Texte établi par Joseph
Liouville, 1837 (première série, tome 2, p. 369-375).
Recherches sur
les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec
la règle et le compas ;
Par M. L. WANTZEL,
Élève-Ingénieur
des Ponts-et-Chaussées.
| {\displaystyle \left\{{\begin{alignedat}{2}x_{1}^{2}+{\rm {A}}x_{1}+{\rm {B}}=&0&x_{2}^{2}+{\rm {A_{1}}}x_{2}+{\rm {B_{1}}}=&0\ldots \\x_{n-1}^{2}+{\rm {A}}_{n-2}x_{n-1}+{\rm {B}}_{n-2}=&0&\qquad x_{n}^{2}+{\rm {A}}_{n-1}x_{n}+{\rm {B}}_{n-1}=&0\\\end{alignedat}}\right.} |
| et {\displaystyle {\rm {B}}} |
|
|
|
|
|
| telle que {\displaystyle {\rm {A_{m}}}} ou {\displaystyle {\rm {B_{m}}}}, prend la forme {\displaystyle {\frac {{\rm {C}}_{m-1}x_{m}+{\rm {D}}_{m-1}}{{\rm {E}}_{m-1}x_{m}+{\rm {F}}_{m-1}}}} si l’on élimine les puissances de {\displaystyle x_{m}} supérieures à la pre |
| , en désignant par {\displaystyle {\rm {{C}_{m-1}}}} |
| par {\displaystyle -{\rm {{E}_{m-1}({\rm {{A}_{m-1}+x_{m})}}}}} |
| dans {\displaystyle {\rm {{A}_{n-1}}}} |
| , ne peut pas être satisfaite par une fonction rationnelle des quantités données et des racines des équations précédentes. Car, s’il en était ainsi, le résultat de la substitution serait une fonction rationnelle de {\displaystyle x_{m},\ldots ,x_{1},p,q,\ldots ,} |
| qu’on peut mettre sous la forme {\displaystyle {\rm {{A}'_{m-1}x_{m}+{\rm {{B}'_{m-1}\,}}}}} |
| , par exemple, était satisfaite identiquement, les deux racines de l’équation {\displaystyle x_{m}^{2}+{\rm {{A}_{m-1}x_{m}+{\rm {{B}_{m-1}=0\,}}}}} |
| et remplacer la racine successivement par ses deux valeurs dans les équations sui |
| équations. |
| , qui donne toutes les solutions d’un problème susceptible d’être résolu au moyen de n équations du second degré, est nécessairement irréductible, c’est-à-dire qu’elle ne peut avoir de racines communes avec une équation de degré moindre dont les coefficients soient des fonctions rationnelles de données {\displaystyle p,q,\ldots .} |
| à coefficients rationnels soit satisfaite par une racine de l’équation {\displaystyle x_{n}^{2}+{\rm {{A}_{n-1}x_{n}+{\rm {{B}_{n-1}=0}}}}} |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| ; pareillement, les coefficients {\displaystyle {\rm {{A}'_{2}}}} et {\displaystyle {\rm {{B}'_{2}}}} peuvent être mis sous la forme {\displaystyle {\rm {{A}'_{1}x_{2}+{\rm {{B}'_{1}}}}}} en prenant pour {\displaystyle x_{2}} l’une ou l’autre des racines de l’équation {\displaystyle x_{2}^{2}+{\rm {{A}_{1}x_{2}+{\rm {{B}_{1}=0}}}}}, correspondantes à chacune des valeurs de {\displaystyle x_{1}}, et par conséquent ils s’annuleront pour les quatre valeurs de {\displaystyle x_{2}} et pour les deux valeurs de {\displaystyle x_{1}} qui résultent de la combinaison des deux premières équations (A). On démontrera de même que {\displaystyle {\rm {{A}'_{3}}}} et {\displaystyle {\rm {{B}'_{3}}}} seront nuls en mettant pour {\displaystyle x_{3}} les {\displaystyle 2^{3}} valeurs tirées des trois premières équations (A) conjointement avec les valeurs correspondantes de {\displaystyle x_{2}} et {\displaystyle x_{1}} ; |
| s’annulera pour les {\displaystyle 2^{n}} |
| ne peut être résolu avec la ligne droite et le cercle. Ainsi la duplication du cube, qui dépend de l’équation {\displaystyle x^{3}-2a^{3}=0} |
| est dans le même cas toutes les fois que le rapport de {\displaystyle b} |
| , dans laquelle {\displaystyle m} |
| . Quand {\displaystyle m} |
