Quantum Versus Classical Decay Laws in Open Chaotic Systems

We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time t_H and the time t_q=t_H/\sqrt{\kappa T} (with \kappa >> 1 and T being the degree of resonance overlapping and the transmission coefficient respectively) associated with the decay. If t_q < t_H the quantum deviation from the classical decay law starts at the time t_q and are due to the openness of the system. Under the opposite condition quantum effects in intrinsic evolution begin to influence the decay at the time t_H. In this case we establish the connection between quantities which describe the time evolution in an open system and their closed counterparts.Comment: 3 pages, REVTeX, no figures, replaced with the published version (misprints corrected, references updated

Trade-Offs Between Size and Degree in Polynomial Calculus

Building on [Clegg et al. \u2796], [Impagliazzo et al. \u2799] established that if an unsatisfiable k-CNF formula over n variables has a refutation of size S in the polynomial calculus resolution proof system, then this formula also has a refutation of degree k + O(?(n log S)). The proof of this works by converting a small-size refutation into a small-degree one, but at the expense of increasing the proof size exponentially. This raises the question of whether it is possible to achieve both small size and small degree in the same refutation, or whether the exponential blow-up is inherent. Using and extending ideas from [Thapen \u2716], who studied the analogous question for the resolution proof system, we prove that a strong size-degree trade-off is necessary

Visualizing 2D Flows with Animated Arrow Plots

Flow fields are often represented by a set of static arrows to illustrate scientific vulgarization, documentary film, meteorology, etc. This simple schematic representation lets an observer intuitively interpret the main properties of a flow: its orientation and velocity magnitude. We propose to generate dynamic versions of such representations for 2D unsteady flow fields. Our algorithm smoothly animates arrows along the flow while controlling their density in the domain over time. Several strategies have been combined to lower the unavoidable popping artifacts arising when arrows appear and disappear and to achieve visually pleasing animations. Disturbing arrow rotations in low velocity regions are also handled by continuously morphing arrow glyphs to semi-transparent discs. To substantiate our method, we provide results for synthetic and real velocity field datasets

Complexity of Distributions and Average-Case Hardness

We address the following question in the average-case complexity: does there exists a language L such that for all easy distributions D the distributional problem (L, D) is easy on the average while there exists some more hard distribution D\u27 such that (L, D\u27) is hard on the average? We consider two complexity measures of distributions: the complexity of sampling and the complexity of computing the distribution function. For the complexity of sampling of distribution, we establish a connection between the above question and the hierarchy theorem for sampling distribution recently studied by Thomas Watson. Using this connection we prove that for every 0 < a < b there exist a language L, an ensemble of distributions D samplable in n^{log^b n} steps and a linear-time algorithm A such that for every ensemble of distribution F that samplable in n^{log^a n} steps, A correctly decides L on all inputs from {0, 1}^n except for a set that has infinitely small F-measure, and for every algorithm B there are infinitely many n such that the set of all elements of {0, 1}^n for which B correctly decides L has infinitely small D-measure. In case of complexity of computing the distribution function we prove the following tight result: for every a > 0 there exist a language L, an ensemble of polynomial-time computable distributions D, and a linear-time algorithm A such that for every computable in n^a steps ensemble of distributions FA correctly decides L on all inputs from {0, 1}^n except for a set that has F-measure at most 2^{-n/2}and for every algorithm B there are infinitely many n such that the set of all elements of {0, 1}^n for which B correctly decides L has D-measure at most 2^{-n+1}

Intuitive modeling of vapourish objects

International audienceAttempts to model gases in computer graphics started in the late 1970s. Since that time, there have been many approaches developed. In this paper we present a non-physical method allowing to create vapourish objects like clouds or smoky characters. The idea is to create few sketches describing the rough shape of the final vapourish object. These sketches will be used as condensation sets of Iterated Function Systems, providing intuitive control over the object. The advantages of the new method are: simplicity, good control of resulting shapes and ease of eventual object animation