A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Composition operators on vector-valued BMOA and related function spaces

A composition operator is a linear operator between spaces of analytic or harmonic functions on the unit disk, which precomposes a function with a fixed self-map of the disk. A fundamental problem is to relate properties of a composition operator to the function-theoretic properties of the self-map. During the recent decades these operators have been very actively studied in connection with various function spaces. The study of composition operators lies in the intersection of two central fields of mathematical analysis; function theory and operator theory. This thesis consists of four research articles and an overview. In the first three articles the weak compactness of composition operators is studied on certain vector-valued function spaces. A vector-valued function takes its values in some complex Banach space. In the first and third article sufficient conditions are given for a composition operator to be weakly compact on different versions of vector-valued BMOA spaces. In the second article characterizations are given for the weak compactness of a composition operator on harmonic Hardy spaces and spaces of Cauchy transforms, provided the functions take values in a reflexive Banach space. Composition operators are also considered on certain weak versions of the above function spaces. In addition, the relationship of different vector-valued function spaces is analyzed. In the fourth article weighted composition operators are studied on the scalar-valued BMOA space and its subspace VMOA. A weighted composition operator is obtained by first applying a composition operator and then a pointwise multiplier. A complete characterization is given for the boundedness and compactness of a weighted composition operator on BMOA and VMOA. Moreover, the essential norm of a weighted composition operator on VMOA is estimated. These results generalize many previously known results about composition operators and pointwise multipliers on these spaces.

Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

The biological functions of mouse twinfilin isoforms

The actin cytoskeleton is essential for many cellular processes, including motility, morphogenesis, endocytosis and signal transduction. Actin can exist in monomeric (G-actin) or filamentous (F-actin) form. Actin filaments are considered to be the functional form of actin, generating the protrusive forces characteristic for the actin cytoskeleton. The structure and dynamics of the actin filament and monomer pools are regulated by a large number of actin-binding proteins in eukaryotic cells. Twinfilin is an evolutionarily conserved small actin monomer binding protein. Twinfilin is composed of two ADF/cofilin-like domains, separated by a short linker and followed by a C-terminal tail. Twinfilin forms a stable, high affinity complex with ADP-G-actin, inhibits the nucleotide exchange on actin monomers, and prevents their assembly into filament ends. Twinfilin was originally identified from yeast and has since then been found from all organisms studied except plants. Not much was known about the role of twinfilin in the actin dynamics in mammalian cells before this study. We set out to unravel the mysteries still covering twinfilins functions using biochemistry, cell biology, and genetics. We identified and characterized two mouse isoforms for the previously identified mouse twinfilin-1. The new isoforms, twinfilin-2a and -2b, are generated from the same gene through alternative promoter usage. The three isoforms have distinctive expression patterns, but are similar biochemically. Twinfilin-1 is the major isoform during development and is expressed in high levels in almost all tissues examined. Twinfilin-2a is also expressed almost ubiquitously, but at lower levels. Twinfilin-2b turned out to be a muscle-specific isoform, with very high expression in heart and skeletal muscle. It seems all mouse tissues express at least two twinfilin isoforms, indicating that twinfilins are important regulators of actin dynamics in all cell and tissue types. A knockout mouse line was generated for twinfilin-2a. The mice homozygous for this knockout were viable and developed normally, indicating that twinfilin-2a is dispensable for mouse development. However, it is important to note that twinfilin-2a shows similar expression pattern to twinfilin-1, suggesting that these proteins play redundant roles in mice. All mouse isoforms were shown to be able to sequester actin filaments and have higher affinity for ADP-G-actin than ATP-G-actin. They are also able to directly interact with heterodimeric capping protein and PI(4,5)P2 similar to yeast twinfilin. In this study we also uncovered a novel function for mouse twinfilins; capping actin filament barbed ends. All mouse twinfilin isoforms were shown to possess this function, while yeast and Drosophila twinfilin were not able to cap filament barbed ends. Twinfilins localize to the cytoplasm but also to actin-rich regions in mammalian cells. The subcellular localizations of the isoforms are regulated differently, indicating that even though twinfilins biochemical functions in vitro are very similar, in vivo they can play different roles through different regulatory pathways. Together, this study show that twinfilins regulate actin filament assembly both by sequestering actin monomers and by capping filament barbed ends, and that mammals have three biochemically similar twinfilin isoforms with partially overlapping expression patterns.

