We show that the ring of Siegel-Jacobi forms of fixed degree and of fixed or bounded ratio between weight and index is not finitely generated. Our main tool is the theory of toroidal b-divisors and their relation to convex geometry. As a byproduct of our methods, we prove a conjecture of Kramer about the representation of all Siegel-Jacobi forms as sections of certain line bundles and we recover a formula due to Tai for the asymptotic dimension of the space of Siegel-Jacobi forms of given ratio between weight and index.

Ana María Botero José Ignacio Burgos Gil David Holmes Robin de Jong

This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived. Numerical examples and applications to simple systems are presented. Previous researches have shown numerically that the systems under study, when arranged in a network, exhibits rich and complex patterns that can dynamically change in response to variations in the environment. We show how this ``adaptation'' process strongly depends on the coupling characteristics of the network. Other potential applications of synchronized chaotic oscillators are discussed.

Juan C. Botero Jean-Jacques E. Slotine

We show that with respect to any bipartite division of modes, pure fermion gaussian states display the same type of structure in its entanglement of modes as that of the BCS wave function, namely, that of a tensor product of entangled two-mode squeezed fermion states. We show that this structure applies to a wider class of "isotropic" mixed fermion states, for which we derive necessary and sufficient conditions for mode entanglement.

Alonso Botero Benni Reznik

Using the geometric entanglement measure, we study the scaling of multipartite entanglement in several 1D models at criticality, specifically the linear harmonic chain and the XY spin chain encompassing both the Ising and XX critical models. Our results provide convincing evidence that 1D models at criticality exhibit a universal logarithmic scaling behavior ~(c/12)log l in the multipartite entanglement per region for a partition of the system into regions of size l, where c is the central charge of the corresponding universality class in conformal field theory.

Alonso Botero Benni Reznik

The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and post-selected ensembles, and if the selections involve entangled states with some other system. We show that the problem is related to the problem of assigning weak values to a continuous family of operators, and give explicit examples where this problem is solvable. Some foundational implications are briefly discussed.

Alonso Botero

We present the solution to the "mean king's problem" in the continuous variable setting. We show that in this setting, the outcome of a randomly-selected projective measurement of any linear combination of the canonical variables x and p can be ascertained with arbitrary precision. Moreover, we show that the solution is in turn a solution to an associated "conjunctive" version of the problem, unique to continuous variables, where the inference task is to ascertain all the joint outcomes of a simultaneous measurement of any number of linear combinations of x and p.

Alonso Botero Yakir Aharonov

In this paper we use the theory of central elements in order to provide a characterization for coextensive varieties. In particular, if the variety is of finite type, congruence-permutable and its class of directly indecomposable members is universal, then coextensivity is equivalent to be a variety of shells.

W. J. Zuluaga Botero

The possibility of programming the control and data planes, enabled by the Software-Defined Networking (SDN) paradigm, represents a fertile ground on top of which novel operation and management mechanisms can be fully explored, being Distributed Denial of Service (DDoS) attack detection based on machine learning techniques the focus of this work. To carry out the detection, this paper proposes ORACLE: cOllaboRation of dAta and Control pLanEs to detect DDoS attacks, an architecture that promotes the coordination of control and data planes to detect network attacks. As its first contribution, this architecture delegates to the data plane the extraction and processing of traffic information collected per flow. This is done in order to ease the calculation and classification of the feature set used in the attack detection, as the needed flow information is already processed when it arrives at the control plane. Besides, as the second contribution, this architecture breaks the limitations to calculate some features that are not possible to implement in a traditional OpenFlow-based environment. In the evaluation of ORACLE, we obtained up to 96% of accuracy in the testing phase, using a K-Nearest Neighbor model.

Sebastián Gómez Macías Luciano Paschoal Gaspary Juan Felipe Botero

In this paper we provide a Stone style duality for monotone semilattices by using the topological duality developed in \cite{Celani2020} for semilattices together with a topological description of their canonical extension. As an application of this duality we obtain a characterization of the congruences of monotone semilattices by means of monotone lower-Vietoris-type topologies.

Ismael Calomino Paula Menchón William J. Zuluaga Botero

In this paper we show that within the context of coextensive varieties, the functor of central elements is representable. In addition, we use the theory of central elements to establish a criterion for fp-coextensive varieties that allows to decide whether the Gaeta Topos classifies indecomposable objects in terms of the indecomposability of the free algebra on one generator.

W. J. Zuluaga Botero