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Diego Maldonado

Publications and source records attributed to Diego Maldonado.

At least 19 recordsLinked to original sources
arXiv2026

Weak porosity in spaces of homogeneous type

Based on the theory of Muckenhoupt weights, short and conceptually simpler proofs are provided for the following two implications: (1) if $(X, d, μ)$ is a space of homogeneous type where $d$-balls are open sets and the Lebesgue differentiation theorem holds true and if $E \subset X$ is a weakly porous set whose maximal $E$-free hole function $ρ_{d, E}$ is doubling, then $\dist{\cdot, E}^{-α} \in A_1(X, d, μ)$ for some $α> 0$; and (2) now without the assumption on the validity of Lebesgue's differentiation theorem, if $\dist{\cdot, E}^{-α} \in A_1(X, d, μ)$ for some $α> 0$, then $ρ_{d, E}$ is doubling.

math.CA↗
arXiv2026

Weighted estimates for fractional integrals with Distances to Bounded Median Porous Sets and applications to Hardy--Sobolev Inequalities

Weighted estimates for the fractional integral operator $I_α$ are established and subsequently applied to derive corresponding Hardy--Sobolev inequalities. The weights are constructed from distance functions to bounded median porous sets and possess mixed homogeneity, which enables us to extend earlier results obtained for porous sets to a significantly broader class of geometries.

math.CA↗
arXiv2025

The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and its Implications for Structure Growth

We present new measurements of cosmic microwave background (CMB) lensing over $9400$ sq. deg. of the sky. These lensing measurements are derived from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) CMB dataset, which consists of five seasons of ACT CMB temperature and polarization observations. We determine the amplitude of the CMB lensing power spectrum at $2.3\%$ precision ($43σ$ significance) using a novel pipeline that minimizes sensitivity to foregrounds and to noise properties. To ensure our results are robust, we analyze an extensive set of null tests, consistency tests, and systematic error estimates and employ a blinded analysis framework. The baseline spectrum is well fit by a lensing amplitude of $A_{\mathrm{lens}}=1.013\pm0.023$ relative to the Planck 2018 CMB power spectra best-fit $Λ$CDM model and $A_{\mathrm{lens}}=1.005\pm0.023$ relative to the $\text{ACT DR4} + \text{WMAP}$ best-fit model. From our lensing power spectrum measurement, we derive constraints on the parameter combination $S^{\mathrm{CMBL}}_8 \equiv σ_8 \left({Ω_m}/{0.3}\right)^{0.25}$ of $S^{\mathrm{CMBL}}_8= 0.818\pm0.022$ from ACT DR6 CMB lensing alone and $S^{\mathrm{CMBL}}_8= 0.813\pm0.018$ when combining ACT DR6 and Planck NPIPE CMB lensing power spectra. These results are in excellent agreement with $Λ$CDM model constraints from Planck or $\text{ACT DR4} + \text{WMAP}$ CMB power spectrum measurements. Our lensing measurements from redshifts $z\sim0.5$--$5$ are thus fully consistent with $Λ$CDM structure growth predictions based on CMB anisotropies probing primarily $z\sim1100$. We find no evidence for a suppression of the amplitude of cosmic structure at low redshifts

astro-ph.CO↗
arXiv2024

The Atacama Cosmology Telescope: DR6 Gravitational Lensing Map and Cosmological Parameters

We present cosmological constraints from a gravitational lensing mass map covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO measurements (from SDSS and 6dF), we obtain the amplitude of matter fluctuations $σ_8 = 0.819 \pm 0.015$ at 1.8% precision, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at 1.6% precision. A joint constraint with CMB lensing measured by the Planck satellite yields even more precise values: $σ_8 = 0.812 \pm 0.013$, $S_8\equivσ_8({Ω_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1 \pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree well with $Λ$CDM-model extrapolations from the CMB anisotropies measured by Planck. To compare these constraints to those from the KiDS, DES, and HSC galaxy surveys, we revisit those data sets with a uniform set of assumptions, and find $S_8$ from all three surveys are lower than that from ACT+Planck lensing by varying levels ranging from 1.7-2.1$σ$. These results motivate further measurements and comparison, not just between the CMB anisotropies and galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We combine our CMB lensing measurements with CMB anisotropies to constrain extensions of $Λ$CDM, limiting the sum of the neutrino masses to $\sum m_ν < 0.13$ eV (95% c.l.), for example. Our results provide independent confirmation that the universe is spatially flat, conforms with general relativity, and is described remarkably well by the $Λ$CDM model, while paving a promising path for neutrino physics with gravitational lensing from upcoming ground-based CMB surveys.

