Improving the prediction of glassy dynamics by pinpointing the local cage Rinske M. Alkemade, 1 Frank Smallenburg, 2 and Laura Filion 1 1) Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University, Utrecht, Netherlands 2) Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France

The relationship between structure and dynamics in glassy fluids remains an intriguing open question. Recent work has shown impressive advances in our ability to predict local dynamics using structural features, most notably due to the use of advanced machine learning techniques. Here we explore whether a simple linear regression algorithm combined with intelligently chosen structural order parameters can reach the accuracy of the current, most advanced machine learning approaches for predicting dynamic propensity. To do this we introduce a method to pinpoint the cage state of the initial configuration -i.e. the configuration consisting of the average particle positions when particle rearrangement is forbidden. We find that, in comparison to both the initial state and the inherent state, the structure of the cage state is highly predictive of the long-time dynamics of the system. Moreover, by combining the cage state information with the initial state, we are able to predict dynamic propensities with unprecedentedly high accuracy over a broad regime of time scales, including the caging regime.

I. INTRODUCTION

Understanding the relation between structure and dynamics in glassy systems has sparked extensive discussion over the last few decades [START_REF] Cavagna | Supercooled liquids for pedestrians[END_REF][START_REF] Berthier | Theoretical perspective on the glass transition and amorphous materials[END_REF][START_REF] Royall | The role of local structure in dynamical arrest[END_REF][START_REF] Tanaka | Revealing key structural features hidden in liquids and glasses[END_REF] . While cooling or compressing a glassy system, we typically observe little to no change in structure, while at the same time observing an extreme decrease in dynamics [START_REF] Ediger | Supercooled liquids and glasses[END_REF] . This decrease in dynamics is highly heterogeneous, with increasingly large regions of slow and fast particles as a function of supercooling [START_REF] Ediger | Can density or entropy fluctuations explain enhanced translational diffusion in glass-forming liquids?[END_REF][START_REF] Berthier | Glasses and aging, a statistical mechanics perspective on[END_REF][START_REF] Candelier | Spatiotemporal hierarchy of relaxation events, dynamical heterogeneities, and structural reorganization in a supercooled liquid[END_REF] .

One of the approaches to probe the apparent discrepancy between structure and dynamics has been the use of machine learning [START_REF] Yang | Machine-learning integrated glassy defect from an intricate configurational-thermodynamicdynamic space[END_REF][START_REF] Ciarella | Dynamics of supercooled liquids from static averaged quantities using machine learning[END_REF][START_REF] Cubuk | Identifying structural flow defects in disordered solids using machine-learning methods[END_REF][START_REF] Schoenholz | A structural approach to relaxation in glassy liquids[END_REF][START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF][START_REF] Boattini | Autonomously revealing hidden local structures in supercooled liquids[END_REF][START_REF] Paret | Assessing the structural heterogeneity of supercooled liquids through community inference[END_REF][START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF][START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF][START_REF] Shiba | Unraveling intricate processes of glassy dynamics from static structure by machine learning relative motion[END_REF][START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF][START_REF] Coslovich | Dimensionality reduction of local structure in glassy binary mixtures[END_REF] . By capturing the local structure of particles in terms of parameters and training algorithms to predict the mobility of particles based on these parameters, the idea is that we can learn what aspects of the structure influence the heterogeneous dynamics.

Over the last two years, the quest for accurate dynamical predictions in glassy systems has led to an explosion of papers introducing new methodologies that compete in predicting the so-called dynamic propensity of simple glassy models. This propensity is defined as the average expected displacement a particle will undergo in a certain time interval when starting from a specific initial configuration [START_REF] Widmer-Cooper | How reproducible are dynamic heterogeneities in a supercooled liquid?[END_REF][START_REF] Widmer-Cooper | On the study of collective dynamics in supercooled liquids through the statistics of the isoconfigurational ensemble[END_REF] . This explosion started in 2020 with the work of Bapst et al. [START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF] , where several machine learning methods were trained to predict the dynamic propensity of a Kob-Andersen system [START_REF] Kob | Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function[END_REF] , with a graph neural network (GNN) performing the best. In 2021, a linear-regression-based algorithm with input parameters that captured structure over several length scales was shown to be able to rival GNNs in predicting the propensity for the same system [START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF] . Since then, several works have improved on this feat, by e.g. using physics-informed parameters as input for a deep neural network [START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF] , by modifying the loss function of a GNN to also consider relative displacements between pairs of particles [START_REF] Shiba | Unraveling intricate processes of glassy dynamics from static structure by machine learning relative motion[END_REF] , or by designing GNNs that preserve roto-translation equivariance [START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF] . These works clearly demonstrate that careful consideration of the physics involved can aid in improving the predictive accuracy of these advanced methods. However, these neural-network based approaches still carry the downside of high complexity. In contrast, due to the simplicity of linear methods, accurately capturing dynamics using linear regression gives a clearer perspective on what structural aspects most strongly drive glassy dynamics. This raises the question: can a clever choice of input parameters boost the performance of linear regression approaches?

Here, we show that this is indeed the case, and apply linear regression to predict the dynamic propensity of three glassforming models: hard spheres, harmonic spheres, and the Kob-Andersen model. The main idea of our method is to consider the structure of the system during the caging regime, where each particle is confined by its neighbors in a reasonably well-defined location. By directly incorporating information about this "cage state", we show that it is possible to drastically improve the ability of linear regression to predict dynamics, to the point where it even exceeds advanced nonlinear machine learning algorithms over a wide range of time scales.

II. MODEL, DESCRIPTORS AND PREDICTION METHOD

A. Model

Each of our three models consists of two species of particles, labeled A and B, with different particle sizes but equal mass m. We denote the number of particles of the two species as N A and N B , such that the total number of particles N = N A + N B . Below we discuss each of the models and the statepoints at which we investigate them individually.

The first model we consider consists of hard-sphere particles of two diameters, denoted σ A and σ B . The hard-sphere potential for two particles i and j is given by

V HS (r) = ∞ for r ≤ σ i j 0 for r > σ i j , (1)
where σ i j = (σ i + σ j )/2. Here, we use a size ratio σ B /σ A = 0.85, and a number ratio N A /N = 0.3. The considered packing fraction of η = 0.58 leads to a structural relaxation time of approximately τ α = 10 4 τ, with τ the unit of time given by τ = mσ 2 A /k B T , k B Boltzmann's constant and T the temperature.

Binary harmonic mixture

The binary harmonic potential is given by [START_REF] Durian | Foam mechanics at the bubble scale[END_REF][START_REF] Berthier | Compressing nearly hard sphere fluids increases glass fragility[END_REF] V Har (r) =

   ε 1 -r σ i j 2 for r ≤ σ i j 0 for r > σ i j , (2)
where again σ i j = (σ i + σ j )/2. Here, we consider the case where σ B /σ A = 1.4, N A /N = 0.5. Our state point of interest is at number density ρσ 3 A = 0.82 and temperature k B T /ε = 0.0045, where the structural relaxation time is approximately τ α = 671τ 26 .

Binary Kob-Andersen mixture

The Kob-Andersen (KA) mixture consists of two particles types A and B interacting via the Lennard-Jones potential: [START_REF] Kob | Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function[END_REF] V KA (r) = 4ε i j σ i j r

12

- σ i j r 6 , (1)
where ε AA : ε AB : ε BB = 1 : 1.5 : 0.5 and σ AA : σ AB : σ BB = 1 : 0.80 : 0.88. Note that (σ AA + σ BB )/2 = σ AB , i.e. the system is non-additive. The composition of the system is N A /N = 0.8. We investigate this system at number density ρσ 3 A = 1.203 and temperature k B T /ε A = 0.44. The relaxation time of the system is approximately τ α 3075τ [START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF] .

B. Generating initial configurations

The HS system is simulated using event-driven molecular dynamics [START_REF] Rapaport | The Event-Driven Approach to N-Body Simulation[END_REF][START_REF] Smallenburg | Efficient event-driven simulations of hard spheres[END_REF] (EDMD) in the microcanonical ensemble, i.e. at fixed number of particles N, volume V and energy E. In order to generate snapshots that can serve as initial configurations, we place N particles in the box at a reduced size, and then grow them over time until the desired packing fraction is reached [START_REF] Donev | Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles. I. algorithmic details[END_REF] . Afterwards, the system is equilibrated for 10τ α .

To simulate both the harmonic and KA systems, we use LAMMPS [START_REF] Thompson | LAMMPS -a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales[END_REF] . First we initialize the system by performing a simulation in the canonical ensemble, i.e. at fixed N, V and T , using a Nose-Hoover thermostat [START_REF] Evans | The Nose-Hoover thermostat[END_REF] at the desired temperature T . Afterwards, we equilibrate the system in the microcanonical ensemble, for 10τ α .

For each system we equilibrate 100 snapshots, where each snapshot contains 2000 particles. FIG. 1. Propensity averaged over all A particles in the system and correlation between the predicted and measured propensity for the same particles, plotted over time for the binary hard sphere mixture at the state point described in this paper. The propensity clearly exhibits three different dynamical regimes: In the ballistic regime, particles have not yet collided with their neighbours, and thus follow a straight ballistic trajectory. In the caging regime, particles move around for an extend period of time in the cage formed by their nearest neighbours. Finally, after particles have escaped the system enters the diffusive regime.

