Quantum computing combines great promise with daunting challenges — the road to devices that solve real-world problems is still long. Now, an implementation of a quantum algorithm maps the problems we want to solve to the devices we already have.
We can describe the local structure of a bounded-degree graph G by counting the number of isomorphic copies in G of each possible k -disk. We can summarize this information in form of a vector that has an entry for each isomorphism class of k -disks. The value of the entry is the ...
You can use the Distance Method parameter to create points based on planar or geodesic measurements when the Point Placement parameter is specified by distance. Topology toolset Enhanced tools: Validate Topology—Specific topologic extents can be validated. Workspace toolset New tools: Enable Editing ...
45 Yuval Peres Coloring a graph arising from a lacunary sequence 59:15 Vojtěch Rödl On two Ramsey type problems for Kt+1-free graphs 47:07 Vilmos Totik Erdős on polynomials And Ben Green The sum-free set constant is ⅓ 1:45:31 Tomasz Łuczak Threshold functions a historical ...
Clearly is non-increasing in . The Riemann-von Mangoldt formula, together with the functional equation, gives us the asymptotic in the case, while the prime number theorem tells us that The various zero free regions for the zeta function can be viewed as slight improvements to (2); for...
When you click Create Similar, the correct tool is launched from the draw gallery. Keep Views in Design Option Modification When non-primary design options are deleted during Accept Primary, all views that were created in these design options can now be preserved. ...
To test whether a graph is empty, one can perform the following obvious algorithm: take k vertices in G at random and check whether they have any edges at all between them. If they do, then the test of course rejects G as being non-empty, while if they don’t, the test accepts G...
How to make a non-planar graph planar? When did tessellations originate? What is the three-dimensional figure represented by each net? What is the name of the 3D shape resembling a thick book? Determine whether the pair of solids are similar, congruent, or neither. What is the trapezium ru...
Another key feature of a brain tumour is its cellular- ity, which can be evaluated with diffusion-weighted MR imaging (DWI). Diffusion tensor imaging (DTI) has proven to be a useful tool for characterising tumours and defin- ing white matter anatomy, as DTI can non-invasively trace neuronal...
Sure, any planar graph can be five-colored. But that result is not sharp: in fact, any planar graph can be four-colored. That is sharp: the same can't be said for any lower number. Sharp (chess) Tactical; risky. Sharp Piercing; keen; severe; painful. A sharp pain; the sharp and...