Weak Modularity Research Articles

Investigation of Salmonella Phage-Bacteria Infection Profiles: Network Structure Reveals a Gradient of Target-Range from Generalist to Specialist Phage Clones in Nested Subsets.

Bacteriophages that lyse Salmonella enterica are potential tools to target and control Salmonella infections. Investigating the host range of Salmonella phages is a key to understand their impact on bacterial ecology, coevolution and inform their use in intervention strategies. Virus–host infection networks have been used to characterize the “predator–prey” interactions between phages and bacteria and provide insights into host range and specificity. Here, we characterize the target-range and infection profiles of 13 Salmonella phage clones against a diverse set of 141 Salmonella strains. The environmental source and taxonomy contributed to the observed infection profiles, and genetically proximal phages shared similar infection profiles. Using in vitro infection data, we analyzed the structure of the Salmonella phage–bacteria infection network. The network has a non-random nested organization and weak modularity suggesting a gradient of target-range from generalist to specialist species with nested subsets, which are also observed within and across the different phage infection profile groups. Our results have implications for our understanding of the coevolutionary mechanisms shaping the ecological interactions between Salmonella phages and their bacterial hosts and can inform strategies for targeting Salmonella enterica with specific phage preparations.

Interacto: A Modern User Interaction Processing Model

Since most software systems provide their users with interactive features, building user interfaces (UI) is one of the core software engineering tasks. It consists in designing, implementing and testing ever more sophisticated and versatile ways for users to interact with software systems, and safely connecting these interactions with commands querying or modifying their state. However, most UI frameworks still rely on a low level model, the bare bone UI event processing model. This model was suitable for the rather simple UIs of the early 80s (menus, buttons, keyboards, mouse clicks), but now exhibits major software engineering flaws for modern, highly interactive UIs. These flaws include lack of separation of concerns, weak modularity and thus low reusability of code for advanced interactions, as well as low testability. To mitigate these flaws, we propose Interacto as a high level user interaction processing model. By reifying the concept of user interaction, Interacto makes it easy to design, implement and test modular and reusable advanced user interactions, and to connect them to commands with built-in undo/redo support. To demonstrate its applicability and generality, we briefly present two open source implementations of Interacto for Java/JavaFX and TypeScript/Angular. We evaluate Interacto interest (1) on a real world case study, where it has been used since 2013, and with (2) a controlled experiment with 44 master students, comparing it with traditionnal UI frameworks.

Dynamics of holomorphic correspondences on Riemann surfaces

We study the global dynamics of holomorphic correspondences [Formula: see text] on a compact Riemann surface [Formula: see text] in the case, so far not well understood, where [Formula: see text] and [Formula: see text] have the same topological degree. In the absence of a mild and necessary obstruction that we call weak modularity, [Formula: see text] admits two canonical probability measures [Formula: see text] and [Formula: see text] which are invariant by [Formula: see text] and [Formula: see text] respectively. If the critical values of [Formula: see text] (respectively, [Formula: see text]) are not periodic, the backward (respectively, forward) orbit of any point [Formula: see text] equidistributes towards [Formula: see text] (respectively, [Formula: see text]), uniformly in [Formula: see text] and exponentially fast.

Dental integration and modularity in pinnipeds

Morphological integration and modularity are important for understanding phenotypic evolution because they constrain variation subjected to selection and enable independent evolution of functional and developmental units. We report dental integration and modularity in representative otariid (Eumetopias jubatus, Callorhinus ursinus) and phocid (Phoca largha, Histriophoca fasciata) species of Pinnipedia. This is the first study of integration and modularity in a secondarily simplified dentition with simple occlusion. Integration was stronger in both otariid species than in either phocid species and related positively to dental occlusion and negatively to both modularity and tooth-size variability across all the species. The canines and third upper incisor were most strongly integrated, comprising a module that likely serves as occlusal guides for the postcanines. There was no or weak modularity among tooth classes. The reported integration is stronger than or similar to that in mammals with complex dentition and refined occlusion. We hypothesise that this strong integration is driven by dental occlusion, and that it is enabled by reduction of modularity that constrains overall integration in complex dentitions. We propose that modularity was reduced in pinnipeds during the transition to aquatic life in association with the origin of pierce-feeding and loss of mastication caused by underwater feeding.

Relations Between the Geometry of Cortical Gyrification and White-Matter Network Architecture

A geometrically based network model of cortico-cortical white-matter connectivity is used in combination with diffusion spectrum MRI (DSI) data to show that white-matter cortical network architecture is founded on a homogeneous, isotropic geometric connection principle. No other special information about single connections or groups of connections is required to generate networks very similar to experimental ones. This model provides excellent agreement with experimental DSI frequency distributions of network measures-degree, clustering coefficient, path length, and betweenness centrality. In the model, these distributions are a result of geometrically induced spatial variations in the values of these measures with deep nodes having more hublike properties than superficial nodes. This leads to experimentally testable predictions of corresponding variations in real cortexes. The convoluted geometry of the cortex is also found to introduce weak modularity, similar to the lobe structure of the cortex, with the boundaries between modules having hublike properties. These findings mean that some putative discoveries regarding the structure of white-matter cortical networks are simply artifacts and/or consequences of geometry. This model may help provide insight into diseases associated with differences in gyrification as well as evolutionary development of the cortex.