C. Dynamic propensity

As a measure of the dynamical heterogeneity we use the dynamic propensity, which is a quantity that captures the average mobility of particles [START_REF] Widmer-Cooper | How reproducible are dynamic heterogeneities in a supercooled liquid?[END_REF][START_REF] Widmer-Cooper | On the study of collective dynamics in supercooled liquids through the statistics of the isoconfigurational ensemble[END_REF] . To measure it, we simulate the dynamical evolution of each initial configuration 50 times, using distinct initial velocities drawn from a Maxwell-Boltzmann distribution at the desired temperature, i.e. we sample the isoconfigurational ensemble [START_REF] Widmer-Cooper | How reproducible are dynamic heterogeneities in a supercooled liquid?[END_REF] . Afterwards the dynamic propensity ∆r i (t) of each particle i is obtained by averaging its absolute displacement over the different runs, i.e.

∆r i (t) = |r i (t) -r i (0)| conf , (3)
where the subscript 'conf' indicates the isoconfigurational average. We measure the dynamic propensity at logarithmic time intervals between t/τ = 0.01 and t/τ = 10τ α . Simulations of the all the three systems are performed in a microcanocical ensemble.

D. Structural Descriptors

To fit the dynamic propensity, we use standard ridge regression combined with structural order parameters, as previously done in Refs. 16 and 32. The structural parameters include rotationally invariant parameters that capture both the local density as well as the local n-fold symmetry. The local density is measured by using radial density functions that capture the density in a shell at distance r and with thickness 2δ from the reference particle. They are defined as

G (0) i (r, δ , s) = ∑ j =i,s j =s e - (r i j -r) 2 2δ 2 , ( 4
)
where i is the reference particle and r i j is the absolute distance between particles i and j. The sum goes over all other particles j in the system that are part of particle species s. In this paper we include the radial functions up to the fifth minimum in the radial distribution.

The other structural descriptors we use are based on bond order parameters which express the local structure in terms of spherical harmonics [START_REF] Steinhardt | Bond-orientational order in liquids and glasses[END_REF][START_REF] Lechner | Accurate determination of crystal structures based on averaged local bond order parameters[END_REF] . To compute the parameters we first compute the complex coefficient

q (0) i (l, m, r, δ ) = 1 Z ∑ i = j e - (r i j -r) 2 2δ 2 Y m l (r i j ). (5)
Here Y m l (r i j ) is the l th spherical harmonic function and m is a function that runs from -l to l. To normalize the coefficient, we use Z, which is given by

Z = ∑ i = j e - (r i j -r) 2 2δ 2 . ( 6
)
Note that due to the exponent, just as with the radial density functions, mainly particles that are within the shell rδ to r + δ contribute to q (0)

i (l, m, r, δ ). The parameters are made rotationally invariant by summing over all possible value of m:

q (0) i (l, r, δ ) = 4π 2l + 1 m=l ∑ m=-l |q (0) i (l, m, r, δ )| 2 . (7)
Note that the q (0) i (l, r, δ ) will mainly pick-up the l-fold symmetry of the particles structure in each shell.

In Ref. 16 it was shown that the prediction of the dynamic propensity via linear regression can be improved when not only the structural parameters of the reference particle itself are included, but also structural parameters averaged over nearest neighbours. These averaged structural parameters are obtained via the following recursive formula:

x (n) i = ∑ j:r i j <r c x (n-1) j e -r i j /r c ∑ j:r i j <r c e -r i j /r c . (8) Here x (n)
i are the structural parameters (which can be both radial density or bond order parameters) of order n for particle i. The sum goes over all particles within a certain radius r c as seen from the reference particle i. This r c is chosen to be located at the second minimum of the radial distribution function, although it was shown in Ref. 16 that its exact value has no substantial influence on the order parameters. Boattini et al showed including parameters up to three generations significantly improves the predictions. Further information on the descriptors can be found in the Supplementary Information (SI).

III. RESULTS

A number of recent studies have made significant progress in predicting the dynamic propensity of particles in glassy fluids based on local structural information using a variety of machine learning algorithms [START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF][START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF][START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF][START_REF] Shiba | Unraveling intricate processes of glassy dynamics from static structure by machine learning relative motion[END_REF][START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF] . The accuracy of such predictions is typically evaluated using the Pearson correlation coefficient [START_REF]) between two datasets X and Y is equal to 1, the two variables are perfectly related via a linear function with positive slope[END_REF] between the predicted and measured dynamic propensities. A typical example of this correlation as a function of time is shown in Fig. 1, where we used linear regression in combination with structural order parameters to predict the propensity in the binary hard-sphere mixture we consider here [START_REF] Alkemade | Comparing machine learning techniques for predicting glassy dynamics[END_REF] . Interestingly, the correlation is weak in three distinct regimes. Two of these regimes are trivial. The first corresponds to the very short-time regime, where dynamics are dominated by the random choice of initial velocities. Especially for hard spheres, the motion of the particles in this regime is entirely unaffected by local structure, and hence fully unpredictable. The second trivial regime that is hard to predict occurs at long time scales t τ α , where the system loses memory of its initial configuration. The intriguing regime, where the correlations are weak, lies at intermediate time scales, and corresponds to the times where particles are trapped inside their local cages, as also indicated by the behavior of the average propensity in Fig. 1. This lower performance of machine-learned algorithms for predicting propensity in the caging regime is not unique to the results of Fig. 1, but has been observed in a variety of studies involving different machine learning methods and different ways to describe the system [START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF][START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF][START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF][START_REF] Alkemade | Comparing machine learning techniques for predicting glassy dynamics[END_REF] , although recent, more advanced machine learning methods have improved significantly the correlation in this regime [START_REF] Shiba | Unraveling intricate processes of glassy dynamics from static structure by machine learning relative motion[END_REF][START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF] .

Observing the weak correlations in the caging regime, a natural question to ask is then: what structural information do we need to include in order to make accurate predictions about the dynamics of our system in this regime? Since during the caging regime, particles on average move around the so called 'cage center', a rather obvious choice would be to consider the expected average distance between a particle's initial position r init i and its typical position while in its cage r cage i . Since the dynamic propensity measures the averaged absolute distance travelled by particles, we would expect this distance between the initial and mean cage position ∆r

cage i = |r cage i -r init i |
to be a good predictor of the dynamic propensity. While this statement seems logically trivial, an important question is: what is a good estimate of the cage center of a given particle?

A common approach in glass literature for predicting dynamical behavior in a glassy system is to quench the system to its inherent state (IS) (see e.g. [START_REF] Schoenholz | A structural approach to relaxation in glassy liquids[END_REF][START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF][START_REF] Widmer-Cooper | Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities[END_REF][START_REF] Tong | Revealing hidden structural order controlling both fast and slow glassy dynamics in supercooled liquids[END_REF] ). The inherent state of a configuration is defined as the local potential energy minimum that one obtains via a rapid energy minimization [START_REF] Stillinger | Hidden structure in liquids[END_REF] . Note, however, that this is not exactly the same as the average position of a particle in its cage, as the average should include the effects of thermal fluctuations as well. As such, a natural alternative choice to estimate the position of the cage center is to simply take the average position of each particle, under the constraint that no significant particle rearrangements have happened. We will refer to this second option as the cage state (CS). To explore these two definitions of ∆r cage , we calculate for each of our initial configurations both the inherent state and cage state positions.

For the inherent state, we use the FIRE algorithm proposed by Bitzek et al. [START_REF] Bitzek | Structural relaxation made simple[END_REF] to minimize the potential energy. In the case of hard spheres, we apply an effective logarithmic interaction potential proposed by Arceri et al. [START_REF] Arceri | Vibrational properties of hard and soft spheres are unified at jamming[END_REF] in order to obtain an effective inherent state. Specifically, we use the effective interaction potential V eff (r) = -k B T log(rσ i j ), with both the forces and interaction energy truncated and shifted to zero at a cutoff radius r c = 1.35σ i j .

To obtain the cage state, we use a Monte Carlo (MC) simulation in the canonical ensemble that measures the average positions of each particle r CS i = r c i , while restricting the movement of each particle to ensure that it stays inside its initial cage. In order to do this, we reject all MC moves that would move the center of a particle outside of its original Voronoi cell. Since we consider binary systems, we use an approximate definition of a Voronoi cell which takes into account the particle sizes. In particular, the approximate Voronoi cell for particle i is defined as the collection of points R for which

R -r init i σ i < R -r init j σ j ∀ j ∈ N (i), (9)
where r init i is the position of particle i in the initial configuration and N (i) are the nearest neighbours of particle i determined by the SANN algorithm [START_REF] Van Meel | A parameterfree, solid-angle based, nearest-neighbor algorithm[END_REF] . For the KA mixture, we set σ i = σ ii , since the individual particle sizes are ill-defined. Note that since the restrictions on the particle positions elim-inate the possibility of long-time diffusion, short simulations are sufficient to sample the restricted phase space. Here, we use MC simulations of 5 • 10 5 initial steps and 10 6 measuring steps.

Note that as an alternative to confining each particle to its initial Voronoi cell, we have also explored the possibility of instead confining each particle to a spherical region with a fixed radius r c . When the size of this sphere is chosen to be close to the size of the particle (and hence similar to the size of the Voronoi cell), we find essentially the same results (as shown in the SI).

