From error bounds to the complexity of first-order descent methods for convex functions

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex functions having a moderately flat profile near the set of minimizers (as those of functions with H\"olderian growth). A counterexample shows that the equivalence is no longer true for extremely flat functions. This fact reveals the relevance of an approach based on KL inequality. In a second stage, we show how KL inequalities can in turn be employed to compute new complexity bounds for a wealth of descent methods for convex problems. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence in the spirit of the famous majorant method of Kantorovich. Our result applies to a very simple abstract scheme that covers a wide class of descent methods. As a byproduct of our study, we also provide new results for the globalization of KL inequalities in the convex framework. Our main results inaugurate a simple methodology: derive an error bound, compute the desingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Our method is illustrated through projection methods for feasibility problems, and through the famous iterative shrinkage thresholding algorithm (ISTA), for which we show that the complexity bound is of the form $O(q^{k})$ where the constituents of the bound only depend on error bound constants obtained for an arbitrary least squares objective with $\ell^1$ regularization

The Early Husserl on Typicality

This paper presents and evaluates the early Husserl’s account of typicality. In the Logical Investigations, Husserl holds that the meaning of ordinary language (common) names is sensitive to typicality: this meaning depends on typical examples which vary in different contexts and are more or less similar to one another. This seems to entail that meanings, which according to Husserl are concepts, are “fluctuating” (schwankend) and vague. Prima facie, such a claim contravenes his theory of ideal meanings, or concepts, which are “fixed” (fest) and sharp. However, Husserl wants to save this theory. He claims that the fluctuation and vagueness in question are not to be found in the meaning itself, or the concept, but rather derive from the act of meaning. Thus, he apparently manages to make room for typicality in ordinary language while accepting only fixed and sharp meanings. After presenting Husserl’s theory, I evaluate it and ask whether he will still be committed, despite his own claims, to accepting prototype concepts to account for typicality in ordinary language

Behavioural indicators of welfare in farmed fish

Behaviour represents a reaction to the environment as fish perceive it and is therefore a key element of fish welfare. This review summarises the main findings on how behavioural changes have been used to assess welfare in farmed fish, using both functional and feeling-based approaches. Changes in foraging behaviour, ventilatory activity, aggression, individual and group swimming behaviour, stereotypic and abnormal behaviour have been linked with acute and chronic stressors in aquaculture and can therefore be regarded as likely indicators of poor welfare. On the contrary, measurements of exploratory behaviour, feed anticipatory activity and reward-related operant behaviour are beginning to be considered as indicators of positive emotions and welfare in fish. Despite the lack of scientific agreement about the existence of sentience in fish, the possibility that they are capable of both positive and negative emotions may contribute to the development of new strategies (e. g. environmental enrichment) to promote good welfare. Numerous studies that use behavioural indicators of welfare show that behavioural changes can be interpreted as either good or poor welfare depending on the fish species. It is therefore essential to understand the species-specific biology before drawing any conclusions in relation to welfare. In addition, different individuals within the same species may exhibit divergent coping strategies towards stressors, and what is tolerated by some individuals may be detrimental to others. Therefore, the assessment of welfare in a few individuals may not represent the average welfare of a group and vice versa. This underlines the need to develop on-farm, operational behavioural welfare indicators that can be easily used to assess not only the individual welfare but also the welfare of the whole group (e. g. spatial distribution). With the ongoing development of video technology and image processing, the on-farm surveillance of behaviour may in the near future represent a low-cost, noninvasive tool to assess the welfare of farmed fish.Fundação para a Ciência e Tecnologia, Portugal [SFRH/BPD/42015/2007]info:eu-repo/semantics/publishedVersio

Non-intrusive in-cylinder pressure sensor for gasoline combustion engines

International audienc

Non-intrusive in-cylinder pressure sensor for gasoline combustion engines

International audienc

A Lasting Symbolic National Threat: The Dispute Over the Name Macedonia

International audienceThe naming dispute between Greece and the Republic of North Macedonia has been ongoing for over 25 years. These two countries claimed the same name, the former for its region, the latter for the entire country. Using the same name for both region and nation has been perceived by Greece as a collective symbolic threat. In this chapter, we will revisit the origins of this symbolic threat and recent developments, then discuss the issue from a theoretical perspective of social representations prompted by a psychosocial analysis. By examining a contemporary conflictual historic episode, we will demonstrate the symbolic effectiveness of social mental productions and their study as a way of expressing social thought.Kalampalikis, N. (2020). A lasting symbolic threat: the dispute over the name Macedonia in Greece. In D. Jodelet, J. Vala & E. Drozda-Senkowska (Eds.), Societies under threat: a pluri-disciplinary approach (pp. 101-112). Cham: Springer