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Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in…

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a…

This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide…

Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the…

We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render…

Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…

Based on large-scale Monte Carlo simulations on lattice the energy probability distribution functions are investigated for a large set of primary sequences in distinct models of copolymers at low temperatures below transitions to compacted…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently…

Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…

Functional networks of complex systems are obtained from the analysis of the temporal activity of their components, and are often used to infer their unknown underlying connectivity. We obtain the equations relating topology and function in…

Complex black-box predictive models may have high performance, but lack of interpretability causes problems like lack of trust, lack of stability, sensitivity to concept drift. On the other hand, achieving satisfactory accuracy of…

A set of density functionals coming from different rungs on Jacob's ladder are employed to evaluate the electronic excited states of three Ru(II) complexes. While most studies on the performance of density functionals compare the vertical…

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…

We develop a connection between mixture and envelope representations of objective functions that arise frequently in statistics. We refer to this connection using the term "hierarchical duality." Our results suggest an interesting and…

Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…

We show that the Laplace approximation of a supremum by Lp-norms has interesting consequences in optimization. For instance, the logarithmic barrier functions (LBF) of a primal convex problem P and its dual appear naturally when using this…