We introduce a new variant of the popular Burrows-Wheeler transform (BWT) called Geometric Burrows-Wheeler Transform (GBWT). Unlike BWT, which merely permutes the text, GBWT converts the text into a set of points in 2-dimensional geometry. Using this transform, we can answer to many open questions in compressed text indexing: (1) Can compressed data structures be designed in external memory with similar performance as the uncompressed counterparts? (2) Can compressed data structures be designed for position restricted pattern matching [16]? We also introduce a reverse transform, called Points2Text, which converts a set of points into text. This transform allows us to derive the first known lower bounds in compressed text indexing. We show strong equivalence between data structural problems in geometric range searching and text pattern matching. This provides a way to derive new results in compressed text indexing by translating the results from range searching.
Studying neural connections and activities in vivo is fundamental to understanding brain functions. Given the cm-size brain and three-dimensional neural circuit dynamics, deep-tissue, high-speed volumetric imaging is highly desirable for brain study. With sub-micrometer spatial resolution, intrinsic optical sectioning, and deep-tissue penetration capability, two-photon microscopy (2PM) has found a niche in neuroscience. However, the current 2PM typically relies on a slow axial scan for volumetric imaging, and the maximal penetration depth is only about 1 mm. Here, we demonstrate that by integrating a gradient-index (GRIN) lens and a tunable acoustic GRIN (TAG) lens into 2PM, both penetration depth and volume-imaging rate can be significantly improved. Specifically, an ∼ 1-cm long GRIN lens allows imaging relay from any target region of a mouse brain, while a TAG lens provides a sub-second volume rate via a 100 kHz ∼ 1 MHz axial scan. This technique enables the study of calcium dynamics in cm-deep brain regions with sub-cellular and sub-second spatiotemporal resolution, paving the way for interrogating deep-brain functional connectome.
Understanding how the brain functions is one of the grand challenges in modern scientific research. Similar to a computer, a functional brain is composed of hardware and software. The major bottleneck lies in the difficulty to directly observe the brain ‘software’, i.e. the rule and operating information used by the brain that might emerge from pan-neuron/synapse connectome. A recognized strategy for probing the functional connectome is to perform volumetric imaging in brains with high spatiotemporal resolution and deep brain penetration. Among various imaging technologies, optical imaging offers appealing combinations including spatial resolution of sub-micrometer to nanometer, temporal resolution of second to millisecond, penetration depth of millimeter or deeper, and molecular contrast based on the abundant choices of fluorescent indicators. Thus, it is ideal for enabling three-dimensional functional brain mapping of small animal models. In this review, we focus on recent technological advances in optical volumetric imaging, with an emphasis on the tools and methods for enhancing imaging speed, depth, and resolution. The review could serve as a quantitative reference for physicists and biologists to choose the techniques better suited for specific applications, as well as to stimulate novel technical developments to advance brain research.
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