arXiv subjects

Alfredo Alcayde

Publications and source records attributed to Alfredo Alcayde.

8 recordsLinked to original sources

arXiv2026

Multivariable Geometric Laplace Transform and Fault Detection in Distributed-Converter Lines

Monitoring a DC line with many distributed power converters is a genuinely spatio-temporal problem: the information about a localized fault travels along the whole conductor and reaches a few measurement points mixed with the dynamics of the line itself. This paper develops a two-dimensional geometric Laplace transform (t,x) -> (s_t,s_x) over a commutative subalgebra of the geometric algebra Cl(4,0), isomorphic to Segre's bicomplex numbers, in which two bivectors B_t and B_x act as independent imaginary units for the temporal and the spatial phase. Because the two phases live in algebraically distinguishable planes, a fault at position x_f leaves a transformed residual that factorizes as F_f(s_t) e^{-s_x x_f}: its temporal nature stays in the first factor and its location can be read as a geometric argument of the second. On this representation we build a transmission-line model of the converter line and its space-time dispersion relation, a distributed control by admittance shaping, including an exact treatment of discrete converter sites (spatial sampling, aliasing, and a per-converter droop realization that is exact on the sub-Nyquist band), and a fault diagnosis chain that detects, localizes and classifies injection-loss, shunt, sensor and local-controller faults, extends to multiple simultaneous faults with automatic order selection, and distinguishes the outage of a plant from a cable defect. As an integral object the transform is known in bicomplex analysis, and with a single independent variable it reduces to the complex Laplace transform; the contribution lies in its geometric embedding and in its operational use for fault diagnosis in distributed-converter networks. All results are reproduced by an accompanying open implementation.

eess.SY↗

arXiv2026

Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control

An intelligent system does not merely reason: it governs its own reasoning - how much to compute, when to stop, which module to activate. Can that role be played by a dynamic internal field - a low-dimensional homeostatic state with explicit physics and certified stability - that modulates cognition without performing it? Ours is a field on the module graph governed by a family of PDEs on the graph Laplacian, advancing with an adaptive-depth reasoner. We certify the stability of the integrator of the whole family - an integrator certificate, not a closed-loop one. New, and proved here: a discrete Schur-Cohn criterion for Verlet with velocity coupling, necessary and sufficient per latent root, with no commutation hypothesis. The answer is threefold: substance no, structure only in part, certifiability yes. The type of the field's physics is irrelevant for accuracy: wave, diffusion, gated mixtures and a 2D Navier-Stokes substrate tie. A twenty-seed preregistered deconfounding campaign bounds the structural claim: at equalized caps the second-order effect is strong in one family (+0.087 [+0.042, +0.132], t=4.0) but is not detected in the other (+0.014 [-0.013, +0.040], n.s.), so part of the original contrast was capacity, not order; and a matched-interface GRU is indistinguishable in the first and nominally exceeds the field in the second (-0.035 [-0.067, -0.002]). What distinguishes the field is not capability but that its one-step operator admits an exact runtime stability check - a difference of kind, not of existence: learned recurrences carry certificates too, sufficient and conservative ones. A kill-gate with a positive control finds no evidence for the field as evidence accumulator (Delta AUC +0.0007 [-0.0065, +0.0079] vs a 0.03 threshold). A dynamic internal field is a viable, certifiable compute governor, but not an enhancer of cognition: it modulates, it does not think.

cs.AI↗

arXiv2026

Where Cognition Lives: Dissecting Emergent from Computed Function in a Minimal Complete Cognitive Architecture

A cognitive architecture is more than the module that reasons: it must also decide how long to think and what deserves the effort. We built a minimal but complete system - a recurrent reasoner with adaptive halting, a homeostatic control field, and a value module - and asked of each part: does this function emerge from gradient descent, or must it be computed? Competence emerges. Stopping appears to emerge too, and to be worth more than everything decidable in advance, but that appearance is instrumentation: payoff at matched mean compute climbs from 0.467 (uniform) through 0.546 (difficulty) to 0.698 (ex-ante value), and the further climb to 0.921 (posterior self-observation) does not survive audit. PonderNet-style halting returns a halting-weighted mixture of hidden states while forced-depth baselines return one, and the language head is trained on the mixture alone; equalizing the readout annihilates the apparent advantage of native execution (residual +0.000 [0.000, 0.000]). Value does not emerge: trained couplings capture zero of a payoff an explicit allocator captures completely (+0.151, routing correlation +0.79), so the second-order decisions that pay must be computed, at least where value is orthogonal to content, as here by construction. On a frozen LLM actuator the same instruments show self-consistency voting to be a measured bound (+0.0236 [+0.0150, +0.0326]) and inter-sample agreement nearly worthless as a stopping signal, its mass concentrating on wrong answers. Every null we assert carries a mechanism and a positive control, and the protocol is part of the contribution. Executing our own falsifiable prediction, value under commitment pays +0.1312 [+0.1124, +0.1502] in a cliff-cost family, some seven times the smooth-family estimate - not because the cliff shifts information ex ante, but because it multiplies the attainable range fivefold (5.1x [3.4, 8.2]).

