An argument for hyperbolic geometry in neural circuits

ImAge quantitates aging and rejuvenation

For efficient, cost-effective and personalized healthcare, biomarkers that capture aspects of functional, biological aging, thus predicting disease risk and lifespan more accurately and reliably than chronological age, are essential. We developed an imaging-based chromatin and epigenetic age (ImAge) that captures intrinsic age-related trajectories of the spatial organization of chromatin and epigenetic marks in single nuclei, in mice. We show that such trajectories readily emerge as principal changes in each individual dataset without regression on chronological age, and that ImAge can be computed using several epigenetic marks and DNA labeling. We find that interventions known to affect biological aging induce corresponding effects on ImAge, including increased ImAge upon chemotherapy treatment and decreased ImAge upon caloric restriction and partial reprogramming by transient OSKM expression in liver and skeletal muscle. Further, ImAge readouts from chronologically identical mice inversely correlated with their locomotor activity, suggesting that ImAge may capture elements of biological and functional age. In sum, we developed ImAge, an imaging-based biomarker of aging with single-cell resolution rooted in the analysis of spatial organization of epigenetic marks.

The Dimensions of dimensionality

Cognitive scientists often infer multidimensional representations from data. Whether the data involve text, neuroimaging, neural networks, or human judgments, researchers frequently infer and analyze latent representational spaces (i.e., embeddings). However, the properties of a latent representation (e.g., prediction performance, interpretability, compactness) depend on the inference procedure, which can vary widely across endeavors. For example, dimensions are not always globally interpretable and the dimensionality of different embeddings may not be readily comparable. Moreover, the dichotomy between multidimensional spaces and purportedly richer representational formats, such as graph representations, is misleading. We review what the different notions of dimension in cognitive science imply for how these latent representations should be used and interpreted.

Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience

Daily experience suggests that we perceive distances near us linearly. However, the actual geometry of spatial representation in the brain is unknown. Here we report that neurons in the CA1 region of rat hippocampus that mediate spatial perception represent space according to a non-linear hyperbolic geometry. This geometry uses an exponential scale and yields greater positional information than a linear scale. We found that the size of the representation matches the optimal predictions for the number of CA1 neurons. The representations also dynamically expanded proportional to the logarithm of time that the animal spent exploring the environment, in correspondence with the maximal mutual information that can be received. The dynamic changes tracked even small variations due to changes in the running speed of the animal. These results demonstrate how neural circuits achieve efficient representations using dynamic hyperbolic geometry.

Geometrical congruence, greedy navigability and myopic transfer in complex networks and brain connectomes

We introduce in network geometry a measure of geometrical congruence (GC) to evaluate the extent a network topology follows an underlying geometry. This requires finding all topological shortest-paths for each nonadjacent node pair in the network: a nontrivial computational task. Hence, we propose an optimized algorithm that reduces 26 years of worst scenario computation to one week parallel computing. Analysing artificial networks with patent geometry we discover that, different from current belief, hyperbolic networks do not show in general high GC and efficient greedy navigability (GN) with respect to the geodesics. The myopic transfer which rules GN works best only when degree-distribution power-law exponent is strictly close to two. Analysing real networks-whose geometry is often latent-GC overcomes GN as marker to differentiate phenotypical states in macroscale structural-MRI brain connectomes, suggesting connectomes might have a latent neurobiological geometry accounting for more information than the visible tridimensional Euclidean.