Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Voronoi Cell Patterns: theoretical model and applications

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris M\'etro stations.Comment: 12 pages, 9 figure

A Halo Model with Environment Dependence: Theoretical Considerations

We present a modification of the standard halo model with the goal of providing an improved description of galaxy clustering. Recent surveys, like the Sloan Digital Sky Survey (SDSS) and the Anglo-Australian Two-degree survey (2dF), have shown that there seems to be a correlation between the clustering of galaxies and their properties such as metallicity and star formation rate, which are believed to be environment-dependent. This environmental dependence is not included in the standard halo model where the host halo mass is the only variable specifying galaxy properties. In our approach, the halo properties i.e., the concentration, and the Halo Occupation Distribution --HOD-- prescription, will not only depend on the halo mass (like in the standard halo model) but also on the halo environment. We examine how different environmental dependence of halo concentration and HOD prescription affect the correlation function. We see that at the level of dark matter, the concentration of haloes affects moderately the dark matter correlation function only at small scales. However the galaxy correlation function is extremely sensitive to the HOD details, even when only the HOD of a small fraction of haloes is modified.Comment: 23 pages, 17 figures. Accepted for publication in MNRA

Process-based Organization Design Model: Theoretical Review and Model Conceptualization

The complexity of today's business world is translated into complexity of the company's organization design (Galbraith, 2002). Organizations are forced to quickly adapt to emerging complexity if they want to survive. The change is addressing all areas of business, especially questioning organizational effectiveness and trying to find optimal solutions for doing business. In accordance with requirements, competitive trends are pushing executives to rethink traditional design configurations. Factors such as increased competition in cost, quality and service, and technical change have forced companies not only to seek out new ways of doing old tasks, but also new ways of organizing either old or new tasks (Cross, 1990). Such focus on the flow of work within organizations, but as well as between them, is emphasizing process orientation as a new management paradigm. Inefficiencies of the two most commonly present structures – functional and divisional, in addition to emerging business trends, place the emphasis on a process-based organization as one of the possible solutions. The process-based organization is lead by the process paradigm, which is focused on the horizontal view of business activities and alignment of organizational systems towards business processes. Regardless of a large interest on business processes, existing organization design theory offers only general guidelines for process-based organizations or more precisely, a process-based organization design model. Consequently, the purpose of the paper is to demystify process-based organization design model. By clearly distinguishing between different levels of process orientation, and by addressing characteristics of the chosen model the paper will lead to better understanding of this way of organizing. Eventually, an operationalized model of process-based organization is developed. Furthermore, the paper elaborates on differences between process-based and other organizational structures and philosophies (e.g. functional, product, matrix, project, team-based). Besides structural elements, which will be in the primary focus, the paper will discuss the alignment of all other important organization design elements for process environment (e.g., management style, reward systems, performance metrics, people practices, organizational culture, etc.). There would be proposed necessary adjustments of organizational elements which should be aligned with the process-based structural solution. In such way, some of the blind spots of process-based organization design model would be revealed, providing practical implications for its implementation and ultimately, offering solution for rising business complexity.organization design, process-based organization, process-based organization design model, business processes

Systematic Theoretical Search for Dibaryons in a Relativistic Model

A relativistic quark potential model is used to do a systematic search for quasi-stable dibaryon states in the $u$, $d$, and $s$ three flavor world. Flavor symmetry breaking and channel coupling effects are included and an adiabatic method and fractional parentage expansion technique are used in the calculations. The relativistic model predicts dibaryon candidates completely consistent with the nonrelativistic model.Comment: 12 pages, latex, no figure