polymer in one direction while it shrinks in the other direction). The absence of this ability to distinguish how hard it is to produce a desired behavior in a molecular system is a limitation in the fields of synthetic chemistry and biology.17. This system is capable of implementing exponential growth and can construct fixed-length linear polymers in poly-logarithmic time30.In the absence of biological measures of complexity we map our system onto a computational framework, by proving theorems regarding the “expressive power” of the model we define. The expressive power of our system is equivalent to context-free grammarsIn our model, each construction begins with an initiator, and grows via the insertion of simple units that we call monomers Fig. . We assucomplementary to each other.We have two finite sets of symbols k monomers, each is described by a quadruple of symbols  and either a plus sign or a minus sign. The plus and minus sign indicate the directionality of the molecules and are used in mapping the model onto a direct DNA implementation, which requires both c. We assume that the total concentration is at most 1. For example, in the exponential growing system described in Fig. There are mentclass2pt{minimNotice that all hairpin sequences are represented in a clockwise ordering, but the ones marked with a “+” and the ones marked with a “−” begin at different locations on the hairpin. The hairpins marked with a “+” begin at one of the toeholds and the hairpins marked with a “−” begin in the middle of the hairpin loop. The insertion of a “+” hairpin generates insertion sites where only “−” hairpins can insert, and vice versa, but the choice of “+” and “−” can be arbitrary.a, b), . Either a and d are complementary to each other or b and c are complementary to each other. Each of these pairs is considered a monomer.The initial state can be described by two pairs of symbols  and  belong to two different monomers. For example, in Fig. An e and f are complementary with each other, then any monomer of the form a, b, c, d) in the middle. insertion site.If there are two consecutive monomers connected in the structure such that the first one ends with the pair e and f are complementary with each other, then any monomer of the form c, d, a, b) in the middle. insertion site.If there are two consecutive monomers connected in the structure such that the first one ends with Only the following insertion rules are possible: x, where x is an exponential random variable with rate c, where c is the concentration of the monomer inserted.If a particular insertion is applicable, it occurs at time polymer is a sequence of tuples of symbols reachable from the initial state, where the first and last tuples are pairs of symbols and the middle tuples are monomers (as defined in rule 2). A terminal polymer is a polymer such that no monomers exist in the system that can be inserted at any of the insertion sites available on that polymer. The length of the polymer is defined as the number of monomers that it contains. For example, in Fig. a and A How do we tell if a polymer is terminal? The only way is to check for the condition, at each site, whether there exists a monomer that can insert according to the insertion rules listed in 5(a) and 5(b). If no monomers can insert, then the polymer is terminal.The detailed description of initiators, monomers, and the insertion rules follows: 32. Toeholds serve as the inputs to dynamic DNA systems and initiate branch migration processes, the random walk process of bond breaking and formation that results in the exchange of one strand in the duplex for another single strand with the same sequence.Given any system described above, there is a direct implementation of monomers into a set of DNA molecules. By encoding the order of the nucleotides in a DNA sequence, we can control the interaction of DNA strands. Subsequences of these strands are called domains and it is their binding (hybridization) and unbinding (disassociation) from complementary domains that determines what a system can do. In DNA nanotechnology, dynamic systems of DNA molecules can be controlled by toeholds, the short sequences of DNA that are complementary to single stranded domains in a target moleculeAny system described in our model can be implemented by designing DNA hairpins and an initiator complex as follows:x (composed of 18 bases) is the long stem of the hairpin. For every monomer c, x, d). The insertion rules defined in the model correspond to all possible reactions that can happen in the corresponding molecular system.For every monomer a, b) and  and divided into two parts , as will be described in section "In addition to the monomer Figure 33. Other design lengths and sequences were explored , but these resulted in a larger system leak (an undesired molecular interaction) than the sequences presented here  is driven by the hybridization of six new base pairs. After that, each new hairpin that is inserted adds nine base pairs to the system. Some of these steps become reversible as the system approaches equilibrium. The free energy and reversibility of toehold-mediated four-way branch migration is explored in depth inWe created a new molecular system that grows linearly, which we compared to the exponential growth system. To achieve this, we used the same monomers as in the exponential growth system, except that we replaced Hairpin 3 with an inactive version called Hairpin 3L. Hairpin 3L contains a poly-T sequence instead of the loops that normally create a new insertion site for Hairpin 1 after Hairpin 3 inserts. As a result, when Hairpins 1, 2, and 3 are inserted, they generate only one new insertion site for Hairpin 1 to bind to, instead of the two insertion sites created by the exponential growth system. This limits the system’s growth to be linear instead of exponential.In addition to the insertional monomers that grow the polymer, we introduce a new type of monomer, which we call a Divide complex, that upon insertion splits the polymer into two pieces. This tool can be used to generate a population of polymers in exponential time Section "".Figure x is complementary to x*. Single-stranded molecules of DNA (henceforth strands) are comprised of concatenated domains. DNA complexes are composed of two or more noncovalently-bound strands. There are two types of toeholds in our system: long toeholds that indicate a stronger desired interaction (six bases in length) and short toeholds that indicate a weaker desired interaction (three bases in length).In each diagram, we utilize a domain abstraction for referring to stretches of consecutive nucleotides that act as a unit in binding to complementary stretches of nucleotides. Domains are represented by Latin letters Fig. . LettersWe confirm exponential growth by measuring the conversion of monomers into a product. We then qualitatively measure the size of products over time. Finally, we verify the predicted structure using Atomic Force Microscopy.We tested each insertion step in the exponential growth mechanism by using the inactivated versions of of Hairpins 2 and 3 in which the binding loop is replaced by an inactive sequence of nucleotides . Hairpin 2L and Hairpin 3L were added to the Initiator and Hairpin 1 both individually (this results in exactly one insertion event) and together with the normal version of the other hairpin (i.e.: Hairpin 2L and Hairpin 3), which results in linear growth. We note that there is more product in lanes 14  and 15  than there is in lanes 12  and 13 .The reactants in lanes 12 and 14 can only proceed through two steps of the polymerization reaction due to the inactivated strands. At equilibrium (after 6 hours) there is more dimerization between the Initiator-Hairpin 1 complex and Hairpin 3L than there is between the Initiator-Hairpin 1 complex and Hairpin 2L. Thus Hairpin 3 appears to have a greater affinity to the Initiator-Hairpin 1 complex than Hairpin 2. This observation implies that the two reactions have different rate constants, Hairpin 2 is either slower to react with