Related papers: Six Birds: Foundations of Emergence Calculus
In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
Extreme-order statistics is applied to the branches of an observer in a many-worlds framework. A unitary evolution operator for a step of time is constructed, generating pseudostochastic behaviour with a power-law distribution when applied…
Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work…
Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…
We establish a canonical normal form for the iterates of a curved differential in curved differential algebras (CDA). This operator calculus clarifies the underlying algebraic structure of CDAs and bypasses the need for complex…
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…
These notes were delivered as a series of NIMROD lectures at the Rutherford Appleton Laboratory by the author in February 1976 (RL-76-022). The purpose of these lectures was primarily two-fold: to discuss the classical theory of free point…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
We present a canonical extension of topological dynamics to transfinite iterations, which makes precise the idea of dynamical phenomena stabilizing at different time-scales. Specifically, consider a sequence of self-maps $F=\{f_n\}$ of a…
We study an extremal projection principle for families of operators ordered by domination, induced by fixed bounded linear mappings acting on a source with an additive baseline. Stability is defined through domination of second--order…
Emergent effect is crucial to understanding the properties of complex systems that do not appear in their basic units, but there has been a lack of theories to measure and understand its mechanisms. In this paper, we consider emergence as a…
We introduce a new class of extremum seeking controllers able to achieve fixed time convergence to the solution of optimization problems defined by static and dynamical systems. Unlike existing approaches in the literature, the convergence…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…
We present a coherent approach to recurrence and transience, starting from a version of the Riesz decomposition theorem for superharmonic elements. Our approach allows straightforward proofs of some known results, entails new theorems, and…
Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however,…
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma…