On the generation of arbitrage-free stock price models using Lie symmetry analysis

AbstractIn Bell and Stelljes (2009) a scheme for constructing explicitly solvable arbitrage-free models for stock prices is proposed. Under this scheme solutions of a second-order (1+1)-partial differential equation, containing a rational parameter p drawn from the interval [1/2,1], are used to generate arbitrage-free models of the stock price. In this paper Lie symmetry analysis is employed to propose candidate models for arbitrage-free stock prices. For all values of p, many solutions of the determining partial differential equation are constructed algorithmically using routines of Lie symmetry analysis. As such the present study significantly extends the work by Bell and Stelljes who found only two arbitrage-free models based on two simple solutions of the determining equation, corresponding to p=1/2 and p=1

Leveraging big data resources and data integration in biology: applying computational systems analyses and machine learning to gain insights into the biology of cancers

Recently, many "molecular profiling" projects have yielded vast amounts of genetic, epigenetic, transcription, protein expression, metabolic and drug response data for cancerous tumours, healthy tissues, and cell lines. We aim to facilitate a multi-scale understanding of these high-dimensional biological data and the complexity of the relationships between the different data types taken from human tumours. Further, we intend to identify molecular disease subtypes of various cancers, uncover the subtype-specific drug targets and identify sets of therapeutic molecules that could potentially be used to inhibit these targets. We collected data from over 20 publicly available resources. We then leverage integrative computational systems analyses, network analyses and machine learning, to gain insights into the pathophysiology of pancreatic cancer and 32 other human cancer types. Here, we uncover aberrations in multiple cell signalling and metabolic pathways that implicate regulatory kinases and the Warburg effect as the likely drivers of the distinct molecular signatures of three established pancreatic cancer subtypes. Then, we apply an integrative clustering method to four different types of molecular data to reveal that pancreatic tumours can be segregated into two distinct subtypes. We define sets of proteins, mRNAs, miRNAs and DNA methylation patterns that could serve as biomarkers to accurately differentiate between the two pancreatic cancer subtypes. Then we confirm the biological relevance of the identified biomarkers by showing that these can be used together with pattern-recognition algorithms to infer the drug sensitivity of pancreatic cancer cell lines accurately. Further, we evaluate the alterations of metabolic pathway genes across 32 human cancers. We find that while alterations of metabolic genes are pervasive across all human cancers, the extent of these gene alterations varies between them. Based on these gene alterations, we define two distinct cancer supertypes that tend to be associated with different clinical outcomes and show that these supertypes are likely to respond differently to anticancer drugs. Overall, we show that the time has already arrived where we can leverage available data resources to potentially elicit more precise and personalised cancer therapies that would yield better clinical outcomes at a much lower cost than is currently being achieved

Some Remarks on the Solution of Linearisable Second-Order Ordinary Differential Equations via Point Transformations

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on such transformations is the class of linearisable second-order ordinary differential equations (ODEs). There are various characterisations of such ODEs. We exploit a particular characterisation and the expanded Lie group method to construct a generic solution for all linearisable second-order ODEs. The general solution of any given equation from this class is then easily obtainable from the generic solution through a point transformation constructed using only two suitably chosen symmetries of the equation. We illustrate the approach with three examples

Protection of traditional knowledge, an incomplete victory, towards inclusion of gender considerations in traditional knowledge protection: a Zambian perspective

This thesis explores the important issue of protection of traditional knowledge from a gendered perspective. More specifically, it seeks to explore the traditional knowledge protection landscape in Zambia in the context of gender sensitivity and gender responsiveness. It further delves into the role of gender considerations in traditional knowledge protection in the achievement of Zambia's national and international development goals. The work relies on desktop research. It draws on primary and secondary sources of information to inform the analysis, provide the necessary background to ground and situate the research. This thesis argues that a gendered approach to TK protection is justified and important. Based on analysis of the prevailing traditional knowledge protection regime in Zambia, the thesis finds and contends that the current protection available is neither gender sensitive nor gender responsive. Further, the current traditional knowledge protection provided in Zambian legislation falls short in various aspects. The role of gender sensitive and gender responsive traditional knowledge protection in the achievement of Zambia's national and international development objectives as expressed in the Zambian Vision 2030 and Sustainable Development Goals is also explored in the work. This thesis suggests that Zambia's traditional knowledge protection regime must be changed to include gender considerations. It presents recommendations for change for Zambia from a legislative perspective partially based on emulating the traditional knowledge protection strategy adopted in Kenya. Gender considerations in traditional knowledge protection legislation in Zambia must be included to ensure that protection is real and effective for women. Through this work it is hoped that attention is drawn to the urgent need for decisive changes in the traditional knowledge protection regime in Zambia in the context of gender sensitivity and gender responsiveness

Chinese FDI and Employment Creation in Zambia

Zambia and China have nurtured their relationship that date back more than four decades ago. This paper looks at the effects of the Chinese foreign direct investment (FDI) on the Zambian labour market. China being the major player in Zambia’s economy is expected to create jobs for the locals who in turn will improve the economy of the country. It is evident that China has increased its FDI inflow to Zambia in the last decade of which mining and construction sectors have received the lions share. The numbers of jobs created by Chinese FDI have also been increasing steadily in the past 10 years especially in the construction and mining industries. However, the paper does not investigate on the quality of both FDI and jobs. Keywords: Foreign direct investment (FDI), job creation, developing country, Zambi

Foot and mouth disease in Zambia: Spatial and temporal distributions of outbreaks, assessment of clusters and implications for control

Zambia has been experiencing low livestock productivity as well as trade restrictions owing to the occurrence of foot and mouth disease (FMD), but little is known about the epidemiology of the disease in these endemic settings. The fundamental questions relate to the spatio-temporal distribution of FMD cases and what determines their occurrence. A retrospective review of FMD cases in Zambia from 1981 to 2012 was conducted using geographical information systems and the SaTScan software package. Information was collected from peer-reviewed journal articles, conference proceedings, laboratory reports, unpublished scientific reports and grey literature. A space–time permutation probability model using a varying time window of one year was used to scan for areas with high infection rates. The spatial scan statistic detected a significant purely spatial cluster around the Mbala–Isoka area between 2009 and 2012, with secondary clusters in Sesheke–Kazungula in 2007 and 2008, the Kafue flats in 2004 and 2005 and Livingstone in 2012. This study provides evidence of the existence of statistically significant FMD clusters and an increase in occurrence in Zambia between 2004 and 2012. The identified clusters agree with areas known to be at high risk of FMD. The FMD virus transmission dynamics and the heterogeneous variability in risk within these locations may need further investigation