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We prove that certain families of compact Coxeter polyhedra in 4- and 5-dimensional hyperbolic space constructed by Makarov give rise to infinitely many commensurability classes of reflection groups in these dimensions., Comment: Final version, to appear in Advances in Mathematics

As the number of empirical studies increases unprecedentedly in line with expansions in higher education, theoretical developments in population studies suffer due to a discoverability crisis of related work. The systematic use of previous research is common in the medical sciences through various types of structured reviews. However, these are less common in the social sciences, despite their potential, especially in cross-disciplinary fields such as migration. We use Google Scholar to examine the niche of housing research within migration studies through a broad range of documents. The contribution of this meta-analysis is threefold. Firstly, we illustrate the association of keywords across the corpus of literature related to migration and housing and map the growth of migration literature since the 1960s. Secondly, we highlight key bridging documents using network measures. Finally, we estimate the distance in reading time between documents. Our findings suggest that the corpus of previous work at the intersection of migration and housing consists of many additive case studies, indicating a gap in integrative approaches replicable across a growing knowledge landscape., Comment: 30 pages, 17 figures, 4 tables

Urban systems are at the core of current sustainability concerns, and their study from a complexity perspective has a long history in several disciplines. We survey this literature and discuss future research directions relevant to sustainable planning, in particular the construction of integrative approaches. We finally illustrate this research program with the coupling of urban simulation models to explore trade-offs between sustainable development goals in systems of cities., Comment: Journ{\'e}es Scientifiques de Rochebrune 2022

We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work with M. Fraczyk and S. Hurtado. We also study in more depth the case of polygons in the hyperbolic plane.

Firm clusters are seen as having a positive effect on innovations, what can be interpreted as economies of scale or knowledge spillovers. The processes underlying the success of these clusters remain difficult to isolate. We propose in this paper a stylised agent-based model to test the role of geographical proximity and informal knowledge exchanges between firms on the emergence of innovations. The model is run on synthetic firm clusters. Sensitivity analysis and systematic model exploration unveil a strong impact of interaction distance on innovations, with a qualitative shift when spatial interactions are more intense. Model bi-objective optimisation shows a compromise between innovation and product diversity, suggesting trade-offs for clusters in practice. This model provides thus a first basis to systematically explore the interplay between firm cluster geography and innovation, from an evolutionary perspective.

We study locally symmetric spaces associated with arithmetic lattices in semisimple Lie groups. We prove the following results about their topology: the minimal number of tetrahedra needed for a triangulation is at most linear in the volume and the Betti numbers are sub-linear in the volume except possibly in middle degree. The proof of these results uses the geometry of these spaces, namely the study of their thin parts. In this regard we prove that these spaces converge in the Benjamini--Schramm sense to their universal covers and give an explicit bound for the volume of the thin part for trace fields of large degree. The main technical ingredients for our proofs are new estimates on orbital integrals, a counting result for elements of small displacement, and a refined version of the Margulis lemma for arithmetic locally symmetric spaces., Comment: 58 pages

The development of public transportation networks and associated transit oriented development policies are efficient tools to mitigate urban sprawl and its negative environmental impacts, especially in terms of commuting emissions. We study in this paper the trajectories in terms of sprawl and public transport accessibility of the nine largest Chinese megacities, from 2000 to 2030 with projected transportation networks and populations. Using the radial profile methodology, we compare the evolution of population distribution with the evolution of accessibility profiles. We show a rebalancing of access in time, suggesting the efficiency of transport network growth regarding transit-oriented development objectives., Comment: 10 pages, 4 figures

Sustainable Development Goals are intrinsically competing, but their embedding into urban systems furthermore emphasises such compromises, due to spatial complexity, the non-optimal nature of such systems, and multi-objective aspects of their agents, among other reasons. We propose in this paper to use a stylised simulation model for systems of cities, focused on innovation diffusion and population dynamics, to show how trade-offs may operate at such a scale. We proceed in particular to a bi-objective optimisation of emissions and innovation utilities, and show that no single urban optimum exists, but a diversity of regimes forming a compromise between the two objectives., Comment: 10 pages, 3 figures