astro-ph.CO↗
arXiv2024

Enhancing LR-FHSS Scalability Through Advanced Sequence Design and Demodulator Allocation

The accelerating growth of the Internet of Things (IoT) and its integration with Low-Earth Orbit (LEO) satellites demand efficient, reliable, and scalable communication protocols. Among these, the Long-Range Frequency Hopping Spread Spectrum (LR-FHSS) modulation, tailored for LEO satellite IoT communications, sparks keen interest. This work presents a joint approach to enhancing the scalability of LR-FHSS, addressing the demand for massive connectivity. We deepen into Frequency Hopping Sequence (FHS) mechanisms within LR-FHSS, spotlighting the potential of leveraging Wide-Gap sequences. Concurrently, we introduce two novel demodulator allocation strategies, namely, ``Early-Decode" and ``Early-Drop," to optimize the utilization of LoRa-specific gateway decoding resources. Our research further validates these findings with extensive simulations, offering a comprehensive look into the future potential of LR-FHSS scalability in IoT settings.

cs.NI↗
arXiv2023

The Hardness of Local Certification of Finite-State Dynamics

Finite-State Dynamics (FSD) is one of the simplest and constrained distributed systems. An FSD is defined by an $n$-node network, with each node maintaining an internal state selected from a finite set. At each time-step, these nodes synchronously update their internal states based solely on the states of their neighboring nodes. Rather than focusing on specific types of local functions, in this article, our primary focus is on the problem of determining the maximum time required for an FSD to reach a stable global state. This global state can be seen as the acceptance state or as the output of a distributed computation. For fixed $k$ and $q$, we define the problem $\text{convergence}(k,q)$, which consists of deciding if a $q$-state FSD converges in at most $k$ time-steps. Our main focus is to study the problem $\text{convergence}$ from the perspective of distributed certification, with a focus on the model of proof-labeling schemes (PLS). First, we study the problem $\text{convergence}$ on arbitrary graphs and show that every PLS has certificates of size $Θ(n^2)$ (up to logarithmic factors). Then, we turn to the restriction of the problem on graphs of maximum degree $Δ$. Roughly, we show that the problem admits a PLS with certificates of size $Δ^{k+1}$, while every PLS requires certificates of size at least $2^{k/6} \cdot 6/k$ on graphs of maximum degree 3.

cs.DC↗
arXiv2023

Local Certification of Majority Dynamics

In majority voting dynamics, a group of $n$ agents in a social network are asked for their preferred candidate in a future election between two possible choices. At each time step, a new poll is taken, and each agent adjusts their vote according to the majority opinion of their network neighbors. After $T$ time steps, the candidate with the majority of votes is the leading contender in the election. In general, it is very hard to predict who will be the leading candidate after a large number of time-steps. We study, from the perspective of local certification, the problem of predicting the leading candidate after a certain number of time-steps, which we call Election-Prediction. We show that in graphs with sub-exponential growth Election-Prediction admits a proof labeling scheme of size $\mathcal{O}(\log n)$. We also find non-trivial upper bounds for graphs with a bounded degree, in which the size of the certificates are sub-linear in $n$. Furthermore, we explore lower bounds for the unrestricted case, showing that locally checkable proofs for Election-Prediction on arbitrary $n$-node graphs have certificates on $Ω(n)$ bits. Finally, we show that our upper bounds are tight even for graphs of constant growth.

cs.DC↗
arXiv2023

The Atacama Cosmology Telescope: High-resolution component-separated maps across one-third of the sky