cs.AI↗

arXiv2026

Geometric Time-Domain Identification of Three-Phase Load Equivalents from Terminal Measurements

This paper presents a geometric time-domain method for identifying three-phase load equivalents from instantaneous voltage and current measurements at the point of common coupling. Measured waveforms are interpreted as trajectories in Euclidean signal spaces, and load-equivalent parameters are recovered from the geometry of those trajectories. The method extends a previously published single-phase geometric identification formulation to three- and four-wire systems and places special emphasis on the three-wire case, where no neutral voltage is measured and the terminal data must satisfy coupled Kirchhoff constraints. The main advance over the earlier analytical formulation is a sampled-data implementation based on local time windows, normalized matrix equations, harmonic-projection derivative and primitive coordinates, explicit geometric identifiability tests, passivity constraints, and energy/Kirchhoff residuals. The method does not force a model when the measured trajectory lacks enough information; instead, it reports low-rank or ill-conditioned windows as low-confidence evidence. Numerical simulations with clean data, measurement noise, window-length sweeps, and sensor delay show that the method accurately identifies informative three-phase trajectories and exposes structurally degenerate cases such as pure single-frequency excitation for higher-order three-wire models. For a given admissible topology the identified circuit closes the instantaneous terminal energy balance of the measured load over the analysis window.

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arXiv2026

Branch-Level Energy Localization in Three-Phase Loads: Resolving Indeterminacy in Time-Domain

This paper develops a branch-level energy-localization framework for three-phase loads. The instantaneous terminal power of an admissible lumped equivalent is decomposed uniquely as Joule dissipation plus magnetic and electric stored-energy rates, branch by branch. Three formal results are established: a Branch-Level Localization Theorem (uniqueness given an admissible topology); a Topology-Indeterminacy Theorem (multiple admissible topologies reproduce identical terminal data with distinct localizations); and a Generalized Energetic Duality Theorem that organizes classical electrical dualities (Norton-Thevenin, series--parallel, L vs C, R vs G) as restrictions to Linear Time Invariant (LTI) sinusoidal regimes of a single time-domain principle in which constant-parameter equivalence is replaced by time-varying parameters. The framework is exercised on six test cases including the de Leon--Cohen open-phase paradox, switched-resistive loads, three-wire delta-versus-wye-virtual indeterminacy, fluctuating-phase loads, and a four-wire nonlinear load with hysteretic, linear, and switched branches. The framework is positioned as complementary to IEEE Std. 1459, CPC, instantaneous p-q, and Fryze-Buchholz-Depenbrock: each answers a different question, and the apparent paradoxes vanish once the question is posed precisely.

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arXiv2020

A new electromechanical analogy approach based on electrostatic coupling for vertical dynamic analysis of planar vehicle models

Analogies between mechanical and electrical systems have been developed and applied for almost a century, and they have proved their usefulness in the study of mechanical and electrical systems. The development of new elements such as the inerter or the memristor is a clear example. However, new applications and possibilities of using these analogues still remain to be explored. In this work, the electrical analogues of different vehicle models are presented. A new and not previously reported analogy between inertial coupling and electrostatic capacitive coupling is found and described. Several examples are provided to highlight the benefits of this analogy. Well-known mechanical systems like the half-car or three three-axle vehicle models are discussed and some numerical results are presented. To the best of the author's knowledge, such systems were never dealt with by using a full electromechanical analogy. The mechanical equations are also derived and compared with those of the electrical domain for harmonic steady state analysis.

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arXiv2020

How to overcome the limitations of p-q Theory: Geometric Algebra Power Theory to the rescue

This paper investigates the recent advances in Geometric Algebra-based power theory (GAPoT) and how this tool provides new insights to solve the flaws of one of the most widespread theory in the time domain, the Instantaneous Reactive Power theory (IRP) and its further enhancements. GAPoT can be applied to single-phase and multi-phase systems to obtain an optimal current decomposition under any distorted voltage source supply and load condition. This could be the case in microgrids or smart grids. Moreover, it is possible to define different strategies based on instantaneous or averaged quantities depending on whether the voltage supply conditions are sinusoidal and symmetrical or not. Several examples illustrate how GAPoT is able to overcome the limitations of IRP theory.

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arXiv2020

Geometric Algebra Power Theory (GAPoT): Revisiting Apparent Power under Non-Sinusoidal Conditions

Traditional power theories and one of their most important concepts --apparent power-- are still a source of debate and, as shown in the literature, they present several flaws that misinterpret the power-transfer phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been applied to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, power theories based on GA are revisited. Several drawbacks and inconsistencies of previous works are identified and modifications to the so-called geometric algebra power theory (GAPoT) are presented. This theory takes into account power components generated by cross-products between current and voltage harmonics in the frequency domain. Compared to other theories based on GA, it is compatible with the traditional definition of apparent power calculated as the product of RMS voltage and current. Also, mathematical developments are done in a multi-dimensional Euclidean space where the energy conservation principle is satisfied. The paper includes a basic example and experimental results in which measurements from a utility supply are analysed. Finally, suggestions for the extension to three-phase systems are drawn.

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