The identification of structuring effects of transportation infrastructure on territorial dynamics remains an open research problem. This issue is one of the aspects of approaches on complexity of territorial dynamics, within which territories and networks would be co-evolving. The aim of this thesis is to challenge this view on interactions between networks and territories, both at the conceptual and empirical level, by integrating them in simulation models of territorial systems., Comment: Doctoral dissertation (2017), Universit\'e Paris 7 Denis Diderot. Translated from French. Several papers compose this PhD thesis; overlap with: arXiv:{1605.08888, 1608.00840, 1608.05266, 1612.08504, 1706.07467, 1706.09244, 1708.06743, 1709.08684, 1712.00805, 1803.11457, 1804.09416, 1804.09430, 1805.05195, 1808.07282, 1809.00861, 1811.04270, 1812.01473, 1812.06008, 1908.02034, 2012.13367, 2102.13501, 2106.11996}

We present the discovery and characterisation of two transiting planets observed by \textit{TESS} in the light curves of the young and bright (V=9.67) star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric space- and ground-based follow-up in order to confirm and characterise the system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm 0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b ($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of $10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c= 18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^ {+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both planets are consistent with worlds made of a solid core surrounded by a volatile envelope. Because of their youth and host star brightness, they both are excellent candidates to perform transmission spectroscopy studies. We expect ongoing atmospheric mass-loss for both planets caused by stellar irradiation. We estimate that the detection of evaporating signatures on H and He would be challenging, but doable with present and future instruments., Comment: Accepted for publication in MNRAS

Understanding the dynamics of road networks has theoretical implications for urban science and practical applications for sustainable long-term planning. Various generative models to explain road network growth have been introduced in the literature. We propose in this paper a systematic benchmark of such models integrating different paradigms (spatial interactions, cost-benefit compromises, biological network growth), focusing on the feasible space of generated network measures. We find a quantitatively high complementarity between the different models. This confirms the necessity of a plurality of urban models, in line with integrative approaches to urban systems., Comment: 9 pages, 2 figures

Context: The current sample of known brown dwarfs (BDs) around FGK-stars is only of the order of a hundred. The ongoing ESA mission Gaia has already collected its nominal 5 yr of mission data and might operate up to 10 yr. Aims: Using detailed simulations, we estimate the number of BDs that could be discovered by Gaia astrometry, radial velocity, and photometric transits around main sequence (V) and subgiants (IV) FGK host stars for a 5 and 10-yr mission. Methods: Using a robust $\Delta \chi^2$ statistic we analyse the BD companion detectability from the Besan\c{c}on Galaxy population synthesis model complemented by Gaia DR2 data for the bright end, using the latest Gaia performance and scanning law, and literature-based BD-parameter distributions. Results: We report here reliable detection numbers ($\Delta \chi^2$>50) for a 5-yr [10-yr] mission. Astrometry alone yields 28,000-42,000 [45,000-55,000] detections out to several hundred pc [>kiloparsec], with the majority around G magnitude 14-15 [14-16] and P>200 d. Gaia radial velocity time series allow detection of 830-1100 [1500-1900] mainly massive BDs (55-80 M_J), most having P <10 d. Systems with at least 3 photometric transits (S/N>3) are expected for 720-1100 [1400-2300] BDs, averaging at 4-5 [5-6] transits per source. Overlap of astrometric and radial velocity detection yield 370-410 [870-950] candidates, transit and radial velocity 17-27 [35-56], and transit and astrometric detection 1-3 [4-6]. Conclusions: Though above numbers have +/- 50% uncertainty due to the uncertain occurrence rate and period distribution of BDs around FGK host stars, Gaia detections will number in the tens-of-thousands, enlarging the current sample by at least two orders of magnitude, allowing to investigate the BD fraction and orbital architectures as a function of host stellar parameters in greater detail than every before., Comment: 24 pages, 17 figures. Updates in this version 2: rewritten Eq. 2, added references Sarro et al. 2013 and Reyl\'e 2018 regarding free floating BDs in introduction, fixed reference to correct Kiefer et al. 2019 paper, expanded funding acknowledgement, added note about G_RVS in DR2 to end of Appendix H, and a few spelling improvements

Systems of cities at the macroscopic scale have their trajectories conditioned by the evolution of infrastructure networks. This leads to complex planning and management situations in the particular case of international transportation infrastructure projects. To understand such dynamics and anticipate future sustainable trajectories, we introduce a co-evolution model between cities and transportation networks at the international scale, which simulates network growth by including transportation governance. The model is applied to synthetic systems of cities and the parameter space systematically explored, showing strong interactions between urban dynamics and governance structure. We also study optimisation patterns as compromises between construction cost and accessibility gain, with possible future applications to sustainable long-term planning of international transport projects., Comment: 9 pages, 4 figures, 1 table

