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Critical behaviour of combinatorial search algorithms, and the unitary-propagation universality class

EUROPHYSICS LETTERS 2004年第1期68卷 153-159页

作者： Deroulers, C Monasson, R ENS CNRS Phys Theor Lab F-75005 Paris France

The probability P(alpha, N) that search algorithms for random satisfiability problems successfully find a solution is studied as a function of the ratio alpha of constraints per variable and the number N of variables. P is shown to be finite if a lies below an algorithm-dependent threshold alpha(A), and exponentially small in N above. The critical behaviour is universal for all algorithms based on the widely used unitary propagation rule: P[(1 + epsilon)-alpha(A), N] similar to exp[-N-1/6 Phi(epsilonN(1/3))]. Exponents are related to the critical behaviour of random graphs, and the scaling function Phi is exactly calculated through a mapping onto a diffusion-and-death problem.

关键词： computer science and technology Classical statistical mechanics Information theory and communication theory

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Dynamics of heuristic optimization algorithms on random graphs

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EUROPEAN PHYSICAL JOURNAL B 2002年第3期28卷 369-381页

作者： Weigt, M Univ Gottingen Inst Theoret Phys D-37073 Gottingen Germany

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, and some environment of it, is covered and removed from the graph. This graph reduction process can be described as a Markovian dynamics in the space of random graphs of arbitrary degree distribution. We discuss some solvable cases, including algorithms already analysed using different techniques, and develop approximation schemes for more complicated cases. The approximations are corroborated by numerical simulations.

关键词： Interdisciplinary applications of physics Probability theory, stochastic processes, and statistics computer science and technology

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Statistical physics analysis of the computational complexity of solving random satisfiability problems using backtrack algorithms

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EUROPEAN PHYSICAL JOURNAL B 2001年第4期22卷 505-531页

作者： Cocco, S Monasson, R ENS Phys Theor Lab CNRS F-75005 Paris France Univ Illinois Dept Phys Chicago IL 60607 USA Univ Chicago James Franck Inst Chicago IL 60637 USA

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated using statistical physics concepts and techniques related to phase transitions, growth processes and (real-space) renormalization flows. 3-SAT is a representative example of hard computational tasks;it consists in knowing whether a set of alphaN randomly drawn logical constraints involving N Boolean variables can be satisfied altogether or not. Widely used solving procedures, as the Davis-Putnam-Loveland-Logemann (DPLL) algorithm, perform a systematic search for a solution, through a sequence of trials and errors represented by a search tree. The size of the search tree accounts for the computational complexity, i.e. the amount of computational efforts, required to achieve resolution. In the present study, we identify, using theory and numerical experiments, easy (size of the search tree scaling polynomially with N) and hard (exponential scaling) regimes as a function of the ratio alpha of constraints per variable. The typical complexity is explicitly calculated in the different regimes, in very good agreement with numerical simulations. Our theoretical approach is based on the analysis of the growth of the branches in the search tree under the operation of DPLL. On each branch, the initial 3-SAT problem is dynamically turned into a more generic 2+p-SAT problem, where p and 1 - p are the fractions of constraints involving three and two variables respectively. The growth of each branch is monitored by the dynamical evolution of alpha and p and is represented by a trajectory in the static phase diagram of the random 2+p-SAT problem. Depending on whether or not the trajectories cross the boundary between satisfiable and unsatisfiable phases, single branches or full trees are generated by DPLL, resulting in easy or hard resolutions. Our picture for the origin of complexity can be applied to other computational problems solved by branch and bound algorithms.

关键词： Computational methods in statistical physics and nonlinear dynamics Thermodynamics computer science and technology

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Stochastic dynamics of adaptive evolutionary search - A study on population-based incremental learning

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EUROPEAN PHYSICAL JOURNAL B 2001年第1期21卷 145-152页

作者： Galic, E Univ Wuerzburg Inst Phys D-97074 Wuerzburg Germany

In this paper the stochastic dynamics of adaptive evolutionary search, as performed by the optimization algorithm Population-Based Incremental Learning, is analyzed with physicists' methods for stochastic processes. The master equation of the process is approximated by van Kampen's small fluctuations assumption. It results in an elegant formalism which allows for an understanding of the macroscopic behaviour of the algorithm together with its fluctuations. We consider the search process to be adaptive since the algorithm iteratively reduces its mutation rate while approaching an optimum. On the one hand, it is this feature which allows the algorithm to quickly converge towards an optimum. On the other hand it results in the possibility to get trapped by a local optimum only. To arrive at a detailed understanding we discuss the influence of fluctuations, as caused by mutation, on this behaviour. Wie study the algorithm for rather small sytem sizes in order to gain an intuitive understanding of the algorithm's performance.

