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A graph is any abstract object that consists of vertices and edges. This entry presents the main attributes of vertices and edges.

The word “pattern” is a very complex term. Generally, it refers to “an arrange- ment that reveals an order, or design, which is meaningful” (cf. Thaker 1999: 427). But a quick look at many of its different domains of application (e.g. theoretical biology, mathematics, aesthetics, linguistics, etc., etc.) proves that “pattern” has a semantic potential richer than one usually expressed by such a definition. For instance, in the framework of the so-called combinatorics on words (cf. at least Lothaire 2012), a pattern is “a word over an alphabet of variables and is meant to describe some kind of repetitive structures” (cf. Rampersard 2017: 98). Therefore, in this first theoretical approach, “the pattern XX over the single variable X is meant to describe the repetition of the same word twice in succession” (cf. Rampersard 2017: 98).

“Homology is probably the most important concept in comparative biology. It has been treated in different ways, however, and more than one concept of homology is probably defensible” (Minelli 1994: 18); “Homology is one of the terms most widely employed in biology. Together with species, gene and a few others, it is likely to occur in texts devoted to the most diverse biological disciplines, from MORPHOLOGY to systematics to molecular genetics.

In the Elements of Geometry, Euclid defines the line as “a length without breadth,” an element without width and depth. The concept of line occurs in propositions, both theorems and proofs, given the postulates that it is possible to draw a straight line between any two points and to extend continuously any line. In Euclid’s Optics, lines are the subject of theorems. Rubin studied the perceptual conditions that could have given an intuitive contribution to the definition of geometrical objects that like in Euclid’s geometry do not occur in experience, yet have a relation with visual constructions. Pictures exploit markings endowed with perceptual linearity and continuity which realize lines. To convey meaning, namely to enable observers seeing the shape of pictured objects, lines obey a grammar that rules their type and combination. Moreover, lines stand for discontinuities that allow observers to sample the structure of the environment.

The conceptual couple CHARACTER/STATE is an ideal candidate to demonstrate the virtues of a morphological way of proceeding that allows historically distinct disciplinary horizons to dialogue in order to achieve a new disciplinary synthesis (Love 2003) and first of all in order to reach a new morphological lexicon, aware of the traditions of reference and of the mutual advantage arising from the dialogue itself.

We introduce some formal definition of Topological Space in the the framework of the so-called classical mathematics.

The concept of chreod was introduced in 1957 by the English theoretical biologist Conrad Hal Waddington (cf. Waddington: 1957; Galperin: 2008). From a linguistic point of view, the word “chreod” is a neologism, or, more precisely, a compound formed by the combination of two Greek words: the verb chre- (“it is necessary, must”) and the substantive -hodos (“way, road”). Therefore, it means literally “obliged pathway” (cf. Fabris 2018: 252, n. 6). Of course, such an etymology covers only a little bit of the semantic repertoire deployed by chreod. But, it is however true that some aspects of the biology of living systems can be described in these terms. Indeed, at the most general level, the idea of chreod as “obliged pathway” finds a good empirical fit to the morphological development of embryonic tissues. With particular reference to this point, it is common to define a chreod as “an orderly sequence of developmental stages”.

The notion of structural stability was first introduced by the Russian math- ematicians Alexandr Andronov and Lev Pontryagin (cf. Andronov and Potryangin 1937). However, there are traces of such a concept in the work of the French math- ematician Henry Poincaré (cf. Poincaré 1880). In more recent years, interesting developments about structural stability included writings of important math- ematicians like Mauricìo Peixoto (cf. at least Peixoto 1960), Stephen Smale (cf. at least Smale 1971) and René Thom (1972, 1980) (see structural morpho- dynamics). From an intuitive point of view, structural stability refers to a particular systemic property known as robustness. Put in general terms, a system is robust “if it is invariant with respect to a set of perturbations” (Alderson and Doyle 2010: 840; Whitacre 2012: 3).

Intuition encompasses questions debated throughout philosophy. This entry treats intuition as a name for cognitive capacities according to the theory in which it is introduced.

The essay analyzes the notion of phenomenon referring to metaphysical, phenomenological and morphological tradition.

Since the first programmatic drafts devoted to MORPHOLOGY, Goethe establishes a very strong connection between the birth of the new science, a dynamic consideration of FORM, and the intent to reach the description of the procedures through which the FORM itself is produced, transformed, and perceived. In fact, the first private entry dedicated to MORPHOLOGY defines it as “Lehre von der Gestalt, der Bildung und Umbildung der organischen Körper”

The term perception denotes the capacity of grasping something that to the common sense belongs to external world, which is the stable and persistent collection of things that are the natural and man-made furniture of the environment. Perception denotes also the capacity of sensing something, like warmth or pain, that is the effect of an external or internal cause localized on or inside one’s own body. Therefore, perception has subjective and objective factors as constituents of its conditions of satisfaction. The activity of perception is describable in terms of the percept, namely the objective constituent of its conditions of satisfaction

