The AddACO: A bio-inspired modified version of the ant colony optimization algorithm to solve travel salesman problems

The Travel Salesman Problem (TSP) consists in finding the minimal-length closed tour that connects the entire group of nodes of a given graph. We propose to solve such a combinatorial optimization problem with the AddACO algorithm: it is a version of the Ant Colony Optimization method that is characterized by a modified probabilistic law at the basis of the exploratory movement of the artificial insects. In particular, the ant decisional rule is here set to amount in a linear convex combination of competing behavioral stimuli and has therefore an additive form (hence the name of our algorithm), rather than the canonical multiplicative one. The AddACO intends to address two conceptual shortcomings that characterize classical ACO methods: (i) the population of artificial insects is in principle allowed to simultaneously minimize/maximize all migratory guidance cues (which is in implausible from a biological/ecological point of view) and (ii) a given edge of the graph has a null probability to be explored if at least one of the movement trait is therein equal to zero, i.e., regardless the intensity of the others (this in principle reduces the exploratory potential of the ant colony). Three possible variants of our method are then specified: the AddACO-V1, which includes pheromone trail and visibility as insect decisional variables, and the AddACO-V2 and the AddACO-V3, which in turn add random effects and inertia, respectively, to the two classical migratory stimuli. The three versions of our algorithm are tested on benchmark middle-scale TPS instances, in order to assess their performance and to find their optimal parameter setting. The best performing variant is finally applied to large-scale TSPs, compared to the naive Ant-Cycle Ant System, proposed by Dorigo and colleagues, and evaluated in terms of quality of the solutions, computational time, and convergence speed. The aim is in fact to show that the proposed transition probability, as long as its conceptual advantages, is competitive from a performance perspective, i.e., if it does not reduce the exploratory capacity of the ant population w.r.t. the canonical one (at least in the case of selected TSPs). A theoretical study of the asymptotic behavior of the AddACO is given in the appendix of the work, whose conclusive section contains some hints for further improvements of our algorithm, also in the perspective of its application to other optimization problems

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

Computational approaches for translational oncology: Concepts and patents

Background: Cancer is a heterogeneous disease, which is based on an intricate network of processes at different spatiotemporal scales, from the genome to the tissue level. Hence the necessity for the biomedical and pharmaceutical research to work in a multiscale fashion. In this respect, a significant help derives from the collaboration with theoretical sciences. Mathematical models can in fact provide insights into tumor-related processes and support clinical oncologists in the design of treatment regime, dosage, schedule and toxicity. Objective and Method: The main objective of this article is to review the recent computational-based patents which tackle some relevant aspects of tumor treatment. We first analyze a series of patents concerning the purposing the purposing or repurposing of anti-tumor compounds. These approaches rely on pharmacokinetics and pharmacodynamics modules, that incorporate data obtained in the different phases of clinical trials. Similar methods are also at the basis of other patents included in this paper, which deal with treatment optimization, in terms of maximizing therapy efficacy while minimizing side effects on the host. A group of patents predicting drug response and tumor evolution by the use of kinetics graphs are commented as well. We finally focus on patents that implement informatics tools to map and screen biological, medical, and pharmaceutical knowledge. Results and Conclusions: Despite promising aspects (and an increasing amount of the relative literature), we found few computational-based patents: There is still a significant effort to do for allowing modelling approaches to become an integral component of the pharmaceutical research

MULTISCALE EXTENSIONS OF THE CELLULAR POTTS MODELS: TOWARD A NESTED-HYBRID APPROACH

Multiscale problems are ubiquitous in all biological phenomena, which emerge from the complex interaction between processes happening at various levels and in particular from the relationship between the subcellular genomic and proteomic dynamics and the behavior of the cell. In order to deals with such an intricate network of organization, this work discusses some innovative extensions of the cellular Potts model (CPM), a discrete, lattice-based, technique able to reproduce and analyze innumerable biological phenomena. The aim is to increase the accuracy of the method and to create a multilevel framework able to deal with the multiscale complexity typical of biological development. The proposed CPM extensions are nally tested with sample applications, that show their potential and biological realism

Extension of tumor fingers: A comparison between an individual-cell based model and a measure theoretic approach

The invasive capability is fundamental in determining the malignancy of a solid tumor. In particular, tumor invasion fronts are characterized by different morphologies, which result both from cell-based processes (such as cell elasticity, adhesive properties and motility) and from subcellular molecular dynamics (such as growth factor internalization, ECM protein digestion and MMP secretion). Of particular relevance is the development of tumors with unstable fingered morphologies: they are in fact more aggressive and hard to be treated than smoother ones as, even if their invasive depth is limited, they are diffcult to be surgically removed. The phenomenon of malignant fingering has been reproduced with several mathematical approaches. In this respect, we here present a qualitative comparison between the results obtained by an individual cell-based model (an extended version of the cellular Potts model) and by a measure-based theoretic method. In particular, we show that in both cases a fundamental role in nger extension is played by intercellular adhesive forces and taxis-like migration

