The Horrocks-Mumford bundle restricted to planes

We study the behavior of the Horrocks-Mumford bundle when restricted to a plane P^2 in P^4, looking for all possible minimal free resolutions for the restricted bundle. To each of the 6 resolutions (4 stable and 2 unstable) we find, we then associate a subvariety of the Grassmannian G(2,4) of planes in P^4. We thus obtain a filtration of the Grassmannian, which we describe in the second part of this work.Comment: 19 pages, typos removed, added details in Propostions 2.1 and 3.

editor’s introduction

The last issue of JNCHC (spring/summer 2019) included a Forum on “Current Challenges to Honors Education.” The essays focused on challenges to honors while this issue’s Forum addresses challenges within honors, especially the challenges we present to our students in courses that are designed to complicate, interrogate, and often defy accepted practices and beliefs. The introduction of risk-taking takes this topic beyond the unthreatening and inviting terrain of challenge into a different territory. Virtually all honors programs and colleges advertise themselves as presenting challenges to their students, but few if any boast that they are risky. Jumping hurdles is a challenge: jumping when you don’t know what is on the other side is risky. Risk involves some possibility of danger, and to varying degrees the essays in this issue’s Forum address not just the challenge but the risk for students, educators, and programs in honors

Organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids

In this work, we present an organocatalytic stereodivergent synthesis of β,β-disubstituted-α-aminoacids using arylidene azlactones as starting materials. The developed two step synthesis involves a sequential catalysis approach, in which two different catalysts act sequentially to control the absolute configuration of two different stereocenters. With an accurate selection of the catalysts absolute configuration it is possible to obtain all the stereoisomers of the product. The first synthetic step is a catalytic asymmetric transfer hydrogenation of the azlactone C=C double bond. A Jacobsen type thiourea and a Hantzsch ester were chosen as chiral catalyst and hydride donor, respectively. Different azlactones, Hantzsch esters and thioureas were synthetized and tested in the asymmetric transfer hydrogenation to achieve the best stereoselectivity. The second step involves a dynamic kinetic resolution on the reduced azlactone, through a nucleophilic addition to the carbonyl moiety promoted by a bifunctional chiral catalyst. A wide range of nucleophiles and organocatalysts were tested; the best results were reached with alcohols as nucleophiles and squaramide-based cinchona alkaloids as a chiral catalysts. With the optimized conditions two stereodivergent syntheses were then performed, enabling the selective obtainment of both diastereoisomeric product with high enantioselectivities

The Interlace Polynomial

In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.Comment: 18 pages, 5 figures, to appear as a chapter in: Graph Polynomials, edited by M. Dehmer et al., CRC Press/Taylor & Francis Group, LL

THE FAILURE OF MARKETABLE PERMIT SYSTEMS AND UNCERTAINTY OF ENVIRONMENTAL POLICY: A SWITCHING REGIME MODEL APPLIED TO THE DUTCH PHOSPHATE QUOTA PROGRAM

A well-known feature of pollution control with tradable quota rights is that the benefits to ownership will capitalize into prices of the quota. Quota present a unique opportunity to examine the effect of risks introduced by governmental programs because all the return to quota is dependent upon these programs. The uncertainty of future regulatory action results from the probability that the stream of incomes could be reduced (portfolio risk) by policy variation or stopped (default risk) by a substantial switch or shock in policy regime. Eliminating the quota program is the extreme case of default risk, as it would terminate the quota benefits. The paper concentrates on the paradox that environmental regulation can provoke economic and environmental inefficiencies because of policy uncertainty. The theory on investment under uncertainty argues that when future returns are uncertain, an opportunity to wait and see has some (quasi) option value. Under uncertainty, investments and disinvestments will take place at respectively higher and lower levels of returns creating an inaction interval. This interval means that returns to quota can vary over a wide range before trade takes place and offers a new, theoretical explanation for the failure of marketable permit systems. The objectives of this paper are threefold. First, the option value theory is employed to forge a natural connection between political uncertainty and quota price volatility. Second, based on the option value theory, a switching regime model is developed for investing and disinvesting in quota. Third, the empirical evidence for the Dutch Phosphate Quota Program indicates that policy risks led to asset fixity. Consequently, the market of tradable phosphate quota was not effective with major negative implications for both economic and environmental efficiency.switching regime, option theory, policy risk, asset fixity, phosphate quota, pork production., Environmental Economics and Policy, Risk and Uncertainty,

Suppressing nonsense--a surprising function for 5-azacytidine.

In this issue of EMBO Molecular Medicine, Bhuvanagiri et al report on a chemical means to convert molecular junk into gold. They identify a chemical inhibitor of a quality control pathway that is best known for its ability to clear cells of rubbish, but that in certain cases can be detrimental because it eliminates “useful” garbage. The chemical inhibitor identified by Bhuvanagiri et al perturbs Nonsense‐Mediated RNA Decay (NMD), a RNA surveillance pathway that targets mRNAs harboring premature termination codons (PTCs) for degradation (Kervestin & Jacobson, 2012)