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         <h2>Abstract</h2>
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-The "computable" numbers may be described briefly as the real
-numbers whose expressions as a decimal are calculable by finite means.
-Although the subject of this paper is ostensibly the computable numbers.
-it is almost equally easy to define and investigate computable functions
-of an integral variable or a real or computable variable, computable
-predicates, and so forth. The fundamental problems involved are,
-however, the same in each case, and I have chosen the computable numbers
-for explicit treatment as involving the least cumbrous technique. I hope
-shortly to give an account of the relations of the computable numbers,
-functions, and so forth to one another. This will include a development
-of the theory of functions of a real variable expressed in terms of computable
-numbers. According to my definition, a number is computable
-if its decimal can be written down by a machine...
+Functional magnetic resonance imaging (fMRI) is an indispensable tool in modern neuroscience, providing a non-invasive window into whole-brain dynamics at millimeter-scale spatial resolution. However, fMRI is constrained by issues such as high operation costs and immobility. With the rapid advancements in cross-modality synthesis and brain decoding, the use of deep neural networks has emerged as a promising solution for inferring whole-brain, high-resolution fMRI features directly from electroencephalography (EEG), a more widely accessible and portable neuroimaging modality. Nonetheless, the complex projection from neural activity to fMRI hemodynamic responses and the spatial ambiguity of EEG pose substantial challenges both in modeling and interpretability. Relatively few studies to date have developed approaches for EEG-fMRI translation, and although they have made significant strides, the inference of fMRI signals in a given study has been limited to a small set of brain areas and to a single condition (i.e., either resting-state or a specific task). The capability to predict fMRI signals in other brain areas, as well as to generalize across conditions, remain critical gaps in the field. To tackle these challenges, we introduce a novel and generalizable framework: **NeuroBOLT**, i.e., **Neuro**-to-**BOL**D **T**ransformer, which leverages multi-dimensional representation learning from temporal, spatial, and spectral domains to translate raw EEG data to the corresponding fMRI activity signals across the brain. Our experiments demonstrate that NeuroBOLT effectively reconstructs resting-state fMRI signals from primary sensory, high-level cognitive areas, and deep subcortical brain regions, achieving state-of-the-art accuracy and significantly advancing the integration of these two modalities.
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