Error, Confidence, and Cost in Engineering Computations

The questions that one should answer in engineering computations - deterministic, probabilistic/randomized, as well as heuristic - are (i) how good the computed results/outputs are and (ii) how much the cost in terms of amount of computation and the amount of storage utilized in getting the outputs is. The absolutely errorfree quantities as well as the completely errorless computations done in a natural process can never be captured by any means that we have at our disposal. While the computations including the input real quantities in nature/natural processes are exact, all the computations that we do using a digital computer or are carried out in an embedded form are never exact. The input data for such computations are also never exact because any measuring instrument has inherent error of a fixed order associated with it and this error, as a matter of hypothesis and not as a matter of assumption, is not less than 0.005 per cent. Here by error we imply relative error bounds. The fact that exact error is never known under any circumstances and any context implies that the term error is nothing but error-bounds. Further, in engineering computations, it is the relative error or, equivalently, the relative error-bounds (and not the absolute error) which is supremely important in providing us the information regarding the quality of the results/outputs. Another important fact is that inconsistency and/or near-consistency in nature, i.e., in problems created from nature is completely nonexistent while in our modelling of the natural problems we may introduce inconsistency or near-inconsistency due to human error or due to inherent non-removable error associated with any measuring device or due to assumptions introduced to make the problem solvable or more easily solvable in practice. Thus if we discover any inconsistency or possibly any near-inconsistency in a mathematical model, it is certainly due to any or all of the three foregoing factors. We do, however, go ahead to solve such inconsistent/near-consistent problems and do get results that could be useful in real-world situations. The talk considers several deterministic, probabilistic, and heuristic algorithms in numerical optimisation, other numerical and statistical computations, and in PAC (probably approximately correct) learning models. It highlights the quality of the results/outputs through specifying relative error-bounds along with the associated confidence level, and the cost, viz., amount of computations and that of storage through complexity. It points out the limitation in error-free computations (wherever possible, i.e., where the number of arithmetic operations is finite and is known a priori) as well as in the usage of interval arithmetic. Further, the interdependence among the error, the confidence, and the cost is discussed.

A digital herbarium for the flora of Karnataka

A herbarium-based database (virtual herbarium) is a referral system for plants that maximizes the usefulness of the collections. The information content of such a database is essentially built on the voucher specimens that the herbarium has in its care. The present article reports on the construction of a `virtual herbarium' for the state-wide collection of flowering plants in the Herbarium JCB housed at the Centre for Ecological Sciences, Indian Institute of Science, Bangalore, that is expected to be launched soon. The taxonomic data on each species include all information presented on the herbarium specimen label, namely species name, author citation, sub-species if any, variety if any, family, subfamily, collection number, locations, date of collection, habitat and the collector's name. The data further comprise `flora' in which the species are described. Additional information includes the nomenclature update according to `The Plant List', a detailed description, phenology, species distribution, threat status and comments on any special features of the taxon. The live images of the species provided in the database form an information synergy on the species. This initiative is the first of its kind for herbaria in peninsular India.

Unusual co-crystal of isonicotinamide: the structural landscape in crystal engineering

The idea of a structural landscape is based on the fact that a large number of crystal structures can be associated with a particular organic molecule. Taken together, all these structures constitute the landscape. The landscape includes polymorphs, pseudopolymorphs and solvates. Under certain circumstances, it may also include multicomponent crystals (or co-crystals) that contain the reference molecule as one of the components. Under still other circumstances, the landscape may include the crystal structures of molecules that are closely related to the reference molecule. The idea of a landscape is to facilitate the understanding of the process of crystallization. It includes all minima that can, in principle, be accessed by the molecule in question as it traverses the path from solution to the crystal. Isonicotinamide is a molecule that is known to form many co-crystals. We report here a 2 : 1 co-crystal of this amide with 3,5-dinitrobenzoic acid, wherein an unusual N-H center dot center dot center dot N hydrogen-bonded pattern is observed. This crystal structure offers some hints about the recognition processes between molecules that might be implicated during crystallization. Also included is a review of other recent results that illustrate the concept of the structural landscape.

Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data

Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called `early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.

Crystal Engineering in the Desiraju Research Group in Bangalore

Over the years, crystal engineering has transformed into a mature and multidisciplinary subject. New understanding, challenges, and opportunities have emerged in the design of complex structures and structure-property evaluation. Revolutionary pathways adopted by many leaders have shaped and directed this subject. In this short essay to celebrate the 60th birthday of Prof. Gautam R. Desiraju, we, his current research group members, contemplate the development of some of the topics explored by our group in the context of the overall subject. These topics, though not entirely new, are of significant interest to the crystal engineering community.