Modal shift in public transport as a consequence of a disruption on a line has in some cases unforeseen consequences such as an increase in congestion in the rest of the network. How information is provided to users and their behavior plays a central role in such configurations. We introduce here a simple and stylised agent-based model aimed at understanding the impact of behavioural parameters on modal shift. The model is applied on a case study based on a stated preference survey for a segment of Paris suburban train network. We systematically explore the parameter space and show non-trivial patterns of congestion for some values of discrete choice parameters linked to perceived wait time and congestion. We also apply a genetic optimisation algorithm to the model to search for optimal compromises between congestion in different modes., Comment: 8 pages, 4 figures

Models focusing on interactions between land-use and transportation mostly assume an exogenous provision of transportation infrastructures. We investigate here co-evolutionary processes between land-use and transportation, at the scale of Mega-City Regions, by introducing a toy model of corresponding processes. In particular, our model is specifically tailored to include governance processes ruling the growth of transportation infrastructure. We show through stylised numerical simulations the potentialities of our model to reproduce a variety of dynamics when co-evolution is taken into account. We then apply the model to a case study, by calibrating it for the Pearl River Delta Mega-city Region (China, 1990-2010). To go beyond this first modelling step, we elaborate on the challenges to overcome to go further towards more complex models integrating co-evolution between transportation networks and territories in urban systems., Comment: 27 pages with supplementary material, 8 figures, 3 tables

Urban systems are intrinsically complex, involving different dimensions and scales, and consequently various approaches and scientific disciplines. In that context, urban simulation models have been coined as essential for the construction of evidence-based and integrated urban sciences. This review and position paper synthesises previous work focused on coupling and integrating urban models on the one hand, and exploring and validating such simulation models on the other hand. These research directions are complementary basis for a research program towards the development of integrated urban theories, with some application perspectives to sustainable territorial planning., Comment: 12 pages, French Regional Conference on Complex Systems 2021

Operational urban transport models require to gather heterogeneous sets of data and often integrate different sub-models. Their systematic validation and reproducible application therefore remains problematic. We propose in this contribution to build transport models from the bottom-up using scientific workflow systems with open-source components and data. These open models are aimed in particular at estimating congestion of public transport in all UK urban areas. This allows us building health indicators related to public transport density in the context of the COVID-19 crisis, and testing related policies., Comment: in Proceedings of 29th Annual GIS Research UK Conference (GISRUK), Cardiff, Wales, UK (Online), 14-16 April 2021

The dynamics and processes of urban morphogenesis are a central issue regarding a long-term sustainability of urban systems. They however imply stakeholders and parameters at multiple temporal and spatial scales simultaneously, leading to intricate interactions between dimensions and scales. We introduce in this paper from a theoretical viewpoint a simple agent-based model of urban morphogenesis at the scale of an urban area, with the feature of integrating the microscopic and the mesoscopic scales. At the local level, developer agents drive urban development conditioned by local properties but also an infrastructure network at a smaller scale. The network evolves more slowly following global properties. Indicators of sustainability including modal shares and urban density suggest an application of the model to multi-objective optimisation. We finally discuss possible implementation, extensions and applications of the model., Comment: 6 pages

Research on links between transport and land-use is by essence interdisciplinary, as a result of the multi-dimensionality and complexity of these objects. In the case of models simulating interactions between transport and land-use, the research landscape is similarly relatively broad and sparse. We propose in this paper a bibliometric analysis of this literature from an interdisciplinary perspective. We first provide a survey of the various disciplines and approaches. We then construct an interdisciplinary corpus of around 10,000 papers, which we analyse in terms of citation network and semantic content. We illustrate therein the diversity of existing approaches, their complementarity, and possible future research directions coupling some of these viewpoints., Comment: 19 pages, 4 figures, 4 tables

