Matrix product states and exactly solvable spin 1/2 Heisenberg chains with nearest neighbor interactions

Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in compact form. The ground state has a very interesting property: all the pairs of spins are equally entangled with each other. Therefore it is possible to engineer long-range entanglement in experimentally realizable spin systems on the one hand and study more closely quantum phase transition in such systems on the other.Comment: 4 pages, RevTex, references added, improved presentation, typos fixe

Exact dimer ground states for a continuous family of quantum spin chains

Using the matrix product formalism, we define a multi-parameter family of spin models on one dimensional chains, with nearest and next-nearest neighbor anti-ferromagnetic interaction for which exact analytical expressions can be found for its doubly degenerate ground states. The family of Hamiltonians which we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a particular point in this parameter space. Like the Majumdar-Ghosh model, the doubly degenerate ground states of our models have a very simple structure, they are the product of entangled states on adjacent sites. In each of these states there is a non-zero staggered magnetization, which vanishes when we take their translation-invariant combination as the new ground states. At the Majumdar-Ghosh point, these entangled states become the spin-singlets pertaining to this model. We will also calculate in closed form the two point correlation functions, both for finite size of the chain and in the thermodynamic limit.Comment: 11 page

Modeling of Whole Genomic Sequencing Implementation using System Dynamics and Game Theory

Biomarker testing is a laboratory test in oncology that is used in the selection of targeted cancer treatments and helping to avoid ineffective treatments. There exist several types of biomarker tests that can be used to detect the presence of particular mutations or variation in gene expression. Whole Genome Sequencing (WGS) is a biomarker test for analyzing the entire genome. WGS can provide more comprehensive diagnostic information, but it is also more expensive than other tests. In this study, System Dynamics and Game Theoretic models are employed to evaluate scenarios, and facilitate organizational decision making regarding WGS implementation. These models evaluate the clinical and economic value of WGS as well as its affordability and accessibility. The evaluated scenarios have covered the timing of implementing WGS using time to diagnosis and total cost.Comment: The IISE Annual Conference & Expo 202

An Agent-based model of stem and cancer cell interaction

Advancements in tissue engineering combined with the disease seeking nature of stem cells have provided new grounds for targeted therapy of cancer. However the discrepancies found in existing literature on the role of un-modified stem cells at tumour sites (Klopp et al. 2011), indicates the need for further research. In vitro approaches provide an insight into actual cell behaviour under given conditions. However these methods are limited by factors such as cost, time and technological advancements in available protocols. In silico tools provide means for quantitative analysis of accumulated data in addition to exploring scenarios and queries otherwise impossible to create in the lab. However these tools can lack in accuracy and realistic correlation with actual biological behaviour. The combination of both in vitro and in silico methods results in a powerful tool that compensates for the limitations of both approaches. An agent-based model (ABM) is a bottom-up approach that uses information regarding cell behaviour at the single cell level to generate emergent cell population results. Through the development of an agent-based model, the resulting effects of known and hypothesised rules regarding individual cell characteristics and cell-to-cell interactions will be simulated. Where possible, the model rules will be informed and the final model predictions validated using results and observations obtained from cell culture experiments run simultaneously, allowing for a one-to-one mapping of in vitro and in silico results. Computational modelling coupled with cell culture experiments will provide an insight into the mechanisms behind stem cell and cancer cell interactions, taking us one step closer to using stem cells as a method of cancer treatment

Robust inference of kinase activity using functional networks

Mass spectrometry enables high-throughput screening of phosphoproteins across a broad range of biological contexts. When complemented by computational algorithms, phospho-proteomic data allows the inference of kinase activity, facilitating the identification of dysregulated kinases in various diseases including cancer, Alzheimer’s disease and Parkinson’s disease. To enhance the reliability of kinase activity inference, we present a network-based framework, RoKAI, that integrates various sources of functional information to capture coordinated changes in signaling. Through computational experiments, we show that phosphorylation of sites in the functional neighborhood of a kinase are significantly predictive of its activity. The incorporation of this knowledge in RoKAI consistently enhances the accuracy of kinase activity inference methods while making them more robust to missing annotations and quantifications. This enables the identification of understudied kinases and will likely lead to the development of novel kinase inhibitors for targeted therapy of many diseases. RoKAI is available as web-based tool at http://rokai.io