Search

The Ethereum blockchain has a \emph{gas system} that associates operations with a cost in gas units. Two central concepts of this system are the \emph{gas limit} assigned by the issuer of a transaction and the \emph{gas used} by a transaction. The former is a budget that must not be exhausted before the completion of the transaction execution; otherwise, the execution fails. Therefore, it seems rather essential to determine the \emph{minimum gas limit} that ensures the execution of a transaction will not abort due to the lack of gas. Despite its practical relevance, this concept has not been properly addressed. In the literature, gas used and minimum gas limit are conflated. This paper proposes a precise notion of minimum gas limit and how it can differ from gas used by a transaction; this is also demonstrated with a quantitative study on real transactions of the Ethereum blockchain. Another significant contribution is the proposition of a fairly precise estimator for each of the two metrics. Again, the confusion between these concepts has led to the creation of estimators only for the gas used by a transaction. We demonstrate that the minimum gas limit for the state of the Ethereum blockchain (after the block) $t$ can serve as a near-perfect estimation for the execution of the transaction at block $t + \Delta$, where $\Delta \leq 11$; the same holds for estimating gas used. These precise estimators can be very valuable in helping the users predict the gas budget of transactions and developers in optimising their smart contracts; over and underestimating gas used and minimum gas limit can lead to a number of practical issues. Overall, this paper serves as an important reference for blockchain developers and users as to how the gas system really works.

The graph coloring game is a famous two-player game (re)introduced by Bodlaender in $1991$. Given a graph $G$ and $k \in \mathbb{N}$, Alice and Bob alternately (starting with Alice) color an uncolored vertex with some color in $\{1,\cdots,k\}$ such that no two adjacent vertices receive a same color. If eventually all vertices are colored, then Alice wins and Bob wins otherwise. The game chromatic number $\chi_g(G)$ is the smallest integer $k$ such that Alice has a winning strategy with $k$ colors in $G$. It has been recently (2020) shown that, given a graph $G$ and $k\in \mathbb{N}$, deciding whether $\chi_g(G)\leq k$ is PSPACE-complete. Surprisingly, this parameter is not well understood even in ``simple" graph classes. Let $P_n$ denote the path with $n\geq 1$ vertices. For instance, in the case of Cartesian grids, it is easy to show that $\chi_g(P_m \times P_n) \leq 5$ since $\chi_g(G)\leq \Delta+1$ for any graph $G$ with maximum degree $\Delta$. However, the exact value is only known for small values of $m$, namely $\chi_g(P_1\times P_n)=3$, $\chi_g(P_2\times P_n)=4$ and $\chi_g(P_3\times P_n) =4$ for $n\geq 4$ [Raspaud, Wu, 2009]. Here, we prove that, for every $n\geq 18$, $\chi_g(P_4\times P_n) =4$., Comment: 22 pages, 22 figures

Research in neutrino physics has been very active, both in experimental advances, with a new generation of detectors in operation and planning, and in theoretical discussions regarding the fundamental nature of the neutrino. This scientific dynamism has attracted many new students to the field. One of the first topics studied in neutrino physics by newcomers is the formalism of neutrino flavor oscillations and its associated phenomenology. We present this work as a compilation of this basic knowledge, through a step-by-step approach that facilitates an efficient understanding of this vast theoretical and experimental landscape., Comment: 14 pages, 4 figures

Recent advances in learning decision-making policies can largely be attributed to training expressive policy models, largely via imitation learning. While imitation learning discards non-expert data, reinforcement learning (RL) can still learn from suboptimal data. However, instantiating RL training of a new policy class often presents a different challenge: most deep RL machinery is co-developed with assumptions on the policy class and backbone, resulting in poor performance when the policy class changes. For instance, SAC utilizes a low-variance reparameterization policy gradient for Gaussian policies, but this is unstable for diffusion policies and intractable for autoregressive categorical policies. To address this issue, we develop an offline RL and online fine-tuning approach called policy-agnostic RL (PA-RL) that can effectively train multiple policy classes, with varying architectures and sizes. We build off the basic idea that a universal supervised learning loss can replace the policy improvement step in RL, as long as it is applied on "optimized" actions. To obtain these optimized actions, we first sample multiple actions from a base policy, and run global optimization (i.e., re-ranking multiple action samples using the Q-function) and local optimization (i.e., running gradient steps on an action sample) to maximize the critic on these candidates. PA-RL enables fine-tuning diffusion and transformer policies with either autoregressive tokens or continuous action outputs, at different sizes, entirely via actor-critic RL. Moreover, PA-RL improves the performance and sample-efficiency by up to 2 times compared to existing offline RL and online fine-tuning methods. We show the first result that successfully fine-tunes OpenVLA, a 7B generalist robot policy, autonomously with Cal-QL, an online RL fine-tuning algorithm, improving from 40% to 70% in the real world in 40 minutes.

