Mathematics: Is God Silent? (Book Review)

Reviewed Title: Mathematics: Is God Silent? by James Nickel (Ross House Books, Vallecito, CA) 1990. xi + 126 pages

The Projective Line Over the Finite Quotient Ring GF(2)[xx]/<x3−x>< x^{3} - x> and Quantum Entanglement I. Theoretical Background

The paper deals with the projective line over the finite factor ring $R\_{\clubsuit} \equiv$ GF(2)[$x$]/$$. The line is endowed with 18 points, spanning the neighbourhoods of three pairwise distant points. As $R\_{\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is not an equivalence relation so that the sets of neighbour points to two distant points overlap. There are nine neighbour points to any point of the line, forming three disjoint families under the reduction modulo either of two maximal ideals of the ring. Two of the families contain four points each and they swap their roles when switching from one ideal to the other; the points of the one family merge with (the image of) the point in question, while the points of the other family go in pairs into the remaining two points of the associated ordinary projective line of order two. The single point of the remaining family is sent to the reference point under both the mappings and its existence stems from a non-trivial character of the Jacobson radical, ${\cal J}\_{\clubsuit}$, of the ring. The factor ring $\widetilde{R}\_{\clubsuit} \equiv R\_{\clubsuit}/ {\cal J}\_{\clubsuit}$ is isomorphic to GF(2) $\otimes$ GF(2). The projective line over $\widetilde{R}\_{\clubsuit}$ features nine points, each of them being surrounded by four neighbour and the same number of distant points, and any two distant points share two neighbours. These remarkable ring geometries are surmised to be of relevance for modelling entangled qubit states, to be discussed in detail in Part II of the paper.Comment: 8 pages, 2 figure

Transforum system innovation towards sustainable food. A review

Innovations in the agri-food sector are needed to create a sustainable food supply. Sustainable food supply requires unexpectedly that densely populated regions remain food producers. A Dutch innovation program has aimed at showing the way forward through creating a number of practice and scientific projects. Generic lessons from the scientific projects in this program are likely to be of interest to agricultural innovation in other densely populated regions in the world. Based on the executed scientific projects, generic lessons across the whole innovation program are derived. We found that the agricultural sector requires evolutionary rather than revolutionary changes to reshaping institutions. Measuring sustainability is possible against benchmarks and requires stakeholder agreement on sustainability values. Results show the importance of multiple social views and multiple stakeholder involvement in agricultural innovation. Findings call for flexible goal rather than process-oriented management of innovation. Findings also emphasise the essential role of profit in anchoring sustainable development in business. The results agree with concepts of evolutionary innovation. We conclude that there is no single best solution to making the agri-food sector more sustainable densely populated areas, but that the combination of a range of solutions and approaches is likely to provide the best way forward

Recente ontwikkelingen in de technische microbiologie

Rede Landbouwhogeschool Wageningen 196

Hidden Markov Models of Evidence Accumulation in Speeded Decision Tasks

Speeded decision tasks are usually modeled within the evidence accumulation framework, enabling inferences on latent cognitive parameters, and capturing dependencies between the observed response times and accuracy. An example is the speed-accuracy trade-off, where people sacrifice speed for accuracy (or vice versa). Different views on this phenomenon lead to the idea that participants may not be able to control this trade-off on a continuum, but rather switch between distinct states (Dutilh, et al., 2010).Hidden Markov models are used to account for switching between distinct states. However, combining evidence accumulation models with a hidden Markov structure is a challenging problem, as evidence accumulation models typically come with identification and computational issues that make them challenging on their own. Thus, hidden Markov models have not used the evidence accumulation framework, giving up on the inference on the latent cognitive parameters, or capturing potential dependencies between response times and accuracy within the states.This article presents a model that uses an evidence accumulation model as part of a hidden Markov structure. This model is considered as a proof of principle that evidence accumulation models can be combined with Markov switching models. As such, the article considers a very simple case of a simplified Linear Ballistic Accumulation. An extensive simulation study was conducted to validate the model's implementation according to principles of robust Bayesian workflow. Example reanalysis of data from Dutilh, et al. (2010) demonstrates the application of the new model. The article concludes with limitations and future extensions or alternatives to the model and its application

Solving ARC visual analogies with neural embeddings and vector arithmetic: A generalized method

Analogical reasoning derives information from known relations and generalizes this information to similar yet unfamiliar situations. One of the first generalized ways in which deep learning models were able to solve verbal analogies was through vector arithmetic of word embeddings, essentially relating words that were mapped to a vector space (e.g., king - man + woman = __?). In comparison, most attempts to solve visual analogies are still predominantly task-specific and less generalizable. This project focuses on visual analogical reasoning and applies the initial generalized mechanism used to solve verbal analogies to the visual realm. Taking the Abstraction and Reasoning Corpus (ARC) as an example to investigate visual analogy solving, we use a variational autoencoder (VAE) to transform ARC items into low-dimensional latent vectors, analogous to the word embeddings used in the verbal approaches. Through simple vector arithmetic, underlying rules of ARC items are discovered and used to solve them. Results indicate that the approach works well on simple items with fewer dimensions (i.e., few colors used, uniform shapes), similar input-to-output examples, and high reconstruction accuracy on the VAE. Predictions on more complex items showed stronger deviations from expected outputs, although, predictions still often approximated parts of the item's rule set. Error patterns indicated that the model works as intended. On the official ARC paradigm, the model achieved a score of 2% (cf. current world record is 21%) and on ConceptARC it scored 8.8%. Although the methodology proposed involves basic dimensionality reduction techniques and standard vector arithmetic, this approach demonstrates promising outcomes on ARC and can easily be generalized to other abstract visual reasoning tasks.Comment: Data and code can be found on https://github.com/foger3/ARC_DeepLearnin

Vermindering stof bij de gedeeltelijk verhoogde strooiselvloer bij kalkoenen

Het beluchten van de gedeeltelijk verhoogde strooiselvloer leidt tot hoge stofconcentraties in de stallucht. In een vergelijkend onderzoek is in een zomerkoppel nagegaan of het omgekeerd beluchten van de strooisellaag (van bovenaf in plaats van onderaf) kan leiden tot lagere stofconcentraties. Het omgekeerd beluchten verliep goed en leidde tot het beoogde resultaat