Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of $N$ sites with free and antiperiodic boundary conditions. The results for the lowest two orders are in perfect agreement with a perturbative conformal field theory scenario proposed by Cardy [Nucl. Phys. B {\bf 270}, 186 (1986)].Comment: 15 page

INTEGRATIVE ANALYSIS OF OMICS DATA IN ADULT GLIOMA AND OTHER TCGA CANCERS TO GUIDE PRECISION MEDICINE

Transcriptomic profiling and gene expression signatures have been widely applied as effective approaches for enhancing the molecular classification, diagnosis, prognosis or prediction of therapeutic response towards personalized therapy for cancer patients. Thanks to modern genome-wide profiling technology, scientists are able to build engines leveraging massive genomic variations and integrating with clinical data to identify “at risk” individuals for the sake of prevention, diagnosis and therapeutic interventions. In my graduate work for my Ph.D. thesis, I have investigated genomic sequencing data mining to comprehensively characterise molecular classifications and aberrant genomic events associated with clinical prognosis and treatment response, through applying high-dimensional omics genomic data to promote the understanding of gene signatures and somatic molecular alterations contributing to cancer progression and clinical outcomes. Following this motivation, my dissertation has been focused on the following three topics in translational genomics. 1) Characterization of transcriptomic plasticity and its association with the tumor microenvironment in glioblastoma (GBM). I have integrated transcriptomic, genomic, protein and clinical data to increase the accuracy of GBM classification, and identify the association between the GBM mesenchymal subtype and reduced tumorpurity, accompanied with increased presence of tumor-associated microglia. Then I have tackled the sole source of microglial as intrinsic tumor bulk but not their corresponding neurosphere cells through both transcriptional and protein level analysis using a panel of sphere-forming glioma cultures and their parent GBM samples.FurthermoreI have demonstrated my hypothesis through longitudinal analysis of paired primary and recurrent GBM samples that the phenotypic alterations of GBM subtypes are not due to intrinsic proneural-to-mesenchymal transition in tumor cells, rather it is intertwined with increased level of microglia upon disease recurrence. Collectively I have elucidated the critical role of tumor microenvironment (Microglia and macrophages from central nervous system) contributing to the intra-tumor heterogeneity and accurate classification of GBM patients based on transcriptomic profiling, which will not only significantly impact on clinical perspective but also pave the way for preclinical cancer research. 2) Identification of prognostic gene signatures that stratify adult diffuse glioma patientsharboring1p/19q co-deletions. I have compared multiple statistical methods and derived a gene signature significantly associated with survival by applying a machine learning algorithm. Then I have identified inflammatory response and acetylation activity that associated with malignant progression of 1p/19q co-deleted glioma. In addition, I showed this signature translates to other types of adult diffuse glioma, suggesting its universality in the pathobiology of other subset gliomas. My efforts on integrative data analysis of this highly curated data set usingoptimizedstatistical models will reflect the pending update to WHO classification system oftumorsin the central nervous system (CNS). 3) Comprehensive characterization of somatic fusion transcripts in Pan-Cancers. I have identified a panel of novel fusion transcripts across all of TCGA cancer types through transcriptomic profiling. Then I have predicted fusion proteins with kinase activity and hub function of pathway network based on the annotation of genetically mobile domains and functional domain architectures. I have evaluated a panel of in -frame gene fusions as potential driver mutations based on network fusion centrality hypothesis. I have also characterised the emerging complexity of genetic architecture in fusion transcripts through integrating genomic structure and somatic variants and delineating the distinct genomic patterns of fusion events across different cancer types. Overall my exploration of the pathogenetic impact and clinical relevance of candidate gene fusions have provided fundamental insights into the management of a subset of cancer patients by predicting the oncogenic signalling and specific drug targets encoded by these fusion genes. Taken together, the translational genomic research I have conducted during my Ph.D. study will shed new light on precision medicine and contribute to the cancer research community. The novel classification concept, gene signature and fusion transcripts I have identified will address several hotly debated issues in translational genomics, such as complex interactions between tumor bulks and their adjacent microenvironments, prognostic markers for clinical diagnostics and personalized therapy, distinct patterns of genomic structure alterations and oncogenic events in different cancer types, therefore facilitating our understanding of genomic alterations and moving us towards the development of precision medicine

Fractional diffusion in Gaussian noisy environment

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic partial equations of the following form: $D_t^\alpha u(t, x)=\textit{B}u+u\cdot W^H$, where $D_t^\alpha$ is the fractional derivative of order $\alpha$ with respect to the time variable $t$, $\textit{B}$ is a second order elliptic operator with respect to the space variable $x\in\mathbb{R}^d$, and $W^H$ a fractional Gaussian noise of Hurst parameter $H=(H_1, \cdots, H_d)$. We obtain conditions satisfied by $\alpha$ and $H$ so that the square integrable solution $u$ exists uniquely