Counting (3+1) - Avoiding permutations

A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The dimension 2 posets $P$ are exactly the ones which have an associated permutation $\pi$ where $i\prec j$ in $P$ if and only if $i<j$ as integers and $i$ comes before $j$ in the one-line notation of $\pi$. So we say that a permutation $\pi$ is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its poset is (\3+\1)-free. This is equivalent to $\pi$ avoiding the permutations 2341 and 4123 in the language of pattern avoidance. We give a complete structural characterization of such permutations. This permits us to find their generating function.Comment: 17 page

Symmetries and collective excitations in large superconducting circuits

The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics. If realizable, quantum coherence in larger circuit networks has great potential for advances in quantum information processing including topological protection from decoherence. Here, we present theory suitable for quantitative modeling of such large circuits and discuss its application to the fluxonium device. Our approach makes use of approximate symmetries exhibited by the circuit, and enables us to obtain new predictions for the energy spectrum of the fluxonium device which can be tested with current experimental technology

Combinatorial Hopf algebra of superclass functions of type DD

We provide a Hopf algebra structure on the space of superclass functions on the unipotent upper triangular group of type D over a finite field based on a supercharacter theory constructed by Andr\'e and Neto. Also, we make further comments with respect to types B and C. Type A was explores by M. Aguiar et. al (2010), thus this paper is a contribution to understand combinatorially the supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with respect to previous version state

Mars climate engineering using orbiting solar reflectors

The manned mission is seen as a first step towards a Mars surface exploration base-station and, later, establishing permanent settlement. The location and use of Mars's natural resources is vital to enable cost-effective long-duration human exploration and exploitation missions as well as subsequent human colonization. Planet resources include various crust-lodged materials, a low-pressure natural atmosphere, assorted forms of utilizable energy, lower gravity than Earth's, and ground placement advantages relative to human operability and living standards. Power resources may include using solar and wind energy, importation of nuclear reactors and the harvesting of geothermal potential. In fact, a new branch of human civilization could be established permanently on Mars in the next century. But, meantime, an inventory and proper social assessment of Mars's prospective energy and material resources is required. This book investigates the possibilities and limitations of various systems supplying manned bases on Mars with energy and other vital resources. The book collects together recent proposals and innovative options and solutions. It is a useful source of condensed information for specialists involved in current and impending Mars-related activities and a good starting point for young researchers

Shared Responsibilities for Nuclear Disarmament: A Global Debate

Presents Sagan's 2009 paper calling for rethinking the balance of responsibilities and the relationship between articles in the Nuclear Non-Proliferation Treaty with seven response papers by international scholars about how to pursue nuclear disarmament

Tectonophysical approach to the description of mining induced seismicity in the Upper Silesia

Seismicity occurring in the Upper Silesian Coal Basin (the USCB) Is induced by deep underground coal mining and is relatively well recorded and recognized. The majority of tremors occurring there, is closely related to mining so only mining induced stresses were considered to be the cause of the tremors. The frequency energy distribution of mine tremors in the USCB has indicated the evident bimodal features: the lower energy mode, closely related to mining and the largest energy indicating the relation to the geological structures of the USCB. Therefore the research has been undertaken to explain if there is any tectonic influence on mine tremors occurrence and to formulate a seismotectonic model of state of deformation and stresses in the rock mass of the USCB responsible together with mining activity for the mine tremors generation. The obtained results indicate that tectonics plays a significant role in the occurrence of at least some of the largest mining tremors in the USCB area and the tectonophysical analysis can explain some relations in their occurrence. On the basis of seismotectonic model constructed for the USCB area we can conclude that the parameters of strain ellipsoid as well as of the seismic moment tensor and regional stress tensor for some mine tremors are almost the same. Some parts of the Upper Silesian Coal Basin (e.g. the zones of large latitudinal faults) are related to the large discontinuities in the deep crustal basement with active shear stresses. The equilibrium disturbance due to the reduction of vertical stress component caused by mining, erosion of the Carpathian overlap or the postglacial rebound may result in unstable behaviour in these zones and one can expect recent horizontal and vertical movements there. We also underline that the application of the optimum method of direct stress (strain) measurement it the rock mass for conditions of the USCB is necessary as well as that the modernization of seismological networks existing there is inevitable

Life on ice, Antarctica and Mars

The study of the origin of life and the prospects for human exploration of Mars are two themes developed in a new 57-minute film, Life on Ice, Antarctica, and Mars, produced by the InnerSpace Foundation and WHRO Television for broadcast by the Public Broadcasting System (PBS). A brief explanation of the film and how it relates to the future human exploration of space is presented

Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimension between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image available (upon request) from the author

Induction of Paralysis and Visual System Injury in Mice by T Cells Specific for Neuromyelitis Optica Autoantigen Aquaporin-4.

While it is recognized that aquaporin-4 (AQP4)-specific T cells and antibodies participate in the pathogenesis of neuromyelitis optica (NMO), a human central nervous system (CNS) autoimmune demyelinating disease, creation of an AQP4-targeted model with both clinical and histologic manifestations of CNS autoimmunity has proven challenging. Immunization of wild-type (WT) mice with AQP4 peptides elicited T cell proliferation, although those T cells could not transfer disease to naïve recipient mice. Recently, two novel AQP4 T cell epitopes, peptide (p) 135-153 and p201-220, were identified when studying immune responses to AQP4 in AQP4-deficient (AQP4-/-) mice, suggesting T cell reactivity to these epitopes is normally controlled by thymic negative selection. AQP4-/- Th17 polarized T cells primed to either p135-153 or p201-220 induced paralysis in recipient WT mice, that was associated with predominantly leptomeningeal inflammation of the spinal cord and optic nerves. Inflammation surrounding optic nerves and involvement of the inner retinal layers (IRL) were manifested by changes in serial optical coherence tomography (OCT). Here, we illustrate the approaches used to create this new in vivo model of AQP4-targeted CNS autoimmunity (ATCA), which can now be employed to study mechanisms that permit development of pathogenic AQP4-specific T cells and how they may cooperate with B cells in NMO pathogenesis