Selected work

Representative Papers

Imperfect Knowledge Management -- A Case Study in a Chilean Manufacturing Company

Jan 31, 2025

Traditional knowledge management (KM) is constrained by a symbolic paradigm rooted in Cartesian dualism—specifically, the epistemic separation of cognition and action—which perpetuates subject–object dichotomies and undermines systemic coherence. Method: This paper proposes Fuzzy Autopoietic Knowledge Management (FAKM), the first KM framework integrating autopoiesis theory, the Viable Systems Model (VSM), and General Systems Theory. FAKM conceptualizes knowledge systems through the lens of “organization–structure duality,” capturing their self-maintaining and self-referential nature while transcending dualistic ontologies. It further incorporates fuzzy logic to model uncertainty and dynamic adaptation inherent in socio-technical systems. Contribution/Results: Empirical validation in manufacturing firms in the Maule Region, Chile, demonstrates that FAKM significantly enhances dynamic coupling between knowledge flows and organizational structure, strengthens endogenous knowledge practice, and improves systemic resilience—thereby offering a theoretically grounded and empirically validated paradigm shift in KM.

7 citationsRead paper

A Behavioural Theory of Probabilistic Algorithms Using Probabilistic Abstract State Machines

Jun 22, 2026

This work addresses the lack of a formal behavioral theory for probabilistic algorithms, which has hindered rigorous characterization of their semantics and execution. Building upon four axiomatic assumptions—stochastic branching time, abstract states, background, and stochastic bounded exploration—the study introduces the first axiomatic behavioral framework for probabilistic algorithms and proposes probabilistic Abstract State Machines (pASMs) as a formal modeling tool. The paper establishes that any algorithm satisfying this framework can be step-by-step behaviorally simulated by a pASM with identical signature and background. This result provides a rigorous behavioral theory for probabilistic algorithms and achieves a semantics-preserving mapping from abstract specifications to concrete computational models.

0 citationsRead paper

Behavioural Theory of Reflective Algorithms II: Reflective Parallel Algorithms

Aug 12, 2025

Existing theories lack a formal foundation for synchronous parallel algorithms capable of self-modifying behavior—termed reflective algorithms (RAs)—which dynamically adapt their computational logic via internal linguistic reflection. Method: We introduce the reflective Abstract State Machine (rASM) model, built upon multisets of terms as primitive values and extended states incorporating updatable rule representations; we develop an axiomatic framework ensuring bounded exploration and formal precision. Contribution/Results: This work establishes the first behaviorally complete theory for RAs: we prove that every RA is behaviorally equivalent to some rASM, thereby providing the first rigorous characterization of linguistic reflection in parallel computation—i.e., the capacity of an algorithm to modify its own operational semantics through manipulation of its internal syntactic representation. The rASM model thus furnishes a sound and expressive formal basis for adaptive, dynamically evolving parallel systems, bridging a critical gap between reflective programming practice and foundational algorithm theory.

0 citationsRead paper

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization

Jul 15, 2025

This paper addresses nonconvex optimization problems characterized by bound constraints, stochastic gradient noise, and multilayer architectures. Method: We propose two adaptive second-order optimization algorithms that extend AdaGrad to both multilayer settings and the additive Schwarz domain decomposition framework, unifying the treatment of noisy gradients and constraints. Grounded in the objective-function-free optimization (OFFO) paradigm, our approach recursively integrates approximate gradient and curvature information. Contribution/Results: We establish the first joint convergence theory for such structured nonconvex problems, guaranteeing—under high probability—convergence to an ε-accurate critical point with an iteration complexity of O(ε⁻²). Extensive experiments demonstrate significant improvements in computational efficiency and robustness on large-scale tasks, including PDE solving and deep neural network training.

0 citationsRead paper

Recent publications

Latest Papers

A Behavioural Theory of Probabilistic Algorithms Using Probabilistic Abstract State Machines

Jun 22, 2026

This work addresses the lack of a formal behavioral theory for probabilistic algorithms, which has hindered rigorous characterization of their semantics and execution. Building upon four axiomatic assumptions—stochastic branching time, abstract states, background, and stochastic bounded exploration—the study introduces the first axiomatic behavioral framework for probabilistic algorithms and proposes probabilistic Abstract State Machines (pASMs) as a formal modeling tool. The paper establishes that any algorithm satisfying this framework can be step-by-step behaviorally simulated by a pASM with identical signature and background. This result provides a rigorous behavioral theory for probabilistic algorithms and achieves a semantics-preserving mapping from abstract specifications to concrete computational models.

0 citationsRead paper

Behavioural Theory of Reflective Algorithms II: Reflective Parallel Algorithms

Aug 12, 2025

Existing theories lack a formal foundation for synchronous parallel algorithms capable of self-modifying behavior—termed reflective algorithms (RAs)—which dynamically adapt their computational logic via internal linguistic reflection. Method: We introduce the reflective Abstract State Machine (rASM) model, built upon multisets of terms as primitive values and extended states incorporating updatable rule representations; we develop an axiomatic framework ensuring bounded exploration and formal precision. Contribution/Results: This work establishes the first behaviorally complete theory for RAs: we prove that every RA is behaviorally equivalent to some rASM, thereby providing the first rigorous characterization of linguistic reflection in parallel computation—i.e., the capacity of an algorithm to modify its own operational semantics through manipulation of its internal syntactic representation. The rASM model thus furnishes a sound and expressive formal basis for adaptive, dynamically evolving parallel systems, bridging a critical gap between reflective programming practice and foundational algorithm theory.

0 citationsRead paper

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization

Jul 15, 2025

This paper addresses nonconvex optimization problems characterized by bound constraints, stochastic gradient noise, and multilayer architectures. Method: We propose two adaptive second-order optimization algorithms that extend AdaGrad to both multilayer settings and the additive Schwarz domain decomposition framework, unifying the treatment of noisy gradients and constraints. Grounded in the objective-function-free optimization (OFFO) paradigm, our approach recursively integrates approximate gradient and curvature information. Contribution/Results: We establish the first joint convergence theory for such structured nonconvex problems, guaranteeing—under high probability—convergence to an ε-accurate critical point with an iteration complexity of O(ε⁻²). Extensive experiments demonstrate significant improvements in computational efficiency and robustness on large-scale tasks, including PDE solving and deep neural network training.

0 citationsRead paper

Imperfect Knowledge Management -- A Case Study in a Chilean Manufacturing Company

Jan 31, 2025

Traditional knowledge management (KM) is constrained by a symbolic paradigm rooted in Cartesian dualism—specifically, the epistemic separation of cognition and action—which perpetuates subject–object dichotomies and undermines systemic coherence. Method: This paper proposes Fuzzy Autopoietic Knowledge Management (FAKM), the first KM framework integrating autopoiesis theory, the Viable Systems Model (VSM), and General Systems Theory. FAKM conceptualizes knowledge systems through the lens of “organization–structure duality,” capturing their self-maintaining and self-referential nature while transcending dualistic ontologies. It further incorporates fuzzy logic to model uncertainty and dynamic adaptation inherent in socio-technical systems. Contribution/Results: Empirical validation in manufacturing firms in the Maule Region, Chile, demonstrates that FAKM significantly enhances dynamic coupling between knowledge flows and organizational structure, strengthens endogenous knowledge practice, and improves systemic resilience—thereby offering a theoretically grounded and empirically validated paradigm shift in KM.

7 citationsRead paper