CONSTRUCTION OF FINITE GROUP

The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) as a homomorphic image of the progenitor 2^(*15) : (15x4), we obtain the group PGL(2; 7) as a homomorphic image of the progenitor 2^7 : D_14, we obtain the group S_6 as a homomorphic image of the progenitor 2^5 : (5 : 4), and we obtain the group S_7 as a homomorphic image of the progenitor 2^(*15) : (15 : 4). Also, have given some unsuccessful progenitors

Conceptualizing and communicating SoTL: A framework for the field

The emerging field of SoTL is an inherently interdisciplinary endeavor which requires embracing a diverse range of research methods and disciplinary differences in world views. This diversity has caused a lack of coherence in its conceptualization and communication, which can be confusing for new scholars. Ongoing debates in the community concern the use of theory and methodology, as well as definitional questions of what constitutes SoTL and the nature of its purpose. This article offers a framework for conceptualizing the field which attempts to broadly delineate the available learning theories underlying and methodologies appropriate to studying teaching and learning, while intending to be hospitable to a broad range of diverse disciplines. Further, the framework illustrates the tacit links between learning theories and methodologies, serving as a guide to potential approaches to SoTL work. The framework is illustrated with example SoTL studies. It is hoped that the framework will help ground future SoTL investigations in appropriate theories and methodologies, and build interdisciplinary communication and understanding in the “trading zone” that is SoTL

The evolution of cauterization: from the hot iron to the Bovie.

The Bovie electrocautery has become a fundamental tool of modern-day surgery, particularly for its integral role in hemostasis, yet despite this landmark invention and its widespread use, there is very little said about the man behind the machine: William T. Bovie. It would be thousands of years from the inception of cautery in medicine until the birth of Dr. Bovie and his device. However, his work in biophysics and collaboration with Dr. Harvey Cushing would revolutionize surgical practice in the early 20th century and forever ingrain his name into the field of surgery

LightPIR: Privacy-Preserving Route Discovery for Payment Channel Networks

Payment channel networks are a promising approach to improve the scalability of cryptocurrencies: they allow to perform transactions in a peer-to-peer fashion, along multi-hop routes in the network, without requiring consensus on the blockchain. However, during the discovery of cost-efficient routes for the transaction, critical information may be revealed about the transacting entities. This paper initiates the study of privacy-preserving route discovery mechanisms for payment channel networks. In particular, we present LightPIR, an approach which allows a source to efficiently discover a shortest path to its destination without revealing any information about the endpoints of the transaction. The two main observations which allow for an efficient solution in LightPIR are that: (1) surprisingly, hub labelling algorithms - which were developed to preprocess "street network like" graphs so one can later efficiently compute shortest paths - also work well for the graphs underlying payment channel networks, and that (2) hub labelling algorithms can be directly combined with private information retrieval. LightPIR relies on a simple hub labeling heuristic on top of existing hub labeling algorithms which leverages the specific topological features of cryptocurrency networks to further minimize storage and bandwidth overheads. In a case study considering the Lightning network, we show that our approach is an order of magnitude more efficient compared to a privacy-preserving baseline based on using private information retrieval on a database that stores all pairs shortest paths

Lightning Creation Games

Payment channel networks (PCNs) are a promising solution to the scalability problem of cryptocurrencies. Any two users connected by a payment channel in the network can theoretically send an unbounded number of instant, costless transactions between them. Users who are not directly connected can also transact with each other in a multi-hop fashion. In this work, we study the incentive structure behind the creation of payment channel networks, particularly from the point of view of a single user that wants to join the network. We define a utility function for a new user in terms of expected revenue, expected fees, and the cost of creating channels, and then provide constant factor approximation algorithms that optimise the utility function given a certain budget. Additionally, we take a step back from a single user to the whole network and examine the parameter spaces under which simple graph topologies form a Nash equilibrium