These two approaches give us two results for ∆r cage , which we denote ∆r IS(CS) for the inherent (cage) state. To compare how effective these measurements are at capturing the actual cage center, we plot in Fig. 2abc the Pearson correlation between the dynamic propensity and both definitions of ∆r cage , for all three glass model systems. Note that since here we consider only a single parameter at a time, no linear regression is required to obtain a correlation. As expected, both the inherent state and the cage state provide significant information about the expected position of a particle during the caging regime. However, clearly ∆r CS is a better predictor of the dynamic propensity in all three cases, reaching correlations stronger than 0.8. This is significantly higher than the results shown in Fig. 1 variable. Evidently, the simple averaging method we used to obtain the cage state indeed manages to eliminate the thermal fluctuations that are present in the initial configuration, without losing significant information about the underlying cage structure. The inherent state performs less well, in particular in the case of harmonic spheres. To shed light on the reason behind this, we measure the radial distribution function g(r) of the initial, inherent, and cage state configurations and compare them in Fig. 2def. In the harmonic and KA models, both the inherent state and cage state increase the degree of local structure in the system, resulting in higher peaks in g(r) -and this degree of additional ordering is stronger for the inherent state than for the cage state. This implies that the inherent state quench pushes the system significantly further away from its local structure than the system would normally sample. In contrast, the cage state procedure only takes into account configurations that the system samples during (constrained) thermal fluctuations. Hence, it is perhaps not surprising that the cage state better reflects the expected dynamics of our systems. We now examine whether knowledge of the cage structure can help us make more accurate predictions of the dynamic propensity even outside the caging regime. To this end, we start with the structural order parameters and linear regression approach described in Refs. 16 and 32. In particular, for each particle, we define a set of approximately 1000 structural parameters describing their local structural environment, and use standard ridge regression in order to fit the dynamic propensity as a function of these structural parameters. A full description of these structural order parameters for each model is provided in the SI. Note that this is the same approach as we used for the data in Fig. 1. As a basis for calculating the local structural descriptors, we now use either the initial, inherent, or cage state, resulting in three sets of structural descriptors for each particle: X init , X IS , and X CS . We then examine how these different sets of input data influence our ability to predict dynamic propensity. The results are shown in Fig. 3abc for the three model systems. In all cases, at short times the initial state of the system provides the best input for predicting propensities. This is understandable, since only the initial state contains information about the exact particle environments in the limit t → 0. At longer time scales, both the inherent and cage state structures outperform the initial state, with the cage state always outperforming the inherent state. This further supports the observation that the cage state, as determined by our MC approach, represents an excellent approximation for the underlying structure of our system when it comes to understanding its dynamics on time scales around the structural relaxation time.

The obvious next step is to combine this information with knowledge of ∆r cage , which we already know provides a strong prediction of dynamics in the caging regime. In Fig. 3def, we plot the correlation between the dynamic propensity and predictions based on linear regression, combining as input X init , X cage , and ∆r cage , for both cage definitions. Overall, we observe a massive improvement in our ability to predict propensity at all time scales beyond the ballistic regime.

The predictive power of our models using information about the cage state is particularly impressive compared to past results. Specifically, the state point of the KA mixture we study here has been used in a variety of previous studies where new methodologies were introduced to attempt accurate prediction of the dynamic propensity. In Fig. 4, we plot our results from Fig. 3f and compare them to the results of Refs. 13, 16-19. Note that the comparison between different predictions is complicated by significant differences in the datasets we used here and the dataset from the work of Bapst et al. [START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF] , which was also used by Boattini, Jung, and Pezzicolo and their respective co-workers [START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF][START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF][START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF] . In particular, for our dataset, we determine dynamics propensities for a set of initial snapshots that are all taken at the same density, and we always measure the dynamic propensity at a fixed set of times. In contrast, the authors of Ref. 13 took the initial snapshots from constant-pressure simulations, and hence the configurations vary slightly in density. Additionally, for each initial configuration, they measured the dynamic propensity at different time intervals, based on the decay of the intermediate scattering function for that specific snapshot. In Fig. 4b, we illustrate this difference by plotting for each of the initial configurations in the training set of Ref. 13 the average propensity as a function of time, and color each point based on the corresponding system density. Hence, in our comparison in Fig. 4a, the time for each point based on this dataset is an average time. Clearly, there is a significant correlation between the density of the snapshot and the mean dynamic propensity, and a significant spread in acquisition times. Additionally, the spread in mean propensities is significantly lower than in our own data (shown in black in Fig. 4b), due to the grouping of initial configurations based on their structural relaxation instead of time. It should be noted that this grouping is not fully consistent with Eq. 3, and implies that some dynamical information is already included in the input data.

Evidently, including information about the cage state -captured in our parameters X CS and ∆r CS -allows our linear regression approach to outperform the current state-of-the-art machine learning methods for predicting dynamic propensity over a wide range of time scales. The GNN-based methods do outperform our predictions in the very short-time regime, where the dynamics are likely dominated by the forces that act on the particles in the initial configuration. This may be an indication that these instantaneous forces cannot be directly recovered from our set of input parameters. In contrast, the three GNN-based approaches plotted (in blue) in Fig. 4 all have information about the relative positions of particles with respect to their neighbors included in the input graph, and hence might be able to learn the net forces on the parti-a) cles with high accuracy. At very long time scales, where the motion of particles becomes more diffusive, the results of the different machine learning approaches appear to converge to similar performance -with the physics-informed approach by Jung et al. [START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF] performing the strongest in this regime. To test whether the improved performance of the GNNs at short time scales is indeed due to them directly learning the initial forces, we adapted our method to also include the net force on each particle in the initial configuration. In Fig. 5 we show the correlation between the dynamic propensity and the initial force in blue, and indeed we see a strong peak at short times. Adding this information into our input data for the full linear regression model, we indeed see a significant improvement at short times (black line). However, the GNNbased methods still achieve a significantly higher accuracy in this regime, and hence appear to be capable of learning more about the short time dynamics than simply the instantaneous forces.

In Fig. 5 we also break down the our prediction of the dynamic propensity into the different relevant aspects of the input data. Overall, we see that the dynamic propensity at short times is indeed dominated by the forces, at intermediate times by the initial distance to the cage center, and at long times by the structural features of the cage state. While this is in principle not surprising, it is impressive to see that the vast majority of the variation in propensity at short and intermediate time intervals can be explained by just two simple measurements. Moreover, the predictive ability of the cage state structure at long times is impressive as well, and demonstrates that it using the cage state, rather than the initial state to make long-time predictions is an excellent strategy. Note that outside of short times, adding in information on the initial state on top of the cage state is fully irrelevant.

IV. CONCLUSIONS

In short, we have demonstrated that the behavior of the dynamic propensity of glassy fluids can be predicted to high accuracy by using information about the cage state of the initial configuration. This cage state is defined as the set of coordinates describing the average position of the particles when the system is constrained to ensure particles cannot escape their local cages. Combining this information with a simple linearregression-based algorithm, we can predict dynamic propensities with accuracies that rival or exceed current state-of-the-art machine learning methods at nearly all times. This suggests that the cage state could be a helpful tool for further studying the underlying structure of glassy fluids. Pearson correlation coefficient between measured and predicted propensity over time, shown for linear regression models trained on different subsets of structural parameters for A particles in a KA system. F net,0 is the absolute net force that a particle feels at t = 0, ∆r CS is the absolute difference between the positions of particles in the initial configuration and the cage state and X CS are the structural parameters evaluated for the cage state. Note that the green line ("All") is the linear regression model trained on the combination of {F net,0 , ∆r CS , X CS }, while the black line ("All +X init ") also includes the structural parameters of the initial configuration in the structural dataset.

6 FIG. 2 .

 62 FIG.2. a,b,c) The Pearson coefficient plotted over time between the propensity and absolute difference between the positions of particles in the initial configuration and the inherent state/cage state (∆r IS/CS ) for the A-particles in hard spheres (a), harmonic spheres (b), and Kob-Andersen (c). d,e,f) The total radial distribution function around A-type particles in the initial configuration, the inherent state, and the cage state, for the same three models.

FIG. 3 .

 3 FIG.3. a,b,c) Pearson correlation coefficient between the dynamic propensity and the prediction of a linear regression model trained on the structural parameters evaluated for the initial-, the inherent-and the cage-state coordinates (i.e. X init , X IS ,X CS ), for the A-particles in hard spheres (a), harmonic spheres (b), and Kob-Andersen (c). d,e,f) Correlation between the measured propensity and the predicted propensity by a linear regression model trained on either only the structural parameters based on the initial positions, or the set of input parameters given by {X init , X IS/CS , ∆r IS/CS } .

F

  FIG.5. Pearson correlation coefficient between measured and predicted propensity over time, shown for linear regression models trained on different subsets of structural parameters for A particles in a KA system. F net,0 is the absolute net force that a particle feels at t = 0, ∆r CS is the absolute difference between the positions of particles in the initial configuration and the cage state and X CS are the structural parameters evaluated for the cage state. Note that the green line ("All") is the linear regression model trained on the combination of {F net,0 , ∆r CS , X CS }, while the black line ("All +X init ") also includes the structural parameters of the initial configuration in the structural dataset.