![{\displaystyle x=k+{\rm {A}}'\,\,{\sqrt[{m'}]{a'}}+{\rm {A}}''\,\,{\sqrt[{m''}]{a''}}+\ldots },m',{\displaystyle m''},{\displaystyle \ldots },2,k,{\displaystyle {\rm {A}}'},{\displaystyle {\rm {A}}''},{\displaystyle \ldots },{\displaystyle a'},{\displaystyle a''},{\displaystyle \ldots },x,x,m,{\displaystyle 2.},{\displaystyle x={\rm {A}}{\sqrt[{m}]{a}}},{\displaystyle ({\sqrt[{m}]{a}})^{p}},{\displaystyle p<m},x,m,{\displaystyle 2.}](image017.gif){kind=small}
| , {\displaystyle m'} |
| et qu’on se soit assuré que cette équation est irréductible ; il s’agit de reconnaître si la solution peut s’obtenir au moyen d’une série d’équations du second degré. |
| {\displaystyle \left\{{\begin{alignedat}{2}x_{1}^{2}+{\rm {A}}x_{1}+{\rm {B=}}&\,0,&x_{2}^{2}+{\rm {A}}_{1}x_{2}+{\rm {B_{1}=}}&\,0\ldots ,\\x_{n-1}^{2}+{\rm {A}}_{n-2}x_{n-1}+{\rm {B}}_{n-2}=&\,0,\qquad &x_{n}^{2}+{\rm {A}}_{n-1}x_{n}+{\rm {B}}_{n-1}=&\,0\end{alignedat}}\right.} |
| , à coefficients rationnels, qui donne toutes les valeurs de {\displaystyle x_{n}} |
| ; si les conditions ne peuvent être vérifiées en donnant des valeurs rationnelles aux indéterminées introduites, le problème ne peut être ramené au second degré. |
| pour l’inconnue de l’avant-dernière équation, puisque {\displaystyle {\rm {B}}_{n-1}=b_{n-1}x_{n-1}+b'_{n-1}} |
| serait nulle, et il faut étudier ce cas séparément. |
| . Prenons de suite les équations du second degré sous la forme {\displaystyle x_{1}^{2}+{\rm {A}}x_{1}+{\rm {B}}=0} |
{\displaystyle 2a_{1}-{\rm {A}}a=0}
| , {\displaystyle a'^{2}+{\rm {A}}aa'-{\rm {A}}+a^{2}{\rm {B}}=p} |
{\displaystyle {\rm {B}}=r,\ \ a={\frac {2q}{4r-{\rm
{A}}^{2}}},\ \ a'={\frac {{\rm {A}}q}{4r-{\rm {A}}^{2}}},\ \ {\rm
{A}}^{3}+p{\rm {A}}^{2}-4r{\rm {A}}+q^{2}-4rp=0.}
| et {\displaystyle a'} |
| pour dernier terme de la deuxième équation du second degré, on a exclu le cas où ce terme serait indépendant de la racine de la première équation ; mais en le traitant directement, on ne trouve aucune solution de la question qui ne soit comprise dans les équations ci-dessus. |
| sera irréductible lorsqu’en cherchant les diviseurs de son premier membre de degrés {\displaystyle 1} |
| à une seule inconnue peut avoir pour racine une fonction de ce genre. Pour cela, il y a plusieurs cas à considérer. 1o Si les coefficients ne dépendent que de nombres donnés entiers ou fractionnaires, il suffira d’appliquer la méthode des racines commensurables. 2o Il peut arriver que les données représentées par les lettres {\displaystyle p} |
| , {\displaystyle q} |
| à une forme telle que ses coefficients soient des fractions entières de {\displaystyle p} |
| par {\displaystyle a_{m}p^{m}+a_{m-1}p^{m-1}+\ldots +a_{0}} |
About
156
Publications
16,272
Reads
2,925
Citations
Introduction
Gonzalo G de Polavieja
currently works at Champalimaud Neuroscience Program. Gonzalo does research
at the boundary of collective behavior, Neuroscience and AI
Skills and Expertise
Research experience
July 2008 - July 2014
Position
Group Leader
Publications (156)
Preprint
Full-text available
| Fernando Martin Maroto |
We show that every finite
semilattice can be represented as an atomized semilattice, an algebraic
structure with additional elements (atoms) that extend the semilattice's
partial order. Each atom maps to one subdirectly irreducible component, and
the set of atoms forms a hypergraph that fully defines the semilattice. An
atomization always exists an...
