The Innocent Pleasure : A Study on Luther's theology of music

The aim of the study is to examine Luther s theology of music from the standpoint of pleasure. The theological assessment of musical pleasure is related to two further questions: the role of emotions in Christianity and the apprehension of beauty. The medieval discussion of these themes is portrayed in the background chapter. Significant traits were: the suspicion felt towards sensuous gratification in music, music as a mathematical discipline, the medieval theory of emotions informed by Stoic apatheia and Platonic-Aristotelian metriopatheia, the notion of beauty as an attribute of God, medieval aesthetics as the aesthetic of proportion and the aesthetic of light and the emergence of the Aristotelian view of science that is based on experience rather than speculation. The treatment of Luther s theology of music is initiated with the notion of gift. Luther says that music is the excellent (or even the best) gift of God. This has sometimes been understood as a mere music-lover s enthusiasm. Luther is, however, not likely to use the word gift loosely. His theology can be depicted as a theology of gift. The Triune God is categorically giving. The notion of gift also includes reciprocity. When we receive the gifts of God, it evokes praise in us. Praising God is predominantly a musical phenomenon. The particular benefit of music in Luther s thought is that it can move human emotions. This emphasis is connected to the overall affectivity of Luther s theology. In contrast to the medieval discussion, Luther ascribes to saints not just emotions but particularly warm and tender affections. The power of music is related to the auditory and vocal character of the Word. Faith comes through hearing the Word that is at once musical and affective perception. Faith is not a mere opinion but the affective trust of the heart. Music can touch the human heart and persuade with its sweetness, like the good news of the Gospel. Music allows us to perceive Luther s theology as a theology of joy and pleasure. Joy is for Luther a gift of the Holy Spirit that fills the heart and bursts out in voice and gestures. Pleasure appears to be a central aspect to Luther s theology. The problem of the Bondage of the Will is precisely the human inability to feel pleasure in God s will. To be pleased in the visible and tangible creation is not something a Christian should avoid. On the contrary, if one is not pleased with the world that God has created, it is a sign of unbelief and ingratitude. The pleasure of music is aesthetic perception. This in turn necessitates the investigation of Luther s aesthetics. Aesthetic evaluation is not just a part of Luther s thought. Eventually his theology as a whole could be portrayed in aesthetic terms. Luther s extremely positive appreciation of music illutrates his theology as an affective acknowledgement of the goodness of the Creation and faith as an aesthetic contentment.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Determination of rational strategies for players in two-target games

This paper addresses some of the basic issues involved in the determination of rational strategies for players in two-target games. We show that unlike single-target games where the task of role assignment and selection of strategies is conceptually straightforward, in two-target games, many factors like the preference ordering of outcomes by players, the relative configuration of the target sets and secured outcome regions, the uncertainty about the parameters of the game, etc., also influence the rational selection of strategies by players. The importance of these issues is illustrated through appropriate examples.

Finite data performance of MUSIC and minimum norm methods

In the direction of arrival (DOA) estimation problem, we encounter both finite data and insufficient knowledge of array characterization. It is therefore important to study how subspace-based methods perform in such conditions. We analyze the finite data performance of the multiple signal classification (MUSIC) and minimum norm (min. norm) methods in the presence of sensor gain and phase errors, and derive expressions for the mean square error (MSE) in the DOA estimates. These expressions are first derived assuming an arbitrary array and then simplified for the special case of an uniform linear array with isotropic sensors. When they are further simplified for the case of finite data only and sensor errors only, they reduce to the recent results given in [9-12]. Computer simulations are used to verify the closeness between the predicted and simulated values of the MSE.

Learning the global maximum with parameterized learning automata

A feedforward network composed of units of teams of parameterized learning automata is considered as a model of a reinforcement teaming system. The internal state vector of each learning automaton is updated using an algorithm consisting of a gradient following term and a random perturbation term. It is shown that the algorithm weakly converges to a solution of the Langevin equation implying that the algorithm globally maximizes an appropriate function. The algorithm is decentralized, and the units do not have any information exchange during updating. Simulation results on common payoff games and pattern recognition problems show that reasonable rates of convergence can be obtained.

Carnatic music analysis: Shadja, swara identification and rAga verification in AlApana using stochastic models

We analyze the AlApana of a Carnatic music piece without the prior knowledge of the singer or the rAga. AlApana is ameans to communicate to the audience, the flavor or the bhAva of the rAga through the permitted notes and its phrases. The input to our analysis is a recording of the vocal AlApana along with the accompanying instrument. The AdhAra shadja(base note) of the singer for that AlApana is estimated through a stochastic model of note frequencies. Based on the shadja, we identify the notes (swaras) used in the AlApana using a semi-continuous GMM. Using the probabilities of each note interval, we recognize swaras of the AlApana. For sampurNa rAgas, we can identify the possible rAga, based on the swaras. We have been able to achieve correct shadja identification, which is crucial to all further steps, in 88.8% of 55 AlApanas. Among them (48 AlApanas of 7 rAgas), we get 91.5% correct swara identification and 62.13% correct R (rAga) accuracy.

