京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18766号 / 理博第4024号 / 新制||理||1580(附属図書館) / 31717 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 伊藤 哲史, 教授 上田 哲生, 教授 雪江 明彦 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The hippocampal CA1 is crucial for myriad types of learning and memory. It is theorized to provide a spatiotemporal framework for the encoding of relevant information during learning, allowing an individual to create a cognitive map of its environment and experiences. To probe CA1 network dynamics that underlie such complex cognitive function, in this work we used recently developed cellular optical imaging techniques that provide high spatial and temporal resolutions. Genetically-encoded calcium indicators offer the ability to record intracellular calcium dynamics, a proxy of neural activity, from hundreds of cells in behaving animals with single cell resolution in genetically-defined cell types. In complement, recently developed genetically-encoded voltage indicators have enabled direct recording of transmembrane voltage of individual genetically-defined cells in behaving animals. The work presented here uses the genetically-encoded calcium indicator GCaMP6f and the genetically-encoded voltage indicator SomArchon to interrogate the activities of individual hippocampal CA1 neurons and their relationship to the dynamics of the broader network during behavior. First, we provide the first in vivo, real-time evidence that two unique populations of CA1 cells encode trace conditioning and extinction learning, two distinct phases of hippocampal-dependent learning. The population of cells responsible for the representation of extinction learning emerges within one session of extinction training. Second, we perform calcium imaging in a mouse model containing a total knockout of NEXMIF, a gene causative of autism spectrum disorder. We reveal that loss of NEXMIF causes over-synchronization of the CA1 circuit, particularly during locomotion, impairing the information encoding capacity of the network. Finally, we conduct voltage imaging of CA1 pyramidal cells and parvalbumin (PV)-positive interneurons, with simultaneous recording of local field potential (LFP), to characterize how cellular-level membrane dynamics and spiking relate to network-level LFP. We demonstrate that in PV neurons, membrane potential oscillations in the theta frequency range show consistent synchrony with LFP theta oscillations and organize spike timing of the PV population relative to LFP theta, indicating that PV interneurons orchestrate theta rhythmicity in the CA1 network. In summary, this dissertation utilizes genetically-encoded optical reporters of neural activity, providing critical insights into the function of the CA1 as a flexible, diverse network of individual neurons.

No description available.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22968号 / 理博第4645号 / 新制||理||1668(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)准教授 市野 篤史, 教授 池田 保, 教授 加藤 周 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We investigate the ultraconnectivity condition on graphs, and provide further connections between critical and ultraconnected graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is preserved by Cartesian products. We completely characterize when adding a vertex to an ultraconnected graph preserves ultraconnectivity. We also derive bounds on the number of vertices which guarantee ultraconnectivity of certain classes of regular graphs. We give results from our exhaustive enumeration of ultraconnected graphs up to 11 vertices. Using techniques involving the Lovász theta parameter for graphs, we prove certain classes of graphs are critical (and hence ultraconnected) in the positive definite partial matrix completion problem.

This paper includes some basic ideas about the computation of a function theta(G), the theta number of a graph G, which is known as the Lovasz number of G. theta(G^c) lies between two hard-to-compute graph numbers omega(G), the size of the largest lique in a graph G, and chi(G), the minimum number of colors need to properly color the vertices of G. Lovasz and Grotschel called this the "Sandwich Theorem". Donald E. Knuth gives four additional definitions of theta, theta_1, theta_2, theta_3, theta_4 and proves that they are all equal. First I am going to describe the proof of the equality of theta, theta_1 and theta_2 and then I will show the calculation of the theta function for some specific graphs: K_n, graphs related to K_n, and C_n. This will help us understand the theta function, an important function for graph theory. Some of the results are calculated in different ways. This will benefit students who have a basic knowledge of graph theory and want to learn more about the theta function.

<p>The main focus of this dissertation is to find and explain the periodic points of certain algebraic functions that are related to some modular functions, which themselves can be represented by continued fractions. Some of these continued fractions are first explored by Srinivasa Ramanujan in early 20th century. Later on, much work has been done in terms of studying the continued fractions, and proving several relations, identities, and giving different representations for them.</p> <p><br></p> <p>The layout of this report is as follows. Chapter 1 has all the basic background knowledge and ingredients about algebraic number theory, class field theory, Ramanujan’s theta functions, etc. In Chapter 2, we look at the Ramanujan-Göllnitz-Gordon continued fraction that we call v(τ) and evaluate it at certain arguments in the field K = Q(√−d), with −d ≡ 1 (mod 8), in which the ideal (2) = ℘₂℘′₂  is a product of two prime ideals. We prove several identities related to itself and with other modular functions. Some of these are new, while some of them are known but with different proofs. These values of v(τ) are shown to generate the inertia field of ℘₂ or ℘′₂ in an extended ring class field over the field K. The conjugates over Q of these same values, together with 0, −1 ± √2, are shown to form the exact set of periodic points of a fixed algebraic function ˆF(x), independent of d. These are analogues of similar results for the Rogers-Ramanujan continued fraction. See [1] and [2]. This joint work with my advisor Dr. Morton, is submitted for publication to the New York Journal.</p> <p><br> In Chapters 3 and 4, we take a similar approach in studying two more continued fractions c(τ) and u(τ), the first of which is more commonly known as the Ramanujan’s cubic continued fraction. We show what fields a value of this continued fraction generates over Q, and we describe how the periodic points for described functions arise as values of these continued fractions. Then in the last chapter, we summarise all these results, give some possible directions for future research as well as mentioning some conjectures.</p>

