Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Momentum distribution in nuclear matter and finite nuclei

A simple method is presented to evaluate the effects of short-range correlations on the momentum distribution of nucleons in nuclear matter within the framework of the Greens function approach. The method provides a very efficient representation of the single-particle Greens function for a correlated system. The reliability of this method is established by comparing its results to those obtained in more elaborate calculations. The sensitivity of the momentum distribution on the nucleon-nucleon interaction and the nuclear density is studied. The momentum distributions of nucleons in finite nuclei are derived from those in nuclear matter using a local-density approximation. These results are compared to those obtained directly for light nuclei like 16O.

High-momentum proton removal from 16 O and the (e,e'p) cross section

The cross section for the removal of high-momentum protons from 16O is calculated for high missing energies. The admixture of high-momentum nucleons in the 16O ground state is obtained by calculating the single-hole spectral function directly in the finite nucleus with the inclusion of short-range and tensor correlations induced by a realistic meson-exchange interaction. The presence of high-momentum nucleons in the transition to final states in 15N at 60¿100 MeV missing energy is converted to the coincidence cross section for the (e,e¿p) reaction by including the coupling to the electromagnetic probe and the final state interactions of the outgoing proton in the same way as in the standard analysis of the experimental data. Detectable cross sections for the removal of a single proton at these high missing energies are obtained which are considerably larger at higher missing momentum than the corresponding cross sections for the p-wave quasihole transitions. Cross sections for these quasihole transitions are compared with the most recent experimental data available.

IRIS BIOMETRIC RECOGNITION SYSTEM EMPLOYING CANNY OPERATOR

Biometrics has become important in security applications. In comparison with many other biometric features, iris recognition has very high recognition accuracy because it depends on iris which is located in a place that still stable throughout human life and the probability to find two identical iris's is close to zero. The identification system consists of several stages including segmentation stage which is the most serious and critical one. The current segmentation methods still have limitation in localizing the iris due to circular shape consideration of the pupil. In this research, Daugman method is done to investigate the segmentation techniques. Eyelid detection is another step that has been included in this study as a part of segmentation stage to localize the iris accurately and remove unwanted area that might be included. The obtained iris region is encoded using haar wavelets to construct the iris code, which contains the most discriminating feature in the iris pattern. Hamming distance is used for comparison of iris templates in the recognition stage. The dataset which is used for the study is UBIRIS database. A comparative study of different edge detector operator is performed. It is observed that canny operator is best suited to extract most of the edges to generate the iris code for comparison. Recognition rate of 89% and rejection rate of 95% is achieved

Annealing inducedlowcoercivity,nanocrystallineCo–Fe–Si thin films exhibitinginversecosine angular variation

Co–Fe–Si based films exhibit high magnetic moments and are highly sought after for applications like soft under layer sinper pendicular recording mediatomagneto-electro-mechanical sensor applications.In this workt he effect of annealing on s tructural,morphologicaland magnetic propertiesofco–Fe–Si thin films wasinvestigated.compositional analysis using x-rayphotoelectron spectroscopy and secondary ion massspectroscopyrevealedanativeoxidesurfacelayerconsistingofoxidesofco,feandsionthe surface. The morphology of theas deposited films shows mound like structures conformingtothe Volmer–Webergrowthmodel.Nanocrystallisationofamorphous films upon annealing was observed by glancing anglex-raydiffraction and transmission electron microscopy.Theevolutionofmagnetic properties with annealing is explained using the Herzermodel.Vibrating sample magnetometry measurements carried out at various angles from01 to 901 to the applied magnetic field were employed to study the angula rvariation of coercivity.The angular variation fits the modified Kondorsky model. Interestingly,the coercivity evolution with annealing deduced frommagneto-opticalKerreffectstudies indicates areversetrendcomparedtomagetisationobservedinthebulk.Thiscanbeattributedtoa domain wallpinningatnativeoxidelayeronthesurfaceofthin films. Theevolutionofsurfacemagnetic properties iscorrelatedwithmorphologyevolutionprobedusingatomicforcemicroscopy.The morphology aswellasthepresenceofthenativeoxidelayerdictatesthesurfacemagneticproperties and this is corroborated by the apparent difference in the bulk and surface magnetic properties

Orthogonal polynomials and recurrence equations, operator equations and factorization

This article surveys the classical orthogonal polynomial systems of the Hahn class, which are solutions of second-order differential, difference or q-difference equations. Orthogonal families satisfy three-term recurrence equations. Example applications of an algorithm to determine whether a three-term recurrence equation has solutions in the Hahn class - implemented in the computer algebra system Maple - are given. Modifications of these families, in particular associated orthogonal systems, satisfy fourth-order operator equations. A factorization of these equations leads to a solution basis.

Elimination in Operator Algebras

A large class of special functions are solutions of systems of linear difference and differential equations with polynomial coefficients. For a given function, these equations considered as operator polynomials generate a left ideal in a noncommutative algebra called Ore algebra. This ideal with finitely many conditions characterizes the function uniquely so that Gröbner basis techniques can be applied. Many problems related to special functions which can be described by such ideals can be solved by performing elimination of appropriate noncommutative variables in these ideals. In this work, we mainly achieve the following: 1. We give an overview of the theoretical algebraic background as well as the algorithmic aspects of different methods using noncommutative Gröbner elimination techniques in Ore algebras in order to solve problems related to special functions. 2. We describe in detail algorithms which are based on Gröbner elimination techniques and perform the creative telescoping method for sums and integrals of special functions. 3. We investigate and compare these algorithms by illustrative examples which are performed by the computer algebra system Maple. This investigation has the objective to test how far noncommutative Gröbner elimination techniques may be efficiently applied to perform creative telescoping.