Zero-Sum Risk-Sensitive Stochastic Differential Games

We study zero-sum risk-sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria. Under certain assumptions, we establish the existence of values and saddle-point equilibria. We obtain our results by studying the corresponding Hamilton-Jacobi-Isaacs equations. Finally, we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations (BSs) that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals that can connect to the base station that offers the best utility. The signal-to-interference-plus-noise ratio (SINR) is used as the quantity that determines the association. We first study the SINR association-game: We determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: 1) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; 2) a cell corresponding to a BS may be the union of disconnected subcells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: We determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation.

Music and symbolic dynamics: the science behind an art

Music signals comprise of atomic notes drawn from a musical scale. The creation of musical sequences often involves splicing the notes in a constrained way resulting in aesthetically appealing patterns. We develop an approach for music signal representation based on symbolic dynamics by translating the lexicographic rules over a musical scale to constraints on a Markov chain. This source representation is useful for machine based music synthesis, in a way, similar to a musician producing original music. In order to mathematically quantify user listening experience, we study the correlation between the max-entropic rate of a musical scale and the subjective aesthetic component. We present our analysis with examples from the south Indian classical music system.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Automatic Tonic Identification in Indian Art Music: Approaches and Evaluation

The tonic is a fundamental concept in Indian art music. It is the base pitch, which an artist chooses in order to construct the melodies during a rg(a) rendition, and all accompanying instruments are tuned using the tonic pitch. Consequently, tonic identification is a fundamental task for most computational analyses of Indian art music, such as intonation analysis, melodic motif analysis and rg recognition. In this paper we review existing approaches for tonic identification in Indian art music and evaluate them on six diverse datasets for a thorough comparison and analysis. We study the performance of each method in different contexts such as the presence/absence of additional metadata, the quality of audio data, the duration of audio data, music tradition (Hindustani/Carnatic) and the gender of the singer (male/female). We show that the approaches that combine multi-pitch analysis with machine learning provide the best performance in most cases (90% identification accuracy on average), and are robust across the aforementioned contexts compared to the approaches based on expert knowledge. In addition, we also show that the performance of the latter can be improved when additional metadata is available to further constrain the problem. Finally, we present a detailed error analysis of each method, providing further insights into the advantages and limitations of the methods.

Three-dimensional localization of multiple acoustic sources in shallow ocean with non-Gaussian noise

In this paper, a low-complexity algorithm SAGE-USL is presented for 3-dimensional (3-D) localization of multiple acoustic sources in a shallow ocean with non-Gaussian ambient noise, using a vertical and a horizontal linear array of sensors. In the proposed method, noise is modeled as a Gaussian mixture. Initial estimates of the unknown parameters (source coordinates, signal waveforms and noise parameters) are obtained by known/conventional methods, and a generalized expectation maximization algorithm is used to update the initial estimates iteratively. Simulation results indicate that convergence is reached in a small number of (<= 10) iterations. Initialization requires one 2-D search and one 1-D search, and the iterative updates require a sequence of 1-D searches. Therefore the computational complexity of the SAGE-USL algorithm is lower than that of conventional techniques such as 3-D MUSIC by several orders of magnitude. We also derive the Cramer-Rao Bound (CRB) for 3-D localization of multiple sources in a range-independent ocean. Simulation results are presented to show that the root-mean-square localization errors of SAGE-USL are close to the corresponding CRBs and significantly lower than those of 3-D MUSIC. (C) 2014 Elsevier Inc. All rights reserved.

MULTI-INSTRUMENT DETECTION IN POLYPHONIC MUSIC USING GAUSSIAN MIXTURE BASED FACTORIAL HMM

We formulate the problem of detecting the constituent instruments in a polyphonic music piece as a joint decoding problem. From monophonic data, parametric Gaussian Mixture Hidden Markov Models (GM-HMM) are obtained for each instrument. We propose a method to use the above models in a factorial framework, termed as Factorial GM-HMM (F-GM-HMM). The states are jointly inferred to explain the evolution of each instrument in the mixture observation sequence. The dependencies are decoupled using variational inference technique. We show that the joint time evolution of all instruments' states can be captured using F-GM-HMM. We compare performance of proposed method with that of Student's-t mixture model (tMM) and GM-HMM in an existing latent variable framework. Experiments on two to five polyphony with 8 instrument models trained on the RWC dataset, tested on RWC and TRIOS datasets show that F-GM-HMM gives an advantage over the other considered models in segments containing co-occurring instruments.

Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.