Koszul Calculus

We present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved for any quadratic algebra.Comment: 40 pages; minor changes; to be published in Glasgow Mathematical Journa

Objects Confiscated During the Nazi Era in Exhibitions of Austrian Federal Museums

Even though the restitution of Nazi-looted property from Austrian federal museums is clearly regulated by law, dealing with objects that are still or have been returned to the collections, or with gaps in exhibitions that have resulted from restitutions, poses challenges for museum work. Through a semiotic analysis of museum media (exhibitions, audio guides, information boards as well as museum shops) in Austrian federal museums in 2020 and 2021, this article investigates whether and how the topics of Nazi-looted property, provenance research, and restitution are represented. The research revealed that these topics, which are inevitably linked to violence, are often completely ignored or only presented in exhibition sections on the histories of the museums, as if the problem belonged to the past.Even though the restitution of Nazi-looted property from Austrian federal museums is clearly regulated by law, dealing with objects that are still or have been returned to the collections, or with gaps in exhibitions that have resulted from restitutions, poses challenges for museum work. Through a semiotic analysis of museum media (exhibitions, audio guides, information boards as well as museum shops) in Austrian federal museums in 2020 and 2021, this article investigates whether and how the topics of Nazi-looted property, provenance research, and restitution are represented. The research revealed that these topics, which are inevitably linked to violence, are often completely ignored or only presented in exhibition sections on the histories of the museums, as if the problem belonged to the past

Leadership Education and Development in STEM High Schools

Leadership. Education. Development. How are we inspiring young adults to grow as good and ethical leaders? Leadership should not be defined by a title or label. It’s about developing the perspective, skills and personal style of the whole individual. Through the LEAD program at IMSA, we believe that leadership can be learned through discussion and application. Thus, we have designed a year long course that takes an intricate look at various definitions, theories, models, and conceptualizations of leadership. Students are challenged to think critically about leadership during peer-to-peer facilitated class discussions, hands-on exercises, and group work

Bankruptcy Weapons to Terminate a Zombie Mortgage

Bankruptcy’s strongest public policy is the possibility of a fresh start for a borrower – a way for a debtor to free himself from the burdens of pre-petition obligations and re-commence his or her financial life. A debtor can surrender property burdened by a lien to the lien-holder and thereby release him or herself from ongoing obligations under the loan. This is true even in cases where the collateral’s value is less than the secured loan – for in bankruptcy, a lender’s secured claim is limited to the value of its lien. In chapter 13, a debtor who elects to keep secured property must pay off the secured claim through an acceptable plan, and if the debtor opts to liquidate the secured property, then the debtor may sell it free and clear of liens if it is authorized to do so under § 363 of the Bankruptcy Code. This straightforward method of wiping the slate clean in bankruptcy has recently been threatened by home mortgage holders’ reluctance to foreclose. If the secured lender refuses to accept a debtor’s surrender and foreclose on its lien, the mere filing of bankruptcy will not operate to release the borrower from legal responsibility for property carrying costs and associated liabilities. In cases of foreclosure delay, the defaulted mortgage becomes impossible to kill off completely, even when a borrower has abandoned the home and sought a bankruptcy fresh start. This undead mortgage prevents the property from entering the flow of commerce and poses a barrier to acquisition by a new owner willing to shoulder its upkeep. Neighborhoods and municipalities also pay the cost of zombie mortgages, as years can drag by with no resident owner paying homeowner association dues or property taxes. Furthermore, vacant, unmaintained properties pose a safety hazard and drive down community property values. Borrowers and communities have tried – with varying success – to address this zombie mortgage apocalypse with creative tools, as have bankruptcy debtors and courts. When mortgage lenders refuse to foreclose real property surrendered in bankruptcy, courts have variously attempted to address the zombie mortgage. One underutilized way to kill off a zombie mortgage is to order the home be sold, free and clear of liens, under § 363 of the Bankruptcy Code. This section permits a trustee (or debtor-in-possession) to sell property free of outstanding liens in certain enumerated cases, including cases of lender assent, cases where the sale price will cover the aggregate value of liens encumbering the property, and cases where a free-and-clear sale would otherwise be available under a legal or equitable proceeding. Each of these options provides an interesting possible route to clearing title and providing a debtor with a fresh start in cases of foreclosure delay. Section 363 sales are also available in cases of a dispute about the underlying obligation, and this raises the possibility that lender misbehavior during the life of a mortgage loan can create lien vulnerability in bankruptcy. This article explores the utility of the various subparts of § 363 as a tool to terminate zombie mortgages in bankruptcy. We believe that this bankruptcy power of sale provides a useful avenue to free debtors from the haunting shadow of a defaulted, un-foreclosed mortgage and associated involuntary homeownership. At the same time, the bankruptcy trustee sale power of § 363 can provide great community and market benefits and alleviate foreclosure crisis fallout by encouraging home occupancy and maintenance, wiping out stale liens, and releasing real property back into the stream of commerce

