It breaks down the design geometries of manufactured objects into discrete, micro-level structures that have their own mathematical values. This can be applied to workflows or processes in automotive, consumer products, industrial, aerospace, marine, and much more. Manufacturing methods such as injecti...
We express information content in a population of sizes of dendritic spines as Shannon entropy, which is a standard tool for estimation of general information67. Although Shannon entropy H is defined only for discrete stochastic variables, it can be also applied to continuous variables with the hel...
Xia. Gbpnet: Universal geometric representation learning on protein structures. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining https://doi.org/10.1145/3534678.3539441 (2022). Deng, C. et al. Vector neurons: a general framework for so (3)-equivariant ...
These structures are a class of spatiotemporal organizations that can be obtained only far from equilibrium, where a system can continuously dissipate entropy in its environment, which compensates the entropy produced by the internal irreversible processes and keeps the system in an organized state. ...
Discrete mathematics and probability Abstract Algebra Abstract algebra is one of the divisions in algebra which discovers the truths relating to algebraic systems independent of the specific nature of some operations. These operations, in specific cases, have certain properties. Thus we can conclude some...
We previously found that the dense phase has a heterogeneous structure in which the binding sites of the IDPs meet at spatially-discrete junctions whose separation depends on the spacing of the binding sites but is less sensitive to their affinity (cp Figure 3 in [50]). Further, the average...
These experiments have some limitations that prompt future directions of study. First, we used novel never-before-seen patterns and faces in these experiments, which is an experimental advantage, but we were limited to a discrete set of patterns and faces. Future studies need to examine the gene...
An environment of entangled qubits placed into a state of collective superposition structures information in a way that looks like waves, with amplitudes associated with each outcome. These amplitudes become the probabilities of the outcomes of a measurement of the system. These waves can build on ...
We say a generator\(g_\theta\)is conditional if it is of the form\(g_\theta : Y \times Z \rightarrow \mathcal {X}\), that is, it accepts an additional input to create a data object. For instance, the additional input can be a class label or, specifically for time series, the...
Object storage is adata storagearchitecture that manages data as discrete units called objects. Unlike traditionalfile systemsthat organize data in hierarchical structures withfilesanddirectories, object storage uses a flat address space. This flat structure eliminates the complexities of navigating nestedfold...