13 papers
Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamics
Mauricio Herrera-Marín
Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fracti…
Learning the exogenous rate but not the distance to criticality in nearly unstable heavy-tailed Hawkes processes
Mauricio Herrera-Marín
In the nearly unstable heavy-tailed regime of Jaisson and Rosenbaum, where the intensity of a linear Hawkes process converges to a rough square-root Volterra process, we ask what a…
Minimax and adaptive inference for branching ratios under long memory
Mauricio Herrera-Marín
The branching ratio of a self-exciting point process determines the branching margin to the critical boundary. We study inference on from a finite record for stationa…
Projection, Memory, and the Validity of Scalar Early-Warning Signals: A Schur--Volterra Theory with an AMOC Application
Mauricio Herrera-Marín
Early-warning signals are usually computed from one or a few observables, although the underlying dynamics are high dimensional. Projection creates a structural ambiguity: the same…
Persistent memory and tail-risk amplification in Atlantic Meridional Overturning Circulation variability: a Volterra integral framework calibrated with CMIP6
Mauricio Herrera-Marín
The Atlantic Meridional Overturning Circulation (AMOC) carries multi-decadal memory that ensemble-mean risk projections do not capture. We quantify this memory and its consequences…
Where should the null live? Surrogate tests for clustering of threshold-derived air-quality indices, with application to PM2.5 exceedances in Chile
Mauricio Herrera-Marín
Air-quality and climate monitoring routinely convert native-resolution measurements into exceedance counts before testing whether high values cluster in time. A surrogate null can…
Memory compression and physical state augmentation favor different AMOC prediction tasks
Mauricio Herrera-Marín
The Atlantic Meridional Overturning Circulation is monitored and emulated through reduced indices, but such projections discard thermohaline structure and may require either explic…
Projected climate memory and inherited warm-tail risk in accelerated European summer warming
Mauricio Herrera-Marín, Alex Godoy-Faúndez, Diego Rivera
European summer warming reflects interactions among background change, persistent ocean--land--circulation states, and same-season variability. We develop an empirical reduced-dyna…
A Spatial Persistence Gradient in European Warming Consistent with North Atlantic Cold-Blob Influence
Mauricio Herrera-Marín, Alex Godoy-Faúndez, Diego Rivera
Europe is warming faster than the global mean, yet the spatial organisation of this acceleration remains incompletely understood. Using ERA5 reanalysis for 1950--2024 across 28 IPC…
Memory operator ensembles indicate proximity to criticality in simulated AMOC transitions
Mauricio Herrera-Marín
Classical early-warning signals assume that recovery slows near a tipping point, but in a well-studied CESM simulation of AMOC collapse, autocorrelation and variance decrease inste…
Regime-Switching Volterra Operators: Modal Stability and Quenched Amplification
Mauricio Herrera-Marín
We develop an operator-theoretic framework for finite-dimensional, regime-dependent Volterra equations with completely monotone memory kernels, dissipative network coupling, and Ha…
Quenched Amplification and Tail Shaping in Networked Systems with Memory and Regime Switching
Mauricio Herrera-Marín
Networked systems operating under intermittent adverse conditions and long memory can remain stable on average while exhibiting rare but extreme trajectory-level excursions. We stu…
Intermittency induced by long memory under stochastic regime switching
Mauricio Herrera-Marín
We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamic…