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Diseño de rúbricas destinadas a la evaluación de los trabajos de fin de grado y de fin de máster en la Facultad de Ciencias Matemáticas de la Universidad Complutense de Madrid. Se presentan modelos tanto para el tutor que dirige el trabajo como para el tribunal que debe evaluar la memoria realizada y su presentación.

CRUE-CSIC (Acuerdos Transformativos 2022), Gender-based crime is one of the most concerning scourges of contemporary society, and governments worldwide have invested lots of economic and human resources to foretell their occurrence and anticipate the aggressions. In this work, we propose to apply Machine Learning (ML) techniques to create models that accurately predict the recidivism risk of a gender-violence offender. We feed the model with data extracted from the official Spanish VioGen system and comprising more than 40,000 reports of gender violence. To evaluate the performance, two new quality measures are proposed to assess the effective police protection that a model supplies and the overload in the invested resources that it generates. The empirical results show a clear outperformance of the ML-centered approach, with an improvement of up to a 25% with respect to the preexisting risk assessment system. Additionally, we propose a hybrid model that combines the statistical prediction methods with the ML method, permitting authorities to implement a smooth transition from the preexisting model to the ML-based model. To the best of our knowledge, this is the first work that achieves an effective ML-based prediction for this type of crimes against an official dataset., Ministerio de Ciencia, Innovación y Universidades (España), Universidad Complutense de Madrid/Banco de Santander, Depto. de Análisis Matemático y Matemática Aplicada, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

When a new type of individual appears in a stable population, the newcomer is typically not advantageous. Due to stochasticity, the new type can grow in numbers, but the newcomers can only become advantageous if they manage to change the environment in such a way that they increase their fitness. This dynamics is observed in several situations in which a relatively stable population is invaded by an alternative strategy, for instance the evolution of cooperation among bacteria, the invasion of cancer in a multicellular organism and the evolution of ideas that contradict social norms. These examples also show that, by generating different versions of itself, the new type increases the probability of winning the struggle for fitness. Our model captures the imposed cooperation whereby the first generation of newcomers dies while changing the environment such that the next generations become more advantageous., Depto. de Biodiversidad, Ecología y Evolución, Fac. de Ciencias Biológicas, TRUE, pub

We compare using visibility the usual Kardar–Parisi–Zhang (KPZ) universality class and a fractional Edward–Wilkinson (EWf) equation with correlated noise, which share the same kinetic roughening exponents. The KPZ universality class is described by an equation in terms of the usual derivatives, uncorrelated noise and therefore is intrinsically local. The second model includes fractional powers of the Laplace operator and correlated noise, both of which are nonlocal. From their scaling properties, one could be tempted to conclude that both dynamics belong to the same universality class, specifically, to the KPZ universality class. However, this is a wrong conclusion that calls the attention against the indiscriminate application of this approach in real systems without taking into consideration basic physical assumptions (e.g. locality). These examples reveal the necessity of finding new algorithms for detecting characteristics that remain unnoticed to classical scaling analysis, where only the two first moments of the interface distribution (mean and variance) are used to classify the dynamics. We show that visibility and, in particular, the kinetic roughening exponents of the visibility interface, are able to distinguish between these two dynamics which are confused by standard techniques., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We consider growing interfaces as dynamical networks whose nodes are the discrete points of the interface and the edges the physical interactions among them. We map the points of the interface formed at each time into a graph by means of a visibility algorithm. As the corresponding interfaces grow, their visibility graphs change over time. We show that the visibility graphs are all scale free for each time. We use the variance of the node degrees as a measure of the dynamical properties of these graphs. This magnitude reveals an unexpected scaling behaviour of these graphs in both the number of nodes and time. This enables to define three robust exponents that characterize any type of dynamics with more detail than the classical scaling analysis applied directly to the physical interfaces. To check the feasibility of this approach we study and classify six different dynamical processes and estimate their critical exponents. We conclude that the dynamics of physical systems far from equilibrium can be determined by its corresponding visibility network. Indeed, this methodology is able to discern among dynamical processes that hitherto have been classified in the same universality class according to the scaling analysis of their interfaces., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Polymorphonuclear neutrophils (PMN) are the most abundant circulating immune cells and represent the first line of immune defense against infection. This review of the biomedical literature of the last 40 years shows that they also have a powerful antitumoral effect under certain circumstances. Typically, the microenvironment surrounding a solid tumor possesses many of the characteristics of chronic inflammation, a condition considered very favorable for tumor growth and spread. However, there are many circumstances that shift the chronic inflammatory state toward an acute inflammatory response around a tumor. This shift seems to convert PMN into very efficient anticancer effector cells. Clinical reports of unexpected antitumoral effects linked to the prolonged use of granulocyte colony-stimulating factor, which stimulates an intense and sustained neutrophilia, suggest that an easy way to fight solid tumors would be to encourage the development of intense peritumoral PMN infiltrates. Specifically designed clinical trials are urgently needed to evaluate the safety and efficacy of such drug-induced neutrophilia in patients with solid tumors. This antitumoral role of neutrophils may provide new avenues for the clinical treatment of cancer., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Background: Mycobacterium tuberculosis is a particularly aggressive microorganism and the host's defense is based on the induction of cellular immunity, in which the creation of a granulomatous structure has an important role. Methodology: We present here a new 2D cellular automata model based on the concept of a multifunctional process that includes key factors such as the chemokine attraction of the cells; the role of innate immunity triggered by natural killers; the presence of neutrophils; apoptosis and necrosis of infected macrophages; the removal of dead cells by macrophages, which induces the production of foamy macrophages (FMs); the life cycle of the bacilli as a determinant for the evolution of infected macrophages; and the immune response. Results: The results obtained after the inclusion of two degrees of tolerance to the inflammatory response triggered by the infection shows that the model can cover a wide spectrum, ranging from highly-tolerant (i.e. mice) to poorly-tolerant hosts (i.e. mini-pigs or humans). Conclusions: This model suggest that stopping bacillary growth at the onset of the infection might be difficult and the important role played by FMs in bacillary drainage in poorly-tolerant hosts together with apoptosis and innate lymphocytes. It also shows the poor ability of the cellular immunity to control the infection, provides a clear protective character to the granuloma, due its ability to attract a sufficient number of cells, and explains why an already infected host can be constantly reinfected., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

