Real root finding for equivariant semi-algebraic systems

Let $R$ be a real closed field. We consider basic semi-algebraic sets defined by $n$-variate equations/inequalities of $s$ symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by $2d < n$. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point with at most $2d-1$ distinct coordinates. Combining this geometric result with efficient algorithms for real root finding (based on the critical point method), one can decide the emptiness of basic semi-algebraic sets defined by $s$ polynomials of degree $d$ in time $(sn)^{O(d)}$. This improves the state-of-the-art which is exponential in $n$. When the variables $x_1, \ldots, x_n$ are quantified and the coefficients of the input system depend on parameters $y_1, \ldots, y_t$, one also demonstrates that the corresponding one-block quantifier elimination problem can be solved in time $(sn)^{O(dt)}$

The Crustacean Fauna (Branchiopoda, Copepoda) of Shallow Freshwater Bodies in Iceland

A survey of shallow freshwaters of Iceland was conducted in June and July 1996. The 34 stations prospected were rainpools, ditches, wetlands. The composition of their crustacean communities, investigated by qualitative net samples, is discussed in relation to water characteristics. One notostracan, Lepidurus arcticus (Pallas, 1793), 17 cladoceran species (5 Daphniidae, 10 Chydoridae, 1 Macrothricidae, 1 Polyphemidae), and 12 copepods (2 Diaptomidae, 7 Cyclopidae, 3 Canthocamptidae) were identified. Two species are reported for the first time from Iceland: the diaptomid Diaptomus (Chaetodiaptomus) rostripes Herbst, 1955 and the chydorid Alona rustica Scott, 1895. Taxonomical comments about different species are added, and their ecological pecularities are given. The species richness as well as the biogeographical features of the freshwater zooplankton of Iceland are discussed in relation to neighbouring Greenland and Northern Europe.Обследование мелких пресных водоемов Исландии проведено в июне-июле 1996 г. Материал собирался в дождевых и талых лужах, канавах, болотах. Среди 30 обнаруженных видов отмечены 1 вид щитней Lepidurus arcticus (Pallas, 1793), 17 видов ветвистоусых ракообразных (5 представителей сем. Daphnidae, 10 Chydoridae, 1 Macrothricidae, 1 Polyphemidae), 12 видов веслоногих ракобразных (2 вида сем. Diaptomidae, 7 Cyclopidae, 3 Canthocamptidae). Два вида указаны впервые для фауны Исландии: Diaptomus (Chaetodiatomus) rostripes Herbst, 1955 и Alona rustica Scott, 1895. Состав ракообразных в водоемах обсуждается в связи с экологической характеристикой последних. Для отдельных видов представлены краткие таксономические и экологические замечания. Обсуждаются видовое разнообразие и биогеографические особенности Исландии в связи с фаунистическими контактами с Гренландией и северной Европой

Perspectives in ground-penetrating radar at high latitudes: From occasional imaging to automated continuous monitoring

International audienceAmong different geophysical methods employed for glacier and permafrost characterization, Ground-Penetrating Radar has been employed many times since its first developments.However these GPR characterization were and are still mostly performed during field campaigns which can be sparse in time, expensive and human resource demanding, and can be limited by the difficulty to access areas.The purpose of this short paper is to present two approaches for northern latitudes features imaging during field mission and discuss the benefits brought by hardware and software improvements to develop the field of long-term monitoring. The main objective of this paper is to highlight the new paradigm that the internet of things brought to the field of surface GPR characterization of high latitude environment