scholarly journals La méthode des élucidations successives

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Claude Lobry
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Natural Language ◽  
Human Brain ◽  
Formal Language ◽  
Formal Model ◽  
Formal Models ◽  
Dynamique Des Populations ◽  
International Audience ◽  
Modelling Process

International audience In the process of elaboration of a model one emphasize on the necessity of confronting the model with the reality which it is supposed to represent. There is another aspect of the modelling process, to my opinion also essential, about which one usually do not speak. It consists in a logico-linguistic work where formal models are used to produce prediction which are not confronted with the reality but serve for falsifying assertions which nevertheless seemed to be derived from the not formalized model. More exactly a first informal model is described in the natural language and, considered in the natural language, seems to say some thing but in a more or less clear way. Then we translate the informal model into a formal model (mathematical model or computer model) where what was argumentation becomes demonstration.The formal model so serves for raising ambiguities of the natural language. But conversely a too much formalized text quickly loses any sense for a human brain what makes necessary the return for a less formal language. It is these successive "translations" between more or less formal languages that I try to analyze on two examples, the first one in population dynamics, the second in mathematics. Dans le processus d’élaboration d’un modèle on insiste beaucoup sur la nécessité de confronter le modèle à la réalité qu’il est sensé représenter. Il est un autre aspect de la modélisation, à mon avis tout aussi essentiel, dont on ne parle pas. Il s’agit d’un travail logico-linguistique où des modèles formels sont utilisés pour produire des prédiction qui ne sont pas confrontées à la réalité mais servent à falsifier des affirmations qui semblaient pourtant se déduire du modèle. Plus précisément un premier modèle informel est décrit dans la langue naturelle et, toujours dans la langue naturelle, semble dire quelques chose mais de façon plus ou moins claire. Alors on traduit le modèle informel en un modèle formel (mathématique ou informatique) où ce qui était argumentation devient démonstration. Le modèle formel sert ainsi à lever des ambiguïtés de la langue naturelle. Mais inversement un texte trop formalisé perd rapidement tout sens pour un cerveau humain ce qui rend nécessaire le retour à une langue moins formelle. Ce sont ces “traductions" successives entre langues plus ou moins formelles que je cherche à analyser sur deux exemples, le premier en dynamique des populations, le second en mathématiques.

scholarly journals Applications de méthodes d’agrégation de variables à l’analyse de modèles spatiaux de dynamique des populations

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Tri Nguyen-Huu ◽  
Pierre Auger
Keyword(s):  
Population Dynamics ◽  
Time Scales ◽  
Discrete Models ◽  
Global Dynamics ◽  
Dynamique Des Populations ◽  
Simplified Models ◽  
Aggregation Of Variables ◽  
Reduced Models ◽  
International Audience ◽  
Different Time Scales

International audience Models in population dynamics can deal with an important number of parameters and variables, which can make them difficult to analyse. Aggregation of variables allow reducing complexity of such models by building simplified models governing fewer variables by use of the existence of different time scales associated to the processes governing the whole system. Those reduced models allows analysing and describing the global dynamics of the system. We present those methods for time discrete models and illustrate their use for the study of spatial host-parasitoids models. Les modèles de dynamique de populations peuvent prendre en compte un nombre important de paramètres et de variables, ce qui les rend difficiles à analyser. Lorsqu’il existe des processus associés à deux échelles de temps différentes, une lente et une rapide, les méthodes d’agrégation de variables permettent de construire un modèle simplifié qui comporte un nombre plus faible de variables. Elles permettent ainsi d’analyser et de décrire un système de manière globale. Nous présentons ces méthodes dans le cas de modèles discrets, puis nous illustrons leur utilisation à l’aide de modèles hôte-parasitoïdes spatialisés.

scholarly journals Migrations in the Rosenzweig-MacArthur model and the "atto-fox" problem

2015 ◽  
Vol Volume 20 - 2015 - Special... ◽  
Author(s):  
Claude Lobry ◽  
Tewfik Sari
Keyword(s):  
Population Dynamics ◽  
Limit Cycle ◽  
Differential System ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Predator Prey ◽  
International Audience

International audience The Rosenzweig-MacArthur model is a system of two ODEs used in population dynamics to modelize the predator-prey relationship. For certain values of the parameters the differential system exhibits a unique stable limit cycle. When the dynamics of the prey is faster than the dynamics of the predator, during oscillations along the limit cycle, the density of preys take so small values that it cannot modelize any actual population. This phenomenon is known as the "atto-fox" problem. In this paper we assume that the populations are living in two patches and are able to migrate from one patch to another. We give conditions for which the migration can prevent the density of prey being too small. Le modèle de Rosenzweig-MacArthur est un système de deux équations différentielles utilisé en dynamique des populations pour modéliser la relation entre un prédateur et sa proie. Pour certaines valeurs des paramètres le système différentiel possède un cycle limite unique stable. Lorsque la dynamique de la proie est plus rapide que celle du prédateur, durant les oscillations le long du cycle, la densité des proies atteint des valeurs tellement petites qu'elle ne peut modéliser une situation issue du monde réel. Ce phénomène est connu sous le nom du problème "atto-fox". Dans cet article on suppose que les populations sont réparties entre deux patches et qu'elles peuvent migrer de l'un à l'autre. Nous donnons des conditions qui assurent que la migration va empêcher la densité des proies de devenir trop petite.

