On the strategy frequency problem in batch Minority Games

Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to calculate these quantities in batch canonical and grand-canonical models. Known analytic theories are easily recovered as limiting cases and, as a further application, the strategy frequency problem for the batch grand-canonical Minority Game with S=2 is solved. The generalization of these ideas to multi-asset models is also presented. Though similarly based on response function techniques, our approach is alternative to the one recently employed by Shayeghi and Coolen for canonical batch Minority Games with arbitrary number of strategies.Comment: 17 page

The differential diagnosis of Huntington's disease-like syndromes: 'red flags' for the clinician

A growing number of progressive heredodegenerative conditions mimic the presentation of Huntington's disease (HD). Differentiating among these HD-like syndromes is necessary when a patient with a combination of movement disorders, cognitive decline, behavioural abnormalities and progressive disease course proves negative to the genetic testing for HD causative mutations, that is, IT15 gene trinucleotide-repeat expansion. The differential diagnosis of HD-like syndromes is complex and may lead to unnecessary and costly investigations. We propose here a guide to this differential diagnosis focusing on a limited number of clinical features (‘red flags’) that can be identified through accurate clinical examination, collection of historical data and a few routine ancillary investigations. These features include the ethnic background of the patient, the involvement of the facio-bucco-lingual and cervical district by the movement disorder, the co-occurrence of cerebellar features and seizures, the presence of peculiar gait patterns and eye movement abnormalities, and an atypical progression of illness. Additional help may derive from the cognitive–behavioural presentation of the patient, as well as by a restricted number of ancillary investigations, mainly MRI and routine blood tests. These red flags should be constantly updated as the phenotypic characterisation and identification of more reliable diagnostic markers for HD-like syndromes progress over the following years

On the transition to efficiency in Minority Games

The existence of a phase transition with diverging susceptibility in batch Minority Games (MGs) is the mark of informationally efficient regimes and is linked to the specifics of the agents' learning rules. Here we study how the standard scenario is affected in a mixed population game in which agents with the `optimal' learning rule (i.e. the one leading to efficiency) coexist with ones whose adaptive dynamics is sub-optimal. Our generic finding is that any non-vanishing intensive fraction of optimal agents guarantees the existence of an efficient phase. Specifically, we calculate the dependence of the critical point on the fraction $q$ of `optimal' agents focusing our analysis on three cases: MGs with market impact correction, grand-canonical MGs and MGs with heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the World through Spin Glasses" in honour of David Sherrington on the occasion of his 65th birthda

Adaptive drivers in a model of urban traffic

We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers' behavioral parameters via numerical simulations and mean-field analytical arguments. We identify a phase transition between a low- and a high-density regime. In the latter, inductive drivers may surprisingly behave worse than randomly selecting drivers.Comment: 7 pages, final versio

Parallel Metropolis chains with cooperative adaptation

Monte Carlo methods, such as Markov chain Monte Carlo (MCMC) algorithms, have become very popular in signal processing over the last years. In this work, we introduce a novel MCMC scheme where parallel MCMC chains interact, adapting cooperatively the parameters of their proposal functions. Furthermore, the novel algorithm distributes the computational effort adaptively, rewarding the chains which are providing better performance and, possibly even stopping other ones. These extinct chains can be reactivated if the algorithm considers necessary. Numerical simulations shows the benefits of the novel scheme

Causal relationships between milk quality and coagulation properties in Italian Holstein-Friesian dairy cattle

Background: Recently, selection for milk technological traits was initiated in the Italian dairy cattle industry based on direct measures of milk coagulation properties (MCP) such as rennet coagulation time (RCT) and curd firmness 30 min after rennet addition (a30) and on some traditional milk quality traits that are used as predictors, such as somatic cell score (SCS) and casein percentage (CAS). The aim of this study was to shed light on the causal relationships between traditional milk quality traits and MCP. Different structural equation models that included causal effects of SCS and CAS on RCT and a30 and of RCT on a30 were implemented in a Bayesian framework. Results: Our results indicate a non-zero magnitude of the causal relationships between the traits studied. Causal effects of SCS and CAS on RCT and a30 were observed, which suggests that the relationship between milk coagulation ability and traditional milk quality traits depends more on phenotypic causal pathways than directly on common genetic influence. While RCT does not seem to be largely controlled by SCS and CAS, some of the variation in a30 depends on the phenotypes of these traits. However, a30 depends heavily on coagulation time. Our results also indicate that, when direct effects of SCS, CAS and RCT are considered simultaneously, most of the overall genetic variability of a30 is mediated by other traits. Conclusions: This study suggests that selection for RCT and a30 should not be performed on correlated traits such as SCS or CAS but on direct measures because the ability of milk to coagulate is improved through the causal effect that the former play on the latter, rather than from a common source of genetic variation. Breaking the causal link (e.g. standardizing SCS or CAS before the milk is processed into cheese) would reduce the impact of the improvement due to selective breeding. Since a30 depends heavily on RCT, the relative emphasis that is put on this trait should be reconsidered and weighted for the fact that the pure measure of a30 almost double-counts RCT