Distribution of periodic points of polynomial diffeomorphisms of C^2

This paper deals with the dynamics of a simple family of holomorphic diffeomorphisms of \C^2: the polynomial automorphisms. This family of maps has been studied by a number of authors. We refer to [BLS] for a general introduction to this class of dynamical systems. An interesting object from the point of view of potential theory is the equilibrium measure $\mu$ of the set $K$ of points with bounded orbits. In [BLS] $\mu$ is also characterized dynamically as the unique measure of maximal entropy. Thus $\mu$ is also an equilibrium measure from the point of view of the thermodynamical formalism. In the present paper we give another dynamical interpretation of $\mu$ as the limit distribution of the periodic points of $f$

Hyperlactation - How left-brained \u27rules\u27 for breastfeeding wreak havoc with a natural process

A variety of arbitrary and often unphysiological rules for breastfeeding are frequently suggested to breastfeeding mothers. Many of these rules duplicate strategies commonly used to increase milk supply, and thus, when undertaken by the many women who already have a generous milk supply, can lead to overproduction. Oversupply, or hyperlactation, is a frequent yet often unrecognized problem that can present with a variety of distressing symptoms for the breastfeeding mother and her infant. Infants may present with symptoms suggesting colic, milk protein allergies, or gastroesophageal reflux, or may present with unusually rapid or slow growth. Mothers may present with tender leaking breasts, sore infected nipples, plugged ducts or mastitis, or even the perception of insufficient milk supply. With an understanding of the pathophysiology of these symptoms, proper diagnosis and breastfeeding management can allow milk production to return to homeostatic levels and provide dramatic symptom relief. March 23, 2012: Author’s note 7 years after publication: Over the 7 years since we wrote this manuscript, we continue to see mothers and babies with these same clinical problems, and we are still learning. Here’s a quick look from 2012 at what we wrote in 2005. Specifics can be found in a link at this site soon. During the last 7 years our treatment strategies have become much more simple and flexible since our earlier strategies encouraged too much of the rigid and rule-based left-brained thinking that often causes or contributes to hyperlactation. In this manuscript, we never once mentioned using hands on the breasts as a strategy for preventing or resolving the problems of hyperlactation, and yet in recent years we’ve found this has revolutionized our management approach. We’ve found that when dealing with hyperlactation, pumping can often be counterproductive. Underweight slow weight gain babies are in a category of their own. Regardless of their symptoms, by definition the underweight baby is NOT drinking too much, and in our experience, typical strategies for addressing hyperlactation can be counterproductive or even dangerous. In particular, staying on one side “to get to the hindmilk” doesn’t work with these sleepy, flow-dependent babies. Side switching may be helpful, but is rarely sufficient, and medical attention is critical. While hyperlactation appears to be increasingly recognized by lactation professionals, left-brained strategies abound, and resolution is often elusive, even by those who correctly identify it. Much more research is needed in all of these areas, as well as in several interesting and related areas discussed in our longer note. Finally, the thoughts and suggestions given here cannot replace appropriate medical attention by a physician or other medical provider. We do not encourage self-treatment, particularly when symptoms are severe. Readers seeking lactation support can locate an International Board Certified Lactation Consultant (IBCLC) in their geographic area at www.ilca.org “Find a Lactation Consultant” http://www.ilca.org/i4a/pages/index.cfm?pageid=343

Testing Gluino Spin with Three-Body Decays

We examine the possibility of distinguishing a supersymmetric gluino from a Kaluza-Klein gluon of universal extra dimensions (UED) at the Large Hadron Collider (LHC). We focus on the case when all kinematically allowed tree-level decays of this particle are 3-body decays into two jets and a massive daughter (typically weak gaugino or Kaluza-Klein weak gauge boson). We show that the shapes of the dijet invariant mass distributions differ significantly in the two models, as long as the mass of the decaying particle mA is substantially larger than the mass of the massive daughter mB. We present a simple analysis estimating the number of events needed to distinguish between the two models under idealized conditions. For example, for mA/mB=10, we find the required number of events to be of order several thousand, which should be available at the LHC within a few years. This conclusion is confirmed by a parton level Monte Carlo study which includes the effects of experimental cuts and the combinatoric background.Comment: 19 pages, 10 figure

