Stratifying multiparameter persistent homology

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter family of spaces obtained from the data. In applications data often depend on several parameters, and in this case one is interested in studying the persistent homology of a multiparameter family of spaces associated to the data. While the theory of persistent homology for one-parameter families is well-understood, the situation for multiparameter families is more delicate. Following Carlsson and Zomorodian we recast the problem in the setting of multigraded algebra, and we propose multigraded Hilbert series, multigraded associated primes and local cohomology as invariants for studying multiparameter persistent homology. Multigraded associated primes provide a stratification of the region where a multigraded module does not vanish, while multigraded Hilbert series and local cohomology give a measure of the size of components of the module supported on different strata. These invariants generalize in a suitable sense the invariant for the one-parameter case.Comment: Minor improvements throughout. In particular: we extended the introduction, added Table 1, which gives a dictionary between terms used in PH and commutative algebra; we streamlined Section 3; we added Proposition 4.49 about the information captured by the cp-rank; we moved the code from the appendix to github. Final version, to appear in SIAG

Coarse graining of slow variables in dynamic simulations of soft matter

A new Brownian dynamics model is presented to describe the coarse grain dynamics of particles with long-lived memory. Instead of solving a set of generalized Langevin equations we introduce a set of variables describing the slowly fluctuating thermodynamic state of the ignored degrees of freedom. These variables give rise to additional transient forces on the simulated particles, whose interpretation provides a new way of thinking about memory effects in soft-matter physics. We illustrate the proposed method by simulating shear thinning of synthetic resins.\u

Nest-Site Selection by Female Black-Capped Chickadees: Settlement Based on Conspecific Attraction?

Female Black-capped Chickadees (Poecile atricapillus) solicit extrapair copulations (EPCs) from neighboring high-ranking males, and these EPCs result in extrapair young. Females might choose to locate their nests near the territory boundaries of attractive males to facilitate access to EPCs. Other hypotheses might also explain choice of nest site, namely (1) habitat characteristics, (2) prey abundance, and (3) previous experience. We tested these four hypotheses in 1996 and 1997. Out of 27 habitat characteristics measured, we found only one that was significantly different between nests and control sites in both years. The abundance of large trees was lower at nest sites than at control sites in each year and when years were pooled. Relative prey abundance did not differ between nests and control sites for either year of the study. We found no different in interyear nest placement based on female experience; experienced females nester farther than 60 m from their previous nest sites in both years of the study. In 1996, females whose neighboring males were higher ranked than their social partner located their nests significantly closer to territory boundaries than did females whose nearest neighbors were lower ranked than their social partner. In 1997, all pairs nested near territory boundaries. We conclude that choice of nest location in Black-capped Chickadees is influenced by conspecific attraction based on mating tactics

Sympatric song variant in mountain chickadees Poecile gambeli does not reduce aggression from black-capped chickadees Poecile atricapillus

When habitats overlap and species compete for resources, negative interactions frequently occur. Character displacement in the form of behavioural, social or morphological divergences between closely related species can act to reduce negative interactions and often arise in regions of geographic overlap. Mountain chickadees  Poecile gambeli have an altered song structure in regions of geographic overlap with the behaviourally dominant black capped chickadee Poecile atricapillus. Similar to European and Asian tits, altered song in mountain chickadees  may decrease aggression from black-capped chickadees. To test this hypothesis, we conducted a playback study in Prince George, BC, Canada, to examine how black-capped chickadees responded to the songs of mountain chickadees recorded in regions where the two species were either sympatric or allopatric. We used principal  component analysis (PCA) to collapse behavioural response variables into a single ‘approach’ variable and a single ‘vocalisation’ variable. We then used mixed-model analysis to determine whether there was a difference in approach or vocalisation response to the two types of mountain chickadee songs (allopatric  songs and variant sympatric songs). Black-capped chickadees responded with equal intensity to both types of mountain chickadee songs, suggesting that the variant mountain chickadee songs from regions of sympatry with black-capped chickadees do not reduce heterospecific aggression. To our knowledge, this is the only instance of a character shift unassociated with reduced aggression in the family Paridae and raises interesting questions about the selective pressures leading to the evolution of this song divergence

Between-Year Survival and Rank Transitions in Male Black-Capped Chickadees (\u3cem\u3ePoecile Atricapillus\u3c/em\u3e): A Multistate Modeling Approach

In dominance-structured animal societies, variation in individual fitness is often related to social status. Like many passerine birds, Black-capped Chickadees (Poecile atricapillus) have a short average adult life-expectancy (Ø2 years); however, the maximum recorded life span is \u3e5× as long. Enhanced annual survival could contribute to greater lifetime reproductive success for male Black-capped Chickadees with high social rank. We used multistate capture–mark–recapture models to estimate annual survival of male Black-capped Chickadees in Ontario using resighting and recapture data collected from 1997 to 2002. Our goal was to evaluate support for an influence of rank on annual survival and estimate its effect size for a food-supplemented study site. We also statistically modeled the probability of between-year rank transitions. Model selection based on Akaike’s information criterion provided support for an effect of rank on survival. However, multimodel inference revealed that the size of the effect was rather small. Over the six study years, model-averaged estimates of the survival benefit of high versus low rank ranged from 5.0 to 7.3%. As expected, survival was strongly year-dependent, with model-averaged estimates of annual survival probability varying between 0.36 and 0.73. Age was an important predictor of the probability of rank transitions. Low-ranked second-year birds were less likely than older low-ranked birds to advance to high rank between years; likewise, high-ranked after-second-year birds were less likely to drop in rank. Other studies have found larger effects of rank on survival than we observed here. Future research should consider how interactions between social and environmental factors influence annual survival

The economics of health

This report presents results from the Economics of Health project funded by the East Midlands Development Agency. The work was undertaken between November 2007 and February 2008. The main aim of the project was to examine the relationship between mental and physical health and employability, labour market participation and economic performance, with specific attention given to the direction of causal relationships

Access to Health Care for Undocumented Migrants: A Comparative Policy Analysis of England and the Netherlands

The presence of undocumented migrants is increasing in many Western countries despite wide-ranging attempts by governments to increase border security. Measures taken to control the influx of immigrants include policies that restrict access to publicly funded health care for undocumented migrants. These restrictions to health care access are controversial, and evidence suggests they do not always have the intended effect. This study provides a comparative analysis of institutional, actor-related, and contextual factors that have influenced health care policy development on undocumented migrants in England and the Netherlands. For undocumented migrants, England restricts its access to care at the point of service, while the Netherlands restricts through the payment system for services. The study includes an analysis of policy papers and semistructured, in-depth interviews with various actors in both countries. Findings confirm the influence of such contextual factors as immigration considerations and cost concerns on health care policy making in this area. However, these factors cannot explain the differences between the two countries. Previously enacted policies, especially the organization of the health care system, affected the kind of restrictions for undocumented migrants. Concerns about the side effects of generous treatment of undocumented migrants on other groups played a substantial role in formulating restrictive policies in both countries. Evidently, policy development and implementation is critically affected by institutional rules, which govern the degree of influence that doctors and professional medical associations have on the policy process