Reduction of mm-Regular Noncrossing Partitions

In this paper, we present a reduction algorithm which transforms $m$-regular partitions of $[n]=\{1, 2, ..., n\}$ to $(m-1)$-regular partitions of $[n-1]$. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions in terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers

Riordan Paths and Derangements

Riordan paths are Motzkin paths without horizontal steps on the x-axis. We establish a correspondence between Riordan paths and $(321,3\bar{1}42)$-avoiding derangements. We also present a combinatorial proof of a recurrence relation for the Riordan numbers in the spirit of the Foata-Zeilberger proof of a recurrence relation on the Schr\"oder numbers.Comment: 9 pages, 2 figure

Assessing effects of permafrost thaw on C fluxes based on multiyear modeling across a permafrost thaw gradient at Stordalen, Sweden

Northern peatlands in permafrost regions contain a large amount of organic carbon (C) in the soil. Climate warming and associated permafrost degradation are expected to have significant impacts on the C balance of these ecosystems, but the magnitude is uncertain. We incorporated a permafrost model, Northern Ecosystem Soil Temperature (NEST), into a biogeochemical model, DeNitrificationDeComposition (DNDC), to model C dynamics in highlatitude peatland ecosystems. The enhanced model was applied to assess effects of permafrost thaw on C fluxes of a subarctic peatland at Stordalen, Sweden. DNDC simulated soil freeze–thaw dynamics, net ecosystem exchange of CO2 (NEE), and CH4 fluxes across three typical land cover types, which represent a gradient in the process of ongoing permafrost thaw at Stordalen. Model results were compared with multiyear field measurements, and the validation indicates that DNDC was able to simulate observed differences in seasonal soil thaw, NEE, and CH4 fluxes across the three land cover types. Consistent with the results from field studies, the modeled C fluxes across the permafrost thaw gradient demonstrate that permafrost thaw and the associated changes in soil hydrology and vegetation not only increase net uptake of C from the atmosphere but also increase the annual to decadal radiative forcing impacts on climate due to increased CH4 emissions. This study indicates the potential of utilizing biogeochemical models, such as DNDC, to predict the soil thermal regime in permafrost areas and to investigate impacts of permafrost thaw on ecosystem C fluxes after incorporating a permafrost component into the model framework

Effective g-factor in Majorana Wires

We use the effective g-factor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a step-like reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the g-factor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zero-bias conductance peak

Estimating Real Production and Expenditures Across Nations: A Proposal for Improving the Penn World Tables

In this paper we propose a new approach to international comparisons of real GDP measured from the output-side. The traditional Geary-Khamis system to measure real GDP from the expenditure-side is modified to include differences in the terms of trade between countries. It is shown that this system has a strictly positive solution under mild assumptions. On the basis of a set of domestic final output, import and export prices and values for 14 European countries and the U.S. it is shown that differences between real GDP measured from the expenditure and output-side can be substantial, especially for small open economies.

Dynamical study of the possible molecular state X(3872) with the s-channel one gluon exchange interaction

The recently observed X(3872) resonance, which is difficult to be assigned a conventional $c\bar{c}$ charmonium state in the quark model, may be interpreted as a molecular state. Such a molecular state is a hidden flavor four quark state because of its charmonium-like quantum numbers. The s-channel one gluon exchange is an interaction which only acts in the hidden flavor multi-quark system. In this paper, we will study the X(3872) and other similiar hidden flavor molecular states in a quark model by taking into account of the s-channel one gluon exchange interaction

Nonlocality of Majorana modes in hybrid nanowires

Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductor-semiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a well-developed Majorana modeThis research was supported by Microsoft, the Danish National Research Foundation, the European Commission, and the Spanish Ministry of Economy and Competitiveness through Grants No. FIS2015-65706-P, No. FIS2015-64654-P, and No. FIS2016-80434-P (AEI/FEDER, EU), the Ramón y Cajal programme Grant No. RYC-2011-09345, and the María de Maeztu Programme for Units of Excellence in R&D (Grant No. MDM-2014-0377). C.M.M. acknowledges support from the Villum Foundation. M.-T.D. acknowledges support from State Key Laboratory of High Performance Computing, Chin