Computational modelling of the behaviour of biomarker particles of colorectal cancer in fecal matter

Colorectal adenocarcinoma is one of the carcinogenic diseases that is increasing the morbidity and mortality rates worldwide. The disease initially occurs through the segregation of biomarker substances in the human system without manifesting symptoms that affect the health of the carrier. Early detection would allow the application of more effective treatments, less invasive procedures and reduce the development of cancer. The purpose of this investigation was the elaboration of a mathematical model and the development of computational simulations to visualize the behavior of biomarker particles in transit through the colon. The flow conditions, properties of the viscous medium and biological regions of interest were established. Constitutive models, numerical conditions and solution strategies were determined. A numerical grid was used to represent the model of the colon and the human feces that carry the bioparticles (biomarkers). The results indicated the trajectories of the bioparticles in the fecal mass and the interactive movement with the natural contractions of the colon. The analysis of the movement of the biomarker particles can provide future less invasive alternatives for the detection in real time of the cancer by means of the implantation of biosensors in the walls of the colon

Emergent SU(3) symmetry in random spin-1 chains

We show that generic SU(2)-invariant random spin-1 chains have phases with an emergent SU(3) symmetry. We map out the full zero-temperature phase diagram and identify two different phases: (i) a conventional random singlet phase (RSP) of strongly bound spin pairs (SU(3) "mesons") and (ii) an unconventional RSP of bound SU(3) "baryons", which are formed, in the great majority, by spin trios located at random positions. The emergent SU(3) symmetry dictates that susceptibilities and correlation functions of both dipolar and quadrupolar spin operators have the same asymptotic behavior.Comment: 5 pages plus 3-page Supplemental Material, 5 figures; published versio

Emergent SU(N) symmetry in disordered SO(N) spin chains

Strongly disordered spin chains invariant under the SO(N) group are shown to display random-singlet phases with emergent SU(N) symmetry without fine tuning. The phases with emergent SU(N) symmetry are of two kinds: one has a ground state formed of randomly distributed singlets of strongly bound pairs of SO(N) spins (a `mesonic' phase), while the other has a ground state composed of singlets made out of strongly bound integer multiples of N SO(N) spins (a `baryonic' phase). The established mechanism is general and we put forward the cases of $\mathrm{N}=2,3,4$ and $6$ as prime candidates for experimental realizations in material compounds and cold-atoms systems. We display universal temperature scaling and critical exponents for susceptibilities distinguishing these phases and characterizing the enlarging of the microscopic symmetries at low energies.Comment: 5 pages, 2 figures, Contribution to the Topical Issue "Recent Advances in the Theory of Disordered Systems", edited by Ferenc Igl\'oi and Heiko Riege

Highly-symmetric random one-dimensional spin models

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure

The Holographic Life of the eta'

In the string holographic dual of large-N_c QCD with N_f flavours of Kruczenski et al, the eta' meson is massless at infinite N_c and dual to a collective fluctuation of N_f D6-brane probes in a supergravity background. Here we identify the string diagrams responsible for the generation of a mass of order N_f/N_c, consistent with the Witten-Veneziano formula, and show that the supregravity limit of these diagrams corresponds to mixings with pseudoscalar glueballs. We argue that the dependence on the theta-angle in the supergravity description occurs only through the combination theta + 2 \sqrt{N_f} eta' / f_pi, as dictated by the U(1) anomaly. We provide a quantitative test by computing the linear term in the eta' potential in two independent ways, with perfect agreement.Comment: 1+26 pages, 8 figures; V4: Appendix added, version published in JHE

Análisis de una propuesta de evaluación en relación con la estructura conceptual de la proporcionalidad

La presente propuesta es una aproximación reflexiva y critica de las prácticas evaluativas que se vienen desarrollando en la enseñanza básica y media en las instituciones de carácter privado de la ciudad de Cali, sustentada desde nuestra propia experiencia como docentes en ejercicio y estudiantes de último semestre en Licenciatura de Matemáticas y Física de la Universidad del Valle, y apoyada en el análisis de unas actividades piloto de intervención y evaluación matemática, en torno a diferentes nociones y conceptos relacionados con la estructura conceptual del tópico de proporción y proporcionalidad en los grados de séptimo de educación básica y décimo de educación media que se realizaron a fin de plantear una serie de interrogantes cruciales en torno a la evaluación, dado su carácter organizador, dinamizador y potencializador del currículo. Esta propuesta se apoyará en el marco metodológico de los organizadores del currículo, donde la evaluación es un eje fundamental en el análisis didáctico que permite la articulación y organización de un currículo significativo para los intereses de los educandos

Small volume expansion of almost supersymmetric large N theories

We consider the small-volume dynamics of nonsupersymmetric orbifold and orientifold field theories defined on a three-torus, in a test of the claimed planar equivalence between these models and appropriate supersymmetric ``parent models". We study one-loop effective potentials over the moduli space of flat connections and find that planar equivalence is preserved for suitable averages over the moduli space. On the other hand, strong nonlinear effects produce local violations of planar equivalence at special points of moduli space. In the case of orbifold models, these effects show that the "twisted" sector dominates the low-energy dynamics.Comment: 20 pages, 3 figures; added references, minor change