arXiv subjects
Publications and source records attributed to Miguel Moreno.
We introduce three new model comparison games that characterize separability by first-order formulas with generalized quantifiers. The first is built on the Ehrenfeucht-Fra\"iss\'e game, the second is a formula-size game, and the third unifies them both and incorporates minor quantifiers.
We give a novel logical characterization of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-attention. We study such transformers over text in the practical setting of floating-point numbers and soft-attention, characterizing them with a new temporal logic. This logic extends propositional logic with a counting global modality over the encoder input and a past modality over the decoder input. We also give an additional characterization of such transformers via a type of distributed automata, and show that our results are not limited to the specific choices in the architecture and can account for changes in, e.g., masking. Finally, we discuss encoder-decoder transformers in the autoregressive setting.
We study the continuous reducibility of isomorphism relations in the space of regresive functions in $\kappa^\kappa$. We show for inaccessible $\kappa$, that if $\mathcal{T}$ is a theory with less than $\kappa$ non-isomorphic models of size $\kappa$ and $\mathcal T'$ is unstable or superstable non-classifiable, then the isomorphism of models of $\mathcal{T}$ is continuous reducible to the isomorphism of models of $\mathcal{T}'$.
The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according to the system's history throughout the simulation. Previous works usually modify the Rulkov model by introducing additional parameters altering its behavior. Here, by contrast, we retain the original equations and allow the control parameters to vary in time, thereby preserving the model's fundamental properties. In this sense, the proposed model is locally equivalent in time to the original one. However, unlike the original model, which reproduces a single neuronal regime per simulation, the new memristive version exhibits both uniform and chaotic transitions among multiple neuronal activity regimes. Its dynamics are examined with respect to the rate at which the memristive function changes and the number of internal states it stores. Three distinct scenarios emerge around a bifurcation point. Before the bifurcation, the system undergoes uniform transitions toward a stable bursting regime. After the bifurcation, it shows uniform transitions toward a final spiking or silent regime. At the bifurcation point, highly complex transitions arise. As examples, we present trajectories in which the neuron chaotically switches between regimes without ever settling, and trajectories for which it requires around 140000 map iterations to reach a stationary regime.
We study the Borel and analytic subsets of the spaces \({}^{\kappa}\kappa\) and \({}^{\kappa}2\) endowed with ideal topologies, where \(\kappa\) is a regular uncountable cardinal. We establish that the Borel hierarchy does not collapse in any ideal topology and prove that every Borel set in such a topology is analytic. In particular, when the ideal contains an unbounded set, the class of analytic sets coincides with the entire powerset. Furthermore, we show that the Approximation Lemma holds for ideal topologies.
We develop Descriptive Set Theory in Generalized Baire Spaces without assuming $κ^{<κ}=κ$. We point out that without this assumption the basic topological concepts of these spaces have to be slightly modified in order to obtain a meaningful theory. This modification has no effect if $κ^{<κ}=κ$. After developing the basic theory we apply it to the question whether the orbits of models of a fixed cardinality $κ$ in the space $κ^κ$ are $κ$-Borel in our generalized sense. It turns out that this question depends, as is the case when $κ^{<κ}=κ$, on stability theoretic properties (structure vs. non-structure) of the first order theory of the model.
We answer one of the main questions in generalized descriptive set theory, the Friedman-Hyttinen-Kulikov conjecture on the Borel reducibility of the Main Gap. We show a correlation between Shelah's Main Gap and generalized Borel reducibility notions of complexity. For any $κ$ satisfying $κ=λ^+=2^λ$ and $2^{\mathfrak{c}}\leqλ=λ^{ω_1}$, we show that if $T$ is a classifiable theory and $T'$ is a non-classifiable theory, then the isomorphism of models of $T'$ is strictly above the isomorphism of models of $T$ with respect to Borel-reducibility. We also show that the following can be forced: for any countable first-order theory in a countable vocabulary, $T$, the isomorphism of models of $T$ is either analytic co-analytic, or analytically-complete.
