Related papers: CAT-generation of ideals
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive…
Despite recent progress, text-to-image models still struggle to generate semantically diverse and compositionally accurate multi-person interaction scenes, often collapsing to repetitive layouts, stereotypical poses, and poorly grounded…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
We find a generating function for interval-closed sets of the product of two chains poset by constructing a bijection to certain bicolored Motzkin paths. We also find a functional equation for the generating function of interval-closed sets…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
Let $P$ be a finite partially ordered set with unique minimal element $\hat{0}$. We study the Betti poset of $P$, created by deleting elements $q\in P$ for which the open interval $(\hat{0}, q)$ is acyclic. Using basic simplicial topology,…
Local to global machinery plays an important role in the study of simplicial complexes, since the seminal work of Garland [G] to our days. In this work we develop a local to global machinery for general posets. We show that the high…
We study ideals generated by $n+1$ powers of general linear forms in $R= k[x_1,\dots,x_n]$. By generalizing the ideas in a recent paper of Diethorn et al., we determine the Betti numbers of such ideals when at least one generator is a…
We construct models, by three-dimensional arrays of ccc posets, where many classical cardinal characteristics of the continuum are pairwise different.
The N cardinality k ideals of any w-element poset (w, k variable) can be enumerated in time O(Nw^3). The corresponding bound for k-element subtrees of a w-element tree is O(Nw^5). An algorithm is described that by the use of wildcards…
In this paper, we consider the completely positive tensor decomposition problem with ideal-sparsity. First, we propose an algorithm to generate the maximal cliques of multi-hypergraphs associated with completely positive tensors. This also…
Grasp detection of novel objects in unstructured environments is a key capability in robotic manipulation. For 2D grasp detection problems where grasps are assumed to lie in the plane, it is common to design a fully convolutional neural…
We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
In this paper we follow our previous research in the area of Computerized Adaptive Testing (CAT). We present three different methods for CAT. One of them, the item response theory, is a well established method, while the other two, Bayesian…
In 1981, Kelly showed that planar posets can have arbitrarily large dimension. However, the posets in Kelly's example have bounded Boolean dimension and bounded local dimension, leading naturally to the questions as to whether either…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
Modern GANs often introduce adversarial supervision on intermediate generator outputs and interpret the resulting multi-stage synthesis as coarse-to-fine hierarchical generation. In this work, we challenge this interpretation. We argue that…
Current approaches in video forecasting attempt to generate videos directly in pixel space using Generative Adversarial Networks (GANs) or Variational Autoencoders (VAEs). However, since these approaches try to model all the structure and…
Computerized adaptive testing (CAT) is an interesting and promising approach to testing human abilities. In our research we use Bayesian networks to create a model of tested humans. We collected data from paper tests performed with grammar…