Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Non-equilibrium dynamics of stochastic point processes with refractoriness

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.Comment: 8 pages, 4 figure

Simulation of truncated normal variables

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance structure.Comment: This 1992 paper appeared in 1995 in Statistics and Computing and the gist of it is contained in Monte Carlo Statistical Methods (2004), but I receive weekly requests for reprints so here it is

Scaling and allometry in the building geometries of Greater London

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal structure. We redress this here by examining scaling relationships in a world city using data on the geometric properties of individual buildings. We first summarise how power laws can be used to approximate the size distributions of buildings, in analogy to city-size distributions which have been widely studied as rank-size and lognormal distributions following Zipf and Gibrat. We then extend this analysis to allometric relationships between buildings in terms of their different geometric size properties. We present some preliminary analysis of building heights from the Emporis database which suggests very strong scaling in world cities. The data base for Greater London is then introduced from which we extract 3.6 million buildings whose scaling properties we explore. We examine key allometric relationships between these different properties illustrating how building shape changes according to size, and we extend this analysis to the classification of buildings according to land use types. We conclude with an analysis of two-point correlation functions of building geometries which supports our non-spatial analysis of scaling.Comment: 28 pages, 8 figure

Network dynamics with a nested node set: sociability in seven villages in Senegal

We propose two complementary ways to deal with a nesting structure in the node set of a network—such a structure may be called a multilevel network, with a node set consisting of several groups. First, within‐group ties are distinguished from between‐group ties by considering them as two distinct but interrelated networks. Second, effects of nodal variables are differentiated according to the levels of the nesting structure, to prevent ecological fallacies. This is elaborated in a study of two repeated observations of a sociability network in seven villages in Senegal, analyzed using the Stochastic Actor‐oriented Model

Enhanced statistical stability in coherent interferometric imaging

http://iopscience.iop.org/0266-5611/International audienc

The gut bacterial community affects immunity but not metabolism in a specialist herbivorous butterfly

1. Plant tissues often lack essential nutritive elements and may contain a range of secondary toxic compounds. As nutritional imbalance in food intake may affect the performances of herbivores, the latter have evolved a variety of physiological mechanisms to cope with the challenges of digesting their plant-based diet. Some of these strategies involve living in association with symbiotic microbes that promote the digestion and detoxification of plant compounds or supply their host with essential nutrients missing from the plant diet. In Lepidoptera, a growing body of evidence has, however, recently challenged the idea that herbivores are nutritionally dependent on their gut microbial community. It is suggested that many of the herbivorous Lepidopteran species may not host a resident microbial community, but rather a transient one, acquired from their environment and diet. Studies directly testing these hypotheses are however scarce and come from an even more limited number of species. 2. By coupling comparative metabarcoding, immune gene expression, and metabolomics analyses with experimental manipulation of the gut microbial community of prediapause larvae of the Glanville fritillary butterfly (Melitaea cinxia, L.), we tested whether the gut microbial community supports early larval growth and survival, or modulates metabolism or immunity during early stages of development. 3. We successfully altered this microbiota through antibiotic treatments and consecutively restored it through fecal transplants from conspecifics. Our study suggests that although the microbiota is involved in the up-regulation of an antimicrobial peptide, it did not affect the life history traits or the metabolism of early instars larvae. 4. This study confirms the poor impact of the microbiota on diverse life history traits of yet another Lepidoptera species. However, it also suggests that potential eco-evolutionary host-symbiont strategies that take place in the gut of herbivorous butterfly hosts might have been disregarded, particularly how the microbiota may affect the host immune system homeostasis.Peer reviewe

Museum epigenomics: Characterizing cytosine methylation in historic museum specimens

Museum genomics has transformed the field of collections‐based research, opening up a range of new research directions for paleontological specimens as well as natural history specimens collected over the past few centuries. Recent work demonstrates that it is possible to characterize epigenetic markers such as DNA methylation in well preserved ancient tissues. This approach has not yet been tested in traditionally prepared natural history specimens such as dried bones and skins, the most common specimen types in vertebrate collections. In this study, we developed and tested methods to characterize cytosine methylation in dried skulls up to 76 years old. Using a combination of ddRAD and bisulphite treatment, we characterized patterns of cytosine methylation in two species of deer mouse (Peromyscus spp.) collected in the same region in Michigan in 1940, 2003, and 2013–2016. We successfully estimated methylation in specimens of all age groups, although older specimens yielded less data and showed greater interindividual variation in data yield than newer specimens. Global methylation estimates were reduced in the oldest specimens (76 years old) relative to the newest specimens (1–3 years old), which may reflect post‐mortem hydrolytic deamination. Methylation was reduced in promoter regions relative to gene bodies and showed greater bimodality in autosomes relative to female X chromosomes, consistent with expectations for methylation in mammalian somatic cells. Our work demonstrates the utility of historic specimens for methylation analyses, as with genomic analyses; however, studies will need to accommodate the large variance in the quantity of data produced by older specimens.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/162784/5/men13115.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162784/4/men13115-sup-0003-AppendixS1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162784/3/men13115-sup-0001-FigS1-S2.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162784/2/men13115_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162784/1/men13115-sup-0002-TableS1-S2.pd

Longitudinal Peer Network Data in Higher Education

This chapter employs a longitudinal social network approach to research small group teaching in higher education. Longitudinal social network analyses can provide in-depth understanding of the social dynamics in small groups. Specifically, it is possible to investigate and disentangle the processes by which students make or break social connections with peers and are influenced by them, as well as how those processes relate to group compositions and personal attributes, such as achievement level. With advanced methods for modelling longitudinal social networks, researchers can identify social processes affecting small group teaching and learning