scholarly journals M-ITRS: Mathematical Model for Identification of Tandem Repeats in DNA Sequence

2018 ◽  
Vol 7 (4) ◽  
pp. 179
Author(s):  
Ajay Kumar ◽  
Sunita Garhwal
Keyword(s):  
Mathematical Model ◽  
Molecular Markers ◽  
Molecular Biology ◽  
Dna Sequence ◽  
Genetic Information ◽  
Tandem Repeats ◽  
Formal Model ◽  
Formal Models ◽  
Tree Adjoining Grammar ◽  
Pushdown Automata

<span lang="EN-US">In DNA, tandem repeat consists of two or more contiguous copies of a pattern of nucleotides. Tandem repeats of the motif are useful in many applications like molecular biology (related to genetic information of inherited diseases), forensic medicines, DNA fingerprinting and molecular markers for cancer. Various researchers designed formal models and grammars to identify two contiguous copies of the pattern. Tree-adjoining grammar cannot be designed for k-copy language. There is a need to design a formal model which will work for more than two contiguous copies of the pattern. In this paper, we have designed deep pushdown automata for k-continuous copies of the pattern for <!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1593603612"> </o:OLEObject> </xml><![endif]-->. The proposed formal model will also identify the tandem repeats without specifying the pattern and its size.</span>

scholarly journals 5PM and DoC - Formal Models for Game Design

2020 ◽  
Vol 23 (2) ◽  
Author(s):  
Rodolfo Mora-Zamora ◽  
Esteban Brenes-Villalobos ◽  
Francisco Durán
Keyword(s):  
Game Design ◽  
Formal Language ◽  
Formal Model ◽  
Fine Tuning ◽  
Formal Models ◽  
Top Down ◽  
Game Mechanics ◽  
Novice Designers ◽  
Part Model

A formal language for game design is an endeavor many academics and industry personalities have been tackling since the mid-nineties. One of the most renowned formal models for game design, the MDA Framework, includes steps to delimit and conceptualize the experience with a top-down approach. There is, however, a significant lack of high detail models for mechanic construction as well as difficulty balancing. In this paper we propose two formal models for novice designers. The 5-Part-Model (5PM) for building and diagnosing game mechanics, and the Dimensions of Challenge (DoC) formal model for balancing and fine-tuning difficulty in games.

scholarly journals A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration

2011 ◽  
Vol 5 (4) ◽  
pp. 335-365 ◽  
Author(s):  
Siewe Nourridine ◽  
Miranda I. Teboh-Ewungkem ◽  
Gideon A. Ngwa
Keyword(s):  
Mathematical Model ◽  
Population Dynamics

scholarly journals Dimensional Changes in Lipid Rafts from Human Brain Cortex Associated to Development of Alzheimer’s Disease. Predictions from an Agent-Based Mathematical Model

2021 ◽  
Vol 22 (22) ◽  
pp. 12181
Author(s):  
Guido Santos ◽  
Mario Díaz
Keyword(s):  
Alzheimer’S Disease ◽  
Mathematical Model ◽  
Alzheimer's Disease ◽  
Human Brain ◽  
Lipid Rafts ◽  
Brain Cortex ◽  
Clinical Symptoms ◽  
Senile Plaques ◽  
Amyloid Β ◽  
Human Brain Cortex

Alzheimer’s disease (AD) is a neurodegenerative disease caused by abnormal functioning of critical physiological processes in nerve cells and aberrant accumulation of protein aggregates in the brain. The initial cause remains elusive—the only unquestionable risk factor for the most frequent variant of the disease is age. Lipid rafts are microdomains present in nerve cell membranes and they are known to play a significant role in the generation of hallmark proteinopathies associated to AD, namely senile plaques, formed by aggregates of amyloid β peptides. Recent studies have demonstrated that human brain cortex lipid rafts are altered during early neuropathological phases of AD as defined by Braak and Braak staging. The lipid composition and physical properties of these domains appear altered even before clinical symptoms are detected. Here, we use a coarse grain molecular dynamics mathematical model to predict the dimensional evolution of these domains using the experimental data reported by our group in human frontal cortex. The model predicts significant size and frequency changes which are detectable at the earliest neuropathological stage (ADI/II) of Alzheimer’s disease. Simulations reveal a lower number and a larger size in lipid rafts from ADV/VI, the most advanced stage of AD. Paralleling these changes, the predictions also indicate that non-rafts domains undergo simultaneous alterations in membrane peroxidability, which support a link between oxidative stress and AD progression. These synergistic changes in lipid rafts dimensions and non-rafts peroxidability are likely to become part of a positive feedback loop linked to an irreversible amyloid burden and neuronal death during the evolution of AD neuropathology.

