Contributions to Speech Analytics based on Speech Recognition and Topic Identification

La última década ha sido testigo de importantes avances en el campo de la tecnología de reconocimiento de voz. Los sistemas comerciales existentes actualmente poseen la capacidad de reconocer habla continua de múltiples locutores, consiguiendo valores aceptables de error, y sin la necesidad de realizar procedimientos explícitos de adaptación. A pesar del buen momento que vive esta tecnología, el reconocimiento de voz dista de ser un problema resuelto. La mayoría de estos sistemas de reconocimiento se ajustan a dominios particulares y su eficacia depende de manera significativa, entre otros muchos aspectos, de la similitud que exista entre el modelo de lenguaje utilizado y la tarea específica para la cual se está empleando. Esta dependencia cobra aún más importancia en aquellos escenarios en los cuales las propiedades estadísticas del lenguaje varían a lo largo del tiempo, como por ejemplo, en dominios de aplicación que involucren habla espontánea y múltiples temáticas. En los últimos años se ha evidenciado un constante esfuerzo por mejorar los sistemas de reconocimiento para tales dominios. Esto se ha hecho, entre otros muchos enfoques, a través de técnicas automáticas de adaptación. Estas técnicas son aplicadas a sistemas ya existentes, dado que exportar el sistema a una nueva tarea o dominio puede requerir tiempo a la vez que resultar costoso. Las técnicas de adaptación requieren fuentes adicionales de información, y en este sentido, el lenguaje hablado puede aportar algunas de ellas. El habla no sólo transmite un mensaje, también transmite información acerca del contexto en el cual se desarrolla la comunicación hablada (e.g. acerca del tema sobre el cual se está hablando). Por tanto, cuando nos comunicamos a través del habla, es posible identificar los elementos del lenguaje que caracterizan el contexto, y al mismo tiempo, rastrear los cambios que ocurren en estos elementos a lo largo del tiempo. Esta información podría ser capturada y aprovechada por medio de técnicas de recuperación de información (information retrieval) y de aprendizaje de máquina (machine learning). Esto podría permitirnos, dentro del desarrollo de mejores sistemas automáticos de reconocimiento de voz, mejorar la adaptación de modelos del lenguaje a las condiciones del contexto, y por tanto, robustecer al sistema de reconocimiento en dominios con condiciones variables (tales como variaciones potenciales en el vocabulario, el estilo y la temática). En este sentido, la principal contribución de esta Tesis es la propuesta y evaluación de un marco de contextualización motivado por el análisis temático y basado en la adaptación dinámica y no supervisada de modelos de lenguaje para el robustecimiento de un sistema automático de reconocimiento de voz. Esta adaptación toma como base distintos enfoque de los sistemas mencionados (de recuperación de información y aprendizaje de máquina) mediante los cuales buscamos identificar las temáticas sobre las cuales se está hablando en una grabación de audio. Dicha identificación, por lo tanto, permite realizar una adaptación del modelo de lenguaje de acuerdo a las condiciones del contexto. El marco de contextualización propuesto se puede dividir en dos sistemas principales: un sistema de identificación de temática y un sistema de adaptación dinámica de modelos de lenguaje. Esta Tesis puede describirse en detalle desde la perspectiva de las contribuciones particulares realizadas en cada uno de los campos que componen el marco propuesto: _ En lo referente al sistema de identificación de temática, nos hemos enfocado en aportar mejoras a las técnicas de pre-procesamiento de documentos, asimismo en contribuir a la definición de criterios más robustos para la selección de index-terms. – La eficiencia de los sistemas basados tanto en técnicas de recuperación de información como en técnicas de aprendizaje de máquina, y específicamente de aquellos sistemas que particularizan en la tarea de identificación de temática, depende, en gran medida, de los mecanismos de preprocesamiento que se aplican a los documentos. Entre las múltiples operaciones que hacen parte de un esquema de preprocesamiento, la selección adecuada de los términos de indexado (index-terms) es crucial para establecer relaciones semánticas y conceptuales entre los términos y los documentos. Este proceso también puede verse afectado, o bien por una mala elección de stopwords, o bien por la falta de precisión en la definición de reglas de lematización. En este sentido, en este trabajo comparamos y evaluamos diferentes criterios para el preprocesamiento de los documentos, así como también distintas estrategias para la selección de los index-terms. Esto nos permite no sólo reducir el tamaño de la estructura de indexación, sino también mejorar el proceso de identificación de temática. – Uno de los aspectos más importantes en cuanto al rendimiento de los sistemas de identificación de temática es la asignación de diferentes pesos a los términos de acuerdo a su contribución al contenido del documento. En este trabajo evaluamos y proponemos enfoques alternativos a los esquemas tradicionales de ponderado de términos (tales como tf-idf ) que nos permitan mejorar la especificidad de los términos, así como también discriminar mejor las temáticas de los documentos. _ Respecto a la adaptación dinámica de modelos de lenguaje, hemos dividimos el proceso de contextualización en varios pasos. – Para la generación de modelos de lenguaje basados en temática, proponemos dos tipos de enfoques: un enfoque supervisado y un enfoque no supervisado. En el primero de