  , despite being based only on a single

			Hard spheres				Harmonic				Kob-Andersen
	a)				b)					c)
		1.0					1.0					1.0
		0.8					0.8					0.8
	Correlation	0.4 0.6			X init	Correlation	0.4 0.6			X init	Correlation	0.4 0.6	X init
		0.2			X IS		0.2			X IS		0.2	X IS
					X CS					X CS			X CS
		0.01 0.0	1	100	10 4		0.01 0.0	1	100	10 4		0.01 0.0	1	100	10 4
				t/τ				t/τ					t/τ
	d)				e)					f)
		1.0					1.0
		0.8					0.8
	Correlation	0.4 0.6		X init		Correlation	0.4 0.6		X init				X init
		0.2		X init , X IS , Δr IS		0.2		X init , X IS , Δr IS			X
				X CS , X CS , Δr CS				X CS , X CS , Δr CS
		0.01 0.0	1	100	10 4		0.01 0.0	1	100	10 4
				t/τ				t/τ

init , X IS , Δr IS X CS , X CS , Δr CS

  Pearson correlation coefficient between the dynamic propensity and the prediction for A particles in a KA system at the statepoint used in this paper, made by different models: linear regression (LR) by Boattini et al.[START_REF] Boattini | Averaging local structure to predict the dynamic propensity in supercooled liquids[END_REF] , multi-layer perceptrop (MLP) by Jung et al.[START_REF] Jung | Predicting dynamic heterogeneity in glass-forming liquids by physics-informed machine learning[END_REF] , graph neural network (GNN) by Bapst et al.[START_REF] Bapst | Unveiling the predictive power of static structure in glassy systems[END_REF] , BOnd TArgetting Network (BOTAN) GNN by Shiba et al.[START_REF] Shiba | Unraveling intricate processes of glassy dynamics from static structure by machine learning relative motion[END_REF] and SE(3)equivariant GNN by Pezzicoli et al.[START_REF] Pezzicoli | SE (3)-equivariant graph neural networks for learning glassy liquids representations[END_REF] . b) Average dynamic propensity per snapshot in the dataset of Ref.13, which was also used in Refs.16, 17, and 19. For each initial snapshot in the training set of Ref.13, we plot the mean propensity in that snapshot at the times reported for that snapshot, and color the point based on the system density. For comparison, we also plot in black the mean propensity taken from our own dataset, where the times and density are the same for each initial configuration. The error bars indicate ±2 times the standard deviation of the mean propensity at each time.

			LR (this work)	GNN (Bapst 2020)
			LR (Boattini 2021)	BOTAN GNN (Shiba 2022)
			MLP (Jung 2022)	• SE(3) GNN (Pezzicoli 2022)
		1.0
			•
		0.9
		0.8
	Correlation	0.7		•	•	•	• • •• • •
		0.6
		0.5
		0.4	0.01	1	100		10 4
					t/τ
	b)
		1.4			ρσ A 3
	Average propensity [Δr/σ	0.4 0.6 0.8 1.0 1.2	1.200		1.204		1.208
		0.2
		0.0
		0.001	0.100	10		1000
					t/τ
	FIG. 4. a)

A ]

ACKNOWLEDGEMENTS

The authors would like to thank Marjolein de Jager for many discussion. L.F. acknowledges funding from NWO for a Vidi grant (Grant No. VI. VIDI.192.102)

DATA AVAILABILITY STATEMENT

Raw data associated with the measurements of the dynamical propensity, as well as all figure data, will be published at the following url [???] prior to publication of the paper.


Luca Maricchiolo
email: luca.maricchiolo@u-pec.fr

Framing urban autopoiesis: street as a track for multiple adaptive cycles

Keywords: urban morphology, urban forming process, public space, adaptation, autopoiesis

Street is the elementary domain of urban complex systems adaptation. It frames all phases of urban evolution, as they can be described by an adaptive cycle conceptual model: a forward loop, including growth and conservation phases, and a back loop, covering release, or crisis, and a reorganization phase.

Urban dynamics are not composed of a unique adaptive cycle, as cities evolve through multiple ones, having different timescales, as well as many periods and durations. The whole of these cycles, deployed on and in streets, unfold street rhythms, which present time is the synchronic representation. This communication will address multiple adaptive cycles intertwining in street life, identifying three main paths: (i) urban fabric forming process; (ii) ground level uses;

(iii) public space appropriations, ephemeral occupations and activities. Diachronic analysis of each path is carried out on the main case study of one street in Rabat, Morocco. It will be discussed by investigating change drivers and mechanisms, adaptation figures and resources, evolutionary phases and rhythms, persistence layouts.

The main goal is to figure out street evolutions dynamics and parameters in the framework of autopoiesis concept, as well as to highlight the role played by street in framing urban autopoiesis.

Introduction

Systematic observation of adaptation phenomena along a street aims at questioning the mechanisms of adaptive process within the theoretical framework of urban autopoiesis. This focuses on street not just as a physical element, but as a component of a systemic process operated by local organisation actions and reactions, of which it represents the founding structure. Street has, thus, a double meaning: it is the spatial structure shaping urban interactions and, at the same time, it is the product of such interactions, the synchronic projection of the whole systemic process.

Systematic observation herein presented concerns adaptation mechanisms and rhythms of a street in Rabat, Morocco, and particularly of a part of Sidi Mohammed Ben Abdallah Avenue. This is carried out through two synergic methodologies of investigation, to highlight actions, outputs, variables and factors that build up the taxonomy of the adaptive process: diachronic and comparative analysis of historical cartography and housing type plans; present analysis of practices and forms in and of the street.

Urban local adaptation: a theoretical framework

City is one of the main examples of a complex adaptive system [START_REF] Batty | Cities: continuity, transformation and emergence[END_REF] . It is a set of interacting elements, whose relations are based on an action-feedback mechanism such as to determine the behaviour of its actors. It is also characterized by two principles, selforganization and amplification of the effects, explaining every configuration as determined by the previous one [START_REF] Bertalanffy | Teoria generale dei sistemi. Fondamenti, sviluppi, applicazioni[END_REF] .

Street is a sub-system of the city, definingand defined bythe territorial location of its actors [START_REF] Pollini | Social Belonging[END_REF] . It affects the possibility and the quality of the whole urban system elements interactions [START_REF] Weber | Economy and society[END_REF] , as it limits a set of relations that are more likely to be established, due to accessibility and proximity. By this, it shapes the ecological participation of its users, as "a state of mutually oriented interdependence of a plurality of actors who are not integrated by bonds of solidarity to form a collectivity but who are objects to one another" [START_REF] Parsons | The social system[END_REF] .

Street system is thus more likely to an ecological system rather than a social one, whose behaviour could be appreciated through ecological resilience mechanisms. This theori-cal model [START_REF] Holling | Quest of a Theory of Adaptive Change[END_REF] postulates two characteristics particularly effective in describing urban dynamics [START_REF] Holling | Resilience and stability of ecological systems[END_REF] : adaptation as a primary evolutionary mechanism; persistence as a measurement of resilience, based on state variable thresholds.

Adaptability provides a basis to analyse self-organisation mechanisms. It is the capacity of a system to reorganize itself within his stability domain, based on the capacity of the actors to use historical memory and drive change towards a desired direction [START_REF] Walker | Resilience, adaptability and transformability in social-ecological systems[END_REF] . In response to environmental forces, actors within a system modify individual action relating to favourable or unfavourable outcomes of previous adaptations, pursuing the maximization of individual effectiveness by the minimization of environmental resistance [START_REF] Van Der Land | Voice, exit and efficacy: dealing with perceived neighbourhood decline without moving out, p. 432[END_REF] .

Adaptation actions are thus communicated to the system, which modifies its behaviour in relation to them [START_REF] Culley | Claiming space in Casablanca: modernist experiments and user-initiated dwelling transformations in Hay Mohammadi[END_REF] . Self-organized whole order emerges from the sedimentation of a myriad of such individual choices, in response to a precise set of housing, production and relational needs 11 .

Adaptation is strictly linked to self-organisation and autopoiesis. Autopoiesis may be referred to how urban structure and morphology are created, transformed, organised and proceeded [START_REF] Bus | Urban Autopoiesis: towards adaptive future cities[END_REF] . Having been defined as the capacity of a living system to recursively reproduce through its own elements [START_REF] Maturana | L'Albero della conoscenza. Un nuovo meccanismo per spiegare le radici biologiche della conoscenza umana[END_REF] , autopoiesis concept can be applied to social, organisation and interaction systems, abstracting from life and defining it as a general form of system-building, using self-referential closure [START_REF] Luhman | The Autopoiesis of Social Systems[END_REF] . Furthermore, Luhmann identifies communication as a founding element of social systems, instead of persons or actions [START_REF] Seldi | Luhmann's theory of autopoietic social system[END_REF] .

Similarly, inner relationspersonal, commercial, business, well-beingare the base elements of urban systems and of street sub-system. Hence, autopoiesis is to be intended as the production process of urban relations as well as of its founding structuresevery artifact making citiesbased on self-referential operations. The duplication of the same elements of a system, as elementary unit replication, is an autopoiesis feature. The criteria of such evolutionwhat element to be duplicated and how, e.g. the reiteration of row houses along a matrix path [START_REF] Bertuglia | Complessità, autoorganizzazione, città[END_REF] depend on system structure, whose selfdetermination is due to self-organization [START_REF] Luhmann | Organisation und Entscheidung[END_REF] .

Local adaptation is an observable phenomenon of system self-organization. Adaptation is concretely acted and registered in system's historical memory, as to shape future sys-tem structure and reproduction. It is an infinitely iterative mechanism, made of successive adaptive cycles made of two proactive phases, i.e. expansion and conservations, and two reactive ones, i.e. release and spontaneous reorganization. Reorganization phase of adaptive cycle includes learning from historical memory, built heritage, functional habits, to manage present transformations and establish new relations or artefacts, whose consequent feedbacks will produce new learning. This builds up a self-referential process, operated within the system, while environment just acts as external force. An autopoietic system is strictly linked to its environment, as it adapts according to external variations, while keeping its internal organization [START_REF] Varela | Principles of biological autonomy[END_REF] .

Across those cycles, some variables of the urban system change to react to external variations, depending on autonomous reorganization. Nevertheless, there are some slowchanging variables, linked to systemic values (e.g. identity, culture and awareness) and to the physical structure of space, that have higher inertia and influence system ability to manage change in a non-destructive way [START_REF] Carpenter | From metaphor to measurement: resilience of what to what?[END_REF] . These are the milestones to define autopoiesis, as, by persistence, they shape system identity.

