The main purpose of this thesis to examine the controllability and observability of the linear discrete fractional systems. First we introduce the problem and continue with the review of some basic definitions and concepts of fractional calculus which are widely used to develop the theory of this subject. In Chapter 3, we give the unique solution of the fractional difference equation involving the Riemann-Liouville operator of real order between zero and one. Additionally we study the sequential fractional difference equations and describe the way to obtain the state-space repre- sentation of the sequential fractional difference equations. In Chapter 4, we study the controllability and observability of time-invariant linear nabla fractional systems.We investigate the time-variant case in Chapter 5 and we define the state transition matrix in fractional calculus. In the last chapter, the results are summarized and directions for future work are stated.

Managing large-scale dynamical systems (e.g., transportation systems, complex information systems, and power networks, etc.) in real-time is very challenging considering their complicated system dynamics, intricate network interactions, large scale, and especially the existence of various uncertainties. To address this issue, intelligent techniques which can quickly design decision-making strategies that are robust to uncertainties are needed. This dissertation aims to conquer these challenges by exploring a data-driven decision-making framework, which leverages big-data techniques and scalable uncertainty evaluation approaches to quickly solve optimal control problems. In particular, following techniques have been developed along this direction: 1) system modeling approaches to simplify the system analysis and design procedures for multiple applications; 2) effective simulation and analytical based approaches to efficiently evaluate system performance and design control strategies under uncertainty; and 3) big-data techniques that allow some computations of control strategies to be completed offline. These techniques and tools for analysis, design and control contribute to a wide range of applications including air traffic flow management, complex information systems, and airborne networks.

Capacity restrictions in stores, maintained by mechanisms like spacing customer intake at certain time intervals, have become familiar features in the time of the pandemic. The effect on total spending is not a linear function of reduced capacity, since shopping in a crowded store under a social distance regime is prone to considerable slowdown. In this thesis, We introduce a simple dynamical model of the evolution of shopping rate as a function of a given customer intake rate, starting with an empty store. The slowdown of each individual customer is incorporated as an additive term to a baseline value shopping time, proportional to the number of other customers in the store. We determine analytically and by simulation the trajectory of the model as it approaches a Little's Law equilibrium, and identify the point of phase change, beyond which equilibrium cannot be achieved. By relating customer shopping rate to the slowdown compared to the baseline, We can calculate the optimal intake rate leading to maximum equilibrium spending. This turns out to be the maximum rate compatible with equilibrium. The slowdown is not enough to justify a lower intake rate. Because the slowdown due to the largest possible number of shoppers is more than compensated for by the increased volume of shopping.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22842号 / 工博第4782号 / 新制||工||1748(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 土居 伸二, 教授 木本 恒暢 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

In this dissertation we develop aspects of ergodic theory for C*-dynamical systems for which the C*-algebras are allowed to be noncommutative. We define four ergodic properties, with analogues in classic ergodic theory, and study C*-dynamical systems possessing these properties. Our analysis will show that, as in the classical case, only certain combinations of these properties are permissable on C*-dynamical systems. In the second half of this work, we construct concrete noncommutative C*-dynamical systems having various permissable combinations of the ergodic properties. This shows that, as in classical ergodic theory, these ergodic properties continue to be meaningful in the noncommutative case, and can be useful to classify and analyse C*-dynamical systems. / Dissertation (MSc)--University of Pretoria, 2013. / gm2014 / Mathematics and Applied Mathematics / unrestricted

In this work, we studied three selected problems in FRW spacetime. In the first part, we analysed the motion of a test particle in the homogeneous and isotropic universe. We presented a framework in which one can derive the uniformly accelerated trajectory and geodesic motion if a scale factor for a given spacetime is provided as a function of coordinate time. By applying the confomal time transformation, we were able to convert second order differential equations of motion in FRW spacetime to first order differential equations. From this, we managed to obtain a formalism to derive the uniformly accelerated trajectory of a test particle in spatially curved FRW spacetime. The second part of this work is devoted to dynamical cosmology. In particular, we analyse the cases of barotropic fluids and non-minimally coupled scalar field in spatially curved FRW spacetime. First, we set up the dynamical systems for an unspecified EoS of a barotropic fluid case and an unspecified positive potential for a non-minimal coupled scalar field case. For both of these systems, we determined well-defined dynamical variables valid for all curvatures. In the framework of these general setups we discovered several characteristic features of the systems, such as invariant subsets, symmetries, critical points and their...

