On set systems determined by intersections

AbstractThe set systems determined by intersections are studied and a sufficient condotion for this property is given. For case of graphs a necessary and sufficient condition is established. Some connections to other results are discussed

Relation between molecular structure and ultrafast photoreactivity with application to molecular switches

Photoinduced ultrafast isomerizations are fundamental reactions in photochemistry and photobiology. This thesis aims for an understanding of the generic forces driving these reactions and a theoretical approach is set up, able to handle realistic systems, whose fast relaxation is mediated by conical intersections. The main focus is on the development of strategies for the prediction and accelerated optimization of conical intersections and their application to artificial compounds with promising physicochemical properties for technical applications as molecular switches. All calculations are based on advanced quantum chemical methods and mixed quantum-classical dynamics. In the first part of this thesis the two-electron two-orbital theory by Michl and Bonacic-Koutecky used in its original formulation to rationalize the structure of conical intersections in charged polyene systems is extended by including the interactions of the active pair of electrons with the remaining closed-shell electrons that are present in any realistic system. A set of conditions, called resonance and heterosymmetry conditions, for the formation of conical intersections in multielectronic systems are derived and verified by calculations on the basic units ethylene, cis-butadiene and 1,3-cyclohexadiene at various geometries and functionalizational patterns. The quantitative results help to understand the role of geometrical deformations and substituent effects for the formation of conical intersections and to derive rules of thumb for their qualitative prediction in arbitrary polyenes. An extension of the rules of thumb to conical intersection seams is formulated. The strategy pursued is to divide the molecular system into basic units and into functional groups. Each unit and its intersection space are treated independently, thereby reducing the dimensionality of the search space compared to the complete molecule. Subsequently, the interconnectivity of the intersection spaces of the different units is determined and an initial guess for the complete seam is constructed. This guess is then fed into a quantum chemistry package to finalize the optimization. The strategy is demonstrated for two multi-functionalized systems, hemithioindigo-hemistilbene and trifluoromethyl-pyrrolylfulgide. In the second part of this thesis state-of-the-art quantum chemical calculations and time-resolved transient and infrared spectroscopy are used to reconstruct the complex multi-channel isomerization mechanisms of hemithioindigo-hemistilbene and trifluoromethyl-indolylfulgide. Both the cis-trans isomerization in hemithioindigo-hemistilbene and the electrocyclic ring closure/opening in indolylfulgide are characterized by a charge transfer in the excited state. The ability of each system to stabilize this charge transfer is essential for the returning to the ground state. The relaxation to the ground state through extended regions of the seam is found to be the decisive step determining the reaction speed and the quantum yield. In the last part of this thesis mixed quantum-classical dynamics simulations at multi-configurational perturbation theory (MS-CASPT2) level, using Tully's fewest switches surface hopping approach, are performed to study the ultrafast photoreactivity of 1,3-cyclohexadiene in the gas-phase. For this purpose a numerical routine for the efficient calculation of non-adiabatic couplings at MS-CASPT2 level is presented. The major part of the excited molecules are found to circumvent the 1B2/2A1 conical intersection and reach the conical intersection seam between the excited state and the ground state instantaneuosly. Time constants for the evolution of the wavepacket on the bright 1B2-state, the relaxation into the 2A1-state and the return to the ground state are extracted. It is demonstrated that the accessibility of the conical intersection seam depends on its energetic and spatial relation to the minimum energy path, as well as on the momentum which is accumulated during relaxation on the excited state potential energy surface

Development of Bus-Stop Time Models in Dense Urban Areas: A Case Study in Washington DC

Bus transit reliability depends on several factors including the route of travel, traffic conditions, time of day, and conditions at the bus stops along the route. The number of passengers alighting or boarding, fare payment method, dwell time (DT), and the location of the bus stop also affect the overall reliability of bus transit service. This study defines a new variable, Total Bus Stop Time (TBST) which includes DT and the time it takes a bus to safely maneuver into a bus stop and the re-entering the main traffic stream. It is thought that, if the TBST is minimized at bus stops, the overall reliability of bus transit along routes could be improved. This study focused on developing a TBST model for bus stops located near intersections and at mid-blocks using ordinary least squares method based on data collection at 60 bus stops, 30 of which were near intersections while the remaining were at mid-blocks in Washington DC. The field data collection was conducted during the morning, mid-day, and evening peak hours. The following variables were observed at each bus stop: bus stop type, number of passengers alighting or boarding, DT, TBST, number of lanes on approach to the bus stop, presence of parking, and bus pad length. The data was analyzed and all statistical inferences were conducted based on 95% confidence interval. The results show that the TBST could be used to aid in improving planning and scheduling of transit bus systems in an urban area

Decentralised control of material or traffic flows in networks using phase-synchronisation

We present a self-organising, decentralised control method for material flows in networks. The concept applies to networks where time sharing mechanisms between conflicting flows in nodes are required and where a coordination of these local switches on a system-wide level can improve the performance. We show that, under certain assumptions, the control of nodes can be mapped to a network of phase-oscillators. By synchronising these oscillators, the desired global coordination is achieved. We illustrate the method in the example of traffic signal control for road networks. The proposed concept is flexible, adaptive, robust and decentralised. It can be transferred to other queuing networks such as production systems. Our control approach makes use of simple synchronisation principles found in various biological systems in order to obtain collective behaviour from local interactions

Risk Assessment Algorithms Based On Recursive Neural Networks

The assessment of highly-risky situations at road intersections have been recently revealed as an important research topic within the context of the automotive industry. In this paper we shall introduce a novel approach to compute risk functions by using a combination of a highly non-linear processing model in conjunction with a powerful information encoding procedure. Specifically, the elements of information either static or dynamic that appear in a road intersection scene are encoded by using directed positional acyclic labeled graphs. The risk assessment problem is then reformulated in terms of an inductive learning task carried out by a recursive neural network. Recursive neural networks are connectionist models capable of solving supervised and non-supervised learning problems represented by directed ordered acyclic graphs. The potential of this novel approach is demonstrated through well predefined scenarios. The major difference of our approach compared to others is expressed by the fact of learning the structure of the risk. Furthermore, the combination of a rich information encoding procedure with a generalized model of dynamical recurrent networks permit us, as we shall demonstrate, a sophisticated processing of information that we believe as being a first step for building future advanced intersection safety system