The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Confidentiality and public protection: ethical dilemmas in qualitative research with adult male sex offenders

This paper considers the ethical tensions present when engaging in in-depth interviews with convicted sex offenders. Many of the issues described below are similar to those found in other sensitive areas of research. However, confidentiality and public protection are matters that require detailed consideration when the desire to know more about men who have committed serious and harmful offences is set against the possibility of a researcher not disclosing previously unknown sensitive information that relates to the risk of someone being harmed.</p

Phase separation transition in liquids and polymers induced by electric field gradients

Spatially uniform electric fields have been used to induce instabilities in liquids and polymers, and to orient and deform ordered phases of block-copolymers. Here we discuss the demixing phase transition occurring in liquid mixtures when they are subject to spatially nonuniform fields. Above the critical value of potential, a phase-separation transition occurs, and two coexisting phases appear separated by a sharp interface. Analytical and numerical composition profiles are given, and the interface location as a function of charge or voltage is found. The possible influence of demixing on the stability of suspensions and on inter-colloid interaction is discussed.Comment: 7 pages, 3 figures. Special issue of the J. Phys. Soc. Ja

Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random-copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales, and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and simulation results to appear in J Phys

Action research and democracy

This contribution explores the relationship between research and learning democracy. Action research is seen as being compatible with the orientation of educational and social work research towards social justice and democracy. Nevertheless, the history of action research is characterized by a tension between democracy and social engineering. In the social-engineering approach, action research is conceptualized as a process of innovation aimed at a specific Bildungsideal. In a democratic approach action research is seen as research based on cooperation between research and practice. However, the notion of democratic action research as opposed to social engineering action research needs to be theorized. So called democratic action research involving the implementation by the researcher of democracy as a model and as a preset goal, reduces cooperation and participation into instruments to reach this goal, and becomes a type of social engineering in itself. We argue that the relationship between action research and democracy is in the acknowledgment of the political dimension of participation: ‘a democratic relationship in which both sides exercise power and shared control over decision-making as well as interpretation’. This implies an open research design and methodology able to understand democracy as a learning process and an ongoing experiment

Novel regulators of PrPC biosynthesis revealed by genome-wide RNA interference

The cellular prion protein PrPC is necessary for prion replication, and its reduction greatly increases life expectancy in animal models of prion infection. Hence the factors controlling the levels of PrPC may represent therapeutic targets against human prion diseases. Here we performed an arrayed whole-transcriptome RNA interference screen to identify modulators of PrPC expression. We cultured human U251-MG glioblastoma cells in the presence of 64'752 unique siRNAs targeting 21'584 annotated human genes, and measured PrPC using a one-pot fluorescence-resonance energy transfer immunoassay in 51'128 individual microplate wells. This screen yielded 743 candidate regulators of PrPC. When downregulated, 563 of these candidates reduced and 180 enhanced PrPC expression. Recursive candidate attrition through multiple secondary screens yielded 54 novel regulators of PrPC, 9 of which were confirmed by CRISPR interference as robust regulators of PrPC biosynthesis and degradation. The phenotypes of 6 of the 9 candidates were inverted in response to transcriptional activation using CRISPRa. The RNA-binding post-transcriptional repressor Pumilio-1 was identified as a potent limiter of PrPC expression through the degradation of PRNP mRNA. Because of its hypothesis-free design, this comprehensive genetic-perturbation screen delivers an unbiased landscape of the genes regulating PrPC levels in cells, most of which were unanticipated, and some of which may be amenable to pharmacological targeting in the context of antiprion therapies

A mathematical model of a criminal-prone society

Criminals are common to all societies. To fight against them the community takes different security measures as, for example, to bring about a police. Thus, crime causes a depletion of the common wealth not only by criminal acts but also because the cost of hiring a police force. In this paper, we present a mathematical model of a criminal-prone self-protected society that is divided into socio-economical classes. We study the effect of a non-null crime rate on a free-of-criminals society which is taken as a reference system. As a consequence, we define a criminal-prone society as one whose free-of-criminals steady state is unstable under small perturbations of a certain socio-economical context. Finally, we compare two alternative strategies to control crime: (i) enhancing police efficiency, either by enlarging its size or by updating its technology, against (ii) either reducing criminal appealing or promoting social classes at ris