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Leonardo de Lima

Publications and source records attributed to Leonardo de Lima.

At least 19 recordsLinked to original sources
arXiv2026

Cosmologically Coupled Black Holes with Regular Horizons

We present the most general and exact solution of Einstein's gravity sourced by an anisotropic fluid describing the cosmological embedding (CE) of a static and spherically-symmetric object, including black holes (BHs) or exotic compact objects, without radial energy influx and in an arbitrary Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology. This is done fully considering backreaction of the local geometry on the cosmological dynamics. Our solution is free of curvature singularities at the would-be BH event horizon, thus solving a main issue of the CE of BH solutions proposed so far. As a byproduct, we derive a new CE of the Schwarzschild BH - distinct from McVitties's original proposal - that is regular everywhere except at the central singularity.

gr-qc↗
arXiv2026

On distance integral and distance Laplacian integral graphs

Let $G$ be a connected graph on $n$ vertices and let $D(G)$ and $D^{L}(G)$ be the distance and the distance Laplacian matrices associated with $G$. A graph $G$ is said to be $D$-integral (resp. $D^L$-integral) if all eigenvalues of $D(G)$ (resp. $D^L(G)$) are integers. In this paper, we obtain various conditions under which the graphs $a\overline{K_m}\nabla C_n$ and $K_{p,p}\nabla C_n$ are distance integral. We also obtain conditions on $m$, $n$ under which the dumbbell graph $\boldsymbol{DB}(W_{m,n})$ is $D^L$-integral.

math.CO↗
arXiv2026

Structured eigenbases and pair state transfer on threshold graphs

Recently, Macharete, Del-Vecchio, Teixeira and de Lima showed that a star and any threshold graph on the same number of vertices share the same eigenbasis relative to the Laplacian matrix. We use this fact to establish two main results in this paper. The first one is a characterization of threshold graphs that are \textit{simply structured}, i.e., their associated Laplacian matrices have eigenbases consisting of vectors with entries from the set $\{-1,0,1\}$. Then, we provide sufficient conditions such that a simply structured threshold graph is weakly Hadamard diagonalizable (WHD). This allows us to list all connected simply structured threshold graphs on at most 20 vertices, and identify those that are WHD. Second, we characterize Laplacian pair state transfer on threshold graphs. In particular, we show that the existence of Laplacian vertex state transfer and Laplacian pair state transfer on a threshold graph are equivalent if and only if it is not a join of a complete graph and an empty graph of certain sizes.

math.CO↗
arXiv2025

Schwarzschild-de Sitter spacetime in regular coordinates with cosmological time

Starting from the Einstein equations in Schwarzschild-de Sitter (SdS) spacetime and imposing Friedmann-Robertson-Walker coordinates at large distances, we find two coordinate systems with time-dependent metrics that are smooth across both the black hole and cosmological horizons. These coordinates require a positive cosmological constant for regularity, and thus they are not de Sitter extensions of the Kruskal-Szekeres or Israel coordinates. One of the coordinate systems was only found in 1999 (Abbassi coordinates), and it has led to conflicting interpretations in the literature, while the other was briefly commented on and promptly dismissed as unphysical or incompatible with SdS. We derive that the second solution is equivalent to the first one, and that both are indeed equivalent descriptions of SdS spacetime. We also derive explicit coordinate transformations linking these coordinate systems to the Kottler coordinates and the maximally extended Lake-Israel coordinates. Among other applications, these results, which extend the largely used cosmological and local coordinates, should be useful for further developments in understanding the exact interplay between black holes and the cosmological background, which has been the focus of a number of recent works.

gr-qc↗
arXiv2025

On some classes of bivalent and trivalent planar graphs

A graph is called bivalent or trivalent if there exists an eigenvector of the graph Laplacian composed from {-1,1} or {-1,0,1}, respectively. These bivalent and trivalent eigenvectors are important for engineering applications, in particular for vibrating systems. In this article, we determine the structure of bivalent and trivalent graphs in the following planar graph families: trees, unicyclic, bicyclic, and cactus.

