The paper provides numerical measures and visualizations of urban segregation based on a new index, the Distortion coefficient. Distortion coefficients are derived from trajectories of contact with ...the city’s population as an individual will encounter an increasing number of persons in a growing distance from their original location. They can be interpreted as measures of how different, or in technical terms, how distorted the view of the city is from any one location. In this paper, we present the theoretical rationale and the procedure leading to the computation of the Distortion coefficients. Through a detailed illustration using Chicago as a case study, we provide the general framework for analyzing and visualizing Distortion. We show that these measures are able to capture complex demographic changes over time and paint a more complete picture of segregation than indices based on imposed scales.
Full text
Available for:
BFBNIB, DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
Rédigé par une historienne et un spécialiste de modélisation mathématique, cet article explore les enjeux épistémologiques de la collaboration interdisciplinaire à travers une étude de cas : ...l’épuration professionnelle du monde du spectacle à la Libération. Dans tout processus de justice, la question de l’équité, ou celle, équivalente, d’éventuelles discriminations, est difficile à instruire. A fortioripour une épuration à caractère disciplinaire, où des artistes ont jugé leurs pairs. L’article montre que le formalisme mathématique, loin de se substituer à l’expertise historique, prolonge celle-ci par les moyens d’un autre langage, abstrait, enrichissant ainsi les modes d’accès au réel en faisant converger plusieurs dispositifs d’enquête. Progressant pas à pas dans la modélisation du problème et dans l’analyse des données, les deux chercheurs prennent soin d’expliciter les approches statistiques et mathématiques de plus en plus complexes qu’ils doivent mobiliser pour détecter des formes jurisprudentielles impossibles à capturer avec des outils classiques – jusqu’à l’idée originale de traiter un processus impliquant des décisions humaines comme un processus algorithmique complexe. Grâce au détournement d’une méthode d’inférence causale conçue pour étudier l’équité de certains processus algorithmiques de type « boîte noire », des résultats inédits, restés jusqu’alors totalement « cachés » dans les données, sont révélés et viennent, en retour, guider l’analyse historique.
We introduce a multidimensional, neural network approach to reveal and measure urban segregation phenomena, based on the self-organizing map algorithm (SOM). The multidimensionality of SOM allows one ...to apprehend a large number of variables simultaneously, defined on census blocks or other types of statistical blocks, and to perform clustering along them. Levels of segregation are then measured through correlations between distances on the neural network and distances on the actual geographical map. Further, the stochasticity of SOM enables one to quantify levels of heterogeneity across census blocks. We illustrate this new method on data available for the city of Paris.
Full text
Available for:
DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this ...process is nonstationary and its probability distribution exhibits rich features. In a finite domain, we define a nontrivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.
Full text
Available for:
CMK, CTK, FMFMET, IJS, NUK, PNG, UL, UM
Let (St)t≥0 be the running maximum of a standard Brownian motion (Bt)t≥0 and Tm≔inf{t;mSt<t},m>0. In this note we calculate the joint distribution of Tm and BTm. The motivation for our work comes ...from a mathematical model for animal foraging. We also present results for Brownian motion with drift.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
First-passage-driven boundary recession De Bruyne, B; Randon-Furling, J; Redner, S
Journal of physics. A, Mathematical and theoretical,
09/2022, Volume:
55, Issue:
35
Journal Article
Peer reviewed
Open access
Abstract
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of ...the particle and the boundary. Phenomenologically rich dynamics arises. In particular, the probability for the particle to first reach the moving boundary for the
n
th time asymptotically scales as
t
−
(
1
+
2
−
n
)
. Because the tail of this distribution becomes progressively fatter, the typical time between successive first passages systematically gets longer. We also find that the number of collisions between the particle and the boundary scales as ln ln
t
, while the time dependence of the boundary position varies as
t
/ln
t
.
Fine-scale data is particularly important for the analysis of multiscalar segregation phenomena. Using dis-aggregated data from an EU data challenge, we show here how to apply a recently developed ...method that measures segregation at multiple scales and provides a visualization of the levels of segregation across scale and space. We illustrate the technique with results for two groups of citizen migrants in the city of Paris.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We combine the processes of resetting and first passage, resulting in first-passage resetting, where the resetting of a random walk to a fixed position is triggered by the first-passage event of the ...walk itself. In an infinite domain, first-passage resetting of isotropic diffusion is non-stationary, and the number of resetting events grows with time according to t. We analytically calculate the resulting spatial probability distribution of the particle, and also obtain the distribution by geometric-path decomposition. In a finite interval, we define an optimization problem that is controlled by first-passage resetting; this scenario is motivated by reliability theory. The goal is to operate a system close to its maximum capacity without experiencing too many breakdowns. However, when a breakdown occurs the system is reset to its minimal operating point. We define and optimize an objective function that maximizes reward for being close to the maximum level of operation and imposes a penalty for each breakdown. We also investigate extensions of this basic model, firstly to include a delay after each reset, and also to two dimensions. Finally, we study the growth dynamics of a domain in which the domain boundary recedes by a specified amount whenever the diffusing particle reaches the boundary, after which a resetting event occurs. We determine the growth rate of the domain for a semi-infinite line and a finite interval and find a wide range of behaviors that depend on how much recession occurs when the particle hits the boundary.
Explicit formulas for the expected volume and expected number of facets of the convex hull of several multidimensional Gaussian random walks are derived in terms of the Gaussian persistence ...probabilities. Special cases include the already known results about the convex hull of a single Gaussian random walk and the d-dimensional Gaussian polytope with or without origin.
Full text
Available for:
EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
PDF
