Related papers: Generalized Circuit Elements
We show that most arithmetic circuit lower bounds and relations between lower bounds naturally fit into the representation-theoretic framework suggested by geometric complexity theory (GCT), including: the partial derivatives technique…
Let M be a filtered module. Some properties of elements of M are "generic" in the following sense: (being open/stable) if an element z of M has a property P then any approximation of z has P; (being dense) any element of M is approximated…
We propose an approach to extracting equivalent circuit models for waveguide-fed, resonant metamaterial elements, such as the complementary, electric inductive-capacitive element (cELC). From the scattering parameters of a single…
We consider a long but finite (ladder) circuit with alternating connections of resistors in series and parallel and derive an explicit expression for its equivalent resistance as a function of the number of repeating blocks, $R_{\rm…
Generalized structural equations models (GSEMs) [Peters and Halpern 2021], are, as the name suggests, a generalization of structural equations models (SEMs). They can deal with (among other things) infinitely many variables with infinite…
In what follows we generalize the notion of a complemented ring to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.
We develop an analytic circuit model for coupled plasmonic dimers separated by small gaps that provides a complete account of the optical resonance wavelength. Using a suitable equivalent circuit, it shows how partially conducting links can…
The Randles circuit (including a parallel resistor and capacitor in series with another resistor) and its generalised topology have widely been employed in electrochemical energy storage systems such as batteries, fuel cells and…
We define the delays of a circuit, as well as the properties of determinism, order, time invariance, constancy, symmetry and the serial connection.
Compositional generalization is one of the main properties which differentiates lexical learning in humans from state-of-art neural networks. We propose a general framework for building models that can generalize compositionally using the…
Recently, topolectrical circuits (TECs) boom in studying the topological states of matter. The resemblance between circuit Laplacians and tight-binding models in condensed matter physics allows for the exploration of exotic topological…
The fields of explainable AI and mechanistic interpretability aim to uncover the internal structure of neural networks, with circuit discovery as a central tool for understanding model computations. Existing approaches, however, rely on…
A complete and harmonized fundamental circuit relational graph with four linear and four memory elements is constructed based on newly defined elements, which provides a guide to developing novel circuit functionalities in the future. In…
General physics approach is applied to analysis of power components in electrical systems under sinusoidal and non-sinusoidal conditions. Physical essence of active, reactive and distorting powers are determinate. It is shown that the all…
Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
There are many possible definitions of derivatives, here we present some and present one that we have called generalized that allows us to put some of the others as a particular case of this but, what interests us is to determine that there…
Component-based design paradigm is of paramount importance due to prolific growth in the complexity of modern-day systems. Since the components are developed primarily by multi-party vendors and often assembled to realize the overall…
After a rich history in medicine, randomisation control trials both simple and complex are in increasing use in other areas such as web-based AB testing and planning and design decisions. A main objective is to be able to measure…
For a multi-component system, general formulas are derived for the dimension of a coexisting region in the phase diagram in various state spaces.