its insertion site or faster to dissociate from its insertion site than Hairpin 3 (or both).The reader may observe the presence of faint extra bands in the lanes that contain only individual hairpins. These are dimerized hairpins that form in small amounts from individual hairpins when the strands are annealed. We minimize their presence by snap cooling. Snap cooling the hairpins results in the same amount of dimerized monomers as gel purification (data not shown). All hairpins except for the Initiator were snap cooled prior to experiments. The Initiator is a gel-purified duplex composed of two molecules of DNA.In order to ensure that polymers were not randomly joining each other over time, we observed the linear systems  and  and the exponential system  when all molecules were added at the same concentration. If the polymers were randomly joining at the ends, we would see a shift in the length of the polymers over time. Figure S4 shows that there is minimal joining as the polymer bands do not shift upward over time.We examined the kinetics of the conversion of monomers into the polymer by adding a fluorophore and quencher pair to the opposite ends of Hairpin 2. Before reaction, the fluorophore is quenched. Upon incorporation of the hairpin into the DNA polymer, the quencher and fluorophore pair are separated, and the fluorescence of the solution increases .We probed both the linear and exponential polymerization over eight different Initiator concentration values. The time course of fluorescence intensity confirmed linear conversion of hairpins in the system with one inactivated strand Fig. A, and ex8. For more details see Supplementary Section S3.In order to derive both the linear and exponential growth equations, we made the approximation that the hairpin concentrations remain constant until 10% of the monomers are consumed as inP, grows as a function of initial Initiator concentration, t, as follows:In a linear growth system, the total mass of polymer product, ata Fig. A.P, grows as a function of initial Initiator concentration, t, as follows:In an exponential growth system, the total mass of polymer product, 8: we adjust the Initiator concentration [I] by an additional term We quantify the leak via spectrofluorimetry experiments in Fig. 3Equations The mean length (in base pairs) of polymers decreases with increasing Initiator concentration above 4% of relative hairpin concentrations. . This is expected because high concentrations of Initiator outcompete existing insertion sites for free hairpins. In the case of Initiator concentration below 4% of relative Hairpin concentrations, the different amounts of leak in the systems are presumably responsible for the different distributions of polymer length between the linear and exponential system. The smaller leak in the linear system (1%) would explain why the linear system produces longer polymers than the exponential system (which has a 4% leak).34. It is unclear whether the leak product is a linear polymer. It may be a highly pseudo-knotted structure.Atomic Force Microscopy of the reaction product confirms the formation of unbranched polymers in the exponential system . In comparing images of both the polymer and the leak product, we find that the leak product is capable of growing much larger than the intended polymer, but the polymer grows faster. Others have shown that polymer growth in the absence of Initiator can provide an upper bound for how big the polymer can growA qualitative difference between the exponential and linear systems is also observed when examining polymer size over time in Fig. Several features of this gel data are worth noticing: First, the exponential system generates longer polymer products sooner than the linear system Fig. , 500 minSecond, the growth rate of the polymers for the exponential system increases drastically, starting at the 30-min point, as seen in the bottom right part of Fig. Third, the length of the polymer tends to have a larger variation in the exponential system. Polymers of size over 2500 base pairs are generated while the average size is still far below 1000 base pairs. The distribution of polymer size is much closer to a normal distribution for the linear system. This phenomenon also fits the expectation for the exponential growth system: longer polymers can grow faster because they have more sites for the insertions to happen in parallel.Although the above three features suggest but do not directly prove exponential growth, all of them are consistent with the expectation that exponential growth progresses. We note that the actual mean of polymer length is larger than that reported here, especially for the exponential system, because of our conservative binning of data .Figure The exponential time lapse gel in Fig. We hypothesize that the fluorescent loading dye bromophenol blue interferes with the fluorescence read-out of our properly initiated polymers. The gel in Fig. The chemical reactions at play in the exponential growth system are modeled and discussed in supplementary material Section S4.Just as a polymer can grow in logarithmic time via parallel insertion, a population of polymers can be generated in logarithmic time using insertional division. Division is implemented by a complex that is identical in sequence to Hairpin 1 except that its loop has a break in it . We confirmed that monomer conversion is logarithmic in time at two different concentrations of Divide complexes .This work is part of a growing push in nanotechnology and material science that is oriented toward fabricating smarter materials that can be programmed and created using molecular reactions. The molecular focus renders these structures as potentially capable of being interfaced with biological compounds and systems. Such materials are capable of complex behaviors and creating programmed and time-varying complex structures, but they will not run the same types of programs that computers run. Rather these molecular systems should be used to do what molecules do best: communicate and process in-vitro and in-vivo information via shape, structure, function and molecular interaction.active self-assembly that is sufficiently expressive as a Pushdown Automaton, to achieve these behaviors and is the first of its kind to be implemented in molecules. We designed and experimentally verified the construction of the first synthetic linear polymer capable of growing exponentially quickly and is also capable of dividing. It is an example of a powerful one-dimensional tool that allows engineers to change the interconnections of molecules after a shape has been assembled, which is an important step toward fully reprogrammable molecular assembly. We demonstrated two different types of behavior using a simple insertion primitive (insertion and splitting), and we have proposed a third behavior (treadmilling) that results from the composition of insertion and division but requires a slightly modified molecular implementation.We have identified a new class of programmable behaviors that use a structured logic for moving molecules relative to each other, with the ability to modify the existing substructure. We constructed a computational model for 39 that can gracefully incorporate the physical domain and physical goals and properties, as well as computational features.In the supplementary material section 42. The new framework will include time, space, movement, rates of change, energy, yield, volume or mass, in addition to the the traditional computational abstractions, which act purely on abstract numerical functions over the integers. We feel that the existing formalisms do not capture enough of the essential ingredients that are needed, for instance, even for the study and foundations for exponential growth, in this combined physical and computational sense. The development of this new type of computational theory could help us understand theoretical issues of exponential growth of programmable physical structures, and would help resolve other theoretical issues for the fabrication and