The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

Atropselective syntheses of (-) and (+) rugulotrosin A utilizing point-to-axial chirality transfer

Chiral, dimeric natural products containing complex structures and interesting biological properties have inspired chemists and biologists for decades. A seven-step total synthesis of the axially chiral, dimeric tetrahydroxanthone natural product rugulotrosin A is described. The synthesis employs a one-pot Suzuki coupling/dimerization to generate the requisite 2,2'-biaryl linkage. Highly selective point-to-axial chirality transfer was achieved using palladium catalysis with achiral phosphine ligands. Single X-ray crystal diffraction data were obtained to confirm both the atropisomeric configuration and absolute stereochemistry of rugulotrosin A. Computational studies are described to rationalize the atropselectivity observed in the key dimerization step. Comparison of the crude fungal extract with synthetic rugulotrosin A and its atropisomer verified that nature generates a single atropisomer of the natural product.P50 GM067041 - NIGMS NIH HHS; R01 GM099920 - NIGMS NIH HHS; GM-067041 - NIGMS NIH HHS; GM-099920 - NIGMS NIH HH

Preparation of amino-substituted indenes and 1,4-dihydronaphthalenes using a one-pot multireaction approach: total synthesis of oxybenzo[c]phenanthridine alkaloids

Allylic trichloroacetimidates bearing a 2-vinyl or 2-allylaryl group have been designed as substrates for a one-pot, two-step multi-bond-forming process leading to the general preparation of aminoindenes and amino-substituted 1,4-dihydronaphthalenes. The synthetic utility of the privileged structures formed from this one-pot process was demonstrated with the total synthesis of four oxybenzo[c]phenanthridine alkaloids, oxychelerythrine, oxysanguinarine, oxynitidine, and oxyavicine. An intramolecular biaryl Heck coupling reaction, catalyzed using the Hermann–Beller palladacycle was used to effect the key step during the synthesis of the natural products

Justice at Sea: Fishers’ politics and marine conservation in coastal Odisha, India

This is a paper about the politics of fishing rights in and around the Gahirmatha marine sanctuary in coastal Odisha, in eastern India. Claims to the resources of this sanctuary are politicised through the creation of a particularly damaging narrative by influential Odiya environmental actors about Bengalis, as illegal immigrants who have hurt the ecosystem through their fishing practices. Anchored within a theoretical framework of justice as recognition, the paper considers the making of a regional Odiya environmentalism that is, potentially, deeply exclusionary. It details how an argument about ‘illegal Bengalis’ depriving ‘indigenous Odiyas’ of their legitimate ‘traditional fishing rights’ derives from particular notions of indigeneity and territory. But the paper also shows that such environmentalism is tenuous, and fits uneasily with the everyday social landscape of fishing in coastal Odisha. It concludes that a wider class conflict between small fishers and the state over a sanctuary sets the context in which questions about legitimate resource rights are raised, sometimes with important effects, like when out at sea

Building professional discourse in emerging markets: Language, context and the challenge of sensemaking

Using ethnographic evidence from the former Soviet republics, this article examines a relatively new and mainly unobserved in the International Business (IB) literature phenomenon of communication disengagement that manifests itself in many emerging markets. We link it to the deficiencies of the local professional business discourse rooted in language limitations reflecting lack of experience with the market economy. This hampers cognitive coherence between foreign and local business entities, adding to the liability of foreignness as certain instances of professional experience fail to find adequate linguistic expression, and complicates cross-cultural adjustments causing multi-national companies (MNCs) financial losses. We contribute to the IB literature by examining cross-border semantic sensemaking through a retrospectively constructed observational study. We argue that a relative inadequacy of the national professional idiom is likely to remain a feature of business environment in post-communist economies for some time and therefore should be factored into business strategies of MNCs. Consequently, we recommend including discursive hazards in the risk evaluation of international projects

Molecularly defined diffuse leptomeningeal glioneuronal tumor (DLGNT) comprises two subgroups with distinct clinical and genetic features

Diffuse leptomeningeal glioneuronal tumors (DLGNT) represent rare CNS neoplasms which have been included in the 2016 update of the WHO classification. The wide spectrum of histopathological and radiological features can make this enigmatic tumor entity difficult to diagnose. In recent years, large-scale genomic and epigenomic analyses have afforded insight into key genetic alterations occurring in multiple types of brain tumors and provide unbiased, complementary tools to improve diagnostic accuracy. Through genome-wide DNA methylation screening of > 25,000 tumors, we discovered a molecularly distinct class comprising 30 tumors, mostly diagnosed histologically as DLGNTs. Copy-number profiles derived from the methylation arrays revealed unifying characteristics, including loss of chromosomal arm 1p in all cases. Furthermore, this molecular DLGNT class can be subdivided into two subgroups [DLGNT methylation class (MC)-1 and DLGNT methylation class (MC)-2], with all DLGNT-MC-2 additionally displaying a gain of chromosomal arm 1q. Co-deletion of 1p/19q, commonly seen in IDH-mutant oligodendroglioma, was frequently observed in DLGNT, especially in DLGNT-MC-1 cases. Both subgroups also had recurrent genetic alterations leading to an aberrant MAPK/ERK pathway, with KIAA1549:BRAF fusion being the most frequent event. Other alterations included fusions of NTRK1/2/3 and TRIM33:RAF1, adding up to an MAPK/ERK pathway activation identified in 80% of cases. In the DLGNT-MC-1 group, age at diagnosis was significantly lower (median 5 vs 14 years, p < 0.01) and clinical course less aggressive (5-year OS 100, vs 43% in DLGNT-MC-2). Our study proposes an additional molecular layer to the current histopathological classification of DLGNT, of particular use for cases without typical morphological or radiological characteristics, such as diffuse growth and radiologic leptomeningeal dissemination. Recurrent 1p deletion and MAPK/ERK pathway activation represent diagnostic biomarkers and therapeutic targets, respectively—laying the foundation for future clinical trials with, e.g., MEK inhibitors that may improve the clinical outcome of patients with DLGNT

Integrated multidimensional sustainability assessment of energy system transformation pathways

Sustainable development embraces a broad spectrum of social, economic and ecological aspects. Thus, a sustainable transformation process of energy systems is inevitably multidimensional and needs to go beyond climate impact and cost considerations. An approach for an integrated and interdisciplinary sustainability assessment of energy system transformation pathways is presented here. It first integrates energy system modeling with a multidimensional impact assessment that focuses on life cycle-based environmental and macroeconomic impacts. Then, stakeholders’ preferences with respect to defined sustainability indicators are inquired, which are finally integrated into a comparative scenario evaluation through a multi-criteria decision analysis (MCDA), all in one consistent assessment framework. As an illustrative example, this holistic approach is applied to the sustainability assessment of ten different transformation strategies for Germany. Applying multi-criteria decision analysis reveals that both ambitious (80%) and highly ambitious (95%) carbon reduction scenarios can achieve top sustainability ranks, depending on the underlying energy transformation pathways and respective scores in other sustainability dimensions. Furthermore, this research highlights an increasingly dominant contribution of energy systems’ upstream chains on total environmental impacts, reveals rather small differences in macroeconomic effects between different scenarios and identifies the transition among societal segments and climate impact minimization as the most important stakeholder preferences