Article
| Antonia H Groneberg |
| Michael B Orger |
Social experiences
greatly define subsequent social behavior. Lack of such experiences,
especially during critical phases of development, can severely impede the
ability to behave adequately in social contexts. To date, it is not well
characterized how early-life social isolation leads to social deficits and
impacts development. In many model speci...
Preprint
Full-text available
| Francisco J. H. Heras |
We explore the
application of linear discriminant analysis (LDA) to the features obtained in
different layers of pretrained deep convolutional neural networks (CNNs). The
advantage of LDA compared to other techniques in dimensionality reduction is
that it reduces dimensions while preserving the global structure of data, so
distances in the low-dime...
Article
Full-text available
| Tiago Costa |
Complex global behavior
patterns can emerge from very simple local interactions between many agents.
However, no local interaction rules have been identified that generate some
patterns observed in nature, for example the rotating balls, rotating tornadoes
and the full-core rotating mills observed in fish collectives. Here we show
that locally inte...
Preprint
Full-text available
| Antonia H Groneberg |
| Michael B. Orger |
Social experiences
greatly define successive social behavior. Lack of such experiences,
especially during critical phases of development, can severely impede the
ability to behave adequately in social contexts. To date it is not well
characterized how early-life social isolation leads to social deficits and
impacts development. In many model specie...
Article
Full-text available
| Francisco J. H. Heras |
A variety of simple
models has been proposed to understand the collective motion of animals.
These models can be insightful but may lack important elements necessary to
predict the motion of each individual in the collective. Adding more detail
increases predictability but can make models too complex to be insightful.
Here we report that deep atten...
Article
Full-text available
| Victòria Brugada-Ramentol |
The sense of ownership,
the feeling that our body belongs to ourselves, relies on multiple sources of
sensory information. Among these sources, the contribution of visuomotor
information is still debated. We tested the effect of active control in the
sense of ownership in the moving Virtual Hand Illusion. Participants reported
sense of ownership an...
Article
Full-text available
| Francisco Romero-Ferrero |
| Gonzalo G de Polavieja |
Understanding of animal
collectives is limited by the ability to track each individual. We describe
an algorithm and software that extract all trajectories from video, with high
identification accuracy for collectives of up to 100 individuals. idtracker.ai
uses two convolutional networks: one that detects when animals touch or cross
and another for...
Article
Full-text available
| Christos C Ioannou |
| Gonzalo G de Polavieja |
How effective groups are
in making decisions is a long-standing question in studying human and animal
behaviour. Despite the limited social and cognitive abilities of younger
people, skills which are often required for collective intelligence, studies
of group performance have been limited to adults. Using a simple task of
estimating the number of...
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The relationship between
individual estimates before and after group discussion in Experiment 1. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The effect of
disagreement (range) in initial estimates on improving group estimates in
Experiment 2. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The effect of question
order and treatment on the disagreement (range) of initial estimates in
Experiment 2. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
Log-likelihood of simple
aggregation rules, the noisy geometric mean model, and confidence intervals
for frequencies of the aggregation rules using the noisy geometric mean
model. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The relationship between
the range of initial estimates and estimates given by the group or calculated
from initial estimates in Experiment 1. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
Fits of different
aggregation rules to the observed data at various levels of added noise in
Experiment 1. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
Distribution of
individual initial estimates in Experiment 2. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The effect of question
order on the absolute error of (initial and group consensus) estimates in
Experiment 2. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The age distribution of
participants in Experiment 1, correlations within groups, and distribution of
individual initial estimates. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The jars of sweets used
in Experiment 1 and Experiment 2. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The use and consequence
of different aggregation rules for different thresholds that define groups as
having a low or high range in Experiment 1. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
Correlations across
treatments in the range of individual initial estimates per group. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The relationship between
participants’ self-rated confidence and error and the change in individuals
estimates between stages. (PDF)
Data
| Christos C Ioannou |
| Gonzalo G de Polavieja |
The distribution of the
difference between the group estimate and the mean of initial estimates.