ellos nos basamos en las etiquetas de temática que originalmente acompañan a los documentos del corpus que empleamos. A partir de estas, agrupamos los documentos que forman parte de la misma temática y generamos modelos de lenguaje a partir de dichos grupos. Sin embargo, uno de los objetivos que se persigue en esta Tesis es evaluar si el uso de estas etiquetas para la generación de modelos es óptimo en términos del rendimiento del reconocedor. Por esta razón, nosotros proponemos un segundo enfoque, un enfoque no supervisado, en el cual el objetivo es agrupar, automáticamente, los documentos en clusters temáticos, basándonos en la similaridad semántica existente entre los documentos. Por medio de enfoques de agrupamiento conseguimos mejorar la cohesión conceptual y semántica en cada uno de los clusters, lo que a su vez nos permitió refinar los modelos de lenguaje basados en temática y mejorar el rendimiento del sistema de reconocimiento. – Desarrollamos diversas estrategias para generar un modelo de lenguaje dependiente del contexto. Nuestro objetivo es que este modelo refleje el contexto semántico del habla, i.e. las temáticas más relevantes que se están discutiendo. Este modelo es generado por medio de la interpolación lineal entre aquellos modelos de lenguaje basados en temática que estén relacionados con las temáticas más relevantes. La estimación de los pesos de interpolación está basada principalmente en el resultado del proceso de identificación de temática. – Finalmente, proponemos una metodología para la adaptación dinámica de un modelo de lenguaje general. El proceso de adaptación tiene en cuenta no sólo al modelo dependiente del contexto sino también a la información entregada por el proceso de identificación de temática. El esquema usado para la adaptación es una interpolación lineal entre el modelo general y el modelo dependiente de contexto. Estudiamos también diferentes enfoques para determinar los pesos de interpolación entre ambos modelos. Una vez definida la base teórica de nuestro marco de contextualización, proponemos su aplicación dentro de un sistema automático de reconocimiento de voz. Para esto, nos enfocamos en dos aspectos: la contextualización de los modelos de lenguaje empleados por el sistema y la incorporación de información semántica en el proceso de adaptación basado en temática. En esta Tesis proponemos un marco experimental basado en una arquitectura de reconocimiento en ‘dos etapas’. En la primera etapa, empleamos sistemas basados en técnicas de recuperación de información y aprendizaje de máquina para identificar las temáticas sobre las cuales se habla en una transcripción de un segmento de audio. Esta transcripción es generada por el sistema de reconocimiento empleando un modelo de lenguaje general. De acuerdo con la relevancia de las temáticas que han sido identificadas, se lleva a cabo la adaptación dinámica del modelo de lenguaje. En la segunda etapa de la arquitectura de reconocimiento, usamos este modelo adaptado para realizar de nuevo el reconocimiento del segmento de audio. Para determinar los beneficios del marco de trabajo propuesto, llevamos a cabo la evaluación de cada uno de los sistemas principales previamente mencionados. Esta evaluación es realizada sobre discursos en el dominio de la política usando la base de datos EPPS (European Parliamentary Plenary Sessions - Sesiones Plenarias del Parlamento Europeo) del proyecto europeo TC-STAR. Analizamos distintas métricas acerca del rendimiento de los sistemas y evaluamos las mejoras propuestas con respecto a los sistemas de referencia. ABSTRACT The last decade has witnessed major advances in speech recognition technology. Today’s commercial systems are able to recognize continuous speech from numerous speakers, with acceptable levels of error and without the need for an explicit adaptation procedure. Despite this progress, speech recognition is far from being a solved problem. Most of these systems are adjusted to a particular domain and their efficacy depends significantly, among many other aspects, on the similarity between the language model used and the task that is being addressed. This dependence is even more important in scenarios where the statistical properties of the language fluctuates throughout the time, for example, in application domains involving spontaneous and multitopic speech. Over the last years there has been an increasing effort in enhancing the speech recognition systems for such domains. This has been done, among other approaches, by means of techniques of automatic adaptation. These techniques are applied to the existing systems, specially since exporting the system to a new task or domain may be both time-consuming and expensive. Adaptation techniques require additional sources of information, and the spoken language could provide some of them. It must be considered that speech not only conveys a message, it also provides information on the context in which the spoken communication takes place (e.g. on the subject on which it is being talked about). Therefore, when we communicate through speech, it could be feasible to identify the elements of the language that characterize the context, and at the same time, to track the changes that occur in those elements over time. This information can be extracted and exploited through techniques of information retrieval and machine learning. This allows us, within the development of more robust speech recognition systems, to enhance the adaptation of language models to the conditions of the context, thus strengthening the recognition system for domains under changing conditions (such as potential variations in vocabulary, style and