design of programmable self-assembled physical problems in chemistry, biology and robotics.As a result, we and other investigators have been seeing that there is a developing type of computational framework, which can be called “Extended Physical Computation”We feel that the connection of essential theory to “Extended Physical Computation” will become increasingly important to explore and develop, as molecular and self-fabricating technologies become progressively more applicable. As a result, we invite theorists to examine the foundations of these issues using physical world parameters, to develop interesting new types of fundamental results and new formalizations, to extend and combine the ideas of effective calculation and growth.Our system is the first to implement “internal” parallel insertion and does not rely on adding layers to “external edges” for growth, and is also the first exponential structure that is linear and is not a tree. This feature of our system provides for improved exponential growth in our system, as our system is not as limited by the external surface area, although there will still be physical limits and constraints.8. Their reaction begins with a root node, where each node generates two child nodes in each generation of growth. The authors point out that, in the absence of steric effects, a linear increase in the number of node species will yield an exponential increase in the size of the binary tree. In practice, steric effects are always present.Our molecular system is not, however, the first exponentially fast growing structure ever synthesized. Yin et al. constructed a binary molecular tree out of DNAA next challenge will be to build reprogrammable molecular shapes in two and three dimensions. Difficulties are likely to arise when scaling our current molecular system to these dimensions. Until we can more precisely control the kinetics of hairpin insertion, we cannot guarantee the proper exponential growth of a shape in these higher dimensions. This is because our polymer is too flexible to accommodate insertions in multiple dimensions without the possibility of self-interactions forming a mis-shaped object. The generation of a well-formed object using an elaboration of our system will require component molecules with rigid structures.A second limitation of our construction is the repeating DNA sequence utilized in the insertion and division primitives. In theory, these structures can be programmed just like tiles in the tile assembly model, but in practice the repeating DNA sequence places a constraint on how many different actions can take place at a given site. One may be able to extend this system by adding more complexity into the hairpin loops—additional structures or sequences that might accommodate other functionalities . The power of our system lies in its ability to grow a structure very quickly with only a few types of monomers by allowing subsets of molecules to move relative to each other. When a system like ours is scaled up its power would be limited, because Brownian motion drives these translocations only on small scales.This work straddles the fields of synthetic biochemistry and theoretical computer science. The fields of synthetic biology and chemistry could greatly benefit from new methods to classify the complexity of molecular systems. There remain many unanswered questions at the intersection of these two sciences. Identifying and implementing the necessary primitives required to implement all active assembly behaviors that chemistry and biology have observed, will provide more insight into how nature works and how we can engineer it.A typical fluorescence kinetics experiment contains Hairpin 2 labeled with a fluorophore and quencher pair on the 3’ and 5’ ends of the strand, respectively. Mixed together with H2 are I, H1 and either the inactivated or regular version of H3 for the linear and exponential systems respectively. H1 is added last to trigger the reaction. As H2 is integrated into the polymer, the quencher and fluorophore pair are separated from each other, yielding an increased fluorescence signal in the solution. At the end of the experiment, another strand of DNA is added into the solution in order to fully displace all unreacted hairpins . This “displacement” strand was added in 15. These sequences were designed using the NUPACK web application44 and our in-house DNA Design software package45 to minimize the presence of any unanticipated secondary structures that might interfere with the kinetics under investigation.The sequences presented in Tables B.1 are based on those used in a previous insertional polymerization motorDNA oligonucleotides were stored in 1All annealing processes were performed with an Eppendorf Mastercycler Gradient thermocycler. The samples were brought down from All Hairpins were snap cooled prior to experiments. This protocol entails heating the strand solution to DNA oligonucleotides used in this study were purchased from Integrated DNA Technologies (IDT), with standard desalting purification, except for strands with a quencher, fluorophore or a 46.Concentrations of individual strand stocks were determined from the measured absorbance at 260 nM using a Nanodrop Biophotometer and using calculated extinction coefficients that account for hypochromicity effects in double-stranded DNAInitiator and Divide complexes were further purified by nondenaturing (ND) polyacrylamide gel electrophoresis (PAGE) as follows: Strands for each sample were prepared with nominally correct stoichiometry at 10 nM and annealed. The acrylamide (19:1 acrylamide:bis) was diluted from Combinatorial gels were run using 12% polyacrylamide and concentrations of all species at 100 nM. Solutions were left to react for 6 hours, then run in an XCell SureLock Mini-Cell Electrophoresis vertical gel box at 150V for 1 hour in TBE running buffer. After a gel was run, it was stained with SYBER Gold dye and imaged using an FLA-5100 fluorescent scanner (Fujifilm Life Science). Time Lapse, Final Value and Divide gels were run in 2% Super Fine Resolution Agarose (from AMRESCO) on a Thermo Scientific Owl Horizontal Gel box. In these experiments, the Initiator is tagged with a 3’ ROX fluorophore on one strand. Thus each properly-initiated polymer has a single ROX tag. Time Lapse reactions contained the following concentrations of species [I] = 80nM, [H1] = 1.5 Atomic Force Microscopy images of polymer taken with 10% Initiator (10 nM) relative to Hairpin (100 nM). 50Spectrofluorimetry studies were done using a SPEX Fluorolog-3 (Horiba) with external water bath and 1.6 mL synthetic quartz cells (Hellma 119-004F). The excitation was at 584 nm, while emission was at 604 nm. In all spectrofluorimetry experiments, the total reaction volume was 1.5 mL, the temperature was Fluorescence is normalized so that one normalized unit of fluorescence corresponds to 1 nM of unquenched fluorophore-labeled strand reporter 2. This normalization is based on the fluorescence levels of annealed samples with a minimal fluorescence measurement taken of the diluted Reporter complex before the experiment was initiated, and a maximal fluorescence value that is extracted from a biexponential fit of the data taken at the end of the experiment, after the displacement strand is added to displace all unreacted fluorophore-quencher pairs.programmable physical systems, a task for theoreticians to explore. Physical sequential Turing machines cannot achieve exponential growth of structure in real time, yet taxonomically less powerful physical formalisms can do this. A need for an “extended” computation/physical theory arises.In this paper, we demonstrate a molecular system for exponentially fast programmed growth using an “internal” insertion approach, which is less limited by physical interference than methods that passively rely on “external” accretion. Exponential growth aids future bottom-up fabrication—the self-manufacture of 2D and 3D molecular devices from simpler components. There is also a discussion in the Supplementary Information.


