Program
13/4/2023
Dynamical systems and statistical mechanics
9:30-10:00 Stefano Iubini
Negative-temperature Fourier transport in one-dimensional systems
Since the pioneering work of Onsager and Ramsey in the 1940s and '50s, physical states at negative absolute temperatures have attracted the curiosity of researchers. In negative-temperature regimes, the average energy is above the infinite-temperature point and high-energy states are more populated than low-energy ones.
While the equilibrium properties of negative-temperature states are now rather well understood, much less is known about their occurrence in out-of-equilibrium setups. In this talk I will focus on one-dimensional diffusive systems and I will show that a phenomenological description in terms of a Fourier law can consistently describe unusual transport regimes where the temperature profiles are entirely or partially in the negative-temperature region.
The case of a two-level paramagnetic system is the simplest example that allows for an analytic description of the nonequilibrium stationary state. More generally, negative-temperature Fourier transport is observed both for deterministic and stochastic dynamics and it can be generalized to coupled transport when two or more thermodynamic currents flow through the system.
10:00-10:30 Michele Baia, Franco Bagnoli
Synchronization, control and data assimilation of the Lorenz system
Master-slave synchronization can occour when some component of master system is fed to a replica. If the master system is a “real” one and the replica is simulated on a computer, this latter can be used to perform measurements impossible on the master one, or to forecast its future dynamics. However, for a real system, it is not possible to perform measurements at any rate, nor sometimes to access the actual variables used for simulations. Moreover, the parameters corresponding to the actual master dynamics has to be determined in some way.
We show that synchronization is possible also using only part of the signal and applying synchronization intermittently in time. We also show that it is possible to exploit the partial synchronization occurring when the parameters of master and slave are not the same to perform a kind of data assimilation, i.e., to determine the parameters of the master system.
Finally, we show that if is even possible to synchronize systems and determine parameters when variables are not accessible, using an ensemble of replicas and “enriching” it with copies of systems that are nearer to the synchronizartion threshold.
Environmental modeling
10:30-11:00 Michele Baia, Alberto Ortolani, Samantha Melani, Carlo Brandini, Franco Bagnoli
Neural Network downscaling of atmospheric projection for supporting climate resilience initiatives
Climate change projections are the main tool to understand what will happen in the future of our environment, in particular regarding the characteristics of extreme events, we will have to face. Beyond their intrinsic uncertainties, due to model approximations, assumptions on coupling and feedback mechanisms, and foreseen forcing scenarios, they provide a picture at a given spatial scale, that can be often not enough to infer what we expect will be the local effects. Downscaling is the process to transfer the information available at a given coarser (spatial or even temporal) scale to a finer one. In some case downscaling can be preferable, in others mandatory, for example when we want projections on river flooding for small catchments not resolved by the coarse available scale. Flooding is obviously related to precipitation and evapotranspiration so atmospheric downscaling can be necessary to force a small hydrological catchment. Another example could be the projections on storm statistics at the urban scale, for some cities known to be increasingly vulnerable to adverse weather. The downscaling can be physical, when a specific model is run at the desired finer resolution, nested in the available coarser grid projection dataset. It can be statistical when statistical relationships are derived and used to go from one resolution to the other. Generally speaking we could think that the latter provides less reliable results than the former one, but the physical downscaling can become very computing demanding with respect to the statistical ones, and sometimes we are obliged to adopt what is feasible or a mix of both.
In SCORE (Smart control of the climate resilience in European coastal cities), a four-year EU-funded H2020 project aiming to increase climate resilience in European coastal cities, we have developed a statistical downscaling methodology to be applied to projection from the EUROCORDEX archive, data in turn physically downscaled on the Euro-Mediterranean domain, starting from projections realised through global circulation climate models. The methodology was based on a convolutional Neural Network (NN) approach, with the idea to model the complex dependencies of some surface target parameters to the available atmospheric and orographic ones, accounting also for seasonal and geographic dependencies as well as for spatial and temporal correlations at the proper scales. The NN algorithm was trained on an available analysis dataset (for a past period) at the target finer spatial resolution and its upscaled version to the projection coarser resolution (we identified as surrogate dataset). Finally we mapped the statistics of the surrogate dataset to the projection dataset, through a probability matching method, to complete the process.