math.CO↗
arXiv2025

A graph-based approach to customer segmentation using the RFM model

The present article proposes a graph-based approach to customer segmentation, combining the RFM analysis with the classical optimization max-$k$-cut problem. We consider each customer as a vertex of a weighted graph, and the edge weights are given by the distances between the vectors corresponding to the $(R,F,M)$-scores of the customers. We design a procedure to build a reduced graph with fewer vertices and edges, and the customer segmentation is obtained by solving the max-$k$-cut for this reduced graph. We prove that the optimal objective function values of the original and the reduced problems are equal. Additionally, we show that an optimal solution to the original problem can be easily obtained from an optimal solution to the reduced problem, which provides an advantage in dealing with computational complexity in large instances. Applying our methodology to a real customer dataset allowed us to identify distinct behaviors between groups and analyze their meaning and value from a business perspective.

math.OC↗
arXiv2024

Location of Zeros of Holomorphic Functions

In this article, various results will be demonstrated that enable the delimitation of a zero-free region for holomorphic functions on a set $K$, studying the behavior of their imaginary or real part on the boundary of $K$. These findings contribute to a deeper understanding of the distribution of zeros, shedding light on the intricate nature of holomorphic functions within the specified set.

math.GM↗
arXiv2023

Positive and Negative Square Energies of Graphs

The energy of a graph $G$ is the sum of the absolute values of the eigenvalues of the adjacency matrix of $G$. Let $s^+(G), s^-(G)$ denote the sum of the squares of the positive and negative eigenvalues of $G$, respectively. It was conjectured by [Elphick, Farber, Goldberg, Wocjan, Discrete Math. (2016)] that if $G$ is a connected graph of order $n$, then $s^+(G)\geq n-1$ and $s^-(G) \geq n-1$. In this paper, we show partial results towards this conjecture. In particular, numerous structural results that may help in proving the conjecture are derived, including the effect of various graph operations. These are then used to establish the conjecture for several graph classes, including graphs with certain fraction of positive eigenvalues and unicyclic graphs.

math.CO↗
arXiv2023

On the Importance of Three-Body Decays of Vector-Like Quarks

It is a common feature of vector-like extensions of the electroweak sector to have near degenerate states, such as electroweak doublets. In simplified models, it is usually assumed that these have decay widths saturated by two-body channels. As a consequence, experimental searches can be done focusing on only one of the states of the doublet. Taking as an example case the light exotic electroweak doublet present in the Minimal Composite Higgs Model, we show that including three-body decays in the pair production process makes this separation unfeasible, since both states of the doublet will be present and contribute significantly to the signal. In addition, by recasting present searches in multileptonic channels, with a simplified cut-and-count analysis, a relevant increase in discovery reach or exclusion potential is obtained; this indeed motivates a more detailed analysis. This study shows how an inclusive search strategy, taking into account both the near degeneracy and the presence of three-body decays, will have greater discovery power and be more natural from a model building perspective.

hep-ph↗
arXiv2022

On graphs with eigenvectors in $\{1, -1, 0\}$ and the max $k$-cut problem

In this paper, we characterize all graphs with eigenvectors of the signless Laplacian and adjacency matrices with components equal to $\{- 1, 0, 1\}.$ We extend the graph parameter max $k$-cut to square matrices and prove a general sharp upper bound, which implies upper bounds on the max $k$-cut of a graph using the smallest signless Laplacian eigenvalue, the smallest adjacency eigenvalue, and the largest Laplacian eigenvalue of the graph. In addition, we construct infinite families of extremal graphs for the obtained upper bounds.

math.CO↗
arXiv2022

Heuristic Algorithm for Univariate Stratification Problem

In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article proposes a heuristic to solve the univariate stratification problem - widely studied in the literature. One of its versions sets the number of strata and the precision level and seeks to determine the limits that define such strata to minimize the sample size allocated to the strata. A heuristic-based on a stochastic optimization method and an exact optimization method was developed to achieve this goal. The performance of this heuristic was evaluated through computational experiments, considering its application in various populations used in other works in the literature, based on 20 scenarios that combine different numbers of strata and levels of precision. From the analysis of the obtained results, it is possible to verify that the heuristic had a performance superior to four algorithms in the literature in more than 94% of the cases, particularly concerning the known algorithms of Kozak and Lavallee-Hidiroglou.

stat.ME↗
arXiv2020

Probing the Top-Higgs Sector with Composite Higgs Models at Present and Future Hadron Colliders

