Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams

We consider the problem of finding the number of matrices over a finite field with a certain rank and with support that avoids a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). For general sets of entries these numbers of matrices are not polynomials in q (Stembridge 98); however, when the set of entries is a Young diagram, the numbers, up to a power of q-1, are polynomials with nonnegative coefficients (Haglund 98). In this paper, we give a number of conditions under which these numbers are polynomials in q, or even polynomials with nonnegative integer coefficients. We extend Haglund's result to complements of skew Young diagrams, and we apply this result to the case when the set of entries is the Rothe diagram of a permutation. In particular, we give a necessary and sufficient condition on the permutation for its Rothe diagram to be the complement of a skew Young diagram up to rearrangement of rows and columns. We end by giving conjectures connecting invertible matrices whose support avoids a Rothe diagram and Poincar\'e polynomials of the strong Bruhat order.Comment: 24 pages, 9 figures, 1 tabl

Modeling Web Services by Iterative Reformulation of Functional and Non-Functional Requirements

Abstract. We propose an approach for incremental modeling of composite Web services. The technique takes into consideration both the functional and nonfunctional requirements of the composition. While the functional requirements are described using symbolic transition systems—transition systems augmented with state variables, function invocations, and guards; non-functional requirements are quantified using thresholds. The approach allows users to specify an abstract and possibly incomplete specification of the desired service (goal) that can be realized by selecting and composing a set of pre-existing services. In the event that such a composition is unrealizable, i.e. the composition is not functionally equivalent to the goal or the non-functional requirements are violated, our system provides the user with the causes for the failure, that can be used to appropriately reformulate the functional and/or non-functional requirements of the goal specification.

Spin swap gate in the presence of qubit inhomogeneity in a double quantum dot

We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse-sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling $J$ negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.Comment: published versio

An epitaxial model for heterogeneous nucleation on potent substrates

© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ΔT ; h decreases; and ΔT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin

Spin interactions and switching in vertically tunnel-coupled quantum dots

We determine the spin exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few Tesla, and perpendicular fields of the order of 10 Tesla for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken technique, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch on and off the spin coupling with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.Comment: 13 pages, 9 figure

Full adoption of the most effective strategies to mitigate methane emissions by ruminants can help meet the 1.5 °C target by 2030 but not 2050

To meet the 1.5 °C target, methane (CH) from ruminants must be reduced by 11 to 30% by 2030 and 24 to 47% by 2050 compared to 2010 levels. A meta-analysis identified strategies to decrease product-based (PB; CH per unit meat or milk) and absolute (ABS) enteric CH emissions while maintaining or increasing animal productivity (AP; weight gain or milk yield). Next, the potential of different adoption rates of one PB or one ABS strategy to contribute to the 1.5 °C target was estimated. The database included findings from 430 peer-reviewed studies, which reported 98 mitigation strategies that can be classified into three categories: animal and feed management, diet formulation, and rumen manipulation. A random-effects meta-analysis weighted by inverse variance was carried out. Three PB strategies—namely, increasing feeding level, decreasing grass maturity, and decreasing dietary forage-to-concentrate ratio—decreased CH per unit meat or milk by on average 12% and increased AP by a median of 17%. Five ABS strategies—namely CH inhibitors, tanniferous forages, electron sinks, oils and fats, and oilseeds—decreased daily methane by on average 21%. Globally, only 100% adoption of the most effective PB and ABS strategies can meet the 1.5 °C target by 2030 but not 2050, because mitigation effects are offset by projected increases in CH due to increasing milk and meat demand. Notably, by 2030 and 2050, low- and middle-income countries may not meet their contribution to the 1.5 °C target for this same reason, whereas high-income countries could meet their contributions due to only a minor projected increase in enteric CH emissions.We thank the GLOBAL NETWORK project for generating part of the database. The GLOBAL NETWORK project (https://globalresearchalliance.org/research/livestock/collaborative-activities/global-research-project/; accessed 20 June 2020) was a multinational initiative funded by the Joint Programming Initiative on Food Security, Agriculture, and Climate Change and was coordinated by the Feed and Nutrition Network (https://globalresearchalliance.org/research/livestock/networks/feed-nutrition-network/; accessed 20 June 2020) within the Livestock Research Group of the Global Research Alliance on Agricultural GHG (https://globalresearchalliance.org; accessed 20 June 2020). We thank MitiGate, which was part of the Animal Change project funded by the EU under Grant Agreement FP7-266018 for sharing their database with us (http://mitigate.ibers.aber.ac.uk/, accessed 1 July 2017). Part of C.A., A.N.H., and S.C.M.’s time in the early stages of this project was funded by the Kravis Scientific Research Fund (New York) and a gift from Sue and Steve Mandel to the Environmental Defense Fund. Another part of C.A.’s work on this project was supported by the National Program for Scientific Research and Advanced Studies - PROCIENCIA within the framework of the "Project for the Improvement and Expansion of the Services of the National System of Science, Technology and Technological Innovation" (Contract No. 016-2019) and by the German Federal Ministry for Economic Cooperation and Development (issued through Deutsche Gesellschaft für Internationale Zusammenarbei) through the research “Programme of Climate Smart Livestock” (Programme 2017.0119.2). Part of A.N.H.’s work was funded by the US Department of Agriculture (Washington, DC) National Institute of Food and Agriculture Federal Appropriations under Project PEN 04539 and Accession no. 1000803. E.K. was supported by the Sesnon Endowed Chair Fund of the University of California, Davis