Globally 800 women die every day from preventable causes related to pregnancy and childbirth. One of the major reasons for high maternal mortality ratios in many developing countries is the low proportion of births attended by Skilled Birth Attendants (SBA). To address the high number of maternal deaths, in 2008 the Government of Pakistan introduced the Community Midwives Program. Under the program, women from across the country were trained and deployed as Community Midwives. In this study, I use six rounds of Pakistan Social and Living Measurement Survey to estimate the impact of this program on maternal healthcare utilization. I find that women residing in districts with higher Community Midwives per capita were 9 percentage points more likely to be attended by a SBA at the time of delivery and were 8 percentage points more likely to give birth at a medical facility as opposed to birthing at home. I find no evidence of impact on take up of prenatal and post‐natal check‐ups. The use of Community Midwives may be a cost effective tool to reduce maternal deaths, especially for developing countries with low health budgets. Ninety four percent of maternal deaths worldwide are from developing countries, with one in every five occurring in the South Asian region.High maternal mortality rates in developing countries such as Pakistan are associated with low proportion of deliveries attended by Skilled Birth Attendants (SBA)  Policy in 2005. One of the major tools employed was the introduction of Community Mid‐Wives (CMWs) as front line health workers. In this study, I estimate the impact of deploying CMWs on maternal healthcare utilization at the time of giving birth, as well as during pregnancy and post‐partum.1.2The Pakistan Demographic and Health Survey (PDHS) of 2006–07 shows that pregnancy related illnesses are the leading cause of death for women of childbearing age PDHS, . PakistaPakistan's MNCH policy of 2005–06 was designed to improve the high maternal, infant and child mortality rates in the country, with the aim of bringing these numbers in line with the Millennium Development Goals. In particular, the program aimed to achieve these goals by increasing utilization of pre‐natal care, institutional births, and presence of skilled attendants at birth. One of the major tools employed was the introduction of CMWs as front line health workers, a concept new to Pakistan's healthcare system. The program was inspired by Indonesia's Village Midwife Program of early 1990s, which introduced more than 50,000 midwives in rural areas of Indonesia . Women from all regions of the country were to be recruited, trained and deployed back in areas of their residence and origin, where they would have both the knowledge about and trust of the local communities, making it easier for the local residents to accept their role. The selected candidates were trained in‐class for a year at one of the certified institutes of Pakistan Nursing Council, followed by 6 months of field training.The eligible candidates for CMW training were females aged 18–35 years who had cleared the national level matriculation exam , Indonesia (6%), Bangladesh (5.7%), and India (5%).While inherently a supply side intervention, the policy also catered to barriers in demand by ensuring CMWs were placed back in areas of their origin upon successful completion of training. Being accustomed to the local language, culture and community would help the CMWs in reaching out to women in their areas and the familiarity would make the local community more receptive to them. Upon deployment, their role was to provide individualized care to the pregnant women throughout the maternity cycle and subsequently to the newborn. It was expected that the interaction of the local women with CMWs would change health‐seeking behaviors by impacting the take up of pre‐ and post‐natal visits, and the rate of skilled birth attendance. Additionally, the CMWs were trained to identify actual or anticipated conditions requiring medical attention and make timely referrals of obstetric and newborn complications, bringing down the number of deaths due to untreated complications.In terms of roll out and implementation, deployment of CMWs to their respective catchment areas started in 2008. By 2013, 45% of the planned 12,000 CMWs were trained, out of which 64% were deployed successfully , to deal with high fertility, maternal mortality and infant mortality rates. Over 50,000 CMWs were introduced in rural areas of Indonesia and the evidence on the effectiveness of the intervention is mixed. Studies have shown the program was ineffective in terms of increasing use of contraception .This, to my knowledge, is the first attempt to study the impact of the program at a national scale. As discussed in the literature review, only a few studies around the world use data to quantitatively assess the impact of frontline, low cost health workers. This study bridges the gap by evaluating the effectiveness of such workers for improving maternal health in developing countries and focuses on Pakistan‐a country with one of the highest number of maternal deaths worldwide.From a policy perspective, the study evaluates whether the deployment and training of CMWs is an effective policy tool for encouraging women to seek maternal health care during pregnancy  and at the time of giving birth . Results of the study provide information on whether this cadre of health workers may help in improving maternal healthcare utilization.22.1The study primarily employs the Pakistan Social and Living Measurement Survey (PSLM). The PSLM is a cross sectional survey conducted each year across the country, alternating between being representative at the district or provincial level.For this study, I use six years of the district level representative data sets for the years between 2004 and 2014. In each of these rounds approximately 75,000 households and their members were interviewed on questions related to employment, education, water and sanitation, household wealth and health, with specific sections on the health of children, and women of childbearing age. In addition, questions pertaining to health utilization and satisfaction regarding available health services were also included in the survey. The relevant outcomes of interest for this study come from the section on women's health, which is administered to women who had given birth in the 3 years prior to the survey. Details of the total sample size of PSLM and the sample of women surveyed for maternal health related questions, over the six rounds used for estimation purposes in this study, are provided in Table I supplement this main data set with data on the deployment of CMWs at the district level. These data were obtained from the MNCH website.Summary statistics for variables used in the study are shown in Table any pre‐natal check‐ups. In the post period a larger proportion of women (61%) report having at least one pre‐natal check‐up during pregnancy. The proportion of women who underwent a post‐natal examination increases from 24% in the pre period to 27% in the post period. In terms of healthcare at the time of delivery, only 42% women had a skilled birth attendant assisting the delivery in the pre‐treatment period. This proportion increased to 45% in the post‐treatment period. We see a big change in the proportion of births occurring at a medical facility (as opposed to home). While only 29% women gave birth at a medical facility in the pre period, 40% of women report delivering at a medical institution in the post period; a change of 11% points. Figure The relevant sample for this study is women who were in the childbearing age (16–50 years) at the time of survey and had given birth in the last three years. This criterion yields a sample size of more than 173,000 observations over six rounds of the