Quantum systems in the d-dimensional Hilbert space are considered. The mutually unbiased bases is a deep problem in this area. The problem of finding all mutually unbiased bases for higher (non-prime) dimension is still open. We derive an alternate approach to mutually unbiased bases by studying a weaker concept which we call weak mutually unbiased bases. We then compare three rather different structures. The first is weak mutually unbiased bases, for which the absolute value of the overlap of any two vectors in two different bases is 1/√k (where k∣d) or 0. The second is maximal lines through the origin in the Z(d) × Z(d) phase space. The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different structures. We give an explicit breakdown of this triality.

Lignocellulosic biomass represents the largest potential volume and lowest cost for biofuel and biochemical production. Harnessing the full potential of the lignocellulosic biomass for low-carbon energy requires the knowledge of efficient breakdown and fractionation of its carbohydrates and lignin. Organic solvent pretreatment is recognized as an emerging way ahead because of its inherent advantages, such as the ability to fractionate lignocellulosic biomass into cellulose, lignin, and hemicellulose components with high purity, as well as easy solvent recovery and solvent reuse. Through all-atom MD simulation, we analyze the conformational transition of diverse lignin molecules in varying concentration of Methanol/water , DMSO/water mixtures and neat DMSO , neat methanol and water. From our work, it appears that in 40 mol% DMSO and 40 mol% methanol mixture (’theta solvent’) hardwood lignin(G/S=1.35) conforms random coil like structure, while 60 mol% DMSO and 60 mol% methanol solution (at 300 K) appears to be ’good solvent’ forhardwood lignin since it conforms extended chain like structure. While 80 mol% methanol is proven to be ’theta solvent’ and 80 mol% DMSO is proven to be ’good solvent’ for softwood lignin. We find that, major functional moieties of both lignin preferentially coordinated by methanol and DMSO molecules in increased organic solvents concentration which induces the conformational transition from crumbled globule to coil and prevent self-aggregation of lignin in binary mixtures. Chain dynamics of lignin explain the relaxation and subsequently elongated in addition of organic solvents into water.

The perception of self-motion draws on inputs from the visual, vestibular and proprioceptive systems. Decades of behavioural research has shed light on constructs such as multisensory weighting, heading perception, and sensory thresholds, that are involved in self-motion perception. Despite the abundance of knowledge generated by behavioural studies, there is a clear lack of research exploring the neural processes associated with full-body, multisensory self-motion perception in humans. Much of what is known about the neural correlates of self-motion perception comes from either the animal literature, or from human neuroimaging studies only administering visual self-motion stimuli. The goal of this thesis was to bridge the gap between understanding the behavioural correlates of full-body self-motion perception, and the underlying neural processes of the human brain. We used a high-fidelity motion simulator to manipulate the interaction of the visual and vestibular systems to gain insights into cognitive processes related to self-motion perception. The present line of research demonstrated that theta, alpha and beta oscillations are the underlying electrophysiological oscillations associated with self-motion perception. Specifically, the three empirical chapters combine to contribute two main findings to our understanding of self-motion perception. First, the beta band is an index of visual-vestibular weighting. We demonstrated that beta event-related synchronization power is associated with visual weighting bias, and beta event-related desynchronization power is associated with vestibular weighting bias. Second, the theta band is associated with direction processing, regardless of whether direction information is provided through the visual or vestibular system. This research is the first of its kind and has opened the door for future research to further develop our understanding of biomarkers related to self-motion perception. / Dissertation / Doctor of Philosophy (PhD) / As we move through the environment, either by walking, or operating a vehicle, our senses collect many different kinds of information that allow us to perceive factors such as, how fast we are moving, which direction we are headed in, or how other objects are moving around us. Many of our senses take in very different information, for example, the vestibular system processes information about our head movements, while our visual system processes information about incoming light waves. Despite how different all of this self-motion information can be, we still manage to have one smooth perception of our bodies moving through the environment. This smooth perception of self-motion is due to our senses sharing information with one another, which is called multisensory integration. Two of the most important senses for collecting information about self-motion are the visual and vestibular systems. To this point, very little is known about the biological processes in the brain while the visual and vestibular systems integrate information about self-motion. Understanding this process is limited because until recently, we have not had the technology or the methodology to adequately record the brain while physically moving people in a virtual environment. Our team developed a ground-breaking set of methodologies to solve this issue, and discovered key insights into brainwave patterns that take place in order for us to perceive ourselves in motion. There were two critical insights from our line of research. First, we identified a specific brainwave frequency (beta oscillations) that indexes integration between the visual and vestibular systems. Second, we demonstrated another brainwave frequency (theta oscillation) that is associated with perceiving which direction we are headed in, regardless of which sense this direction information is coming from. Our research lays the foundation for our understanding of biological processes of self-motion perception and can be applied to diagnosing vestibular disorders or improving pilot simulator training.