Using first-principles DFT calculations, we analyze the origin of the different crystal structures, optical and magnetic properties of two basic families of layered fluoride materials with formula A2MF4 (M = Ag, Cu, Ni, Mn; A = K, Cs, Rb). On one hand, Cs2AgF4 and K2CuF4 compounds (both with d9 metal cations) crystallize in an orthorhombic structure with Cmca space group and MA - F - MB bridge angle of 180, and they exhibit a weak ferromagnetism (FM) in the layer plane. On the other hand, K2NiF4 or K2MnF4 compounds (with d8 and d5 metal cations, respectively) have a tetragonal I4/mmm space group with 180 bridge angle and exhibit antiferromagnetism (AFM) in the layer plane. Firstly, we show that, contrary to what is claimed in the literature, the Cmca structure of Cs2AgF4 and K2CuF4 is not related to a cooperative Jahn-Teller effect among elongated MF64- units. Instead, first-principles calculations carried out in the I4/mmm parent phase of these two compounds show that MF64- units are axially compressed because the electrostatic potential from the rest of lattice ions force the hole to lie in the 3z2 - r2 molecular orbital (z being perpendicular to the layer plane). This fact increases the metal-ligand distance in the layer plane and makes that covalency in the bridging ligand has a residual character (clearly smaller than in K2NiF4 or KNiF3) stabilizing for only a few meV (7.9 meV for Cs2AgF4) an AFM order. However, this I4/mmm parent phase of Cs2AgF4 is unstable thus evolving towards the experimental Cmca structure with an energy gain of 140 meV, FM ordering and orthorhombic MF64- units.
We study the $κ$-Borel-reducibility of isomorphism relations of complete first order theories by using coloured trees. Under some cardinality assumptions, we show the following: For all theories T and T', if T is classifiable and T' is unsuperstable, then the isomorphism of models of T' is strictly above the isomorphism of models of T with respect to $κ$-Borel-reducibility.
The radiative response of any object is governed by a surface parameter known as emissivity. Tuning the emissivity of surfaces has been of great interest in many applications involving thermal radiation such as thermophotovoltaics, thermal management systems, and passive radiative cooling. Although several surface engineering techniques (e.g., surface functionalization) have been pursued to alter the emissivity, there exists a knowledge gap in precisely predicting the emissivity of a surface prior to the modification/fabrication process. Predicting emissivity by a physics-based modeling approach is challenging due to surface's contributing factors, complex interactions and interdependence, and measuring the emissivity requires a tedious procedure for every sample. Thus, a new approach is much-needed to systematically predict the emissivity and expand the applications of thermal radiation. In this work, we demonstrate the immense advantage of employing artificial intelligence (AI) techniques to predict the emissivity of complex surfaces. For this aim, we fabricated 116 bulk aluminum 6061 samples with various surface characteristics using femtosecond laser surface processing (FLSP). A comprehensive dataset was established by collecting surface characteristic data, laser operating parameters, and measured emissivities for all samples. We demonstrated the application of AI in two distinct scenarios. First, the range of emissivity of an unknown sample was shown to be estimated correctly solely based on its 3D surface morphology image. Second, the emissivity of a sample was precisely predicted based on its surface characteristics data and fabrication parameters. The implementation of the AI techniques resulted in the highly accurate prediction of emissivity by showing excellent agreement with the measurements.
We study the Borel-reducibility of isomorphism relations in the generalized Baire space $κ^κ$. In the main result we show for inaccessible $κ$, that if $T$ is a classifiable theory and $T'$ is superstable with the strong dimensional order property (S-DOP), then the isomorphism of models of $T$ is Borel reducible to the isomorphism of models of $T'$. In fact we show the consistency of the following: If $κ$ is inaccessible and $T$ is a superstable theory with S-DOP, then the isomorphism of models of $T$ is $Σ_1^1$-complete.
