Strong-majority bootstrap percolation on regular graphs with low dissemination threshold

International audienceConsider the following model of strong-majority bootstrap percolation on a graph. Let r ≥ 1 be some integer, and p ∈ [0, 1]. Initially, every vertex is active with probability p, independently from all other vertices. Then, at every step of the process, each vertex v of degree deg(v) becomes active if at least (deg(v) + r)/2 of its neighbours are active. Given any arbitrarily small p > 0 and any integer r, we construct a family of d = d(p, r)-regular graphs such that with high probability all vertices become active in the end. In particular, the case r = 1 answers a question and disproves a conjecture of Rapaport, Suchan, Todinca and Verstraëte [38]

Thermodynamics of percolation in interacting systems

Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it remains unknown how the dynamics characterized by percolation is related to the thermodynamics of phase transitions. It is non-trivial to formalize thermodynamics for most complex systems, not to mention calculating thermodynamic quantities and verifying scaling relations during percolation. In this work, we develop a formalism to quantify the thermodynamics of percolation in interacting systems, which is rooted in a discovery that percolation transition is a process for the system to lose the freedom degrees associated with ground state configurations. We derive asymptotic formulas to accurately calculate entropy and specific heat under our framework, which enables us to detect phase transitions and demonstrate the Rushbrooke equality (i.e., $\alpha+2\beta+\gamma=2$) in six representative complex systems (e.g., Bernoulli and bootstrap percolation, classical and quantum synchronization, non-linear oscillations with damping, and cellular morphogenesis). These results suggest the general applicability of our framework in analyzing diverse interacting systems and percolation processes

Cancer therapeutic potential of combinatorial immuno- and vaso-modulatory interventions

Currently, most of the basic mechanisms governing tumor-immune system interactions, in combination with modulations of tumor-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumor growth, where the main novelty is the modeling of the interplay between functional tumor vasculature and effector cell recruitment dynamics. Parameters are calibrated on the basis of different in vivo immunocompromised Rag1-/- and wild-type (WT) BALB/c murine tumor growth experiments. The model analysis supports that tumor vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immuno-stimulations. We find that improved levels of functional tumor vasculature, potentially mediated by normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumor burden reduction and growth control. Normalization of tumor blood vessels opens a therapeutic window of opportunity to augment the antitumor immune responses, as well as to reduce the intratumoral immunosuppression and induced-hypoxia due to vascular abnormalities. The potential success of normalizing tumor-associated vasculature closely depends on the effector cell recruitment dynamics and tumor sizes. Furthermore, an arbitrary increase of initial effector cell concentration does not necessarily imply a better tumor control. We evidence the existence of an optimal concentration range of effector cells for tumor shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immuno- and vaso-modulatory interventions

Diffuse and Localized Functional Dysconnectivity in Schizophrenia: a Bootstrapped Top-Down Approach

Schizophrenia (SZ) is a brain disorder leading to detached mind's normally integrated processes. Hence, the exploration of the symptoms in relation to functional connectivity (FC) had great relevance in the field. FC can be investigated on different levels, going from global features to single edges between regions, revealing diffuse and localized dysconnection patterns. In this context, SZ is characterized by a diverse global integration with reduced connectivity in specific areas of the Default Mode Network (DMN). However, the assessment of FC presents various sources of uncertainty. This study proposes a multi-level approach for more robust group-comparison. FC between 74 AAL brain areas of 15 healthy controls (HC) and 12 SZ subjects were used. Multi-level analyses and graph topological indexes evaluation were carried out by the previously published SPIDER-NET tool. Robustness was augmented by bootstrapped (BOOT) data and the stability was evaluated by removing one (RST1) or two subjects (RST2). The DMN subgraph was evaluated, toegether with overall local indexes and connection weights to enhance common activations/deactivations. At a global level, expected trends were found. The robustness assessment tests highlighted more stable results for BOOT compared to the direct data testing. Conversely, significant results were found in the analysis at lower levels. The DMN highlighted reduced connectivity and strength as well as increased deactivation in the SZ group. At local level, 13 areas were found to be significantly different ($p<0.05$), highlighting a greater divergence in the frontal lobe. These results were confirmed analyzing the negative edges, suggesting inverted connectivity between prefronto-temporal areas. In conclusion, multi-level analysis supported by BOOT is highly recommended, especially when diffuse and localized dysconnections must be investigated in limited samples.Comment: 28 pages, 8 figure