Morphological classification of galaxies becomes increasingly challenging with redshift. We apply a hybrid supervised-unsupervised method to classify $\sim 14,000$ galaxies in the CANDELS fields at $0.2 \leq z \leq 2.4$ into spheroid, disk, and irregular systems. Unlike previous works, our method is applied to redshift bins of width 0.2. Comparison between models applied to a wide redshift range versus bin-specific models reveals significant differences in galaxy morphology beyond $z \geq 1$ and a consistent $\sim 25\%$ disagreement. This suggests that using a single model across wide redshift ranges may introduce biases due to the large time intervals involved compared to galaxy evolution timescales. Using the FERENGI code to assess the impact of cosmological effects, we find that flux dimming and smaller angular scales may lead to the misclassification of up to $18\%$ of disk galaxies as spheroids or irregulars. Contrary to previous studies, we find an almost constant fraction of disks ($\sim 60\%$) and spheroids ($\sim 30\%$) across redshifts. We attribute discrepancies with earlier works, which suggest a decreasing fraction of disks beyond $z \sim 1$, to the biases introduced by visual classification. Our claim is further strengthened by the striking agreement to the results reported by Lee et al. (2024) using an objective, unsupervised method applied to James Webb Space Telescope data. Exploring mass dependence, we observe a $\sim 40\%$ increase in the fraction of massive ($M_{\rm stellar} \geq 10^{10.5}{\rm M}_{\odot}$) spheroids with decreasing redshift, well balanced with a decrease of $\sim 20\%$ in the fraction of $M_{\rm stellar} \geq 10^{10.5}{\rm M}_{\odot}$ disks, suggesting that merging massive disk galaxies may form spheroidal systems., Comment: 15 pages, 11 figures, 3 tables

We present a brief introduction to a class of interactive fuzzy numbers, called f correlated fuzzy numbers, which consist of pairs of fuzzy numbers where one is dependent on the other by a continuous montone injector function. We present some results of operations with these numbers, obtaining equations that can directly calculate the results of these operations using only basic operations with real numbers, intervals on the real line and the function that relates the fuzzy numbers being considered., Comment: 5 pages, no figures

This paper presents some concepts of the theory of interactive fuzzy numbers, and mainly, a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers. We start from the foundations of general fuzzy mathematics and go through operations and the notion of interactivity for fuzzy numbers. The main result is that $f$-correlation preserve the shape of certains fuzzy numbers. More specificaly, if two fuzzy numbers are $f$ correlated, and one is a LR-type fuzzy number, the other is also a LR-type fuzzy number. This paper also presents some operations with the $f$-correlated fuzzy numbers wich are interesting to applications like biomathematics., Comment: 6 pages, no figures

Evaluating text-to-image generative models remains a challenge, despite the remarkable progress being made in their overall performances. While existing metrics like CLIPScore work for coarse evaluations, they lack the sensitivity to distinguish finer differences as model performance rapidly improves. In this work, we focus on the text rendering aspect of these models, which provides a lens for evaluating a generative model's fine-grained instruction-following capabilities. To this end, we introduce a new evaluation framework called TypeScore to sensitively assess a model's ability to generate images with high-fidelity embedded text by following precise instructions. We argue that this text generation capability serves as a proxy for general instruction-following ability in image synthesis. TypeScore uses an additional image description model and leverages an ensemble dissimilarity measure between the original and extracted text to evaluate the fidelity of the rendered text. Our proposed metric demonstrates greater resolution than CLIPScore to differentiate popular image generation models across a range of instructions with diverse text styles. Our study also evaluates how well these vision-language models (VLMs) adhere to stylistic instructions, disentangling style evaluation from embedded-text fidelity. Through human evaluation studies, we quantitatively meta-evaluate the effectiveness of the metric. Comprehensive analysis is conducted to explore factors such as text length, captioning models, and current progress towards human parity on this task. The framework provides insights into remaining gaps in instruction-following for image generation with embedded text.

Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of $\mathfrak{sl}_2 (K)$, or equivalently, the $\mathbb{Z}_2$-graded identities for the pair $(M_3(K), \mathfrak{sl}_2 (K))$. We work with the canonical grading on $\mathfrak{sl}_2 (K)$ and the only nontrivial $\mathbb{Z}_2$-grading of the associative algebra $M_3(K)$ induced by that on $\mathfrak{sl}_2(K)$., Comment: 20 pages, no figures

We establish a compactness result for solutions of a certain class of hypoelliptic equations. This result allows us to show the existence of global weak solutions to the non-homogeneous Landau-Fermi-Dirac equation with Coulomb potential.

We compare ambient and outer Lipschitz geometry of Lipschitz normally embedded H\"older triangles in $\mathbb{R}^4$. In contrast to the case of $\mathbb{R}^3$ there are infinitely many equivalence classes. The equivalence classes are related to the so-called microknots., Comment: arXiv admin note: text overlap with arXiv:2311.18570

The decays of the Z boson and CP-even or CP-odd scalar bosons into quark-antiquark pairs have been calculated at NLO in the framework of Implicit Regularization (IReg) , which operates strictly in the physical dimension and complies with the BPHZ procedure. The presence of the {\gamma}5 matrix is dealt without the need of gauge symmetry restoring counterterms and the Kinoshita-Lee-Nauenberg (KLN) theorem is verified. The results are compared to the ones obtained in the Dimensional Reduction scheme (DRed)., Comment: presented in the eQCD 2024 conference Acta Physica Polonica B Proceedings Supplement 17, 6-A14 (2024)

The Moderately Discontinuous Homology (MD-Homology, for short) was created recently in 2022 by Fern\'andez de Bobadilla at al. and it captures deep Lipschitz phenomena. However, to become a definitive powerful tool, it must be widely comprehended. In this paper, we investigate the MD-Homology of definable surface germs for the inner and outer metrics. We completely determine the MD-Homology of surfaces for the inner metric and we present a great variety of interesting MD-Homology of surfaces for the outer metric, for instance, we determine the MD-Homology of some bubbles, snake surfaces, and horns. Furthermore, we explicit the diversity of MD-Homology of surfaces for the outer metric in general, showing how hard it is to completely solve the outer classification problem. On the other hand, we show that, under specific conditions, the weakly outer Lipschitz equivalence determines completely the MD-Homology of surfaces for the outer metric, showing that these two subjects are quite related., Comment: 36 pages

We analyze the network of transactions among cities based on the electronic invoice database for the municipalities in the Cear\'a state, Brazil. It consists of approximately 3.7 billion records, registered during the period between the years 2016 to 2019. All the transactions are grouped in a unique dataset and represented as an asymmetrical adjacency matrix corresponding to a directed graph with connections weighted by the number of transactions among cities. Due to the large size of Cear\'a state, its unequal distribution of wealth, and spatially heterogeneous population, we initially determine communities of cities based on their mutual intensity of trades and verify to which extent their economic interests reflect a community cohesiveness. For the first task, we use the Infomap algorithm to detect the partition which provides the shortest description length and captures the optimal community structure of the network in terms of its associated flow dynamics. Surprisingly, the partition identified has five modules, whose two-dimensional geographical projections are all simply-connected domains. We proceed with the analysis of traded products by building bipartite structures represented in terms of adjacency matrices between municipalities and products, considering selling and buying. Using the revealed comparative advantage (RCA) concept, we define a non-monetary and binary activity index that can distinguish the RCA of a city in a class of goods or services as evidenced by trade flows. Finally, through the pairwise Maximum Entropy Model, we can associate to the largest communities their corresponding binary Ising-like Hamiltonian models. In an analogy with critical phenomena, our results reveal that each community operates at a "temperature" that is close to the corresponding "critical point", suggesting a high degree of "economic cohesiveness" in its trade network of cities., Comment: 29 pages, 10 figures

