Context:Brain metastases are the most common type of intracranial neoplasm, with the total number outnumbering primary brain tumors by a ratio of 10:1 and occur in about 25% of cancer patients. However, controversies exist regarding demographic and clinical profile of brain metastases.Aims:The purpose of this study was to analyze retrospectively the demographic and clinical profile of patients with brain metastases.Settings and Design:Retrospective, single institutional study.Materials and Methods:A retrospective study of 72 patients with brain metastasis was carried out from November 2010 to October 2012. The data pertaining to these patients was entered in a standardized case record form. These include History; clinical examination and other investigations including computed tomography/magnetic resonance imaging scan of the brain.Statistical Analysis:A statistical analysis was performed on the data collected using the MedCalc version 11.Results:Brain metastases were more common in male and occur in 6th decade of life mostly. There was no relationship of occupation or socio-economic status with the incidence of brain metastases. Carcinoma lung was the most common primary giving rise to brain metastases followed by breast. Adenocarcinoma accounts for most common histology of the primary that give rise to metastases. Multiple metastases were more common than the single group. Supratentorial lesions were more common than infratentorial lesions. Among them, parietal lobe was the most common site of involvement.Conclusions:The present study highlights that the incidence of brain metastasis is common in elderly population and mostly due to primary lung. Adenocarcinoma was the most common histology of primary. Majority of lesions has been observed at parietal lobe.

We introduce a novel approach for solving the problem of identifying regions in the framework of Method of Regions by considering singularities and the associated Landau equations given a multiscale Feynman diagram. These equations are then analyzed by an expansion in a small threshold parameter via the Power Geometry technique. This effectively leads to the analysis of Newton Polytopes which are evaluated using a Mathematica based convex hull program. Furthermore, the elements of the Gröbner Basis of the Landau Equations give a family of transformations, which when applied, reveal regions like potential and Glauber. Several one-loop and two-loop examples are studied and benchmarked using our algorithm which we call ASPIRE.In this section, we set up the formalism for identifying the different regions using the singular structure of the Feynman integral. This process can be automated using ideas from power geometry. However, for the sake of completeness, we also summarize the technique of Pak and Smirnov in a subsequent sub-section. Method of RegionsThe technique of the MoR was proposed in an attempt to analytically approximate various processes within perturbation theory [7,22,23,24]. The idea of the MoR is to provide an expansion of the integrand in ratio of the scales involved, usually in the form of low-energy scale to high-energy scale. This results in expressing the original Feynman integral as a sum over simpler integrals, all of which need to be integrated over their corresponding domains, which are called regions.

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Waddington’s epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

The ASPIRE program, which is based on the Landau singularities and the method of Power geometry to unveil the regions required for the evaluation of a given Feynman diagram asymptotically in a given limit, also allows for the evaluation of scaling coming from the top facets. In this work, we relate the scaling having equal components of the top facets of the Newton polytope to the maximal cut of given Feynman integrals. We have therefore connected two independent approaches to the analysis of Feynman diagrams.