Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Design of Matched Zero-Index Metamaterials Using Non-Magnetic Inclusions in Epsilon-Near-Zero (ENZ) Media

In this work, we study the electrodynamics of metamaterials that consist of resonant non-magnetic inclusions embedded in an epsilon-near-zero (ENZ) host medium. It is shown that the inclusions can be designed in such a way that both the effective permittivity and permeability of the composite structure are simultaneously zero. Two different metamaterial configurations are studied and analyzed in detail. For a particular class of problems, it is analytically proven that such matched zero-index metamaterials may help improving the transmission through a waveguide bend, and that the scattering parameters may be completely independent of the specific arrangement of the inclusions and of the granularity of the crystal. The proposed concepts are numerically demonstrated at microwaves with a metamaterial realization based on an artificial plasma.Comment: 38 pages, 10 Figures, under revie

Is Climate Change Predictable? Really?

This project is the first application of a completely different approach to climate modeling, in which new prognostic equations are used to directly compute the evolution of two-point correlations. This project addresses three questions that are critical for the credibility of the science base for climate prediction: (1) What is the variability spectrum at equilibrium? (2) What is the rate of relaxation when subjected to external perturbations? (3) Can variations due to natural processes be distinguished from those due to transient external forces? The technical approach starts with the evolution equation for the probability distribution function and arrives at a prognostic equation for ensemble-mean two-point correlations, bypassing the detailed weather calculation. This work will expand our basic understanding of the theoretical limits of climate prediction and stimulate new experiments to perform with conventional climate models. It will furnish statistical estimates that are inaccessible with conventional climate simulations and likely will raise important new questions about the very nature of climate change and about how (and whether) climate change can be predicted. Solid progress on such issues is vital to the credibility of the science base for climate change research and will provide policymakers evaluating tradeoffs among energy technology options and their attendant environmental and economic consequences

Quantum walks on quotient graphs

A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup used to construct it. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A {\bf 74}, 042334 (2006)] that the hitting time can be infinite. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with fast hitting times correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speed-up.Comment: 18 pages, 7 figures in EPS forma

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.Comment: 18 page

Nonvascularized human skin chronic allograft rejection.

A 65-year-old man had extensive burns of the lower legs in 1991, at the age of 40 years. He was treated by nonvascularized and de-epithelialized, allogeneic split-thickness skin allograft and cyclosporine monotherapy for 2 months. Ulcers developed between 10 and 25 years after transplantation and a surgical debridement on the lower extremities was required. Analyses of the removed tissue allografts showed chronic antibody-mediated and cellular rejection with extensive and dense fibrosis, and diffuse capillary C4d deposits. An anti-DRB1*08:01, donor-specific antibody was present. A unique clinical condition with late immunopathological features of human skin chronic allograft rejection is reported

Prosthetic resurfacing of engaging posterior capitellar defects in recurrent posterolateral rotatory instability of the elbow

Background Posterolateral rotatory instability (PLRI) is a common mechanism of recurrent elbow instability. While the essential lesion is a deficiency in the lateral ulnar collateral ligament (LUCL), there are often associated concomitant bony lesions, such as an Osborne-Cotterill lesions (posterior capitellar fractures) and marginal radial head fractures, that compromise stability. Currently, there is no standard treatment for posterior capitellar deficiency associated with recurrent PLRI. Methods We conducted a retrospective review of five patients with recurrent PLRI of the elbow associated with a posterior capitellar impaction fracture engaging with the radial head during normal range of motion. The patients were treated surgically with LUCL reconstruction or repair and off-label reconstruction of the capitellar joint surface using a small metal prosthesis designed for metatarsal head resurfacing (HemiCAP toe classic). Results Five patients (three adolescent males, two adult females) were treated between 2007 and 2018. At a median follow-up of 5 years, all patients had complete relief of their symptomatic instability. No patients had pain at rest, but two patients had mild pain (visual analog scale 1–3) during physical activity. Three patients rated their elbow as normal, one as almost normal, and one as greatly improved. On short-term radiographic follow-up there were no signs of implant loosening. None of the patients needed reoperation. Conclusions Recurrent PLRI of the elbow associated with an engaging posterior capitellar lesion can be treated successfully by LUCL reconstruction and repair and filling of the capitellar defect with a metal prosthesis. This treatment option has excellent clinical results in the short-medium term. Level of evidenceIV

The Ursinus Weekly, February 15, 1954

Student exchange consultant will speak here, Wed. • Psychologist tells of work with children • Sororities to try different rushing policy • Groups II, III prepare for one-act plays in March • Fine arts seminar sponsored by Y to begin tonight • Godley relates tale of sunken treasure • Debating team to make first appearance, Feb. 17 • Mrs. Seth Bakes speaks at Color Day ceremonies • MSGA-WSGA to confer on Student Union • Spring play chosen; Try-outs start, Thurs. • Y cabinet retreat yields plans for second semester • Curator of Audubon shrine addresses YM-YWCA group • Editorials: Leave it to the girls! • I know a man • Grizzlies lose to Delaware, 85-71; Drexel 74-70; Haverford, a question • J.V.s beat Drexel; Heller scores 15 • Delaware rallies to tie U.C. grapplers, 14 allhttps://digitalcommons.ursinus.edu/weekly/1488/thumbnail.jp

Compactification, topology change and surgery theory

We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any topology change in dimensions $\geq 5$ may be achieved via a causally continuous cobordism. This extends the known result for 4 dimensions. Therefore, there is no selection rule for compactification at the level of causal continuity. Theorems from surgery theory and handle theory are seen to be very relevant for understanding topology change in higher dimensions. Compactification via parallelisable cobordisms is particularly amenable to study with these tools.Comment: 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected case adde

Octonionic representations of Clifford algebras and triality

The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the non-associativity and non-commutativity of this division algebra are answered. Octonionic representations for Clifford algebras lead to a notion of octonionic spinors and are used to give octonionic representations of the respective orthogonal groups. Finally, the triality automorphisms are shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page