Secondary education reform in Lesotho and Zimbabwe and the needs of rural girls: Pronouncements, policy and practice

Analysis of the educational needs of rural girls in Lesotho and Zimbabwe suggests a number of shortcomings in the current form of secondary education, and ways in which it might be modified so as to serve this sizeable group of students better. Several of the shortcomings, notably in relation to curricular irrelevance and excessive focus on examinations, have long been recognised, including by politicians. Yet political pronouncements are seldom translated into policy, and even where policy is formulated, reforms are seldom implemented in schools. This paper makes use of interviews with educational decision-makers in the two southern African countries and a range of documentary sources to explore why, despite the considerable differences between the two contexts, much needed educational reforms have been implemented in neither

Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model in e+e- Interactions at \sqrt{s} = 189 GeV

A search for the lightest neutral scalar and neutral pseudoscalar Higgs bosons in the Minimal Supersymmetric Standard Model is performed using 176.4 pb^-1 of integrated luminosity collected by L3 at a center-of-mass energy of 189 GeV. No signal is observed, and the data are consistent with the expected Standard Model background. Lower limits on the masses of the lightest neutral scalar and pseudoscalar Higgs bosons are given as a function of tan(beta). Lower mass limits for tan(beta)>1 are set at the 95% confidence level to be m_h > 77.1 GeV and m_A > 77.1 GeV

Search for Extra Dimensions in Boson and Fermion Pair Production in e+e- Interactions at LEP

Extra spatial dimensions are proposed by recent theories that postulate the scale of gravity to be of the same order as the electroweak scale. A sizeable interaction between gravitons and Standard Model particles is then predicted. Effects of these new interactions in boson and fermion pair production are searched for in the data sample collected at centre-of-mass energies above the Z pole by the L3 detector at LEP. In addition, the direct production of a graviton associated with a Z boson is investigated. No statistically significant hints for the existence of these effects are found and lower limits in excess of 1 TeV are derived on the scale of this new theory of gravity

Measurement of the Probability of Gluon Splitting into Charmed Quarks in Hadronic Z Decays

We have measured the probability, n(g->cc~), of a gluon splitting into a charm-quark pair using 1.7 million hadronic Z decays collected by the L3 detector. Two independent methods have been applied to events with a three-jet topology. One method relies on tagging charmed hadrons by identifying a lepton in the lowest energy jet. The other method uses a neural network based on global event shape parameters. Combining both methods, we measure n(g->cc~)= [2.45 +/- 0.29 +/- 0.53]%