Urban evolution processes occur at different scales, with intricate interactions between levels and relatively distinct type of processes. To what extent actual urban dynamics include an actual strong coupling between scales, in the sense of both top-down and bottom-up feedbacks, remains an open issue with important practical implications for the sustainable management of territories. We introduce in this paper a multi-scalar simulation model of urban growth, coupling a system of cities interaction model at the macroscopic scale with morphogenesis models for the evolution of urban form at the scale of metropolitan areas. Strong coupling between scales is achieved through an update of model parameters at each scale depending on trajectories at the other scale. The model is applied and explored on synthetic systems of cities. Simulation results show a non-trivial effect of the strong coupling. As a consequence, an optimal action on policy parameters such as containing urban sprawl is shifted. We also run a multi-objective optimization algorithm on the model, showing showing that compromise between scales are captured. Our approach opens new research directions towards more operational urban dynamics models including a strong feedback between scales., Comment: 15 pages, 7 figures, 1 table

Modeling and simulation in urban and regional studies has always given a significant place to models relating the dynamics of territories with transportation networks. These include for example Land-use Transport Interaction models, but this question has been investigated from different viewpoints and disciplines. We propose in this paper a systematic review to construct a corpus of such models, followed by a meta-analysis of model characteristics. A statistical analysis provides links between temporal and spatial scale of models, their level of interdisciplinarity, and the paper year, with disciplines, type of model and methodology. We unveil in particular strong disciplinary discrepancies in the type of approach taken. This study provides a basis for novel and interdisciplinary approaches to modeling interactions between transportation networks and territories., Comment: 18 pages, 3 figures, 7 tables

Mining frequent itemsets and association rules is an essential task within data mining and data analysis. In this paper, we introduce PrefRec, a recursive algorithm for finding frequent itemsets and association rules. Its main advantage is its recursiveness with respect to the items. It is particularly efficient for updating the mining process when new items are added to the database or when some are excluded. We present in a complete way the logic of the algorithm, and give some of its applications. After that, we carry out an experimental study on the effectiveness of PrefRec. We first compare the execution times with some very popular frequent itemset mining algorithms. Then, we do experiments to test the updating capabilities of our algorithm.

The increase in the number of publications has made more difficult for authors to situate their work within previous literature, especially on subjects studied from different disciplinary viewpoints. Besides, new data analysis techniques and new bibliometrics data sources provide an opportunity to map and navigate scientific landscapes. We introduce here an open-source and open-access web application designed for the multi-dimensional exploration of a journal content, including the mapping of geographical, semantic and citations networks. The application is profiled and implemented for the geography journal Cybergeo, a generalist geography journal which receives contributions from multiple sub-disciplines. We suggest that such initiatives are crucial to promote open science and reflexivity., Comment: 6 pages, 3 figures. Translated from French

This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new constraints in terms of limited energy and raw material resources or possible catastrophic events such as pandemics are challenging further urban expansion, it is important to consolidate the theories from various scientific disciplines to estimate to what extent the urban dynamics can be modified. While briefly reviewing the contributions to urban theories provided by the new developments in complexity sciences, we first advocate for the soundness of urban theories. Second, we develop our original approach considering spatial interaction and evolutionary path dependence as major features in the general behavior of urban entities. Third, we test these principles grounded in an evolutionary theory of urban systems by experimenting four dynamic models of urban growth calibrated on harmonized empirical data sets with comparisons across the whole world., Comment: 16 pages, 2 figures

We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the number of tetrahedra tends to infinity, these manifolds are connected and have a single boundary component. We prove a law of large numbers for the genus of this boundary component, we show that the Heegaard genus of these manifolds is linear in the number of tetrahedra and we bound their first Betti number. We also show that, asymptotically almost surely as the number of tetrahedra tends to infinity, our manifolds admit a unique hyperbolic metric with totally geodesic boundary. We prove a law of large numbers for the volume of this metric, prove that the associated Laplacian has a uniform spectral gap and show that the diameter of our manifolds is logarithmic as a function of their volume. Finally, we determine the Benjamini--Schramm limit of our sequence of random manifolds.

We define a twisted $L^2$-torsion on the character variety of 3-manifold $M$ and study some of its properties. In the case where $M$ is hyperbolic of finite volume, we prove that the $L^2$-torsion is a real analytic function on a neighborhood of any lift of the holonomy representation.