The neocortex covers 90% of the human cerebral cortex [41] and is responsible for higher cognitive function and socio-cognitive skills in all mammals. It is known to be structured in layers and in some species or cortical areas, in columns. A balanced network model was built, which incorporated these structural organizations and in particular, the layers, minicolumns and hypercolumns. The dynamics of eight different network models were studied, based on combinations of structural organizations that they have. The eigenvalue spectra of their matrices was calculated showing that layered networks have eigenvalues outside their bulk distribution in contrast to networks with columns and no layers. It was demonstrated, through simulations, that networks with layers are unstable and have a lower threshold to synchronization, thus, making them more susceptible to switch to synchronous and regular activity regimes [10]. Moreover, introduction of minicolumns to these networks was observed to partially counterbalance synchrony and regularity, in the network and neuron activity, respectively. Layered networks, principally the ones without minicolumns, also have higher degree correlations and a reduced size of potential pre- and post- connections, which induces correlations in the neuronal activity and oscillations.

Title: Dynamical symmetry breaking in models with strong Yukawa in- teractions Author: Petr Beneš Department: Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University Supervisor: Ing. Jiří Hošek, DrSc., Department of Theoretical Physics, Nu- clear Physics Institute, Academy of Sciences of the Czech Repub- lic Abstract: The primary aim of the thesis is to explore the possibility of spon- taneous symmetry breaking by strong Yukawa dynamics. Tech- nically, the symmetry is assumed to be broken by formation of symmetry-breaking parts of both the scalar and the fermion prop- agators, rather than by the scalar vacuum expectation values. The idea is first introduced on an example of a toy model with the underlying symmetry being an Abelian one and later applied to a realistic model of electroweak interaction. In addition, the thesis also deals with some more general, model-independent is- sues, applicable not only to the discussed model of strong Yukawa dynamics, but to a wider class of models with dynamical mass generation. First of these issues is the problem of fermion flavor mixing in the presence of fermion self-energies with a general mo- mentum dependence. It is in particular shown how to define the CKM matrix in such models and argued that it can come out in principle...

This study was directed toward the development of a bistable wall attachment Flip-Flop device which was capable of directionally controlling particle flow. The particles were transported by a fluid stream which under the influence of wall attachment. The dominant criteria in the development of the device was the achievement of the highest recovery of particles at the active output, without destroying the wall attachment of the fluid stream The experiment was conducted in several distinct stages; each of which was concerned with at least one aspect of wa1l attachment or particle flow. Results derived from one test were used to develop the criteria for the next experimental arrangement. Two experimental models were constructed: one of plywood with only one attachment wall, and one of plexiglas which had two attachment walls and was bistable. The plywood model was used in testing wall attachment and particle recovery as a function of the attachment wall angle. From these tests it was concluded that the optimum wall angle was 18 degrees from the center line of the device. Observations of particle action in the plywood model led to the incorporation of additional features in the plexiglas model. They were: an extended nozzle, the elimination of the separation bubble, and the development of smooth transitions at the corners. The plexiglas model was used to investigate optimum splitter location, the effect of jet velocity on recovery efficiency, the effect of vents on the performance of the device, and the performance of the device using a water jet. In the last stages of testing, moving parts and additional output features were used in conjunction with the bistable device to improve the collection efficiency. Some observations resulting from the data gathered in the various tests include: 1. The higher the jet velocity, the greater the wall attachment. 2. The higher the density and viscosity of the fluid stream the greater the recovery of particles at the active output. 3. Particles with large inertial forces were controlled less by the attached jet stream. The addition 0f vents in the device may produce greater particle recovery. 5. The use of moving parts and variations in the output leg design can produce 100 percent particle recovery. This study indicated that it was possible to control the directional flow of particles with the bistable wall attachment device which was developed. However, the pure fluid bistable device could not achieve 100 percent recovery of particles. The addition of moving parts or variations in the output leg design can produce 100 percent recovery of the particles. The use of a bistable device could provide simplicity, reliability and adaptability in transporting materials for industrial processes.

Indiana University-Purdue University Indianapolis (IUPUI) / Associated to any finite simple graph $\Gamma$ is the {\em chromatic polynomial} $\P_\Gamma(q)$ whose complex zeros are called the {\em chromatic zeros} of $\Gamma$. A hierarchical lattice is a sequence of finite simple graphs $\{\Gamma_n\}_{n=0}^\infty$ built recursively using a substitution rule expressed in terms of a generating graph. For each $n$, let $\mu_n$ denote the probability measure that assigns a Dirac measure to each chromatic zero of $\Gamma_n$. Under a mild hypothesis on the generating graph, we prove that the sequence $\mu_n$ converges to some measure $\mu$ as $n$ tends to infinity. We call $\mu$ the {\em limiting measure of chromatic zeros} associated to $\{\Gamma_n\}_{n=0}^\infty$. In the case of the Diamond Hierarchical Lattice we prove that the support of $\mu$ has Hausdorff dimension two. The main techniques used come from holomorphic dynamics and more specifically the theories of activity/bifurcation currents and arithmetic dynamics. We prove a new equidistribution theorem that can be used to relate the chromatic zeros of a hierarchical lattice to the activity current of a particular marked point. We expect that this equidistribution theorem will have several other applications, and describe one such example in statistical mechanics about the Lee-Yang-Fisher zeros for the Cayley Tree.