(PDF)
Article
Full-text available
| Andres Laan |
Theoretical studies of
ecosystem models have generally concluded that large numbers of species will
not stably coexist if the species are all competing for the same limited set
of resources. Here, we describe a simple multi-trait model of competition where
the presence of N resources will lead to the stable coexistence of up to 2 N
species. Our mo...
Data
| Andres Laan |
Preprint
Full-text available
| Francisco J. H. Heras |
A variety of simple
models has been proposed to understand the collective motion of animals.
These models can be insightful but lack important elements necessary to
predict the motion of each individual in the collective. Adding more detail
increases predictability but can make models too complex to be insightful.
Here we report that deep attention...
Data
| Andres Laan |
Data
| Andres Laan |
Article
| Gonzalo G de Polavieja |
A new study on the
zebrafish has discovered a population of forebrain neurons necessary for
social orienting, providing a foundation for dissecting social brain networks
in this powerful vertebrate model.
Article
Full-text available
| Andres Laan |
Most animals fight by
repeating complex stereotypic behaviours, yet the internal structure of these
behaviours has rarely been dissected in detail. We characterized the internal
structure of fighting behaviours by developing a machine learning pipeline that
measures and classifies the behaviour of individual unmarked animals on a
sub-second time sc...
Preprint
Full-text available
| Andres Laan |
Animals often assess each
other by paying special attention to signals, which help to communicate the
quality of each individual. When there is a conflict of interest between the
signaler and the receiver, then the signaler has an incentive to cheat by producing
signals which exaggerate its apparent quality. One opportunity for cheating
might be to...
Article
Full-text available
| Angel Carlos Roman |
| Gonzalo G de Polavieja |
Background: Animals can
show very different behaviors even in isogenic populations, but the
underlying mechanisms to generate this variability remain elusive. We use the
zebrafish (Danio rerio) as a model to test the influence of histone
modifications on behavior. Results: We find that laboratory and isogenic
zebrafish larvae show consistent ind...
Data
| Angel Carlos Roman |
| Gonzalo G de Polavieja |
Data
| Angel Carlos Roman |
| Gonzalo G de Polavieja |
Article
Full-text available
| Fernando Martin Maroto |
Machine learning
algorithms use error function minimization to fit a large set of parameters
in a preexisting model. However, error minimization eventually leads to a
memorization of the training dataset, losing the ability to generalize to
other datasets. To achieve generalization something else is needed, for
example a regularization method or st...
Preprint
Full-text available
| Francisco Romero-Ferrero |
| Gonzalo G de Polavieja |
Our understanding of
collective animal behavior is limited by our ability to track each of the
individuals. We describe an algorithm and software, idtracker.ai, that
extracts from video all trajectories with correct identities at a high
accuracy for collectives of up to 100 individuals. It uses two deep networks,
one detecting when animals touch or...
Article
Full-text available
| Julián Vicente-Page |
According to the classic
results of Galton and Condorcet, as well as in modern decision-making models,
accuracy in groups increases with group size. However, these studies do not
consider the naturally occurring situation in which individuals dynamically
re-evaluate their decision with a possible change of opinion. The dynamics of
re-evaluation in...
Preprint
Full-text available
| Andres Laan |
Ecological models of
community dynamics fall into two main categories. The neutral theory of
biodiversity correctly predicts various large-scale ecosystem characteristics
such as the species abundance distributions. On a smaller scale, the niche
theory of species competition explains population dynamics and interactions
between two to a dozen speci...
Preprint
Full-text available
| Andres Laan |
Most animals fight by
repeating complex stereotypic behaviors, yet the internal structure of these
behaviors has rarely been dissected in detail. We characterized the internal
structure of fighting behaviors by developing a machine learning pipeline
that measures and classifies the behavior of individual unmarked animals on a
sub-second timescale....
Article
Full-text available
| Andres Laan |
The total knowledge
contained within a collective supersedes the knowledge of even its most
intelligent member. Yet the collective knowledge will remain inaccessible to
us unless we are able to find efficient knowledge aggregation methods that
produce reliable decisions based on the behavior or opinions of the
collective’s members. It is often stat...
Article
Full-text available
| Alfonso Pérez-Escudero |
Decision-making theories
explain animal behaviour, including human behaviour, as a response to
estimations about the environment. In the case of collective behaviour, they
have given quantitative predictions of how animals follow the majority
option. However, they have so far failed to explain that in some species and
contexts social cohesion incre...