A cup-cap duality in Koszul calculus

We introduce a cup-cap duality in the Koszul calculus of N-homogeneous algebras. As an application, we prove that the graded symmetry of the Koszul cap product is a consequence of the graded commutativity of the Koszul cup product. We propose a conceptual approach that may lead to a proof of the graded commutativity, based on derived categories in the framework of DG algebras and DG bimodules. Various enriched structures are developed in a weaker situation corresponding to N>2.Comment: 30 page

The Garifuna Journey Study Guide

Garifuna tradition bearers, artists, and technicians collaborated with filmmakers Andrea E. Leland and Kathy Berger to produce The Garifuna Journey, a documentary focused on the story of resistance and continuity of culture. The National Garifuna Council of Belize also worked on the project with the goal of cultural retrieval, as little had been documented and collected for its own archives. With direction from tradition bearers in Belize, video footage and audio taped oral histories were collected, transcribed, and returned to the Belize community. The documentary was produced from these materials, focused on the Garifuna experience in Belize.https://digitalcommons.colum.edu/leland_study/1000/thumbnail.jp

Bowel Ischemia: A Rare Complication of Thiopental Treatment for Status Epilepticus

Background: Refractory status epilepticus (RSE) treatment is usually performed with comainduction using an appropriate general anesthetic. Most frequent complications are represented by hypotension and infection. Other side-effects may however be encountered. Observations: We describe two patients suffering from acute bowel ischemia after thiopental (THP) treatment for RSE. A 73-year-old man with a complex-patial RSE following an acute stroke received THP (303 mg/kg over 48 h); 36 h after THP discontinuation, he presented abdominal tenderness and lactate elevation. Necrosis of the terminal ileum and colon was seen during surgical exploration; he deceased shortly thereafter. A 21 year-old woman had a cryptogenic de novo generalized-convulsive RSE resistant to 5 attempts of EEG burst-suppression. During the 6th attempt, after THP (840 mg/kg over 150 h) together with mild hypothermia, she developed an ileus with elevated serum lactate; caecum necrosis was observed during surgery. Hypernatremia, acidosis and hyperlactatemia heralded this complication in both patients. Conclusion: In these two patients, mechanical vascular ischemia may have resulted from drug-induced paralytic ileus. To our knowledge, this is the first report describing this potential fatal side effect in adults with RS

New Constraints on Supersymmetry Using Neutrino Telescopes

We demonstrate that megaton-mass neutrino telescopes are able to observe the signal from long-lived particles beyond the Standard Model, in particular the stau, the supersymmetric partner of the tau lepton. Its signature is an excess of charged particle tracks with horizontal arrival directions and energy deposits between 0.1 and 1 TeV inside the detector. We exploit this previously-overlooked signature to search for stau particles in the publicly available IceCube data. The data shows no evidence of physics beyond the Standard Model. We derive a new lower limit on the stau mass of $320$ GeV (95\% C.L.) and estimate that this new approach, when applied to the full data set available to the IceCube collaboration, will reach world-leading sensitivity to the stau mass ($m_{\tilde{\tau}}=450\,\mathrm{GeV}$)