An [Formula: see text]-dimensional knot text] is called doubly slice if it occurs as the cross section of some unknotted knot. For every unknown which knots are slice, and this remains one biggest unsolved problems in high-dimensional theory. text], we use signatures coming from text]-cohomology to develop new obstructions for with metabelian groups be slice. each construct an infinite family o...

Adapting the ideas of L. Keen and C. Series used in their study Riley slice Schottky groups generated by two parabolics, we explicitly identify `half-space' neighbourhoods pleating rays which lie completely slice. This gives a provable method to determine if point is or not. We also discuss family Farey polynomials rational root set determines slice; this leads dynamical systems interpretation ...

Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertica...

PURPOSE A ghost correction strategy for Simultaneous Multi-Slice (SMS) EPI methods that provides improved ghosting artifact reduction compared to conventional methods is presented. Conventional Nyquist ghost correction methods for SMS-EPI rely on navigator data that contain phase errors from all slices in the simultaneously acquired slice-group. These navigator data may contain spatially nonlin...

Hamiltonian Monte Carlo and slice sampling are amongst the most widely used and studied classes of Markov Chain Monte Carlo samplers. We connect these two methods and present Hamiltonian slice sampling, which allows slice sampling to be carried out along Hamiltonian trajectories, or transformations thereof. Hamiltonian slice sampling clarifies a class of model priors that induce closed-form sli...

We show that a Boolean degree~$d$ function on the slice $\binom{[n]}{k}$ is junta if $k \geq 2d$, and this bound sharp. prove similar result for $A$-valued functions arbitrary finite $A$, an infinite analog of slice.