Data
| Alfonso Pérez-Escudero |
Data
| Mikko Juusola |
| Jouni Takalo |
Simulated voltage
responses of a biophysically realistic R1-R6 photoreceptor model to very
bright 20 Hz, 50 Hz, 100 Hz, 200 Hz and 500 Hz GWN light stimuli at BG1.
Data
| Mikko Juusola |
| Jouni Takalo |
Intracellular voltage
responses of the same R1-R6 photoreceptor to very bright 20 Hz, 50 Hz, 100
Hz, 200 Hz and 500 Hz bursty light stimuli at BG0 (darkness).
Data
| Mikko Juusola |
| Jouni Takalo |
Intracellular voltage
responses of the same R1-R6 photoreceptor to very bright 20 Hz, 50 Hz, 100
Hz, 200 Hz and 500 Hz bursty light stimuli at BG0.5.
Data
| Mikko Juusola |
| Jouni Takalo |
Simulated voltage
responses of a biophysically realistic R1-R6 photoreceptor model to very
bright 20 Hz, 50 Hz, 100 Hz, 200 Hz and 500 Hz bursty light stimuli at BG0.5.
Data
| Mikko Juusola |
| Jouni Takalo |
Intracellular voltage
responses of the same R1-R6 photoreceptor to very bright 20 Hz, 50 Hz, 100
Hz, 200 Hz and 500 Hz bursty light stimuli at BG1.
Data
| Mikko Juusola |
| Jouni Takalo |
Intracellular voltage
responses of the same R1-R6 photoreceptor to very bright 20 Hz, 50 Hz, 100
Hz, 200 Hz and 500 Hz bursty light stimuli at BG1.5.
Data
| Mikko Juusola |
| Jouni Takalo |
Simulated voltage
responses of a biophysically realistic R1-R6 photoreceptor model to very
bright 20 Hz, 50 Hz, 100 Hz, 200 Hz and 500 Hz bursty light stimuli at BG0
(darkness).
Data
| Mikko Juusola |
| Jouni Takalo |
Simulated voltage
responses of a biophysically realistic R1-R6 photoreceptor model to very
bright 20 Hz, 50 Hz, 100 Hz, 200 Hz and 500 Hz GWN light stimuli at BG1.5.
Article
Full-text available
| Mikko Juusola |
| Jouni Takalo |
Article
| Matthieu Louis |
Insects are capable of
spectacular achievements through collective behavior, but examples of such
behavior in fruit flies are rare. New research indicates that Drosophila
larvae engage in coordinated digging to feed collectively.
Preprint
| Angel-Carlos Román |
| Gonzalo G de Polavieja |
Animals can show very
different behaviors even in isogenic populations, but the underlying
mechanisms to generate this variability remain elusive. We found that
laboratory and isogenic zebrafish ( Danio rerio ) larvae showed consistent
individual behaviors when swimming freely in identical wells or in reaction
to stimuli. We also found that this be...
Preprint
Full-text available
| Mikko Juusola |
| Jouni Takalo |
Small fly eyes should not
see fine image details. Because flies exhibit saccadic visual behaviors and
their compound eyes have relatively few ommatidia (sampling points), their
photoreceptors would be expected to generate blurry and coarse retinal images
of the world. Here we demonstrate that Drosophila see the world far better
than predicted from...
Article
Full-text available
| Mikko Juusola |
| Jouni Takalo |
Small fly eyes should not
see fine image details. Because flies exhibit saccadic visual behaviors and
their compound eyes have relatively few ommatidia (sampling points), their
photoreceptors would be expected to generate blurry and coarse retinal images
of the world. Here we demonstrate that Drosophila see the world far better
than predicted from...
Article
Full-text available
| Andress Laan |
Animals moving in groups
coordinate their motion to remain cohesive. A large amount of data and
analysis of movement coordination has been obtained in several species, but
we are lacking theoretical frameworks that can derive the form of
coordination rules. Here, we examine whether optimal control theory can
predict the rules underlying social inte...
Data
| Andress Laan |
Article
| Michael B Orger |
A great challenge in
neuroscience is understanding how activity in the brain gives rise to
behavior. The zebrafish is an ideal vertebrate model to address this
challenge, thanks to the capacity, at the larval stage, for precise
behavioral measurements, genetic manipulations, and recording and
manipulation of neural activity noninvasively and at sin...