Systematic observation aims at grasping such specific characteristics of both street structure and organization: identifying adaptive cycles and highlighting their periods, actions of adaptation, outputs, persistence and change factors. Observation focuses on three main domains: urban forming process, ground floor activities and public space practices; they deploy physical, relational and functional factors making urban unicity, and managing shift from a state regime to another 20 .

The goal is to outline autopoiesis trajectoryhow street evolved producing new relations ad artefactsas well as the founding role street had in framing it.

Observation: street adaption phenomena

Rabat, Morocco: Avenue Sidi Mohammed Ben Abdallah in Yacoub el Mansour district

Rabat has had a quite recent metropolitan growth. Fitted in its traditional form until it became the capital of the French protectorate in 1914, it didn't reach significant dimensions even with the first colonial plan by Henri Prost. The metropolitan extension begun A first category of street adaptation consists in permanent occupation of public space through informal new hard-wall volumes for shops. In free spaces, and particularly in the gap between the orthogonal plot and the diagonal street axis, small constructions were built either as extensions or new installations, detached from the front by a small passage. In some cases, the addition of commercial volumes constitutes a new urban front, sometimes arcaded, which overlap a new gallery on the rhythmic scan of the plots, unifying closest blocks through a gate on perpendicular ways.

A second category of street section adaptation differs for technology and temporality of appropriation. A series of light constructions stands in front of the hard-walled volumes: kiosks in recycled material, metallic and textile tents, glass and aluminium verandas, wooden platforms, are either extensions of ground floors activities or independent business directly installed on sidewalks.

The third category of adaptation is the ephemeral occupation. Café's terraces occupy sidewalks seasonally, parking lots allow the installation of hawkers for weekly markets, boutiques thresholds are employed by boxes and showcases on daytime; during the month of Ramadan, the square becomes a space for prayer, commerce is reduced, restaurants close during the day, removing their tables from sidewalks to extend those onto the roadway after ftour. The five-to-ten meters band facing urban front hosts a mix of uses, very flexible in uses, which can be ordered as a succession of temporalities [START_REF] Mangin | Le droit au rez-de-ville[END_REF] . The ambiguity -even regulatory -of space expresses a great diversity of rhythms and geometries. The experience of the street is an overlap of noises, sensations, sounds and en-counters, featured by several variables, as duration, uses, type of merchandise, extension (punctual or linear), shape and construction.

Observation results

The diachronic analysis and present observation unfold multiple adaptive cycle deployed on and in the street. These have been classified on three categories on the basis of the spatial domain of deployment and the temporal scale of duration. Phenomena restitution highlights further parameters associated to each cycle: the crisis triggering back loop phases, main adaptation actions, the temporal scale of the cycle and the forms and figures that spontaneous reorganization has taken. The quality of the transformation is measured according to change rate of the ten above mentioned variables, adopted as adaptation indicators. Moreover, among these, each adaptive process is based on some factors acting as a resource for adaptation, linked to slow variables of change, thus steering the adaptation [START_REF] Wildavsky | Searching for safety[END_REF] .

A taxonomy of adaptive cycles allows to relate adaptive actions with outputs, resources for adaptation and persistence variables.

( From the taxonomy of local adaptation phenomena, through chronological localisation of few events [START_REF] Maricchiolo | Historicizing spontaneous city. Michel Ecochard and the «habitat pour le plus grand nombre» in Morocco[END_REF] , we can draw a diagram of temporal deployment of the adaptive cycles of the avenue. Although the set of information is not precisely quantifiable for the entire period, the diagram provides qualitative insights on persistence rhythms and duration.

The notion of persistence, declined on a local temporal scale, identifies variables that persist in at least one adaptive cycle. Local persistence variables are slow variables on a larger time scale. General persistence is a limit case of the long periodicity of change.

(Table 02 - -Small plots scale, allowing easier installation, management and transformation as relate to the population economic means;

-Tight rhythm of plot patterns, strengthening neighbourhood relations;

-Buffer and redundant spaces, providing physical resources for adaptation;

-Urban structure, translating fractal Medina's structure to easily establish space progression and hierarchy from main axis to inner public space, which are consistent with local urban tradition;

-Horizontality of management process, due to lack of public control and weak regulation, admitting informal action.

There are obviously mutual relations between persistence characters and adaptation factors, as, generally, slow changing variables depend on system identity. Some of those remained consistent across change, influencing adaptation and being exploited as resources in further configurations. Some others have been spontaneously recreated, as the linear disposition of commercial activities along the avenue to the detriment of initial local centralities, as well as of the less attractive main square.

The nature of persistence variables can be discussed in the theoretical framework of

Conclusion

Adaptation actions and outputs profile an autopoiesis and describe the role of the street as an accumulation path. This leads to draw few conclusions and research perspectives from a design point of view.

Firstly, self-referential closure revealed the deepest identity of the city, reproducing living secular habits that had inspired Ecochard planning [START_REF] Cohen | Casablanca. Mythes et figures d'une aventure urbaine[END_REF] . Autopoietic public space carries a metis 31 value [START_REF] Avermate | Nomadic experts and travelling perspectives: colonial modernity and the epistemological shift in Modern architecture culture[END_REF] , that arises from intuitive adaptive ability [START_REF] Detienne | Les ruses de l'intelligence. La mètis des Grecs[END_REF] and could unfold future adaptation paths. Modeling of autopoietic features, as well as mapping of adaptation by parametric tools, should provide a strong basis for urban design, foreshadowing adaptive possibilities facing present time uncertainty.

Furthermore, the autopoietic trajectory displays a trend towards human-scaled urban space. Self-organized process does not follow an a priori project, but it acts according to the ability of each element to adapt its behaviour by taking advantage of environmental change [START_REF] Bertuglia | [END_REF] : persistence is not just inertia, is more likely an active organization, an energetic effort to maintain the identity, and consequently the form [START_REF] Morin | Il metodo 1. La natura della natura[END_REF] . There is, thus, an implicit idea of purpose in urban self-organization [START_REF] Ruiz | Sistemas urbanos complejos[END_REF] ; in Rabat inhabitants realized their own urban aspirations through informal actions [START_REF] Navez-Bouchanine | Stratégies residentielles dans la ville fragmentée. Le cas de la ville marocaine[END_REF] . The expressed trend offers a gaze on contemporary city and complexity intuitive management: it outlines a model of a tight urban fabric, made of small buildings and spaces, intense rhythms, pedestrian paths, proximity, densification, functional mixité, and it conveys an idea of a certain ambiguity in space regulation and a strong simultaneity in uses, being relevant for consumption reduction.

Finally, street confirms the founding role it had in urban history [START_REF] Romano | Liberi di costruire[END_REF] . As it had marked the formative processes of European medieval city, systematically based on the pioneering colonization of a matrix path, persisted in subsequent evolutions, the comparison with the Rabat case-study highlights the recurrence of the same transition process, passing through the settlement of small single units along a street, their implementation, the recasting of adjacent units, the genesis of linear collective housing [START_REF] Caniggia | Lettura dell'edilizia di base[END_REF] . Self-organization depends on likelihood of relations established within the urban system. Hence, defining ecological participation, street is an accumulation path for systemic interactions, and as such it frames autopoiesis and directs morphogenesis.

place in the framework of author's research and teaching activities at the International University of from 2017 to 2021. Ahmed Amahzoune cooperated in the data systematization at the International University of Rabat.

  scheme for multiple floors houses, establish a new expansion phase based on the outcome of the previous cycle spontaneous reorganization. In 1971 the Ecochard plots ended to be considered as temporary, and in 1973 the first post-independence Rabat urban plan incorporates the former evolutionary habitat[START_REF] Chaline | Urbanisme et développemnt. évaluation des schémas directeurs d'Ankara, du Caire[END_REF] . Thus, dwellings continued to be built on 8 meters or smaller plots, settling 3 to 4 floors terraced houses known as modern Moroccan houses (maisons modernes marocaines)[START_REF] Belfquih | Mécanismes et formes de croissance urbaine au Maroc. Cas de l'agglomeration Rabat-Salé[END_REF] . Street evolution keeps a consistent urban structure, based on the original 6 to 8 meters plots, accommodating medium height individual row houses.

(

  Fig. 08 -Public space appropriations. Photocollage -Source: Author, 2022) Direct observation on day and night time allows to grasp two further variables to describe the whole adaptation process: (ix) public space hierarchy, evident in the gain of importance of the main axis, a former circulation path expected to remain aside of public centralities; (x) public space occupation, challenging the street regulation. (Fig. 09 -Sidi Mohammed Ben Abdallah avenue in Rabat: diagram of ground floors activities -Source: Ahmed Amahzoune and Luca Maricchiolo, 2022)

