Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH

Let \psi_\K be the Chebyshev function of a number field \K. Under GRH we prove an explicit upper bound for |\psi_\K(x)-x| in terms of the degree and the discriminant of \K. The new bound improves significantly on previous known results.Comment: Some misprints corrected. This is the final version which will appear in Mathematics of Computatio

Zeros of Dedekind zeta functions under GRH

Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $[T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.Comment: Some misprints corrected, simplified proof for a lemma. This version will appear in Mathematics of Computatio

Primes and prime ideals in short intervals

We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.Comment: minor change to Proposition

L'éducation en Chine à l'ère des réformes

Juin 1989, un étudiant chinois se dresse face à un char place Tiananmen : le monde entier découvre une jeunesse pleine d’espoir mobilisée par le devoir de faire évoluer la société et avancer les idéaux de liberté et de démocratie. Juin 2006, plusieurs milliers d’étudiants de l’université de Zhengzhou (province centrale du Henan) manifestent violemment sur leur campus dans la nuit du 15 : ils ont appris que le diplôme qui leur sera délivré mentionne seulement le nom de leur institut privé et n..

The community ecology perspective of omics data

The measurement of uncharacterized pools of biological molecules through techniques such as metabarcoding, metagenomics, metatranscriptomics, metabolomics, and metaproteomics produces large, multivariate datasets. Analyses of these datasets have successfully been borrowed from community ecology to characterize the molecular diversity of samples (ɑ-diversity) and to assess how these profiles change in response to experimental treatments or across gradients (β-diversity). However, sample preparation and data collection methods generate biases and noise which confound molecular diversity estimates and require special attention. Here, we examine how technical biases and noise that are introduced into multivariate molecular data affect the estimation of the components of diversity (i.e., total number of different molecular species, or entities; total number of molecules; and the abundance distribution of molecular entities). We then explore under which conditions these biases affect the measurement of ɑ- and β-diversity and highlight how novel methods commonly used in community ecology can be adopted to improve the interpretation and integration of multivariate molecular data. Video Abstract

The ecological causes of functional distinctiveness in communities

Recent work has shown that evaluating functional trait distinctiveness, the average trait distance of a species to other species in a community offers promising insights into biodiversity dynamics and ecosystem functioning. However, the ecological mechanisms underlying the emergence and persistence of functionally distinct species are poorly understood. Here, we address the issue by considering a heterogeneous fitness landscape whereby functional dimensions encompass peaks representing trait combinations yielding positive population growth rates in a community. We identify four ecological cases contributing to the emergence and persistence of functionally distinct species. First, environmental heterogeneity or alternative phenotypic designs can drive positive population growth of functionally distinct species. Second, sink populations with negative population growth can deviate from local fitness peaks and be functionally distinct. Third, species found at the margin of the fitness landscape can persist but be functionally distinct. Fourth, biotic interactions (positive or negative) can dynamically alter the fitness landscape. We offer examples of these four cases and guidelines to distinguish between them. In addition to these deterministic processes, we explore how stochastic dispersal limitation can yield functional distinctiveness. Our framework offers a novel perspective on the relationship between fitness landscape heterogeneity and the functional composition of ecological assemblages

Functional diversity and redundancy of freshwater fish communities across biogeographic and environmental gradients

AimFunctional redundancy occurs when species share overlapping ecological functions and is considered an important component of ecosystem resilience. However, much of what we know about functional redundancy comes from relatively species‐rich terrestrial and marine environments. Here, we examined patterns of functional redundancy among Ontario freshwater fish communities with species richness levels ranging from 4 to 30 species across lakes of differing size, depth, productivities and thermal characteristics.LocationSix thousand nine hundred and seventy‐seven lakes in Ontario, Canada.MethodsWe examined functional redundancy by quantifying the relationship between functional diversity and species richness in lakes across Ontario and within smaller biogeographic regions. We used null models to test whether fish communities had greater redundancy than expected from random assemblages. We then used generalized additive models (GAMs) to predict how patterns of redundancy vary across environmental variables. At last, we compared species‐level functional rarity metrics across fish thermal preference groups, body sizes and species occurrence rates.ResultsThe functional diversity and species richness relationship were saturating among fish communities at the provincial scale but varied between smaller regions with differing biogeographic histories. Most communities fell within expectations from weighted null models of the functional diversity and species richness relationship. The GAMs indicated that fish communities in the largest, deepest and warmest lakes showed the greatest overall functional redundancy. No differences were observed in functional rarity measures between thermal preference groups, across body sizes or across species occurrence rates.Main conclusionsAlthough lakes in this study were relatively depauperate of fish species, Ontario fish communities exhibited functional redundancy at the provincial scale, with variation regionally. North‐eastern communities showed the least saturating relationship overall as predicted by historical biogeographic patterns of freshwater fish colonization. Overall, this study provides a broad perspective of freshwater fish diversity patterns and highlights the importance of investigating redundancy from different perspectives and multiple spatial scales.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146304/1/ddi12812_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146304/2/ddi12812.pd