The Big Match in Small Space

In this paper we study how to play (stochastic) games optimally using little space. We focus on repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games. The prototypical example of these games is the well known Big Match of Gillete (1957). These games may not allow optimal strategies but they always have {\epsilon}-optimal strategies. In this paper we design {\epsilon}-optimal strategies for Player 1 in these games that use only O(log log T ) space. Furthermore, we construct strategies for Player 1 that use space s(T), for an arbitrary small unbounded non-decreasing function s, and which guarantee an {\epsilon}-optimal value for Player 1 in the limit superior sense. The previously known strategies use space {\Omega}(logT) and it was known that no strategy can use constant space if it is {\epsilon}-optimal even in the limit superior sense. We also give a complementary lower bound. Furthermore, we also show that no Markov strategy, even extended with finite memory, can ensure value greater than 0 in the Big Match, answering a question posed by Abraham Neyman

Young Binary Stars and Associated Disks

The typical product of the star formation process is a binary star. Binaries have provided the first dynamical measures of the masses of pre-main-sequence (PMS) stars, providing support for the calibrations of PMS evolutionary tracks. Surprisingly, in some star-forming regions PMS binary frequencies are higher than among main-sequence solar-type stars. The difference in PMS and main-sequence binary frequencies is apparently not an evolutionary effect; recent attention has focussed on correlations between binary frequency and stellar density or cloud temperatures. Accretion disks are common among young binary stars. Binaries with separations between 1 AU and 100 AU have substantially less submillimeter emission than closer or wider binaries, suggesting that they have truncated their disks. Evidence of dynamical clearing has been seen in several binaries. Remarkably, PMS binaries of all separations show evidence of circumstellar disks and continued accretion. This suggests that the circumstellar disks are replenished from circumbinary disks or envelopes. The frequent presence of disks suggests that planet formation can occur in binary environments, and formation of planets in wide binaries is already established by their discovery. Circumbinary disk masses around very short period binaries are ample to form planetary systems such as our own. The nature of planetary systems among the most common binaries, with separations between 10 AU and 100 AU, is less clear given the observed reduction in disk mass, though they may have disk masses adequate for the formation of terrestrial-like planets.Comment: 32 pages, including 6 Postscript figures (TeX, uses psfig.sty); to appear in "Protostars & Planets IV". Gif figures with captions and high-res Postscript color figure available at http://hven.swarthmore.edu/~jensen/preprints/ppiv.htm

Separation and Concentration without Clogging Using a High-Throughput Tunable Filter

We present a detailed experimental study of a hydrodynamic filtration microchip and show how chip performance can be tuned and clogging avoided by adjusting the flow rates. We demonstrate concentration and separation of microspheres at throughputs as high as 29  ml/min and with 96% pureness. Results of streakline visualizations show that the thickness of a tunable filtration layer dictates the cutoff size and that two different concentration mechanisms exist. Particles larger than pores are concentrated by low-velocity rolling over the filtration pillars, while particles smaller than pores are concentrated by lateral drift across the filtration layer. Results of microscopic particle image velocimetry and particle-tracking velocimetry show that the degree of lateral migration can be quantified by the slip velocity between the particle and the surrounding fluid. Finally, by utilizing differences in inertia and separation mode, we demonstrate size-based separation of particles in a mixtureacceptedVersio

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple

Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin–orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree–Fock or Kohn–Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange–correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10−5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnFn, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost