Persistent homology applied to the activity of grid cells in the Medial Entorhinal Cortex suggests that this activity lies on a toroidal manifold. By analyzing real data and a simple model, we show that neural oscillations play a key role in the appearance of this toroidal topology. To quantitatively monitor how changes in spike trains influence the topology of the data, we first define a robust measure for the degree of toroidality of a dataset. Using this measure, we find that small perturbations ([Formula: see text]100 ms) of spike times have little influence on both the toroidality and the hexagonality of the ratemaps. Jittering spikes by [Formula: see text]100-500 ms, however, destroys the toroidal topology, while still having little impact on grid scores. These critical jittering time scales fall in the range of the periods of oscillations between the theta and eta bands. We thus hypothesized that these oscillatory modulations of neuronal spiking play a key role in the appearance and robustness of toroidal topology and the hexagonal spatial selectivity is not sufficient. We confirmed this hypothesis using a simple model for the activity of grid cells, consisting of an ensemble of independent rate-modulated Poisson processes. When these rates were modulated by oscillations, the network behaved similarly to the real data in exhibiting toroidal topology, even when the position of the fields were perturbed. In the absence of oscillations, this similarity was substantially lower. Furthermore, we find that the experimentally recorded spike trains indeed exhibit temporal modulations at the eta and theta bands, and that the ratio of the power in the eta band to that of the theta band, [Formula: see text], correlates with the critical jittering time at which the toroidal topology disappears.

In Fig 2, two of the panels of Fig 2B are duplicates of panel Fig 2A.Please see the correct Fig 2 here.

The semantic capabilities of large language models (LLMs) have the potential to enable rich analytics and reasoning over vast knowledge corpora. Unfortunately, existing systems either empirically optimize expensive LLM-powered operations with no performance guarantees , or limit their support to simple batched-inference primitives. We introduce semantic operators , the first formalism with statistical accuracy guarantees for general-purpose AI-based operations with natural language parameters (e.g., filtering, sorting, joining or aggregating records using natural language criteria). Each operator can be implemented by multiple AI algorithms , which compose individual model invocations to orchestrate the model over the data. Our programming model specifies the expected behavior of each operator with a high-quality reference algorithm , and we develop an optimization framework that reduces cost, while providing accuracy guarantees for individual operators. Using this approach, we propose several novel optimizations to accelerate semantic filtering, joining, group-by and top-k operations by up to 1, 000×. We implement semantic operators in the LOTUS system and demonstrate LOTUS' effectiveness on real, bulk-semantic processing applications, including fact-checking, biomedical multi-label classification, search, and topic analysis. We show that the semantic operator model is expressive, capturing state-of-the-art AI pipelines in a few operator calls, and making it easy to express new pipelines that match or exceed quality of recent LLM-based analytic systems by up to 170%, while offering accuracy guarantees. Overall, LOTUS programs match or exceed the accuracy of state-of-the-art AI pipelines for each task while running up to 3.6× faster than the highest-quality baselines. LOTUS is publicly available at https://github.com/lotus-data/lotus.

Exploiting the relationships among data is a classical query optimization technique. As persistent data is increasingly being created and maintained programmatically, prior work that infers data relationships from data statistics misses an important opportunity. We present Coco, the first tool that identifies data relationships by analyzing database-backed applications. Once identified, Coco leverages the constraints to optimize the application's physical design and query execution. Instead of developing a fixed set of predefined rewriting rules, Coco employs an enumerate-test-verify technique to automatically exploit the discovered data constraints to improve query execution. Each resulting rewrite is provably equivalent to the original query. Using 14 real-world web applications, our experiments show that Coco can discover numerous data constraints from code analysis and improve real-world application performance significantly.