arXiv subjects

Eve Bodnia

Publications and source records attributed to Eve Bodnia.

3 recordsLinked to original sources

arXiv2026

Emergent topological structure in spontaneous brain-organoid activity

Neural activity is widely held to organize on low-dimensional structure embedded in a high-dimensional state space. Persistent homology reads such structure directly from the pattern of pairwise correlations, without assuming in advance which variables are relevant. We apply persistent homology to microelectrode-array (MEA) recordings of spontaneous activity from human (Lancaster) and mouse (Paşca) cortical organoids, spanning $26$--$234$ simultaneously sorted units, and ask whether topological data analysis resolves structure at the node counts that neural recordings actually deliver. Building weighted networks in correlation space and characterizing them by Vietoris--Rips filtration, we find that the first homology ($H_1$, loops) rises significantly above a rate- and population-preserving null in $14$ of $18$ datasets. This loop structure occupies a non-redundant core: it is robust to random removal of units yet disrupted by targeted removal of the units that carry it. Topological richness grows with network size, and second homology ($H_2$) emerges significantly above the null only in the larger networks. These results show that persistent homology resolves structured topology in neural recordings at the scale experiments actually deliver.

q-bio.NC↗

arXiv2026

Compression is all you need: Modeling Mathematics

Human mathematics (HM), the mathematics humans discover and value, is a vanishingly small subset of formal mathematics (FM), the totality of all valid deductions. We argue that HM is distinguished by its compressibility through hierarchically nested definitions, lemmas, and theorems. We model this with monoids. A mathematical deduction is a string of primitive symbols; a definition or theorem is a named substring or macro whose use compresses the string. In the free abelian monoid $A_n$, a logarithmically sparse macro set achieves exponential expansion of expressivity. In the free non-abelian monoid $F_n$, even a polynomially-dense macro set only yields linear expansion; superlinear expansion requires near-maximal density. We test these models against MathLib, a large Lean~4 library of mathematics that we take as a proxy for HM. Each element has a depth (layers of definitional nesting), a wrapped length (tokens in its definition), and an unwrapped length (primitive symbols after fully expanding all references). We find unwrapped length grows exponentially with both depth and wrapped length; wrapped length is approximately constant across all depths. These results are consistent with $A_n$ and inconsistent with $F_n$, supporting the thesis that HM occupies a polynomially-growing subset of the exponentially growing space FM. We discuss how compression, measured on the MathLib dependency graph, and a PageRank-style analysis of that graph can quantify mathematical interest and help direct automated reasoning toward the compressible regions where human mathematics lives.

cs.AI↗

arXiv2024

The quest for CMB signatures of Conformal Cyclic Cosmology

Circles of low-variance and Hawking points in the Cosmic Microwave Background (CMB), resulting from black hole mergers and black hole evaporation, respectively, in a previous cycle of the universe, have been predicted as possible evidence for the Conformal Cyclic Cosmology model (CCC) introduced by R. Penrose. We present a high-resolution search for such low-variance circles in the Planck and WMAP CMB data, and introduce HawkingNet, our machine learning open-source software based on a ResNet18 algorithm, to search for Hawking points in the CMB. We find that spots consisting of a few unusually bright (high-temperature) or dark (low-temperature) pixels, erroneously lead to regions with many low-variance circles, and consequently sets of near-concentric low-variance circles, when applying the search criteria used in previous work [V.G. Gurzadyan, R. Penrose]. After removing those spots from the data, no statistically significant low-variance circles can be found. Concerning Hawking points, also no statistically significant evidence is found when using a Gaussian temperature amplitude model over 1 degree opening angle and after accounting for spots of unusual brightness. That the unusual spots in the data are themselves remnants of Hawking points is not supported by low-variance and/or low-temperature circles around them. The absence of such statistically-significant distinct features in the currently available CMB data does not disprove the CCC model, but implies that higher resolution CMB data and/or refined CCC based predictions are needed to pursue the search for CCC signatures further

astro-ph.CO↗