Pictures are a presentation whose structure is decomposable into a surface, an arrangement of markings, the appearance of something in front of, before or behind the surface, the reference to a scene of the real or a possible world, whose aspects and concrete or abstract states of affairs are displayed by the appearance. Pictures are a kind of markings, namely patterns perceived on a surface, which do not yet convey information about it. Markings depend on surfaces. No marking exists without a surface, while the opposite is true. There is a variety of markings according to the technique and the tools chosen to produce them. Surfaces serve as a medium either as a support or as that which affords the properties for particular manipulations. The appearances, which occur on the basis of markings, regard the configurational property of pictures. Philosophical and psychological theories address issues concerning the struc- ture of pictures with distinct approaches.

Analogy is a mode of reasoning that is employed in problem solving, logic, science and art. The scheme of analogical reasoning is centred on the detection of similarity or common features across domains. Copi and Cohen (2005), Keynes (1921), Carnap (1980) suggested what analogical reasoning consists of. De Finetti (1938) proposed an alternative treatment of analogy as inference on what is invariant across statistical distributions of distinct event kinds. In problem solving theory, cognitive models of the content and the structural mapping of analogy has been built. Science and art has provided important test beds for models.

Il saggio si propone di evidenziare l’operatività, nella prospettiva di un’ontologia fenomenologica e dialettica, del nesso tra fenomeno ed essenza a partire dal reciproco implicarsi del visibile e dell’invisibile, e come alla luce della sua tematizzazione attuata da Merleau-Ponty sia possibile riprendere l’eredità vivente della metafisica.

The author discusses the reading of Sophocles Antigone by Giuseppe Nicolaci and this becomes the opportunity to address the issue of the birth of ethics. Antigone is thus summoned as a partner of a question that Nicolaci considers starting from Kant and Lacan.

Una ricognizione del contributo di Deleuze alla riflessione stetica contemporanea

SARS-CoV-2 is able to re-structure chromatin organization and alters the epigenomic landscape of the host genome, though the mechanisms that produce such changes are still poorly understood. Here, we investigate with polymer physics chromatin re-organization of the host genome, in space and time upon SARS-CoV-2 viral infection. We show that re-structuring of A/B compartments is well explained by a re-modulation of intra-compartment homotypic affinities, which leads to the weakening of A-A interactions and enhances A-B mixing. At TAD level, re-arrangements are physically described by a general reduction of the loop extrusion activity coupled with an alteration of chromatin phase-separation properties, resulting in more intermingling between different TADs and spread in space of TADs themselves. In addition, the architecture of loci relevant to the antiviral interferon (IFN) response, such as DDX58 or IFIT, results more variable within the 3D single-molecule population of the infected model, suggesting that viral infection leads to a loss of chromatin structural specificity. Analysis of time trajectories of pairwise gene-enhancer and higher-order contacts reveals that such variability derives from a more fluctuating dynamics in infected case, suggesting that SARS-CoV-2 alters gene regulation by impacting the stability of the contact network in time. Overall, our study provides the first polymer-physics based 4D reconstruction of SARS-CoV-2 infected genome with mechanistic insights on the consequent gene mis-regulation.

Extrachromosomal DNAs (ecDNAs) are found in the nucleus of an array of human cancer cells where they can form clusters that were associated to oncogene overexpression, as they carry genes and cis -regulatory elements. Yet, the mechanisms of aggregation and gene amplification beyond copy-number effects remain mostly unclear. Here, we investigate, at the single molecule level, MYC -harboring ecDNAs of COLO320-DM colorectal cancer cells by use of a minimal polymer model of the interactions of ecDNA BRD4 binding sites and BRD4 molecules. We find that BRD4 induces ecDNAs phase separation, resulting in the self-assembly of clusters whose predicted structure is validated against HiChIP data (Hung et al., 2021). Clusters establish in-trans associated contact domains (I-TADs) enriched, beyond copy number, in regulatory contacts among specific ecDNA regions, encompassing its PVT1-MYC fusions but not its other canonical MYC copy. That explains why the fusions originate most of ecDNA MYC transcripts (Hung et al., 2021), and shows that ecDNA clustering per se is important but not sufficient to amplify oncogene expression beyond copy-number, reconciling opposite views on the role of clusters (Hung et al., 2021; Zhu et al., 2021; Purshouse et al. 2022). Regulatory contacts become strongly enriched as soon as half a dozen ecDNAs aggregate, then saturate because of steric hindrance, highlighting that even cells with few ecDNAs can experience pathogenic MYC upregulations. To help drug design and therapeutic applications, with the model we dissect the effects of JQ1, a BET inhibitor. We find that JQ1 reverses ecDNA phase separation hence abolishing I-TADs and extra regulatory contacts, explaining how in COLO320-DM cells it reduces MYC transcription (Hung et al., 2021).