Computational principles of single neuron adaptation

Cortical neurons continuously transform sets of incoming spike trains into output spike trains. This input-output transformation is referred to as single-neuron computation and constitutes one of the most fundamental process in the brain. A deep understanding of single-neuron dynamics is therefore required to study how neural circuits support complex behaviors such as sensory perception, learning and memory. The results presented in this thesis focus on single-neuron computation. In particular, I address the question of how and why cortical neurons adapt their coding strategies to the statistical properties of their inputs. A new spiking model and a new fitting procedure are introduced that enable reliable nonparametric feature extraction from in vitro intracellular recordings. By applying this method to a new set of data from L5 pyramidal neurons, I found that cortical neurons adapt their firing rate over multiple timescales, ranging from tens of milliseconds to tens of second. This behavior results from two cellular processes, which are triggered by the emission of individual action potentials and decay according to a power-law. An analysis performed on in vivo intracellular recordings further indicates that power-law adaptation is near-optimally tuned to efficiently encode natural inputs received by single neurons in biologically relevant situations. These results shade light on the functional role of spike-frequency adaptation in the cortex. The second part of this thesis focuses on the long-standing question of whether cortical neurons act as temporal integrators or coincidence detectors. According to standard theories relying on simplified spiking models, cortical neurons are expected to feature both coding strategies, depending on the statistical properties of their inputs. A model-based analysis performed on a second set of in vitro recordings demonstrates that the spike initiation dynamics implements a complex form of adaptation to make cortical neurons act as coincidence detectors, regardless of the input statistics. This result indicates that cortical neurons are well-suited to support a temporal code in which the relevant information is carried by the precise timing of spikes. The spiking model introduced in this thesis was not designed to study a particular aspect of single-neuron computation and achieves good performances in predicting the spiking activity of different neuronal types. The proposed method for parameter estimation is efficient and only requires a limited amount of data. If applied on large datasets, the mathematical framework presented in this thesis could therefore lead to automated high-throughput single-neuron characterization

Mathematical control theory and Finance

Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio

A circuit model for diffusive breast imaging and a numerical algorithm for its inverse problem

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 67-70).by Julie L. Wonus.M.Eng

Improving Network Reductions for Power System Analysis

abstract: The power system is the largest man-made physical network in the world. Performing analysis of a large bulk system is computationally complex, especially when the study involves engineering, economic and environmental considerations. For instance, running a unit-commitment (UC) over a large system involves a huge number of constraints and integer variables. One way to reduce the computational expense is to perform the analysis on a small equivalent (reduced) model instead on the original (full) model. The research reported here focuses on improving the network reduction methods so that the calculated results obtained from the reduced model better approximate the performance of the original model. An optimization-based Ward reduction (OP-Ward) and two new generator placement methods in network reduction are introduced and numerical test results on large systems provide proof of concept. In addition to dc-type reductions (ignoring reactive power, resistance elements in the network, etc.), the new methods applicable to ac domain are introduced. For conventional reduction methods (Ward-type methods, REI-type methods), eliminating external generator buses (PV buses) is a tough problem, because it is difficult to accurately approximate the external reactive support in the reduced model. Recently, the holomorphic embedding (HE) based load-flow method (HELM) was proposed, which theoretically guarantees convergence given that the power flow equations are structure in accordance with Stahl’s theory requirements. In this work, a holomorphic embedding based network reduction (HE reduction) method is proposed which takes advantage of the HELM technique. Test results shows that the HE reduction method can approximate the original system performance very accurately even when the operating condition changes.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201