Related papers: Boltzmann Samplers for Colored Combinatorial Objec…
We consider a combinatorial property isolated in the field of ideal convergence, a P-property for two ideals on natural numbers. We show that among selected ideals induced by disjoint families, not all pairs satisfy P-property for two…
The possibility of employing restricted Boltzmann machine (RBM) for collaborative filtering has been known for about a decade. However, there has been hardly any work on this topic since 2007. This work revisits the application of RBM in…
This paper presents a novel framework for modeling and conditional generation of 3D articulated objects. Troubled by flexibility-quality tradeoffs, existing methods are often limited to using predefined structures or retrieving shapes from…
Inspired by structural colors in avian species, various synthetic strategies have been developed to produce non-iridescent, saturated colors using nanoparticle assemblies. Mixtures of nanoparticles varying in particle chemistry (or complex…
Modeling subtractive color mixture (e.g., the way that paints mix) is difficult when working with colors described only by three-dimensional color space values, such as RGB. Although RGB values are sufficient to describe a specific color…
An $(m,n)$-mixed graph generalizes the notions of oriented graphs and edge-coloured graphs to a graph object with $m$ arc types and $n$ edge types. A simple colouring of such a graph is a non-trivial homomorphism to a reflexive target. We…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with…
Colors observed in nature are very important to form our perception of an object as well as its design. The desire to reproduce vivid colors such as those found in birds, fishes, flowers and insects has driven extensive research into…
We consider object detection using a generic model for natural shapes. A common approach for object recognition involves matching object models directly to images. Another approach involves building intermediate representations via a…
Given a graph G (or more generally a matroid embedded in a projective space), we construct a sequence of varieties whose geometry encodes combinatorial information about G. For example, the chromatic polynomial of G (giving at each m>0 the…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
We present a perceptional mathematical model for image and signal analysis. A resemblance measure is defined, and submitted to an innovating combinatorial optimization algorithm. Numerical Simulations are also presented
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
The paper by No\'e et al. [F. No\'e, S. Olsson, J. K\"ohler and H. Wu, Science, 365:6457 (2019)] introduced the concept of Boltzmann Generators (BGs), a deep generative model that can produce unbiased independent samples of many-body…
We propose a framework to continuously learn object-centric representations for visual learning and understanding. Existing object-centric representations either rely on supervisions that individualize objects in the scene, or perform…
Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a…
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…
We propose a generative model that can infer a distribution for the underlying spatial signal conditioned on sparse samples e.g. plausible images given a few observed pixels. In contrast to sequential autoregressive generative models, our…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…