Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

Biophysical, Grazing-Season Management, and Animal Traits Effects on Individual Animal Performance of Cow-Calf Systems: Insights from a Long-Term Experiment in the US Western Great Plains

Beef grazing systems require information on management, biophysical, and individual animal influences on performance metrics. However, long-term controlled experiments are lacking to comprehensively ascertain these individual and likely interacting influences. We used a legacy data set from the USDA Agricultural Research Service where individual weight gains were determined from on and off weights of Hereford cows and calves grazing native northern mixed-grass prairie, during the June through September season, from 1975-2001 near Cheyenne, Wyoming, USA. The herd size varied from a minimum of 10 to a maximum of 48 pairs across years. Management (on and off grazing dates and stocking rate, kg BW/ha), biophysical (forage production estimated through NDVI LANDSAT time series, temperature, and precipitation variability), and individual animal (cow age, cow body weight at beginning of grazing season, and calf gender) influences were evaluated for effects on calf weight gain (WG, kg/head). Linear mixed models were used for analyses where the above mentioned were fixed factors, and year and individual cow were random ones. Calf performance was influenced by three animal traits: gender with steer WG 4 kg more than heifer, cow body weight with calf WG increased 2kg for each 100kg of cow body weight, and cow age as optimum calf WG occurred with 5-year-old cows. Management influenced calf WG through the on and off dates. Delaying the start of a grazing season decreased calf WG by 0.80 kg per delayed day. On the contrary, extending the grazing season increased calf WG by about the same amount. Biophysical effects on calf WG were not significant suggesting that the cow performance was mitigating these effects of variability. Results suggest that calf individual performance in this resilient rangeland ecosystem relies on cows’ body weight at beginning of the grazing, their age, and the timing to enter and remove animals from pastures

Quantitative Trait Loci (QTL) for Forage Traits in Intermediate Wheatgrass When Grown as Spaced-Plants versus Monoculture and Polyculture Swards

It has been hypothesized that the genetic control of forage traits, especially biomass, for grass plants growing as spaced-plants versus swards is different. Likewise, the genetic control of compatibility in grass–legume polyculture mixtures is assumed to be different than for forage production in a grass monoculture. However, these hypotheses are largely unvalidated, especially at the DNA level. This study used an intermediate wheatgrass mapping population to examine the effect of three competition environments (spaced-plants, polyculture, and monoculture) on classical quantitative genetic parameters and quantitative trait loci (QTL) identification for biomass, morphology, and forage nutritive value. Moderate to high heritable variation was observed for biomass, morphological traits, and nutritive value within all three environments (H ranged from 0.50 to 0.87). Genetic correlations (rG) among environments for morphology and nutritive value were predominantly high, however, were moderately-low (0.30 to 0.48) for biomass. Six biomass QTL were identified, including three on linkage groups (LG) 1, 6, and 15 that were only expressed in the monoculture environment. Moreover, three biomass QTL on LG 10, 14, and 15 exhibited significant QTL by environment interactions. This study verified that the genetic control of grass biomass in a monoculture versus a grass–legume mixture is only partially the same, with additional genes expressed in monoculture, and that biomass in widely spaced-plants versus swards is predominantly under different genetic control. These results indicate that selection for improved grass biomass will be most successful when conducted within the targeted monoculture or polyculture sward environment per se

Trichinella Surveillance in Black Bears (Ursus Americanus) from Oregon, USA

We used serology and muscle digestion to test black bears (Ursus americanus) from western Oregon, USA, for Trichinella. Results indicate black bears in Oregon are not part of a sylvatic cycle for Trichinella, and risk of human exposure to Trichinella larvae from eating black bear meat from Oregon appears low

Chiral potentials, perturbation theory, and the 1S0 channel of NN scattering

We use nucleon-nucleon phase shifts obtained from experimental data, together with the chiral expansion for the long-distance part of the NN interaction, to obtain information about the short-distance piece of the NN potential that is at work in the 1S0 channel. We find that if the scale R that defines the separation between "long-" and "short-" distance is chosen to be \lsim 1.8 fm then the energy dependence produced by short-distance dynamics is well approximated by a two-term polynomial for Tlab < 200 MeV. We also find that a quantitative description of NN dynamics is possible, at least in this channel, if one treats the long-distance parts of the chiral NN potential in perturbation theory. However, in order to achieve this we have to choose a separation scale R that is larger than 1.0 fm.Comment: 19 pages, 4 figure

Secondary structure of Ac-Alan_n-LysH+^+ polyalanine peptides (nn=5,10,15) in vacuo: Helical or not?