The emergence of interconnected urban networks is a crucial feature of globalisation processes. Understanding the drivers behind the growth of such networks - in particular urban firm networks -, is essential for the economic resilience of urban systems. We introduce in this paper a generative network model for firm networks at the urban area level including several complementary processes: the economic size of urban areas at origin and destination, industrial sector proximity between firms, the strength of links from the past, as well as the geographical and socio-cultural distance. An empirical network analysis on European firm ownership data confirms the relevance of each of these factors. We then simulate network growth for synthetic systems of cities, unveiling stylized facts such as a transition from a local to a global regime or a maximal integration achieved at an intermediate interaction range. We calibrate the model on the European network, outperforming statistical models and showing a strong role of path-dependency. Potential applications of the model include the study of mitigation policies to deal with exogenous shocks such as economic crisis or potential lockdowns of countries, which we illustrate with an application on stylized scenarios., Comment: 19 pages, 9 figures, 7 tables

The spatial distribution of population and activities within urban areas, or urban form at the mesoscopic scale, is the outcome of multiple antagonist processes. We propose in this paper to benchmark different models of urban morphogenesis, to systematically compare the urban forms they can produce. Different types of approaches are included, such as a reaction-diffusion model, a gravity-based model, and correlated percolation. Applying a diversity search algorithm, we estimate the feasible space of each model within a space of urban form indicators, in comparison of empirical values for worldwide urban areas. We find a complementarity of the different types of processes, advocating for a plurality of urban models., Comment: 14 pages, 5 figures

The sensitivity analysis and validation of simulation models require specific approaches in the case of spatial models. We describe the spatialdata scala library providing such tools, including synthetic generators for urban configurations at different scales, spatial networks, and spatial point processes. These can be used to parametrize geosimulation models on synthetic configurations, and evaluate the sensitivity of model outcomes to spatial configuration. The library also includes methods to perturb real data, and spatial statistics indicators, urban form indicators, and network indicators. It is embedded into the OpenMOLE platform for model exploration, fostering the application of such methods without technical constraints., Comment: GISRUK 2020 Proceedings

An increased interdisciplinarity in science projects has been highlighted as crucial to tackle complex real-world challenges, but also as beneficial for the development of disciplines themselves. This paper introduces a parcimonious agent-based model of interdisciplinary relationships in collective entreprises of knowledge discovery, to investigate the impact of scientist-level decisions and preferences on global interdisciplinarity patterns. Under the assumption of simple rules for individual researcher project management, such as trade-offs between invested time overhead and knowledge benefit, model simulations show that individual choices influence the distribution of compromise points between emergent level of disciplinary depth and interdisciplinarity in a non-linear way. Different structures for collaboration networks may also yield various outcomes in terms of global interdisciplinarity. We conclude that independently of the research field, the organization of research, and more particularly the local balancing between vertical and horizontal research, already influences the final positioning of research results and the extent of the knowledge front. This suggests direct applications to research policies with a bottom-up leverage on the interactions between disciplines., Comment: 14 pages, 2 figures

The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international comparisons of the evolution of cities often produce uncertain results because national territorial frameworks are not always in strict correspondence with the dynamics of urban systems. We propose to provide various compositions of systems of cities to better take into account the dynamic networking of cities that go beyond regional and national territorial boundaries. Different models conceived for explaining city size and urban growth distributions enable to establish a correspondence between urban trajectories when observed at the level of cities and systems of cities. We test the validity and representativeness of several dynamic models of complex urban systems and their variations across regions of the world, at the macroscopic scale of systems of cities. The originality of the approach is in considering spatial interaction and evolutionary path dependence as major features in the general behavior of urban entities. The models studied include diverse and complementary processes, such as economic exchanges, diffusion of innovations and physical network flows. Complex systems' dynamics is in principle unpredictable, but contextualizing it regarding demographic, income and resource components may help in minimizing the forecasting errors., Comment: 25 pages, 9 figures, 4 tables

The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be investigated. We propose here such a model for urban dynamics at the macroscopic scale, in which the diffusion of innovations between cities captures transformation processes (mutations) and transmission processes (diffusion), using two coupled spatial interaction models. Explorations of the model on synthetic systems of cities show the role of spatial interaction and innovation diffusion ranges on measures of diversity and utility, and the existence of intermediate ranges yielding an optimal utility. Multi-objective optimization shows how the model produces a compromise between utility and diversity. This model paves the way towards more elaborated formalizations of urban evolution., Comment: 8 pages, 3 figures

