Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect ...copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris–Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A. These segments are validated by the TCGA BRCA cohort dataset except for those found for Luminal A.
On Self-Aggregations of Min-Subgroups Bejines, Carlos; Ardanza-Trevijano, Sergio; Elorza, Jorge
Axioms,
08/2021, Volume:
10, Issue:
3
Journal Article
Peer reviewed
Open access
Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in ...mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions. However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.
Numerous problems encountered in computational biology can be formulated as optimization problems. In this context, optimization of drug release characteristics or dosing schedules for anticancer ...agents has become a prominent area not only for the development of new drugs, but also for established drugs. However, in complex systems, optimization of drug exposure is not a trivial task and cannot be efficiently addressed through trial-error simulation exercises. Finding a solution to those problems is a challenging task which requires more advanced strategies like optimal control theory. In this work, we perform an optimal control analysis on a previously developed computational model for the testosterone effects of triptorelin in prostate cancer patients with the goal of finding optimal drug-release characteristics. We demonstrate how numerical control optimization of non-linear models can be used to find better therapeutic approaches in order to improve the final outcome of the patients.
Aggregation of fuzzy graphs Talavera, Francisco Javier; Bejines, Carlos; Ardanza-Trevijano, Sergio ...
International journal of approximate reasoning,
September 2024, 2024-09-00, Volume:
172
Journal Article
Peer reviewed
Open access
Our study is centered on the aggregation of fuzzy graphs, looking for conditions under which the aggregation process yields another fuzzy graph. We conduct an in-depth analysis of the preservation of ...several important properties and structures inherent to fuzzy graphs, like paths, cycles, or bridges. In addition we obtain appropriate criteria for when the aggregation of complete fuzzy graphs is again a complete fuzzy graph.
Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life-specific experiences. How humans organize semantic information remains poorly ...understood. In an effort to better understand this issue, we conducted a verbal fluency experiment on 200 participants with the aim of inferring and representing the conceptual storage structure of the natural category of animals as a network. This was done by formulating a statistical framework for co-occurring concepts that aims to infer significant concept–concept associations and represent them as a graph. The resulting network was analyzed and enriched by means of a missing links recovery criterion based on modularity. Both network models were compared to a thresholded co-occurrence approach. They were evaluated using a random subset of verbal fluency tests and comparing the network outcomes (linked pairs are clustering transitions and disconnected pairs are switching transitions) to the outcomes of two expert human raters. Results show that the network models proposed in this study overcome a thresholded co-occurrence approach, and their outcomes are in high agreement with human evaluations. Finally, the interplay between conceptual structure and retrieval mechanisms is discussed.
Recent developments have meant that network theory is making an important contribution to the topological study of biological networks, such as protein-protein interaction (PPI) networks. The ...identification of differentially expressed genes in DNA array experiments is a source of information regarding the molecular pathways involved in disease. Thus, considering PPI analysis and gene expression studies together may provide a better understanding of multifactorial neurodegenerative diseases such as Multiple Sclerosis (MS) and Alzheimer disease (AD). The aim of this study was to assess whether the parameters of degree and betweenness, two fundamental measures in network theory, are properties that differentiate between implicated (seed-proteins) and non-implicated nodes (neighbors) in MS and AD. We used experimentally validated PPI information to obtain the neighbors for each seed group and we studied these parameters in four networks: MS-blood network; MS-brain network; AD-blood network; and AD-brain network.
Specific features of seed-proteins were revealed, whereby they displayed a lower average degree in both diseases and tissues, and a higher betweenness in AD-brain and MS-blood networks. Additionally, the heterogeneity of the processes involved indicate that these findings are not pathway specific but rather that they are spread over different pathways.
Our findings show differential centrality properties of proteins whose gene expression is impaired in neurodegenerative diseases.
Preface Ardanza-Trevijano, Sergio; Chasco, María Jesús; Hofmann, Karl H. ...
Topology and its applications,
06/2012, Volume:
159, Issue:
9
Journal Article
We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping ...process by means of both simulations and experiments. States with equal packing fraction obtained with different tapping intensities are distinguished after the introduction of a filtration parameter which determines the particles (nodes in the network) that are joined by an edge. We first use numerical simulations to characterize the effect of the precision in the particles localization by artificially adding different levels of noise in this magnitude. The outcomes obtained for the simulations are then compared with the experimental results allowing a clear distinction of experimental packings that have the same density. This is accomplished by just using the position of the particles and no other information about the possible contacts, or magnitude of forces.
In this paper, for a given space
X, a structural category
C
, and a faithful functor η from
C
to the category of spaces, we introduce a notion of (
C
, η)-bundle which contains as particular cases, ...the notions of covering space, of overlaying space (introduced by Fox), of suspension foliation and other well-known topological structures.
The new notion allows us to use sheaf theory and category theory in order to obtain some classification theorems which appear in terms of equivalences of categories. We prove that the category (
C
, η)-bundle(X) of (
C
, η)-bundles over
X is equivalent to the category
pro(πCX,
C)
, which is determined by the fundamental groupoid of
X and the structural category
C
. As particular cases we obtain the standard classification of covering spaces, Fox's classification theorem for overlays with a finite number of leaves and the standard classification of suspension foliations.
This paper illustrates the importance of the fundamental progroupoid of a space
X, which plays in shape theory the role of the standard fundamental groupoid. If the space
X satisfies some additional properties, the progroupoid
πCX can be reduced to a surjective progroup, a groupoid or a group. In some cases a surjective progroupoid can be replaced by a topological prodiscrete group. In all these cases the category
pro(πCX,
C)
also reduces to well-known categories.
PDF
