5,108 research outputs found
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
We consider 3-monopoles symmetric under inversion symmetry. We show that the
moduli space of these monopoles is an Atiyah-Hitchin submanifold of the
3-monopole moduli space. This allows what is known about 2-monopole dynamics to
be translated into results about the dynamics of 3-monopoles. Using a numerical
ADHMN construction we compute the monopole energy density at various points on
two interesting geodesics. The first is a geodesic over the two-dimensional
rounded cone submanifold corresponding to right angle scattering and the second
is a closed geodesic for three orbiting monopoles.Comment: latex, 22 pages, 2 figures. To appear in Nonlinearit
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Study of industrial titania synthesis using a hybrid particle-number and detailed particle model
We apply a hybrid particle model to study synthesis of particulate titania under representative industrial conditions. The hybrid particle model employs a particle-number description for small particles, and resolves complicated particle morphology where required using a detailed particle model. This enables resolution of particle property distributions under fast process dynamics. Robustness is demonstrated in a network of reactors used to simulate the industrial process. The detailed particle model resolves properties of the particles that determine end product quality and post-processing efficiency, including primary particle size and degree of aggregate cohesion. Sensitivity of these properties to process design choices is quantified, showing that higher temperature injections produce more sintered particles; more frequent injections narrow the geometric standard deviation of primary particle diameter; and chlorine dilution reduces particle size and size variance. Structures of a typical industrial particle are compared visually with simulated particles, illustrating similar aggregate features with slightly larger primary particles
Premise Selection and External Provers for HOL4
Learning-assisted automated reasoning has recently gained popularity among
the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an
add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system
that provides machine learning-based premise selection and automated reasoning
also for HOL4. We efficiently record the HOL4 dependencies and extract features
from the theorem statements, which form a basis for premise selection.
HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof
formats, which are then processed by the ATPs. We discuss the different
evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure
the performance of HOLyHammer on the HOL4 standard library. The results are
combined accordingly and compared with the HOL Light experiments, showing a
comparably high quality of predictions. The system directly benefits HOL4 users
by automatically finding proofs dependencies that can be reconstructed by
Metis
Symmetric Instantons and Skyrme Fields
By explicit construction of the ADHM data, we prove the existence of a charge
seven instanton with icosahedral symmetry. By computing the holonomy of this
instanton we obtain a Skyrme field which approximates the minimal energy charge
seven Skyrmion. We also present a one parameter family of tetrahedrally
symmetric instantons whose holonomy gives a family of Skyrme fields which
models a Skyrmion scattering process, where seven well-separated Skyrmions
collide to form the icosahedrally symmetric Skyrmion.Comment: 22 pages plus 1 figure in GIF forma
Prostate involvement during sexually transmitted infections as measured by prostate-specific antigen concentration
Background:We investigated prostate involvement during sexually transmitted infections by measuring serum prostate-specific antigen (PSA) as a marker of prostate infection, inflammation, and/or cell damage in young, male US military members.Methods:We measured PSA before and during infection for 299 chlamydia, 112 gonorrhoea, and 59 non-chlamydial, non-gonococcal urethritis (NCNGU) cases, and 256 controls.Results:Chlamydia and gonorrhoea, but not NCNGU, cases were more likely to have a large rise (â©ľ40%) in PSA than controls (33.6%, 19.1%, and 8.2% vs 8.8%, P<0.0001, 0.021, and 0.92, respectively).Conclusion:Chlamydia and gonorrhoea may infect the prostate of some infected men
Empirically modelled Pc3 activity based on solar wind parameters
It is known that under certain solar wind (SW)/interplanetary magnetic
field (IMF) conditions (e.g. high SW speed, low cone angle) the occurrence of
ground-level Pc3–4 pulsations is more likely. In this paper we demonstrate
that in the event of anomalously low SW particle density, Pc3 activity is
extremely low regardless of otherwise favourable SW speed and cone angle. We
re-investigate the SW control of Pc3 pulsation activity through a statistical
analysis and two empirical models with emphasis on the influence of SW
density on Pc3 activity. We utilise SW and IMF measurements from the OMNI
project and ground-based magnetometer measurements from the MM100 array to
relate SW and IMF measurements to the occurrence of Pc3 activity. Multiple
linear regression and artificial neural network models are used in iterative
processes in order to identify sets of SW-based input parameters, which
optimally reproduce a set of Pc3 activity data. The inclusion of SW density
in the parameter set significantly improves the models. Not only the density
itself, but other density related parameters, such as the dynamic pressure of
the SW, or the standoff distance of the magnetopause work equally well in the
model. The disappearance of Pc3s during low-density events can have at least
four reasons according to the existing upstream wave theory: 1. Pausing the
ion-cyclotron resonance that generates the upstream ultra low frequency waves
in the absence of protons, 2. Weakening of the bow shock that implies less
efficient reflection, 3. The SW becomes sub-Alfvénic and hence it is not
able to sweep back the waves propagating upstream with the Alfvén-speed,
and 4. The increase of the standoff distance of the magnetopause (and of the
bow shock). Although the models cannot account for the lack of Pc3s during
intervals when the SW density is extremely low, the resulting sets of optimal
model inputs support the generation of mid latitude Pc3 activity
predominantly through upstream waves
Empirically modelled Pc3 activity based on solar wind parameters
It is known that under certain solar wind (SW)/interplanetary magnetic field (IMF) conditions (e.g. high SW speed, low cone angle) the occurrence of ground-level Pc3–4 pulsations is more likely. In this paper we demonstrate that in the event of anomalously low SW particle density, Pc3 activity is extremely low regardless of otherwise favourable SW speed and cone angle. We re-investigate the SW control of Pc3 pulsation activity through a statistical analysis and two empirical models with emphasis on the influence of SW density on Pc3 activity. We utilise SW and IMF measurements from the OMNI project and ground-based magnetometer measurements from the MM100 array to relate SW and IMF measurements to the occurrence of Pc3 activity. Multiple linear regression and artificial neural network models are used in iterative processes in order to identify sets of SW-based input parameters, which optimally reproduce a set of Pc3 activity data. The inclusion of SW density in the parameter set significantly improves the models. Not only the density itself, but other density related parameters, such as the dynamic pressure of the SW, or the standoff distance of the magnetopause work equally well in the model. The disappearance of Pc3s during low-density events can have at least four reasons according to the existing upstream wave theory: 1. Pausing the ion-cyclotron resonance that generates the upstream ultra low frequency waves in the absence of protons, 2. Weakening of the bow shock that implies less efficient reflection, 3. The SW becomes sub-Alfvénic and hence it is not able to sweep back the waves propagating upstream with the Alfvén-speed, and 4. The increase of the standoff distance of the magnetopause (and of the bow shock). Although the models cannot account for the lack of Pc3s during intervals when the SW density is extremely low, the resulting sets of optimal model inputs support the generation of mid latitude Pc3 activity predominantly through upstream waves
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