67 resultados para Automatic theorem proving
Resumo:
There are many published methods available for creating keyphrases for documents. Previous work in the field has shown that in a significant proportion of cases author selected keyphrases are not appropriate for the document they accompany. This requires the use of such automated methods to improve the use of keyphrases. Often the keyphrases are not updated when the focus of a paper changes or include keyphrases that are more classificatory than explanatory. The published methods are all evaluated using different corpora, typically one relevant to their field of study. This not only makes it difficult to incorporate the useful elements of algorithms in future work but also makes comparing the results of each method inefficient and ineffective. This paper describes the work undertaken to compare five methods across a common baseline of six corpora. The methods chosen were term frequency, inverse document frequency, the C-Value, the NC-Value, and a synonym based approach. These methods were compared to evaluate performance and quality of results, and to provide a future benchmark. It is shown that, with the comparison metric used for this study Term Frequency and Inverse Document Frequency were the best algorithms, with the synonym based approach following them. Further work in the area is required to determine an appropriate (or more appropriate) comparison metric.
Resumo:
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. It is shown that this nonequilibrium canonical distribution implies some important results from nonequilibrium thermodynamics, specifically, the fluctuation theorem and the Jarzynski equality. Those results are therefore expected to be more widely applicable, for example, to macroscopic systems.
Resumo:
Flood extents caused by fluvial floods in urban and rural areas may be predicted by hydraulic models. Assimilation may be used to correct the model state and improve the estimates of the model parameters or external forcing. One common observation assimilated is the water level at various points along the modelled reach. Distributed water levels may be estimated indirectly along the flood extents in Synthetic Aperture Radar (SAR) images by intersecting the extents with the floodplain topography. It is necessary to select a subset of levels for assimilation because adjacent levels along the flood extent will be strongly correlated. A method for selecting such a subset automatically and in near real-time is described, which would allow the SAR water levels to be used in a forecasting model. The method first selects candidate waterline points in flooded rural areas having low slope. The waterline levels and positions are corrected for the effects of double reflections between the water surface and emergent vegetation at the flood edge. Waterline points are also selected in flooded urban areas away from radar shadow and layover caused by buildings, with levels similar to those in adjacent rural areas. The resulting points are thinned to reduce spatial autocorrelation using a top-down clustering approach. The method was developed using a TerraSAR-X image from a particular case study involving urban and rural flooding. The waterline points extracted proved to be spatially uncorrelated, with levels reasonably similar to those determined manually from aerial photographs, and in good agreement with those of nearby gauges.
Resumo:
Straightforward mathematical techniques are used innovatively to form a coherent theoretical system to deal with chemical equilibrium problems. For a systematic theory it is necessary to establish a system to connect different concepts. This paper shows the usefulness and consistence of the system by applications of the theorems introduced previously. Some theorems are shown somewhat unexpectedly to be mathematically correlated and relationships are obtained in a coherent manner. It has been shown that theorem 1 plays an important part in interconnecting most of the theorems. The usefulness of theorem 2 is illustrated by proving it to be consistent with theorem 3. A set of uniform mathematical expressions are associated with theorem 3. A variety of mathematical techniques based on theorems 1–3 are shown to establish the direction of equilibrium shift. The equilibrium properties expressed in initial and equilibrium conditions are shown to be connected via theorem 5. Theorem 6 is connected with theorem 4 through the mathematical representation of theorem 1.
Resumo:
This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.
Resumo:
Keyphrases are added to documents to help identify the areas of interest they contain. However, in a significant proportion of papers author selected keyphrases are not appropriate for the document they accompany: for instance, they can be classificatory rather than explanatory, or they are not updated when the focus of the paper changes. As such, automated methods for improving the use of keyphrases are needed, and various methods have been published. However, each method was evaluated using a different corpus, typically one relevant to the field of study of the method’s authors. This not only makes it difficult to incorporate the useful elements of algorithms in future work, but also makes comparing the results of each method inefficient and ineffective. This paper describes the work undertaken to compare five methods across a common baseline of corpora. The methods chosen were Term Frequency, Inverse Document Frequency, the C-Value, the NC-Value, and a Synonym based approach. These methods were analysed to evaluate performance and quality of results, and to provide a future benchmark. It is shown that Term Frequency and Inverse Document Frequency were the best algorithms, with the Synonym approach following them. Following these findings, a study was undertaken into the value of using human evaluators to judge the outputs. The Synonym method was compared to the original author keyphrases of the Reuters’ News Corpus. The findings show that authors of Reuters’ news articles provide good keyphrases but that more often than not they do not provide any keyphrases.
Resumo:
The ability to create accurate geometric models of neuronal morphology is important for understanding the role of shape in information processing. Despite a significant amount of research on automating neuron reconstructions from image stacks obtained via microscopy, in practice most data are still collected manually. This paper describes Neuromantic, an open source system for three dimensional digital tracing of neurites. Neuromantic reconstructions are comparable in quality to those of existing commercial and freeware systems while balancing speed and accuracy of manual reconstruction. The combination of semi-automatic tracing, intuitive editing, and ability of visualizing large image stacks on standard computing platforms provides a versatile tool that can help address the reconstructions availability bottleneck. Practical considerations for reducing the computational time and space requirements of the extended algorithm are also discussed.
Resumo:
Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.
Resumo:
Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.
Resumo:
Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted
Resumo:
Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature. We also demonstrate advantages over two alternative methods of simulation-based inference.