scholarly journals Méthode d'agrégation des variables appliquée à la dynamique des populations

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Pierre Auger ◽  
Abderrahim El Abdllaoui ◽  
Rachid Mchich
Keyword(s):  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Globally Asymptotically Stable ◽  
Density Dependent ◽  
Migration Rates ◽  
First Case ◽  
International Audience ◽  
Predator Model ◽  
Predator System

International audience We present the method of aggregation of variables in the case of ordinary differential equations. We apply the method to a prey - predator model in a multi - patchy environment. In this model, preys can go to a refuge and therefore escape to predation. The predator must return regularly to his terrier to feed his progeny. We study the effect of density-dependent migration on the global stability of the prey-predator system. We consider constant migration rates, but also density-dependent migration rates. We prove that the positif equilibrium is globally asymptotically stable in the first case, and that its stability changes in the second case. The fact that we consider density-dependent migration rates leads to the existence of a stable limit cycle via a Hopf bifurcation. Nous présentons les grandes lignes de laméthode d'agrégation des variables dans les systèmes d'équations différentielles ordinaires. Nous appliquons laméthode à un modèle proie-prédateur spatialisé. Dans ce modèle, les proies peuvent échapper à la prédation en se réfugiant sur un site. Le prédateur doit aussi retourner régulièrement dans son terrier pour nourrir sa progéniture. Nous étudions les effets de migration dépendant de la densité des populations sur la stabilité globale du système proie-prédateur. Nous considérons des taux de migration constants, puis densité-dépendants. Dans le cas de taux constants il existe un équilibre positif toujours stable alors que dans le cas de taux de migration densité-dépendants, il existe un cycle limite stable via une bifurcation de Hopf.

scholarly journals How host phenology impacts multi-season epidemic cycles

2021 ◽  
Author(s):  
Hannelore MacDonald ◽  
Dustin Brisson
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Population Cycles ◽  
Seasonal Activity ◽  
Host Interactions ◽  
Host Phenology ◽  
Demographic Impact ◽  
Host Parasite ◽  
Parasite Populations ◽  
Parasite Dynamics

Parasite-host interactions can result in periodic population dynamics when parasites over-exploit host populations. The timing of host seasonal activity, or host phenology, determines the frequency and demographic impact of parasite-host interactions which may govern if the parasite can sufficiently over-exploit their hosts to drive population cycles. We describe a mathematical model of a monocyclic, obligate-killer parasite system with seasonal host activity to investigate the consequences of host phenology on host-parasite dynamics. The results suggest that parasites can reach the densities necessary to destabilize host dynamics and drive cycling in only some phenological scenarios, such as environments with short seasons and synchronous host emergence. Further, only parasite lineages that are sufficiently adapted to phenological scenarios with short seasons and synchronous host emergence can achieve the densities necessary to over-exploit hosts and produce population cycles. Host-parasite cycles can also generate an eco-evolutionary feedback that slows parasite adaptation to the phenological environment as rare advantageous phenotypes are driven to extinction when introduced in phases of the cycle where host populations are small and parasite populations are large. The results demonstrate that seasonal environments can drive population cycling in a restricted set of phenological patterns and provides further evidence that the rate of adaptive evolution depends on underlying ecological dynamics.

Prominence Semantics for Modality

2021 ◽  
pp. 153-168
Author(s):  
Una Stojnić
Keyword(s):  
Natural Language ◽  
Classical Logic ◽  
Formal Model ◽  
Logical Form ◽  
Context Sensitivity ◽  
Adequate Account ◽  
Language Discourse ◽  
Satisfactory Account ◽  
Demonstrative Pronouns

This chapter develops a formal model of context-sensitivity of modal discourse. Much like demonstrative pronouns, modals are prominence-sensitive, selecting the most prominent candidate interpretation. The prominence ranking of candidate interpretations is recorded in the conversational record, and is maintained through the effects of discourse conventions represented in the logical form of a discourse. In this way arguments are individuated as structured discourses that underwrite a particular propositional pattern. It is shown that such account provably preserves classical logic. Further, this chapter argues that its model offers a more satisfactory account of the individuation of argument patterns in natural language discourse then the competing alternatives. Any adequate account, it is here argued, will have to take into account not just the contribution of individual sentences, but also of discourse conventions. Indeed, the contribution of discourse conventions is crucial for determining the contribution of individual sentences in the first place.

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