Article
Full-text available
| Romain J G Clément |
| Jens Krause |
Collective cognition has
received much attention in recent years but most of the empirical work has
focused on comparing individuals and groups within single populations,
thereby not addressing evolutionary origins of collective cognition. Here, we
investigated collective cognition in multiple populations that are subject to
different levels of pre...
Article
Full-text available
| Robert C. Hinz |
The striking patterns of
collective animal behavior, including ant trails, bird flocks, and fish
schools, can result from local interactions among animals without centralized
control. Several of these rules of interaction have been proposed, but it has
proven difficult to discriminate which ones are implemented in nature. As a
method to better disc...
Article
| Andres Laan |
Evolutionary game theory
has been the theoretical tool of choice for analysis of social interactions
in general and aggressive interaction in particular. Many important game
theory models of aggression are formulated based on assumptions about short
timescale behavior but are tested trough measuring long timescale behavior.
The resulting methodolog...
Article
Full-text available
| Victòria Brugada-Ramentol |
Feeling embodiment over
our body or body part has a major role in the understanding of the self and
control of self-actions. Even though it is crucial in our daily life,
embodiment is not an homogenous phenotype across population, as quantified by
implicit and explicit measures (i.e., neuroimaging or self-reports). Studies
have shown differences in...
Data
| Mathieu Duteil |
| Andrew J King |
Electronic Supplementary
Material: Details of fish rearing conditions and three Supplementary Figures
(Figures S1-S3) are provided
Article
Full-text available
| Mathieu Duteil |
| Andrew J King |
Ocean acidification
(OA)-caused by rising concentrations of carbon dioxide (CO2)-is thought to be
a major threat to marine ecosystems and has been shown to induce behavioural
alterations in fish. Here we show behavioural resilience to nearfuture OA in
a commercially important and migratory marine finfish, the Sea bass
(Dicentrarchus labrax). Sea ba...
Article
| Simona Gradari |
| José Luis Trejo |
Doublecortin
(DCX)-Calretinin (CLR) immunolabeling of the hippocampal dentate gyrus of a 4
month old male mice (Mus musculus). DCX+ (red) and CLR+ (green) neurons in a
section from a control (no treatment) mouse, where both DCX+/CLR+ and
DCX+/CLR+ can be appreciated. This dual labeling lets to count two different
subpopulation of immature, differen...
Preprint
| Alfonso Pérez-Escudero |
In adverse conditions,
individuals follow the majority more strongly. This phenomenon is very
general across social species, but explanations have been particular to the
species and context, including antipredatory responses, deflection of
responsibility, or increase in uncertainty. Here we show that the impact of
social information in realistic de...
Article
| Simona Gradari |
| José Luis Trejo |
The influence of the
learning process on the persistence of the newly acquired behavior is
relevant both for our knowledge of the learning/memory mechanisms and for the
educational policy. However, it is unclear whether during an operant
conditioning process with a continuous reinforcement paradigm, individual
differences in acquisition are also as...
Article
Full-text available
| Mathieu Duteil |
| Andrew J King |
Ocean acidification
(OA)—caused by rising concentrations of carbon dioxide (CO2)—is thought to be
a major threat to marine ecosystems and has been shown to induce behavioural
alterations in fish. Here we show behavioural resilience to near-future OA in
a commercially important migratory marine finfish, the European sea bass
(Dicentrarchus labrax)....
Article
Full-text available
| Mathieu Duteil |
| Andrew J King |
Ocean acidification
(OA)—caused by rising concentrations of carbon dioxide (CO2)—is thought to be
a major threat to marine ecosystems and has been shown to induce behavioural
alterations in fish. Here we show behavioural resilience to near-future OA in
a commercially important migratory marine finfish, the European sea bass
(Dicentrarchus labrax)....
Article
Full-text available
| Przemyslaw A. Grabowicz |
| Krishna P. Gummadi |
Humans, like many other
animal species, often make choices under social influence. Experiments in
ants and fishes have shown that individuals choose according to estimations
of which option to take given private and social information. Principled
approaches based on probabilistic estimations by agents give mathematical
formulas explaining experimen...
Article
Full-text available
| Gabriel Madirolas |
Groups can make precise
collective estimations in cases like the weight of an object or the number of
items in a volume. However, in others tasks, for example those requiring
memory or mental calculation, subjects often give estimations with large
deviations from factual values. Allowing members of the group to communicate
their estimations has the...
