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  Item type:Ítem,

  Redes neuronales de álgebra geométrica para la simulación de la ecuación de aguas poco profundas

  (Universidad Distrital Francisco José de Caldas)

  Patiño Bonilla, Juan Pablo

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  Gómez Vasco, Carlos Andrés

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  Gómez Vasco, Carlos Andrés [0000-0003-1473-0568]

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  The Shallow Water Equations (SWE) are the standard mathematical framework for simulating free-surface geophysical flows; tsunamis, coastal flooding, and large-scale atmospheric and oceanic currents, yet their traditional numerical solution faces considerable computational bottlenecks, particularly over complex topographies. This work evaluates an alternative based on Geometric Algebra Neural Networks (RNAG), architectures that replace classical vector products with the Clifford geometric product, seeking an inductive bias that respects the vector and rotational structure of the flow. Three architectures were implemented and compared, a conventional convolutional network (BasicCNN), a physics-informed network (ShallowWaterPINN), and a geometric algebra network (ShallowWaterClifford), trained on a synthetic dataset generated with SpeedyWeather.jl, and evaluated both on one-step prediction and on the stability of autoregressive rollout simulation. Results show a non-trivial pattern: ShallowWaterPINN achieved the lowest one-step prediction error, in both vector and scalar fields, while ShallowWaterClifford, despite a less accurate one-step fit, produced the lowest rollout error among the three architectures. This reversal suggests that the geometric structure of Clifford Algebra does not provide an advantage in instantaneous accuracy, but may better contain error propagation under autoregressive composition, a property particularly relevant for simulators intended for sustained use. The comparatively poor performance of BasicCNN is explained by an early interruption of its training, rather than by an architectural limitation.

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  Caracterización conformacional en el simportador NIS: parámetro de orden para lípidos

  (Universidad Distrital Francisco José de Caldas)

  Herrera Martinez, Laura Yeraldin

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  Flórez Pérez, José Manuel

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  Leyva Rojas, José Alfonso

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  The sodium/iodide symporter (NIS) is a membrane glycoprotein essential for active iodide uptake in thyroid tissue. The main objective of this research is to characterize the ion translocation mechanism mediated by NIS through the implementation of a mechanical-statistical order parameter. The methodology is based on classical molecular dynamics simulations using the GROMACS package and the CHARMM36 empirical force field. Using a computational protocol developed in Python and MDAnalysis, the radial distances of charged lipids (PAPS, POPI, POPA) to the protein’s center of mass were extracted, simultaneously evaluating the local bending of transmembrane segments (TMS) with the HELANAL algorithm. The results show distinct kinematic behaviors: POPA lipids exhibit exceptional positional stability due to low steric hindrance, in contrast to the greater positional freedom of PAPS lipids and the position-dependent dynamics of POPI. The integration of these kinematics with local curvature allowed the formulation of a convolution field (Φi) as a collective variable. This parameter revealed an exclusive and significant dynamic coupling in three microdomains of the TMS7 segment, demonstrating that the composition and position of the lipid environment exert a direct allosteric modulation on the functional architecture of the symporter’s hydrophobic cavity.

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  Item type:Ítem,

  Aplicativo web para la gestión de espacios de estacionamiento en zonas urbanas de Fusagasugá mediante el monitoreo en tiempo real

  (Universidad Distrital Francisco José de Caldas)

  Bolaños Camacho, Edward Santiago

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  Hernández Rodríguez, Jorge Eduardo

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  Hernandez Rodriguez, Jorge Eduardo [0000-0002-7129-7919]

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  The objective of this thesis was to help address the challenges of finding and managing parking spaces in urban areas, a common problem in cities due to population growth and the increase in the number of vehicles. To this end, a web application was developed to manage parking in the municipality of Fusagasugá. The system allows for the registration of users and vehicles, real-time monitoring of parking duration, automatic calculation of fees, and oversight of space occupancy. It also facilitates the administrative control of parking lots and the tracking of cases of nonpayment.

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  Item type:Ítem,

  Clasificación del riesgo crediticio mediante Máquinas de Boltzmann: un enfoque de aprendizaje automático y profundo

  (Universidad Distrital Francisco José de Caldas)

  Gomez Rojas, Andres Fernando

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  Gómez Vasco, Carlos Andrés

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  Gómez Vasco, Carlos Andrés [0000-0003-1473-0568]

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  This undergraduate thesis develops a credit risk rating model based on Boltzmann Machines, carried out as an internship in the financial sector. The proposal integrates principles of statistical physics and machine learning, establishing the correspondence between Restricted Boltzmann Machines and the Hopfield model as a framework for interpreting the architecture and its parameters. The development included the implementation of the models from scratch, the discretisation of financial, educational and judicial variables into binary attributes, the numerical verification of the algorithms against exact values, and experimental validation on a public benchmark dataset. The system produces a probability of default that is mapped to an AAA to CCC rating scale through isotonic calibration, together with an auditable scorecard that decomposes each decision by attribute. The results show that the model is competitive with standard industry techniques and that its additive decomposition of the decision meets the explainability requirements of the financial sector.

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  Item type:Ítem,

  SY103A INVAII

  (Universidad Distrital Francisco José de Caldas)

  Licenciatura en Matemáticas

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  Consejo Curricular Licenciatura en Matemáticas

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  Syllabus, Version 2026, for the course “Classroom Research II”, offered in the third semester of the Bachelor of Science in Mathematics program at the Francisco José de Caldas District University

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