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Emergent spatial patterns of coexistence in species-rich plant communities

Statistical physics has proved essential to analyze multiagent environments. Motivated by the empirical observation of various nonequilibrium features in Barro Colorado and other ecological systems, we analyze a plant-species abundance model of neutral competition, presenting analytical evidence of scale-invariant plant clusters and nontrivial emergent modular correlations. Such first theoretical confirmation of a scale-invariant region, based on percolation processes, reproduces the key feat...

The Validity of Machine Learning Procedures in Orthodontics: What Is Still Missing?

Artificial intelligence (AI) models and procedures hold remarkable predictive efficiency in the medical domain through their ability to discover hidden, non-obvious clinical patterns in data. However, due to the sparsity, noise, and time-dependency of medical data, AI procedures are raising unprecedented issues related to the mismatch between doctors’ mentalreasoning and the statistical answers provided by algorithms. Electronic systems can reproduce or even amplify noise hidden in the data, ...

Refining Mean-field Approximations by Dynamic State Truncation

Mean-field models are an established method to analyze large stochastic systems with N interacting objects by means of simple deterministic equations that are asymptotically correct when N tends to infinity. For finite N, mean-field equations provide an approximation whose accuracy is model-and parameter-dependent. Recent research has focused on refining the approximation by computing suitable quantities associated with expansions of order $1/N$ and $1/N2$ to the mean-field equation. In this ...

Differential Equivalence for Linear Differential Algebraic Equations

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this article, we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that h...

Computation of Input Disturbance Sets for Constrained Output Reachability

— Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data through set-membership identification. However, the problem of computing a suitable input disturbance set in case the set of possible output values is assigned a priori has received relatively little attention. This problem arises in many contexts, such as in...

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