-

  Chronological diagram. Section A (top) shows major deployment of adaptation actions. Section B (bottom) displays changing (discontinuous) or persistent (continuous) variables -Source: Author, 2022) Discussion Adaptation, persistence and change Synoptic view of the adaptive processes of Sidi Mohammed Ben Abdallah avenue in Rabat allows to grasp the evolutionary trajectories of the urban street system. adaptive cycles, specialized for resources, drivers and activated processes, overlap on different time periods, showing indicators of local variability and persistence. Local variability identifies fast changing variables. On the contrary, local persistence describes slow changing variables, thus state variables whose transformation, over the decades, has been sporadic, slower or fainter. As a limit state of slow change, the following variables of street structure are identifiable as persistent: Plot pattern: from pioneering phase (design) to nowadays, plot patterns kept its initial structure, acting as a resource for change and as a main factor influencing urban form adaptation in its shapes -Urban structure: despite hard transformations, public space geometry remained almost unchanged, as it is recognizable by comparing Ecochard plan with Google aerial photos. Furthermore, those processes describe a global densification trend, in land and housing density increase, in primary functions, in street activities and frequentations. Densification trend testifies to a positive feedbacks chain, expressed in the categories of population attractiveness, commercial appeal, economic growth. Positive feedbacks feed adaptive process, which generated further positive feedbacks, stimulating the whole process, according to the effects amplification principle. Adaptive factors in cultural and economic fields are the resources for such positive dynamics:

  urban self-organization and autopoiesis. Adaptation feedbacks rule the production of new relations and the success of the existing ones. The evolution of the analysed street is built up through replication of urban syntaxeshierarchies, paths, activitiesand artefactspatterns, buildings, ephemeral objectsmatching both self-determination and self-referentiality principles. First, the process has not managed by planning, being driven by inhabitants after Ecochard founding plan in 1948. Then, although driven by external forces, as demographic, political and economic changes, it is locally operated on local sources: adaptation draw solutions from Ecochard design, as well as from traditional city: main transformation towards hierarchical progression from commercial road to inner fabric depends on the relationship between diversity and intimacy expressed in the fractal structure of the traditional city: matrix path of the souk was spontaneously recreated along the avenue Sidi Mohammed Ben Abdallah. (Fig. 10 -Self-referential closure. (i) Street and skyline rhythm: a. Sidi Mohammed Ben Abdallah avenue; b. Rabat ancient medina; (ii) Dwelling typologies evolution, from Ecochard to present time; (iii) Public space shape: a. Sidi Mohammed Ben Abdallah avenue; b. Rabat ancient medina; (iv) Commercial typologies: a. Sidi Mohammed Ben Abdallah avenue; b. Rabat ancient medina -Source: Author, 2015-2022)

Table 01 -

 01 Taxonomy of street adaptations -Source: Author, 2022)

	Adaptive	Action of	Outputs of	Drivers	Local	Local	Adaptation
	Cycle	adaptation	adaptation		change	persistence	resources
	Urban forming	Saturation	Roofing of	Urban	Dwelling	urban	Buffer space
	process 1	(densification)	inner patios	population	types	structure, plots	exceeding
				growth		pattern,	initial needs
						urban form
			Substitution of	Private means	Dwelling	Urban	Plots space,
			initial barracks	increase	types,	structure,	urban
			with ground-		urban form	Plots pattern	infrastructure
			floor hard-
			walled houses
	Urban forming	Rise up	Building of 3-	Urban	Dwelling	Urban	Basement,
	process 2	(densification)	to-4 floors row	population	types,	structure,	redundancy of
			houses on low-	growth,	urban form,	plots pattern,	urban
			rise initial	private means	facades		infrastructure
			patio houses	increase	porosity		exceeding
							initial needs
	Urban forming	Subdivision	Split of row	Urban	Dwelling	Urban	Staircase
	process 3	(densification)	house into	population	types	structure,	sharing
			collective	growth,		plots pattern,
			housing with	Households		urban form,
			one apartment	composition		facades
			per floor	evolution		porosity
	Urban forming	Recasting	Unification of	Increase of	Dwelling	Urban	Juxtaposition,
	process 4		adjacent row	private means	types, Facades	structure,	small scaled
			house in a		porosity or	plots pattern,	plots
			multi-plot		pattern	Urban form
			collective
			building
	Ground level	Intensification	Increase of	Urban	Ground floor	Urban	Buffer space
	transformation	(densification)	housing	population	density,	structure,	exceeding
	1		capacity	growth	dwelling types	Plots pattern,	initial needs
						urban form,
						functional
						diversity,
						Accessibility
	Ground level	Change of use Attribution to	Economical	Functional	Urban	Redundant
	transformation		productive	needs	diversity,	structure,	space in the
	2		activity to		dwelling types	Plots pattern,	house, small
			ground floor			urban form,	scaled plots
						ground floor
						density,
						accessibility
	Ground level	Extroversion	Opening of	Economical	Accessibility.	Urban	Boundary of
	transformation	of commercial	showcases and	needs	Public space	structure, Plots	urban space,
	3	space	windows		hierarchy,	pattern, urban	small-scaled
					dwelling types	form,	plots, urban
						functional	paths
						diversity,	hierarchy
						ground floor
						density
			External	Economical	Accessibility,	Urban	Redundant
			private	needs	Ground floor	structure, Plots	space on
			appropriation		density	pattern, urban	sidewalks
						form,
						functional
						diversity
	Public space	Permanent	Commercial	Economical	Plots pattern,	Urban	Redundant
	appropriation	occupation	building	needs	urban form,	structure,	space of urban
	1	(densification)	construction		public space	functional	pattern gaps
			on main axes		hierarchy and	diversity,
					occupation	dwelling types
	Public space	Temporary	Kiosks, tents,	Economical	Public space	Urban	Redundant
	appropriation	occupation	verandas,	needs	hierarchy and	structure, plots	space of urban
	2	(densification)	platform		occupation,	pattern, urban	pattern gaps,

fabric, on one side of the street, made of Modern patio houses on 8 meters squared plots organised in clusters, centred on a small square; the settlement of trame sanitaire plots on the other side, to recover Douar Debbagh slum, depending on minimal public intervention principle: a 6 meters square pattern, equipped with hydraulic network and a toilet, on which small barracks with conical straw roof are built prior to the selfconstruction of hard-wall houses. (Fig. 02 -Horizontal city: Service de l'habitat, Rabat Yacoub el Mansour, General plan of the site between avenue « D » and avenue Sidi Mohammed Ben Abdallah, 1951 -Source: Archives du Maroc)The main avenue is more a circulation route rather than a structuring path, faithful to the modern principle of the separation of flows, as highlighted by geometric misalignment between the axis and the plots.

K. Fabbricatti, Le sfide della città interculturale. La teoria della resilienza per il governo dei cambiamenti, Milano: FrancoAngeli, 2013

Acknowledgments

Some observation results hereby presented have been collected on the occasion of the seminar "Atlas partagé des rez-de-ville", held at the International University Rabat in 2018, in the context of the international research project "Rez-de-ville. Formel/informel, besoins des deux" led by David Mangin at EAVT Paris-Est. Further observations took


Chiara Roma

Morphological persistence in Zadar historical centre reconstruction

As an Italian exclave in Dalmatia, Zadar was bombed by the Allied army during World War II for almost a year, from November 1943 to October 1944, leading to the destruction of a large part of the old Venetian city. Once gone to the Socialist Federal Republic of Yugoslavia in 1947, the city managed the reconstruction of the historic centre. A design competition, inspired by the Yugoslav Academy of Sciences and Arts, was launched in 1953, with the aim of developing an organic plan for the whole historic fabric. This has been the opportunity to discuss different approaches and to define a strategy for reconstruction moving away from both identical reconstruction and modern breakout. This paper aims at questioning the doctrines of reconstruction and restoration at urban scale challenged by the reconstruction of the historic centre of Zadar. It proposes a critical review of such process by comparing some proposals of the competition. Thus, it focuses on the final masterplan, developed under the coordination of the architect Bruno Milic to highlight its specific features and question it through restoration principles, as expressed by Cesare Brandi and the Venice Charter. The critical review is based on the documentary sources of the presented proposals as well as on literature issues relevant to the debate of the time. It relies, as well, on a comparative approach with other emblematic experiences of post-war reconstruction in Europe, to reveal the particular features of the modern historic centre of Zadar. In the panorama of post-war reconstruction approaches, Zadar reconstruction process achieves a rare philological interpretation of restoration on an urban scale, integrating gaps and stratifying the urban historical landscape without neither hiding history nor renouncing to its own present time.

Introduction

Founded in IX century B.C., Zadar was conquered by the Romans in II century and rebuilt as a typical Roman city, which cardo-decumanic structure shaped the forming process in the following centuries. The medieval city developed on the sediment of the Roman insulae, welcoming the emergence of pre-Romanesque and Romanesque religious architecture up to the XII century. Conquered by Venice in the XIII century, several Renaissance and Baroque buildings were set in the medieval fabric on the Roman grid, and the fortress at the entrance to the peninsula was built. Zadar finally passed to the Austro-Hungarian Empire in XVIII century, without undergoing major transformations, till the Italian domination begins at the beginning of the XX century 1 . In 1939, the Zadar Regulation Plan ruled the expansion of the city outside the peninsula, and it envisaged the restructuration of the historical centre, involving the reshape of public spaces in front of main buildings. This plan has not been implemented due to the outbreak of war, so the historical centre remains intact till World War II2 . During war, after Italian armistice in 1943, Zadar was bombed by the Allied Army to prevent it from passing to the Germans. The city was hit seventy-two times between November 1973 and October 1944, leading the eighty percent of peninsula heritage being destroyed or seriously damaged, and the population passing from 30,000 to 6,000 inhabitants3 . Hence, the reconstruction of the historic centre of Zadar became a main issue in postwar period, once Zadar passed to the SFR of Yugoslavia in 1947. It was also the opportunity to foster the debate on post-war reconstruction in Europe, whose practices

were not yet characterized by a coherent theoretical framework. Zadar reconstruction has risen in relation to different instances: the socialist ideal, aiming at building a new society through urban planning; the adoption of modern architecture principles, without any yielding to stylistic historicism; the preservation of the historical structure and of the built heritage of the city4 . Dealing with these issues, it has been a breeding ground for the development of an original methodology in urban restoration. (Fig. 1)

