Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

This paper develops nonparametric estimation for discrete choice models based on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution $G$. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution $G$, to estimate choice probabilities. We provide an important theoretical support for the use of the proposed methodology by investigating consistency of the posterior distribution for a general nonparametric prior on the mixing distribution. Consistency is defined according to an $L_1$-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy-to-use blocked Gibbs sampling procedures. These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes. A simulation study is also performed to investigate the performance of the proposed methods.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ233 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models

This paper develops nonparametric estimation for discrete choice models based on the Mixed Multinomial Logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution G. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate the unknown choice probabilities. Theoretical support for the use of the proposed methodology is provided by establishing strong consistency of a general nonparametric prior on G under simple sufficient conditions. Consistency is defined according to a L1-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy to use blocked Gibbs sampling procedures. A simulation study is also performed to illustrate the proposed methods and the exibility they achieve with respect to parametric Gaussian MMNL models.Bayesian consistency, Bayesian nonparametrics, Blocked Gibbs sampler, Discrete choice models, Mixed Multinomial Logit, Random probability measures, Stick-breaking priors

Ефективність симбіотичної азотфіксації в агроценозах України

Проведено порівняльну оцінку ефективності виробничих і перспективних штамів бульбочкових бактерій колекції Південної дослідної станції ІСГМ УААН у симбіозі з сучасними сортами бобових культур. Визначені високоефективні комбінації “сорти – штами”. Показано доцільність передпосівної інокуляції насіння бобових культур на фоні ґрунтової популяції ризобій.Проведена сравнительная оценка эффективности производственных и перспективных штаммов клубеньковых бактерий коллекции Южной опытной станции ИСХМ УААН в симбиозе с современными сортами бобовых культур. Определены высокоэффективные комбинации “сорта – штаммы”. Показана целесообразность предпосевной инокуляции семян бобовых культур на фоне почвенной популяции ризобий.The comparative estimation of rhisobia strains (from the collection of the Southern Experimental Station of Institute of Agricultural Microbiology UAAS) efficiency in symbiosis with modern legume cultivars was done. Highly effective complemented „cultivars – strains” combinations have been determined. It was shown the expediency of legume seeds pre-sowing treatment on background of soil rhisobia population

The Baryon Content of Cosmic Structures

We make an inventory of the baryonic and gravitating mass in structures ranging from the smallest galaxies to rich clusters of galaxies. We find that the fraction of baryons converted to stars reaches a maximum between M500 = 1E12 and 1E13 Msun, suggesting that star formation is most efficient in bright galaxies in groups. The fraction of baryons detected in all forms deviates monotonically from the cosmic baryon fraction as a function of mass. On the largest scales of clusters, most of the expected baryons are detected, while in the smallest dwarf galaxies, fewer than 1% are detected. Where these missing baryons reside is unclear.Comment: ApJ Letters, in pres

Surface Phase Transitions Induced by Electron Mediated Adatom-Adatom Interaction

We propose that the indirect adatom-adatom interaction mediated by the conduction electrons of a metallic surface is responsible for the $\sqrt{3}\times \sqrt{3}\Leftrightarrow 3\times 3$ structural phase transitions observed in Sn/Ge (111) and Pb/Ge (111). When the indirect interaction overwhelms the local stress field imposed by the substrate registry, the system suffers a phonon instability, resulting in a structural phase transition in the adlayer. Our theory is capable of explaining all the salient features of the $\sqrt{3}\times \sqrt{3}\Leftrightarrow 3\times 3$ transitions observed in Sn/Ge (111) and Pb/Ge (111), and is in principle applicable to a wide class of systems whose surfaces are metallic before the transition.Comment: 4 pages, 5 figure

