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S. M. Simpson's first mill in Ellison, just east of what is now the Kelowna-Vernon airport.
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Photo shows individuals with zap-straps on their wrists beside RCMP and Vancouver Police with crowd on the other side of fence. Prof. Frank Tester (UBC School of Social Work) is standing in background (wearing black beret).
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This theorem says that the true electron density of a molecule has a convergent Taylor expansion away from the positions of the nuclei. We discuss this, and an open problem about its structure at the nuclei.
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Our primary motivation for persistent homology is in its applications to shape similarity measures. Multidimensional or multiparameter persistence comes into play in that context when two objects are to be simultaneously compared according to several features. The ideas go back to early 1900s when Paretoâ s optimal points of multiple functions were studied with applications to economy on mind. In our previous work, we developed an algorithm that produces an acyclic partial matching (A, B, C) on the cells of a given simplicial complex, in the way that it is compatible with a vector-valued function given on its vertices. This implies the construction can be used to build a reduced filtered complex with the same multidimensional persistent homology as of the original one filtered by the sublevel sets of the function. Until now, any simplex added to C by our algorithm has been defined as critical. It was legitimate to do so, because an application- driven extension of Formanâ s discrete Morse theory to multi-parameter functions has not been carried out yet. In particular, no definition of a general combinatorial critical cell has been given in this context. We now propose new definitions of a multidimensional discrete Morse function (for short, mdm function), of its gradient field, its regular and critical cells. We next show that the function f used as input for our algorithm gives rise to an mdm function g with the same order of sublevel sets and the same partial matching as the one produced by our algorithm. This is a joint work with Madjid Allili, Claudia Landi, and Filippo Masoni.
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'Description obtained from the Annotated Catalogue of the H. Colin Slim Stravinsky Collection: ''Autographed sepia photograph taken in 1944, probably by Paola Foa ... (including inscribed lower margin), in English in black ink, May 1946, to Harry Freistadt (1908-64).'''
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This stone inscription in Chinese is located at Ziwei Palace (紫微宮遺址), Jiyuan, Henan, China. Dimensions: 112.5 cm (H) ✕ 62.5 cm (W) ✕ 17.5 cm (D). Further details are provided in the accompanying metadata spreadsheet, "Inscription metadata for Cluster 2.1 (2017): Jiyuan Shi (China)" under ID ZW-10.
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Finding a maximum clique in a graph is one of the most basic computational problems on graphs. The various applications of this problem has motivated the design of algorithms which today can successfully solve real-world instances with thousands of vertices. However, from a theoretical point a view, it is widely believed that this is a hard problem: in particular that determining whether a graph on n vertices contains a k-clique requires time $n^{\Omega(k)}$. In terms of upper bounds, it is easy to determine this in time roughly $n^k$ by checking if any of the sets of vertices of size k forms a clique.<br><br> We analyse the running time of the most successful algorithms used in practice: colour-based branch-and-bound strategies and à stergård's algorithm based on Russian doll search. When analysing such algorithms, it is convenient to view the execution trace as a proof establishing the maximal clique size for the input graph. In particular, if this graph does not have a k-clique, then the trace provides an efficiently verifiable proof in so-called regular resolution of the statement that the graph is k-clique-free. We show that for any $k \ll n^{1/4}$ if the input graph is a k-clique-free random graph sampled from the right distribution then the size of such regular resolution proofs, and hence the running time of these algorithm, is at least $n^{\Omega(k)}$.
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