We study the Hankel determinant of the generalized Jacobi weight (x − t)x(1 − x) for x ∈ [0, 1] with α, β > 0, t < 0 and γ ∈ R. Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of Hankel determinant is characterized by a τ -function for the Painlevé VI system.

We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances, these sources are not perfect ...

An input constrained channel S is de ned as the set of words generated by a nite labeled directed graph It is shown that every nite state encoder with nite antici pation i e with nite decoding delay for S can be obtained through state splitting rounds applied to some deterministic graph presentation of S followed by a reduction of equivalent states Furthermore each splitting round can be restri...

One of the main themes in the area of Terminologi-cal Reasoning has been to identify description logics (DLs) that are both very expressive and decidable. A recent paper by Schild showed that this issue can be prootably addressed by relying on a correspondence between DLs and propositional dynamic logics (PDL). However Schild left open three important problems, related to the translation into P...

A number of properties of Young raising operators as applied to S-functions and Schur Q-functions are noted. The order of evaluating the action of inverse raising operators is found to require careful specification and the maximum power of the operators bij is determined. The operation of the inverse raising operator on a partition .A is found to be the same as for its conjugate t A new definit...

We formulate the notion of uniformization of colorings of ladder systems on subsets of trees. We prove that Suslin trees have this property and also Aronszajn trees in the presence of Martin’s Axiom. As an application we show that if a tree has this property, then every countable discrete family of subsets of the tree can be separated by a family of pairwise disjoint open sets. Such trees are t...

A new approach to protein sequencing is described. It consists of two steps: (i) ladder-generating chemistry, the controlled generation from a polypeptide chain by wet chemistry of a family of sequence-defining peptide fragments, each differing from the next by one amino acid; and (ii) data readout, a one-step readout of the resulting protein sequencing ladder by matrix-assisted laser-desorptio...

We present the Video Ladder Network (VLN) for video prediction. VLN is a neural encoder-decoder model augmented by both recurrent and feedforward lateral connections at all layers. The model achieves competitive results on the Moving MNIST dataset while having very simple structure and providing fast inference.

The use of unsupervised data in addition to supervised data has lead to a significant improvement when training discriminative neural networks. However, the best results were achieved with a training process that is divided in two parts: first an unsupervised pre-training step is done for initializing the weights of the network and after these weights are refined with the use of supervised data...