survey. The four outcomes of interest are binary indicators for (i) pre‐natal checkup, (ii) post‐natal checkup, (iii) birth attended by a SBA and (iv) birth at a medical institution. Table In terms of access to health services, Table Statistics in Table 2.22.2.1pre‐period averages of these variables, using Ordinary Least Squares as follows:CMWd is the treatment variable defined as the average number of CMWs per 10,000 of the population in district d, ECd represents a vector of controls capturing the average economic conditions of households in the districts in the pre‐period, MHd represents a vector of controls capturing average pre‐period rates of maternal health practices and εd represents the random error term.The Government of Pakistan implemented the policy at the national level, with varying dose of treatment for each district. There is, however, concern that the treatment may be endogenous. For example, if districts with worse maternal health care receive a higher dose of the treatment, the estimate of the impact will likely be biased. To address this concern, I follow the approach taken by Bollen et al.  to accouI test whether district characteristics in the pre‐period (averaged using 2004 and 2006 rounds of the PSLM survey) predict the deployment of CMWs. I test whether the average rates of the main outcomes of interest  in the years prior to the introduction of CMWs predict the number of CMWs deployed per 10,000 of the population in the district. In addition, I check whether other characteristics such as the economic well‐being of the district  with television (TV), proportion of rural HHs) and outreach of existing health facilities (proportion of HHs visited by LHWs) are predictive of the treatment.β1 from Equation .p‐value of 0.58 on joint test of significance).p‐value of 0.41 on joint test of significance).Table Equation  would bei indicates the individual, and d indicates districts. yid is the outcome of interest . CMWd is the continuous treatment variable defined as CMWs deployed per 10,000 of population in district d, taking on a value of zero for pre‐treatment periods. Xid are individual and household level controls while Zid are other controls related to the area of residence and the available health facilities, and δt are survey year fixed effects  in estimation of Equation  is statistically insignificant, allowing us to assume that the treatment (and the intensity of the treatment) is not endogenous.Table 2.2.2one prenatal checkup during pregnancy, (ii) having a post‐natal checkup within 6 weeks of delivery, (iii) having a skilled birth attendant present at the time of delivery and, (iv) delivering the baby at a medical facility .I use a difference‐in‐differences approach with a continuous treatment variable and use variation in treatment intensity to evaluate the effect of the program. More precisely, I use the difference in “dose” of the treatment, measured by CMWs deployed per 10,000 of the population in the district, to determine the impact of the program using pre‐ and post‐period data. The main outcomes of interest are binary and are defined as: (i) having undergone at least γd are district fixed effects and all other variables are as defined for Equation .The probit model estimated for the main outcomes of interest is as follows:33.1CMWd for estimations in Panel A.I estimate the impact of CMWs on maternal health care utilization using individual level micro data from six rounds of the PSLM. Table I begin by looking at utilization behavior prior to and after delivery. In Columns 1 and 2, I find no evidence of a significant impact of CMW's deployment in the district on the probability of women seeking pre‐ and post‐natal check‐ups. The coefficients though positive are imprecisely estimated.Next, I look at the impact of CMWs on whether the women are attended by a SBA at the time of delivering the child. A positive coefficient in Column 3 of Table Table Results in Table 3.2Twenty two of the districts received no CMWs under the program. I exclude these districts from the sample and re‐estimate Equation . ResultsThe recall period for maternal healthcare related questions in the PSLM survey is 3 years. To address the concern of the 2008–09 round of PSLM overlapping with the year of the CMW intervention, I exclude the 2008–09 PSLM sample from my data and re‐estimate Equation  would be available, and reduce the deaths due to undiagnosed or untreated complications.The results in Table Results in Table community midwives was to bridge any local and cultural barriers so that they are easily accepted in their roles by the local communities. However, it appears that despite increased contact with skilled birth attendants at the time of birth, women are not convinced about the importance of post‐natal checkups. Affordability is unlikely to be a barrier here since CMWs are allowed to charge only a very nominal fee from their patients and their basic compensation comes from the Government  and facilities  may potentially improve pre and post‐natal check‐ups as well. Increase in post‐natal check‐ups may potentially also lead to gains in infant health as well, since CMWs are also trained to provide newborn care. Further research may help inform policy makers how the ultimate goal of reducing maternal and infant mortality was impacted by the CMWs. This study is also limited in not being able to speak to the possible mechanisms which might be leading to a significant impact on utilization at the time of birth but not on pre and post‐natal check‐ups. With more informative data, these questions may be answered to provide insights for better future implementation.The author declares that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.This study received the designation of ‘Not Human Subject Research’ from the Institutional Review Board of Georgia State University.


Fiber optic infrastructure is essential in the transmission of data of all kinds, both for the long haul and shorter distances in cities. Optical fibers are also preferred for data infrastructures inside buildings, especially in highly secured organizations and government facilities. This paper focuses on a reference measurement and analysis of optical fiber cables sensitivity to acoustic waves. Measurement was carried out in an anechoic chamber to ensure stable conditions of acoustic pressure in the range from 20 Hz to 20 kHz. The frequency response, the signal-to-noise ratio per frequency, and the Speech Transmission Index are evaluated for various types of optical fiber cables and different ceiling tiles, followed by their comparison. The influence of the means of fixing the cable is also studied. The results prove that optical fiber-based infrastructure in buildings can be exploited as a sensitive microphone. Some data transmissions are not encrypted and even if they are, there is a high risk that in near future, these data will be decryptable by quantum computers. Therefore, the hot topics today are quantum encryption and post-quantum encryption. A relatively unexplored area is fiber optic sensing for vibrations in the acoustic, thus, audible spectrum.Nowadays, optical fibers are increasingly often used for both data and non-data transmission. Many research groups focus on protection of fiber based infrastructures against data eavesdropping that can be done by several techniques4. Acoustic sensing has recently been a highly studied area7 because of the security of fiber optic based information systems and networks. Acoustic sensing techniques can be divided on the basis of the methods used.Mechanical vibrations and acoustic noise acting on the optical fiber cause changes in the strain and the refractive index of the fiber core. These changes can subsequently be detected by several methods and converted into an electrical signal followed by acoustic reproduction. Information