Threshold graph limits and random threshold graphs

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.Comment: 47 pages, 8 figure

Threshold

My decisions in the studio are tied to my experiences outside of the studio, intertwining the complex relationship of memory and sentience. Each work precariously balances between softness and rigidity, vessel and sculpture, monumentality and intimacy. These tensions transform the familiar into the enigmatic and are an integral part of my philosophical approach to making. Soft curves and billowing planes are punctuated by the structure of defined edges, hard angles, and areas of dark shadows. This duality suggests two worlds, one of feeling, intuition, sensuality, and dreams, the other of intellect, reason, structure, form, rhythm, and geometry. By contradicting the visual with the tactile, the surface emphasizes the coupling of softness and rigidity. My surfaces are inspired by looking closely at our physical world, by exploring a Piñon tree as if was a whole forest or wandering through the colorful streets of “old town” Turkey, layers of heavily pigmented paint transforming the mundane into the extraordinary. I am drawn to the crusted and the weathered; objects that have had time transform their visual depth and speak about a layering of living. The forms relate to architectural spaces, intimacies of passageways opening to sacred spaces, eroded canyons, and the human body conceptualized as a landscape. I am interested in how light and shadow dictate our movements, how they affect the physical sensation in our body as we maneuver through interior spaces and natural landscapes. My intent is to create beautiful objects that elicit, as the viewer\u27s eye explores the form, a similar corporeal sensation to powerful physical spaces. By creating vessels that use volume and containment, qualities inherent to pottery, I explore content beyond utility. A vessel has a universality that has a certain familiarity to the viewer making my work more approachable and, by borrowing the language of pottery (i.e. lips, feet, etc), the vessel reemphasizes the reference to the body. Solid forms and unseen voids not only reference physical spaces, but allude to the play between our physical and psychological worlds. Interior spaces do not invite the viewer to fill the space with use, but rather, reference the shadows of our psyche. By limiting visual entry to enclosed volumes, my work evokes mystery, intrigue, and most importantly, the imagination. 7 images are attached below as Additional files

Crossed Threshold Resummation

We show that certain general properties of threshold and joint resummations in Drell-Yan cross sections hold as well for their crossed analogs in semi-inclusive deep-inelastic scattering and double-inclusive leptonic annihilation. We show that all plus-distribution corrections near threshold show the same structure, and are determined to all logarithmic order by two anomalous dimensions, one of which is a generalization of the D-term previously derived in Drell-Yan. We also discuss the possibility of universality in power corrections implied by the resummation.Comment: 8 page

Universal threshold enhancement

By assuming certain analytic properties of the propagator, it is shown that universal features of the spectral function including threshold enhancement arise if a pole describing a particle at high temperature approaches in the complex energy plane the threshold position of its two-body decay with the variation of T. The case is considered, when one can disregard any other decay processes. The quality of the proposed description is demonstrated by comparing it with the detailed large N solution of the linear sigma model around the pole-threshold coincidence.Comment: 4 pages, 2 figure

Threshold Factorization Redux

We reanalyze the factorization theorems for Drell-Yan process and for deep inelastic scattering near threshold, as constructed in the framework of the soft-collinear effective theory (SCET), from a new, consistent perspective. In order to formulate the factorization near threshold in SCET, we should include an additional degree of freedom with small energy, collinear to the beam direction. The corresponding collinear-soft mode is included to describe the parton distribution function (PDF) near threshold. The soft function is modified by subtracting the contribution of the collinear-soft modes in order to avoid double counting on the overlap region. As a result, the proper soft function becomes infrared finite, and all the factorized parts are free of rapidity divergence. Furthermore, the separation of the relevant scales in each factorized part becomes manifest. We apply the same idea to the dihadron production in $e^+ e^-$ annihilation near threshold, and show that the resultant soft function is also free of infrared and rapidity divergences.Comment: 20 pages, 2 figures; matches published versio