On Musical Self-Similarity : Intersemiosis as Synecdoche and Analogy

Self-similarity, a concept taken from mathematics, is gradually becoming a keyword in musicology. Although a polysemic term, self-similarity often refers to the multi-scalar feature repetition in a set of relationships, and it is commonly valued as an indication for musical coherence and consistency . This investigation provides a theory of musical meaning formation in the context of intersemiosis, that is, the translation of meaning from one cognitive domain to another cognitive domain (e.g. from mathematics to music, or to speech or graphic forms). From this perspective, the degree of coherence of a musical system relies on a synecdochic intersemiosis: a system of related signs within other comparable and correlated systems. This research analyzes the modalities of such correlations, exploring their general and particular traits, and their operational bounds. Looking forward in this direction, the notion of analogy is used as a rich concept through its two definitions quoted by the Classical literature: proportion and paradigm, enormously valuable in establishing measurement, likeness and affinity criteria. Using quantitative qualitative methods, evidence is presented to justify a parallel study of different modalities of musical self-similarity. For this purpose, original arguments by Benoît B. Mandelbrot are revised, alongside a systematic critique of the literature on the subject. Furthermore, connecting Charles S. Peirce s synechism with Mandelbrot s fractality is one of the main developments of the present study. This study provides elements for explaining Bolognesi s (1983) conjecture, that states that the most primitive, intuitive and basic musical device is self-reference, extending its functions and operations to self-similar surfaces. In this sense, this research suggests that, with various modalities of self-similarity, synecdochic intersemiosis acts as system of systems in coordination with greater or lesser development of structural consistency, and with a greater or lesser contextual dependence.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Honey flows through fertile valleys : The cognitive and evolutionary foundations of paradise representations

The aim of the study is to explain how paradise beliefs are born from the viewpoint of mental functions of the human mind. The focus is on the observation that paradise beliefs across the world are mutually more similar than dissimilar. By using recent theories and results from the cognitive and evolutionary study of religion as well as from studies of environmental preferences, I suggest that this is because pan-human unconscious motivations, the architecture of mind, and the way the human mind processes information constrain the possible repertoire of paradise beliefs. The study is divided into two parts, theoretical and empirical. The arguments in the theoretical part are tested with data in the empirical part with two data sets. The first data set was collected using an Internet survey. The second data set was derived from literary sources. The first data test the assumption that intuitive conceptions of an environment of dreams generally follow the outlines set by evolved environmental preferences, but that they can be tweaked by modifying the presence of desirable elements. The second data test the assumption that familiarity is a dominant factor determining the content of paradise beliefs. The results of the study show that in addition to the widely studied belief in supernatural agents, belief in supernatural environments wells from the natural functioning of the human mind attesting the view that religious thinking and ideas are natural for human species and are produced by the same mental mechanisms as other cultural information. The results also help us to understand that the mental structures behind the belief in the supernatural have a wider scope than has been previously acknowledged.

Coordinated Verb Pairs in Texts

This dissertation discusses the relation between lexis, grammar and textual organisation. The major premise adopted here is that grammatical structures are motivated both by semantic potential of words and by text-pragmatic demands. In other words, it is argued that grammatical structures form the interface between lexis and textual organisation, and that linguistic analysis should not concentrate on analysing grammatical structures in isolation, independent of context. From this point of view, grammatical structures are said to be 'well-formed' only in relation to the context they occur in. This study is based on a corpus of three million words of recent Finnish fiction from which all the occurrences of the coordinated verb pairs ([V ja V] -pairs]) containing one of the intransitive motion verbs 'lähteä' (to go), 'mennä' (to go), 'päästä' (to get into), 'nousta' (to get up), and 'laskea' (to go down), were extracted. This set of verbs was established using methods described in earlier work by Lagus & Airola (2001, and 2005). The quantitative analysis of the [V ja V] -pairs was used to carry out a qualitative analysis of individual texts. In analysing the texts, an analogy was made between musical and textual structure. The results show among others that individual verbs specialise in different functions when occurring in coordinated verb pairs. One aspect was that those verb pairs including the verb 'nousta' tend to function as markers of textual boundaries and thus reflect the organisation of narrative substance. The verb 'mennä' has weakened literal meanings, but strengthened modal meanings when occurring in [V ja V] -pairs, and, in many cases, the verb 'lähteä' in [V ja V] -pairs function as an aspectual marker rather than a pure verb of motion. That there is a gradient from the concrete sense of motion into more differentiated senses of a verb in [V ja V] -pairs alongside the structure-creating potential of the [V ja V] -pairs themselves suggest an ongoing grammaticalisation process of the patterns discussed.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Moderneja ryijyjä, metritavaraa ja käsityötä : Tekstiilitaide ja nykyaikaistuva taideteollisuus Suomessa maailmansotien välisenä aikana

