A converse to the Grace--Walsh--Szeg\H{o} theorem

We prove that the symmetrizer of a permutation group preserves stability of a polynomial if and only if the group is orbit homogeneous. A consequence is that the hypothesis of permutation invariance in the Grace-Walsh-Szeg\H{o} Coincidence Theorem cannot be relaxed. In the process we obtain a new characterization of the \emph{Grace-like polynomials} introduced by D. Ruelle, and prove that the class of such polynomials can be endowed with a natural multiplication.Comment: 7 page

Role-similarity based functional prediction in networked systems: Application to the yeast proteome

We propose a general method to predict functions of vertices where: 1. The wiring of the network is somehow related to the vertex functionality. 2. A fraction of the vertices are functionally classified. The method is influenced by role-similarity measures of social network analysis. The two versions of our prediction scheme is tested on model networks were the functions of the vertices are designed to match their network surroundings. We also apply these methods to the proteome of the yeast Saccharomyces cerevisiae and find the results compatible with more specialized methods

Discrete concavity and the half-plane property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M-concave functions in the literature. In the language of tropical geometry we study the tropicalization of the space of polynomials with the half-plane property, and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's hive theorem which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected

Core-periphery organization of complex networks

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. For example do geographical networks have a strong core-periphery structure, while the core-periphery structure of social networks (despite their positive degree-degree correlations) is rather weak. We proceed to study radial statistics of the core, i.e. properties of the n-neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n-neighborhoods at a certain distance from the core suggesting an effective radius for non-trivial network processes

Nonequilibrium phase transition in the coevolution of networks and opinions

Models of the convergence of opinion in social systems have been the subject of a considerable amount of recent attention in the physics literature. These models divide into two classes, those in which individuals form their beliefs based on the opinions of their neighbors in a social network of personal acquaintances, and those in which, conversely, network connections form between individuals of similar beliefs. While both of these processes can give rise to realistic levels of agreement between acquaintances, practical experience suggests that opinion formation in the real world is not a result of one process or the other, but a combination of the two. Here we present a simple model of this combination, with a single parameter controlling the balance of the two processes. We find that the model undergoes a continuous phase transition as this parameter is varied, from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. We characterize the static and dynamical properties of this transition

ANALISIS TOKOH DAN PENOKOHAN DALAM NOVEL CINTA KITA YANG RASA (Karya Ariani Octavia)

The purpose of this research is to describe: Analysis of the role of characters and characterizations in Ariana Octavia's Novel Cinta Kita Yang Rasa. This research is a descriptive qualitative research. The method used is descriptive method. The source of the data is Ariana Octavia's Novel, Analysis of Characters and Characteristics. 1st print and from the internet. Data collection techniques used reading and note-taking techniques. The data analysis technique used is the Seiddel via Maleong qualitative analysis which includes three components, namely data reduction, data presentation, and conclusion drawing. The research procedure consisted of several stages, namely data collection, data selection, analyzing the selected data, and making research reports. Based on the results of the research it can be concluded: in the novel Analysis of Characters and Characteristics in the Novel Cinta Kita Yang Rasa by Ariana Octavia wants to convey characters and characterizations that are very useful for readers by animating the contents of the stories in them, so that they can become more alive and add variety and avoid Monotonous things that can bore readers in the novel Analysis of Character and Characteristics in the Novel Cinta Kita Yang Rasa by Ariana Octavia

Symmetry-allowed phase transitions realized by the two-dimensional fully frustrated XY class

A 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new groundstate in addition to the checkerboard groundstates of the standard 2D FFXY model. The spin configuration of this additional groundstate is obtained. Associated with this groundstate there are additional phase transitions. An order parameter accounting for these new transitions is proposed. The transitions associated with the new order parameter are suggested to be similar to a 2D liquid-gas transition which implies Z_2-Ising like transitions. This suggests that the class of 2D FFXY models belongs within a U(1) x Z_2 x Z_2-designation of possible transitions, which implies that there are seven different possible single and combined transitions. MC-simulations for the generalized fully frustrated XY (GFFXY) model on a square lattice are used to investigate which of these possibilities can be realized in practice: five of the seven are encountered. Four critical points are deduced from the MC-simulations, three consistent with central charge c=3/2 and one with c=1. The implications for the standard 2D FFXY-model are discussed in particular with respect to the long standing controversy concerning the characteristics of its phase transitions.Comment: 8 pages, 8 figure