Der Momentum-Effekt und Momentum-Handelsstrategien

Diese Arbeit weist Momentum-Renditen für europäische Aktien im Zeitraum von 1991 bis 2010 nach, die – je nach Top/Flop-Prozentsatz – vor Kosten zwischen 6 und 19% p.a. liegen. Gleichzeitig liegen mit hohen Standardabweichungen, negativen Schiefe-Werten und hohen Drawdowns drei wesentliche Risikofaktoren vor. Für die Kernuntersuchungen des Top/Flop-Wertes von 5% treten die höchsten Momentum-Renditen von mehr als 10% p.a. für Ranking-Perioden von 80 bis 100 und Holding-Perioden von 60 bis 90 Handelstagen auf. Grundsätzlich sind die extremsten Aktien der Ranking-Periode entscheidend für die Ausprägung des Momentum-Effekts. Gleichzeitig steigen mit zunehmender Eingrenzung des Top/Flop-Wertes die Risiken, was eine Erklärung hoher Momentum-Renditen aus Sicht der Risikoaversions-Theorie nahelegt. Auch die Berücksichtigung zusätzlicher Filterbedingungen (Gleitende Durchschnitte, Handelsvolumen, Low Volatility) ermöglicht leicht höhere Momentum-Renditen bei entsprechend höheren Risiken. Zwischen dem Momentum-Effekt und dem Auftreten von Kurslücken besteht dagegen kein klarer Zusammenhang. Für die praktische Anwendung sind Momentum-Strategien mit dynamischer Positionsverwaltung während der Haltedauer interessant. Untersucht wurden Strategien anhand der eigens programmierten Simulationsverfahren Stopout und Castout sowie eines kombinierten Verfahrens. Im Ergebnis sind – je nach Präferenz des Investors – das Castout- und das kombinierte Verfahren optimal. Für das Rebalancing der Portfolios empfiehlt es sich, zu den entsprechenden Terminen jeweils nur die Short-Seite auf den Startwert zurückzusetzen. Weiterhin zeigen die Untersuchungen, dass deutliche Long-Übergewichtungen bei Momentum-Strategien grundsätzlich von Vorteil sind. Potenzielle Verbesserungen der Ergebnisse können durch weitere Stopp-Abstände, eine Verringerung des Top/Flop-Wertes oder eine längere Ranking-Periode erzielt werden. Weiterhin sind für die Praxis Long-only-Strategien auf Basis von Doppelranking-Verfahren attraktiv, bei denen das Zweitranking nach Standardabweichung oder Rendite/Standardabweichungs-Ratio erfolgt.

Structural Dynamics Model of a Cartesian Robot

Methods are developed for predicting vibration response characteristics of systems which change configuration during operation. A cartesian robot, an example of such a position-dependent system, served as a test case for these methods and was studied in detail. The chosen system model was formulated using the technique of Component Mode Synthesis (CMS). The model assumes that he system is slowly varying, and connects the carriages to each other and to the robot structure at the slowly varying connection points. The modal data required for each component is obtained experimentally in order to get a realistic model. The analysis results in prediction of vibrations that are produced by the inertia forces as well as gravity and friction forces which arise when the robot carriages move with some prescribed motion. Computer simulations and experimental determinations are conducted in order to calculate the vibrations at the robot end-effector. Comparisons are shown to validate the model in two ways: for fixed configuration the mode shapes and natural frequencies are examined, and then for changing configuration the residual vibration at the end of the mode is evaluated. A preliminary study was done on a geometrically nonlinear system which also has position-dependency. The system consisted of a flexible four-bar linkage with elastic input and output shafts. The behavior of the rocker-beam is analyzed for different boundary conditions to show how some limiting cases are obtained. A dimensional analysis leads to an evaluation of the consequences of dynamic similarity on the resulting vibration.

Investigating shape representation in area V4 with HMAX: Orientation and Grating selectivities

The question of how shape is represented is of central interest to understanding visual processing in cortex. While tuning properties of the cells in early part of the ventral visual stream, thought to be responsible for object recognition in the primate, are comparatively well understood, several different theories have been proposed regarding tuning in higher visual areas, such as V4. We used the model of object recognition in cortex presented by Riesenhuber and Poggio (1999), where more complex shape tuning in higher layers is the result of combining afferent inputs tuned to simpler features, and compared the tuning properties of model units in intermediate layers to those of V4 neurons from the literature. In particular, we investigated the issue of shape representation in visual area V1 and V4 using oriented bars and various types of gratings (polar, hyperbolic, and Cartesian), as used in several physiology experiments. Our computational model was able to reproduce several physiological findings, such as the broadening distribution of the orientation bandwidths and the emergence of a bias toward non-Cartesian stimuli. Interestingly, the simulation results suggest that some V4 neurons receive input from afferents with spatially separated receptive fields, leading to experimentally testable predictions. However, the simulations also show that the stimulus set of Cartesian and non-Cartesian gratings is not sufficiently complex to probe shape tuning in higher areas, necessitating the use of more complex stimulus sets.

Lecture notes B pdf

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Lecture notes B

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Exercises B

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