The projective translation equation and unramified 2-dimensional flows with rational vector fields

Let X=(x,y). Previously we have found all rational solutions of the 2-dimensional projective translation equation, or PrTE, (1-z)f(X)=f(f(Xz)(1-z)/z); here f(X)=(u(x,y),v(x,y)) is a pair of two (real or complex) functions. Solutions of this functional equation are called projective flows. A vector field of a rational flow is a pair of 2-homogenic rational functions. On the other hand, only special pairs of 2-homogenic rational functions give rise to rational flows. In this paper we are interested in all non-singular (satisfying the boundary condition) and unramified (without branching points, i.e. single-valued functions in C^2\{union of curves}) projective flows whose vector field is still rational. We prove that, up to conjugation with 1-homogenic birational plane transformation, these are of 6 types: 1) the identity flow; 2) one flow for each non-negative integer N - these flows are rational of level N; 3) the level 1 exponential flow, which is also conjugate to the level 1 tangent flow; 4) the level 3 flow expressable in terms of Dixonian (equianharmonic) elliptic functions; 5) the level 4 flow expressable in terms of lemniscatic elliptic functions; 6) the level 6 flow expressable in terms of Dixonian elliptic functions again. This reveals another aspect of the PrTE: in the latter four cases this equation is equivalent and provides a uniform framework to addition formulas for exponential, tangent, or special elliptic functions (also addition formulas for polynomials and the logarithm, though the latter appears only in branched flows). Moreover, the PrTE turns out to have a connection with Polya-Eggenberger urn models. Another purpose of this study is expository, and we provide the list of open problems and directions in the theory of PrTE; for example, we define the notion of quasi-rational projective flows which includes curves of arbitrary genus.Comment: 34 pages, 2 figure

CENP-A Is Dispensable for Mitotic Centromere Function after Initial Centromere/Kinetochore Assembly

Human centromeres are defined by chromatin containing the histone H3 variant CENP-A assembled onto repetitive alphoid DNA sequences. By inducing rapid, complete degradation of endogenous CENP-A, we now demonstrate that once the first steps of centromere assembly have been completed in G1/S, continued CENP-A binding is not required for maintaining kinetochore attachment to centromeres or for centromere function in the next mitosis. Degradation of CENP-A prior to kinetochore assembly is found to block deposition of CENP-C and CENP-N, but not CENP-T, thereby producing defective kinetochores and failure of chromosome segregation. Without the continuing presence of CENP-A, CENP-B binding to alphoid DNA sequences becomes essential to preserve anchoring of CENP-C and the kinetochore to each centromere. Thus, there is a reciprocal interdependency of CENP-A chromatin and the underlying repetitive centromere DNA sequences bound by CENP-B in the maintenance of human chromosome segregation

Towards a public analysis database for LHC new physics searches using MadAnalysis 5

We present the implementation, in the MadAnalysis 5 framework, of several ATLAS and CMS searches for supersymmetry in data recorded during the first run of the LHC. We provide extensive details on the validation of our implementations and propose to create a public analysis database within this framework.Comment: 20 pages, 15 figures, 5 recast codes; version accepted by EPJC (Dec 22, 2014) including a new section with guidelines for the experimental collaborations as well as for potential contributors to the PAD; complementary information can be found at http://madanalysis.irmp.ucl.ac.be/wiki/PhysicsAnalysisDatabas

Spinal Progenitor-Laden Bridges Support Earlier Axon Regeneration Following Spinal Cord Injury.

Impact statementSpinal cord injury (SCI) results in loss of tissue innervation below the injury. Spinal progenitors have a greater ability to repair the damage and can be injected into the injury, but their regenerative potential is hampered by their poor survival after transplantation. Biomaterials can create a cell delivery platform and generate a more hospitable microenvironment for the progenitors within the injury. In this work, polymeric bridges are used to deliver embryonic spinal progenitors to the injury, resulting in increased progenitor survival and subsequent regeneration and functional recovery, thus demonstrating the importance of combined therapeutic approaches for SCI

UMass Amherst Collections 2013

During the Campus Master Planning effort the need to better understand and plan for the UMass Amherst collections was identified and an ad-hoc committee was created to help advance a better understanding of the existing collections and how best to plan for the future. The committee was comprised of Directors/ curators of campus academic collections, Campus Planning staff and other related campus professionals. The first task of the committee was to develop a basis for creating a planning framework for the academic collections. The Committee defined existing collections and set a framework and common language that enabled the classification and quantification of collections space on cam­pus. The UMass Amherst Collections 2013 report summarizes each collection, its mission and the contact person responsible for the collection. The term collection was defined to include all the campus holdings that are used for academic, research and outreach purposes, with the exception of the Libraries, which had recently completed a facilities Master Plan outlining strategies for future facilities