We leverage recent insights from second-order optimisation for neural networks to construct a Kronecker factored Laplace approximation to the posterior over the weights of a trained network. Our approximation requires no modification of the training procedure, enabling practitioners to estimate the uncertainty of their models currently used in production without having to retrain them. We exten...

Each king on an n×n chessboard is said to attack its own square and its neighboring squares, i.e., the nine or fewer squares within one move of the king. A set of kings is said to form an irredundant set if each attacks a square attacked by no other king in the set. We prove that the maximum size of an irredundant set of kings is bounded between (n− 1)=3 and n=3, and that the minimum size of a ...

We study the finite-size corrections of the dimer model on a square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of ; we also show that such unusual finite-size behavior can be fully explained in the framework of the logarithmic conformal field theory.

We are given a two-dimensional square grid of size N N, where N := 2 n and n 0. A space lling curve (SFC) is a numbering of the cells of this grid with numbers from c + 1 to c + N 2 , for some c 0. We call a SFC recursive (RSFC) if it can be recursively divided into four square RSFCs of equal size. Examples of well-known RSFCs include the Hilbert curve, the z-curve, and the Gray code. We prove ...

We compare strawman designs for two Square Kilometre Array demonstrators, the Extended New Technology Demonstrator (xNTD) and the Canadian Large Adaptive Reflector (CLAR), in the context of survey capability and suitability for addressing key survey science programmes. We first show that, all else being equal, the survey speed for detecting point sources is proportional to the product of field-...

We prove that the sum of entries of the suitably normalized groundstate vector of the O(1) loop model with periodic boundary conditions on a periodic strip of size 2n is equal to the total number of n×n alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the O(1) model with the partition function of the inhomogeneous six-vertex mode...

background: during radiotherapy treatment, critical organs are shielded using lead and cerrobend blocks. the objective of this study is to compare the effects of lead and cerrobend shielding blocks on incident photon beam. methods: collimator scatter factors were measured for open square fields (3 x 3 cm to 40 x 40 cm) defined by collimator jaws and for fields blocked down to smaller asymmetric...

introduction evaluation of the delivered dose of externally wedged photon beams by external diode dosimeters during the treatment process requires the estimation of exit surface dose correction factors in various wedge angles and field sizes. materials and methods a system of absorbed dose evaluation, using p-type diode dosimeters placed on the exit surface of a phantom, was characterized for e...

The statistical analysis of spatial data is usually done under Gaussian assumption for the underlying random field model. When this assumption is not satisfied, block bootstrap methods can be used to analyze spatial data. One of the crucial problems in this setting is specifying the block sizes. In this paper, we present asymptotic optimal block size for separate block bootstrap to estimate the...