8 citations · 11 across the 19 of their papers we have counts for
25 papers
Stable Regularity Lemmas: Efficient Algorithms and Essentially Tight Littlestone Bounds
Leonardo N. Coregliano, Fernando G. Jeronimo
In this paper, we determine the precise asymptotics of the number of parts of stable regularity equipartitions in terms of the Littlestone dimension: every graph of Littlestone…
High-arity Sample Compression
Leonardo N. Coregliano, William Opich
Recently, a series of works have started studying variations of concepts from learning theory for product spaces, which can be collected under the name high-arity learning theory.…
Some model-theoretic consequences of high-arity uniform convergence, part I
Leonardo N. Coregliano, Maryanthe Malliaris
We show that certain families of sets in (or ) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately defina…
Sample completion, structured correlation, and Netflix problems
Leonardo N. Coregliano, Maryanthe Malliaris
We develop a new high-dimensional statistical learning model which can take advantage of structured correlation in data even in the presence of randomness. We completely characteri…
A packing lemma for VCN-dimension and learning high-dimensional data
Leonardo N. Coregliano, Maryanthe Malliaris
Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, t…
Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones +2
A central and longstanding open problem in coding theory is the rate-versus-distance trade-off for binary error-correcting codes. In a seminal work, Delsarte introduced a family of…
Bigraph percolation problems
Leonardo N. Coregliano
A bigraph is weakly norming if the th root of the density of in is a norm in the space of bounded measurable functions …
On the equivalence of quasirandomness and exchangeable representations independent from lower-order variables
Leonardo N. Coregliano, Henry P. Towsner
It is often convenient to represent a process for randomly generating a graph as a graphon. (More precisely, these give \emph{vertex exchangeable} processes -- those processes in w…
How to get the random graph with non-uniform probabilities?
Leonardo N. Coregliano, Jarosław Swaczyna, Agnieszka Widz
The Rado Graph, sometimes also known as the (countable) Random Graph, can be generated almost surely by putting an edge between any pair of vertices with some fixed probability $p…
High-arity PAC learning via exchangeability
Leonardo N. Coregliano, Maryanthe Malliaris
We develop a theory of high-arity PAC learning, which is statistical learning in the presence of "structured correlation". In this theory, hypotheses are either graphs, hypergraphs…
Exact Completeness of LP Hierarchies for Linear Codes
Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones
Determining the maximum size of a binary code of blocklength and distance remains an elusive open question even when restricted to the important class of linear…
Weak randomness in graphons and theons
Leonardo N. Coregliano, Maryanthe Malliaris
Call a hereditary family of graphs strongly persistent if there exists a graphon such that in all subgraphons of , is precisely the class of…
Left-cut-percolation and induced-Sidorenko bigraphs
Leonardo N. Coregliano
A Sidorenko bigraph is one whose density in a bigraphon is minimized precisely when is constant. Several techniques of the literature to prove the Sidorenko property consis…
Countable Ramsey
Leonardo N. Coregliano, Maryanthe Malliaris
The celebrated Erdős-Hajnal Conjecture says that in any proper hereditary class of finite graphs we are guaranteed to have a clique or anti-clique of size , which is a much be…
A Complete Linear Programming Hierarchy for Linear Codes
Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones
A longstanding open problem in coding theory is to determine the best (asymptotic) rate of binary codes with minimum constant (relative) distance . An existential lower…
Biregularity in Sidorenko's Conjecture
Leonardo N. Coregliano, Alexander A. Razborov
Sidorenko's Conjecture says that the minimum density of a bigraph in a bigraphon of a given edge density is attained when is a constant function. A consequence of a res…
Natural quasirandomness properties
Leonardo N. Coregliano, Alexander A. Razborov
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permuta…
On the abstract chromatic number and its computability for finitely axiomatizable theories
Leonardo N. Coregliano
The celebrated Erdős--Stone--Simonovits theorem characterizes the asymptotic maximum edge density in -free graphs as , where $χ(\mathc…
Tighter Bounds on the Independence Number of the Birkhoff Graph
Leonardo Nagami Coregliano, Fernando Granha Jeronimo
The Birkhoff graph is the Cayley graph of the symmetric group , where two permutations are adjacent if they differ by a single cycle. Our main result is a tigh…
Semantic Limits of Dense Combinatorial Objects
Leonardo N. Coregliano, Alexander A. Razborov
The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag alg…
Packing densities of layered permutations and the minimum number of monotone sequences in layered permutations
Josefran de Oliveira Bastos, Leonardo Nagami Coregliano
In this paper, we present two new results of layered permutation densities. The first one generalizes theorems from Hästö (2003) and Warren (2004) to compute the permutation packin…
A continuous time stochastic model for biological neural nets
Leonardo Nagami Coregliano
We propose a new stochastic model for biological neural nets which is a continuous time version of the model proposed by Galves and Löcherbach in [A. Galves and E. Löcherbach, "In…
On the maximum density of fixed strongly connected subtournaments
Leonardo N. Coregliano, Roberto F. Parente, Cristiane M. Sato
We study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for five tournaments as well as…
Quasi-Carousel Tournaments
Leonardo Nagami Coregliano
A tournament is called locally transitive if the outneighbourhood and the inneighbourhood of every vertex are transitive. Equivalently, a tournament is locally transitive if it avo…