相关论文: A Scrapbook of Inadmissible Line Complexes For the…
The admissibility problem in integral geometry asks for which collections of affine subspaces the Radon transform remains injective. In the discrete setting, this becomes a purely combinatorial question about recovering a function on a…
We consider the X-ray transform in a projective space over a finite field. It is well known (after E. Bolker) that this transform is injective. We formulate an analog of I.M. Gelfand's admissibility problem for the Radon transform, which…
We consider the Radon transform along lines in an $n$ dimensional vector space over the two element field. It is well known that this transform is injective and highly overdetermined. We classify the minimal collections of lines for which…
We formally define algorithmic capture of combinatorial tasks as the ability of a transformer to extrapolate to arbitrary task sizes with controllable error and logarithmic sample adaptation, providing a sharp scaling criterion for…
The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…
In extension problems of partial graph drawings one is given an incomplete drawing of an input graph $G$ and is asked to complete the drawing while maintaining certain properties. A prominent area where such problems arise is that of…
In the context of positive infinite-dimensional linear systems, we systematically study $L^p$-admissible control and observation operators with respect to the limit-cases $p=\infty$ and $p=1$, respectively. This requires an in-depth…
We consider the problem of translating between irreducible closed sets and implicational bases in closure systems. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph…
Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
This paper examines several measures of space complexity of variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept every word in the language of…
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but…
The Restricted Invertibility problem is the problem of selecting the largest subset of columns of a given matrix $X$, while keeping the smallest singular value of the extracted submatrix above a certain threshold. In this paper, we address…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…