Related papers: Neural Codes and the Factor Complex
We give a complete combinatorial characterization of weakly $d$-Tverberg complexes. These complexes record which intersection combinatorics of convex hulls necessarily arise in any sufficiently large general position point set in $\mathbb…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term…
Spike patterns have been reported to encode sensory information in several brain areas. Here we assess the role of specific patterns in the neural code, by comparing the amount of information transmitted with different choices of the…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
This paper extends and generalizes previous works on constructing combinatorial multivector fields from continuous systems (see [10]) and the construction of combinatorial vector fields from data (see [2]) by introducing an optimization…
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex…
We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time…
It is widely believed that complex machine learning models generally encode features through linear representations. This is the foundational hypothesis behind a vast body of work on interpretability. A key challenge toward extracting…
We provide an exact estimate on the maximal subword complexity for quasiperiodic infinite words. To this end we give a representation of the set of finite and of infinite words having a certain quasiperiod q via a finite language derived…
The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
Place cells are neurons that act as biological position sensors, associated with and firing in response to regions of an environment to situate an organism in space. These associations are recorded in (combinatorial) neural codes,…
We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…
We introduce new types of local algorithms, which we call "ASI Algorithms", and use them to demonstrate a link between descriptive and computable combinatorics. This allows us to unify arguments from the two fields, and also sometimes to…
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix…