Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe

A thermodynamic adsorption/entrapment model for selenium(IV) coprecipitation with calcite

Selenium is an environmentally relevant trace element, while the radioisotope 79Se is of particular concern in the context of nuclear waste disposal safety. Oxidized selenium species are relatively soluble and show only weak adsorption at common mineral surfaces. However, a possible sorption mechanism for selenium in the geosphere is the structural incorporation of selenium(IV) (selenite, SeO3 2) into calcite (CaCO3). In this study we investigate the interactions between selenite and calcite by a series of experimental and computational methods with the aim to quantify selenite incorporation into calcite at standard conditions. We further seek to describe the thermodynamics of selenite-doped calcite, and selenite coprecipitation with calcite. The structure of the incorporated species is investigated using Se K-edge EXAFS (isotropic and polarization dependent) and results are compared to density functional theory (DFT) calculations. These investigations confirm structural incorporation of selenite into calcite by the substitution of carbonate for selenite, leading to the formation of a Ca(SeO3)X(CO3)(1-X)solid solution.Coprecipitation experiments at low supersaturation indicate a linear increase of the selenite to carbonate ratio in the solid with the increase of the selenite to carbonate ratio in the contact solution. This relationship can be described under the assumption of an ideal mixing between calcite and a virtual CaSeO3 endmember, whose standard Gibbs free energy (G0(CaSeO3_exp) = 953 ± 6 kJ/mol, log10(KSP(CaSeO3_exp)) = 6.7 ± 1.0) is defined by linear extrapolation of the excess free energy from the dilute Henry’s law domain to X(CaSeO3) = 1. In contrast to this experimental result, DFT and force field calculations predict the virtual bulk CaSeO3 endmember to be significantly less stable and more soluble: G0(CaSeO3 bulk) = 912 ± 10 kJ/mol and log10(KSP(CaSeO3_bulk)) = 0.5 ± 1.7. To explain this discrepancy we introduce a thermodynamic adsorption/entrapment concept. This concept is based on the idea that the experimental value of 953 ± 6 kJ/mol reflects the Gibbs free energy of CaSeO3 within the surface layer, while the value obtained from atomistic calculations reflects bulk thermodynamic properties. In coprecipitation experiments performed at steady-state conditions the difference between these values is compensated by the supersaturation. Thus, if the Gibbs free energies of the bulk CaCO3 and CaSeO3 endmembers are substituted with the Gibbs free energies of the surface endmembers, the coprecipitation experiment can still be treated within the formalism of equilibrium thermodynamics. This concept leads to a number of important consequences, which can be tested both experimentally and theoretically.We show that selenite adsorption at the calcite surface and selenite coprecipitation with calcite under supersaturated conditions can be described with the same partition coefficient. This implies that the coprecipitation can be viewed as a sequence of adsorption and entrapment events. On the other hand, our aragonite recrystallization experiments show that at near equilibrium conditions the calcite growth is inhibited in the presence of selenite. Consistent with these observations, our DFT calculations show that the substitution of carbonate for selenite is energetically more favorable at the surface than inside the bulk. The whole set of the experimental and atomistic simulation results leads to the conclusion that the calcite–CaSeO3 solid solution can only grow continuously if the aqueous solution is supersaturated with respect to the bulk solid solution. Under these conditions selenite coprecipitates with calcite at a partition coefficient of D = 0.02 ± 0.01. If the solution is undersaturated with respect to the bulk solid solution, only surface ion-exchange occurs. Elevated selenite concentrations in bulk calcite therefore reflect non-equilibrium conditions

Gamma and pulsed electron radiolysis studies of CyMe4BTBP and CyMe4BTPhen: Identification of radiolysis products and effects on the hydrometallurgical separation of trivalent actinides and lanthanides

The radiolytic stability of the highly selective ligands CyMe4BTBP and CyMe4BTPhen against ionizing gamma radiation was studied in 1-octanol solution. CyMe4BTBP and CyMe4BTPhen are important extractants for a potential treatment of used nuclear fuel. They were studied under identical experimental conditions to directly compare the effects of gamma and pulsed electron radiolysis on the ligands and systematically study the influence of structural changes in the ligand backbone. Distribution ratios of Am3+, Cm3+ and Eu3+, the residual concentration of CyMe4BTBP and CyMe4BTPhen in solution, and the formation of radiolysis products were studied as a function of absorbed gamma dose and presence of an acidic aqueous phase during irradiation. Quantitative and semi-quantitative analyses were used to elucidate the radiolysis mechanism for both ligands. Addition products of alpha-hydroxyoctyl radicals formed through radiolysis of the 1-octanol diluent to the ligand molecules were identified as the predominant radiolysis products. These addition products also extract trivalent metal ions, as distribution ratios remained high although the parent molecule concentrations decreased. Therefore, the utilization time of a solvent using these extractants under the harsh conditions of used nuclear fuel treatment could be considerably longer than expected. Understanding the radiolysis mechanism is crucial for designing more radiation resistant extractants

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters

Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$\lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B,$$ with $A$ and $B$ satisfying $A > -1$, $B>-1$, $A+B < -1$. The asymptotic analysis is based on the non-Hermitian orthogonality of these polynomials, and uses the Deift/Zhou steepest descent analysis for matrix Riemann-Hilbert problems. As a corollary, asymptotic zero behavior is derived. We show that in a generic case the zeros distribute on the set of critical trajectories $\Gamma$ of a certain quadratic differential according to the equilibrium measure on $\Gamma$ in an external field. However, when either $\alpha_n$, $\beta_n$ or $\alpha_n+\beta_n$ are geometrically close to $\Z$, part of the zeros accumulate along a different trajectory of the same quadratic differential.Comment: 31 pages, 12 figures. Some references added. To appear in Journal D'Analyse Mathematiqu

Motor expertise modulates the unconscious processing of human body postures

Little is known about the cognitive background of unconscious visuomotor control of complex sports movements. Therefore, we investigated the extent to which novices and skilled high-jump athletes are able to identify visually presented body postures of the high jump unconsciously. We also asked whether or not the manner of processing differs (qualitatively or quantitatively) between these groups as a function of their motor expertise. A priming experiment with not consciously perceivable stimuli was designed to determine whether subliminal priming of movement phases (same vs. different movement phases) or temporal order (i.e. natural vs. reversed movement order) affects target processing. Participants had to decide which phase of the high jump (approach vs. flight phase) a target photograph was taken from. We found a main effect of temporal order for skilled athletes, that is, faster reaction times for prime-target pairs that reflected the natural movement order as opposed to the reversed movement order. This result indicates that temporal-order information pertaining to the domain of expertise plays a critical role in athletes’ perceptual capacities. For novices, data analyses revealed an interaction between temporal order and movement phases. That is, only the reversed movement order of flight-approach pictures increased processing time. Taken together, the results suggest that the structure of cognitive movement representation modulates unconscious processing of movement pictures and points to a functional role of motor representations in visual perception

Retention and diffusion of radioactive and toxic species on cementitious systems: Main outcome of the CEBAMA project

Cement-based materials are key components in radioactive waste repository barrier systems. To improve the available knowledge base, the European CEBAMA (Cement-based materials) project aimed to provide insight on general processes and phenomena that can be easily transferred to different applications. A bottom up approach was used to study radionuclide retention by cementitious materials, encompassing both individual cement mineral phases and hardened cement pastes. Solubility experiments were conducted with Be, Mo and Se under high pH conditions to provide realistic solubility limits and radionuclide speciation schemes as a prerequisite for meaningful adsorption studies. A number of retention mechanisms were addressed including adsorption, solid solution formation and precipitation of radionuclides within new solid phases formed during cement hydration and evolution. Sorption/desorption experiments were carried out on several anionic radionuclides and/or toxic elements which have received less attention to date, namely: Be, Mo, Tc, I, Se, Cl, Ra and 14C. Solid solution formation between radionuclides in a range of oxidation states (Se, I and Mo) with the main aqueous components (OH−, SO4 −2, Cl−) of cementitious systems on AFm phases were also investigated

Cognitive loading affects motor awareness and movement kinematics but not locomotor trajectories during goal-directed walking in a virtual reality environment.