Modern ryijys, fabric by the yard and handicrafts. Finnish textile art and modernizing applied art during the inter-war years Textile art was in the 1920s and 1930s in the front rank of Finnish applied art and design. Modern ryijys, tapestries and fabrics by the yard by contemporary textile artists were on show in Finland and abroad. Textile art had also become interesting commercially, especially in interior textiles of modern homes. The research uses sources of the Ornamo Association of Decorative Artists, for example the Ornamo year books published from 1927, the Finnish Society of Crafts and Design and the country s only school of applied arts, the Central School of Arts and Crafts and the Museum of Applied Arts maintained by the society and also the national specialist organisation the Friends of Finnish Handicraft. It also refers to the magazines Käsiteollisuus and Kotiliesi. The art historical dissertation studies the renaissance of weaving art of the inter-war years in Finland. It problematizes the relation of the succesfull and appreciated textile art to the concept of breakthrough of Modernism (Functionalism). With the material from textile artists activities it questions the prevailing idea of slow modernization of Finnish applied art and design and challenges the polarization of craft and industry in the discourses of Modernisms of design. The public discussions about modernization of design and applied art where textile art and especially the ryijy got sometimes into difficult positions are interpreted as power struggles. After taking independence in 1917 the Finnish tradition of ryijy rugs was set as a symbol of the original culture of the young nation. The research studies the development of the so called art ryijy and the notions and meanings of hand weaving in the national context and also in relation to contemporary events in international applied art and design. It highlights the continuity of hand crafted production of textiles and the strong position of textile artists working in this field. The research opens new perspectives to Finnish textile artists by showing their activities as entrepreneurs in their own weaving studios or design studios and referring to their many relations and functions as pattern designers and educators in the growing handicraft industries.

Kognitiva system i namngivningen av finländska handelsfartyg 1838-1938

This dissertation is an onomastic study of Finland s stock of ship names (nautonomasticon) recorded over the period 1838 1938. The primary material investigated consists of 2 066 examples of ship names from the fleets of coastal towns, distributed over five sample years. The material is supplemented with two bodies of comparative data; one that consists of 2 535 examples of boat names from the archipelago area at the corresponding time, and another that comprises 482 examples of eighteenth century Finnish ship names. This study clarifies the categories of names that appear the frequency of the names, formation, morphology, linguistic origin, functions, and semantic qualities. By comparing the material with boat names from previous centuries, and from other countries, the characteristics of Finnish vessel names are further highlighted. Additional clarification is brought to the chronological, regional, and social variations, and to the emergence of various forms of systematic naming. This dissertation builds on older research from other countries, and uses traditional onomastic methods alongside a more modern methodology. The approach is interdisciplinary, meaning that the names are explored using facts not only from nautical history, but also from a range of other historical disciplines such as economics, culture, art, and literature. In addition, the approach is socio-onomastic, i.e. that the variations in names are studied in a societal context. Using a synchronised perspective, cognitive linguistic theories have provided the tools for this exploration into the metaphorical and the prototypical meaning of the names, and the semantic domains that the names create. The quantitative analysis has revealed the overall picture of Finnish boat names. Personal names, names from mythology, and place names, emerge as significant categories, alongside nonproprial names in Swedish and Finnish. The interdisciplinary perspective has made it possible to explain certain trends in the stock of boat names, for example, the predisposition towards names from classical mythology, the breakthrough of names taken from the national epos Kalevala, names in the Finnish language from around the middle of the nineteenth century, and the continuing rise of place names during the latter part of the period 1838 1938. The socio-onomastic perspective has also identified clear differences between those ship names used in towns, and those ship names used in the archipelago, and it has clarified how naming conventions tend to spread from town centres to peripheral areas. The cognitive linguistic methods have revealed that the greater part of the vessel names can be interpreted as metaphors, in particular personifications, and that many names are related in their content and also form semantic networks and cognitive systems. The results indicate that there is a mental nautonomasticon that consists of a standard set of traditional ship names, but they also reveal the existence of conscious or unconscious cognitive systems (rules and conventions) that guide the naming of boats.