In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, we prove an adapted version of A'Campo-L\^e's Theorem for foliations, i.e., the algebraic multiplicity equal to one is a topological invariant in dimension two. This result is further generalized to higher dimensions under mild conditions; as a consequence, we prove that saddle-nodes are topologically invariant. We prove that the algebraic multiplicity is a topological invariant in several classes of foliations that contain, for instance, the generalized curves and the foliations of second type. Additionally, we address a fundamental result by Rosas-Bazan, which states that the existence of a homeomorphism extending through a neighborhood of the exceptional divisor of the first blow-up implies the topological invariance of the algebraic multiplicity. We show that the result holds if the homeomorphism extends locally near a singularity, even if it does not extend over the entire divisor., Comment: The title was changed, the paper was rewritten and Section 4 and Subsection 5.1 are new; 20 pages

Determining the carrying capacity of urban tourism destinations and public spaces is essential for sustainable management. This paper presents an online tool that calculates pedestrian carrying capacities for user-defined areas based on OpenStreetMap (OSM) data. The tool considers physical, real, and effective carrying capacities by incorporating parameters such as area per pedestrian, rotation factor, corrective factors, and management capacity. The carrying capacity calculator aids in balancing environmental, economic, social, and experiential factors to prevent overcrowding and preserve the quality of life for residents and visitors. This tool is particularly useful for tourism destination management, urban planning, and event management, ensuring positive visitor experiences and sustainable infrastructure development. We detail the implementation of the calculator, its underlying algorithm, and its application to the Santa Maria Maior parish in Lisbon, highlighting its effectiveness in managing urban tourism and public spaces.

Galaxies infalling into clusters undergo both star-formation quenching and morphological transformation due to environmental effects. We investigate these processes and their timescales using a local sample of 20,191 cluster and 11,674 field galaxies from SDSS. By analysing morphology as a function of distance from the star-formation main sequence, we show that environmental influence is especially pronounced for low-mass galaxies, which emerge from the green valley with early-type morphologies before their star formation is fully suppressed. Using the galaxies' positions in the clusters' Projected Phase Space, we examine the evolution of blue cloud, green valley, and red sequence fractions as a function of time since infall. Interestingly, the green valley fraction remains constant with time since infall, suggesting a balanced flow of galaxies in and out of this class. We estimate that galaxies less massive than $10^{10}\rm M_{\odot}$ spend approximately 0.4 Gyr in the green valley. By comparing quenched and early-type populations, we provide further evidence for the ``slow-then-rapid'' quenching model and suggest that it can also be applied to morphological transitions. Our results indicate that morphological transformation occurs at larger radii than complete star-formation quenching. About 75% of galaxies undergoing morphological transition in clusters are spirals evolving into S0s, suggesting that infalling galaxies retain their disks, while massive ellipticals are relics of early merger events. Finally, we show it takes approximately 2.5 and 1.2 Gyr after the delay-time ($\sim 3.8 {\rm Gyr}$) for the population of low mass galaxies in clusters to reach a 50% threshold in quenched and early-type fraction, respectively. These findings suggest morphological transition precedes full star formation quenching, with both processes possibly being causally linked., Comment: 14 pages, 10 figures

Strongly correlated electrons systems may exhibit a variety of interesting phenomena, for instance, superconductivity and pseudogap, as is the case of cuprates and pnictides. In strongly correlated electron systems, it is considered essential to understand, not only the nature of the pseudogap, but also the relationship between superconductivity and the pseudogap. In order to address this question, in the present work, we investigated a one-band Hubbard model treated by the Green's function method within an n-pole approximation. In the strongly correlated regime, antiferromagnetic correlations give rise to nearly flat band regions in the nodal points of the quasiparticle bands. As a consequence, a pseudogap emerges at the antinodal points of the Fermi surface. The obtained results indicate that the same antiferromagnetic correlations responsible for a pseudogap, can also favor superconductivity, providing an increase in the superconducting critical temperature Tc., Comment: 16 pages, 9 figures

We investigate the formation of particular patterns when light passes through glass. Experimentally, we use various glass plates, registering each reflected and transmitted outcome. Thus, we find the condition to form a common pattern, namely, randomly scratched plates produce the halos. We engineer other optical patterns by means of the specular holography method. Using the Defocusing Microscopy technique, we study the geometric properties of the glass, establishing the physical and mathematical model for a simulation. Our computational results agree well with the experimental ones, leading us to conclude that the pattern formation is governed by specular reflection on various points along the scratches. Our findings give an initial explanation for the pattern formation on glass, in particular for the halo design.