Industrial symbiosis involves creating integrated cycles of by-products and waste between networks of industrial actors in order to maximize economic value, while at the same time minimizing environmental strain. In such a network, the global environmental strain is no longer equal to the sum of the environmental strain of the individual actors, but it is dependent on how well the network performs as a whole. The development of methods to understand, manage or optimize such networks remains an open issue. In this paper we put forward a simulation model of by-product flow between industrial actors. The goal is to introduce a method for modelling symbiotic exchanges from a macro perspective. The model takes into account the effect of two main mechanisms on a multi-objective optimization of symbiotic processes. First it allows us to study the effect of geographical properties of the economic system, said differently, where actors are divided in space. Second, it allows us to study the effect of clustering complementary actors together as a function of distance, by means of a spatial correlation between the actors' by-products. Our simulations unveil patterns that are relevant for macro-level policy. First, our results show that the geographical properties are an important factor for the macro performance of symbiotic processes. Second, spatial correlations, which can be interpreted as planned clusters such as Eco-industrial parks, can lead to a very effective macro performance, but only if these are strictly implemented. Finally, we provide a proof of concept by comparing the model to real world data from the European Pollutant Release and Transfer Register database using georeferencing of the companies in the dataset. This work opens up research opportunities in interactive data-driven models and platforms to support real-world implementation of industrial symbiosis., Comment: 23 pages, 9 figures, 2 tables

The metaphor of cities as organisms has a long history in urban planning, and a few urban modeling approaches have explicitly been linked to Artificial Life. We propose in that paper to explore the extent of Artificial Life and Artificial Intelligence application to urban issues, by constructing and exploring a citation network of around 225,000 papers. It shows that most of the literature is indeed application of methodologies and a rather strong modularity of approaches. We finally develop ALife concepts which have a strong potential for the development of new urban theories., Comment: 8 pages, 2 figures, 1 table

The concept of hierarchy in complex systems is tightly linked to co-evolutionary processes. We propose here to explore it in the case of the co-evolution between transportation networks and territories. More precisely, we extend a co-evolution model for systems of cities and infrastructure networks, and systematically study its behavior following specific hierarchy indicators we introduce. We show that population hierarchy and network hierarchy are tightly linked, but that a broad range of regimes can exist. Model exploration furthermore yields non-trivial stylized facts which can be taken into account for territorial planning on such long time scales with co-evolutionary processes., Comment: 16 pages, 4 figures, 1 table

At the end of the five years of work in our GeoDiverCity program, we brought together a diversity of authors from different disciplines. Each person was invited to present an important question about the theories and models of urbanization. They are representative of a variety of currents in urban research. Rather than repeat here the contents of all chapters, we propose two ways to synthesize the scientific contributions of this book. In a first part we replace them in relation to a few principles that were experimented in our program, and in a second part we situate them with respect to a broader view of international literature on these topics., Comment: 31 pages, 3 figures, 2 tables

The generation of synthetic data is an essential tool to study complex systems, allowing for example to test models of these in precisely controlled settings, or to parametrize simulation models when data is missing. This paper focuses on the generation of synthetic data with an emphasis on correlation structure. We introduce a new methodology to generate such correlated synthetic data. It is implemented in the field of socio-spatial systems, more precisely by coupling an urban growth model with a transportation network generation model. We also show the genericity of the method with an application on financial time-series. The simulation results show that the generation of correlated synthetic data for such systems is indeed feasible within a broad range of correlations, and suggest applications of such synthetic datasets., Comment: 18 pages, 5 figures

Vibrational properties of molecular crystals are constantly used as structural fingerprints, in order to identify both the chemical nature and the structural arrangement of molecules. The simulation of these properties is typically very costly, especially when dealing with response properties of materials to e.g. electric fields, which require a good description of the perturbed electronic density. In this work, we use Gaussian process regression (GPR) to predict the static polarizability and dielectric susceptibility of molecules and molecular crystals. We combine this framework with ab initio molecular dynamics to predict their anharmonic vibrational Raman spectra. We stress the importance of data representation, symmetry, and locality, by comparing the performance of different flavors of GPR. In particular, we show the advantages of using a recently developed symmetry-adapted version of GPR. As an examplary application, we choose Paracetamol as an isolated molecule and in different crystal forms. We obtain accurate vibrational Raman spectra in all cases with less than 1000 training points, and obtain improvements when using a GPR trained on the molecular monomer as a baseline for the crystal GPR models. Finally, we show that our methodology is transferable across polymorphic forms: we can train the model on data for one structure, and still be able to accurately predict the spectrum for a second polymorph. This procedure provides an independent route to access electronic structure properties when performing force-evaluations on empirical force-fields or machine-learned potential energy surfaces.

Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the complex interplay of individual and collective actions and reactions with simpler mathematical or computer mechanisms, making it easier to understand the relationships between the causes and the consequences of these interactions and to make predictions. As the formalism of mathematical models offering analytical solutions is often not suitable for representing social complexity, more and more agent-based computer models are being used. For a long time, the limited computing capacities of computers have hampered programming models that would take into account the interactions between large numbers of geographically located entities (persons or territories). In principle, these models should inform the conditions for the emergence of certain patterns defined at a macro-geographic level from the interactions occurring at a micro-geographic level, in systems whose behaviors are too complex to be understood directly by a human brain. Moreover, it is also necessary to analyze the dynamic behavior of these models with nonlinear feedback effects and verify that they produce plausible results at all stages of their simulation. This essential work of exploring the dynamics of modeled systems remained in its infancy until the late 2010s. Since then, algorithms combining more sophisticated methods, including genetic algorithms and the use of distributed intensive computing, have made it possible to make a significant qualitative leap forward in the exploration and validation of models. The result is an epistemological turn for the human and social sciences, as indicated by the latest applications realized with the help of the OpenMOLE platform presented here., Comment: 16 pages

Context. Since 1998, a planet-search around main sequence stars within 50~pc in the southern hemisphere has been carried out with the CORALIE spectrograph at La Silla Observatory. Aims. With an observing time span of more than 20 years, the CORALIE survey is able to detect long term trends in data with masses and separations large enough to select ideal targets for direct imaging. Detecting these giant companion candidates will allow us to start bridging the gap between radial velocity detected exoplanets and directly imaged planets and brown dwarfs. Methods. Long-term precise Doppler measurements with the CORALIE spectrograph reveal radial velocity signatures of massive planetary companions and brown dwarfs on long-period orbits. Results. In this paper we report the discovery of new companions orbiting HD~181234, HD~13724, HD~25015, HD~92987 and HD~50499. We also report updated orbital parameters for HD~50499b, HD~92788b and HD~98649b. In addition, we confirm the recent detection of HD~92788c. The newly reported companions span a period range of 15.6 to 40.4 years and a mass domain of 2.93 to 26.77 $M_{\mathrm{Jup}}$, the latter of which straddles the nominal boundary between planets and brown dwarfs. Conclusion. We have reported the detection of five new companions and updated parameters of four known extrasolar planets. We identify at least some of these companions to be promising candidates for imaging and further characterisation., Comment: 18 pages, 11 figures, accepted to A&A

Network percolation has recently been proposed as a method to characterize the global structure of an urban system form the bottom-up. This paper proposes to extend urban network percolation in a multi-dimensional way, to take into account both urban form (spatial distribution of population) and urban functions (here as properties of transportation networks). The method is applied to the European urban system to reconstruct endogenous urban regions. The variable parametrization allows to consider patterns of optimization for two stylized contradictory sustainability indicators (economic performance and greenhouse gases emissions). This suggests a customizable spatial design of policies to develop sustainable territories., Comment: 12 pages, 7 figures

At large scales, typologies of urban form and corresponding generating processes remain an open question with important implications regarding urban planning policies and sustainability. We propose in this paper to generate urban configurations at large scales, typically of districts, with morphogenesis models, and compare these to real configurations according to morphological indicators. Real values are computed on a large sample of districts taken in European urban areas. We calibrate each model and show their complementarity to approach the variety of real urban configurations, paving the way to multi-model approaches of urban morphogenesis., Comment: 8 pages, 4 figures, 1 table

Interactions between transportation networks and territories are the subject of open scientific debates, in particular regarding the possible existence of structuring effects of networks, and linked to crucial practical issues of territorial development. We propose an entry on these through co-evolution, and more particularly by the modeling of co-evolution processes between transportation networks and territories. We construct a multi-disciplinary definition of co-evolution which is proper to territorial systems and which can be tested empirically. We then develop the lessons learnt from the development of two types of models, macroscopic interaction models in systems of cities and mesoscopic morphogenesis models through co-evolution. This research opens the perspective of multi-scale models that could be applied to territorial prospective., Comment: Translated from French, "Mod\'elisation des interactions entre r\'eseaux de transport et territoires : une approche par la co-\'evolution", Journ\'ee d'Etude Pacte-Citeres 2018, Grenoble, 15 novembre 2018. 10 pages