such as the audio component of a video call, a conversation between people in a room or a phone call can be intercepted even before it is converted into digital form and encrypted. Thus, optical fiber infrastructures, mainly inside buildings, can be used as sensitive microphones, posing a significant security risk. The roots of fiber optic acoustic sensing date back to the 1970s, when the first audible sound sensing experiments were realized8. The scattering spots in the fiber cause the fiber to act as a distributed interferometer. The intensity of the reflected light is measured as a function of time after transmitting the laser pulse. DAS detects pico-strain-level signatures in the fiber induced by vibroacoustic disturbances caused by an event near the optical cable. These perturbations change the scattering in the fiber core at a molecular scale, originating from the sub-wavelength heterogeneities formed when the fiber is drawn. Further research is focused on the Phase-sensitive Optical Time-Domain Reflectometry (9.Fiber strain changes can be detected in Rayleigh backscattering. The distributed acoustic sensing technique (DAS) uses this effect, where a coherent laser pulse is transmitted along an optical fiber10. Doppler-induced frequency or phase shift of a propagating light wave is detectable in schemes of optical interferometers where the instantaneous interference phase in the time domain is converted to the electric signal11. The frequency shift is detectable in an arrangement Fabry–Perot (FPI), Mach–Zehnder (MZI) or Michelson (MI) interferometers formed by optical fibers with necessary optical elements included in the optical setup.Changes in the refractive index of the fiber core caused by external mechanical vibrations and acoustic noise lead to Doppler shifts of light waves travelling through an optical fiber. This phenomenon can be explained as a Doppler effect in a flexible and expandable waveguide16 and dependences of the cavity length and the materials used can be compared. Such microphones can also be used for multipoint sensing, for example, using a 1:4 splitter17.The FPI is very often used for the arrangement of point-optical microphones. Variety of FPI based microphone designs are available18 where the multimode–singlemode–multimode (MSM) structure and direct measurement detection are used to detect acoustic vibrations. Fiber Bragg grating (FBG) microstructures19 incorporated in the sensing optical fiber can be used as mirrors for the FPI where an optical cavity is formed between two or more FBGs. The FPI arrangement is suitable for the use as microphones and hydrophones as well21. Several works based on the FPI arrangement have been devoted to voice sensing with ethylene propylene diene terpolymer film and the aluminium surface17 and based on cellulose triacetate diaphragm13. There are also unique variants of the detection schemes in the arrangement with the FPI. They include an experiment using a laser feedback interferometer, where changes of the refractive index of the sensing fiber lead to changes of optical frequency of the detecting laser22. An important disadvantage of the FPI-based techniques for acoustic sensing is the limited possibility of measuring at one only or very low number of points on the optical fiber. The other disadvantage is the need for a specially modified fiber, e.g. with FBG microstructures.A special use of the FPI is possible23 which again requires a special fiber, or to use conventional fibers for acoustic monitoring of gas turbines24. It is also possible to use the open cavity and the collimators in the sensing arm of the MZI for sound sensing25.Arrangements using the MZI for acoustic sensing are used for example, it is possible to use microfiber MZI26 but also as sensors for audible frequencies27. Implementations in sensing seismic vibration have been also reported28 as well as possible use in monitoring of marine structures29. It is also worth noting that research is carried out that deals with improving the noise stability of the MI30. The star topology of the fiber optic infrastructure inside buildings gives the opportunity to build the MI arrangement. A single optical fiber usually runs from the room with the central optical switch to the room with a piece of terminal equipment. The fiber can thus sense acoustic signals along its entire route and can be connected as a measuring arm of an MI arrangement.Arrangements of the MI are often used as hydrophones sensing ultrasoundIn this paper, we set up an experimental MI that allows the detection of acoustic signals through an optical fiber guided by different types of corridors. We focused on measuring the sensitivity of this arrangement to defined acoustic signals in a fully anechoic laboratory. The experiments examined the influence of several factors such as the optical fiber position and types of optical fibers on the quality of the detected signal regarding a level of speech intelligibility. The properties of the acquired signals were analyzed, the individual measurements’ frequency responses were compared, and signal-to-noise ratios were investigated. In our work, we also measure and evaluate the Speech Transmission Index (STI), which is the prevailing way to objectively assess the expected intelligibility of speech signals after passing through a system.3132.The Michelson interferometer is widely utilized for its flexibility of use. A fiber arrangement contains only a single coupler through which coherent light is distributed from the laser source to the sensing and reference arm, as seen in Fig. 34 Among other issues, the review discusses current methods of demodulation in fiber interferometers. Another article35 deals with noise removal using MZI, MI, and 36.For the detection of mechanical and acoustic vibrations, MI is often used, as stated, for example, in the review by Li et al.38. The phase fluctuations of the laser can be observed as additive noise in the detected interference phase. Considering the phase noise of the laser as the input signal and the noise in the detected interference phase as the output signal, the interferometer acts as a feed-forward high-pass comb filter as shown in Fig. Due to the self-heterodyne effect, the phase noise of the laser needs to be taken into account in both MI and MZIs the magnitude of the transfer function can be expressed:The transfer function of such a system can be expressed asPractically, this means that the longer the length difference 39 describing the calibration of the optical fiber sensor; it contains only basic measurements, neither measurements of human speech nor a comparison of intelligibility to reference microphones.A characterization of optical fibers and cables as acoustic sensors mainly for speech is probably of the greatest interest in real infrastructures, for example for the sake of security. Despite this fact, our experiment consists of sensing acoustic vibrations in a maximally controlled environment. Our measurements are thus performed in an anechoic room. This allows us to separate inherent factors from those affecting the quality of the signal in the real case. As far as we know, only a single similar experiment was carried out, Zhang et al.For measuring the transmission of acoustic vibrations to the fiber we have set up a heterodyne Michelson interferometer (MI) configuration shown in Fig. The heterodyne MI setup used is an extension to a classical homodyne MI shown in Fig. To allow for a greater versatility in signal processing, the demodulation of the beatnote signal is carried out off-line on sets of digitally recorded RF signal samples. As illustrated in Fig. quations  and 5b)\document40. Doing so extends the interval of possible phase angle values seamlessly from To get the interference phase The anechoic chamber utilized for the measurements has a volume