Creation and Growth of Components in a Random Hypergraph Process

Denote by an $\ell$-component a connected $b$-uniform hypergraph with $k$ edges and $k(b-1) - \ell$ vertices. We prove that the expected number of creations of $\ell$-component during a random hypergraph process tends to 1 as $\ell$ and $b$ tend to $\infty$ with the total number of vertices $n$ such that $\ell = o(\sqrt[3]{\frac{n}{b}})$. Under the same conditions, we also show that the expected number of vertices that ever belong to an $\ell$-component is approximately $12^{1/3} (b-1)^{1/3} \ell^{1/3} n^{2/3}$. As an immediate consequence, it follows that with high probability the largest $\ell$-component during the process is of size $O((b-1)^{1/3} \ell^{1/3} n^{2/3})$. Our results give insight about the size of giant components inside the phase transition of random hypergraphs.Comment: R\'{e}sum\'{e} \'{e}tend

Mountain maple and balsam fir early response to partial and clear-cut harvesting under aspen stands of northern Quebec

This study is a component of the Sylviculture et am

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Pulsating White Dwarf Stars and Precision Asteroseismology

Galactic history is written in the white dwarf stars. Their surface properties hint at interiors composed of matter under extreme conditions. In the forty years since their discovery, pulsating white dwarf stars have moved from side-show curiosities to center stage as important tools for unraveling the deep mysteries of the Universe. Innovative observational techniques and theoretical modeling tools have breathed life into precision asteroseismology. We are just learning to use this powerful tool, confronting theoretical models with observed frequencies and their time rate-of-change. With this tool, we calibrate white dwarf cosmochronology; we explore equations of state; we measure stellar masses, rotation rates, and nuclear reaction rates; we explore the physics of interior crystallization; we study the structure of the progenitors of Type Ia supernovae, and we test models of dark matter. The white dwarf pulsations are at once the heartbeat of galactic history and a window into unexplored and exotic physics.Comment: 70 pages, 11 figures, to be published in Annual Review of Astronomy and Astrophysics 200

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although the MYC oncogene has been implicated in cancer, a systematic assessment of alterations of MYC, related transcription factors, and co-regulatory proteins, forming the proximal MYC network (PMN), across human cancers is lacking. Using computational approaches, we define genomic and proteomic features associated with MYC and the PMN across the 33 cancers of The Cancer Genome Atlas. Pan-cancer, 28% of all samples had at least one of the MYC paralogs amplified. In contrast, the MYC antagonists MGA and MNT were the most frequently mutated or deleted members, proposing a role as tumor suppressors. MYC alterations were mutually exclusive with PIK3CA, PTEN, APC, or BRAF alterations, suggesting that MYC is a distinct oncogenic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such as immune response and growth factor signaling; chromatin, translation, and DNA replication/repair were conserved pan-cancer. This analysis reveals insights into MYC biology and is a reference for biomarkers and therapeutics for cancers with alterations of MYC or the PMN. We present a computational study determining the frequency and extent of alterations of the MYC network across the 33 human cancers of TCGA. These data, together with MYC, positively correlated pathways as well as mutually exclusive cancer genes, will be a resource for understanding MYC-driven cancers and designing of therapeutics