11:00-11:30 Coffee break
11:30-12:00 Andrea Orlandi, Alberto Baldi, Franco Bagnoli, Alberto Ortolani, Samantha Melani
Geophysical numerical prediction: “grand challenges” with strong complexity and high
dimensionality
In Geophysics, the application of numerical integration techniques and their fusion with Earth observation and data processing resources have been key elements for the development and operational implementation of Numerical Weather Prediction (NWP) and Oceanographic Forecasting systems, so as for the development of Climate Prediction. The resulting computational problems are to be considered as computational “grand challenges”, not only for the presence of many non-linear mechanisms covering wide
ranges of scales with several feedback interactions among them, but also due to the huge dimensionality of the models to be studied.
However, relevant milestones in this field have been posed by studying Low Order Models (LOMs), obtained by suitably reducing the original dimensionality, but retaining the main nonlinearities and feedbacks. Someone of these initial studies gained the role of cornerstones in the more general complex systems discipline, as those due to Edward Lorenz, and their developments are still present in many
contemporary research works. In NWP research studies, LOMs are still today precious instruments for the study of numerical modelling approaches and for the investigation of novel Data Assimilation (DA) techniques performing the optimal blending of numerical models with observed data. Moreover, LOMs can have a relevant role also in the didactics of basic elements of the nowadays vast and complex discipline of
NWP.
Some examples are reported from studies performed by exploiting the estimation of the rate of divergence of perturbed predictions (Breeding technique) for the adaptive optimization of DA approaches applied for the optimal initialization of some relevant LOMs.
A conclusive short mention will be given of the recent developments and perspectives brought by the growing role of Big Data Processing and Machine Learning techniques in the fields NWP and Climate Prediction.
Biophysics
12:00-12:30 Valentina Buonfiglio
A Small Ensemble of Myosin Motors at Work: Fitting Experimental Data with a Stochastic Model
We developed a stochastic model to interpret the experimental output of a synthetic nanomachine mimicking the striated muscle. The nanomachine is constituted by the minimum number of myosin molecules needed to reproduce the collective mechanism of muscle myosin in the sarcomere. The mechanical output of the machine is measured with a Dual Laser Optical Tweezers which act as a force transducer. The small ensemble of molecular myosin motors in interaction with an actin filament is capable of performing isometric contraction in solution with physiological ATP concentration. A stochastic model that assumes one detached and two different force-generating attached states, allows to predict the force distribution resulting from the cumulative action of the motors. The computed distribution can be superposed to the homologous experimental profile via a non-linear fitting procedure. The fitting scheme is first validated against synthetically generated data and then applied to experimental distributions of the force. Accounting for the fluctuations of the force exerted by the ensemble of motors makes it possible to directly estimate the force exerted by individual myosin-actin interactions and to compute the associated duty ratio. This challenge cannot be successfully faced when solely relying on a mean field description of the scrutinized dynamics. Analysing the performance of the small ensemble of motors with a reverse engineering procedure made it possible to recover single motor properties and can pave the way for the study of the performance of unknown myosin isoforms.
12:30-13:00 Simona Olmi
Exact neural mass model for synaptic-based working memory
Working Memory (WM) is the ability to temporarily store and manipulate stimuli representations that are no longer available to the senses. We have developed an innovative coarse-grained population model able to mimic several operations associated to WM. The novelty of the model consists in reproducing exactly the dynamics of spiking neural networks with realistic synaptic plasticity composed of hundreds of thousands of neurons in terms of a few macroscopic variables. These variables give access to experimentally measurable quantities such as local field potentials and electroencephalographic signals. Memory operations are joined to sustained or transient oscillations emerging in different frequency bands, in accordance with experimental results for primate and humans performing WM tasks. We have designed an architecture composed of many excitatory populations and a common inhibitory pool able to store and retain several memory items. The capacity of our multi-item architecture is around 3–5 items, a value similar to the WM capacities measured in many experiments. Furthermore, the maximal capacity is achievable only for presentation rates within an optimal frequency range. Finally, we have defined a measure of the memory load analogous to the event-related potentials employed to test humans’ WM capacity during visual memory tasks.
