A Pseudopolynomial Algorithm for Alexandrov's Theorem

Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution leads to the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time. Along the way, we develop pseudopolynomial algorithms for computing shortest paths and weighted Delaunay triangulations on a polyhedral surface, even when the surface edges are not shortest paths.Comment: 25 pages; new Delaunay triangulation algorithm, minor other changes; an abbreviated v2 was at WADS 200

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

Оценивание устойчивого развития окружающей среды на субнациональном уровне в Украине

Рассмотрены существующие методы оценивания устойчивого развития окружающей среды (самостоятельные индикаторы, а также их системы и индексы). Предложен индекс устойчивого развития окружающей среды для оценивания взаимоотношений с окружающей средой на уровне регионов Украины, учитывающий национальные приоритеты в экологической политике. По предложенному региональному индексу получены экологические профили и рейтинг областей Украины.Розглянуто існуючі методи оцінювання сталого розвитку довкілля (самостійні індикатори, а також їх системи та індекси). Запропоновано індекс сталого розвитку довкілля для оцінювання взаємовідносин із навколишнім середовищем на рівні регіонів України, який враховує національні пріоритети в екологічній політиці. За запропонованим регіональним індексом отримано екологічні профілі і рейтинг областей України.The existing methods for assessment of the environment sustainable development (independent indicators, their systems and indices) are considered. The environment sustainability index for assessment of relations with the environment at a regional level for Ukraine is proposed, which takes into account the national priorities in ecological policy. Ecological profiles and rating of the Ukrainian regions are obtained according to the proposed regional index

Test of a theoretical equation of state for elemental solids and liquids

We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the nuclei and electrons. We also point out that at low pressures the neglect of anharmonic and electron-phonon terms, both contained in this formalism, results in errors of less than 5% in the thermal parts of the thermodynamic functions. Then we explicitly display the forms of the remaining terms in the EOS, commenting on the use of experiment and electronic structure theory to evaluate them. We also construct an EOS for Aluminum and compare the resulting Hugoniot with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity et al. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.Comment: Minor revisions for consistency with published versio

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

Shortest Path Problems on a Polyhedral Surface

We develop algorithms to compute shortest path edge sequences, Voronoi diagrams, the Fréchet distance, and the diameter for a polyhedral surface

The valence-fluctuating ground state of plutonium

A central issue in material science is to obtain understanding of the electronic correlations that control complex materials. Such electronic correlations frequently arise because of the competition of localized and itinerant electronic degrees of freedom. Although the respective limits of well-localized or entirely itinerant ground states are well understood, the intermediate regime that controls the functional properties of complex materials continues to challenge theoretical understanding. We have used neutron spectroscopy to investigate plutonium, which is a prototypical material at the brink between bonding and nonbonding configurations. Our study reveals that the ground state of plutonium is governed by valence fluctuations, that is, a quantum mechanical superposition of localized and itinerant electronic configurations as recently predicted by dynamical mean field theory. Our results not only resolve the long-standing controversy between experiment and theory on plutonium’s magnetism but also suggest an improved understanding of the effects of such electronic dichotomy in complex materials.JRC.E.6-Actinide researc

Renewable Energy

This chapter presents an in-depth examination of major renewable energy technologies, including their installed capacity and energy supply in 2009 , the current state of market and technology development, their economic and financial feasibility in 2009 and in the near future, as well as major issues they may face relative to their sustainability or implementation. Renewable energy sources have been important for humankind since the beginning of civilization. For centuries, biomass has been used for heating, cooking, steam generation, and power production; solar energy has been used for heating and drying; geothermal energy has been used for hot water supplies; hydropower, for movement; and wind energy, for pumping and irrigation. For many decades renewable energy sources have also been used to produce electricity or other modern energy carriers

Ancillary Therapy and Supportive Care of Chronic Graft-versus-Host Disease: National Institutes of Health Consensus Development Project on Criteria for Clinical Trials in Chronic Graft-versus-Host Disease: V. Ancillary Therapy and Supportive Care Working Group Report

AbstractThe Ancillary Therapy and Supportive Care Working Group had 3 goals: (1) to establish guidelines for ancillary therapy and supportive care in chronic graft-versus-host disease (GVHD), including treatment for symptoms and recommendations for patient education, preventive measures, and appropriate follow-up; (2) to provide guidelines for the prevention and management of infections and other common complications of treatment for chronic GVHD; and (3) to highlight the areas with the greatest need for clinical research. The definition of “ancillary therapy and supportive care” embraces the most frequent immunosuppressive or anti-inflammatory interventions used with topical intent and any other interventions directed at organ-specific control of symptoms or complications resulting from GVHD and its therapy. Also included in the definition are educational, preventive, and psychosocial interventions with this same objective. Recommendations are organized according to the strength and quality of evidence supporting them and cover the most commonly involved organs, including the skin, mouth, female genital tract, eyes, gastrointestinal tract, and lungs. Recommendations are provided for prevention of infections, osteoporosis, and steroid myopathy and management of neurocognitive and psychosocial adverse effects related to chronic GVHD. Optimal care of patients with chronic GVHD often requires a multidisciplinary approach

Tacrolimus versus Cyclosporine after Hematopoietic Cell Transplantation for Acquired Aplastic Anemia

AbstractCombinations of cyclosporine (CSP) with methotrexate (MTX) have been widely used for immunosuppression after allogeneic transplantation for acquired aplastic anemia. We compared outcomes with tacrolimus (TAC)+MTX versus CSP+MTX after transplantation from HLA-identical siblings (SIB) or unrelated donors (URD) in a retrospective cohort of 949 patients with severe aplastic anemia. Study endpoints included hematopoietic recovery, graft failure, acute graft-versus-host disease (GVHD), chronic GVHD, and mortality. TAC+MTX was used more frequently in older patients and, in recent years, in both SIB and URD groups. In multivariate analysis, TAC+MTX was associated with a lower risk of mortality in URD recipients and with slightly earlier absolute neutrophil count recovery in SIB recipients. Other outcomes did not differ statistically between the 2 regimens. No firm conclusions were reached regarding the relative merits of TAC+MTX versus CSP+MTX after hematopoietic cell transplantation for acquired aplastic anemia. Prospective studies would be needed to determine whether the use of TAC+MTX is associated with lower risk of mortality in URD recipients with acquired aplastic anemia