Approximation schemes for network, clustering and queueing models

In this dissertation, we consider important optimization problems that arise in three different domains, namely network models, clustering problems and queueing models. To be more specific, we focus on devising efficient traffic routing models, deriving exact convex reformulation to the well-known K-means clustering problem and studying the classical Naor’s observable queues under uncertain parameters. In the following chapters, we discuss these problems in detail, design efficient and tractable solution methodologies, and assess the quality of proposed solutions. In the first part of the dissertation, we analyze a limited-adaptability traffic routing model for the Austin road network. Routing a person through a traffic network presents a tension between selecting a fixed route that is easy to navigate and selecting an aggressively adaptive route that minimizes the expected travel time. We develop non-aggressive adaptive routes in the middle-ground seeking the best of both these extremes. Specifically, these routes still adapt to changing traffic condition, however we limit the total number of allowable adjustments. This improves the user experience, by providing a continuum of options between saving travel time and minimizing navigation. We design strategies to model single and multiple route adjustments, and investigate enumerative techniques to solve these models. We also develop tractable algorithms with easily computable lower and upper bounds to handle real-size traffic data. We finally present the numerical results highlighting the benefit of different levels of adaptability in terms of reducing the expected travel time. In the second part of the dissertation, we study the well-known classical K-means clustering problem. We show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite programming (SDP) relaxation that is tighter than the current SDP relaxation schemes in the literature. In contrast to the existing schemes, our proposed SDP formulation gives rise to solutions that can be leveraged to identify the clusters. We devise a new approximation algorithm for K-means clustering that utilizes the improved formulation and empirically illustrate its superiority over the state-of-the-art solution schemes. Finally, we study an extension of Naor’s analysis [74] on the joining or balking problem in observable M/M/1 queues, relaxing the principal assumption of deterministic arrival and service rates. While all the Markovian assumptions still hold, we assume the arrival and service rates are uncertain and study this problem under stochastic and distributionally robust settings. In the former setting, the exact rates are unknown but we assume the distribution of rates are known to all the decision makers. We derive the optimal joining threshold strategies from the perspective of an individual customer, a social optimizer and a revenue maximizer, such that expected profit rate is maximized. In the distributionally robust setting, we go a step further to assume the true distributions are unknown and the decision makers have access to only a finite set of training samples. Similar to the stochastic setting, we derive optimal thresholds such that the worst-case expected profit rates are maximized. Finally, we compare our observations, both theoretically and numerically, with Naor’s classical results.Operations Research and Industrial Engineerin

Probabilistic game approaches for network cost allocation

In a restructured power market, the network cost is to be allocated between multiple players utilizing the system in varying capacities. Cooperative game approaches based on Shapley value and Nucleolus provide stable models for embedded cost allocation of power networks. Varying network usage necessitates the introduction of probabilistic approaches to cooperative games. This paper proposes a variety of probabilistic cooperative game approaches. These have variably been modeled based upon the probability of existence of players, the probability of existence of coalitions, and the probability of players joining a particular coalition along with their joining in a particular sequence. Application of these approaches to power networks reflects the system usage in a more justified way. Consistent and stable results qualify the application of probabilistic cooperative game approaches for cost allocation of power networks.Cooperative games, embedded cost allocation, probabilistic games, transmission pricing

A CRITICAL REVIEW ON NUTRACEUTICALS IN MADHUMEHA (DIABETES)

Diabetes mellitus is a well-known clinical syndrome since antiquity. Ayurveda mainly focuses on the role of diet in Prameha and Madhumeha, which is akin to Diabetes. Nutraceuticals are food or food products that provide health and medical benefits, including the prevention and treatment of disease. Traditional Indian diets are functional and used both as food and medicine. Although in recent scientific studies these diets are evaluated for rich source of dietary fiber (whole grains and vegetables), antioxidants and other active principles suitable for diabetes. Primarily, they have been selected and used based on fundamental principles of Ayurveda, such as their Rasa, Guna, Virya, Vipaka, Prabhava, and so on. Reviewing the characteristic properties along with important antidiabetic properties of conventional system of medicine, accentuates the role of these diets in Diabetes. The correlation further emphasizes the way to include or to evaluate more Nutraceuticals for the benefit of Diabetic population. Diabetes is a complex disease with multiple variations. Nutraceuticals too have variant properties and belong to various dietetic groups, such as Kodrava (grain variety: Paspolum scrobiculatum Linn.), Adhaki (red gram: Cajamus indicus Spreng.), Yava (Barley: Hordeum vulgare Linn.), Mudga (green gram: Phaseolus radiatus Linn.), Kuluttha (horse gram: Dolichos biflorus Linn.), Amalaki (Indian goose berry: Emblica officinalis Gaertn.), Meti (fenugreek: Trigonella foenum-graecum Linn.), Karavellaka (bitter gourd: Momordica charantia Linn.), Jambu (java plum: Syzygium cumini (Linn.) Skeels.), Navapatola (young: Tricosanthes dioica Roxb.), Matsyakshi (Alternanthera sessiles Linn.) R. Br. etc

