Not sure how much detail you need but generally there exist implicit and explicit integrators for numerically solving (integrating) ODE. The implicit ones, like the one used here, tend to be more stable. The ideas behind SSM come from control theory ideas that used integrators with stability guarantees so that the rest of the neural network can focus on other aspects of the problem.
This is an odd definition for tacit knowledge. My understanding is that it's more caught up in the intuition of concepts/systems that's difficult to codify because it's very contextual. This "tribal knowledge" perspective seems more like processes and facts that aren't documented. Not because of the inherent difficulty but instead because of priorities. Not that there isn't some intersection between the two.
A diverse set of biological processes have been implicated in the pathophysiology of Alzheimer’s disease (AD) and related dementias. However, there is limited understanding of the peripheral biological mechanisms relevant in the earliest phases of the disease. Here, we used a large-scale proteomics platform to examine the association of 4877 plasma proteins with 25-year dementia risk in 10,981 middle-aged adults. We found 32 dementia-associated plasma proteins that were involved in proteostasis, immunity, synaptic function, and extracellular matrix organization. We then replicated the association between 15 of these proteins and clinically relevant neurocognitive outcomes in two independent cohorts. We demonstrated that 12 of these 32 dementia-associated proteins were associated with cerebrospinal fluid (CSF) biomarkers of AD, neurodegeneration, or neuroinflammation. We found that eight of these candidate protein markers were abnormally expressed in human postmortem brain tissue from patients with AD, although some of the proteins that were most strongly associated with dementia risk, such as GDF15, were not detected in these brain tissue samples. Using network analyses, we found a protein signature for dementia risk that was characterized by dysregulation of specific immune and proteostasis/autophagy pathways in adults in midlife ~20 years before dementia onset, as well as abnormal coagulation and complement signaling ~10 years before dementia onset. Bidirectional two-sample Mendelian randomization genetically validated nine of our candidate proteins as markers of AD in midlife and inferred causality of SERPINA3 in AD pathogenesis. Last, we prioritized a set of candidate markers for AD and dementia risk prediction in midlife.
Singular integrals are a lovely topic, especially from a Fourier analytic perspective. Taking the Fourier transform, F(H(f))(x) = -i * sgn(x) * F(f)(x), which implies H^2 = - I. H has the Fourier multiplier -i * sgn(x). The Riesz transforms R_j are a higher dimensional generalization of the Hilbert transform with Fourier multipliers -i * x_j/|x_j|, which leads to the nice property sum R_j^2 = -I.
A syntax-producing machine harnessing the power of duality will still never have access to semantic content. For this reason I have difficulty saying that it understands things beyond a colloquial sense.
I'm probably flaunting my ignorance here, but how isn't this an extremely tenuous connection? The graphs are unconvincing beyond a "... Maybe? I guess?" and comparing brain activity to NN activity seems dubious.
I'd be curious what other sounds look like for both.
