Related papers: Some combinatorial problems arising in the dimer m…
The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
Combinatorial optimization augmented machine learning (COAML) has recently emerged as a powerful paradigm for integrating predictive models with combinatorial decision-making. By embedding combinatorial optimization oracles into learning…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
There has been rapidly growing demand of polymeric materials coming from different aspects of modern life because of the highly diverse physical and chemical properties of polymers. Polymer informatics is an interdisciplinary research field…
Social choice has become a foundational component of modern machine learning systems. From auctions and resource allocation to the alignment of large generative models, machine learning pipelines increasingly aggregate heterogeneous…
The predominance of machine learning models in many spheres of human activity has led to a growing demand for their transparency. The transparency of models makes it possible to discern some factors, such as security or non-discrimination.…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
The dimer problem arose in a thermodynamic study of diatomic molecules, and was abstracted into one of the most basic and natural problems in both statistical mechanics and combinatoric mathematics. Given a rectangular lattice of volume V…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
Modeling with multi-omics data presents multiple challenges such as the high-dimensionality of the problem ($p \gg n$), the presence of interactions between features, and the need for integration between multiple data sources. We establish…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
With the emergence of foundation models, deep learning-based object detectors have shown practical usability in closed set scenarios. However, for real-world tasks, object detectors often operate in open environments, where crucial factors…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…
The threat of global warming and the demand for reliable climate predictions pose a formidable challenge being the climate system multiscale, high-dimensional and nonlinear. Spatiotemporal recurrences of the system hint to the presence of a…
Lecture notes from a minicourse given at the ICTP in May 2002.
A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of…