Effective Condition Number Bounds for Convex Regularization

We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the $\ell_1$-analysis setting. Using results from conic integral geometry, we show that the bounds can be made to depend only on a random projection, or restriction, of the analysis operator to a lower dimensional space, and can still be effective if these operators are ill-conditioned. As an application, we get new bounds for the undersampling phase transition of composite convex regularizers. Key tools in the analysis are Slepian's inequality and the kinematic formula from integral geometry.Comment: 17 pages, 4 figures . arXiv admin note: text overlap with arXiv:1408.301

Effective condition number bounds for convex regularization

We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the ℓ 1 -analysis setting. Using results from conic integral geometry, we show that the bounds can be made to depend only on a random projection, or restriction, of the analysis operator to a lower dimensional space, and can still be effective if these operators are ill-conditioned. As an application, we get new bounds for the undersampling phase transition of composite convex regularizers. Key tools in the analysis are Slepian's inequality and the kinematic formula from integral geometry

Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in Rd\mathbb{R}^d

We introduce a class of UV-regularized two-body interactions for fermions in $\mathbb{R}^d$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step toward this result, we also prove a propagation bound of Lieb-Robinson type for Schr\"odinger operators. We apply the propagation bound to prove the existence of infinite-volume dynamics as a strongly continuous group of automorphisms on the CAR algebra.Comment: Corrected equation (1.5) in the introductio

Geophysical and geological analysis of fault activity and seismic history of the Obion River Area, New Madrid Seismic Zone (NMSZ), Western Tennessee, USA

Thesis advisor: John EbelThe New Madrid Seismic Zone (NMSZ) is well known for producing some of the largest intra-cratonic earthquakes within the North American Plate. The common hypothesis for the geological structure within the NMSZ is that stress is released across three major faults: the Cottonwood Grove Fault, the New Madrid North Fault, and the Reelfoot Thrust Fault. Evidence exists that would suggest an alternative model of geologic deformation in the area: that stress is being released across more than these three faults. A geologic and geophysical investigation was done to investigate a hypothetical fault west of Dyersburg, TN to test the alternative multi-fault hypothesis. A seismically created sand blow was logged in close proximity to the fault projection. Weathering of the sand blow indicated that the age of the sand blow came from a seismic event prior to the 1811-1812 earthquakes. There was no evidence to confirm this sand blow was created by a hypothetical fault in close proximity. A seismic exploration of the area was done across four seismic lines, primarily mapping Quaternary-age Mississippi River flood plain deposits. These seismic surveys yielded no evidence to suggest the presence of an additional fault. Across all surveys no evidence was found to conclusively support any existing theory on fault movement in the NMSZ.Thesis (MS) — Boston College, 2014.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Earth and Environmental Sciences

Large pTp_T Hadroproduction of ZZ as a Probe of Gluon Distribution inside Proton

The transverse momentum distribution of single vector boson production at hadron colliders provides useful ways of testing the Standard Model and searching new physics beyond the Standard Model. We study large $p_{_T}$ hadroproduction of $Z$-boson as a probe of gluon distributions inside proton. We investigate how to get initial gluon-involving contributions, or how to subtract quark-quark (or -antiquark) contributions from total cross section. We also investigated the simultaneous measurement of the rapidity and the transverse momentum of the produced $Z$ boson, to obtain momentum fractions of initial partons. And we extracted relevant uncertainties involving in experimental and theoretical analyses. This large $p_{_T}$ hadroproduction of $Z$ can be used as constraints on analyses of global parton (gluon and quarks) distribution functions inside proton.Comment: (a) 13 pages(LaTeX) + 1 figure ps file(3 pages):compressed, uuencoded (b) accepted by Phys.Lett.B. (c) some figures are combined and one is omitted. (d) conclusion part is included into abstrac

Singing with Moses and the Lamb: Social Memory and Radical Discipleship in John’s Apocalypse

The Apocalypse reads as a kind of “discipleship manual” for the ekklesiai living in Asia Minor under Roman administration. It calls for followers of the Lamb to reject easy compliance with the world of empire, and to embrace instead a costly alternative of witness and resistance. This study applies learnings from social memory theory to illuminate the political struggle in the Apocalypse: it considers how memory functions in antiquity to build a shared narrative of “Romanness;” how the Apocalypse’s strategy of drawing on Hebrew scriptures articulates a “counter-discourse” to Roman hegemony; how worship recalls this distinctive memory and re-narrates the world through it; and finally, how memory functions in the important imperative to “remember and repent” (2:5, 3:3). The study concludes that John is quite aware of the dynamics of power at work in his social world and memory is one basis on which he confronts this power. Through memory, the Apocalypse nurtures an alternative way of seeing the world, forges an alternative identity to “being Roman,” and animates an alternative life-practice. Deep memory is crucial for the ekklesiai to embody the way of the Lamb as a sustained alternative to ordinary civic life in the empire