There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Economic Control of Quality of Manufactured Product.

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

In this work, we investigate linear model based multivariable control schemes for proton exchange membrane fuel cells (PEMFCs). Much of the literature relies on a mechanistic model to design model predictive controllers; however, this can be a difficult and time-consuming exercise for a PEMFC. An effective approach for developing models for control purposes is to use time series analysis and develop control oriented state space models directly from input-output data. In the present work, we develop an innovation form of state space model from input-output perturbation data obtained from a PEMFC. We then demonstrate the development of infinite horizon unconstrained linear model predictive controllers (LMPC) using these models, and compare their performance to IMC based PI control. We conduct servo and regulatory control studies on an experimental single cell PEMFC system, and demonstrate that the proposed control schemes regulate the power obtained from the fuel cell as desired even in the presence of disturbances.

/pdf/experimental-evaluation-of-linear-model-based-control-35osw01dvl.pdf

Experimental evaluation of linear model based control strategies for PEMFCs

A computerized method for designing a discrete droplet microfluidic system: (a) provides an initial set of droplet based networks; (b) codes each droplet based network into a data structure such that all the data structures form a current set of data structures; (c) creates new data structures by performing one or more genetic operators on the current set of data structures; (d) adds new data structures to the current set of data structures; (e) creates a new set of data structures that satisfies one or more design parameters; (f) replaces the current set of data structures with the new set of data structures; (g) repeats steps (c), (d), (e) and (f) until the new set of data structures has been created a third number of times; and (h) displays/outputs the current set of data structures as possible designs for the discrete droplet microfluidic system to one or more output devices.

System and method for simulation and design of discrete droplet microfluidic systems

/pdf/nonlinear-dynamics-in-a-microfluidic-loop-device-chaos-and-4dgo40lodu.pdf

Nonlinear dynamics in a microfluidic loop device: Chaos and Fractals

Background: The prevalence of preterm birth (PTB) is high in lower and middle-income countries (LMIC) such as India. In LMIC, since a large proportion seeks antenatal care for the first time beyond 14-weeks of pregnancy, accurate estimation of gestational age (GA) using measures derived from ultrasonography scans in the second and third trimesters is of paramount importance. Different models have been developed globally to estimate GA, and currently, LMIC uses Hadlock9s formula derived from data based on a North American cohort. This study aimed to develop a population-specific model using data from GARBH-Ini, a multidimensional and ongoing pregnancy cohort established in a district hospital in North India for studying PTB.

Methods: Data obtained by longitudinal ultrasonography across all trimesters of pregnancy was used to develop and validate GA models for second and third trimesters. The first trimester GA estimated by ultrasonography was considered the Gold Standard. The second and third trimester GA model named, Garbhini-GA2 is a multivariate random forest model using five ultrasonographic parameters routinely measured during this period. Garbhini-GA2 model was compared to Hadlock and INTERGROWTH-21st models in the TEST set by estimating root mean-squared error, bias and PTB rate.

Findings: Garbhini-GA2 reduced the GA estimation error by 23-45% compared to the published models. Furthermore, the PTB rate estimated using Garbhini-GA2 was more accurate when compared to published formulae that overestimated the rate by 1.5-2.0 times. 

Interpretation: The Garbhini-GA2 model developed is the first of its kind developed solely using Indian population data. The higher accuracy of GA estimation by Garbhini-GA2 emphasises the need to apply population-specific GA formulae to improve antenatal care and better PTB rate estimates.

/pdf/development-of-second-and-third-trimester-population-1gzoh80bhk.pdf

Development of second and third-trimester population-specific machine learning pregnancy dating model (Garbhini-GA2) derived from the GARBH-Ini cohort in north India

The ability to manipulate drops is essential for integrating multiple processes in droplet microfluidics-based lab-on-a-chip devices. Examples of such droplet manipulation operations include sorting, sequencing, synchronization, and so forth. Microfluidic networks are promising platforms for performing these functionalities. This work explores the design of entry times of drops, a set of operating parameters, in a microfluidic network to achieve a desired functionality. Here, we specifically focus on sorting of drops at the exit of the network. For the first time, droplet microfluidic networks are perceived as hybrid dynamical systems. This viewpoint allows us to develop a methodology for designing the entry times of drops in microfluidic networks to achieve desired functionalities through the notion of constraint satisfaction. The solution to this constraint satisfaction problem provides entry times that result in the desired functionality. The proposed method allows one to establish the existence/nonexistence of entry time solutions for a desired functionality. 

Raghunathan Rengaswamy

Papers

Experimental evaluation of linear model based control strategies for PEMFCs

System and method for simulation and design of discrete droplet microfluidic systems

Nonlinear dynamics in a microfluidic loop device: Chaos and Fractals

Development of second and third-trimester population-specific machine learning pregnancy dating model (Garbhini-GA2) derived from the GARBH-Ini cohort in north India

Droplet microfluidic networks as hybrid dynamical systems: Inlet spacing optimization for sorting of drops