MULTISCALE MODEL OF TUMOR-DERIVED CAPILLARY-LIKE NETWORK FORMATION

Solid tumors recruit and form blood vessels, used for maintenance and growth as well as for formation and spread of metastases. Vascularization is therefore a pivotal switch in cancer malignancy: an accurate analysis of its driving processes is a big issue for the development of treatments. In vitro experiments have demonstrated that cultured tumor-derived endothelial cells (TECs) are able to organize in a connected network, which mimics an in vivo capillary-plexus. The process, called tubulogenesis, is promoted by the activity of soluble peptides (such as VEGFs), as well as by the following intracellular calcium signals. We here propose a multilevel approach, reproducing selected features of the experimental system: it incorporates a continuous model of microscopic VEGF-induced events in a discrete mesoscopic Cellular Potts Model (CPM). The two components are interfaced, producing a multiscale framework characterized by a constant ux of information from ner to coarser levels. The simulation results, in agreement with experimental analysis, allow to identify the key mechanisms of network formation. In particular, we provide evidence that the nascent pattern is characterized by precise topological properties, regulated by the initial cell density in conjunction with the degree of the chemotactic response and the directional persistence of cell migration

MAIN FEATURES OF A 3D GIS FOR A MONUMENTAL COMPLEX WITH AN HISTORICAL-CULTURAL RELEVANCE

The last achievements of technologies in geomatics especially in survey and restitution of 3D models (UAV/drones and laser scanner technologies) generated new procedures and higher standards of quality in representation of archaeological sites. Together with Geomatics, the recent development of Information and Communication Technologies (ICT) strongly contribute to document and the Cultural Heritage (CH). The representation and documentation of CH using these new technologies has became necessary in order to satisfy different needs: – for restorers in order to acquire a deep knowledge of the cultural good and to define possible strategies of restoration; – for the conservation of information, allowing to preserve the 3D geometry of the monumental complex with the integration of descriptions about architectural elements; – for touristic aims, giving the opportunity of sharing CH information on web, allowing users to visit and explore, in a virtual way, monumental complexes, acquiring information details about architectural elements or the history of monumental complex. Looking through these new scenarios, the development of a 3D Geographic Information System (GIS) applied to a cultural good could be, today, an added value of fundamental importance for full description and data management of monumental complexes. In this work, the main features necessary for the correct construction of a 3D GIS of a monumental complex will be analyzed, with a particular focus on the possibilities for creating a standardized procedure to follow

Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles

The description of the cell spatial pattern and characteristic distances is fundamental in a wide range of physio-pathological biological phenomena, from morphogenesis to cancer growth. Discrete particle models are widely used in this field, since they are focused on the cell-level of abstraction and are able to preserve the identity of single individuals reproducing their behavior. In particular, a fundamental role in determining the usefulness and the realism of a particle mathematical approach is played by the choice of the intercellular pairwise interaction kernel and by the estimate of its parameters. The aim of the paper is to demonstrate how the concept of H-stability, deriving from statistical mechanics, can have important implications in this respect. For any given interaction kernel, it in fact allows to a priori predict the regions of the free parameter space that result in stable configurations of the system characterized by a finite and strictly positive minimal interparticle distance, which is fundamental when dealing with biological phenomena. The proposed analytical arguments are indeed able to restrict the range of possible variations of selected model coefficients, whose exact estimate however requires further investigations (e.g., fitting with empirical data), as illustrated in this paper by series of representative simulations dealing with cell colony reorganization, sorting phenomena and zebrafish embryonic development

Collective migration and patterning during early development of zebrafish posterior lateral line

The morphogenesis of zebrafish posterior lateral line (PLL) is a good predictive model largely used in biology to study cell coordinated reorganization and collective migration regulating pathologies and human embryonic processes. PLL development involves the formation of a placode formed by epithelial cells with mesenchymal characteristics which migrates within the animal myoseptum while cyclically assembling and depositing rosette-like clusters (progenitors of neuromast structures). The overall process mainly relies on the activity of specific diffusive chemicals, which trigger collective directional migration and patterning. Cell proliferation and cascade of phenotypic transitions play a fundamental role as well. The investigation on the mechanisms regulating such a complex morphogenesis has become a research topic, in the last decades, also for the mathematical community. In this respect, we present a multiscale hybrid model integrating a discrete approach for the cellular level and a continuous description for the molecular scale. The resulting numerical simulations are then able to reproduce both the evolution of wild-type (i.e. normal) embryos and the pathological behaviour resulting form experimental manipulations involving laser ablation. A qualitative analysis of the dependence of these model outcomes from cell-cell mutual interactions, cell chemical sensitivity and internalization rates is included. The aim is first to validate the model, as well as the estimated parameter values, and then to predict what happens in situations not tested yet experimentally. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'