of 90 mmentclasspt{minimathe effect of the panel type,the effect of the cable/fiber type,the effect of the cable/fiber position with respect to the ceilings panels,the effect of the FM2 mirror position.In the given setup, we aim at the following comparisons: frequency response of the system using a swept sine excitation signal,signal-to-noise ratio per frequency (SNRf) using a stepped sine excitation signal,the Speech Transmission Index for Public Address systems (STIPA).Measurement of the frequency responses using the swept sine signal, as well as the estimation of speech intelligibility using the STIPA protocol are common techniques in signal processing and system analysis, see the description below. The metrics are measured on audio signals obtained from the acquired I/Q signals using phase demodulation. The signals are downsampled to To measure and both visually and numerically evaluate the sensing capabilities in different setups, we performed three types of measurements, resulting in the following quantities: N is denoted We treat all the  signals as column vectors, i.e. a signal S is using its impulse response 41S to produce an output 44 as One of the most common means to characterize properties of a linear time-invariant system f. In our experiments, we used 53 values of the target frequency f logarithmically spread from 50 Hz up to 20 kHz. To analyze the signal from acquired at the fiber, we first divide the acquired signal into segments, corresponding to the input signal as described above. Then, each segment f) and noise f.The second input test signal consists of 50 subsequent time segments, each of them is occupied by a single, pure sinusoid of a prescribed frequency a, b, such a sum generates a sinusoid with fixed frequency f and arbitrary amplitude and phase)a, b are parameters to be optimized such that the energy of the noise M is the length of a single step in the sequence, in our case 45 asIn more detail, we search for the signal f asThen, we may easily compute SNRf for the specific frequency 46. The standardized test signal contains pink noise, amplitude-modulated in seven non-overlapping bands. The bands, frequencies and modulation depths are prescribed such that the resulting noise signal is statistically similar to male speech. At the output, the signal is analyzed in terms of loss of amplitude and modulation depth, and a final number  in the interval from 0 to 1 is computed. See Fig. STIPA is an established method for objective assessment of speech intelligibility after passing the speech signal through a systemno panel (none),standard panel (standard),AMF ECOMIN Filigran acoustic panel (acoustic).The results are presented in terms of the frequency response in Fig. 47 for the visualizations, using of 1/12th-octave.First, we present the comparison for particular choices of the panel:As expected, we observe in Fig. We observe in Fig. Finally, we focus on SNRf in Fig. standard Patch Cord G.657.A1 (PC)—FTTX 12 fibers G.657.A1 (FTTX)—KDP flat drop 2 fibers G.657.A1 (KDF)—2.0 KDP 24 fibers G.657.A1 (KDP)—Excel LSOH 24 G.652D fibers OS2 (Excel)—For the analysis, we chose the position of the cable hanging above the panel since this setting eliminates possible inaccuracies in arrangement of different cables. Based on the observation above, we focus on the results of the step analysis in Fig. For the comparison of cable type, we tested the following possibilities:As expected, we see that the cables with a thicker coating  exhibit a drop of SNRf on lower frequencies, compared to the thinner options . On the other hand, the remarkable observation is the relatively high value of SNRf in the case of the FTTX cable around 2 kHz. The increased sensitivity of the FTTX cable compared to others is most likely caused by the material composition of the cable jacket. It is a hard PE plastic that transmits acoustic vibrations to the fibers.hanging above the grid, with no panels present, for reference (no panel),hanging above the panel (hanging),lying in a coil on the panel (coil),lying on the panel in a circle around the perimeter (circle),lying on a polyurethane foam on the panel in a circle around the perimeter (foam).Clearly, the foam layer serves as a damping element in the whole system, similar to a low-pass filter. While this is more pronounced in terms of frequency response ,FM in the middle of the FUT lying on the panel (lying),FM in the middle of the FUT vertically glued to the panel ,FM in the middle of the FUT in a plastic bell (bell),FM in the middle of the FUT glued to a non-playing speaker (speaker).Finally, we evaluate the effect of the FM2 mirror position, aiming to investigate whether the mirror itself serves as an optical microphone, or an amplifier for the effect of the whole FUT. We test the following setups, see Fig. The results of the step analysis in Fig. 46 is 0.02–0.03, and, during the swap of the panels, it could happen that the fiber changed its position or shape slightly.Concerning the speech transmission in terms of STIPA, the values for all the setups are displayed in Table In terms of the cable position, the lowest STI is observed with a hanging cable and with the cable placed on foam blocks. In these cases, the cable is blocked from mechanical vibrations coming from the panel itself. These vibrations are generated by the acoustic waves from the audio source, and play a crucial role in a surprisingly high increase of the STI value. The STI in these two cases is even greater than when panels are removed. The panel plays the role of a resonator here.The cable type seems to be an imperative factor in the transmission of speech. While the best STI score by far has been achieved with the FTTX cable (0.66), the KDP cable is much more resistant to vibrations, reaching the lowest STI of 0.23. The ranking of the cables corresponds with the frequency-dependent SNRf analysis presented in Fig. In the setup with a Faraday mirror, its position affects the resulting STI, but this effect is not as pronounced as the effect of the cable type. The best score of STI 0.65 has been achieved with the mirror lying on the panel. Yet, such a high value should be probably attributed to the fact that only in this particular setup, the resonator effect of the panel, as described above, happened. See Fig. In the paper, we focused on the design of a reference method for measuring the sensitivity of optical cables to acoustic vibrations in the audible spectrum. In addition to evaluating the sensitivity of several different fiber optic cables, the influence of the ceiling panel type on the transmission quality was also evaluated. The most sensitive optical fiber sensor systems as well as standard audio microphones were used for the measurements, thanks to which it was possible to obtain relevant information about acoustic wave propagation. In order to consider the measurement as a reference, anechoic chamber/room was used and three different signal processing methods were proposed. The results show that optical cable infrastructures inside buildings can be used as sensitive microphones and can pick up human speech.In future work, we would like to focus more on the post-processing of the acquired audio signals and, with the use of suitable algorithms, achieve an improvement in the quality of the obtained audio signals. We would also like to focus on measurements in real conditions, i.e. in a room with existing optical infrastructure primarily used for data transmission. In real conditions, degradation of the measurement quality can be expected due to a large number of different sources of interference. However, thanks to the data obtained from the reference measurement in the anechoic chamber, we believe that with appropriate post-processing we will be able to suppress some of the interferences and increase the quality and intelligibility of audio.


