The Complemented System Approach: A Novel Method for Calculating the X-ray Scattering from Computer Simulations

In this paper, we review the main problem concerning the calculation of X-ray scattering of simulated model systems, namely their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue by complementing the missing surroundings of each particle with an average image of the system. The method was designed to operate directly on particle configurations without an intermediate step (e.g., calculation of pair distribution functions): in this way, all information contained in the configurations was preserved. A comparison of the results against those of other known methods showed that the new method combined several favourable properties: an arbitrary q-scale, scattering curves free of truncation artifacts and good behaviour down to the theoretical lower limit of the q-scale. A test of computational efficiency was also performed to establish a relative scale between the speeds of all known methods: the reciprocal lattice approach, the brute force method, the Fourier transform approach and the newly presented complemented system approach.Comment: 6 pages, 5 figures. Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://link.aip.org/link/?jcp/133/17412

Tactical diagrammatic reasoning

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction in the construction of proofs and of providing explanations of solutions expressed in the proofs remain to be addressed. In this paper we take an interactive proof assistant for Euler diagrams, Speedith, and add tactics to its reasoning engine, providing a level of automation in the construction of proofs. By adding tactics to Speedith's repertoire of inferences, we ease the interaction between the user and the system and capture a higher level explanation of the essence of the proof. We analysed the design options for tactics by using metrics which relate to human readability, such as the number of inferences and the amount of clutter present in diagrams. Thus, in contrast to the normal case with sentential tactics, our tactics are designed to not only prove the theorem, but also to support explanation

SEPIA: Search for Proofs Using Inferred Automata

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.Comment: To appear at 25th International Conference on Automated Deductio

The Use of Reddit as an Inexpensive Source for High-Quality Data

Today, researchers have the ability to conduct their investigations in a number of different manners, including both traditional testing using university subject pool participants and the more recent method of online recruitment. Although the use of internet participants is becoming more popular, this area of research is still very much in its infancy and needs further examination. Additionally, alternative web-based platforms need to be investigated because much of the literature has focused on using Amazon.com’s Mechanical Turk (MTurk). Therefore, the current study recruited an internet population using the website Reddit, and compared them to a traditional undergraduate sample to learn more about this web-based platform. The results demonstrated similarities and distinctions between the two samples. Furthermore, previous findings in the psychological well-being literature were replicated. As a whole, the participants recruited from Reddit provided high-quality data that were inexpensive and comparable to the responses gathered using undergraduate participants. We conclude that this website appears to be a promising tool for the field of psychological assessment, research, and evaluation. Accessed 4,072 times on https://pareonline.net from May 30, 2017 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Electrochemistry of Crystalline Mixed Conductors: Concepts and Exampleswith SrTiO3

The electrochemistry of mixed conductors is outlined. In particular the impact of grain boundaries on the transport perpendicular to the grain boundary plane is studied. Fe-doped SrTiO3 bicrystals were used as prototype mixed conductor. Experimental results obtained by optical spectroscopy (chemical diffusion) and electrochemical impedance spectroscopy (electrical transport) are analysed in terms of continuum models. A unified approach based on the use of “chemical capacitors” is briefly explained. For the description of grain boundary, the Schottky model acting on electronic and ionic charge carriers is used

Nonlinear diffusion in two-dimensional ordered porous media based on a free volume theory.

A continuum nonlinear diffusion model is developed to describe molecular transport in ordered porous media. An existing generic van der Waals equation of state based free volume theory of binary diffusion coefficients is modified and introduced into the two-dimensional diffusion equation. The resulting diffusion equation is solved numerically with the alternating-direction fully implicit method under Neumann boundary conditions. Two types of pore structure symmetries are considered, hexagonal and cubic. The former is modeled as parallel channels while in case of the latter equal-sized channels are placed perpendicularly thus creating an interconnected network. First, general features of transport in both systems are explored, followed by the analysis of the impact of molecular properties on diffusion inside and out of the porous matrix. The influence of pore size on the diffusion-controlled release kinetics is assessed and the findings used to comment recent experimental studies of drug release profiles from ordered mesoporous silicates

Exploring and conceptualising attestation

When formalising the rules of trust in the remote attesta- tion of TPM-based computer systems it is paramount that the rules are precisely understood, supporting unambiguous communication of infor- mation about system requirements between engineers. We present a dia- grammatic approach to modelling rules of trust using an extended version of concept diagrams. Within the context of our proof-of-concept Net- work Function Virtualisation and Attestation environment, these rules allow different level of trust to be explored and, importantly, allow us to identify when a computer system should not be trusted. To ensure that the modelling approach can be applied to general systems, we in- clude generic patterns for extending our domain model and rules of trust. Consequently, through the use of a formal, yet accessible, diagrammatic notation, domain experts can define rules of trust for their systems.Leverhulme Trust gran

Mining State-Based Models from Proof Corpora

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201

Investigating diagrammatic reasoning with deep neural networks

Diagrams in mechanised reasoning systems are typically en- coded into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. We present a new method of using Deep artificial Neu- ral Networks (DNN) to learn continuous, vector-form representations of diagrams without any human input, and entirely from datasets of dia- grammatic reasoning problems. Based on this DNN, we developed a novel reasoning system, Euler-Net, to solve syllogisms with Euler diagrams. Euler-Net takes two Euler diagrams representing the premises in a syl- logism as input, and outputs either a categorical (subset, intersection or disjoint) or diagrammatic conclusion (generating an Euler diagram rep- resenting the conclusion) to the syllogism. Euler-Net can achieve 99.5% accuracy for generating syllogism conclusion. We analyse the learned representations of the diagrams, and show that meaningful information can be extracted from such neural representations. We propose that our framework can be applied to other types of diagrams, especially the ones we don’t know how to formalise symbolically. Furthermore, we propose to investigate the relation between our artificial DNN and human neural circuitry when performing diagrammatic reasoning