Engineering and Scientific Applications: Using MatLab(Registered Trademark) for Data Processing and Visualization

MatLab(R) (MATrix LABoratory) is a numerical computation and simulation tool that is used by thousands Scientists and Engineers in many cou ntries. MatLab does purely numerical calculations, which can be used as a glorified calculator or interpreter programming language; its re al strength is in matrix manipulations. Computer algebra functionalities are achieved within the MatLab environment using "symbolic" toolbo x. This feature is similar to computer algebra programs, provided by Maple or Mathematica to calculate with mathematical equations using s ymbolic operations. MatLab in its interpreter programming language fo rm (command interface) is similar with well known programming languag es such as C/C++, support data structures and cell arrays to define c lasses in object oriented programming. As such, MatLab is equipped with most ofthe essential constructs of a higher programming language. M atLab is packaged with an editor and debugging functionality useful t o perform analysis of large MatLab programs and find errors. We belie ve there are many ways to approach real-world problems; prescribed methods to ensure foregoing solutions are incorporated in design and ana lysis of data processing and visualization can benefit engineers and scientist in gaining wider insight in actual implementation of their perspective experiments. This presentation will focus on data processing and visualizations aspects of engineering and scientific applicati ons. Specifically, it will discuss methods and techniques to perform intermediate-level data processing covering engineering and scientifi c problems. MatLab programming techniques including reading various data files formats to produce customized publication-quality graphics, importing engineering and/or scientific data, organizing data in tabu lar format, exporting data to be used by other software programs such as Microsoft Excel, data presentation and visualization will be discussed. The presentation will emphasize creating practIcal scripts (pro grams) that extend the basic features of MatLab TOPICS mclude (1) Ma trix and vector analysis and manipulations (2) Mathematical functions (3) Symbolic calculations & functions (4) Import/export data files (5) Program lOgic and flow control (6) Writing function and passing parameters (7) Test application program

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b , where A is an m by x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as 4x(sub 1) + 6x(sub 2) + 5x (sub 3) = 10, where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or a minimum norm solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning

Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning

Experimental observation of extreme multistability in an electronic system of two coupled R\"{o}ssler oscillators

We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems. We construct and couple two analog circuits based on a modified coupled R\"{o}ssler system and demonstrate the occurrence of extreme multistability through a controlled switching to different attractor states purely through a change in initial conditions for a fixed set of system parameters. Numerical studies of the coupled model equations are in agreement with our experimental findings.Comment: to be published in Phys. Rev.

Cholesterol Corrects Altered Conformation of MHC-II Protein in Leishmania donovani Infected Macrophages: Implication in Therapy

Previously we reported that Kala-azar patients show progressive decrease in serum cholesterol as a function of splenic parasite burden. Splenic macrophages (MΦ) of Leishmania donovani (LD) infected mice show decrease in membrane cholesterol, while LD infected macrophages (I-MΦ) show defective T cell stimulating ability that could be corrected by liposomal delivery of cholesterol. T helper cells recognize peptide antigen in the context of class II MHC molecule. It is known that the conformation of a large number of membrane proteins is dependent on membrane cholesterol. In this investigation we tried to understand the influence of decreased membrane cholesterol in I-MΦ on the conformation of MHC-II protein and peptide-MHC-II stability, and its bearing on the antigen specific T-cell activatio

Restoration of IFNγR Subunit Assembly, IFNγ Signaling and Parasite Clearance in Leishmania donovani Infected Macrophages: Role of Membrane Cholesterol

Despite the presence of significant levels of systemic Interferon gamma (IFNγ), the host protective cytokine, Kala-azar patients display high parasite load with downregulated IFNγ signaling in Leishmania donovani (LD) infected macrophages (LD-MØs); the cause of such aberrant phenomenon is unknown. Here we reveal for the first time the mechanistic basis of impaired IFNγ signaling in parasitized murine macrophages. Our study clearly shows that in LD-MØs IFNγ receptor (IFNγR) expression and their ligand-affinity remained unaltered. The intracellular parasites did not pose any generalized defect in LD-MØs as IL-10 mediated signal transducer and activator of transcription 3 (STAT3) phosphorylation remained unaltered with respect to normal. Previously, we showed that LD-MØs are more fluid than normal MØs due to quenching of membrane cholesterol. The decreased rigidity in LD-MØs was not due to parasite derived lipophosphoglycan (LPG) because purified LPG failed to alter fluidity in normal MØs. IFNγR subunit 1 (IFNγR1) and subunit 2 (IFNγR2) colocalize in raft upon IFNγ stimulation of normal MØs, but this was absent in LD-MØs. Oddly enough, such association of IFNγR1 and IFNγR2 could be restored upon liposomal delivery of cholesterol as evident from the fluorescence resonance energy transfer (FRET) experiment and co-immunoprecipitation studies. Furthermore, liposomal cholesterol treatment together with IFNγ allowed reassociation of signaling assembly (phospho-JAK1, JAK2 and STAT1) in LD-MØs, appropriate signaling, and subsequent parasite killing. This effect was cholesterol specific because cholesterol analogue 4-cholestene-3-one failed to restore the response. The presence of cholesterol binding motifs [(L/V)-X1–5-Y-X1–5-(R/K)] in the transmembrane domain of IFNγR1 was also noted. The interaction of peptides representing this motif of IFNγR1 was studied with cholesterol-liposome and analogue-liposome with difference of two orders of magnitude in respective affinity (KD: 4.27×10−9 M versus 2.69×10−7 M). These observations reinforce the importance of cholesterol in the regulation of function of IFNγR1 proteins. This study clearly demonstrates that during its intracellular life-cycle LD perturbs IFNγR1 and IFNγR2 assembly and subsequent ligand driven signaling by quenching MØ membrane cholesterol

Knowledge Priorities on Climate Change and Water in the Upper Indus Basin: A Horizon Scanning Exercise to Identify the Top 100 Research Questions in Social and Natural Sciences

River systems originating from the Upper Indus Basin (UIB) are dominated by runoff from snow and glacier melt and summer monsoonal rainfall. These water resources are highly stressed as huge populations of people living in this region depend on them, including for agriculture, domestic use, and energy production. Projections suggest that the UIB region will be affected by considerable (yet poorly quantified) changes to the seasonality and composition of runoff in the future, which are likely to have considerable impacts on these supplies. Given how directly and indirectly communities and ecosystems are dependent on these resources and the growing pressure on them due to ever-increasing demands, the impacts of climate change pose considerable adaptation challenges. The strong linkages between hydroclimate, cryosphere, water resources, and human activities within the UIB suggest that a multi- and inter-disciplinary research approach integrating the social and natural/environmental sciences is critical for successful adaptation to ongoing and future hydrological and climate change. Here we use a horizon scanning technique to identify the Top 100 questions related to the most pressing knowledge gaps and research priorities in social and natural sciences on climate change and water in the UIB. These questions are on the margins of current thinking and investigation and are clustered into 14 themes, covering three overarching topics of ‘governance, policy, and sustainable solutions’, ‘socioeconomic processes and livelihoods’, and ‘integrated Earth System processes’. Raising awareness of these cutting-edge knowledge gaps and opportunities will hopefully encourage researchers, funding bodies, practitioners, and policy makers to address them