Related papers: Boltzmann Samplers for Colored Combinatorial Objec…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems:…
What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natural candidate, and we formulate a purely combinatorial…
This paper is devoted to the random generation of particular colored necklaces for which the number of beads of a given color is constrained (these necklaces are called v-balanced). We propose an efficient sampler (its expected time…
Scene modeling is very crucial for robots that need to perceive, reason about and manipulate the objects in their environments. In this paper, we adapt and extend Boltzmann Machines (BMs) for contextualized scene modeling. Although there…
Color modelling and extraction is an important topic in fashion, art, and design. Recommender systems, color-based retrieval, decorating, and fashion design can benefit from color extraction tools. Research has shown that modeling color so…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
To be useful in everyday environments, robots must be able to observe and learn about objects. Recent datasets enable progress for classifying data into known object categories; however, it is unclear how to collect reliable object data…
In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of…
We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n…
Compositional representations are thought to enable humans to generalize across combinatorially vast state spaces. Models with learnable object slots, which encode information about objects in separate latent codes, have shown promise for…
It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be…
We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…
Compositing an object into an image involves multiple non-trivial sub-tasks such as object placement and scaling, color/lighting harmonization, viewpoint/geometry adjustment, and shadow/reflection generation. Recent generative image…
Collaborative filtering is an effective recommendation technique wherein the preference of an individual can potentially be predicted based on preferences of other members. Early algorithms often relied on the strong locality in the…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models.…
The production of color language is essential for grounded language generation. Color descriptions have many challenging properties: they can be vague, compositionally complex, and denotationally rich. We present an effective approach to…