The LHC has proven to be one of the most ambitious and powerful particle colliders to date, being capable to explore the TeV energy scale and to produce a particle compatible with the Higgs boson, such discovery was confirmed in 2012 by the CMS and ATLAS experiments. While exploring possibilities for physics beyond the Standard Model, the ATLAS collaboration further searches for heavy resonances decaying into a Higgs boson pair. The understanding of the final states involving the decays of a pair of Higgs bosons are crucial channels in the search of heavy resonances, which are predicted by theories encompassed in minimal supersymmetric Standard Model extensions or other theories beyond the Standard Model. A pair of highly collimated tau leptons in the final state challenges the reconstruction of Higgs particles due to the partial overlap of the hadronic tau jets in the detector. Particularly, in this work, we studied the boosted topology of the decay chain X → hh → b¯bτ+τ− in a fully hadronic final state, implementing a reconstruction technique for the invariant mass of a boosted tau pair, applying the collinear mass approximation method and compare the results with the visible decay system.

We present a family of exact planar hairy neutral black hole solutions in extended supergravity with Fayet-Iliopoulos (FI) terms. We consider a model where the magnetic part of FI sector vanishes and obtain the superpotential at finite temperature in analytic form. Then, we discuss the thermodynamics and some holographic properties of these solutions. We regularize the action by two different methods, one with gravitational and scalar counterterms and the other using the thermal superpotential as a counterterm, and compute the holographic stress tensor. We also construct the c-function of the corresponding RG flow and obtain an exact holographic β-function for this model.

In recent times, biopolymer materials have been studied due to their wide range of applications and sustainability. Among these, biopolymer-based hydrogels are fundamental in medical research, such as neural tissue engineering. Cellulose-based materials with tailored properties can be obtained by combining the growth of cotton in tissue culture with molecularly-designed glucose building-block feeding. This project aims to study the nanoscale effects of biological incorporation of fluorine-based molecules on cotton and characterize the nanomechanical properties of various biopolymer-based hydrogels for neural tissue growth using environmental Atomic Force Microscopy (e-AFM). We present a protocol for synthesizing cotton fibers using enzymatic digestion to yield nanofibrils. Both digested and non-digested cotton fibers were measured using e-AFM, including imaging and nanoindentation (for non-digested fibers) under different relative humidities. Collagen-, PEGDA-, GelMA-, and Alginate-based hydrogels prepared for neural tissue engineering were measured under liquid conditions. Results indicate that both control and modified cotton macrofibers have microto nano-structures arranged along their elongation axis, with noticeable heterogeneities in their local mechanics, presumably due to their internal arrangement. In modified samples, the fluorine atom may also contribute to these differences. Control cotton nanofibers swell at specific spots when exposed to higher relative humidity, suggesting a semicrystalline structure. Modified cellulose nanofibers exhibit heterogeneous swelling, with almost periodic changes in stiffness and height, likely due to the fluorine atom’s interference with their wettability. Biopolymer-based hydrogels showed rugosity (RMS) values around 2 nm, except for Collagen, which had an RMS of around 15 nm, potentially due to UV light exposure. The Young’s moduli of the gels ranged between 0.53 and 4.1 MPa.

Dirac materials, hosting linearly dispersing quasiparticles at low energies, exhibit an emergent Lorentz symmetry close to a quantum critical point (QCP) separating semimetallic state from a strongly-coupled gapped insulator or superconductor. This feature appears to be quite robust even in the open Dirac systems coupled to an environment, featuring non-Hermitian (NH) Dirac fermions: close to a strongly coupled QCP, a Yukawa-Lorentz symmetry emerges in terms of a unique terminal velocity for both the fermion and the bosonic order parameter fluctuations, while the system can either retain non-Hermiticity or completely decouple from the environment thus recovering Hermiticity as an emergent phenomenon. In this thesis, we propose a minimal model describing a non-Hermitian (NH) twodimensional tilted Dirac semimetal (DSM), by introducing masslike anti-Hermitian Dirac operators to the tilted Dirac Hamiltonian. We calculate density of states (DOS) and optical conductivity (OC), where because of NH and tilt dependence on these observables, we show that tilt can be used as a probe for non-Hermiticity in the low-energy regime. Additionally, we show that such a Yukawa-Lorentz symmetry can emerge at the quantum criticality even when the NH Dirac Hamiltonian includes a tilt term at the lattice scale. As we demonstrate by performing a leading order ϵ = 3−d expansion close to d = 3 upper critical dimension of the theory, a tilt term becomes irrelevant close to the QCP separating the NH Dirac semimetal and a gapped (insulating or superconducting) phase. Such a behavior also extends to the case of the linear-in-momentum non-tilt perturbation, introducing the velocity anisotropy for the Dirac quasiparticles, which also becomes irrelevant at the QCP. These predictions can be numerically tested in quantum Monte Carlo lattice simulations of the NH Hubbard-like models hosting low-energy NH tilted Dirac fermions.

El transporte óptimo ha sido tema de interés durante los últimos años [Villani, 2008] por sus aplicaciones en gestión de operaciones y en procesamiento de imágenes. En particular, en [Ekeland and Queyranne, 2015] se plantea un modelo de transporte óptimo para la extracción de un pozo minero a cielo abierto. El objetivo de este trabajo es presentar un modelo similar al descrito anteriormente, pero agregando restricciones de capacidad de extracción. Utilizando el esquema de dualidad de [Pennanen and Perkkiö, 2019] para problemas en el espacio de medidas de Radón, se consiguen condiciones de optimalidad para las soluciones, las cuales generan un pozo. Numéricamente se consiguen resultados para la optimalidad del pozo en el problema discretizado tanto para el problema irrestricto como para el problema con la restricción de capacidad.

