Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from f+; g. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

A Study of Some Centrality Measures in Graphs

Centrality is in fact one of the fundamental notions in graph theory which has established its close connection with various other areas like Social networks, Flow networks, Facility location problems etc. Even though a plethora of centrality measures have been introduced from time to time, according to the changing demands, the term is not well defined and we can only give some common qualities that a centrality measure is expected to have. Nodes with high centrality scores are often more likely to be very powerful, indispensable, influential, easy propagators of information, significant in maintaining the cohesion of the group and are easily susceptible to anything that disseminate in the network.

Oligo(p-Phenylenevinylene) Derived Organogels: A Novel Class of Functional Supramolecular Materials

The main objective of the present study is to have a detailed investigation on the gelation properties, morphology and optical properties of small π-conjugated oligomers. For this purpose we have chosen oligo(p-phenylenevinylene)s (OPVs), a class of molecules which have received considerable attention due to their unique optical and electronic properties. Though a large number of reports are available in the literature on the self-assembly properties of tailor made OPVs, none of them pertain to the design of nanostructures based on organogels. In view of this, we aimed at the creation of functional chromophoric assemblies of π-conjugated OPVs through the formation of organogels, with the objective of crafting nanoscopic assemblies of different size and shape thereby modulating their optical and electronic properties.In order to fulfill the above objectives, the design and synthesis of a variety of OPVs with appropriate structural variations were planned. The design principle involves the derivatization of OPVs with weak H-bonding hydroxymethyl end groups and with long aliphatic hydrocarbon side chains. The noncovalent interactions in these molecules were expected to lead the formation of supramolecular assembly and gels in hydrocarbon solvents. In such an event, detailed study of gelation and extensive analysis of the morphology of the gel structures were planned using advanced microscopic techniques. Since OPVs are strongly fluorescent molecules, gelation is expected to perturb the optical properties. Therefore, detailed study on the gelation induced optical properties as a way to probe the nature and stability of the selfassembly was planned. Apart from this, the potential use of the modulation of the optical properties for the purpose of light harvesting was aimed. The approach to this problem was to entrap an appropriate energy trap to the OPV gel matrix which may lead to the efficient energy transfer from the OPV gel based donor to the entrapped acceptor. The final question that we wanted to address in this investigation was the creation of helical nanostructures through proper modification of the OPV backbone With chiral handles.The present thesis is a detailed and systematic approach to the realization of the above objectives which are presented in different chapters of the thesis.

On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Reinforcement Learning approaches to Economic Dispatch problem

This paper presents Reinforcement Learning (RL) approaches to Economic Dispatch problem. In this paper, formulation of Economic Dispatch as a multi stage decision making problem is carried out, then two variants of RL algorithms are presented. A third algorithm which takes into consideration the transmission losses is also explained. Efficiency and flexibility of the proposed algorithms are demonstrated through different representative systems: a three generator system with given generation cost table, IEEE 30 bus system with quadratic cost functions, 10 generator system having piecewise quadratic cost functions and a 20 generator system considering transmission losses. A comparison of the computation times of different algorithms is also carried out.

Reinforcement Learning Solution for Unit Commitment Problem Considering Minimum Start Up and Shut Down Times

Unit Commitment Problem (UCP) in power system refers to the problem of determining the on/ off status of generating units that minimize the operating cost during a given time horizon. Since various system and generation constraints are to be satisfied while finding the optimum schedule, UCP turns to be a constrained optimization problem in power system scheduling. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision making task and an efficient Reinforcement Learning solution is formulated considering minimum up time /down time constraints. The correctness and efficiency of the developed solutions are verified for standard test systems

Reinforcement Learning solution for Unit Commitment Problem through pursuit method

Unit commitment is an optimization task in electric power generation control sector. It involves scheduling the ON/OFF status of the generating units to meet the load demand with minimum generation cost satisfying the different constraints existing in the system. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision task and Reinforcement Learning solution is formulated through one efficient exploration strategy: Pursuit method. The correctness and efficiency of the developed solutions are verified for standard test systems