We show all problems can be solved with a unified algorithm with an iteration of matrix multiplications. We present intuitive theory results on cardinality estimation and time complexity considering graph size, shape and density. Finally, we characterize parallel computational complexity and speedup per ...
where D(·, ·) is a distance function, T is the number of steps of the whole training trajectory, optθ is the update rule for model parameters, and θSt , θTt denote the model parameters trained on S and Tat time step t, respectively. Since our goal is to match the parameters s...
Note that aiming at maximal cliques reduces the number of factors, but at the same time the complexity is increased; for example, this can amount to an exponential explosion in the number of terms that have to be learned in the case of discrete variables. At the same time, using large ...
Black circles represent regional localities, with sizes corresponding to the relative numbers of different carbon-bearing minerals found at those localities. The network rendering reveals important information regarding the diversity and distribution of carbon minerals through space and time. In particular,...
branching complexity is often explored through the extraction of neurite attachment points (somata-neurite intersection points) and end points (neurite terminal points). As adopted by NeurphologyJ71, morphological dilation and erosion may be used to detect these points respectively (Supplementary Fig.4a...
The total number of infected and recovered nodes at time t, denoted as F(t) which is an indicator to evaluate the influence of the seed nodes. Clearly, F(t) converges to a stable number \(F(t_c)\), where \(t_c\) is the time when no nodes get infected. The spreading process ...
For over two years we've been iterating out a virtually limitless workspace that blends the mesmerizing complexity of fractals with contemporary mind-mapping technique. 📢Major Update:Neurite Desktop Why Fractals? The Mandelbrot Set is not just an aesthetic choice - fractal logic is ingrained into...
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of 1.0–1.3% observed across the Hereford, Angus and Brahman genomes. Similarly, the QUAST26software (v5.0.2) calculated that the two assemblies cover 93.9% (N’Dama) and 94.0% (Ankole) of the ARS-UCD1.2 Hereford genome, again consistent with the 94.2% and 96.2% of the Angus and ...
We show that the Graph Isomorphism (GI) problem and the more general problems of String Isomorphism (SI) andCoset Intersection (CI) can be solved in quasipolynomial(exp((logn)O(1))) time. The best previous bound for GI was exp(O( √n log n)), where n is the number of verti...