A classical theorem of Hechler asserts that the structure $\left(ω^ω,\le^*\right)$ is universal in the sense that for any $σ$-directed poset P with no maximal element, there is a ccc forcing extension in which $\left(ω^ω,\le^*\right)$ contains a cofinal order-isomorphic copy of P. In this paper, we prove a consistency result concerning the universality of the higher analogue $\left(κ^κ,\le^S\right)$: Theorem. Assume GCH. For every regular uncountable cardinal $κ$, there is a cofinality-preserving GCH-preserving forcing extension in which for every analytic quasi-order Q over $κ^κ$ and every stationary subset S of $κ$, there is a Lipschitz map reducing Q to $(κ^κ,\le^S)$.
We introduce a generalization of stationary set reflection which we call "filter reflection", and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection from ZFC, and present applications of filter reflection to the study of canonical equivalence relations of the higher Cantor and Baire spaces.
We prove under $V=L$ that the inclusion modulo the non-stationary ideal is a $Σ_1^1$-complete quasi-order in the generalized Borel-reducibility hierarchy ($κ>ω$). This improvement to known results in $L$ has many new consequences concerning the $Σ_1^1$-completeness of quasi-orders and equivalence relations such as the embeddability of dense linear orders as well as the equivalence modulo various versions of the non-stationary ideal. This serves as a partial or complete answer to several open problems stated in literature. Additionally the theorem is applied to prove a dichotomy in $L$: If the isomorphism of a countable first-order theory (not necessarily complete) is not $Δ_1^1$, then it is $Σ_1^1$-complete. We also study the case $V\ne L$ and prove $Σ_1^1$-completeness results for weakly ineffable and weakly compact $κ$.
Technologically useful and robust graphene-based interfaces for devices require the introduction of highly selective, stable, and covalently bonded functionalities on the graphene surface, whilst essentially retaining the electronic properties of the pristine layer. This work demonstrates that highly controlled, ultrahigh vacuum covalent chemical functionalization of graphene sheets with a thiol-terminated molecule provides a robust and tunable platform for the development of hybrid nanostructures in different environments. We employ this facile strategy to covalently couple two representative systems of broad interest: metal nanoparticles, via S-metal bonds, and thiol-modified DNA aptamers, via disulfide bridges. Both systems, which have been characterized by a multi-technique approach, remain firmly anchored to the graphene surface even after several washing cycles. Atomic force microscopy images demonstrate that the conjugated aptamer retains the functionality required to recognize a target protein. This methodology opens a new route to the integration of high-quality graphene layers into diverse technological platforms, including plasmonics, optoelectronics, or biosensing. With respect to the latter, the viability of a thiol-functionalized chemical vapor deposition graphene-based solution-gated field-effect transistor array was assessed.
Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal $κ$. We show the consistency of $E^{λ^{++},λ^{++}}_{λ\text{-club}}$, the relation of equivalence modulo the non-stationary ideal restricted to $S^{λ^{++}}_λ$ in the space $(λ^{++})^{λ^{++}}$, being continuously reducible to $E^{2,λ^{++}}_{λ^+\text{-club}}$, the relation of equivalence modulo the non-stationary ideal restricted to $S^{λ^{++}}_{λ^+}$ in the space $2^{λ^{++}}$. Then we show the consistency of $E^{2,κ}_{reg}$, the relation of equivalence modulo the non-stationary ideal restricted to regular cardinals in the space $2^κ$, being $Σ_1^1$-complete. We finish by showing, for $Π_2^1$-indescribable $κ$, that the isomorphism relation between dense linear orders of cardinality $κ$ is $Σ_1^1$-complete.
We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is strictly above the isomorphism of models of T with respect to Borel-reducibility. In fact, we can also ensure that a range of equivalence relations modulo various non-stationary ideals are strictly between those isomorphism relations. The isomorphism relations are considered on models of some fixed uncountable cardinality obeying certain restrictions.
We study the Borel reducibility of isomorphism relations in the generalized Baire space $κ^κ$. In the main result we show for inaccessible $κ$, that if $T$ is a classifiable theory and $T'$ is stable with OCP, then the isomorphism of models of $T$ is Borel reducible to the isomorphism of models of $T'$.