topic). In this sense, the main contribution of this Thesis is the proposal and evaluation of a framework of topic-motivated contextualization based on the dynamic and non-supervised adaptation of language models for the enhancement of an automatic speech recognition system. This adaptation is based on an combined approach (from the perspective of both information retrieval and machine learning fields) whereby we identify the topics that are being discussed in an audio recording. The topic identification, therefore, enables the system to perform an adaptation of the language model according to the contextual conditions. The proposed framework can be divided in two major systems: a topic identification system and a dynamic language model adaptation system. This Thesis can be outlined from the perspective of the particular contributions made in each of the fields that composes the proposed framework: _ Regarding the topic identification system, we have focused on the enhancement of the document preprocessing techniques in addition to contributing in the definition of more robust criteria for the selection of index-terms. – Within both information retrieval and machine learning based approaches, the efficiency of topic identification systems, depends, to a large extent, on the mechanisms of preprocessing applied to the documents. Among the many operations that encloses the preprocessing procedures, an adequate selection of index-terms is critical to establish conceptual and semantic relationships between terms and documents. This process might also be weakened by a poor choice of stopwords or lack of precision in defining stemming rules. In this regard we compare and evaluate different criteria for preprocessing the documents, as well as for improving the selection of the index-terms. This allows us to not only reduce the size of the indexing structure but also to strengthen the topic identification process. – One of the most crucial aspects, in relation to the performance of topic identification systems, is to assign different weights to different terms depending on their contribution to the content of the document. In this sense we evaluate and propose alternative approaches to traditional weighting schemes (such as tf-idf ) that allow us to improve the specificity of terms, and to better identify the topics that are related to documents. _ Regarding the dynamic language model adaptation, we divide the contextualization process into different steps. – We propose supervised and unsupervised approaches for the generation of topic-based language models. The first of them is intended to generate topic-based language models by grouping the documents, in the training set, according to the original topic labels of the corpus. Nevertheless, a goal of this Thesis is to evaluate whether or not the use of these labels to generate language models is optimal in terms of recognition accuracy. For this reason, we propose a second approach, an unsupervised one, in which the objective is to group the data in the training set into automatic topic clusters based on the semantic similarity between the documents. By means of clustering approaches we expect to obtain a more cohesive association of the documents that are related by similar concepts, thus improving the coverage of the topic-based language models and enhancing the performance of the recognition system. – We develop various strategies in order to create a context-dependent language model. Our aim is that this model reflects the semantic context of the current utterance, i.e. the most relevant topics that are being discussed. This model is generated by means of a linear interpolation between the topic-based language models related to the most relevant topics. The estimation of the interpolation weights is based mainly on the outcome of the topic identification process. – Finally, we propose a methodology for the dynamic adaptation of a background language model. The adaptation process takes into account the context-dependent model as well as the information provided by the topic identification process. The scheme used for the adaptation is a linear interpolation between the background model and the context-dependent one. We also study different approaches to determine the interpolation weights used in this adaptation scheme. Once we defined the basis of our topic-motivated contextualization framework, we propose its application into an automatic speech recognition system. We focus on two aspects: the contextualization of the language models used by the system, and the incorporation of semantic-related information into a topic-based adaptation process. To achieve this, we propose an experimental framework based in ‘a two stages’ recognition architecture. In the first stage of the architecture, Information Retrieval and Machine Learning techniques are used to identify the topics in a transcription of an audio segment. This transcription is generated by the recognition system using a background language model. According to the confidence on the topics that have been identified, the dynamic language model adaptation is carried out. In the second stage of the recognition architecture, an adapted language model is used to re-decode the utterance. To test the benefits of the proposed framework, we carry out the evaluation of each of the major systems aforementioned. The evaluation is conducted on speeches of political domain using the EPPS (European Parliamentary Plenary Sessions) database from the European TC-STAR project. We analyse several performance metrics that allow us to compare the improvements of the proposed systems against the baseline ones.

Overexpression of Mdm2 in mice reveals a p53-independent role for Mdm2 in tumorigenesis

The Mdm2 proto-oncogene is amplified to high copy numbers in human sarcomas and is overexpressed in a wide variety of other human cancers. Because Mdm2 protein forms a complex with the p53 tumor suppressor protein and down-regulates p53 function, the oncogenic potential of Mdm2 is presumed to be p53-dependent. To model these conditions in mice, we have used the entire Mdm2 gene, under transcriptional control of its native promoter region, as a transgene to create mice that overexpress Mdm2. The transgenic mice are predisposed to spontaneous tumor formation, and the incidence of sarcomas observed in the Mdm2-transgenic mice in the presence or absence of functional p53 demonstrates that, in addition to Mdm2-mediated inactivation of p53, there exists a p53-independent role for Mdm2 in tumorigenesis.

Seasonal dynamics of an aquatic macroinvertebrate assembly (Hydrobiological case study of Lake Balaton No. 2)

In 2002, 2003 and 2004, we took macoinvertebrate samples on a total of 36 occasions at the Badacsony bay of Lake Balaton. Our sampling site was characterised by areas of open water (in 2003 and 2004 full of reed-grass) as well as by areas covered by common reed (Phragmites australis) and narrowleaf cattail (Typha angustifolia). Samples were taken both from water body and benthic ooze by use of a stiff hand net. We have gained our data from processing 208 individual samples. We took samples frequently from early spring until late autumn for a deeper understanding of the processes of seasonal dynamics. The main seasonal patterns and temporal changes of diversity were described. We constructed a weather-dependent simulation model of the processes of seasonal dynamics in the interest of a possible further utilization of our data in climate change research. We described the total number of individuals, biovolume and diversity of all macroinvertebrate species with a single index and used the temporal trends of this index for simulation modelling. Our discrete deterministic model includes only the impact of temperature, other interactions might only appear concealed. Running the model for different climate change scenarios it became possible to estimate conditions for the 2070-2100 period. The results, however, should be treated very prudently not only because our model is very simple but also because the scenarios are the results of different models.

Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.

Burn healing is dependent on burn site : a quantitative analysis from a porcine burn model

This retrospective review examines healing in different sites on a porcine burn model; 24 pairs of burns on 18 pigs from other animal trials were selected for analysis. Each pair of burns was located on the either the cranial or the caudal part of the thoracic ribs region, on the same side of the animal. The burns were 40-50 cm(2) in size and of uniform deep-dermal partial thickness. Caudal burns healed significantly better than cranial burns, demonstrated by earlier closure of wounds, less scar formation and better cosmesis. To our knowledge, this is the first detailed study reporting that burn healing is affected by location on a porcine burn model. We recommend that similar symmetrical burns should be used for future comparative assessments of burn healing.

BM18 : a novel androgen-dependent human prostate cancer xenograft model derived from a bone metastasis

BACKGROUND Androgen-dependent prostate cancer (PrCa) xenograft models are required to study PrCa biology in the clinically relevant in vivo environment. METHODS Human PrCa tissue from a femoral bone metastasis biopsy (BM18) was grown and passaged subcutaneously through male severe combined immune-deficient (SCID) mice. Human mitochondria (hMt), prostate specific antigen (PSA), androgen receptor (AR), cytokeratin-18 (CK-18), pan-cytokeratin, and high molecular weight-cytokeratin (HMW-CK) were assessed using immunohistochemistry (IHC). Surgical castration was performed to examine androgen dependence. Serum was collected pre- and post-castration for monitoring of PSA levels. RESULTS: BM18 stained positively for hMt, PSA, AR, CK-18, pan keratin, and negatively for HMW-CK, consistent with the staining observed in the original patient material. Androgen-deprivation induced tumor regression in 10/10 castrated male SCID mice. Serum PSA levels positively correlated with BM18 tumor size. CONCLUSIONS BM18 expresses PSA and AR, and rapidly regresses in response to androgen withdrawal. This provides a new clinically significant PrCa model for the study of androgen-dependent growth.

