Int. J. Topol., Volume 2, Issue 2 (June 2025) – 5 articles

Persistent homology is a powerful tool in topological data analysis that captures the multi-scale topological features of data. In this work, we provide a mathematical introduction to persistent homology and demonstrate its application to protein–protein interaction networks. We combine persistent homology with algebraic connectivity, a graph-theoretic measure of network robustness, to analyze the topology and stability of PPI networks. An example is provided to illustrate the methodology and its potential applications in systems biology. Full article

A multicomplex structure is defined from an ordered lattice of multigraphs. This structure will help us to observe the features of persistent homology in this context, its interaction with the ordering, and the repercussions of merging multigraphs in the calculation of Betti numbers. For the latter, an extended version of the incremental algorithm is provided. The ideas developed here are mainly oriented to the original example described by the author and others in the context of the formalization of the notion of embodiment in Neuroscience. Full article

Raynaud’s Phenomenon (RP), characterized by episodic reductions in peripheral blood flow, leads to significant discomfort and functional impairment. Existing therapeutic strategies focus on pharmacological treatments, external heat supplementation and exercise-based rehabilitation, but fail to address biomechanical contributions to vascular dysfunction. We introduce a computational approach rooted in topological transformations of hand prehension, hypothesizing that specific hand postures can generate transient geometric structures that enhance thermal and hemodynamic properties. We examine whether a flexed hand posture—where fingers are brought together to form a closed-loop toroidal shape—may modify heat transfer patterns and blood microcirculation. Using a combination of heat diffusion equations, fluid dynamics models and topological transformations, we implement a heat transfer and blood flow simulation to examine the differential thermodynamic behavior of the open and closed hand postures. We show that the closed-hand posture may preserve significantly more heat than the open-hand posture, reducing temperature loss by an average of 1.1 ± 0.3 °C compared to 3.2 ± 0.5 °C in the open-hand condition (p < 0.01). Microvascular circulation is also enhanced, with a 53% increase in blood flow in the closed-hand configuration (p < 0.01). Therefore, our findings support the hypothesis that maintaining a closed-hand posture may help mitigate RP symptoms by preserving warmth, reducing cold-induced vasoconstriction and optimizing peripheral flow. Overall, our topologically framed approach provides quantitative evidence that postural modifications may influence peripheral vascular function through biomechanical and thermodynamic mechanisms, elucidating how shape-induced transformations may affect physiological and pathological dynamics. Full article

We establish a comprehensive framework demonstrating that physical reality can be understood as a holographic encoding of underlying computational structures. Our central thesis is that different geometric realizations of the same physical system represent equivalent holographic encodings of a unique computational structure. We formalize quantum complexity as a physical observable, establish its mathematical properties, and demonstrate its correspondence with geometric descriptions. This framework naturally generalizes holographic principles beyond AdS/CFT correspondence, with direct applications to black hole physics and quantum information theory. We derive specific, quantifiable predictions with numerical estimates for experimental verification. Our results suggest that computational structure, rather than geometry, may be the more fundamental concept in physics. Full article

We find that the whole set of known baryons of spin parity $J^P={{\displaystyle \frac{1}{2}}}^{+}$ (the ground state) and $J^P={{\displaystyle \frac{3}{2}}}^{+}$ (the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finite group $G=(192, 187)$. A subset of the theory is the small group $(48, 29)\cong GL(2, 3)$ whose conjugacy classes are in correspondence with the baryon families of Gell-Mann’s octet and decuplet. G has many of its irreducible characters that are minimal and informationally complete quantum measurements that we assign to the baryon families. Since G is isomorphic to the group of braiding matrices of $SU{\left(2\right)}_2$ Ising anyons, we explore the view that baryonic matter has a topological origin. We are interested in the holographic gravity dual $Ad{S}_3/QF{T}_2$ of the Ising model. This dual corresponds to a strongly coupled pure Einstein gravity with central charge $c=1/2$ and AdS radius of the order of the Planck scale. Some physical issues related to our approach are discussed. Full article