Tête-à-tête avec Ian Smillie

Version anglaise disponible dans la Bibliothèque numérique du CRDI: In conversation : Ian Smilli

In conversation : Ian Smillie

French version available in IDRC Digital Library: Tête-à-tête avec Ian Smilli

Probing Supersymmetry With Third-Generation Cascade Decays

The chiral structure of supersymmetric particle couplings involving third generation Standard Model fermions depends on left-right squark and slepton mixings as well as gaugino-higgsino mixings. The shapes and intercorrelations of invariant mass distributions of a first or second generation lepton with bottoms and taus arising from adjacent branches of SUSY cascade decays are shown to be a sensitive probe of this chiral structure. All possible cascade decays that can give rise to such correlations within the MSSM are considered. For bottom-lepton correlations the distinctive structure of the invariant mass distributions distinguishes between decays originating from stop or sbottom squarks through either an intermediate chargino or neutralino. For decay through a chargino the spins of the stop and chargino are established by the form of the distribution. When the bottom charge is signed through soft muon tagging, the structure of the same-sign and opposite-sign invariant mass distributions depends on a set function of left-right and gaugino-higgsino mixings, as well as establishes the spins of all the superpartners in the sequential two-body cascade decay. Tau-lepton and tau-tau invariant mass distributions arising from MSSM cascade decays are likewise systematically considered with particular attention to their dependence on tau polarization. All possible tau-lepton and tau-tau distributions are plotted using a semi-analytic model for hadronic one-prong taus. Algorithms for fitting tau-tau and tau-lepton distributions to data are suggested.Comment: 35 pages, 17 .eps figure

Spin Discrimination in Three-Body Decays

The identification of the correct model for physics beyond the Standard Model requires the determination of the spin of new particles. We investigate to which extent the spin of a new particle $X$ can be identified in scenarios where it decays dominantly in three-body decays $X\to f\bar{f} Y$. Here we assume that $Y$ is a candidate for dark matter and escapes direct detection at a high energy collider such as the LHC. We show that in the case that all intermediate particles are heavy, one can get information on the spins of $X$ and $Y$ at the LHC by exploiting the invariant mass distribution of the two standard model fermions. We develop a model-independent strategy to determine the spins without prior knowledge of the unknown couplings and test it in a series of Monte Carlo studies.Comment: 31+1 pages, 4 figures, 8 tables, JHEP.cls include

Spin Measurements in Cascade Decays at the LHC

We systematically study the possibility of determining the spin of new particles after their discovery at the LHC. We concentrate on angular correlations in cascade decays. Motivated by constraints of electroweak precision tests and the potential of providing a Cold Dark Matter candidate, we focus on scenarios of new physics in which some discrete symmetry guarantees the existence of stable neutral particles which escape the detector. More specifically, we compare supersymmetry with another generic scenario in which new physics particles have the same spin as their Standard Model partners. A survey of possibilities of observing spin correlations in a broad range of decay channels is carried out, with interesting ones identified. Rather than confining ourselves to one "collider friendly" benchmark point (such as SPS1a), we describe the parameter region in which any particular decay channel is effective. We conduct a more detailed study of chargino's spin determination in the decay channel $\tilde{q}\to q + \tilde{C}^\pm \to q + W^\pm + LSP$. A scan over the chargino and neutralino masses is performed. We find that as long as the spectrum is not too degenerate the prospects for spin determination in this channel are rather good.Comment: 36 pages, references added, 1 figure modifie

Missing Momentum Reconstruction and Spin Measurements at Hadron Colliders

We study methods for reconstructing the momenta of invisible particles in cascade decay chains at hadron colliders. We focus on scenarios, such as SUSY and UED, in which new physics particles are pair produced. Their subsequent decays lead to two decay chains ending with neutral stable particles escaping detection. Assuming that the masses of the decaying particles are already measured, we obtain the momenta by imposing the mass-shell constraints. Using this information, we develop techniques of determining spins of particles in theories beyond the standard model. Unlike the methods relying on Lorentz invariant variables, this method can be used to determine the spin of the particle which initiates the decay chain. We present two complementary ways of applying our method by using more inclusive variables relying on kinematic information from one decay chain, as well as constructing correlation variables based on the kinematics of both decay chains in the same event.Comment: Version to appear in JHE