The primary purpose of this study was to investigate the effects of cognitive loading on movement kinematics and trajectory formation during goal-directed walking in a virtual reality (VR) environment. The secondary objective was to measure how participants corrected their trajectories for perturbed feedback and how participants' awareness of such perturbations changed under cognitive loading. We asked 14 healthy young adults to walk towards four different target locations in a VR environment while their movements were tracked and played back in real-time on a large projection screen. In 75% of all trials we introduced angular deviations of ±5° to ±30° between the veridical walking trajectory and the visual feedback. Participants performed a second experimental block under cognitive load (serial-7 subtraction, counter-balanced across participants). We measured walking kinematics (joint-angles, velocity profiles) and motor performance (end-point-compensation, trajectory-deviations). Motor awareness was determined by asking participants to rate the veracity of the feedback after every trial. In-line with previous findings in natural settings, participants displayed stereotypical walking trajectories in a VR environment. Our results extend these findings as they demonstrate that taxing cognitive resources did not affect trajectory formation and deviations although it interfered with the participants' movement kinematics, in particular walking velocity. Additionally, we report that motor awareness was selectively impaired by the secondary task in trials with high perceptual uncertainty. Compared with data on eye and arm movements our findings lend support to the hypothesis that the central nervous system (CNS) uses common mechanisms to govern goal-directed movements, including locomotion. We discuss our results with respect to the use of VR methods in gait control and rehabilitation

Emotional facial activation induced by unconsciously perceived dynamic facial expressions

Do facial expressions of emotion influence us when not consciously perceived? Methods to investigate this question have typically relied on brief presentation of static images. In contrast, real facial expressions are dynamic and unfold over several seconds. Recent studies demonstrate that gaze contingent crowding (GCC) can block awareness of dynamic expressions while still inducing behavioural priming effects. The current experiment tested for the first time whether dynamic facial expressions presented using this method can induce unconscious facial activation. Videos of dynamic happy and angry expressions were presented outside participants' conscious awareness while EMG measurements captured activation of the zygomaticus major (active when smiling) and the corrugator supercilii (active when frowning). Forced-choice classification of expressions confirmed they were not consciously perceived, while EMG revealed significant differential activation of facial muscles consistent with the expressions presented. This successful demonstration opens new avenues for research examining the unconscious emotional influences of facial expressions

Visuo-tactile integration in autism: atypical temporal binding may underlie greater reliance on proprioceptive information

BackgroundEvidence indicates that social functioning deficits and sensory sensitivities in autism spectrum disorder (ASD) are related to atypical sensory integration. The exact mechanisms underlying these integration difficulties are unknown; however, two leading accounts are (1) an over-reliance on proprioception and (2) atypical visuo-tactile temporal binding. We directly tested these theories by selectively manipulating proprioceptive alignment and visuo-tactile synchrony to assess the extent that these impact upon body ownership.MethodsChildren with ASD and typically developing controls placed their hand into a multisensory illusion apparatus, which presented two, identical live video images of their own hand in the same plane as their actual hand. One virtual hand was aligned proprioceptively with the actual hand (the veridical hand), and the other was displaced to the left or right. While a brushstroke was applied to the participants’ actual (hidden) hand, they observed the two virtual images of their hand also being stroked and were asked to identify their real hand. During brushing, one of three different temporal delays was applied to either the displaced hand or the veridical hand. Thus, only one virtual hand had synchronous visuo-tactile inputs.ResultsResults showed that visuo-tactile synchrony overrides incongruent proprioceptive inputs in typically developing children but not in autistic children. Evidence for both temporally extended visuo-tactile binding and a greater reliance on proprioception are discussed.ConclusionsThis is the first study to provide definitive evidence for temporally extended visuo-tactile binding in ASD. This may result in reduced processing of amodal inputs (i.e. temporal synchrony) over modal-specific information (i.e. proprioception). This would likely lead to failures in appropriately binding information from related events, which would impact upon sensitivity to sensory stimuli, body representation and social processes such as empathy and imitation

The impact of the Great Exhibition of 1851 on the development of technical education during the second half of the nineteenth century

This paper examines the contribution made by the mechanics’ institute movement in Britain just prior to, and following, the opening of the Great Exhibition of 1851 in London. It argues that far from making little contribution to education, as often portrayed by historians, the movement was ideally positioned to respond to the findings of the Exhibition, which were that foreign goods on display were often more advanced than those produced in Britain. The paper highlights, through a regional study, how well suited mechanics’ institutes were in organising their own exhibitions, providing the idea of this first international exhibition. Subsequently, many offered nationally recognised technical subject examinations through relevant education as well as informing government commissions, prior to the passing of the Technical Instruction Acts in 1889 and the Local Taxation Act of 1890. These acts effectively put mechanics’ institutes into state ownership as the first step in developing further education for all in Britai