We study the production of $t{\bar t}h$ and $t{\bar t}hh$ at hadron colliders, in the minimal Composite Higgs Models, based on the coset $SO(5)/SO(4)$. We explore the fermionic representations ${\bf 5}$ and ${\bf 14}$. A detailed phenomenological analysis is performed, covering the energy range of the LHC and its High Luminosity upgrade, as well as that of a future 100 TeV hadron collider. Both resonant and non-resonant production are considered, stressing the interplay and complementary interest of these channels with each other and double Higgs production. We provide sets of representative points with detailed experimental outcomes in terms of modification of the cross sections as well as resonance masses and branching ratios. For non-resonant production, we gauge the relative importance of Yukawa, Higgs trilinear, and contact $t\bar{t}hh$ vertices to these processes, and consider the prospect for distinguishing the fermion representations from each other and from the Standard Model. In the production of top partners, we find that the three-body decay channel $W^+ W^- t$ becomes significant in certain regions of parameter space having a degenerate spectrum, and is further enhanced with energy. This motivates both higher energy machines as well as the need to go beyond the current analysis performed for the searches for these resonances.

hep-ph↗
arXiv2020

On the Graovac-Ghorbani index for bicyclic graphs with no pendant vertices

Let $G=(V,E)$ be a simple undirected and connected graph on $n$ vertices. The Graovac--Ghorbani index of a graph $G$ is defined as $$ABC_{GG}(G)= \sum_{uv \in E(G)} \sqrt{\frac{n_{u}+n_{v}-2} {n_{u} n_{v}}},$$ where $n_u$ is the number of vertices closer to vertex $u$ than vertex $v$ of the edge $uv \in E(G)$ and $n_{v}$ is defined analogously. It is well-known that all bicyclic graphs with no pendant vertices are composed by three families of graphs, which we denote by $\mathcal{B}_{n} = B_1(n) \cup B_2(n) \cup B_3(n).$ In this paper, we give an lower bound to the $ABC_{GG}$ index for all graphs in $B_1(n)$ and prove it is sharp by presenting its extremal graphs. Additionally, we conjecture a sharp lower bound to the $ABC_{GG}$ index for all graphs in $\mathcal{B}_{n}.$

math.GM↗
arXiv2019

On graphs with adjacency and signless Laplacian matrix eigenvectors entries in $\{-1, +1\}$

Let $G$ be a simple graph. In 1986, Herbert Wilf asked what kind of graphs have an eigenvector with entries formed only by $\pm 1$? In this paper, we answer this question for the adjacency, Laplacian and signless Laplacian matrix of a graph. Besides, we generalize the concept of an exact graph to the adjacency and signless Laplacian matrices. Infinity families of exact graphs for all those matrices are presented.

math.SP↗
arXiv2019

The Super-Planckian Axion Strikes Back

We present a novel framework for obtaining large hierarchies in axion decay constants as well as trans-Planckian field excursions, with no need for tuning or a large number of fields. We consider a model with two or more CFTs with a common cutoff, that are linked by a gauged diagonal symmetry. This construction is dual to the geometry of a warped space with two or more throats glued at a common brane, allowing for calculability. Many applications of our setup are possible,such as ultra-light axions, natural inflation, and relaxion models.

hep-ph↗
arXiv2018

A warped relaxion

We construct a UV completion of the relaxion in a warped extra dimension. We identify the relaxion with the zero mode of the fifth component of a bulk gauge field and show how hierarchically different decay constants for this field can be achieved by different localizations of anomalous terms in the warped space. This framework may also find applications for other axion-like fields. The cutoff of the relaxion model is identified as the scale of the IR brane where the Higgs lives, which can be as high as $10^6$ GeV, while above this scale warping takes over in protecting the Higgs mass.

hep-ph↗
arXiv2017

Minimally extended SILH

Higgs boson compositeness is a phenomenologically viable scenario addressing the hierarchy problem. In minimal models, the Higgs boson is the only degree of freedom of the strong sector below the strong interaction scale. We present here the simplest extension of such a framework with an additional composite spin-zero singlet. To this end, we adopt an effective field theory approach and develop a set of rules to estimate the size of the various operator coefficients, relating them to the parameters of the strong sector and its structural features. As a result, we obtain the patterns of new interactions affecting both the new singlet and the Higgs boson's physics. We identify the characteristics of the singlet field which cause its effects on Higgs physics to dominate over the ones inherited from the composite nature of the Higgs boson. Our effective field theory construction is supported by comparisons with explicit UV models.

hep-ph↗