arXiv subjects

Florian Martin

Publications and source records attributed to Florian Martin.

3 recordsLinked to original sources

arXiv2026

Sorry for the late reply: Response times and reciprocity in WhatsApp and Instagram chats

Chat communication is often fast-paced, creating the expectation of quick replies. While the timing of exchanges is known to foster closeness and enjoyment, it remains largely unexplored whether chat partners with strong ties reciprocate each other's response times. Using 3.4 million messages from 889 chats across 97 donations of anonymous WhatsApp and Instagram chats, we analyzed response times, their balance between chat partners, and its stability over time. To our knowledge, this is the first study to examine response speed as an expression of reciprocity, bridging a key aspect of online communication with a fundamental principle of social interactions. We found that around 70% of WhatsApp and 44% of Instagram messages were answered within five minutes, confirming the fast pace of instant messaging. Overall, the response speed between chat partners was similar. The response speed similarity was evident both in the overall response-time distributions of chat partners assessed with Jensen-Shannon distance and in the steep regression slopes (0.786 for WhatsApp and 0.796 for Instagram) linking one person's probability of responding within five minutes to the partner's corresponding probability. Importantly, the dispersion of response time similarity over months showed that this balance persists over time. Our results position response time balance as a marker of reciprocity in computer-mediated communication, offering a new way to quantitatively study this fundamental principle of social interaction. We suggest using response speed balance as a complementary metric in the analysis of relationship dynamics, such as the strengthening or weakening of social ties.

cs.SI↗

arXiv2021

Trimmed Spline Surfaces with Accurate Boundary Control

We introduce trimmed NURBS surfaces with accurate boundary control, briefly called ABC-surfaces, as a solution to the notorious problem of constructing watertight or smooth ($G^1$ and $G^2)$ multi-patch surfaces within the function range of standard CAD/CAM systems and the associated file exchange formats. Our construction is based on the appropriate blend of a base surface, which traces out the intended global shape, and a series of reparametrized ribbons, which dominate the shape near the boundary.

cs.GR↗

arXiv2015

Synergy, suppression and immorality: forward differences of the entropy function

Conditional mutual information is important in the selection and interpretation of graphical models. Its empirical version is well known as a generalised likelihood ratio test and that it may be represented as a difference in entropy. We consider the forward difference expansion of the entropy function defined on all subsets of the variables under study. The elements of this expansion are invariant to permutation of their suffices and relate higher order mutual informations to lower order ones. The third order difference is expressible as an, apparently assymmetric, difference between a marginal and a conditional mutual information. Its role in the decomposition for explained information provides a technical definition for synergy between three random variables. Positive values occur when two variables provide alternative explanations for a third; negative values, termed synergies, occur when the sum of explained information is greater than the sum of its parts. Synergies tend to be infrequent; they connect the seemingly unrelated concepts of suppressor variables in regression, on the one hand, and unshielded colliders in Bayes networks (immoralities), on the other. We give novel characterizations of these phenomena that generalise to categorical variables and to higher dimensions. We propose an algorithm for systematically computing low order differences from a given graph. Examples from small scale real-life studies indicate the potential of these techniques for empirical statistical analysis.

stat.ME↗