Conditional network measures using multivariate partial coherence analysis for spike train data with application to multi-electrode array recordings

This thesis proposes a novel approach for functional connectivity studies of neuronal signal recordings based on statistical signal processing analysis in the frequency domain using Multivariate Partial Coherence (MVPC) combined with network theory measures. MVPC is applied to spike trains signals to make inferences about the underlying network structure. The presence of connections between single unit spike trains is estimated using both coherence and MVPC analysis. Scalability of MVPC analysis is investigated through application to simulated spike train data with up to 100 simultaneous spike trains generated from a network of excitatory and inhibitory cortical neurons. Stable MVPC estimates were obtained with up to 198 predictors in partial coherence estimates, using a combination of simulated cortical neuron data and additional Poisson spike train predictors. MVPC provides higher order partial coherence analysis for multi-channel spike trains signals, removing effects of common influences in pairwise connectivity estimates. Network measures applied to binary and weighted adjacency measures derived from coherence and partial coherence are compared to determine the differences in unconditional and conditional networks of spike train interactions. A combination of MVPC analysis along with network theory analysis provides a systematic approach for multi-channel spike train signals. The proposed method is applied to simulated and multi-electrode array (MEA) spike train data. The MEA data consists of 19 single unit channels recorded from a study of connectivity in a model of kainic acid (KA) induced epileptiform activity for mesial temporal lobe epilepsy (mTLE) in a rat. The network theory analysis uses basic measures on both conditional and unconditional network, which highlights the differences in network structure and characteristics between the two representations. Complex analysis on conditional networks is useful in describing the properties of integration and segregation in the network

Average Number of Coherent Modes for Pulse Random Fields

Some consequences of spatio-temporal symmetry for the deterministic decomposition of complex light fields into factorized components are considered. This enables to reveal interrelations between spatial and temporal coherence properties of wave. An estimation of average number of the decomposition terms is obtained in the case of statistical ensemble of light pulses.Comment: LaTeX, 10 pages, no figures; to be published in Proc. SPIE; E-mail: [email protected]

Weak Cat-Operads

An operad (this paper deals with non-symmetric operads)may be conceived as a partial algebra with a family of insertion operations, Gerstenhaber's circle-i products, which satisfy two kinds of associativity, one of them involving commutativity. A Cat-operad is an operad enriched over the category Cat of small categories, as a 2-category with small hom-categories is a category enriched over Cat. The notion of weak Cat-operad is to the notion of Cat-operad what the notion of bicategory is to the notion of 2-category. The equations of operads like associativity of insertions are replaced by isomorphisms in a category. The goal of this paper is to formulate conditions concerning these isomorphisms that ensure coherence, in the sense that all diagrams of canonical arrows commute. This is the sense in which the notions of monoidal category and bicategory are coherent. The coherence proof in the paper is much simplified by indexing the insertion operations in a context-independent way, and not in the usual manner. This proof, which is in the style of term rewriting, involves an argument with normal forms that generalizes what is established with the completeness proof for the standard presentation of symmetric groups. This generalization may be of an independent interest, and related to matters other than those studied in this paper. Some of the coherence conditions for weak Cat-operads lead to the hemiassociahedron, which is a polyhedron related to, but different from, the three-dimensional associahedron and permutohedron.Comment: 38 pages, version prepared for publication in Logical Methods in Computer Science, the authors' last version is v

Types and forgetfulness in categorical linguistics and quantum mechanics

The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an illustration. Taking as a starting point the question of whether the evaluation of such a type system 'loses information', we consider the parametrized typing associated with connectives from this viewpoint. The answer to this question implies that, within full categorical models of meaning, the objects associated with types must exhibit a simple but subtle categorical property known as self-similarity. We investigate the category theory behind this, with explicit reference to typed systems, and their monoidal closed structure. We then demonstrate close connections between such self-similar structures and dagger Frobenius algebras. In particular, we demonstrate that the categorical structures implied by the polymorphically typed connectives give rise to a (lax unitless) form of the special forms of Frobenius algebras known as classical structures, used heavily in abstract categorical approaches to quantum mechanics.Comment: 37 pages, 4 figure

A Critical Examination of BonJour’s, Haack’s, and Dancy’s Theory of Empirical Justification

In this paper, we shall describe and critically evaluate four contemporary theories which attempt to solve the problem of the infinite regress of reasons: BonJour's ‘impure’ coherentism, BonJour's foundationalism, Haack's ‘foundherentism’ and Dancy's pure coherentism. These theories are initially put forward as theories about the justification of our empirical beliefs; however, in fact they also attempt to provide a successful response to the question of their own ‘metajustification.’ Yet, it will be argued that 1) none of the examined theories is successful as a theory of justification of our empirical beliefs, and that 2) they also fall short of being adequate theories of metajustification. It will be further suggested that the failure of these views on justification is not coincidental, but is actually a consequence of deeper and tacitly held problematic epistemological assumptions (namely, the requirements of justificatory generality and epistemic priority), whose acceptance paves the way towards a generalized scepticism about empirical justification

Updating Data Semantics

This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing terms like maybe and if interact: they iterate, and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox, and that exposing that opens the door to a solution to the puzzle. And third, to explore the reach of that solution. Along the way, the paper highlights a number of pleasing properties of two elegant semantic theories, explores some meta-theoretic properties of dynamic notions of meaning, dips its toe into some hazardous waters, and offers characterization theorems for the space of meanings an indicative conditional can have