Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

A Government-Binding Based Parser for Warlpiri, a Free-Word Order Language

Free-word order languages have long posed significant problems for standard parsing algorithms. This thesis presents an implemented parser, based on Government-Binding (GB) theory, for a particular free-word order language, Warlpiri, an aboriginal language of central Australia. The words in a sentence of a free-word order language may swap about relatively freely with little effect on meaning: the permutations of a sentence mean essentially the same thing. It is assumed that this similarity in meaning is directly reflected in the syntax. The parser presented here properly processes free word order because it assigns the same syntactic structure to the permutations of a single sentence. The parser also handles fixed word order, as well as other phenomena. On the view presented here, there is no such thing as a "configurational" or "non-configurational" language. Rather, there is a spectrum of languages that are more or less ordered. The operation of this parsing system is quite different in character from that of more traditional rule-based parsing systems, e.g., context-free parsers. In this system, parsing is carried out via the construction of two different structures, one encoding precedence information and one encoding hierarchical information. This bipartite representation is the key to handling both free- and fixed-order phenomena. This thesis first presents an overview of the portion of Warlpiri that can be parsed. Following this is a description of the linguistic theory on which the parser is based. The chapter after that describes the representations and algorithms of the parser. In conclusion, the parser is compared to related work. The appendix contains a substantial list of test cases ??th grammatical and ungrammatical ??at the parser has actually processed.

The Computation of Color

This thesis takes an interdisciplinary approach to the study of color vision, focussing on the phenomenon of color constancy formulated as a computational problem. The primary contributions of the thesis are (1) the demonstration of a formal framework for lightness algorithms; (2) the derivation of a new lightness algorithm based on regularization theory; (3) the synthesis of an adaptive lightness algorithm using "learning" techniques; (4) the development of an image segmentation algorithm that uses luminance and color information to mark material boundaries; and (5) an experimental investigation into the cues that human observers use to judge the color of the illuminant. Other computational approaches to color are reviewed and some of their links to psychophysics and physiology are explored.

Computational Structure of Human Language

The central thesis of this report is that human language is NP-complete. That is, the process of comprehending and producing utterances is bounded above by the class NP, and below by NP-hardness. This constructive complexity thesis has two empirical consequences. The first is to predict that a linguistic theory outside NP is unnaturally powerful. The second is to predict that a linguistic theory easier than NP-hard is descriptively inadequate. To prove the lower bound, I show that the following three subproblems of language comprehension are all NP-hard: decide whether a given sound is possible sound of a given language; disambiguate a sequence of words; and compute the antecedents of pronouns. The proofs are based directly on the empirical facts of the language user's knowledge, under an appropriate idealization. Therefore, they are invariant across linguistic theories. (For this reason, no knowledge of linguistic theory is needed to understand the proofs, only knowledge of English.) To illustrate the usefulness of the upper bound, I show that two widely-accepted analyses of the language user's knowledge (of syntactic ellipsis and phonological dependencies) lead to complexity outside of NP (PSPACE-hard and Undecidable, respectively). Next, guided by the complexity proofs, I construct alternate linguisitic analyses that are strictly superior on descriptive grounds, as well as being less complex computationally (in NP). The report also presents a new framework for linguistic theorizing, that resolves important puzzles in generative linguistics, and guides the mathematical investigation of human language.

Alignment by Maximization of Mutual Information

A new information-theoretic approach is presented for finding the pose of an object in an image. The technique does not require information about the surface properties of the object, besides its shape, and is robust with respect to variations of illumination. In our derivation, few assumptions are made about the nature of the imaging process. As a result the algorithms are quite general and can foreseeably be used in a wide variety of imaging situations. Experiments are presented that demonstrate the approach registering magnetic resonance (MR) images with computed tomography (CT) images, aligning a complex 3D object model to real scenes including clutter and occlusion, tracking a human head in a video sequence and aligning a view-based 2D object model to real images. The method is based on a formulation of the mutual information between the model and the image called EMMA. As applied here the technique is intensity-based, rather than feature-based. It works well in domains where edge or gradient-magnitude based methods have difficulty, yet it is more robust than traditional correlation. Additionally, it has an efficient implementation that is based on stochastic approximation. Finally, we will describe a number of additional real-world applications that can be solved efficiently and reliably using EMMA. EMMA can be used in machine learning to find maximally informative projections of high-dimensional data. EMMA can also be used to detect and correct corruption in magnetic resonance images (MRI).

Improving Multi-class Text Classification with Naive Bayes

There are numerous text documents available in electronic form. More and more are becoming available every day. Such documents represent a massive amount of information that is easily accessible. Seeking value in this huge collection requires organization; much of the work of organizing documents can be automated through text classification. The accuracy and our understanding of such systems greatly influences their usefulness. In this paper, we seek 1) to advance the understanding of commonly used text classification techniques, and 2) through that understanding, improve the tools that are available for text classification. We begin by clarifying the assumptions made in the derivation of Naive Bayes, noting basic properties and proposing ways for its extension and improvement. Next, we investigate the quality of Naive Bayes parameter estimates and their impact on classification. Our analysis leads to a theorem which gives an explanation for the improvements that can be found in multiclass classification with Naive Bayes using Error-Correcting Output Codes. We use experimental evidence on two commonly-used data sets to exhibit an application of the theorem. Finally, we show fundamental flaws in a commonly-used feature selection algorithm and develop a statistics-based framework for text feature selection. Greater understanding of Naive Bayes and the properties of text allows us to make better use of it in text classification.

A Hierarchical Cache Coherent Protocol

As the number of processors in distributed-memory multiprocessors grows, efficiently supporting a shared-memory programming model becomes difficult. We have designed the Protocol for Hierarchical Directories (PHD) to allow shared-memory support for systems containing massive numbers of processors. PHD eliminates bandwidth problems by using a scalable network, decreases hot-spots by not relying on a single point to distribute blocks, and uses a scalable amount of space for its directories. PHD provides a shared-memory model by synthesizing a global shared memory from the local memories of processors. PHD supports sequentially consistent read, write, and test- and-set operations. This thesis also introduces a method of describing locality for hierarchical protocols and employs this method in the derivation of an abstract model of the protocol behavior. An embedded model, based on the work of Johnson[ISCA19], describes the protocol behavior when mapped to a k-ary n-cube. The thesis uses these two models to study the average height in the hierarchy that operations reach, the longest path messages travel, the number of messages that operations generate, the inter-transaction issue time, and the protocol overhead for different locality parameters, degrees of multithreading, and machine sizes. We determine that multithreading is only useful for approximately two to four threads; any additional interleaving does not decrease the overall latency. For small machines and high locality applications, this limitation is due mainly to the length of the running threads. For large machines with medium to low locality, this limitation is due mainly to the protocol overhead being too large. Our study using the embedded model shows that in situations where the run length between references to shared memory is at least an order of magnitude longer than the time to process a single state transition in the protocol, applications exhibit good performance. If separate controllers for processing protocol requests are included, the protocol scales to 32k processor machines as long as the application exhibits hierarchical locality: at least 22% of the global references must be able to be satisfied locally; at most 35% of the global references are allowed to reach the top level of the hierarchy.

Procedures as a Representation for Data in a Computer Program for Understanding Natural Language

This paper describes a system for the computer understanding of English. The system answers questions, executes commands, and accepts information in normal English dialog. It uses semantic information and context to understand discourse and to disambiguate sentences. It combines a complete syntactic analysis of each sentence with a "heuristic understander" which uses different kinds of information about a sentence, other parts of the discourse, and general information about the world in deciding what the sentence means. It is based on the belief that a computer cannot deal reasonably with language unless it can "understand" the subject it is discussing. The program is given a detailed model of the knowledge needed by a simple robot having only a hand and an eye. We can give it instructions to manipulate toy objects, interrogate it about the scene, and give it information it will use in deduction. In addition to knowing the properties of toy objects, the program has a simple model of its own mentality. It can remember and discuss its plans and actions as well as carry them out. It enters into a dialog with a person, responding to English sentences with actions and English replies, and asking for clarification when its heuristic programs cannot understand a sentence through use of context and physical knowledge.

Verb Classes and Alternations in Bangla, German, English, and Korean

In this report, we investigate the relationship between the semantic and syntactic properties of verbs. Our work is based on the English Verb Classes and Alternations of (Levin, 1993). We explore how these classes are manifested in other languages, in particular, in Bangla, German, and Korean. Our report includes a survey and classification of several hundred verbs from these languages into the cross-linguistic equivalents of Levin's classes. We also explore ways in which our findings may be used to enhance WordNet in two ways: making the English syntactic information of WordNet more fine-grained, and making WordNet multilingual.

Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

La adquisición de la interrogación: las interrogativas parciales en catalán y castellano = The acquisition of interrogatives:Wh-questions in Catalan and Spanish

En este trabajo se describe la naturaleza y secuencia de adquisición de las preguntas interrogativas parciales en niños de habla catalana y/o castellana dentro de un marco de análisis según el cual la adquisición de las estructuras lingüísticas se construye gradualmente desde estructuras concretas hasta estructuras más abstractas. La muestra utilizada se compone de 10 niños y niñas procedentes de corpus longitudinales cuyas edades van de los 17 meses a los 3 años. El análisis se ha realizado atendiendo a la estructura sintáctica de la oración, los errores, los pronombres y adverbios interrogativos, y la tipología verbal. Los resultados muestran que la secuencia de adquisición pasa por un momento inicial caracterizado por producciones estereotipadas o fórmulas, durante el cual sólo aparecen algunas partículas interrogativas en estructuras muy concretas. Posteriormente la interrogación aparece con otros pronombres y adverbios y se diversifica a otros verbos, además, no se observan errores en la construcción sintáctica. Estos resultados suponen un hecho diferencial respecto de estudios previos en lengua inglesa

Aprendizaje léxico y desarrollo de la gramática: vocabulario verbal, aceleración morfológica y complejidad sintáctica

This paper studies the initial development of certain language components. More precisely, we analyse the relation between three aspects that are closely involved in the grammar of the verb: morphological productivity, syntactic complexity, and verb vocabulary learning. The study is based on data about the relationship between lexical development and grammatical development, and also on proposals that a critical mass of vocabulary is needed in order to develop a grammatical component. The sample comprised six subjects who are monolingual or bilingual in Catalan andlor Spanish. Results show a morphological spurt some time afer the learning of a certain quantity of verbs. Moreover, syntactic complexity is only evident some months after this morphological spurt

Construcción de un instrumento para identificar el perfil de emprendedores bogotanos de la última década

El proyecto de investigación que se trabaja centra su atención en la siguiente cuestión: determinar un instrumento de recolección que permita identificar cuáles son las competencias que caracterizan a los emprendedores bogotanos creadores de empresas de rápido crecimiento. La presente es una investigación cualitativa que busca la mejor manera de preparar a los futuros emprendedores desde la educación superior. Si se conocen las competencias que acompañan al emprendedor se puede comprender mejor su capacidad de crear empresa y así buscar una mejor manera de preparar a los futuros emprendedores. Esto es importante para la economía de un país en general, máxime cuando se dan situaciones de depresión económica como el desempleo que se vive en la actualidad. “La creación y el desarrollo de nuevas empresas contribuye decisivamente a lograr el deseado bienestar para la sociedad, dado que permite incrementar el nivel de empleo, impulsar la innovación y mejorar la competitividad” (Acs, Audretch, & Braunerhjelm, 2006, pág. 83). La investigación abarca la búsqueda de competencias a nivel mundial basándose en estudios realizados por diferentes autores (Alles, Durán, Goleman, Shipmann, Varela, Boyatsis, Mc. Clelland y Blancero). El objetivo es desarrollar un instrumento que permita recolectar información de emprendedores bogotanos exitosos, con base en la clasificación de competencias que se realice a lo largo de la investigación.

Comparación de cuatro escalas de riesgo en pacientes que consultaron por síncope al servicio de urgencias

Introducción: El síncope es un motivo frecuente de consulta en Urgencias, definir el estudio y el destino de estos pacientes es motivo de controversia. Se han diseñado varias escalas para estratificación del riesgo en pacientes con esta entidad. En este estudio se comparan las características operativas de 4 escalas para la decisión de hospitalizar pacientes con síncope que consultan a un servicio de urgencias de una institución de III y IV Nivel Métodos. Estudio analítico transversal, en el que se aplicaron las 4 escalas de riesgo a pacientes que consultaron por síncope al servicio de Urgencias durante un período de 6 meses y que fueron hospitalizados en la institución donde se realizó. Se evaluaron los resultados aplicando el programa Epidat 3.1 para sensibilidad y especificidad, índice de Youden. Resultados. Se incluyeron en total 91 pacientes. La sensibilidad de las escalas San Francisco, OESIL, EGSYS y la institucional para el requerimiento de hospitalización fue de 79%, 87%. 63% y 95% respectivamente y la especificidad fue de 52%, 40%, 64% y 14%. EL riesgo de mortalidad no fue adecuadamente detectado por la escala de San Francisco.. Conclusiones. Ninguna de las escalas aplicadas a los pacientes hospitalizados que consultaron por síncope a urgencias superó el juicio clínico para definir la hospitalización. Sin embargo, la escala OESIL y la institucional pueden ayudar a corroborar la decisión clínica de hospitalizar en esta población.