关键词： computer science and technology Dynamics of evolution Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

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Monte Carlo validation in diagnostic radiological imaging

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MEDICAL PHYSICS 2000年第6期27卷 1294-1304页

作者： Boone, JM Buonocore, MH Cooper, VN Univ Calif Davis Dept Radiol Sacramento CA 95817 USA

Monte Carlo analysis in the radiological sciences has been used for several decades, however with the ever-increasing power of desktop computers, the utility of Monte Carlo simulation is increasing. A Monte Carlo code called the Simple Investigative Environment for Radiological Research Applications (SIERRA) is described mathematically, and is then compared against an array of published and unpublished results determined by other means. A series of 32 comparisons between data sets, 22 from independent Monte Carlo simulations and 10 from physically measured data, were assessed. The compared parameters included depth dose curves, lateral energy scattering profiles, scatter to primary ratios, normalized glandular doses, angular scattering distributions, and computed tomography dose index (CTDI) values. Three of the 32 comparison data sets were excluded as they were identified as outliers. Of the remaining 29 data sets compared, the mean differences ranged from - 14.8% to + 17.2%, and the average of the mean differences was 0.12% (sigma=1.64%), and the median difference was 1.57%. Fifty percent of the comparisons showed mean differences of similar to 5% or less, and 93% of the comparisons showed mean differences of 12% or less. We conclude that for research applications in diagnostic radiology, the SIERRA Monte Carlo code demonstrates accuracy and precision to well within acceptable levels. (C) 2000 American Association of Physicists in Medicine. [S0094-2405(00)01506-6].

关键词： Computed radiography General statistical methods Monte Carlo methods dosimetry computerised tomography X-ray scattering Monte Carlo methods Dosimetry Data sets Physicists computer simulation computer science and technology Medical diagnosis Medical imaging Image analysis

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On-chip clock technology for ultrafast digital superconducting electronics

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APPLIED PHYSICS LETTERS 2000年第25期76卷 3819-3821页

作者： Gupta, D Zhang, YM Hypres Inc Elmsford NY 10523 USA Conductus Inc Sunnyvale CA 94086 USA

An on-chip, low-jitter clock technology is essential for future multi-GHz digital electronics. In this article, we describe an on-chip clock technology for superconducting rapid single flux quantum (RSFQ) circuits built around an unshunted long Josephson junction (LJJ) oscillator that acts as a master clock source. The clock technology also includes clock frequency divider and selector circuits as well as a clock distribution network. These LJJ oscillators, implemented in linear and annular geometries using 3 mu m Nb technology, have quality factors of 10(6). This clock technology potentially has widespread use in 10-100 GHz superconducting digital circuits and systems, including analog-to-digital converters, time-to-digital converters, correlators, and processors for ultrahigh performance computers. (C) 2000 American Institute of Physics. [S0003-6951(00)04325-4].

关键词： Clocks Superconductivity Ultrafast technology computer science and technology Oscillators

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Collective intelligence for control of distributed dynamical systems

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EUROPHYSICS LETTERS 2000年第6期49卷 708-714页

作者： Wolpert, DH Wheeler, KR Tumer, K NASA Ames Res Ctr Moffett Field CA 94035 USA

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, The American Economic Review, 84 (1994) 406;D. Challet and Y. C. Zhang, Physica A, 256 (1998) 514). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not "work at;cross purposes", in that, their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local fi ee energy functions. We show that;a system designed with that theory performs nearly optimally for the bar problem.

关键词： Neural networks, fuzzy logic, artificial intelligence computer science and technology Other topics of general interest to physicists

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A STUDY OF QUALITY OF BREMSSTRAHLUNG SPECTRA RECONSTRUCTED FROM TRANSMISSION MEASUREMENTS

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MEDICAL PHYSICS 1990年第2期17卷 227-233页

作者： PIERMATTEI, A ARCOVITO, G AZARIO, L BACCI, C BIANCIARDI, L DESAPIO, E GIACCO, C UNIV ROME LA SAPIENZA DEPARTIMENTO FIS I-00185 ROME ITALY UNIV ROME LA SAPIENZA IST RADIOL I-00185 ROME ITALY IST NAZL TUMORI ROME ITALY OSPED SAN CAMILLO LELLIS ROME ITALY

A numerical method for the reconstruction of bremsstrahlung spectra has been applied to the analysis of simulated data. The method is found to be reliable in reconstructing x-ray spectra of maximum energy up to 10 MeV. Measurements of aluminum transmission data carried out for five linear accelerators have also been analyzed by this method to determine the fractional energy fluence. The values of the Spencer-Attix water/air stopping power ratio, SW,airS.A., reported as a function of the ratios TPR1020, are in good agreement with computed results. Quality index values were correlated to mean incident energies of x-ray beams used in radiotherapy. The experimental setup has also provided information regarding the softening effect on the off-axis beam, which can be used in clinical computer dosimetry to correct conventional zero field size tissue maximum ratio.