Zadar reconstruction process

The reconstruction of the historical centre has been faced even before the end of the war, as the first studies for an urban plan already begun in 1944 5 . In 1947, when the city passed from Italy to the SFR of Yugoslavia, a first plan drawn up by the architects Milovan Kovačević, Božidar Rašica and Zdenko Strižić was approved 6 . The masterplan, adopting modernist principles consistent to socialist ideals, foresees the restoration of main historical monuments, whose surroundings should be freed from rubble or preexisting structures to enhance the plastic value. Intact insulae were as well recognised, leading to the conservation of some preserved fabric. New buildings were freely arranged in the greenery, namely on the south coast, so as to stand, as historical monuments, in a continuous and fluid space. The reference to CIAM principles draws on some radical ideas, as the reduction of historical identity to a series of emblematic elements standing on a neutral ground, echoing Le Corbusier paratactical representation of Paris as a series of main monuments and cruciform towers standing over a cancelled urban fabric 7 . The radical inspiration of the plan leads to its prompt suspension, which arrives in 1948. Nevertheless, the plan provides the legal basis for carrying out the removal of rubble, which ends up aggravating the damage, as entire insulae were destroyed during this operation 8 . At the beginning of the fifties, the Yugoslav Academy of Sciences and Arts, on the occasion of the restoration of the Romanesque Saint Mary's convent, promoted the need for an organic plan of the historic centre. Hence, three architects of the academy -Josip Seissel, Drago Galić and Andrija Mohorovičićdeveloped the guidelines which became the basis for a design competition 9 . Launched in 1953 by the Municipality, the Yugoslav national competition for the regulatory basis of the city of Zadar sets the objective of drafting an organic plan for the reconstruction and the development of the historic core of Zadar, fostering a unitary intervention with the aim of "renovating the existing part of the city so that the whole represents a complex architectural and urban organization" 10 . The tender articulates different objectives in order of priority, regarding the development of the city as a cultural, educational, administrative, touristic, industrial, handcrafts and trade centre 11 . Furthermore, the competition declared the ambition of stimulating a cultural debate on urban planning, wishing to make Zadar a model in Europe for post-war reconstruction. The announcement raises some cultural issues, problematizing questions to which proposals are called to offer a hypothesis. It requests to preserve the remaining urban fabric, keep the ancient urban structure, make existing buildings the cores of new urban sequences in accordance with the general scale of the city, and convert the centre into pedestrian. The Academy of Arts points out the value of urban memory in present time. It expects participants to integrate historical elements in contemporary design and preserve the stratifications of the city without falling into historicism nor limiting design innovation, fostering, by that, a methodological approach inherent in restoration practice. On the one hand, the emphasis is placed on the recognition of the cultural value of the city, with the aim of redeveloping it valorising what was saved from war. The solid analytical basis provided to participants reflects this orientation 12 : the city is divided into fifty-seven blocks, for each of which are defined the guidelines for interventions 13 . The announcement provides a detailed survey of the historic fabric of the peninsula, going from maps at 1/25,000 to plans at 1/500, and including the elevations of the street fronts. Furthermore, the documentation is provided with a detailed inventory of the heritage and with a diagnostic of the existing building status, On the other hand, the hierarchy of the sought design features is revealed by the evaluation criteria 14 : the prefiguration of a balanced urban complex, characterized by the harmonious relationship between built and unbuilt space; the design of modest dimensions public spaces, adapted to the medieval architectural heritage, to Mediterranean climate and lifestyle; the new morphology, to better integrate the historic street network; the waterfront proposal, which height and shape should not obscure main landmarks of the city's identity. Fourteen entries have been submitted to the competition, twelve of which met the criteria. Three ex-aequo winners have been elected: Berislav Kaloðera with the proposal n. 16124; Bruno Milić and Miroslav Kollenz with the proposal n. 39393; Vlado 9 Ivana Lazanja, "The reconstruction of the Croatian coastal city of Zadar", in Luc Verpoest and Nicholas Bullock (ed.), Living with History, 1914-1964: Rebuilding

Alternative approaches

The competition specifics considerably frame design towards a prevalent conservation of the historic layout and the integration of the existing in an organic vision of the whole. Nonetheless, a variety of approaches emerges from the comparative reading of the presented proposals, while commission's judgments mostly appreciate proposals that are more respectful of the existing. The research of Antonija Mlikota 1516 , based on the primary sources of the competition, is a precious reference to acknowledge the presented projects, whose comparative analysis allows to draw some critical reflections. These point out four main design hypotheses. (i) The hypothesis of the reconstruction ab nihilo, founded on the reduction of historical identity to the preservation of a series of extraordinary buildings; around, a new system of urban relation should be re-established. It seems to be in harmony with the Modern educational tendencies, affirmed, for instance, in the plans for the reconstruction of Saint-Dié des Vosges by Le Corbusier or Le Havre by Auguste Perret. According to this stance, design is a tool for the construction of identityalthough structured by a series of punctiform emergenciesrather than for the enhancement of the existing one. The churches, the ramparts and the archaeological site of Zadar become the focal points of a self-standing design, unconcerned with the urban forming process, providing for a massive dose of demolition of the ordinary fabric. The envisaged new morphologies refer to opposite, whilst equivalent, radical approach to reconstruction, replacing ancient fabric by modern isolated buildings 17 , closed blocks fabric 18 , or new patterns emphasising around main monuments 19 ; their implant, according to the jury, would establish a fake historical nucleus, denying the history and the culture of Zadar 20 . (ii) The hypothesis of the interpretative reconstruction, which maintains the historical plot while reshaping typo-morphologies. Moving from a comprehension of the identity of the fabric, some proposals respect ordinary fabric scale and typologies to develop innovative solutions, harmonious with the context. Therefore, some proposals receive averagely good appreciations, since they are considered globally consistent with the request of the tender. They respect layouts and morphologies, adapting new architectures to preserved historical monuments, responding to the expectation of a noninvasive completion of the urban fabric. At the same time, some derogations to the continuity of the existing city are proposed: the introduction of morphological variations, as buildings jutting out onto the coast profile or new commercial axes 21 ; the redefinition of squares proportions 22 or hierarchies 23 ; the new relationship between monumental buildings and the ordinary fabric, freeing up spaces previously defined by 15 building fronts 24 . These have been criticised for to the non-compliance with historical sequences; particularly interesting is the refusal of new concentrations of activities inconsistent with the matrix path and hierarchy, to avoid the upsetting of urban dynamics and pedestrian flows. (iii) The hypothesis of philological reconstruction, which echoes some methodological principles of restoration theory. According to the jury evaluations, the three winning projects propose a similar approach. They keep the Roman street pattern to install new architectural typologies in respect of the urban alignments and shapes. The proposals given by Kaloðera and Milić are carried with a scientific approach which anchors design to the analysis of the formative process of the historical fabric, foreseen low rise typologies consistent to historic city space. They propose a Mediterranean-type spatiality made of a strong articulation between masses and voids, public and semipublic spaces, such as courtyards, arcades, passages. New buildings for forum area and the waterfront comply with the fabric scale and do not hide historical landmarks. Milić's proposal was praised for the accordance of building heights to medieval row houses, and for designing forum area under reserve of archaeological excavations. Kaloðera proposes greater typo-morphological freedom, by a composition of modern buildings into the street pattern, respecting alignments without reconstituting the entire perimeter of the block, to keep more open spaces and greater ventilation. This stronger modern imprint has been appreciated for articulating the monotone ancient street pattern with modern composition. The proposal from the Urban Planning Institute of Croatia also takes up the Roman network, respecting the scale and the layout of the streets. However, it adopts a too decisive approach to urban morphology: the serial repetition of the open block typology and the provision of some large, monumental squares moves away from the idea of an ancient Mediterranean city. (iv) Finally, a single proposal adopts a stronger philological approach 25 , closer to restoration practice: it stands at pure conservation of the existing building, foreseeing the liberation of the demolished areas and their transformation in parks, seeming to be neutral colour filling of lacunae. Its negative evaluation is due to the lack of new housing.