Conference
Paper
Full-text available
| Mathieu Duteil |
| Andrew J King |
Ocean acidification (OA),
caused by rising concentrations of carbon dioxide (CO2), is thought to be a
major threat to marine ecosystems and has been shown to induce behavioural
alterations in various species of fish. Recent investigations into the effects
of near-future OA conditions on the behaviour of early life stages of marine
fish have provide...
Article
Full-text available
| Germán Sumbre |
Article
| Anthony I Dell |
| Ulrich Brose |
The behavior of
individuals determines the strength and outcome of ecological interactions,
which drive population, community, and ecosystem organization. Bio-logging,
such as telemetry and animal-borne imaging, provides essential individual
viewpoints, tracks, and life histories, but requires capture of individuals
and is often impractical to scal...
Article
Full-text available
| Gonzalo G de Polavieja |
Human groups can perform
extraordinary accurate estimations compared to individuals by simply using
the mean, median or geometric mean of the individual estimations [Galton
1907, Surowiecki 2005, Page 2008]. However, this is true only for some tasks
and in general these collective estimations show strong biases. The method
fails also when allowing...
Data
Full-text available
| A.I. Dell |
| Ulrich Brose |
Article
Full-text available
| Alfonso Pérez-Escudero |
| Gonzalo G de Polavieja |
Animals in groups touch
each other, move in paths that cross, and interact in complex ways. Current
video tracking methods sometimes switch identities of unmarked individuals
during these interactions. These errors propagate and result in random
assignments after a few minutes unless manually corrected. We present
idTracker, a multitracking algorit...
Article
Full-text available
| Alfonso Pérez-Escudero |
Decisions in a group
often result in imitation and aggregation, which are enhanced in panic,
dangerous, stressful or negative situations. Current explanations of this
enhancement are restricted to particular contexts, such as anti-predatory
behavior, deflection of responsibility in humans, or cases in which the
negative situation is associated with...
Article
| Marta Rivera-Alba |
The placement of neuronal
cell bodies relative to the neuropile differs among species and brain areas.
Cell bodies can be either embedded as in mammalian cortex or segregated as in
invertebrates and some other vertebrate brain areas. Why are there such different
arrangements? Here we suggest that the observed arrangements may simply be a
reflection...
Article
Full-text available
| Amanda Sorribes |
| Karl Æ Karlsson |
Zebrafish (Danio rerio)
are used extensively in sleep research; both to further understanding of
sleep in general and also as a model of human sleep. To date, sleep studies
have been performed in larval and adult zebrafish but no efforts have been
made to document the ontogeny of zebrafish sleep-wake cycles. Because sleep
differs across phylogeny a...
Article
Full-text available
| Alfonso Pérez-Escudero |
| Gonzalo G de Polavieja |
Miller et al. (1)
demonstrate, by confronting groups of fish with three options, that
information can be effectively integrated, allowing consensus despite no
individual being aware of the consensus option. The different ways in which
the conflict can be resolved allow testing of collective decision-making
theories.
Article
Full-text available
| Thomas Pietri |
| Germán Sumbre |
Rett syndrome (RTT) is an
X-linked neurodevelopmental disorder and one of the most common causes of
mental retardation in affected girls. Other symptoms include a rapid
regression of motor and cognitive skills after an apparently early normal
development. Sporadic mutations in the transcription factor MECP2 has been
shown to be present in more than...
Article
| Sara Arganda |
Article
| Blanchard Florence |
Article
Full-text available
| Sara Arganda |
A diversity of
decision-making systems has been observed in animal collectives. In some
species, choices depend on the differences of the numbers of animals that
have chosen each of the available options, whereas in other species on the
relative differences (a behavior known as Weber's law), or follow more
complex rules. We here show that this dive...
Article
Full-text available
| Gabriel Madirolas |
Decisions by humans
depend on their estimations given some uncertain sensory data. These
decisions can also be influenced by the behavior of others. Here we present a
mathematical model to quantify this influence, inviting a further study on
the cognitive consequences of social information. We also expect that the
present model can be used for a be...
Article
| Marta Rivera-Alba |
| Gonzalo G de Polavieja |
Article
Full-text available
| Marta Rivera-Alba |
| Gonzalo G de Polavieja |
Wiring economy has
successfully explained the individual placement of neurons in simple nervous
systems like that of Caenorhabditis elegans [1-3] and the locations of
coarser structures like cortical areas in complex vertebrate brains [4].