关键词： x-ray spectrum, attenuation analysis, dosimetry, quality indexes Dosimetry/exposure assessment PHOTON BEAMS BREMSSTRAHLUNG MEV RANGE 01−10 RADIOTHERAPY LINEAR ACCELERATORS RADIATION QUALITY NUMERICAL ANALYSIS ATTENUATION X−RAY DOSIMETRY Data analysis Transmission measurement Aluminium computer science and technology Linear accelerators Numerical analysis Spectrum analysis Collisional energy loss Water vapor Radiation therapy

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A VIDEO-BASED PATIENT CONTOUR ACQUISITION-SYSTEM FOR THE DESIGN OF RADIOTHERAPY COMPENSATORS

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MEDICAL PHYSICS 1989年第3期16卷 425-430页

作者： ANDREW, JW ALDRICH, JE HALE, ME BERRY, JA CANC TREATMENT & RES FDN NOVA SCOTIA DEPT MED PHYS 5820 UNIV AVE HALIFAX B3H 1V7 NS CANADA DALHOUSIE UNIV DEPT RADIAT ONCOL HALIFAX B3H 1V7 NS CANADA

Recent advances in computer and video technology have enabled significant advances in the field of surface topography measurement. This paper will describe a digital video patient contour acquisition system for the design of radiotherapy beam compensators. The system is mounted on a tray which slides into the collimator of a radiotherapy simulator. The tray holds a source which projects a 1-mm wide fan beam of light along the simulator beam axis onto the patient. The tray also holds a small solid state video camera which views the projected line of light on the patient surface. Video images are digitized and processed on an 80386 based IBM PC-compatible computer. Transverse contours are obtained from one digitized video image or, in case of opposed fields, from two or more image frames taken at different gantry angles. Entire surfaces are measured by scanning the bed longitudinally and acquiring a number of transverse contours. Posterior surfaces are obtained by scanning a mold. A printer produces a template for making the compensator from sheet lead.

关键词： Therapeutic applications, including brachytherapy Optimization Monte Carlo methods RADIOTHERAPY VIDEO TECHNIQUES CONTOURS TOPOGRAPHY DIGITAL SYSTEMS DESIGN BEAM PROFILES PATIENTS 87.53.10.f 87.54.2 Medical imaging computer simulation Surface measurements Radiation therapy computer science and technology Topography computer systems Collimators Radiotherapy compensators Radiotherapy sources

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RADIATION-THERAPY AND CLINICAL PHYSICS PRACTICES IN THE MIDWEST (1982-1986)

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MEDICAL PHYSICS 1989年第4期16卷 648-652页

作者： DEWERD, LA LIGHT, MC LISS, MM MESINA, CF MIDWEST CTR RADIOL PHYS 1530 MED SCI CTR MADISON WI 53706 USA

As a part of an on-site physics review procedure, the Midwest Center for Radiological Physics (MWCRP) interviewed midwest clinical radiotherapy physicists and radiation therapists in institutions that participated in federally funded Cancer Control Programs. Information from 77 institutions was complied regarding types of megavoltage units, daily patient load, radiotherapy personnel, treatment planning responsibilities, dosimetric practices, and treatment planning computers. Even though some practices, such as frequency of patient charge checks, were consistent throughout the midwest, other practices varied considerably such as patient load with the number of megavoltage units. This information may be useful eigher for planning a new facility, considering the needs for staff, or for comparing existing practices and responsibilities.

关键词： Biomedical instrumentation and transducers, including micro-electro-mechanical systems (MEMS) Medical imaging Biomedical imaging USA RADIOTHERAPY WISCONSIN MEDICAL PERSONNEL RADIOLOGICAL PERSONNEL REVIEWS MONITORING LINEAR ACCELERATORS DOSIMETRY HOSPITALS 87.53 Radiation therapy Medical treatment planning Physicists Cancer computer science and technology Dosimetry Medical radiation safety Radiation monitoring

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