arXiv subjects

Félix Balado

Publications and source records attributed to Félix Balado.

6 recordsLinked to original sources

arXiv2026

Systematic Enumeration of Fundamental Quantities Involving Runs in Binary Strings

We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same enumerations when runs of ones and runs of zeros are jointly considered. We give the connections between these two types of run enumeration, and with the problem of compositions. We also analyse the same enumerations with a Hamming weight constraint. We discuss which of the many number sequences that emerge from these problems are already known and listed in the OEIS. Additionally, we extend our main enumerative results to the probabilistic scenario in which binary strings are outcomes of independent and identically distributed Bernoulli variables.

math.CO↗

arXiv2025

Diffusion Model-based Data Augmentation Method for Fetal Head Ultrasound Segmentation

Medical image data is less accessible than in other domains due to privacy and regulatory constraints. In addition, labeling requires costly, time-intensive manual image annotation by clinical experts. To overcome these challenges, synthetic medical data generation offers a promising solution. Generative AI (GenAI), employing generative deep learning models, has proven effective at producing realistic synthetic images. This study proposes a novel mask-guided GenAI approach using diffusion models to generate synthetic fetal head ultrasound images paired with segmentation masks. These synthetic pairs augment real datasets for supervised fine-tuning of the Segment Anything Model (SAM). Our results show that the synthetic data captures real image features effectively, and this approach reaches state-of-the-art fetal head segmentation, especially when trained with a limited number of real image-mask pairs. In particular, the segmentation reaches Dice Scores of 94.66\% and 94.38\% using a handful of ultrasound images from the Spanish and African cohorts, respectively. Our code, models, and data are available on GitHub.

eess.IV↗

arXiv2023

Runs of Ones in Binary Strings

We give three different computations of the total number of runs of length $i$ in binary $n$-strings, and we discuss the connection of this problem with the compositions of $n$.

math.CO↗

arXiv2023

General Distributions of Number Representation Elements

We provide general expressions for the joint distributions of the $k$ most significant $b$-ary digits and of the $k$ leading continued fraction coefficients of outcomes of an arbitrary continuous random variable. Our analysis highlights the connections between the two problems. In particular, we give the general convergence law of the distribution of the $j$-th significant digit, which is the counterpart of the general convergence law of the distribution of the $j$-th continued fraction coefficient (Gauss-Kuz'min law). We also particularise our general results for Benford and Pareto random variables. The former particularisation allows us to show the central role played by Benford variables in the asymptotics of the general expressions, among other results. The particularisation for Pareto variables -- which include Benford variables as a special case -- is specially relevant in the context of pervasive scale-invariant phenomena, where Pareto variables occur much more frequently than Benford variables. This suggests that the Pareto expressions that we produce have wider applicability than their Benford counterparts in modelling most significant digits and leading continued fraction coefficients of real data. Our results may find practical application in all areas where Benford's law has been previously used.

math.PR↗

arXiv2017

Asymptotically Optimum Perfect Universal Steganography of Finite Memoryless Sources

A solution to the problem of asymptotically optimum perfect universal steganography of finite memoryless sources with a passive warden is provided, which is then extended to contemplate a distortion constraint. The solution rests on the fact that Slepian's Variant I permutation coding implements first-order perfect universal steganography of finite host signals with optimum embedding rate. The duality between perfect universal steganography with asymptotically optimum embedding rate and lossless universal source coding with asymptotically optimum compression rate is evinced in practice by showing that permutation coding can be implemented by means of adaptive arithmetic coding. Next, a distortion constraint between the host signal and the information-carrying signal is considered. Such a constraint is essential whenever real-world host signals with memory (e.g., images, audio, or video) are decorrelated to conform to the memoryless assumption. The constrained version of the problem requires trading off embedding rate and distortion. Partitioned permutation coding is shown to be a practical way to implement this trade-off, performing close to an unattainable upper bound on the rate-distortion function of the problem.

cs.IT↗

arXiv2011

Capacity of DNA Data Embedding Under Substitution Mutations

A number of methods have been proposed over the last decade for encoding information using deoxyribonucleic acid (DNA), giving rise to the emerging area of DNA data embedding. Since a DNA sequence is conceptually equivalent to a sequence of quaternary symbols (bases), DNA data embedding (diversely called DNA watermarking or DNA steganography) can be seen as a digital communications problem where channel errors are tantamount to mutations of DNA bases. Depending on the use of coding or noncoding DNA hosts, which, respectively, denote DNA segments that can or cannot be translated into proteins, DNA data embedding is essentially a problem of communications with or without side information at the encoder. In this paper the Shannon capacity of DNA data embedding is obtained for the case in which DNA sequences are subject to substitution mutations modelled using the Kimura model from molecular evolution studies. Inferences are also drawn with respect to the biological implications of some of the results presented.

cs.IT↗