The low-frequency range of vibrational spectra is sensitive to collective vibrations of the lattice. In molecular crystals, it can be decisive to identify the structure of different polymorphs, and in addition, it plays an important role on the magnitude of the temperature-dependent component of vibrational free energy differences between these crystals. In this work we study the vibrational Raman spectra and vibrational density of states of different polymorphs of the flexible Aspirin and Paracetamol crystals based on dispersion-corrected density-functional theory, density-functional perturbation theory, and $ab\,initio$ molecular dynamics. We examine the effect of quasi-harmonic lattice expansion and compare the results of harmonic theory and the time correlation formalism for vibrational spectra. Lattice expansion strongly affects the collective vibrations below 300 cm$^{-1}$, but it is significantly less important at higher frequencies, while thermal nuclear motion can be important in the full vibrational range. We also observe that the inclusion or neglect of many-body van der Waals dispersion interactions do not cause large differences in the low-frequency range of Raman spectra or vibrational density of states, provided the lattice constants are fixed. We obtain quantitative agreement with experimental room-temperature Raman spectra below 300 cm$^{-1}$ for all polymorphs studied. Examining the two-dimensional correlations between different vibrations, we find which modes show a larger degree of anharmonic coupling to others, providing a possible route to assess the accuracy of harmonic free energy evaluations in different cases.

The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We develop from a theoretical viewpoint some arguments illustrating ontological complexity, in the sense of the diversity and multidimensionality of possible representations, and then complexity in the sense of emergence, i.e. the necessity of the existence of several autonomous levels. We then propose numerical experiments to explore properties of complexity (dynamical complexity and co-evolution) within two simple models of urban morphogenesis. We finally suggest other dimensions of complexity which could be typical of territorial systems., Comment: 11 pages, 3 figures. Translated from French, "Espace et complexit\'es des syst\`emes territoriaux", Journ\'ees de Rochebrune 2019

We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type $F$. Our methods imply similar results for $\ell^2$-torsion as well as a strong profiniteness statement for Novikov-Shubin invariants., Comment: small changes in introduction and proof of prop 2.7

Although simulation models of geographical systems in general and agent-based models in particular represent a fantastic opportunity to explore socio-spatial behaviours and to test a variety of scenarios for public policy, the validity of generative models is uncertain unless their results are proven robust and representative of 'real-world' conditions. Sensitivity analysis usually includes the analysis of the effect of stochasticity on the variability of results, as well as the effects of small parameter changes. However, initial spatial conditions are usually not modified systematically in geographical models, thus leaving unexplored the effect of initial spatial arrangements on the interactions of agents with one another as well as with their environment. In this paper, we present a method to assess the effect of some initial spatial conditions on simulation models, using a systematic spatial configuration generator in order to create density grids with which spatial simulation models are initialised. We show, with the example of two classical agent-based models (Schelling's models of segregation and Sugarscape's model of unequal societies) and a straightforward open-source work-flow using high performance computing, that the effect of initial spatial arrangements is significant on the two models. Furthermore, this effect is sometimes larger than the effect of parameters' value change., Comment: 23 pages, 10 figures, 4 tables

Recent years have witnessed an exceptional extension of public transportation networks in People's Republic of China, both at a national scale with the construction of the first HSR railway network of the world, and at local scales with numerous cities developing high coverage subway networks often from scratch. This chapter studies these mutations, both from a quantitative perspective with the study of the evolution of population accessibility landscapes, at a national level and for several cities, and from a qualitative perspective with fieldwork observations. We confirm that rebalancing planning objectives are well achieved in terms of accessibility at both scales, when all planned lines will be achieved but already in a significant manner. We finally hypothesize possible paths for the coupled network-territory systems, given the extent without precedent of such mutations., Comment: 17 pages, 6 figures, 1 table

Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter some links between three types of complexity, namely emergence, computational complexity and informational complexity. We discuss the implication of these links on the necessity of reflexivity to produce a knowledge of the complex, and how this connects to the interdisciplinary of approaches in particular for socio-technical systems. We finally synthesize this positioning as a proposal of an epistemological framework called applied perspectivism, and discuss the implications for the study of urban systems., Comment: 9 pages

We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a congruence hyperbolic 3--orbifold asymptotically vanishes relatively to hyperbolic volume.