First-Come-First-Served for Online Slot Allocation and Huffman Coding

Can one choose a good Huffman code on the fly, without knowing the underlying distribution? Online Slot Allocation (OSA) models this and similar problems: There are n slots, each with a known cost. There are n items. Requests for items are drawn i.i.d. from a fixed but hidden probability distribution p. After each request, if the item, i, was not previously requested, then the algorithm (knowing the slot costs and the requests so far, but not p) must place the item in some vacant slot j(i). The goal is to minimize the sum, over the items, of the probability of the item times the cost of its assigned slot. The optimal offline algorithm is trivial: put the most probable item in the cheapest slot, the second most probable item in the second cheapest slot, etc. The optimal online algorithm is First Come First Served (FCFS): put the first requested item in the cheapest slot, the second (distinct) requested item in the second cheapest slot, etc. The optimal competitive ratios for any online algorithm are 1+H(n-1) ~ ln n for general costs and 2 for concave costs. For logarithmic costs, the ratio is, asymptotically, 1: FCFS gives cost opt + O(log opt). For Huffman coding, FCFS yields an online algorithm (one that allocates codewords on demand, without knowing the underlying probability distribution) that guarantees asymptotically optimal cost: at most opt + 2 log(1+opt) + 2.Comment: ACM-SIAM Symposium on Discrete Algorithms (SODA) 201

Discrete Poincaré Lemma

This paper proves a discrete analogue of the Poincar´e lemma in the context of a discrete exterior calculus based on simplicial cochains. The proof requires the construction of a generalized cone operator, p : Ck(K) -> Ck+1(K), as the geometric cone of a simplex cannot, in general, be interpreted as a chain in the simplicial complex. The corresponding cocone operator H : Ck(K) -> Ck−1(K) can be shown to be a homotopy operator, and this yields the discrete Poincar´e lemma. The generalized cone operator is a combinatorial operator that can be constructed for any simplicial complex that can be grown by a process of local augmentation. In particular, regular triangulations and tetrahedralizations of R2 and R3 are presented, for which the discrete Poincar´e lemma is globally valid

DASCH 100-yr light curves of high-mass X-ray binaries

We analyzed the 100-yr light curves of Galactic high-mass X-ray binaries using the Harvard photographic plate collection, made accessible through the DASCH project (Digital Access to a Sky Century at Harvard). As scanning is still in progress, we focus on the four objects that are currently well covered: the supergiant X-ray binary Cyg X-1 (V1357 Cyg), and the Be X-ray binaries 1H 1936+541 (BD+53 2262), RX J1744.7-2713 (HD 161103), and RX J2030.5+4751 (SAO 49725), the latter two objects being similar to gamma Cas. The star associated with Cyg X-1 does not show evidence for variability with an amplitude higher than 0.3 magnitude over a hundred years. We found significant variability of one magnitude with timescales of more than 10 years for SAO 49725, as well as a possible period of 500-600 days and an amplitude of 0.05 magnitude that might be the orbital, or super-orbital period of the system. The data is insufficient to conclude for HD 161103 but suggests a similar long-term variability. We thus observe an additional characteristic of gamma Cas-like objects: their long-term variability. This variability seems to be due to the slow evolution of a decretion disk around the Be star, but may be triggered by the presence of a compact object in the system, possibly a white dwarf. This characteristic could be used to identify further similar objects otherwise difficult to detect.Comment: Accepted for publication in Proceedings of Science (INTEGRAL 2012), Eds. A. Goldwurm, F. Lebrun and C. Winkler, based on a presentation at the 9th INTEGRAL Workshop "An INTEGRAL view of the high-energy sky (the first 10 years)", October 15-19, 2012, Paris, Franc

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue

Measurement of the Radius of Neutron Stars with High S/N Quiescent Low-mass X-ray Binaries in Globular Clusters

This paper presents the measurement of the neutron star (NS) radius using the thermal spectra from quiescent low-mass X-ray binaries (qLMXBs) inside globular clusters (GCs). Recent observations of NSs have presented evidence that cold ultra dense matter -- present in the core of NSs -- is best described by "normal matter" equations of state (EoSs). Such EoSs predict that the radii of NSs, Rns, are quasi-constant (within measurement errors, of ~10%) for astrophysically relevant masses (Mns > 0.5 Msun). The present work adopts this theoretical prediction as an assumption, and uses it to constrain a single Rns value from five qLMXB targets with available high signal-to-noise X-ray spectroscopic data. Employing a Markov-Chain Monte-Carlo approach, we produce the marginalized posterior distribution for Rns, constrained to be the same value for all five NSs in the sample. An effort was made to include all quantifiable sources of uncertainty into the uncertainty of the quoted radius measurement. These include the uncertainties in the distances to the GCs, the uncertainties due to the Galactic absorption in the direction of the GCs, and the possibility of a hard power-law spectral component for count excesses at high photon energy, which are observed in some qLMXBs in the Galactic plane. Using conservative assumptions,we found that the radius, common to the five qLMXBs and constant for a wide range of masses, lies in the low range of possible NS radii, Rns=9.1(+1.3)(-1.5) km (90%-confidence). Such a value is consistent with low-res equations of state. We compare this result with previous radius measurements of NSs from various analyses of different types of systems. In addition, we compare the spectral analyses of individual qLMXBs to previous works.Comment: Accepted to Apj. 31 pages, 17 figures, 8 table

Non-monotonic density dependence of the diffusion of DNA fragments in low-salt suspensions

The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking non-monotonic dependence of the long-time self-diffusion on the concentration of the DNA in low-salt conditions. This generic non-monotonic behavior results from both the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, and from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.Comment: 4 pages, 2 figures. Physical Review E, accepted on November 24, 200