Attribute reduction and missing value imputing with ANN: prediction of learning disabilities

Learning disability (LD) is a neurological condition that affects a child’s brain and impairs his ability to carry out one or many specific tasks. LD affects about 10% of children enrolled in schools. There is no cure for learning disabilities and they are lifelong. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. Just as there are many different types of LDs, there are a variety of tests that may be done to pinpoint the problem The information gained from an evaluation is crucial for finding out how the parents and the school authorities can provide the best possible learning environment for child. This paper proposes a new approach in artificial neural network (ANN) for identifying LD in children at early stages so as to solve the problems faced by them and to get the benefits to the students, their parents and school authorities. In this study, we propose a closest fit algorithm data preprocessing with ANN classification to handle missing attribute values. This algorithm imputes the missing values in the preprocessing stage. Ignoring of missing attribute values is a common trend in all classifying algorithms. But, in this paper, we use an algorithm in a systematic approach for classification, which gives a satisfactory result in the prediction of LD. It acts as a tool for predicting the LD accurately, and good information of the child is made available to the concerned

Raman and FTIR studies of the structural aspects of Nasicon-type crystals; AFeTi(PO4)3 [A ¼ Ca, Cd]

Raman and FTIR spectra of CaFeTi(PO4)3 and CdFeTi(PO4)3 are recorded and analyzed. The observed bands are assigned in terms of vibrations of TiO6 octahedra and PO4 tetrahedra. The symmetry of TiO6 octrahedra and PO4 tetrahedra is lowered from their free ion symmetry. The presence of Fe3+ ion disrupts the Ti–O–P–O–Ti chain and leads to the distortion of TiO6 octrahedra and PO4 tetrahedra. The PO4 3 tetrahedra in both crystals are linearly distorted. The covalency bonding factor of PO4 3 polyanion of both the crystals are calculated from the Raman spectra and compared to that of other Nasicon-type systems. The numerical values of covalency bonding factor indicates that there is a reduction in redox energy and cell voltage and is attributed to strong covalency of PO4 3 polyanionin

Learning analysis by reduction from positive data

Analysis by reduction is a linguistically motivated method for checking correctness of a sentence. It can be modelled by restarting automata. In this paper we propose a method for learning restarting automata which are strictly locally testable (SLT-R-automata). The method is based on the concept of identification in the limit from positive examples only. Also we characterize the class of languages accepted by SLT-R-automata with respect to the Chomsky hierarchy.

A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Künstliche Randbedingungen und Algebraische Äquivalenzen in der Elastizitätstheorie

In dieser Arbeit werden zwei Aspekte bei Randwertproblemen der linearen Elastizitätstheorie untersucht: die Approximation von Lösungen auf unbeschränkten Gebieten und die Änderung von Symmetrieklassen unter speziellen Transformationen. Ausgangspunkt der Dissertation ist das von Specovius-Neugebauer und Nazarov in "Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type"(Math. Meth. Appl. Sci, 2004; 27) eingeführte Verfahren zur Untersuchung von Petrovsky-Systemen zweiter Ordnung in Außenraumgebieten und Gebieten mit konischen Ausgängen mit Hilfe der Methode der künstlichen Randbedingungen. Dabei werden für die Ermittlung von Lösungen der Randwertprobleme die unbeschränkten Gebiete durch das Abschneiden mit einer Kugel beschränkt, und es wird eine künstliche Randbedingung konstruiert, um die Lösung des Problems möglichst gut zu approximieren. Das Verfahren wird dahingehend verändert, dass das abschneidende Gebiet ein Polyeder ist, da es für die Lösung des Approximationsproblems mit üblichen Finite-Element-Diskretisierungen von Vorteil sei, wenn das zu triangulierende Gebiet einen polygonalen Rand besitzt. Zu Beginn der Arbeit werden die wichtigsten funktionalanalytischen Begriffe und Ergebnisse der Theorie elliptischer Differentialoperatoren vorgestellt. Danach folgt der Hauptteil der Arbeit, der sich in drei Bereiche untergliedert. Als erstes wird für abschneidende Polyedergebiete eine formale Konstruktion der künstlichen Randbedingungen angegeben. Danach folgt der Nachweis der Existenz und Eindeutigkeit der Lösung des approximativen Randwertproblems auf dem abgeschnittenen Gebiet und im Anschluss wird eine Abschätzung für den resultierenden Abschneidefehler geliefert. An die theoretischen Ausführungen schließt sich die Betrachtung von Anwendungsbereiche an. Hier werden ebene Rissprobleme und Polarisationsmatrizen dreidimensionaler Außenraumprobleme der Elastizitätstheorie erläutert. Der letzte Abschnitt behandelt den zweiten Aspekt der Arbeit, den Bereich der Algebraischen Äquivalenzen. Hier geht es um die Transformation von Symmetrieklassen, um die Kenntnis der Fundamentallösung der Elastizitätsprobleme für transversalisotrope Medien auch für Medien zu nutzen, die nicht von transversalisotroper Struktur sind. Eine allgemeine Darstellung aller Klassen konnte hier nicht geliefert werden. Als Beispiel für das Vorgehen wird eine Klasse von orthotropen Medien im dreidimensionalen Fall angegeben, die sich auf den Fall der Transversalisotropie reduzieren lässt.

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

Noise Reduction Using Low Weight and Constant Weight Coding Techniques

Signalling off-chip requires significant current. As a result, a chip's power-supply current changes drastically during certain output-bus transitions. These current fluctuations cause a voltage drop between the chip and circuit board due to the parasitic inductance of the power-supply package leads. Digital designers often go to great lengths to reduce this "transmitted" noise. Cray, for instance, carefully balances output signals using a technique called differential signalling to guarantee a chip has constant output current. Transmitted-noise reduction costs Cray a factor of two in output pins and wires. Coding achieves similar results at smaller costs.

Using Recurrent Networks for Dimensionality Reduction

This report explores how recurrent neural networks can be exploited for learning high-dimensional mappings. Since recurrent networks are as powerful as Turing machines, an interesting question is how recurrent networks can be used to simplify the problem of learning from examples. The main problem with learning high-dimensional functions is the curse of dimensionality which roughly states that the number of examples needed to learn a function increases exponentially with input dimension. This thesis proposes a way of avoiding this problem by using a recurrent network to decompose a high-dimensional function into many lower dimensional functions connected in a feedback loop.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

3D Object Recognition: Symmetry and Virtual Views

Many 3D objects in the world around us are strongly constrained. For instance, not only cultural artifacts but also many natural objects are bilaterally symmetric. Thoretical arguments suggest and psychophysical experiments confirm that humans may be better in the recognition of symmetric objects. The hypothesis of symmetry-induced virtual views together with a network model that successfully accounts for human recognition of generic 3D objects leads to predictions that we have verified with psychophysical experiments.

Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Operational Cost Reduction in WDM Networks using Lighttours

Wavelength division multiplexing (WDM) networks have been adopted as a near-future solution for the broadband Internet. In previous work we proposed a new architecture, named enhanced grooming (G+), that extends the capabilities of traditional optical routes (lightpaths). In this paper, we compare the operational expenditures incurred by routing a set of demands using lightpaths with that of lighttours. The comparison is done by solving an integer linear programming (ILP) problem based on a path formulation. Results show that, under the assumption of single-hop routing, almost 15% of the operational cost can be reduced with our architecture. In multi-hop routing the operation cost is reduced in 7.1% and at the same time the ratio of operational cost to number of optical-electro-optical conversions is reduced for our architecture. This means that ISPs could provide the same satisfaction in terms of delay to the end-user with a lower investment in the network architecture

Asymmetric tunnels in P2MP LSPs as a label space reduction method

The objective of traffic engineering is to optimize network resource utilization. Although several works have been published about minimizing network resource utilization, few works have focused on LSR (label switched router) label space. This paper proposes an algorithm that takes advantage of the MPLS label stack features in order to reduce the number of labels used in LSPs. Some tunnelling methods and their MPLS implementation drawbacks are also discussed. The described algorithm sets up NHLFE (next hop label forwarding entry) tables in each LSR, creating asymmetric tunnels when possible. Experimental results show that the described algorithm achieves a great reduction factor in the label space. The presented works apply for both types of connections: P2MP (point-to-multipoint) and P2P (point-to-point)