As for isolated chlorophyll, the vibronic coupling is found to have a strong influence on the high-frequency vibrational sideband in the absorption spectrum, giving rise to a band splitting. In contrast, in the CD spectrum the interplay of vibronic coupling and static disorder leads to a strong suppression of the vibrational sideband in excellent agreement with the experimental data. The conservative nature of the CD spectrum in the low-energy region is found to be caused by a delicate balance of the intermonomer excitonic coupling between the purely electronic QAn electron-vibrational coupling model that includes the vibronic (non-adiabatic) coupling between the QThe online version contains supplementary material available at 10.1007/s11120-022-00946-3. Non-adiabatic couplings between different excited electronic states of chlorophyll (Chl) and related pigments in photosynthetic antennae give rise to a fast internal conversion of excitation energy to the first excited state Sa and to a much lesser extent in bacteriochlorophyll a  Spano  and onlyi to the system-bath coupling Hamiltonian From mentclass2pt{minimFor the calculation of linear absorption spectra we introduce the lower and upper triangular part of the vectorial transition dipole operator in the exciton basis, n of a single monomer unit a from the electronic ground state are given as a, where the position is identified with the center of mass, and the corresponding electronic transition dipole moment: a  spectra not only the electronic transition dipole moments, which under the assumption of localized excitation of electronic state y to Eq.  we formuThe correlation functions a from the literature, we adopt the model parameters of the monomer specified in Reimers et al.  region of the spectra. According to Reimers et al. . For the excitonic couplings between the electronic transitions of the different monomer units we used the following estimates: For the coupling between the Qa and b and the additional factor k-th and the c. The resulting values of the excitonic coupling in the subspace of QIn the case of the Qs et al. , leadingn in Eq. , where in in Eq.  the Huann in Eq. . This reAs mentioned in  Section  “Monomer Hamiltonian” we only take a very limited number of vibrational excitations into account. While only a single intramolecular vibration can be excited to its first vibrational eigenstate, excitation of up to four vibrational quanta of the vibronic coupling mode is possible in the framework of our treatment. The applied restriction with respect to the number of intramolecular vibrational excitations can be justified by the small Huang–Rhys factors of the respective modes. Even though there is no displacement of the vibronic coupling mode upon electronic excitation, the vibronic coupling leads to an effective displacement in the diagonalized Hamiltonian. As the corresponding Huang–Rhys factor is estimated to be larger than the Huang–Rhys factors of the individual intramolecular vibrational modes, we take four excited vibrational eigenstates into account to ensure convergence. Please note that simultaneous excitation of an intramolecular vibrational mode and of the vibronic coupling mode is feasible in our treatment. Such combined excitations gain relevance in the side band region of absorption and CD spectra. However, including them drastically increases the numerical effort, making convergence tests with respect to the number of vibrational modes, included in the model, and with respect to restrictions regarding the number of vibrationally excited basis states difficult. We therefore applied such tests only at an earlier stage of the development of our model, where simultaneous excitation of an intramolecular vibrational mode and of the vibronic coupling mode had not been included yet. Some of the respective results are shown in Section IB of the SI.It is worth mentioning that the vibronic coupling relies on the concept of a conical intersection. For the description of conical intersections separable tuning and a coupling modes can be identified Robb , where oa monomers in ether  and from a calculation where the coupling between the 0-0 QThe lower part in Fig. a dimer in WSCP, we are ready to discuss the comparison of our calculated spectra with the experimental data in Fig. a in ether) by Reimers et al. . In thes et al.  could bea these low-intensity transitions can compensate their small dipole strength by a much smaller energy difference with respect to the QExcellent agreement between theory and experiment is obtained for the CD spectrum Below is the link to the electronic supplementary material.


Ka of each component. This approach can be expanded to layered systems to generate many varied systems by changing composition and rates of pH change, adapting their microstructure and so allowing access to a far greater range of morphologies and complexity than can be achieved in single component systems.We use a pH‐driven annealing process to convert between co‐assembled and self‐sorted networks in multicomponent gels. The initially formed gels at low pH are co‐assembled, with the two components coexisting within the same self‐assembled structures. We use an enzymatic approach to increase the pH, resulting in a gel‐to‐sol transition, followed by a hydrolysis to lower the pH once again. As the pH decreases, a self‐sorted network is formed by a two‐stage gelation process determined by the p Annealing changes the assembly of fibres and leads to self‐sorting in the case of multicomponent systems. When a multilayer gel is formed, annealing can be used to form hybrid materials. There is significant current interest in systems that evolve and change with time,Most current examples focus on a single self‐assembling component. This component self‐assembles in different ways controlled by the solution conditions. Hence, the changes in the global system control the self‐assembled structures present and hence changes in, for example pH, result directly in whether structures such as micelles or persistent fibers are formed, the latter of which would typically lead to a gel phase.In terms of multicomponent systems, the situation is more complex. Where both components can adopt different self‐assembled structures, it is possible to form structures which comprise either both or either of the components to give co‐assembled or self‐sorted systems respectively  which results in an increase in solubility and a structural shift from fibrous structures to wormlike micellar structures.2 and ammonia are formed, which often results in gas bubbles being formed in the gels. We stress that these bubbles do not affect the reproducibility of the data discussed below.Similar gels are formed on addition of an aqueous solution containing urease, urea and methyl formate as described elsewhere for single component systems.Ka of FmocFF. There is an inflection in the rheology data when the apparent pKa of 1ThNapFF is reached. Hence, the transition back to a gel phase occurs in a multistep fashion which can be linked directly to the apparent pKa of each component.Ka of one unit is sufficient for self‐sorting to occur in such systems.Following the entire process for the multicomponent system with time Figure c shows tTo confirm whether co‐assembly or self‐sorting are occurring in the initially formed and pH‐annealed systems, we used a number of techniques. Circular dichroism (CD) spectra Figure a and 3b 1H NMR spectroscopy was used to follow the pH increase and pH decrease using the integrations of the gelators , slowing down the rate of pH increase. Due to the broad resonances, it was not possible to integrate the FmocFF and 1ThNapFF separately . However, the resonances of the 6 and 7 position of the cyclohexyl moiety of 1ThNapFF were resolvable. When the pH of a two‐component sample is increased with urea‐urease alone, the combined integral of the aromatic protons of both gelators, and the 6 and 7 position of 1ThNapFF increase at the same rate  of the gelators are soluble at the first time point in the urea‐urease methyl formate sample, although accurate integration is not possible due to the short relaxation delays necessary to capture the system at early time points when it is evolving rapidly . When the pH of a 2 mg mL−1 sample of 1ThNapFF alone decreases in the presence of urea‐urease and methyl formate, the aromatic and cyclohexyl protons decrease in intensity at the same rate . Overall, these data show that we initially have a co‐assembled network which dissolves as the pH increases and then a self‐sorted network is formed on pH decrease.s Figure c preclude Figure c, suggese Figure d, the inWe can tune the rate of pH change  and hence the properties of the material  by varying the amounts of methyl formate, urea, or urease used. A decrease in the concentration of either urea or urease resulted in decrease in the rate of the pH increase during annealing. The rate of pH change can further be controlled by increasing the concentration of methyl formate. Since 1ThNapFF forms wormlike micelles at high pHThis annealing approach can be used to change the composition of a gel. For all of the discussion below, we highlight that we are using NMR data and rheological data to show that we can control the exact composition in a spatially resolved manner and that this leads to changes in the mechanical properties. The rheological properties evolve over long time periods  and so we focus here on differences not on absolute values.First, to exemplify the methodology, a layered gel was formed, with the bottom layer formed from only 1ThNapFF and the top layer from FmocFF. No urea, urease and methyl formate were included and so no annealing is expected. After 16 hours, the gel was sliced into 6 segments and the composition determined by NMR . As expected, after slicing into segments, each of the segments contained only 1ThNapFF or FmocFF  should be addressed to the authors.Supporting InformationClick here for additional data file.