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

Solid–interstitial fluid interaction, which depends on tissue permeability, is significant to the strain-rate-dependent mechanical behavior of humeral head (shoulder) cartilage. Due to anatomical and biomechanical similarities to that of the human shoulder, kangaroos present a suitable animal model. Therefore, indentation experiments were conducted on kangaroo shoulder cartilage tissues from low (10−4/s) to moderately high (10−2/s) strain-rates. A porohyperelastic model was developed based on the experimental characterization; and a permeability function that takes into account the effect of strain-rate on permeability (strain-rate-dependent permeability) was introduced into the model to investigate the effect of rate-dependent fluid flow on tissue response. The prediction of the model with the strain-rate-dependent permeability was compared with those of the models using constant permeability and strain-dependent permeability. Compared to the model with constant permeability, the models with strain-dependent and strain-rate-dependent permeability were able to better capture the experimental variation at all strain-rates (p<0.05). Significant differences were not identified between models with strain-dependent and strain-rate-dependent permeability at strain-rate of 5×10−3/s (p=0.179). However, at strain-rate of 10−2/s, the model with strain-rate-dependent permeability was significantly better at capturing the experimental results (p<0.005). The findings thus revealed the significance of rate-dependent fluid flow on tissue behavior at large strain-rates, which provides insights into the mechanical deformation mechanisms of cartilage tissues.

Size-dependent melting of nanoparticles: Hundred years of thermodynamic model

Thermodynamic model first published in 1909, is being used extensively to understand the size-dependent melting of nanoparticles. Pawlow deduced an expression for the size-dependent melting temperature of small particles based on the thermodynamic model which was then modified and applied to different nanostructures such as nanowires, prism-shaped nanoparticles, etc. The model has also been modified to understand the melting of supported nanoparticles and superheating of embedded nanoparticles. In this article, we have reviewed the melting behaviour of nanostructures reported in the literature since 1909.

Mechanism of aromatic hydroxylation *1, , *2, , *3: Properties of a model for pyridine nucleotide-dependent flavoprotein hydroxylases

A model (NADH-phenazine methosulfate-O2) formally similar to pyridine nucleotide-dependent flavoprotein hydroxylases catalyzed the hydroxylation of several aromatic compounds. The hydroxylation was maximal at acid pH and was inhibited by ovine Superoxide dismutase, suggesting that perhydroxyl radicals might be intermediates in this process. The stoichiometry of the reaction indicated that a univalent reduction of oxygen was occurring. The correlation between the concentration of semiquinone and hydroxylation, and the inhibition of hydroxylation by ethanol which inhibited semiquinone oxidation, suggested the involvement of phenazine methosulfate-semiquinone. Activation of hydroxylation by Fe3+ and Cu2+ supported the contention that univalently reduced species of oxygen was involved in hydroxylation. Catalase was without effect on the hydroxylation by the model, ruling out H2O2 as an intermediate. A reaction sequence, involving a two-electron reduction of phenazine methosulfate to reduced phenazine methosulfate followed by disproportionation with phenazine methosulfate to generate the semiquinone, was proposed. The semiquinone could donate an electron to O2 to generate O2 which could be subsequently protonated to form the perhydroxyl radical.

Spatially dependent correlation functions in the Anderson model

We report results from a first principles calculation of spatially dependent correlation functions around a magnetic impurity in metals described by the nondegenerate Anderson model. Our computations are based on a combination of perturbative scaling theory and numerical renormalization group methods. Results for the conduction election charge density around the impurity and correlation functions involving the conduction electron and impurity charge and spin densities will be presented. The behavior in various regimes including the mixed valent regime will be explored.

Time-Dependent Dynamics of a Planar Galaxy Model

Time-dependent models of collisionless stellar systems with harmonic potentials allowing for an essentially exact analytic description have recently been described. These include oscillating spheres and spheroids. This paper extends the analysis to time-dependent elliptic discs. Although restricted to two space dimensions, the systems are richer in that their parameters form a 10-dimensional phase space (in contrast to six for the earlier models). Apart from total energy and angular momentum, two additional conserved quantities emerge naturally. These can be chosen as the areas of extremal sections of the ellipsoidal region of phase space occupied by the system (their product gives the conserved volume). The present paper describes the construction of these models. An application to a tidal encounter is given which allows one to go beyond the impulse approximation and demonstrates the effects of rotation of the perturbed system on energy and angular-momentum transfer. The angular-momentum transfer is shown to scale inversely as the cube of the encounter velocity for an initial configuration of the perturbed galaxy with zero quadrupole moment.

Spatially dependent zero-frequency response functions and correlation functions in the Kondo model

We present the details of a formalism for calculating spatially varying zero-frequency response functions and equal-time correlation functions in models of magnetic and mixed-valence impurities of metals. The method is based on a combination of perturbative, thermodynamic scaling theory [H. R. Krishna-murthy and C. Jayaprakash, Phys. Rev. B 30, 2806 (1984)] and a nonperturbative technique such as the Wilson renormalization group. We illustrate the formalism for the spin-1/2 Kondo problem and present results for the conduction-spin-density�impurity-spin correlation function and conduction-electron charge density near the impurity. We also discuss qualitative features that emerge from our calculations and discuss how they can be carried over to the case of realistic models for transition-metal impurities.