Observations of the millimeter sky contain valuable information on a number of signals, including the blackbody cosmic microwave background (CMB), Galactic emissions, and the Compton-$y$ distortion due to the thermal Sunyaev-Zel'dovich (tSZ) effect. Extracting new insight into cosmological and astrophysical questions often requires combining multi-wavelength observations to spectrally isolate one component. In this work, we present a new arcminute-resolution Compton-$y$ map, which traces out the line-of-sight-integrated electron pressure, as well as maps of the CMB in intensity and E-mode polarization, across a third of the sky (around 13,000 sq.~deg.). We produce these through a joint analysis of data from the Atacama Cosmology Telescope (ACT) Data Release 4 and 6 at frequencies of roughly 93, 148, and 225 GHz, together with data from the \textit{Planck} satellite at frequencies between 30 GHz and 545 GHz. We present detailed verification of an internal linear combination pipeline implemented in a needlet frame that allows us to efficiently suppress Galactic contamination and account for spatial variations in the ACT instrument noise. These maps provide a significant advance, in noise levels and resolution, over the existing \textit{Planck} component-separated maps and will enable a host of science goals including studies of cluster and galaxy astrophysics, inferences of the cosmic velocity field, primordial non-Gaussianity searches, and gravitational lensing reconstruction of the CMB.

astro-ph.CO↗
arXiv2019

On the Complexity of the Stability Problem of Binary Freezing Totalistic Cellular Automata

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbors. We classify all the Cellular Automata in the class of TFCA, grouping them in five different classes: the Trivial rules, Turing Universal rules,Algebraic rules, Topological rules and Fractal Growing rules. At the same time, we study in this family the Stability problem, consisting in deciding whether an inactive cell becomes active, given an initial configuration.We exploit the properties of the automata in each group to show that: - For Algebraic and Topological Rules the Stability problem is in $\text{NC}$. - For Turing Universal rules the Stability problem is $\text{P}$-Complete.

cs.DS↗
arXiv2019

On the Complexity of Asynchronous Freezing Cellular Automata

In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each time-step only one cell is updated. Given configuration, we say that a cell is unstable if there exists a sequential updating scheme that changes its state. In this context, we define the problem AsyncUnstability, which consists in deciding if a cell is unstable or not. In general AsyncUnstability is in NP, and we study in which cases we can solve the problem by a more efficient algorithm. We begin showing that AsyncUnstability is in NL for any one-dimensional FCA. Then we focus on the family of life-like freezing CA (LFCA), which is a family of two-dimensional two-state FCA that generalize the freezing version of the game of life, known as life without death. We study the complexity of AsyncUnstability for all LFCA in the triangular and square grids, showing that almost all of them can be solved in NC, except for one rule for which the problem is NP-complete.

cs.CC↗
arXiv2018

Universality in Freezing Cellular Automata

Cellular Automata have been used since their introduction as a discrete tool of modelization. In many of the physical processes one may modelize thus (such as bootstrap percolation, forest fire or epidemic propagation models, life without death, etc), each local change is irreversible. The class of freezing Cellular Automata (FCA) captures this feature. In a freezing cellular automaton the states are ordered and the cells can only decrease their state according to this "freezing-order". We investigate the dynamics of such systems through the questions of simulation and universality in this class: is there a Freezing Cellular Automaton (FCA) that is able to simulate any Freezing Cellular Automata, i.e. an intrinsically universal FCA? We show that the answer to that question is sensitive to both the number of changes cells are allowed to make, and geometric features of the space. In dimension 1, there is no universal FCA. In dimension 2, if either the number of changes is at least 2, or the neighborhood is Moore, then there are universal FCA. On the other hand, there is no universal FCA with one change and Von Neumann neighborhood. We also show that monotonicity of the local rule with respect to the freezing-order (a common feature of bootstrap percolation) is also an obstacle to universality.

cs.CC↗
arXiv2017

Nontrivial Turmites are Turing-universal

A Turmit is a Turing machine that works over a two-dimensional grid, that is, an agent that moves, reads and writes symbols over the cells of the grid. Its state is an arrow and, depending on the symbol that it reads, it turns to the left or to the right, switching the symbol at the same time. Several symbols are admitted, and the rule is specified by the turning sense that the machine has over each symbol. Turmites are a generalization of Langtons ant, and they present very complex and diverse behaviors. We prove that any Turmite, except for those whose rule does not depend on the symbol, can simulate any Turing Machine. We also prove the P-completeness of prediction their future behavior by explicitly giving a log-space reduction from the Topological Circuit Value Problem. A similar result was already established for Langtons ant; here we use a similar technique but prove a stronger notion of simulation, and for a more general family.

cs.CC↗
arXiv2013

A remark on an endpoint Kato-Ponce inequality

This note introduces bilinear estimates intended as a step towards an $L^\infty$-endpoint Kato-Ponce inequality. In particular, a bilinear version of the classical Gagliardo-Nirenberg interpolation inequalities for a product of functions is proved.

math.AP↗