For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where  $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...

Using a probabilistic interpretation of Papoulis' generalized sampling theorem, an iterative algorithm has been devised for 3D reconstruction of a Lam-bertian surface at sub-pixel accuracy. The problem has been formulated as an optimization one in a Bayesian framework. The latter allows for introducing a priori information on the solution, using Markov Random Fields (MRF). The estimated 3D feat...

We extend results of A. Haken to give an exponential lower bound on the size of resolution proofs for propositional formulas encoding a generalized pigeonhole principle. These propositional formulas express the fact that there is no one-one mapping from c ·n objects to n objects when c > 1. As a corollary, resolution proof systems do not p -simulate constant formula depth Frege proof systems.

The interpretation of logical metonymies like begin the book has traditionally been explained by assuming the existence of complex lexical entries containing information about event knowledge (qualia roles: reading the book/writing the book). Qualia structure provides concrete constraints on interpretation, which are however too rigid to be cognitively plausible. We suggest generalized event kn...

We have recently proposed augmenting clauses in a Boolean database with groups of permutations, the augmented clauses then standing for the set of all clauses constructed by acting on the original clause with a permutation in the group. This approach has many attractive theoretical properties, including representational generality and reductions from exponential to polynomial proof length in a ...

We present an algorithm which assigns interpretations to several major types of ellipsis structures through a generalized procedure of syntactic reconstruction. Ellipsis structures are taken to be sequences of lexically realized arguments and/or adjuncts of an empty verbal head. Reconstruction is characterized as the specification of a (partial) correspondence relation between the unrealized he...

Learned image compression has recently shown the potential to outperform standard codecs. State-of-the-art rate-distortion (R-D) performance been achieved by context-adaptive entropy coding approaches in which hyperprior and autoregressive models are jointly utilized effectively capture spatial dependencies latent representations. However, latents feature maps of same resolution previous works,...