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Register a new userStochastic modeling of a serial killer
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We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of Devils staircase type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis.
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Autocatalytic networks have been used to model the emergence of self-organizing structure capable of sustaining life and undergoing biological evolution. Here, we model the emergence of cognitive structure capable of undergoing cultural evolution. Mental representations of knowledge and experiences play the role of catalytic molecules, and interactions amongst them (e.g., the forging of new associations) play the role of reactions, and result in representational redescription. The approach tags mental representations with their source, i.e., whether they were acquired through social learning, individual learning (of pre-existing information), or creative thought (resulting in the generation of new information). This makes it possible to model how cognitive structure emerges, and to trace lineages of cumulative culture step by step. We develop a formal representation of the cultural transition from Oldowan to Acheulean tool technology using Reflexively Autocatalytifc and Food set generated (RAF) networks. Unlike more primitive Oldowan stone tools, the Acheulean hand axe required not only the capacity to envision and bring into being something that did not yet exist, but hierarchically structured thought and action, and the generation of new mental representations: the concepts EDGING, THINNING, SHAPING, and a meta-concept, HAND AXE. We show how this constituted a key transition towards the emergence of semantic networks that were self-organizing, self-sustaining, and autocatalytic, and discuss how such networks replicated through social interaction. The model provides a promising approach to unraveling one of the greatest anthropological mysteries: that of why development of the Acheulean hand axe was followed by over a million years of cultural stasis.
We discuss statistical issues in cases of serial killer nurses, focussing on the Dutch case of the nurse Lucia de Berk, arrested under suspicion of murder in 2001, convicted to life imprisonment, but declared innocent in 2010; and the case of the English nurse Ben Geen, arrested in 2004, also given a life sentence. At the trial of Ben Geen, a statistical expert was refused permission to present evidence on statistical biases concerning the way suspicious cases were identified by a hospital team of investigators. The judge ruled that the experts written evidence was merely common sense. An application to the CCRC to review the case was turned down, since the application only presented statistical evidence but did not re-address the medical evidence presented at the original trials. This rejection has been successfully challenged in court, and the CCRC has withdrawn it. The paper includes some striking new statistical findings on the Ben Geen case as well as giving advice to statisticians involved in future cases, which are not infrequent. Statisticians need to be warned of the pitfalls which await them.
Recent research has found that select scientists have a disproportional share of highly cited papers. Researchers reasoned that this could not have happened if success in science was random and introduced a hidden parameter Q, or talent, to explain this finding. So, the talented high-Q scientists have many high impact papers. Here I show that an upgrade of an old random citation copying model could also explain this finding. In the new model the probability of citation copying is not the same for all papers but is proportional to the logarithm of the total number of citations to all papers of its author. Numerical simulations of the model give results similar to the empirical findings of the Q-factor article.
The recently proposed generalized epidemic modeling framework (GEMF) cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article builds an algorithm for exact, continuous-time numerical simulation of GEMF-based processes. Moreover the implementation of this algorithm, GEMFsim, is available in popular scientific programming platforms such as MATLAB, R, Python, and C; GEMFsim facilitates simulating stochastic spreading models that fit in GEMF framework. Using these simulations one can examine the accuracy of mean-field-type approximations that are commonly used for analytical study of spreading processes on complex networks.
Computers has been endowed with a part of human-like intelligence owing to the rapid development of the artificial intelligence technology represented by the neural networks. Facing the challenge to make machines more imaginative, we consider a quantum stochastic neural network (QSNN), and propose a learning algorithm to update the parameters governing the network evolution. The QSNN can be applied to a class of classification problems, we investigate its performance in sentence classification and find that the coherent part of the quantum evolution can accelerate training, and improve the accuracy of verses recognition which can be deemed as a quantum enhanced associative memory. In addition, the coherent QSNN is found more robust against both label noise and device noise so that it is a more adaptive option for practical implementation.
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