When is the inverse of an invertible convex function itself convex?

We provide a sufficient condition for an invertible (locally strongly) convex vector-valued function on $\mathbb{R}^N$ to have a (locally strongly) convex inverse. We show under suitable conditions that if the gradient of each component of the inverse has negative entries, then this inverse is (locally strongly) convex if the original is

Sobolev regularity and an enhanced Jensen inequality

We derive a new criterion for a real-valued function $u$ to be in the Sobolev space $W^{1,2}(\R^n)$. This criterion consists of comparing the value of a functional $\int f(u)$ with the values of the same functional applied to convolutions of $u$ with a Dirac sequence. The difference of these values converges to zero as the convolutions approach $u$, and we prove that the rate of convergence to zero is connected to regularity: $u\in W^{1,2}$ if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization problem with constraints, where regularity of minimizers cannot be deduced from the Euler-Lagrange equation.Comment: 10 page

A consistent treatment of link and writhe for open rods, and their relation to end rotation

We combine and extend the work of Alexander & Antman \cite{alexander.82} and Fuller \cite{fuller.71,fuller.78} to give a framework within which precise definitions can be given of topological and geometrical quantities characterising the contortion of open rods undergoing large deformations under end loading. We use these definitions to examine the extension of known results for closed rods to open rods. In particular, we formulate the analogue of the celebrated formula $Lk=Tw+Wr$ (link equals twist plus writhe) for open rods and propose an end rotation, through which the applied end moment does work, in the form of an integral over the length of the rod. The results serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations.Comment: 17 pages, 4 figure

Bounding ζ(s)\zeta(s) in the critical strip

Assuming the Riemann Hypothesis, we make use of the recently discovered \cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\log\left(\tfrac{4 + x^2}{(\alpha-1/2)^2 + x^2}\right)$ to find upper and lower bounds with explicit constants for $\log|\zeta(\alpha + it)|$ in the critical strip, extending the work of Chandee and Soundararajan \cite{CS}

Rare enemies and rare friends: adaptations that make other adaptations maladaptive

We show that certain adaptations can make other adaptations maladaptive. For example, one line of defence against an enemy can make an otherwise valuable, but subsequent line of defence detrimental. This can occur through indirect rare enemy effects

The adaptiveness of defence strategies against cuckoo parasitism

Most bird species of the Eurasian Cuckoo, 'Cuculuscanorus', often display egg-discrimination behaviour butchick-rejection behaviour has never been reported.In this paper, we analyse ahost-cuckoo association in which both population dynamics andevolutionary dynamics are explored in a discrete-time model.We introduce four host types, each with their own defence behaviour, displayingeither egg or chick rejection, neither or both. We also introducefitness functions for each of these host types.Although we can characterise the long term behaviour in many cases by a simpleheuristic argument which is in accordance with common views in ecology, thereare a number of other phenomena that are not explained within thisframework: we describe stable oscillatory behaviour and coexistence oftwo defensive host types. We analyse the scenariosin which chick rejection may establish itself and give a first explanationas to why this defence trait has never been recorded in nature.We find that chick rejectors generally are at an intrinsicdisadvantage with respect to a host type that rejects eggs.Hosts benefit more from rejecting cuckoo eggs than cuckoo chicks, and ourmodel suggests that this is chiefly responsible for the absence of chickrejection. Moreover, even though it seems that chick rejection must beuseful as an extra defence, it is shown that hosts with both defencestrategies are less likely to establish themselves in competitionwith egg-rejectors than hosts which reject chicks only.These results provide insight in the extent to whichadaptations may be perfected by natural selection

Understanding start-up problems in yeast glycolysis

Yeast glycolysis has been the focus of research for decades, yet a number of dynamical aspects of yeast glycolysis remain poorly understood at present. If nutrients are scarce, yeast will provide its catabolic and energetic needs with other pathways, but the enzymes catalysing upper glycolytic fluxes are still expressed. We conjecture that this overexpression facilitates the rapid transition to glycolysis in case of a sudden increase in nutrient concentration. However, if starved yeast is presented with abundant glucose, it can enter into an imbalanced state where glycolytic intermediates keep accumulating, leading to arrested growth and cell death. The bistability between regularly functioning and imbalanced phenotypes has been shown to depend on redox balance. We shed new light on these phenomena with a mathematical analysis of an ordinary differential equation model, including NADH to account for the redox balance. In order to gain qualitative insight, most of the analysis is parameter-free, i.e., without assigning a numerical value to any of the parameters. The model has a subtle bifurcation at the switch between an inviable equilibrium state and stable flux through glycolysis. This switch occurs if the ratio between the flux through upper glycolysis and ATP consumption rate of the cell exceeds a fixed threshold. If the enzymes of upper glycolysis would be barely expressed, our model predicts that there will be no glycolytic flux, even if external glucose would be at growth-permissable levels. The existence of the imbalanced state can be found for certain parameter conditions independent of the mentioned bifurcation. The parameter-free analysis proved too complex to directly gain insight into the imbalanced states, but the starting point of a branch of imbalanced states can be shown to exist in detail. Moreover, the analysis offers the key ingredients necessary for successful numerical continuation, which highlight the existence of this bistability and the influence of the redox balance

LifeCLEF Bird Identification Task 2017

International audienceThe LifeCLEF challenge BirdCLEF offers a large-scale proving ground for system-oriented evaluation of bird species identification based on audio recordings of their sounds. One of its strengths is that it uses data collected through Xeno-canto, the worldwide community of bird sound recordists. This ensures that BirdCLEF is close to the conditions of real-world application, in particular with regard to the number of species in the training set (1500). The main novelty of the 2017 edition of BirdCLEF was the inclusion of soundscape recordings containing time-coded bird species annotations in addition to the usual Xeno-canto recordings that focus on a single foreground species. This paper reports an overview of the systems developed by the five participating research groups, the methodology of the evaluation of their performance, and an analysis and discussion of the results obtained

LifeCLEF Bird Identification Task 2016: The arrival of Deep learning

International audienceThe LifeCLEF bird identification challenge provides a large-scale testbed for the system-oriented evaluation of bird species identification based on audio recordings. One of its main strength is that the data used for the evaluation is collected through Xeno-Canto, the largest network of bird sound recordists in the world. This makes the task closer to the conditions of a real-world application than previous, similar initiatives. The main novelty of the 2016-th edition of the challenge was the inclusion of soundscape recordings in addition to the usual xeno-canto recordings that focus on a single foreground species. This paper reports the methodology of the conducted evaluation, the overview of the systems experimented by the 6 participating research groups and a synthetic analysis of the obtained results

LifeCLEF Bird Identification Task 2014

International audienceThe LifeCLEF bird identification task provides a testbed for a system-oriented evaluation of 501 bird species identification. The main originality of this data is that it was specifically built through a citizen science initiative conducted by Xeno-Canto, an international social net-work of amateur and expert ornithologists. This makes the task closer to the conditions of a real-world application than previous, similar ini-tiatives. This overview presents the resources and the assessments of the task, summarizes the retrieval approaches employed by the participating groups, and provides an analysis of the main evaluation results. With a total of ten groups from seven countries and with a total of twenty-nine runs submitted, involving distinct and original methods, this first year task confirms the interest of the audio retrieval community for biodiver-sity and ornithology, and highlights further challenging studies in bird identification