The Freudian unconscious in the context of the cognitive orientation

For decades psychoanalysis was the discipline studying the unconscious, and other branches of study lacked competence to take a stand on the issues concerning the unconscious. From 1980s onwards intense study of the unconscious has been taken place in the scope of cognitive orientation. Thus, nowadays it is talked about both pyschoanalytic and cognitive unconscious. The aim of this thesis is to integrate psychoanalytic and cognitive views. When the "Freudian" conception of the unconscious is considered, there are four entangled issues: 1) what is the unconscious like, 2) how does the unconsciuos give rise to psychic disorders 3) why and how certain contents are missing from consciousness (repression of contents), 4) the emergence of those contents (becoming conscious of the repressed). The conventional psychoanalytic answer to the first question - and "the cornerstone of psychoanalysis" - is "the unconscious is mental". The issues 2)-4) depend radically on the answer given to the 1): "psychoanalytic" conceptualizations on them rest on the "cornerstone". That ground was challended in study I: it was argued that it has never been clear what does it mean that the unconscious is mental. Thus, it was stated that in the current state of art psychoanalysis should drop out the ephitet "mental" before the term unconscious. That claim creates a pressure to reappraise the convential "psychoanalytic" answers to the other questions, and that reappraisal was the aim of studies II and III. In study II the question 2) is approached in terms of implicit knowledge. Study III focuses on mechanisms, which determine which contents appear in the scope of consciousness, and also cause missing of contents from there (the questions 3) and 4)). In the core of study III there are distinctions concerning the processess occuring in the levels of the brain, consciousness, self-consciousness, and narrative self-consciousness. Studies I-III set "psychoanalytic" topics in the frames of cognitive view. The picture emerging from those studies is not especially useful for a clinican (psychotherapist). Studies IV and V focused that issue. Study IV is a rather serious critique toward neuropsychoanalysis. In it it was claimed that repressive functions of conscious states are in the core of clinical psychoanalysis, and functions in general cannot be reduced to neurophysiological terminology. Thus, the limits of neuropsychoanalysis are more strict than it has been realized: crucial clinical issues remain outside its scope. In study V it was focused on the confusing state of things that although unconscious fantasies do not exist, the idea on them has been an important conceptual tool for clinicans. When put in a larger context, the aim of study V is similar to that of study IV: to determine the relation between psychotherapists' and neuroscientists' terminologies. Studies III, IV and V apply the philosopher Daniel Dennett's model on different levels of explanation.

Neurochemical regulation of auditory information processing studied with EEG/MEG: application to schizophrenia

Cognitive impairments of attention, memory and executive functions are a fundamental feature of the pathophysiology of schizophrenia. The neurophysiological and neurochemical changes in the auditory cortex are shown to underlie cognitive impairmentsin schizophrenia patients. Functional state of the neural substrate of auditory information processing could be objectively and non-invasively probed with auditory event-related potentials (ERPs) and event- related fields (ERFs). In the current work, we explored the neurochemical effect on the neural origins of auditory information processing in relation to schizophrenia. By means of ERPs/ERFs we aimed to determine how neural substrates of auditory information processing are modulated by antipsychotic medication in schizophrenia spectrum patients (Studies I, II) and by neuropharmacological challenges in healthy human subjects (Studies III, IV). First, with auditory ERPs we investigated the effects of olanzapine (Study I) and risperidone (Study II) in a group of patients with schizophrenia spectrum disorders. After 2 and 4 weeks of treatment, olanzapine has no significant effects on mismatch negativity(MMN) and P300, which, as it has been suggested, respectively reflect preattentive and attention-dependent information processing. After 2 weeks of treatment, risperidone has no significant effect on P300, however risperidone reduces P200 amplitude. This latter effect of risperidone on neural resources responsible for P200 generation could be partly explained through the action of dopamine. Subsequently, we used simultaneous EEG/MEG to investigate the effects of memantine (Study III) and methylphenidate (Study IV) in healthy subjects. We found that memantine modulates MMN response without changing other ERP components. This could be interpreted as being due to the possible influence of memantine through the NMDA receptors on auditory change- detection mechanism, with processing of auditory stimuli remaining otherwise unchanged. Further, we found that methylphenidate does not modulate the MMN response. This finding could indicate no association between catecholaminergic activities and electrophysiological measures of preattentive auditory discrimination processes reflected in the MMN. However, methylphenidate decreases the P200 amplitudes. This could be interpreted as a modulation of auditory information processing reflected in P200 by dopaminergic and noradrenergic systems. Taken together, our set of studies indicates a complex pattern of neurochemical influences produced by the antipsychotic drugs in the neural substrate of auditory information processing in patients with schizophrenia spectrum disorders and by the pharmacological challenges in healthy subjects studied with ERPs and ERFs.