Graphene oxide based synaptic memristor device for neuromorphic computing

Brain-inspired neuromorphic computing which consist neurons and synapses, with an ability to perform complex information processing has unfolded a new paradigm of computing to overcome the von Neumann bottleneck. Electronic synaptic memristor devices which can compete with the biological synapses are indeed significant for neuromorphic computing. In this work, we demonstrate our efforts to develop and realize the graphene oxide (GO) based memristor device as a synaptic device, which mimic as a biological synapse. Indeed, this device exhibits the essential synaptic learning behavior including analog memory characteristics, potentiation and depression. Furthermore, spike-timing-dependent-plasticity learning rule is mimicked by engineering the pre- and post-synaptic spikes. In addition, non-volatile properties such as endurance, retentivity, multilevel switching of the device are explored. These results suggest that Ag/GO/FTO memristor device would indeed be a potential candidate for future neuromorphic computing applications. Keywords: RRAM, Graphene oxide, neuromorphic computing, synaptic device, potentiation, depressionComment: Nanotechnology (accepted) (IOP publishing

Synthesis of industrially important platform chemicals via olefin metathesis of palash fatty acid methyl esters

The study signifies the importance of olefin metathesis in developing industrially important platform chemicals from a non-edible renewable resource, palash oil using Grubb’s second generation catalyst. The reaction conditions were optimized by varying the concentration of the catalyst, 0.03-0.05 mM and the temperature, 45-100 °C of the reaction. Maximum yield of the metathesized products, as analysed using GC/GC-MS were obtained employing lower concentration of the catalyst, 0.03 Mm and temperature, 45 °C for 36 h. The metathesized products showed the formation of hydrocarbons namely 9-octadecene (10.9%) and cyclodecacyclotetradecene (27%) as major. The formation of cyclodecacyclotetradecene was observed for the first time. The study also describes the possible routes and the molecules involved in the formation of the metathesized products

Hummingbird: An Energy-Efficient GPS Receiver for Small Satellites

Global positioning system (GPS) is the most widely adopted localization technique for satellites in low earth orbits (LEOs). To enable many state-of-the-art applications on satellites, the exact position of the satellites is necessary. With the increasing demand for small satellites, the need for a low-power GPS for satellites is also increasing. However, building low-power GPS receivers for small satellites poses significant challenges, mainly due to the high speeds (similar to 7.8 km/s) of satellites and low available energy. While duty cycling the receiver is a possible solution, the high relative Doppler shift among the GPS satellites and the small satellite contributes to an increase in Time to First Fix (TTFF), which negatively impacts energy consumption. Further, if the satellite tumbles, the GPS receiver may not be able to receive signals properly from the GPS satellites, thus leading to an even longer TTFF. In the worst case, the situation may result in no GPS fix due to disorientation of the receiver antenna. In this work, we elucidate the design of a low-cost, low-power GPS receiver for small satellites. We also propose an energy optimization algorithm to improve the TTFF. With the extensive evaluation of our GPS receiver on an operational nanosatellite, we show that up to 96.16% of energy savings can be achieved using our algorithm without significantly compromising (similar to 10 m) the positioning accuracy

Metathesis of 9-octadecenoic acid methyl ester: diversity and mechanism of product formation at various Grubbs’ catalyst concentrations

Self-metathesis of 9-octadecenoic acid methyl ester was carried out with varying the concentration of Grubbs’ second generation catalyst from 0.03 mmol to 0.18 mmol at 40-45 °C for 36 h. Only two products (9-octadecene 30%, and dimethyl-9-octadecene-dienoate 23%) resulted when 0.06 mmol of catalyst was employed, while at other concentrations four metathesized products were observed. 9-Octadecene generated at 0.03, 0.06 and 0.12 mmol completely disappeared and dimethyl-9-octadecene-dienoate (64%) was observed in major amounts at 0.18 mmol concentration

Geospatial Epidemiology of chicken-pox disease in India between 2015-2021: A GIS based analysis

Introduction: In this paper, we introduce geographical information systems (GIS) as a tool to study trends in disease spread in time and space. Based on data gathered by the integrated disease surveillance programme (IDSP), we can see where outbreaks of Chickenpox have occurred. Objective: The aim of this study is to assess the trends in chickenpox diseases in India between January 2015 and April 2021 using GIS maps. Methods: For the collection of secondary data relating to chickenpox, a free app called collect 5 was used for collecting data weekly from the IDSP website and then storing them in an online server. In this project, variables that needed to be processed with QGIS were combined with table attributes of many shapefiles of India and presented as maps. Results: Between Jan 2015 and May 2021, 1269 chickenpox outbreaks (27,257 cases) have been recorded. Thirty-one deaths have been confirmed, with most occurring in Bihar and Uttar Pradesh. Nineteen states did not report any deaths. According to the seasonally adjusted trend, the number of cases was highest during the months of January and March. Conclusion:  In summary, geographic information systems have become an invaluable tool for mapping the hotspots of acute epidemics and planning public health interventions to prevent the spread of these diseases