arXiv subjects

Luís Diogo

Publications and source records attributed to Luís Diogo.

5 recordsLinked to original sources

arXiv2026

The 2026 Algorithmic Information Theory Data Compression Challenge

Lossless data compression remains central to computer science, with direct impact on storage, communication bandwidth, computational cost, and energy consumption. It is also closely related to Algorithmic Information Theory, where compressibility provides an operational measure of structure and non-randomness. This paper presents the 2026 Algorithmic Information Theory Data Compression Challenge, a benchmark for evaluating general-purpose lossless compressors under realistic constraints. Submissions were encouraged to use arithmetic or range coding, limited to at most 8 GB of memory, and required to include a decompressor no larger than 1 MB. The benchmark comprised sixteen heterogeneous files, split into public training and hidden testing datasets. In total, 117 valid submitted compressors were evaluated alongside established reference compressors using compression ratio, compression and decompression time, Weissman score, and Pareto-frontier analysis. The results show that performance depends strongly on the optimization criterion: fast compressors achieved the best speed-oriented scores, whereas modelling-intensive compressors produced smaller outputs at higher computational cost. A Normalized Compression Distance analysis further revealed clusters of related submissions and distinguished incremental variants from more independent implementations. Selected submissions were described for their methodological novelty or competitive performance and further tested on four large external datasets, where several achieved competitive or superior results relative to established compressors. Overall, the challenge confirms the importance of probabilistic modelling, hidden testing, and external datasets for assessing compression performance and generalization. Benchmark resources, leaderboard data, binaries, and selected source code are publicly available at https://aitdcc.github.io.

cs.IT↗

arXiv2024

Augmentations, annuli, and Alexander polynomials

The augmentation variety of a knot is the locus, in the 3-dimensional coefficient space of the knot contact homology dg-algebra, where the algebra admits a unital chain map to the complex numbers. We explain how to express the Alexander polynomial of a knot in terms of the augmentation variety: it is the exponential of the integral of a ratio of two partial derivatives. The expression is derived from a description of the Alexander polynomial as a count of Floer strips and holomorphic annuli, in the cotangent bundle of Euclidean 3-space, stretching between a Lagrangian with the topology of the knot complement and the zero-section, and from a description of the boundary of the moduli space of such annuli with one positive puncture.

math.SG↗

arXiv2023

Monotone Lagrangians in cotangent bundles of spheres

We study the compact monotone Fukaya category of $T^*S^n$, for $n\geq 2$, and show that it is split-generated by two classes of objects: the zero-section $S^n$ (equipped with suitable bounding cochains) and a 1-parameter family of monotone Lagrangian tori $(S^1\times S^{n-1})_τ$, with monotonicity constants $τ>0$ (equipped with rank 1 unitary local systems). As a consequence, any closed orientable spin monotone Lagrangian (possibly equipped with auxiliary data) with non-trivial Floer cohomology is non-displaceable from either $S^n$ or one of the $(S^1\times S^{n-1})_τ$. In the case of $T^*S^3$, the monotone Lagrangians $(S^1\times S^2)_τ$ can be replaced by a family of monotone tori $T^3_τ$.

math.SG↗

arXiv2019

Symplectic Homology of complements of smooth divisors

If $(X, ω)$ is a symplectic manifold, and $Σ$ is a smooth symplectic submanifold Poincaré dual to a positive multiple of $ω$, $X \setminus Σ$ admits a compactification as a Liouville domain, which we then complete to $(W, dλ)$. Under monotonicity assumptions on $X$ and on $Σ$, we construct a chain complex whose homology computes the Symplectic Homology of $W$. We show the differential is given in terms of Morse contributions, terms computed from Gromov-Witten invariants of $X$ relative to $Σ$ and terms computed from the Gromov-Witten invariants of $Σ$. We use a Morse-Bott model for symplectic homology. Our proof involves comparing Floer cylinders with punctures to pseudoholomorphic curves in in the symplectization of the unit normal bundle to $Σ$.

math.SG↗

arXiv2018

Morse-Bott Split Symplectic Homology

We introduce a chain complex associated to a Liouville domain $(\overline{W}, dλ)$ whose boundary $Y$ admits a Boothby--Wang contact form (i.e. is a prequantization space). The differential counts cascades of Floer solutions in the completion $W$ of $\overline{W}$, in the spirit of Morse--Bott homology (as in work of Bourgeois, Frauenfelder arXiv:math/0309373 and Bourgeois-Oancea arXiv:0704.1039). The homology of this complex is the symplectic homology of the completion $W$. We identify a class of simple cascades and show that their moduli spaces are cut out transversely for generic choice of auxiliary data. If $X$ is obtained by collapsing the boundary along Reeb orbits and $Σ$ is the quotient of $Y$ by the $S^1$-action induced by the Reeb flow, we also establish transversality for certain moduli spaces of holomorphic spheres in $X$ and in $Σ$. Finally, under monotonicity assumptions on $X$ and $Σ$, we show that for generic data, the differential in our chain complex counts elements of moduli spaces that are transverse. Furthermore, by some index estimates, we show that very few combinatorial types of cascades can appear in the differential.

math.SG↗