However, it remains unclear whether wiring economy can explain the placement
of individual neurons in brains l...
Data
| Alfonso Pérez-Escudero |
Comparison between
different models for the condition with two different replicas.
Experimentally measured statistics of final configurations of fish choices
from 20 experimental repetitions [43] (blue histograms). Red line: results
from model in Eq. 20 in the main text (, = 0.35, 0.7, 0.5, 0.52, 0.69, 0.75,
0.43, 0.55, 0.78, 0.43 for each row from...
Data
Full-text available
| Alfonso Pérez-Escudero |
Derivation of the model
with more options. This file contains the derivation of the model for the
more general case of different options (instead of only 2, as presented in
the main text). (PDF)
Data
| Alfonso Pérez-Escudero |
Comparison between model
including dependencies and stickleback choices in symmetric set-up. (A)
Schematic diagram of symmetric set-up with a group of sticklebacks (in black)
choosing between two identical refugia and with different numbers of replica
fish (in red) going to and . (B) Experimentally measured statistics of final
configurations of fis...
Data
| Alfonso Pérez-Escudero |
Goodness of fit of the
model including dependencies for different values of . Red: Symmetric case
(data in Fig. S4). Green: Case with different replicas at each side (data in
Fig. 9. The parameters are re-optimized for each value of ). Blue: Asymmetric
set-up with predator on one side (data in Fig. S5; Parameter is re-optimized
for each value of )....
Data
| Alfonso Pérez-Escudero |
Comparison between
different models for the symmetric set-up. Experimentally measured statistics
of final configurations of fish choices from 20 experimental repetitions [42]
(blue histograms). Red line: results from our single-parameter model assuming
independence in Eq. 17 in the main text (). Green line: Enhanced model
assuming independence with...
Data
| Alfonso Pérez-Escudero |
Comparison between
different models in the asymmetrical set-up. Experimentally measured
statistics of final configurations of fish choices from 20 experimental
repetitions [42] (blue histograms). Red line: results from model neglecting
dependencies in Eq. 22 in the main text (, ). Green line: Enhanced model
neglecting dependencies with different re...
Data
| Alfonso Pérez-Escudero |
Comparison between model
including dependencies and stickleback choices in asymmetric set-up. A)
Schematic diagram of asymmetric set-up (predator at , large fish depicted in
red) with a group of sticklebacks (in black) choosing between two refugia,
and replica fish (small fish depicted in red) going to . (B) Experimentally
measured statistics of fi...
Data
| Alfonso Pérez-Escudero |
Algorithm for the model
that neglects dependencies. This file contains Matlab code that runs the
model without dependencies. Please, change extension from .txt to .m to make
it operative. It can be run without any input argument. Once the extension is
changed to .m, simply type ProtocolS1 in Matlab's command window to get
results for default parame...
Data
| Alfonso Pérez-Escudero |
Algorithm for the model
that takes dependencies into account. This file contains Matlab code that
runs the model with dependencies. Please, change extension from .txt to .m to
make it operative. It can be run without any input argument. Once the
extension is changed to .m, simply type ProtocolS2 in Matlab's command window
to get results for default...
Article
Full-text available
| Alfonso Pérez-Escudero |
Animals living in groups
make movement decisions that depend, among other factors, on social
interactions with other group members. Our present understanding of social
rules in animal collectives is mainly based on empirical fits to
observations, with less emphasis in obtaining first-principles approaches
that allow their derivation. Here we show t...
Data
| Amanda Sorribes |
| Gonzalo G de Polavieja |
Short and long-term
memory. Flies of three commonly used genotypes (Canton-S (CS), yellow-white
(yw) and w1118) and of two ages (3 days and 4 weeks) and tethered flight data
from reference [21] were tested for (A) short-term and (B) long-term memory.
Significance levels are computed by comparison of actual and shuffled data
(white bars). Note that...
Data
| Amanda Sorribes |
| Gonzalo G de Polavieja |
The fit method correctly
estimates the underlying parameters k and λ of the Weibull distribution.
To test that the fitting technique used to obtain the parameters k and λ
for real fly data is accurate, we performed two different kinds of fits (‘Linear’
and ‘Non-linear’) to artificial data with known parameters. 50 (red), 100
(orange) 150 (green) 20...