The modern historic centre of Zadar

As a result of the competition, in 1955 Bruno Milić was commissioned to draw up a regulatory plan considering the other two awarded works. The plan integrating some analyses and strategies from other works and from the jury. The methodological leap lies in the rejection of two antithetical modelsmodern breakthrough as well as historicismtowards a project based on the method. Among the main planning trends in post-war Europe, Milić's synthesis goes through a via media of urban design, used to be run by some Italian 26 , Portuguese 27 or Spanish 28 practices, but, at the time, less common in Central Europe. Zadar aurea mediocritas primarly defines itself in relation 24 Design proposal n. 201153 25 Design proposal n. 99066 26 For instance: Ludovico Quaroni and Mario Ridolfi, Quartiere Tiburtino, Roma, 1949-1954; Adalberto Libera, Unità di abitazione orizzontale, Roma, 1950Roma, -1954;;Giancarlo De Carlo, Collegi universitari, Urbino, 1962-1983;Vittorio Gragotti, Quartiere residenziale a Cannaregio, Venice, 1981-1985 27 Alvaro Siza, Quinta da Malagueira, Evora, 1973 28 Josep Martorell, Oriol Bohigas, David Mackay andAlbert Puigdomènech, Vila Olimpica del Poblenou, Barcelona, 1992 to the compatibility with the historical and landscape context, even, perhaps, by renouncing to an innovative impulse that would slip into self-referentiality. The plan reads and interprets the city in a contemporary key, keeping distinctive urban spaces, street pattern and squares, dimensions, proportions, and volumetric relationships. Architectures are shaped with respect to historical monuments, as to preserve views and to valorise pre-existing buildings. The overlay of masses and voids articulates inner courtyards and vibrant ground-floors, while external fronts shape urban sequences, combining modern dwelling typologies with Mediterranean spatiality. (Fig. 2) Milić's plan was presented in 1955, but it has never officially approved by the City of Zadar; indeed, it has finally been rejected in 1958. A new competition, launched in 1959 by the invitation of major Croatian architects, ended without any result 29 . Hence, the guidelines for reconstruction have been finally developed by the jury 30 , and an ad hoc commission managed design and construction, combining three strategies: the restoration of damaged buildings, the stylistic reconstruction for iconic monuments, the contemporary graft in accordance with the existing. In the absence of any official regulatory plan, Milić one was still an essential reference: the guidelines comply with its principles, which have often been implemented by architectural design: residential building 53/15, designed in 1954 by Alfred Albini, and the Krsevan block, by Neven Šegvić in 1954, takes up the meander configuration of Milić's plan; similarly, the residential building for tankers by Božidar Rašica, winner of the west coast development competition in 1955 31 . The 1959 guidelines developed a specific model for the reconstruction of the Kalelarga matrix path, introducing galleries on ground floor -not foreseen in Milic's plan -and some passages towards the courtyards: these variations, however, emphasize the imbrication of spaces typical of Mediterranean urban. The model assigned the different plots: blocks A, B and D, which define Kalelarga urban fronts, are designed by Bruno Milić and Ivo Bartolić; blocks C, along Kalelarga, H and I, which define the void of the Forum, are assigned to Božidar Rašica; the block E, the Archeological Museum in front of the Church of San Donatus, is designed by Mladen Kauzlarić. Blocks F and G, envisaged on the site of the forum to close the square towards the sea, will not be built 32 . (Fig. 3) (Fig. 4) The architectures have a synthetic, minimalist language, taking up modern stylistic features in dialectical relation with historical buildings. Thus, the achieved reconstruction complies with the aim suggested by the Academy statement and Milić plan: it keeps contemporary interventions exceptional and recognizable, while enhancing the preservable heritage and fostering the legibility of urban stratification.

Conclusion: on reconstruction epistemology.

Zadar reconstruction process adheres in a pertinent and potentially fruitful way to the methodological approach of restoration, particularly in the philological approach having 29 Antonija Mlikota, "Četrnaest arhitektonskih i urbanističkih vizija povijesne jezgre Zadra nastalih 1953 godine", Ars Adriatica, 5, 2015, pp. 163-192, p. 186 30 Antonija Mlikota, Obnova i izgradnja povijesne jezgre Zadra nakon razaranja u Drugom svjetskom ratu, PhD thesis, Faculty of Philosophy, University of Zagreb, Zagreb, p.134 31 Natječaju za arhitektonsko i urbanističko rješenje zapadne obale povijesne jezgre Zadra, 1955 32 Anđela Galić, Stambena Arhitektura Zadra 1950-ih i 1960-ih, Master thesis, Faculty of Philosophy, University of Zagreb, 2017, p. 25 been theorised by Cesare Brandi and the Venice Charter. Restoration is, according to Brandi, "any intervention intended to restore efficiency to a product of human activity" [START_REF] Brandi | Teoria del restauro[END_REF] . Its conceptualisation will differ depending on the nature of the product of human activity, and particularly on the recognition of it as work of art. It follows that "restoration is the methodological moment of recognition of the work of art, in its physical substance and in its dual aesthetic and historical polarity, in view of its transmission to the future" 34 . The process initiated by the Yugoslav Academy of Sciences and Art is founded on the acknowledgement of the artistic value of Zadar built heritage, in its both aesthetic and historical meanings. The competition announcement and the evaluation criteria are particularly concerned by the recognition of the cultural value of the surviving heritage, as well as by the way to restore efficiency and transmit it to the future. Furthermore, academy approach cares about basic issues of restoration, as: (i) is the conservation of the matter of the work of art, in its both structure and appearance [START_REF] Brandi | Teoria del restauro[END_REF] , applying to existing buildings and viewpoints preservation; (ii) the reconstitution of the potential unity of the work of art, to be researched in the wish to complete the fabric as a whole without making a false 36 ; (iii) the respect of work of art duration and the timing of restoration in present time [START_REF] Brandi | Teoria del restauro[END_REF] . Some further principles should be drawn from the Venice Charter 38 , which defines the methodological milestones of restoration operations : (i) the philological certainty of the history of the work aimed at its comprehensibility; (ii) the respect for the stratification of all historical epochs (against the prerogative of a real or presumed state of origin); (iii) the recognizability of the restoration work, while respecting the legibility of the whole; (iv) the exceptional nature of the completion or integration intervention, within a primary purpose of the restoration which is the conservation and transmission to subsequent generations; (v) the reversibility of the intervention. Restoration principles do not belong to urban design discipline, emerging in architecture and art restauration practices. City is not a unitary work of art, it is like a work of art composed of parts, each one with its time and duration. Thus, the historicity of urban landscape is made of the relation between every historical present of the forming process of its parts and the current present that recognizes it. The importance accorded to the duration of forming process and to the stratification of the whole makes reconstruction process both historical and aesthetic instances of postwar heritage: the first, through the methodological approach based on scientific and documentary knowledge as a requisite for design; the second, in the aim of philological valorisation of every present time, including contemporary fillings. As a result, every layer is still visible and recognizable in Zadar historical landscape. The outcome is appreciable in nowadays urban quality and touristic attractivity, talking about the success of a post-war reconstruction which offers an original point of view on the European scene. Original, as it stands out form the practice of assuming destruction as a cathartic event for the emergence of a new story, which also boasts a thriving tradition in modern Europe, from Catania 39 to Lisbon 40 ; instead, it deals with the medieval practice of spontaneous settlement on previous eras ruins 41 , continuing the stratification of landscape within a consistent plot. In this way, it enriches the epistemology of urban design, including the scientific methodology of restoration to produce a design method attentive to the past without abjuring the historical present that generated it. 41 For instance, Split medieval forming process over Diocletian Palace ruins

CaptionsFig. 1 -

 1 Fig. 1 -Zadar after World War II bombing, 1944 quarter page

  Europe after the First and Second World Wars and the Role of Heritage Preservation, Leuven University Press, Leuven, 2021, pp. 279-287, p. 283 10 People's Committee of the City Municipality of Zadar (ed.), Natjeÿaj za Regulacionu osnovu grada Zadr, Zadar, 1953 11 Ines Merćep, "Natjecaj za regulacijsku osnovu Zadra iz 1953. Pedeset godina poslije", Prostor, 13 (1,29), may 2005, pp. 67-78 12 People's Committee of the City Municipality of Zadar (ed.), Natjeÿaj za Regulacionu osnovu grada Zadr, Zadar, 1953 13 Antonija Mlikota, Četrnaest arhitektonskih i urbanističkih vizija povijesne jezgre Zadra nastalih 1953 godine, in: Ars Adriatica, 5, 2015, pp. 163-192, p. 164 14 Ines Merćep, "Natjecaj za regulacijsku osnovu Zadra iz 1953. Pedeset godina poslije", Prostor, 13 (1,29), may 2005, pp. 67-78, p. 72 Ivanović, Radovan Mišcević, Branko Petrović and Branko Vasiljević (Urban Planning Institute of Croatia) with the proposal n. 50105.

  Antonija Mlikota, Obnova i izgradnja povijesne jezgre Zadra nakon razaranja u Drugom svjetskom ratu, PhD thesis, Faculty of Philosophy, University of Zagreb, Zagreb, 2013 16 Antonija Mlikota, "Četrnaest arhitektonskih i urbanističkih vizija povijesne jezgre Zadra nastalih 1953 godine", Ars Adriatica, 5, 2015, pp. 163-192 17 Design proposal n. 35281 18 Design proposal n. 77711 19 Design proposal n. 77771 20 Antonija Mlikota, "Četrnaest arhitektonskih i urbanističkih vizija povijesne jezgre Zadra nastalih 1953 godine", Ars Adriatica, 5, 2015, pp. 163-192, p. 165 21 Design proposal n. 74174 22 Design proposal n. 123121

23

Design proposal n. Z-00001

Marko Rukavina and Mladen Obad Šćitaroci, "Urban Integration of Archaeological Heritage in Zadar", Annales,

(2), 2017, pp. 227-464

Dražen Arbutina, "Regulacijski plan Zadra iz 1939 godine", Prostor, 9 (1, 21), dec. 2002, pp. 15-30

Damir Magaš, "Prostorni razvoj Zadra 1945-1991", in Tado Oršolić (ed.), Zadar i okolica od Drugog svjetskog rata do Domovinskog rata, conference proceedings, Croatian Academy of Sciences and Arts, University ofZadar, Zadar, 2009, pp. 1-55

Dražen Arbutina, "Zadar's unfinished modernisation", in Maroje Mrduljaš, Vladimir Kulić (ed.), Unfinished modernisations, between utopia and pragmatism, UHA/CCA,Zagreb, 2012, pp. 445-455

Dragan Boltar, "Zadar -izgradnja centra", Arhitektura, 15 (3-4), 1961, pp. 40-48

Ivana Lazanja, "The reconstruction of the Croatian coastal city of Zadar", in Luca Verpoest and Nicholas Bullock (ed.), Living withHistory, 1914History, -1964: : Rebuilding Europe after the First and Second World Wars and the Role of Heritage Preservation, Leuven University Press,Leuven, 2021, pp. 279-287

Chiara Roma, Le Corbusier e le suggestioni dei ruderi, Quodlibet, Macerata, 2020, p. 55

Modrijan, Petar. "Portreti: Ivo Petricioli, Čuvar zadarskog blaga", Zadar, Biseri Jadrana: Edicija za kulturu putovanja,Zagreb, 2004, 144-147