The polyalanine-based peptide series Ac-Ala_n-LysH+ (n=5-20) is a prime example that a secondary structure motif which is well-known from the solution phase (here: helices) can be formed in vacuo. We here revisit this conclusion for n=5,10,15, using density-functional theory (van der Waals corrected generalized gradient approximation), and gas-phase infrared vibrational spectroscopy. For the longer molecules (n=10,15) \alpha-helical models provide good qualitative agreement (theory vs. experiment) already in the harmonic approximation. For n=5, the lowest energy conformer is not a simple helix, but competes closely with \alpha-helical motifs at 300K. Close agreement between infrared spectra from experiment and ab initio molecular dynamics (including anharmonic effects) supports our findings.Comment: 4 pages, 4 figures, Submitted to JPC Letter

From Demonstrations to Task-Space Specifications:Using Causal Analysis to Extract Rule Parameterization from Demonstrations

Learning models of user behaviour is an important problem that is broadly applicable across many application domains requiring human-robot interaction. In this work, we show that it is possible to learn generative models for distinct user behavioural types, extracted from human demonstrations, by enforcing clustering of preferred task solutions within the latent space. We use these models to differentiate between user types and to find cases with overlapping solutions. Moreover, we can alter an initially guessed solution to satisfy the preferences that constitute a particular user type by backpropagating through the learned differentiable models. An advantage of structuring generative models in this way is that we can extract causal relationships between symbols that might form part of the user's specification of the task, as manifested in the demonstrations. We further parameterize these specifications through constraint optimization in order to find a safety envelope under which motion planning can be performed. We show that the proposed method is capable of correctly distinguishing between three user types, who differ in degrees of cautiousness in their motion, while performing the task of moving objects with a kinesthetically driven robot in a tabletop environment. Our method successfully identifies the correct type, within the specified time, in 99% [97.8 - 99.8] of the cases, which outperforms an IRL baseline. We also show that our proposed method correctly changes a default trajectory to one satisfying a particular user specification even with unseen objects. The resulting trajectory is shown to be directly implementable on a PR2 humanoid robot completing the same task.Comment: arXiv admin note: substantial text overlap with arXiv:1903.0126

International Commercial Arbitration: Fifty Years After the New York Convention

a one-day conference held at the Dean Rusk Center on January 30, 2009. The event, co-sponsored by the Georgia Journal of International and Comparative Law, featured Gary Born as keynote speaker and other leaders in the field of international commercial arbitration including Robert Davidson, Executive Director of JAMS Arbitration Practice; William K. Slate, II, President, American Arbitration Association; and Anne Marie Whitesell, Former Secretary General of the ICC International Court of Arbitration

Creative destruction over the business cycle: a stochastic frontier analysis

[[abstract]]This paper examines the within-industry distributions of jobs created and destructed across plants in terms of technical efficiency, technical efficiency change, scale effect, and technical change. It further investigates how these distributions vary with economic activity. By applying the stochastic frontier analysis to plant-level longitudinal data on Taiwan’s 23 two-digit manufacturing industries spanning the period 1992–2003, we find that jobs created (destructed) are disproportionately clustered at plants with lower technical efficiency but higher rate of technical change. A fall in economic activities is associated with a statistically significant decrease (increase) in the fraction of newly created (destructed) jobs accounted for by plants with a higher rate of technical change, indicating that creative destruction is more pronounced during economic contractions.[[journaltype]]國外[[incitationindex]]SSCI[[ispeerreviewed]]Y[[countrycodes]]US