Demonstrating the Usefulness of CAELinux for Computer Aided Engineering using an Example of the Three Dimensional Reconstruction of a Pig Liver

CAELinux is a Linux distribution which is bundled with free software packages related to Computer Aided Engineering (CAE). The free software packages include software that can build a three dimensional solid model, programs that can mesh a geometry, software for carrying out Finite Element Analysis (FEA), programs that can carry out image processing etc. Present work has two goals: 1) To give a brief description of CAELinux 2) To demonstrate that CAELinux could be useful for Computer Aided Engineering, using an example of the three dimensional reconstruction of a pig liver from a stack of CT-scan images. One can note that instead of using CAELinux, using commercial software for reconstructing the liver would cost a lot of money. One can also note that CAELinux is a free and open source operating system and all software packages that are included in the operating system are also free. Hence one can conclude that CAELinux could be a very useful tool in application areas like surgical simulation which require three dimensional reconstructions of biological organs. Also, one can see that CAELinux could be a very useful tool for Computer Aided Engineering, in general.

Point Spread Function Engineering for Super-Resolution Single-Photon and Multiphoton Fluorescence Microscopy

Super-resolution imaging techniques are of paramount interest for applications in bioimaging and fluorescence microscopy. Recent advances in bioimaging demand application-tailored point spread functions. Here, we present some approaches for generating application-tailored point spread functions along with fast imaging capabilities. Aperture engineering techniques provide interesting solutions for obtaining desired system point spread functions. Specially designed spatial filters—realized by optical mask—are outlined both in a single-lens and 4Pi configuration. Applications include depth imaging, multifocal imaging, and super-resolution imaging. Such an approach is suitable for fruitful integration with most existing state-of-art imaging microscopy modalities.

Nanoindentation in Crystal Engineering: Quantifying Mechanical Properties of Molecular Crystals

Nanoindentation is a technique for measuring the elastic modulus and hardness of small amounts of materials. This method, which has been used extensively for characterizing metallic and inorganic solids, is now being applied to organic and metalorganic crystals, and has also become relevant to the subject of crystal engineering, which is concerned with the design of molecular solids with desired properties and functions. Through nanoindentation it is possible to correlate molecular-level properties such as crystal packing, interaction characteristics, and the inherent anisotropy with micro/macroscopic events such as desolvation, domain coexistence, layer migration, polymorphism, and solid-state reactivity. Recent developments and exciting opportunities in this area are highlighted in this Minireview.

Engineering Gold Nanoparticle Interaction by PAMAM Dendrimer

Bare faceted gold nanoparticles (AuNPs) have a tendency to aggregate through a preferred attachment of the 111] surfaces. We have used fully atomistic classical molecular dynamics simulations to obtain a quantitative estimate of this surface interaction using umbrella sampling (US) at various temperatures. To tune this surface interaction, we use polyamidoamine (PAMAM) dendrimer to coat the gold surface under various conditions. We observe a spontaneous adsorption of the protonated as well as nonprotonated PAMAM dendrimer on the AuNP surface. The adsorbed dendrimer on the nanoparticle surface strongly alters the interaction between the nanoparticles. We calculate the interaction between dendrimercoated AuNPs using US and show how the interaction between two bare faceted AuNPs can be tuned as a function of dendrimer concentration and charge (pH dependent) With appropriate choice of the dendrimer concentration and charge, two strongly interacting AuNPs can be made effectively noninteracting. Our simulation results demonstrate a strategy to tune the nanoparticle interaction, which can help in engineering self-assembly of such nanoparticles.

Scaffolds for bone tissue engineering: role of surface patterning on osteoblast response

The fabrication of tissue engineering scaffolds necessitates amalgamation of a multitude of attributes including a desirable porosity to encourage vascular invasion, desired surface chemistry for controlled deposition of calcium phosphate-based mineral as well as ability to support attachment, proliferation, and differentiation of lineage specific progenitor cells. Scaffold fabrication often includes additional surface treatments to bring about desired changes in the surface chemistry. In this perspective, this review documents the important natural and synthetic scaffolds fabricated for bone tissue engineering applications in tandem with the surface treatment techniques to maneuver the biocompatibility of engineered scaffolds. This review begins with a discussion on the fundamental concepts related to biocompatibility as well as the characteristics of the biological micro-environment. The primary focus is to discuss the effects of surface micro/nano patterning on the modulation of bone cell response. Apart from reviewing a host of experimental studies reporting the functionality of osteoblast-like bone cells and stem cells on surface modified or textured bioceramic/biopolymer scaffolds, theoretical insights to predict cell behavior on a scaffold with different topographical features are also briefly analyzed.

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.

Crystal engineering: from molecule to crystal

How do molecules aggregate in solution, and how do these aggregates consolidate themselves in crystals? What is the relationship between the structure of a molecule and the structure of the crystal it forms? Why do some molecules adopt more than one crystal structure? Why do some crystal structures contain solvent? How does one design a crystal structure with a specified topology of molecules, or a specified coordination of molecules and/or ions, or with a specified property? What are the relationships between crystal structures and properties for molecular crystals? These are some of the questions that are being addressed today by the crystal engineering community, a group that draws from the larger communities of organic, inorganic, and physical chemists, crystallographers, and solid state scientists. This Perspective provides a brief historical introduction to crystal engineering itself and an assessment of the importance and utility of the supramolecular synthon, which is one of the most important concepts in the practical use and implementation of crystal design. It also provides a look to the future from the viewpoint of the author, and indicates some directions in which this field might be moving.