Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems

We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a class G of graphs, an (F,G)-system is a boolean dynamical system with local transitions functions lying in F and graphs in G. We show that, if local transition functions are given by lookup tables, then the following complexity classification holds: Let F be a class of boolean functions closed under superposition and let G be a graph class closed under taking minors. If F contains all min-functions, all max-functions, or all self-dual and monotone functions, and G contains all planar graphs, then it is #P-complete to compute the number of fixed points in an (F,G)-system; otherwise it is computable in polynomial time. We also prove a dichotomy theorem for the case that local transition functions are given by formulas (over logical bases). This theorem has a significantly more complicated structure than the theorem for lookup tables. A corresponding theorem for boolean circuits coincides with the theorem for formulas.Comment: 16 pages, extended abstract presented at 10th Italian Conference on Theoretical Computer Science (ICTCS'2007

On the kHz QPO frequency correlations in bright neutron star X-ray binaries

We re-examine the correlation between the frequencies of upper and lower kHz quasi-periodic oscillations (QPO) in bright neutron-star low-mass X-ray binaries. By including the kHz QPO frequencies of the X-ray binary Cir X-1 and two accreting millisecond pulsars in our sample, we show that the full sample does not support the class of theoretical models based on a single resonance, while models based on relativistic precession or Alfven waves describe the data better. Moreover, we show that the fact that all sources follow roughly the same correlation over a finite frequency range creates a correlation between the linear parameters of the fits to any sub-sample.Comment: Accepted for publication in MNRAS; 7 pages, 4 figure

Cluster Computing and the Power of Edge Recognition

We study the robustness--the invariance under definition changes--of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with respect to some length-respecting total order with efficient adjacency checks. The definition of CL#P is heavily influenced by the defining paper's focus on (global) orders. In contrast, we define a cluster class, CLU#P, to capture what seems to us a more natural model of cluster computing. We prove that the naturalness is costless: CL#P = CLU#P. Then we exploit the more natural, flexible features of CLU#P to prove new robustness results for CL#P and to expand what is known about the closure properties of CL#P. The complexity of recognizing edges--of an ordered collection of computation paths or of a cluster of accepting computation paths--is central to this study. Most particularly, our proofs exploit the power of unique discovery of edges--the ability of nondeterministic functions to, in certain settings, discover on exactly one (in some cases, on at most one) computation path a critical piece of information regarding edges of orderings or clusters

Swift X-ray Telescope study of the Black Hole Binary MAXI J1659-152: Variability from a two component accretion flow

We present an energy dependent X-ray variability study of the 2010 outburst of the black hole X-ray binary MAXI J1659-152 with the Swift X-ray Telescope (XRT). The broad-band noise components and the quasi periodic oscillations (QPO) observed in the power spectra show a strong and varied energy dependence. Combining Swift XRT data with data from the Rossi X-ray Timing Explorer, we report, for the first time, an rms spectrum (fractional rms amplitude as a function of energy) of these components in the 0.5-30 keV energy range. We find that the strength of the low-frequency component (< 0.1 Hz) decreases with energy, contrary to the higher frequency components (> 0.1 Hz) whose strengths increase with energy. In the context of the propagating fluctuations model for X-ray variability, we suggest that the low-frequency component originates in the accretion disk (which dominates emission below ~ 2 keV) and the higher frequency components are formed in the hot flow (which dominates emission above ~ 2 keV). As the properties of the QPO suggest that it may have a different driving mechanism, we investigate the Lense-Thirring precession of the hot flow as a candidate model. We also report on the QPO coherence evolution for the first time in the energy band below 2 keV. While there are strong indications that the QPO is less coherent at energies below 2 keV than above 2 keV, the coherence increases with intensity similar to what is observed at energies above 2 keV in other black-hole X-ray binaries.Comment: 12 pages, 6 Figures, 2 Tables, Accepted for publication in Astrophysical Journa

Tuning the Diversity of Open-Ended Responses from the Crowd

Crowdsourcing can solve problems that current fully automated systems cannot. Its effectiveness depends on the reliability, accuracy, and speed of the crowd workers that drive it. These objectives are frequently at odds with one another. For instance, how much time should workers be given to discover and propose new solutions versus deliberate over those currently proposed? How do we determine if discovering a new answer is appropriate at all? And how do we manage workers who lack the expertise or attention needed to provide useful input to a given task? We present a mechanism that uses distinct payoffs for three possible worker actions---propose,vote, or abstain---to provide workers with the necessary incentives to guarantee an effective (or even optimal) balance between searching for new answers, assessing those currently available, and, when they have insufficient expertise or insight for the task at hand, abstaining. We provide a novel game theoretic analysis for this mechanism and test it experimentally on an image---labeling problem and show that it allows a system to reliably control the balance betweendiscovering new answers and converging to existing ones