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

Photonic band structure of highly deformable, self-assembling systems

We calculate the photonic band structure at normal incidence of highly deformable, self-assembling systems - cholesteric elastomers subjected to external stress. Cholesterics display brilliant reflection and lasing owing to gaps in their photonic band structure. The band structure of cholesteric elastomers varies sensitively with strain, showing new gaps opening up and shifting in frequency. A novel prediction of a total band gap is made, and is expected to occur in the vicinity of the previously observed de Vries bandgap, which is only for one polarisation

Bubble Formation in Additive Manufacturing of Borosilicate Glass

Entrapped bubbles are an important problem in conventional glass manufacturing. It is also a significant factor determining the quality of glass products produced using additive manufacturing (AM). This paper reports on the bubble formation and entrapment in filament-fed AM printing of borosilicate glass. This process involves maintaining a local molten region using a CO2 laser. A 2 mm filament is fed continuously into the molten region while CNC stages position the workpiece relative to the laser and filament feed. Two different bubble regimes are identified in experiments with borosilicate glass. These regimes can be related to different physical phenomena, specifically, bubble entrapment at defects in the filaments and bubble formation due to reboil. These can be overcome by selecting defect free filaments and by minimizing the temperature inside the molten region to prevent breaking down the glass. Understanding these mechanisms allows bubble-free glass to be printed. Finally, residual stress in the deposited glass pieces is removed using post-deposition annealing and validated using a polariscope

Additive Manufacturing of Transparent Fused Quartz

This paper investigates a filament-fed process for additive manufacturing (AM) of fused quartz. Glasses such as fused quartz have significant scientific and engineering applications, which include optics, communications, electronics, and hermetic seals. AM has several attractive benefits such as increased design freedom, faster prototyping, and lower processing costs for small production volumes. However, current research into glass AM has focused primarily on nonoptical applications. Fused quartz is studied here because of its desirability for use in high-quality optics due to its high transmissivity and thermal stability. Fused quartz filaments are fed into a CO2 laser-generated molten region, smoothly depositing material onto the workpiece. Spectroscopy and pyrometry are used to measure the thermal radiation incandescently emitted from the molten region. The effects of the laser power and scan speed are determined by measuring the morphology of single tracks. Thin walls are printed to study the effects of layer-to-layer height. This information is used to deposit solid pieces including a cylindrical-convex shape capable of focusing visible light. The transmittance and index homogeneity of the printed fused quartz are measured. These results show that the filament-fed process has the potential to print transmissive optics

Fundamental limits of super-resolution microscopy by dielectric microspheres and microfibers

In recent years, optical super-resolution by microspheres and microfibers emerged as a new paradigm in nanoscale label-free and fluorescence imaging. However, the mechanisms of such imaging are still not completely understood and the resolution values are debated. In this work, the fundamental limits of super-resolution imaging by high-index barium-titanate microspheres and silica microfibers are studied using nanoplasmonic arrays made from Au and Al. A rigorous resolution analysis is developed based on the object's convolution with the point-spread function that has width well below the conventional (∼λ/2) diffraction limit, where λ is the illumination wavelength. A resolution of ∼λ/6-λ/7 is demonstrated for imaging nanoplasmonic arrays by microspheres. Similar resolution was demonstrated for microfibers in the direction perpendicular to the fiber axis with hundreds of times larger field-of-view in comparison to microspheres. Using numerical solution of Maxwell's equations, it is shown that extraordinary close point objects can be resolved in the far field, if they oscillate out of phase. Possible super-resolution using resonant excitation of whispering gallery modes is also studied. Keywords: Optical super-resolution; near-field microscopy; confocal microscop

Two problems related to prescribed curvature measures

Existence of convex body with prescribed generalized curvature measures is discussed, this result is obtained by making use of Guan-Li-Li's innovative techniques. In surprise, that methods has also brought us to promote Ivochkina's $C^2$ estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo

Accessible reasoning with diagrams: From cognition to automation

High-tech systems are ubiquitous and often safety and se- curity critical: reasoning about their correctness is paramount. Thus, precise modelling and formal reasoning are necessary in order to convey knowledge unambiguously and accurately. Whilst mathematical mod- elling adds great rigour, it is opaque to many stakeholders which leads to errors in data handling, delays in product release, for example. This is a major motivation for the development of diagrammatic approaches to formalisation and reasoning about models of knowledge. In this paper, we present an interactive theorem prover, called iCon, for a highly expressive diagrammatic logic that is capable of modelling OWL 2 ontologies and, thus, has practical relevance. Significantly, this work is the first to design diagrammatic inference rules using insights into what humans find accessible. Specifically, we conducted an experiment about relative cognitive benefits of primitive (small step) and derived (big step) inferences, and use the results to guide the implementation of inference rules in iCon

Poly(sulfur-random-(1,3-diisopropenylbenzene)) Based Mid-Wavelength Infrared Polarizer: Optical Property Experimental and Theoretical Analysis

Development of polymer based mid-wavelength infrared (MWIR) optics has been limited mainly due to high optical loss of organic polymers used in general optical components. In this study, a MWIR polarization grating based on a sulfuric polymer poly(sulfur-random-(1,3-diisopropenylbenzene)) with a low loss in the MWIR range was fabricated using a simple two-step process: imprint and metal deposition. Fourier-transform infrared (FTIR) spectroscopy measurement showed that this polymeric MWIR polarizer selectively transmitted the polarized IR in transverse magnetic (TM) mode over the transverse electric (TE) mode at normal incidence. The measured extinction ratios (  = The ratio of transmissions in TM and TE) were 208, 176, and 212 at the wavelength of 3, 4, and 5 μm, respectively. The computational simulation and analytical model confirmed that the enhanced TM transmission efficiency and followed a Fabry-Pérot (FP) resonance mode within the created sulfuric polymer film. This polymeric MWIR polarizer demonstrated a great potential for broader applications in IR photonics to realize low-cost and durable optical components

Self-Assembly of Supramolecular Triblock Copolymer Complexes

Four different poly(tert-butoxystyrene)-b-polystyrene-b-poly(4-vinylpyridine) (PtBOS-b-PS-b-P4VP) linear triblock copolymers, with the P4VP weight fraction varying from 0.08 to 0.39, were synthesized via sequential anionic polymerization. The values of the unknown interaction parameters between styrene and tert-butoxystyrene and between tert-butoxystyrene and 4-vinylpyridine were determined from random copolymer blend miscibility studies and found to satisfy 0.031<χS,tBOS<0.034 and 0.39<χ4VP,tBOS<0.43, the latter being slightly larger than the known 0.30<χS,4VP≤0.35 value range. All triblock copolymers synthesized adopted a P4VP/PS core/shell cylindrical self-assembled morphology. From these four triblock copolymers supramolecular complexes were prepared by hydrogen bonding a stoichiometric amount of pentadecylphenol (PDP) to the P4VP blocks. Three of these complexes formed a triple lamellar ordered state with additional short length scale ordering inside the P4VP(PDP) layers. The self-assembled state of the supramolecular complex based on the triblock copolymer with the largest fraction of P4VP consisted of alternating layers of PtBOS and P4VP(PDP) layers with PS cylinders inside the latter layers. The difference in morphology between the triblock copolymers and the supramolecular complexes is due to two effects: (i) a change in effective composition and, (ii) a reduction in interfacial tension between the PS and P4VP containing domains. The small angle X-ray scattering patterns of the supramolecules systems are very temperature sensitive. A striking feature is the disappearance of the first order scattering peak of the triple lamellar state in certain temperature intervals, while the higher order peaks (including the third order) remain. This is argued to be due to the thermal sensitivity of the hydrogen bonding and thus directly related to the very nature of these systems.