There is evidence that polymorphonuclear neutrophils (PMNs) can exert severe antineoplastic effects. Cross-talk between tumour cells and endothelial cells (ECs) is necessary for the accumulation of PMN around a tumour. This work reports the ability of two PMN-sensitive, human, permanent cell lines-colorectal adenocarcinoma (HT-29) and pharyngeal squamous-cell carcinoma (FaDu) cells-to act as inflammatory foci. PMNs were cytotoxic to both lines, the adhesion of the PMNs to the tumour cells being important in this effect. The tumour cells released appreciable amounts of IL-8 and GRO alpha, and induced the transmigration of PMN through human microvascular-EC monolayers. Conditioning media associated with both lines induced the adhesion of PMN and the surface expression of ICAM-1 in microvascular-EC. In addition, FaDu-conditioning-medium strongly induced the production of proinflammatory cytokines by microvascular-EC. These results support the idea that tumour cells might normally induce a potent acute inflammatory response, leading to their own destruction., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Tumour growth can be described in terms of mathematical models from different points of view due to its multiscale nature. Dynamic scaling is a heuristic discipline that exploits the geometrical features of growing fronts using different concepts from the theory of stochastic processes and fractal geometry. This work is concerned with some problems that arise in the study of tumour-host interfaces. The behaviour of their fluctuations leads to some stochastic evolution equations, which are studied here in the radial symmetry case. Some questions concerning the dynamic scaling of these models and their comparison with experimental results are addressed., European Contract, Universidad Complutense de Madrid, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This paper describes some experiments on the manner in which external pressure affects cell colony growth in general, and tumour growth in particular. More precisely, our results show that cell colony borders growing under high-pressure conditions have geometrical and dynamical properties that are markedly different from those corresponding to growth under homeostatic, normal pressure conditions. These behaviours are characterized by means of the so-called dynamical exponents of each type of growth. These are shown to correspond to statistical properties of solutions of some stochastic partial differential equations that account for the evolution of the interface between the expanding colony and the surrounding medium., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

6th International Workshop on Fractal Mathematics Applied to Soil and Related Heterogeneous Systems. JUL 02-06, 2004 El Barco de Avila, SPAIN, This paper reports experimental results regarding the scaling properties of wetting fronts during the hydration of repacked bentonite clay with a wide range of pore sizes (over five decades). The process of hydration in this swelling, heterogeneous, porous medium was analyzed using a Hele-Shaw hydration cell. In highly disordered media, anomalous diffusion of the hydration interface and the effect of capillary forces are best understood using a volume filling structure model. This concept of porous media also allows the changes in the position of the mean position of the interface and the water volume intake over time to be explained. The change in the mean interface position follows the expression < h(x,t)> proportional to t(y) with gamma being time dependent until pinning occurs. This is the first report of the pinning of a water interface in a natural porous medium as a consequence of the medium heterogeneity and capillary force disorder produced by the randomness of its pore sizes. The hydration process produced interfaces with a characteristic roughness described by an exponent of 0.63. The results obtained from these experiments reveal a phenomenology unexplained by current theoretical models. The process cannot be classified into any known universality class of dynamics., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This work is concerned with a model which has been proposed to describe the growth of solid tumors. More precisely, the model under consideration provides a procedure to extract information about the growth dynamics from the analysis of the geometrical properties of the interface tumor-host tissue. In particular, it is suggested that the tumor boundary should evolve according to some stochastic evolution equation. This is herein compared with other dynamic equations related to the growth of rough surfaces, and a number of questions concerning the asymptotics of the corresponding solutions (and its relation to that of their deterministic counterparts) are discussed., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Tumor growth is a surface phenomenon of the molecular beam epitaxy universality class in which diffusion at the surface is the determining factor. This Letter reports experiments performed in mice showing that these dynamics can, however, be changed. By stimulating the immune response, we induced strong neutrophilia around the tumor. The neutrophils hindered cell surface diffusion so much that they induced new dynamics compatible with the slower quenched-disorder Edwards-Wilkinson universality class. Important clinical effects were also seen, including remarkably high tumor necrosis (around 80%-90% of the tumor), a general increase in survival time [the death ratio in the control group is 15.76 times higher than in the treated group (equivalent to a Cox's model hazard ratio of 0.85; 95% confidence interval 0.76-0.95, p=0.004)], and even the total elimination of some tumors., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

The main goal of this letter is the scaling analysis of multivalued interfaces showing anomalous height fluctuations. A model of two-fluid transport through porous media is studied by means of dynamical scaling techniques. When the displacement is unstable, the interfaces are multivalued. In this paper we compare three definitions of the height function h(x, t). In our model we prove the kind of scaling to depend on the height function definition, and those anomalous fluctuations not to exist actually, as would be in many models and experiments exhibiting multivalued interfaces., Madrid Ciencia y Tecnología, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Scaling techniques were used to analyze the fractal nature of colonies of 15 cell lines growing in vitro as well as of 16 types of tumor developing in vivo. All cell colonies were found to exhibit exactly the same growth dynamics - which correspond to the molecular beam epitaxy (MBE) universality class. MBE dynamics are characterized by 1), a linear growth rate, 2), the constraint of cell proliferation to the colony/tumor border, and 3), surface diffusion of cells at the growing edge. These characteristics were experimentally verified in the studied colonies. That these should show MBE dynamics is in strong contrast with the currently established concept of tumor growth: the kinetics of this type of proliferation rules out exponential or Gompertzian growth. Rather, a clear linear growth regime is followed. The importance of new cell movements - cell diffusion at the tumor border - lies in the fact that tumor growth must be conceived as a competition for space between the tumor and the host, and not for nutrients or other factors. Strong experimental evidence is presented for 16 types of tumor, the growth of which cell surface diffusion may be the main mechanism responsible in vivo. These results explain most of the clinical and biological features of colonies and tumors, offer new theoretical frameworks, and challenge the wisdom of some current clinical strategies., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Presentamos un marco para describir el transporte de trazadores en medios heterogéneos, tales como los medios porosos tales como las bentonitas. En estos medios, la aproximación de campo medio no es válida ya que exiten ciertas restricciones geométricas y el transporte es anómalo., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

The growth of a cultivated typical brain tumor is studied in this work. The tumor is analyzed both dynamically and morphologically. We have measured its fractal dimension to be d(f) = 1.21 +/- 0.05. From its dynamical behavior we determine the scaling critical exponents of this circular symmetry system which are compatible with the linear molecular beam epitaxy universality class. A very important feature of tumor profiles is that they are super-rough, which constitutes the first (1 + 1)-dimensional experiment in literature with super-roughness. The results obtained from the dynamics study make manifest two very surprising features of tumor growth: Its dynamics is mainly due to contour cells and the tendency of an interface cell to duplicate is a function of the local curvature. [S0031-9007(98)07545-0]., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub