The dynamic topological order problem is that of efficiently updating a topological order after an edge insertion. This can be solved using a standard topological sort algorithm in O(v+e+b) time, for a batch of b edge insertions. However, this always traverses the entire graph when processing a batch of insertions, even if only a few edges are added. Dynamic topological order algorithms travers...

In Bayesian Network Structure Learning (BNSL), we are given a variable set and parent scores for each aim to compute DAG, called network, that maximizes the sum of scores, possibly under some structural constraints. Even very restricted special cases BNSL computationally hard, and, thus, in practice heuristics such as local search used. typical algorithm, solution ask whether there is better wi...

This paper introduces an algorithm for determining data clusters called TILO/PRC (Topologically Intrinsic Lexicographic Ordering/Pinch Ratio Clustering). The theoretical foundation for this algorithm, developed in [14], uses ideas from topology (particularly knot theory) suggesting that it should be very flexible and robust with respect to noise. The TILO portion of the algorithm progressively ...

Topological insulators are emerging materials with insulating bulk and symmetry protected nontrivial surface states. One of the most fascinating transport behaviors in a topological insulator is quantized anomalous Hall insulator, which has been observed magnetic-topological-insulator-based devices. In this work, we report successful doping rare earth element Tb into ${\mathrm{Bi}}_{1.08}{\math...

Let X be a geometrically connected scheme over a field K. Then, the absolute Galois group GK of K acts on the algebraic fundamental group π 1 (X ⊗K,x). This lecture explains the following: 1. This action is an analogy of “geometric monodromy of deformation family” in the topology. 2. Lie algebraization of the fundamental group is effective to extract some information from this action. 1 Algebra...

AbstractThis paper considers the problem of unsupervised 3D object reconstruction from in-the-wild single-view images. Due to ambiguity and intrinsic ill-posedness, this is inherently difficult solve therefore requires strong regularization achieve disentanglement different latent factors. Unlike existing works that introduce explicit regularizations into objective functions, we look a space fo...

In stochastic (dynamic) traffic assignment (DTA), route choice (RC) formulations with implicit set require less memory than their explicit counterparts. To compute turn probabilities, however, a topological ordering of the nodes is needed, which negatively impacts stability convergence and consistency equilibrium. This paper formulates general framework for RC module efficient DTA (ESDTA) witho...