arXiv subjects

Basile Grammaticos

Publications and source records attributed to Basile Grammaticos.

7 recordsLinked to original sources

arXiv2024

On the duration of face-to-face contacts

The analysis of social networks, in particular those describing face-to-face interactions between individuals, is complex due to the intertwining of the topological and temporal aspects. We revisit them both, using public data recorded by the sociopatterns wearable sensors in some very different sociological environments, putting particular emphasis on the contact duration timelines. As well known, the distribution of the contact duration for all the interactions within a group is broad, with tails that resemble each other, but not precisely, in different contexts. By separating each interacting pair, we find that the fluctuations of the contact duration around the mean-interaction time follow however a very similar pattern. This common robust behavior is observed on 7 different datasets. It suggests that, although the set of persons we interact with and the mean-time spent together, depend strongly on the environment, our tendency to allocate more or less time than usual with a given individual is invariant, i.e. governed by some rules that lie outside the social context. Additional data reveal the same fluctuations in a baboon population. This new metric, which we call the relation *contrast*, can be used to build and test agent-based models, or as an input for describing long duration contacts in epidemiological studies.

physics.soc-ph↗

arXiv2023

Deautonomisation by singularity confinement and degree growth

In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement. These observations are of a link between two a priori unrelated notions: firstly the dynamical degree of the mapping and secondly the evolution of parameters required for its singularity structure to remain unchanged under a sufficiently general deautonomisation. We explain this correspondence for a large class of birational mappings of the plane via the spaces of initial conditions for their deautonomised versions. We show that even for non-integrable mappings in this class, the surfaces forming these spaces have effective anticanonical divisors and one can define a period map parametrising them, similar to that in the theory of rational surfaces associated with discrete Painlev\'e equations. This provides a bridge between the evolution of coefficients in the deautonomised mapping and the induced dynamics on the Picard lattice which encode the dynamical degree.

nlin.SI↗

arXiv2022

Predicting regrowth of low-grade gliomas after radiotherapy

Diffuse low grade gliomas are invasive and incurable brain tumours that inevitably transform into higher grade ones. A classical treatment to delay this transition is radiotherapy (RT). Following RT, the tumour gradually shrinks during a period of typically 6 months to 4 years before regrowing. To improve the patient's health-related quality of life and help clinicians build personalised follow-ups, one would benefit from predictions of the time during which the tumour is expected to decrease. The challenge is to provide a reliable estimate of this regrowth time shortly after RT (i.e. with few data), although patients react differently to the treatment. To this end, we analyse the tumour size dynamics from a batch of 20 high-quality longitudinal data, and propose a simple and robust analytical model, with just 4 parameters. From the study of their correlations, we build a statistical constraint that helps determine the regrowth time even for patients for which we have only a few measurements of the tumour size. We validate the procedure on the data and predict the regrowth time at the moment of the first MRI after RT, with precision of, typically, 6 months. Using virtual patients, we study whether some forecast is still possible just three months after RT. We obtain some reliable estimates of the regrowth time in 75\% of the cases, in particular for all "fast-responders". The remaining 25\% represent cases where the actual regrowth time is large and can be safely estimated with another measurement a year later. These results show the feasibility of making personalised predictions of the tumour regrowth time shortly after RT.

physics.med-ph↗

arXiv2021

Radiotherapy Effects on Diffuse Low-Grade Gliomas: Confronting Theory With Clinical Data

Diffuse low grade gliomas are slowly growing tumors that always recur after treatment. In this paper, we revisit the modeling of the tumor radius evolution before and after the radiotherapy process and propose a novel model that is simple, yet biologically motivated, and that remedies some shortcomings of previously proposed ones. We confront it with clinical data consisting in time-series of tumor radius for 43 patient records, using a stochastic optimization technique and obtain very good fits in all the cases. Since our model describes the evolution of the tumor from the very first glioma cell, it gives access to the possible age of the tumor. Using the technique of profile-likelihood to extract all the information from the data, we build confidence intervals for the tumor birth age and confirm the fact that low-grade glioma seem to appear in the late teenage years. Moreover, an approximate analytical expression of the temporal evolution of the tumor radius allows us to explain the correlations observed in the data.

physics.med-ph↗

arXiv2018

Quantitative characterization of the imaging limits of diffuse low-grade oligodendrogliomas

Background : Supratentorial diffuse low-grade gliomas in adults extend beyond maximal visible MRI-defined abnormalities, and a gap exists between the imaging signal changes and the actual tumor margins. Direct quantitative comparisons between imaging and histological analyses are lacking to date. However, they are of the utmost importance if one wishes to develop realistic models for diffuse glioma growth. Methods : In this study, we quantitatively compare the cell concentration and the edema fraction from human histological biopsy samples (BSs) performed inside and outside imaging abnormalities during serial imaging-based stereotactic biopsy of diffuse low-grade gliomas. Results : The cell concentration was significantly higher in BSs located inside (1189 $\pm$ 378 cell/mm$^2$) than outside (740 $\pm$ 124 cell/mm$^2$) MRI-defined abnormalities (p=0.0003). The edema fraction was significantly higher in BSs located inside (mean, 45 $\pm$ 23%) than outside (mean, 5 $\pm$ 9%) MRI-defined abnormalities (p<0.0001). At borders of the MRI-defined abnormalities, 20% of the tissue surface area was occupied by edema, and only 3% by tumor cells. The cycling cell concentration was significantly higher in BSs located inside (10 $\pm$ 12 cell/mm$^2$) compared to outside (0.5 $\pm$ 0.9 cell/mm$^2$) MRI-defined abnormalities (p=0.0001). Conclusions : We show that the margins of T2-weighted signal changes are mainly correlated with the edema fraction. In 62.5% of patients, the cycling tumor cell fraction (defined as the ratio of the cycling tumor cell concentration to the total number of tumor cells) was higher at the limits of the MRI-defined abnormalities than closer to the center of the tumor. In the remaining patients, the cycling tumor cell fraction increased towards the center of the tumor.

q-bio.TO↗

arXiv2007

Integrable lattice equations and their growth properties

In this paper we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show that while for generic, nonintegrable equations, the degree grows exponentially fast, for integrable lattice equations the degree growth is polynomial. The growth criterion is used in order to obtain the integrable deautonomisations of the equations examined. In the case of linearisable lattice equations we show that the degree growth is slower than in the case of equations integrable through Inverse Scattering Transform techniques.

math-ph↗

arXiv2007

Integrable systems without the Painlevé property

We examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we investigate whether the singularity confinement property is satisfied for the discrete analogues of the non-Painlevé continuous linearisable systems. We find that while these discrete systems are themselves linearisable, they possess nonconfined singularities.

math-ph↗