Angular momentum and an invariant quasilocal energy in general relativity

Owing to its transformation property under local boosts, the Brown-York quasilocal energy surface density is the analogue of E in the special relativity formula: E^2-p^2=m^2. In this paper I will motivate the general relativistic version of this formula, and thereby arrive at a geometrically natural definition of an `invariant quasilocal energy', or IQE. In analogy with the invariant mass m, the IQE is invariant under local boosts of the set of observers on a given two-surface S in spacetime. A reference energy subtraction procedure is required, but in contrast to the Brown-York procedure, S is isometrically embedded into a four-dimensional reference spacetime. This virtually eliminates the embeddability problem inherent in the use of a three-dimensional reference space, but introduces a new one: such embeddings are not unique, leading to an ambiguity in the reference IQE. However, in this codimension-two setting there are two curvatures associated with S: the curvatures of its tangent and normal bundles. Taking advantage of this fact, I will suggest a possible way to resolve the embedding ambiguity, which at the same time will be seen to incorporate angular momentum into the energy at the quasilocal level. I will analyze the IQE in the following cases: both the spatial and future null infinity limits of a large sphere in asymptotically flat spacetimes; a small sphere shrinking toward a point along either spatial or null directions; and finally, in asymptotically anti-de Sitter spacetimes. The last case reveals a striking similarity between the reference IQE and a certain counterterm energy recently proposed in the context of the conjectured AdS/CFT correspondence.Comment: 54 pages LaTeX, no figures, includes brief summary of results, submitted to Physical Review

Velocity-selective sublevel resonance of atoms with an array of current-carrying wires

Resonance transitions between the Zeeman sublevels of optically-polarized Rb atoms traveling through a spatially periodic magnetic field are investigated in a radio-frequency (rf) range of sub-MHz. The atomic motion induces the resonance when the Zeeman splitting is equal to the frequency at which the moving atoms feel the magnetic field oscillating. Additional temporal oscillation of the spatially periodic field splits a motion-induced resonance peak into two by an amount of this oscillation frequency. At higher oscillation frequencies, it is more suitable to consider that the resonance is mainly driven by the temporal field oscillation, with its velocity-dependence or Doppler shift caused by the atomic motion through the periodic field. A theoretical description of motion-induced resonance is also given, with emphasis on the translational energy change associated with the internal transition.Comment: 7 pages, 3 figures, final versio

V605 Aquilae: a born again star, a nova or both?

V605 Aquilae is today widely assumed to have been the result of a final helium shell flash occurring on a single post-asymptotic giant branch star. The fact that the outbursting star is in the middle of an old planetary nebula and that the ejecta associated with the outburst is hydrogen deficient supports this diagnosis. However, the material ejected during that outburst is also extremely neon rich, suggesting that it derives from an oxygen-neon-magnesium star, as is the case in the so-called neon novae. We have therefore attempted to construct a scenario that explains all the observations of the nebula and its central star, including the ejecta abundances. We find two scenarios that have the potential to explain the observations, although neither is a perfect match. The first scenario invokes the merger of a main sequence star and a massive oxygen-neon-magnesium white dwarf. The second invokes an oxygen-neon-magnesium classical nova that takes place shortly after a final helium shell flash. The main drawback of the first scenario is the inability to determine whether the ejecta would have the observed composition and whether a merger could result in the observed hydrogen-deficient stellar abundances observed in the star today. The second scenario is based on better understood physics, but, through a population synthesis technique, we determine that its frequency of occurrence should be very low and possibly lower than what is implied by the number of observed systems. While we could not envisage a scenario that naturally explains this object, this is the second final flash star which, upon closer scrutiny, is found to have hydrogen-deficient ejecta with abnormally high neon abundances. These findings are in stark contrast with the predictions of the final helium shell flash and beg for an alternative explanation.Comment: 8 pages, 1 figures, 2 tables, accepted for MNRAS. Better title and minor corrections compared to previous versio

Self-assembly of ultra-small micelles from amphiphilic lipopeptoids

Poly(N-substituted glycine) “peptoids” constitute a promising class of peptide-mimetic materials. We introduce the self-assembly of lipopeptoids into spherical micelles ca. 5 nm in diameter as well as larger assemblies by varying the peptoid sequence design. Our results point to design rules for the self-assembly of peptoid nanostructures, enabling the creation of stable, ultra-small peptidomimetic nanospheres

A Mission to Explore the Pioneer Anomaly

The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8.74 \pm 1.33)\times 10^{-10} {\rm m/s^2}$. This signal has become known as the Pioneer anomaly. The inability to explain the anomalous behavior of the Pioneers with conventional physics has contributed to growing discussion about its origin. There is now an increasing number of proposals that attempt to explain the anomaly outside conventional physics. This progress emphasizes the need for a new experiment to explore the detected signal. Furthermore, the recent extensive efforts led to the conclusion that only a dedicated experiment could ultimately determine the nature of the found signal. We discuss the Pioneer anomaly and present the next steps towards an understanding of its origin. We specifically focus on the development of a mission to explore the Pioneer Anomaly in a dedicated experiment conducted in deep space.Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020", 19-21 April 2005, ESTEC, Noordwijk, The Netherland