Related papers: A Hierarchy for Constant Communication Complexity
We study ternary sequences associated with a multidimensional continued fraction algorithm introduced by the first author. The algorithm is defined by two matrices and we show that it is measurably isomorphic to the shift on the set…
The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of…
Boolean function $F(x,y)$ for $x,y \in \{0,1\}^n$ is an XOR function if $F(x,y)=f(x\oplus y)$ for some function $f$ on $n$ input bits, where $\oplus$ is a bit-wise XOR. XOR functions are relevant in communication complexity, partially for…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
The complexity of an infinite word can be measured in several ways, the two most common measures being the subword complexity and the abelian complexity. In 2015, Rigo and Salimov introduced a family of intermediate complexities indexed by…
Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphism on homology. In the other, the weak equivalences are maps…
Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data.…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…
We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory.…
We exhibit an $n$-bit communication problem with a constant-cost randomized protocol but which requires $n^{\Omega(1)}$ deterministic (or even non-deterministic) queries to an Equality oracle. Therefore, even constant-cost randomized…
Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions…
We consider four categories: the category of diagrams of small categories indexed by a given small category O, the (comma) category of small categories over O, the category of diagrams of simplicial sets indexed by O, and the category of…
Similarity is a fundamental measure in network analyses and machine learning algorithms, with wide applications ranging from personalized recommendation to socio-economic dynamics. We argue that an effective similarity measurement should…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
This paper proposes a novel method that can replace compression-based dissimilarity measure (CDM) in composer estimation task. The main features of the proposed method are clarity and scalability. First, since the proposed method is…
One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as…
Hierarchical classification addresses the problem of classifying items into a hierarchy of classes. An important issue in hierarchical classification is the evaluation of different classification algorithms, which is complicated by the…
The classical Dold-Kan correspondence is known to admit a categorification in the form of an equivalence between the $\infty$-categories of $2$-simplicial stable $\infty$-categories and connective chain complexes of stable…