Finding the αn-th largest element

We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3.     

Solvation thermodynamics: theory and applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.     

Seeing chance: perceptual reasoning as an epistemic resource for grounding compound event spaces

The mathematics subject matter of probability is notoriously challenging, and in particular the content of random compound events. When students analyze experiments, they often omit to discern variations as distinct events, e.g., HT and TH in the case of flipping a pair of coins, and thus infer erroneous predictions. Educators have addressed this conceptual difficulty by engaging students in actual experiments whose outcomes contradict the erroneous predictions. Yet whereas empirical activities per se are crucial for any probability design, because they introduce the pivotal contents of randomness, variance, sample size, and relations among them, empirical activities may not be the unique or best means for students to accept the logic of combinatorial analysis. Instead, learners may avail of their own pre-analytic perceptual judgments of the random generator itself so as to arrive at predictions that agree rather than conflict with mathematical analysis. I support this view first by detailing its philosophical, theoretical, and didactical foundations and then by presenting empirical findings from a design-based research project. Twenty-eight students aged 9?C11 participated in tutorial, task-based clinical interviews that utilized an innovative random generator. Their predictions were mathematically correct even though initially they did not discern variations. Students were then led to recognize the formal event space as a semiotic means of objectifying these presymbolic notions. I elaborate on the thesis via micro-ethnographic analysis of key episodes from a paradigmatic case study.     

X-Ray Crystallography and Free Energy Calculations Reveal the Binding Mechanism of A2A Adenosine Receptor Antagonists

We present a robust protocol based on iterations of free energy perturbation (FEP) calculations, chemical synthesis, biophysical mapping and X-ray crystallography to reveal the binding mode of an antagonist series to the A_2A adenosine receptor (AR). Eight A_2AAR binding site mutations from biophysical mapping experiments were initially analyzed with sidechain FEP simulations, performed on alternate binding modes. The results distinctively supported one binding mode, which was subsequently used to design new chromone derivatives. Their affinities for the A_2AAR were experimentally determined and investigated through a cycle of ligand-FEP calculations, validating the binding orientation of the different chemical substituents proposed. Subsequent X-ray crystallography of the A_2AAR with a low and a high affinity chromone derivative confirmed the predicted binding orientation. The new molecules and structures here reported were driven by free energy calculations, and provide new insights on antagonist binding to the A_2AAR, an emerging target in immuno-oncology.     

Determination of the α parameter for the decay Ξ− → Λπ−

The α parameter for Ξ^? → Λπ^? decay has been determined to be α_Ξ^?=?0.462 ± 0.015, from a sample of 1.5 × 10⁵ events recorded in the CERN SPS hyperon beam. This value is 2.5 standard deviations higher than the current world average.     

First observation ofΩ * resonances

In a experiment at the CERN SPS charged hyperon beam using incident Ξ^?, we have obtained evidence for the production of two Ω^* resonances decaying into Ξ^?π⁺ K ^?, with the following parameters:M ₁=2251±12,Γ ₁=48±20 MeV/c², 78 ±23 events, andM ₂=2284±12,Γ ₂=26±23 MeV/c² 45±10 events. The first state is also observed as a 4.2σ effect in a subsample which contains an additionalK ⁺ orK ⁰ in the final state. Production cross sections and branching ratios to Ξ^* K ^? and Ξ^? K ^* are presented.     

A new upper limit for the branching ratio (Ξ− → nπ−)(Ξ− → Λπ−)

From a sample of 735 000 Ξ^? decays, we have obtained a new upper limit for the branching ratio $\text{(Ξ}{}^{\mathrm{?}}\text{→}\text{n}\text{π}{}^{\mathrm{?}}\text{)}\text{(Ξ}{}^{\mathrm{?}}\text{→ Λπ}{}^{\mathrm{?}}\text{)}$. The result is 1.9 × 10^?5 at the 90% confidence level.     

Soft π−p and pp elastic scattering in the energy range 30 to 345 GeV

Differential cross sections for π^?p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/c)² ? |t| ? 0.04 (GeV/c)². From the analysis of the data, the ratio ? (t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.The results on the real parts confirm the validity of the forward dispersion relations at high energies. Using the dispersion relations, it was shown that the experimental data on ?_{π?p(t = 0)} require a continuous rise of the total πp cross sections, at least up to the energy of 2000 GeV, thus revealing a close similarity in high-energy behaviour of πp and pp interactions.The results on the slope parameters from this experiment together with the analysis of the available world data demonstrate that the existing experimental data are consistent with the hypothesis of a universal shrinkage of the hadronic diffraction cone at high energies. The value of the asymptotic shrinkage parameter α_p^′ was found to be independent of the kind of the incident hadron and of the momentum transfer in the t range |t| ? 0.2 (GeV/c)² : 2α_{p^′ = ± 3 (GeV/c)^?2}.