Constructing graphs with no immersion of large complete graphs

In 1989, Lescure and Meyniel proved, for $d=5, 6$, that every $d$-chromatic graph contains an immersion of $K_d$, and in 2003 Abu-Khzam and Langston conjectured that this holds for all $d$. In 2010, DeVos, Kawarabayashi, Mohar, and Okamura proved this conjecture for $d = 7$. In each proof, the $d$-chromatic assumption was not fully utilized, as the proofs only use the fact that a $d$-critical graph has minimum degree at least $d - 1$. DeVos, Dvo\v{r}\'ak, Fox, McDonald, Mohar, and Scheide show the stronger conjecture that a graph with minimum degree $d-1$ has an immersion of $K_d$ fails for $d=10$ and $d\geq 12$ with a finite number of examples for each value of $d$, and small chromatic number relative to $d$, but it is shown that a minimum degree of $200d$ does guarantee an immersion of $K_d$. In this paper we show that the stronger conjecture is false for $d=8,9,11$ and give infinite families of examples with minimum degree $d-1$ and chromatic number $d-3$ or $d-2$ that do not contain an immersion of $K_d$. Our examples can be up to $(d-2)$-edge-connected. We show, using Haj\'os' Construction, that there is an infinite class of non-$(d-1)$-colorable graphs that contain an immersion of $K_d$. We conclude with some open questions, and the conjecture that a graph $G$ with minimum degree $d - 1$ and more than $\frac{|V(G)|}{1+m(d+1)}$ vertices of degree at least $md$ has an immersion of $K_d$

LEAD Program Evaluation: Recidivism Report

The LEAD program was established in 2011 as a means of diverting those suspected of low-level drug and prostitution criminal activity to case management and other supportive services instead of jail and prosecution. The primary aim of the LEAD program is to reduce criminal recidivism. Secondary aims include reductions in criminal justice service utilization and associated costs as well as improvements for psychosocial, housing and quality-of-life outcomes. Because LEAD is the first known pre-booking diversion program of its kind in the United States, an evaluation is critically needed to inform key stakeholders, policy makers, and other interested parties of its impact. The evaluation of the LEAD program described in this report represents a response to this need.Background: This report was written by the University of Washington LEAD Evaluation Team at the request of the LEAD Policy Coordinating Group and fulfills the first of three LEAD evaluation aims. Purpose: This report describes findings from a quantitative analysis comparing outcomes for LEAD participants versus "system-as-usual" control participants on shorter- and longer-term changes on recidivism outcomes, including arrests (i.e., being taken into custody by legal authority) and criminal charges (i.e., filing of a criminal case in court). Arrests and criminal charges were chosen as the recidivism outcomes because they likely reflect individual behavior more than convictions, which are more heavily impacted by criminal justice system variables external to the individual. Findings: Analyses indicated statistically significant recidivism improvement for the LEAD group compared to the control group on some shorter- and longer-term outcomes

Editorial: water governance in a climate change world: appraising systemic and adaptive effectiveness

and other research outputs Editorial: water governance in a climate change world: appraising systemic and adaptive effectivenes

Spin Dependence of Massive Lepton Pair Production in Proton-Proton Collisions

We calculate the transverse momentum distribution for the production of massive lepton-pairs in longitudinally polarized proton-proton reactions at collider energies within the context of perturbative quantum chromodynamics. For values of the transverse momentum Q_T greater than roughly half the pair mass Q, Q_T > Q/2, we show that the differential cross section is dominated by subprocesses initiated by incident gluons, provided that the polarized gluon density is not too small. Massive lepton-pair differential cross sections should be a good source of independent constraints on the polarized gluon density, free from the experimental and theoretical complications of photon isolation that beset studies of prompt photon production. We provide predictions for the spin-averaged and spin-dependent differential cross sections as a function of Q_T at energies relevant for the Relativistic Heavy Ion Collider (RHIC) at Brookhaven, and we compare these with predictions for real prompt photon production.Comment: 34 pages, RevTeX including 17 figures in .ps file

Massive Lepton Pairs as a Prompt Photon Surrogate

We discuss the transverse momentum distribution for the production of massive lepton-pairs in hadron reactions at fixed target and collider energies within the context of next-to-leading order perturbative quantum chromodynamics. For values of the transverse momentum $Q_T$ greater than the pair mass $Q$, $Q_T > Q$, we show that the differential cross section is dominated by subprocesses initiated by incident gluons. Massive lepton-pair differential cross sections are an advantageous source of constraints on the gluon density, free from the experimental and theoretical complications of photon isolation that beset studies of prompt photon production. We compare calculations with data and provide predictions for the differential cross section as a function of $Q_T$ in proton-antiproton reactions at center-of-mass energies of 1.8 TeV, and in proton-nucleon reactions at fixed target and LHC energies.Comment: 36 pages, RevTeX, including 16 ps files of figures; minor changes in wording; one reference added. Version to appear in Phys Rev

A stochastic model for early placental development

In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely under-stood and are difficult to study in vivo. In this paper we model the early development of the placenta in the human, based on the hypothesis that this is driven by dynamics dominated by a chemo-attractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model for these events, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that placental shape is highly variable and disruption of spiral arteries can exert profound effects on placental shape, particularly if this disruption is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, which predisposes to pregnancy complications

Novel Quark Fragmentation Functions and the Nucleon's Transversity Distribution

We define twist-two and twist-three quark fragmentation functions in Quantum Chromodynamics (QCD) and study their physical implications. Using this formalism we show how the nucleon's transversity distribution can be measured in single pion inclusive electroproduction.Comment: 10 pages, uses PHYZZX macro package, 2 PostScript figures (added using FIGURES). MIT-CTP-215

Next-to-leading-order corrections to exclusive processes in kTk_T factorization

We calculate next-to-leading-order (NLO) corrections to exclusive processes in $k_T$ factorization theorem, taking $\pi\gamma^*\to\gamma$ as an example. Partons off-shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms $\ln^2k_T$ and $\ln^2 x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation, and the latter absorbed into a jet function and organized by the threshold resummation. The NLO corrections are found to be only few-percent for $\pi\gamma^*\to\gamma$, if setting the factorization scale to the momentum transfer from the virtual photon.Comment: 13 pages; version to appear in Physical Review

Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering

Motivated by the need to correct the potentially large kinematic errors in approximations used in the standard formulation of perturbative QCD, we reformulate deeply inelastic lepton-proton scattering in terms of gauge invariant, universal parton correlation functions which depend on all components of parton four-momentum. Currently, different hard QCD processes are described by very different perturbative formalisms, each relying on its own set of kinematical approximations. In this paper we show how to set up formalism that avoids approximations on final-state momenta, and thus has a very general domain of applicability. The use of exact kinematics introduces a number of significant conceptual shifts already at leading order, and tightly constrains the formalism. We show how to define parton correlation functions that generalize the concepts of parton density, fragmentation function, and soft factor. After setting up a general subtraction formalism, we obtain a factorization theorem. To avoid complications with Ward identities the full derivation is restricted to abelian gauge theories; even so the resulting structure is highly suggestive of a similar treatment for non-abelian gauge theories.Comment: 44 pages, 69 figures typos fixed, clarifications and second appendix adde