Project X and a muon facility at Fermilab

An integrated program is described, starting with muon experiments in the Booster era, continuing with a 2 MW target station, a 4 GeV Neutrino Factory and a 3 TeV Muon Collider, all driven by Project X. This idea provides an integrated approach to the Intensity and Energy Frontiers at Fermilab.Comment: 3 pp. 11th International Workshop on Neutrino Factories, Superbeams and Betabeams: NuFact 09. 20-25 Jul 2009. Chicago, Illinoi

Asymptotic genealogy of a critical branching process

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.Comment: 30 page

Thanks to 2D and maybe even beyond: 115 GeV and 140 GeV almost Standard Model Higgs without problems

I address: (1) dynamical, likely local Higgs mass generation as resolution to the 4D hierarchy and vacuum energy problems, (2) possibility that top condensation may be explained by an interplay among the gluon and scalar sectors, (3) the Higgs Mass Zero Crossing (HMZC) scale, most likely equal to {\Lambda}_EWSB, in accord with standard cosmology or classic inflation, and (4) two preferred Higgs regions centered at 116.5 GeV and 140.5 GeV with related high energy models. I show that SM in 2D could simultaneously satisfy (a) complete radiative generation of the Higgs mass via top loop and (b) cancelation of the remaining leading order corrections to the scalar propagator. The Higgs mass, m_H, parameterized with k=1 (2), in the leading order is 113.0{\pm}1.0 GeV (143.4{\pm}1.3 GeV). I show that the SM top condensation is consistent with the gluon and Higgs mediated top-anti top interactions at tree level. I predict the QCD fine structure constant with the mean value only 0.25% away from the world average value at {\sqrt}s=M_Z. The SM driven theory at energies larger than the HMZC scale necessary includes effective tachyonic Higgs (Popovic 2001). Here, I map the SM physical Higgs mass to the low energy HMZC scale (0.8-1.8 TeV). I show that the very "long lived" SM necessitates Higgs lighter than 146.5{\pm}2 GeV such that there is a single HMZC scale at energies smaller than the Planck mass. I present candidate m_H=138.1{\pm}1.8 GeV for the SM valid up to an energy scale, nearly equal Planck mass, obtained from a conjecture which minimizes the parameters of the Higgs potential. I introduce a class of models potentially exactly removing tachyons. I analyze Composite Particles Models (CPM) (Popovic 2002) where top quark is composite, composed of 3 fundamental fermions, and Higgs scalar is composite, composed of 2 fundamental fermions, with m_H=2/3 m_t=115.4{\pm}0.9 GeV.Comment: 52 Pages, 11 Figures, 1 Table, 155 References, document created on July 24, 2010, document submitted to the Physical Review D on July 25, 201

Scaling limits of spatial compartment models for chemical reaction networks

We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has different effects depending on whether the movement of each type of species is faster or slower than the effective reaction dynamics on this molecular type. We obtain results for both when the system is without and with conserved quantities, which are linear combinations of species evolving only on the slower time scale.Comment: Published at http://dx.doi.org/10.1214/14-AAP1070 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The coalescent point process of branching trees

We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process $(A_i; i\ge 1)$, where $A_i$ is the coalescence time between individuals i and i+1. There is a Markov process of point measures $(B_i; i\ge 1)$ keeping track of more ancestral relationships, such that $A_i$ is also the first point mass of $B_i$. This process of point measures is also closely related to an inhomogeneous spine decomposition of the lineage of the first surviving particle in generation h in a planar BGW tree conditioned to survive h generations. The decomposition involves a point measure $\rho$ storing the number of subtrees on the right-hand side of the spine. Under appropriate conditions, we prove convergence of this point measure to a point measure on $\mathbb{R}_+$ associated with the limiting continuous-state branching (CSB) process. We prove the associated invariance principle for the coalescent point process, after we discretize the limiting CSB population by considering only points with coalescence times greater than $\varepsilon$.Comment: Published in at http://dx.doi.org/10.1214/11-AAP820 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Capital Augmenting and Labor Augmenting Approach in Measuring Contribution of Human Capital and Education to Economic Growth

In this paper an effort has been made to unveil some hidden and implicit assumptions that has been used in different models dealing with analysis and measurement of contribution of human capital to economic growth. In order to do it we started from the general production function with heterogeneous labor input and general production function with heterogeneous human and physical capital. By introducing different assumptions regarding the partial elasticity of substitution between different factors of production we derived different models for human capital contribution. Apart from making hidden assumptions of existing models explicit we also derived several others models that can be used for the same purposes.Economic Growth, Growth Accounting, Human Capital, Capital of Education, Partial Elasticity of Sustitution