Halgurd Taher, Alessandro Torcini, and Simona Olmi. ""Exact neural mass model for synaptic-based working memory."" PLOS Computational Biology 16, no. 12 (2020): e1008533.
13:00-14:30 Lunch and discussion
Biophysics
14:30-15:00 Arkady Pikowski
Statistical Theory of Asymmetric Damage Segregation in Clonal Cell Populations
Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions.
15:00-15:30 Alessandro Torcini
Next Generation Neural Mass Models
I will first give a brief overview of the next generation neural mass models, which represent a complete new perspective for the development of exact mean field models of heterogenous spiking neural networks [1]. Then I will report recent results on the application of this formalism to reproduce relevant phenomena in neuroscience ranging from cross-frequency coupling [2] to theta-nested gamma oscillations [3], from slow and fast gamma oscillations [4] to synaptic-based working memory [5]. I will finally show how these neural masses can be extended to capture fluctuations driven phenomena induced by dynamical sources of disorder, naturally present in brain circuits, such as background noise and current fluctuations due to the sparsness in the connections [6-8].
[1] Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons, TB Luke, E Barreto, P So, Neural computation 25 (12), 3207-3234 1482013 (2013); Derivation of a neural field model from a network of theta neurons, CR Laing, Physical Review E 90 (1), 010901 (2014); Montbrió, Ernest, Diego Pazó, Alex Roxin. “Macroscopic description for networks of spiking neurons.” Physical Review X 5.2 (2015): 021028.
[2] A.Ceni, S. Olmi, AT, D. Angulo Garcia, “Cross frequency coupling in next generation inhibitory neural mass models”, Chaos , 30, 053121 (2020)
[3] M. Segneri, H.Bi, S. Olmi, AT, “Theta-nested gamma oscillations in next generation neural mass models”, Frontiers in Computational Neuroscience , 14:47 (2020)
[4] H. Bi, M. Segneri, M. di Volo, AT, “Coexistence of fast and slow gamma oscillations in one population of inhibitory spiking neurons”, Physical Review Research ,2, 013042 (2020)
[5] H. Taher, AT, S. Olmi, “Exact neural mass model for synaptic-based working memory”, PLOS Computational Biology , 16(12): e1008533 (2020)
[6] M. di Volo, AT, “Transition from asynchronous to oscillatory dynamics in balanced spiking networks with instantaneous synapses”, Phys. Rev. Lett. 121 , 128301 (2018)
[7] D. Goldobin, M diVolo, AT, “A reduction methodology for fluctuation driven population dynamics”, Physical Review Letters 127,038301 (2021) [
[8] M. di Volo, M. Segneri, D. Goldobin, A. Politi, AT, “Coherent oscillations in balanced neural networks driven by endogenous fluctuations”, Chaos 32, 023120 (2022) "
15:30-16:00 Coffee break
16:00-17:00 Andreas Guskos, Jarosław Rybicki, Arkadiusz Marcinkowski
Cellular Automata, Fractals and Poetic Machines [INTERACTIVE SESSION]
Mathematical formulas, such as cellular automata or fractals, produce very complex images that can be attractive for artists as a material for creating visual art. The interest is also enhanced by the intuitive feeling that these mathematical structures are deeply associated with the law of nature. Over past few months new A.I. algorithms have been introduced to the wider audience. The A.I. is capable of creating visual content, text and performing other complex tasks based on a set of simple descriptions. In this presentation we will show artworks created using of the cellular automata, fractals and A.I. interfaces.