On the Orthocomplementation of State–Property–Systems of Contextual Systems

We adopt an operational approach to quantum mechanics in which a physical system is defined by the mathematical structure of its set of states and properties. We present a model in which the maximal change of state of the system due to interaction with the measurement context is controlled by a parameter which corresponds with the number N of possible outcomes in an experiment. In the case N=2 the system reduces to a model for the spin measurements on a quantum spin-1/2 particle. In the limit N→∞ the system is classical, i.e. the experiments are deterministic and its set of properties is a Boolean lattice. For intermediate situations the change of state due to measurement is neither ‘maximal’ (i.e. quantum) nor ‘zero’ (i.e. classical). We show that two of the axioms used in Piron’s representation theorem for quantum mechanics are violated, namely the covering law and weak modularity. Next, we discuss a modified version of the model for which it is even impossible to define an orthocomplementation on the set of properties. Another interesting feature for the intermediate situations of this model is that the probability of a state transition in general not only depends on the two states involved, but also on the measurement context which induces the state transition.

Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity

A network of 32 or 64 connected neural masses, each representing a large population of interacting excitatory and inhibitory neurons and generating an electroencephalography/magnetoencephalography like output signal, was used to demonstrate how an interaction between dynamics and connectivity might explain the emergence of complex network features, in particular modularity. Network evolution was modeled by two processes: (i) synchronization dependent plasticity (SDP) and (ii) growth dependent plasticity (GDP). In the case of SDP, connections between neural masses were strengthened when they were strongly synchronized, and were weakened when they were not. GDP was modeled as a homeostatic process with random, distance dependent outgrowth of new connections between neural masses. GDP alone resulted in stable networks with distance dependent connection strengths, typical small-world features, but no degree correlations and only weak modularity. SDP applied to random networks induced clustering, but no clear modules. Stronger modularity evolved only through an interaction of SDP and GDP, with the number and size of the modules depending on the relative strength of both processes, as well as on the size of the network. Lesioning part of the network, after a stable state was achieved, resulted in a temporary disruption of the network structure. The model gives a possible scenario to explain how modularity can arise in developing brain networks, and makes predictions about the time course of network changes during development and following acute lesions.

A Helly theorem in weakly modular space

The d-convex sets in a metric space are those subsets which include the metric interval between any two of its elements. Weak modularity is a certain interval property for triples of points. The d-convexity of a discrete weakly modular space X coincides with the geodesic convexity of the graph formed by the two-point intervals in X. The Helly number of such a space X turns out to be the same as the clique number of the associated graph. This result thus entails a Helly theorem for quasi-median graphs, pseudo-modular graphs, and bridged graphs.

Rise and fall of modular orthodoxy

The premise of cortical modularity is based on strong dissociations caused by focal lesions. These dissociations are rare, and their explanatory power and theoretical importance are vastly overrated. The effects of brain lesions must be considered in their totality, rather than in idiosyncratic selectivity. These effects are more consistent with a continuous, graded functional neocortical geometry, than with a modular neocortex. Distinction must be drawn between strong intrinsic modularity, and weak emergent modularity. Strong intrinsic modularity is more characteristic of the thalamus than of the cortex. The advent of neocortex may have represented an evolutionary escape from strong modularity as the dominant principle of neural organization, and a shift toward a more interactive principle of neural organization dominated by emergent properties. The latter may take the form of weak modularity, reflective of cognitive skill routinization. The extent of weak, emergent modularization may be asymmetric, more pronounced in the left hemisphere, while the right hemisphere is essentially amodular.

Classical foundations of quantum logic

We construct a languageL for a classical first-order predicate calculus with monadic predicates only, extended by means of a family of statistical quantifiers. Then, a formal semantic model\(\mathfrak{M}\) is put forward forL which is compatible with a physical interpretation and embodies a truth theory which provides the statistical quantifiers with properties that fit their interpretation; in this framework, the truth mode of physical laws is suitably characterized and a probability-frequency correlation principle is established. By making use ofL and\(\mathfrak{M}\), a set of basic physical laws is stated that hold both in classical physics (CP) and in quantum physics (QP), which allow the selection of suitable subsets of primitive predicates ofL (the setℒP of pure states; the setsℰo andℰE of operational and exact effects, respectively) and the introduction on these subsets of binary relations (a preclusion relation # onℒP, an order relation < onℰE. By assuming further physical laws, (ℰE, <) turns out to be a complete orthocomplemented lattice [mixtures and atomicity of (ℰE, <) also can be introduced by means of suitable physical assumptions]. Two languagesLEx andLES are constructed that can be mapped intoL; the mapping induces on them mathematical structures, some kind of truth function, an interpretation. The formulas ofLEx can be interpreted as statements about properties of a physical object, and the truth function onLEx is two valued. The formulas ofLES can be endowed with two different interpretations as statements about the frequency of some physical property in some class (state) of physical objects; consequently, a two-valued truth function and a multivalued fuzzy-truth function are defined onLES. In all cases the algebras of propositions of these “logics” are complete orthocomplemented lattices isomorphic to (ℰE, <). These results hold both in CP and in QP; further physical assumptions endow the lattice (ℰE, <), henceLEx andLE/S, with further properties, such as distributivity in CP and weak modularity and covering law in QP. In the latter case,LES andLES, together with their interpretations, can be considered different models of the same basic mathematical structure, and can be identified with standard (elementary) quantum logics. These are therefore founded on the classical extended languageL with semantic model\(\mathfrak{M}\).

Semimodularity and weak modularity in subalgebra lattices of completely simple semigroups

Semimodularity and weak modularity in subalgebra lattices of completely simple semigroups

Propositional systems and measurements—I

A direct approach to propositional systems, influenced by the exposition of Jauch & Piron (1968), is formulated. Further motivations and interpretations in experimental terms are given and worked out explicitly. The orthocomplementation is introduced independent of weak modularity by two postulates on the set of questions. Weak modularity and atomicity are reduced to requirements on the set of preparation procedures. It is shown that preparative measurements are not needed in order to impose the covering law. The latter can also be reduced to a postulate on the set of preparations.