Project Management is becoming increasingly crucial in competitive environments such as manufacturing and the service industries. The resource-constrained multi-project scheduling problem (RCMPSP) consists of assigning start times to jobs corresponding to two or more projects that must be executed simultaneously while respecting the precedence between jobs and limited resources. The existing rise in the study of the RCMPSP resulted in numerous works on the topic while proposing different problem features. This thesis presented a study of the RCMPSP and its variants, the base problem is initially described, and the solution methods and benchmarks used to solve RCMPSPs are classified and analyzed. The implications of the RCMPS with practice and its connection are also discussed. In addition, this research analyzed different variants of the problem based on aspects related to jobs, projects, relationships, resources, and time management, and based on the problem variants considered in the reviewed works, a taxonomy allowing (i) the identification and positioning of each RCMPSP variant and (ii) the analysis of the current state-of-the-art of the problem was proposed. Subsequently, it delved into the research of one of the most studied variants in the literature, RCMPSP with local resources (RCMPSP-L), describing the problem in detail and exposing its corresponding mathematical formulation. To solve the RCMPSP-L, a hybrid algorithm that integrates ant colony optimization with a hill-climbing first-improvement algorithm was proposed, and the experimentation process was carried out using a set of instances taken from the MPSPLib. The proposed algorithm presented low variability values, the construction phase provided good-quality solutions, and the local search constantly improved the constructive algorithm, with the results compared with other well-known approaches in the literature, evidencing that for different existing metrics, the proposed approach presents competitive results. Later, new variants of the problem that consider resource mixed accessibility, total resource allocation, delay costs, and resource costs were presented: RCMPSP-MT-W and RCMPSP-MT-W+RC, respectively, both variants described and mathematically formulated. A hybrid algorithm that integrates priority rules, simulated annealing, and tabu search as part of an iterated local search was proposed to solve the variants, where simple perturbation and joint perturbation were proposed as different perturbation intensities as part of the ILS. To validate the model and the algorithm, 36 instances based on the MPSPLib library were modified, and the results show that the application of joint perturbation yields better or equal results than simple perturbation, making greater use of resources with global accessibility, and although it may not be the only factor, the global accessibility of resources may imply greater freedom of allocation, allowing better results to be obtained.

La segmentación automática de lesiones de esclerosis múltiple en imágenes de resonancia magnética es una tarea fundamental para el diagnóstico, el monitoreo de la enfermedad y la evaluación de tratamientos. No obstante, la presencia del efecto del volumen parcial, el solapamiento de intensidades entre tejidos y el alto desbalance de clases, dificultan la segmentación de las lesiones de EM. En esta tesis se propone una nueva función de pérdida, denominada Mahalanobis Distance Loss (MDL), basada en el Mapa de Distancias de Mahalanobis (MDM), también propuesto, que integra información espacial y textural mediante características radiómicas extraídas de la modalidad FLAIR. A diferencia de los mapas de distancia construidos con la distancia euclidiana, el MDM incorpora dependencias estadísticas entre características, capturando mejor las variaciones sutiles en regiones ambiguas cercanas a los bordes de las lesiones. La MDL es combinada con la Generalized Dice Loss mediante un parámetro $\epsilon$ que regula el equilibrio entre solapamiento global y precisión en los bordes. La evaluación en los conjuntos de datos públicos ISBI-MS y MSSEG2016, utilizando una U-Net, demuestra que la función de pérdida propuesta supera a las basadas en mapas de distancia euclidiana, como Boundary Loss y Hausdorff Loss, en métricas de solapamiento (Dice, precisión), de borde (HD95, ASSD) y de detección bajo desbalance de clases (AUC-PR), además de reducir los falsos positivos. Los resultados validan que incorporar información de textura en la función de pérdida mediante el MDM mejora la segmentación automática de lesiones de EM y ofrece un marco prometedor para generalizar estas ideas a otros tipos de lesiones, tejidos y órganos.

El presente estudio aborda el desarrollo de un sistema operativo de respuesta ante emergencias Search and Rescue (SAR) en ambientes marítimos, basado en el uso de Modelos Hidrodinámicos Globales (MHG) y un Modelo Hidrodinámico Local (MHL), específicamente FVCOM. Se diseñaron algoritmos para procesar las salidas de estos modelos y utilizarlas como entrada en el Estimador Múltiple de Deriva de Partículas (EMDP), con el objetivo de delimitar zonas de búsqueda ante eventos de deriva en el mar. La evaluación del sistema se realizó utilizando datos del accidente aéreo del 2 de septiembre de 2011, ocurrido entre Isla Santa Clara e Isla Robinson Crusoe. Los resultados evidencian una buena concordancia entre trayectorias simuladas y observadas, con variaciones asociadas a las condiciones océano-atmosféricas. Se observó mejor desempeño de los modelos influenciados por mareas en condiciones de calma, y de los modelos impulsados por viento cuando este superó los 7 km·h⁻¹. El uso del MHL permitió una resolución espacial fina (hasta 46 m), capturando con mayor precisión la distribución de trayectorias. Este trabajo representa el primer aporte científico en Chile orientado a emergencias SAR marítimas, y propone una herramienta de apoyo eficiente para autoridades responsables en la toma de decisiones.