arXiv subjects

C. Escudero

Publications and source records attributed to C. Escudero.

12 recordsLinked to original sources

arXiv2024

Optimal Trade Characterizations in Multi-Asset Crypto-Financial Markets

This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This generalizes previous results that used convexity, and also guarantees the robustness against arbitrage of so-designed automatic market makers. The theoretical results are illustrated by families of examples given by generalized means, and also by numerical simulations in certain concrete cases. These simulations along with the mathematical analysis suggest that the quasilinear-trade-function based automatic market makers might replicate the functioning of those based on convex functions, in particular regarding their resilience to arbitrage.

math.OC↗

arXiv2021

The Fornax Cluster through S-PLUS

The Southern Photometric Local Universe Survey (S-PLUS) aims to map $\approx$ 9300 deg$^2$ of the Southern sky using the Javalambre filter system of 12 optical bands, 5 Sloan-like filters and 7 narrow-band filters centered on several prominent stellar features ([OII], Ca H+K, D4000, H$_δ$, Mgb, H$_α$ and CaT). S-PLUS is carried out with the T80-South, a new robotic 0.826-m telescope located on CTIO, equipped with a wide FoV camera (2 deg$^2$). In this poster we introduce project #59 of the S-PLUS collaboration aimed at studying the Fornax galaxy cluster covering an sky area of $\approx$ 11 $\times$ 7 deg$^2$, and with homogeneous photometry in the 12 optical bands of S-PLUS (Coordinator: A. Smith Castelli).

astro-ph.GA↗

arXiv2019

Galaxias de bajo brillo superficial: analogas a los satélites de Andrómeda en Pegasus I?

Here we show the preliminary results of a study where there seems to be a bias effect in the size distributions of the detected low-surface brightness (LSB) galaxies in different environments. In this sense, more distant groups/clusters would lack small effective radius objects, while large systems would not found in the Local Group and nearby environments. While there may be an actual shortage of large LSB galaxies in low-density environments like the Local Group, the non-detection of small (and faint) systems at large distances is clearly a selection effect. As an example, LSB galaxies with similar sizes to those of the satellites of Andromeda in the Local Group, will be certainly missed in a visual identification at the distance of Pegasus I.

astro-ph.GA↗

arXiv2018

Encounter-controlled coalescence and annihilation on a one-dimensional growing domain

The kinetics of encounter-controlled processes in growing domains is markedly different from that in a static domain. Here, we consider the specific example of diffusion limited coalescence and annihilation reactions in one-dimensional space. In the static case, such reactions are among the few systems amenable to exact solution, which can be obtained by means of a well-known method of intervals. In the case of a uniformly growing domain, we show that a double transformation in time and space allows one to extend this method to compute the main quantities characterizing the spatial and temporal behavior. We show that a sufficiently fast domain growth brings about drastic changes in the behavior. In this case, the reactions stop prematurely, as a result of which the survival probability of the reacting particles tends to a finite value at long times and their spatial distribution freezes before reaching the fully self-ordered state. We obtain exact results for the survival probability and for key properties characterizing the degree of self-ordering induced by the chemical reactions, i.e., the interparticle distribution function and the pair correlation function. These results are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2018

Reaction-diffusion kinetics in growing domains

Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become indispensable tools. In population dynamics, say, such approaches are utilized to study many systems, e.g., colonies of microorganisms or ecological systems. While the majority of studies focus on the case of a static domain, the time-dependent case is also important, as it allows one to deal with situations where the domain growth takes place over time scales that are relevant for the computation of reaction rates and of the associated reactant distributions. Such situations are indeed frequently encountered in the field of developmental biology, notably in connection with pattern formation, embryo growth or morphogen gradient formation. In this chapter, we review some recent advances in the study of pure diffusion processes in growing domains. These results are subsequently taken as a starting point to study the kinetics of a simple reaction-diffusion process, i.e., the encounter-controlled annihilation reaction. The outcome of the present work is expected to pave the way for the study of more complex reaction-diffusion systems of possible relevance in various fields of research.

cond-mat.stat-mech↗

arXiv2018

Propiedades fotométricas de las galaxias enanas de bajo brillo superficial en la zona central del grupo Pegasus I

Here we show the preliminary results of a photometric study of low surface brightness objects with $μ_{g'}~\gtrsim~25$~mag/arcsec$^2$. These objects are present in several fields obtained with GEMINI-GMOS, in the central region of the Pegasus I group. We found that their photometric characteristics are similar to the so-called dwarf spheroidal galaxies or to the ultra low surface brightness galaxies.

astro-ph.GA↗

arXiv2016

Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties

We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time $τ(t)$, which we define via the relation $\dot τ=1/a^2$, where $a(t)$ is the expansion scale factor. If the medium expansion is driven by a power law [$a(t) \propto t^γ$ with $γ>0$], we find interesting crossover effects in the mixing effectiveness of the diffusion process when the characteristic exponent $γ$ is varied. Crossover effects are also found at the level of the survival probability and of the moments of the first passage-time distribution with two different regimes separated by the critical value $γ=1/2$. The case of an exponential scale factor is analyzed separately both for expanding and contracting media. In the latter situation, a stationary probability distribution arises in the long time limit.

cond-mat.stat-mech↗

arXiv2010

Discretization-related issues in the KPZ equation: Consistency, Galilean-invariance violation, and fluctuation--dissipation relation

In order to perform numerical simulations of the KPZ equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf--Cole transformation applied to a diffusion equation (with \emph{multiplicative} noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen. On the other hand, since the discretization is an operation performed on \emph{space} and the Hopf--Cole transformation is \emph{local} both in space and time, the former should be the same regardless of the field to which it is applied. It is shown that whereas some discretization schemes pass both consistency tests, known examples in the literature do not. The requirement of consistency for the discretization of Lyapunov functionals is argued to be a natural and safe starting point in choosing spatial discretization schemes. We also analyze the relation between real-space and pseudo-spectral discrete representations. In addition we discuss the relevance of the Galilean invariance violation in these consistent discretization schemes, and the alleged conflict of standard discretization with the fluctuation--dissipation theorem, peculiar of 1D.

cond-mat.stat-mech↗

arXiv2005

Geometrical aspects of isoscaling

The property of isoscaling in nuclear fragmentation is studied using a simple bond percolation model with ``isospin'' added as an extra degree of freedom. It is shown analytically, first, that isoscaling is expected to exist in such a simple model with the only assumption of fair sampling with homogeneous probabilities. Second, numerical percolations of hundreds of thousands of grids of different sizes and with different $N$ to $Z$ ratios confirm this prediction with remarkable agreement. It is thus concluded that isoscaling emerges from the simple assumption of fair sampling with homogeneous probabilities, a requirement which, if put in the nomenclature of the minimum information theory, translates simply into the existence of equiprobable configurations in maximum entropy states.

nucl-th↗

arXiv2004

Effects of internal fluctuations on the spreading of Hantavirus

We study the spread of Hantavirus over a host population of deer mice using a population dynamics model. We show that taking into account the internal fluctuations in the mouse population due to its discrete character strongly alters the behaviour of the system. In addition to the familiar transition present in the deterministic model, the inclusion of internal fluctuations leads to the emergence of an additional deterministically hidden transition. We determine parameter values that lead to maximal propagation of the disease, and discuss some implications for disease prevention policies.

q-bio.PE↗

arXiv2003

Extinction in population dynamics

We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead to certain extinction. Standard continuum mean field models in one dimension yield a critical refuge length L_c such that a population in a refuge larger than this is assured survival. Herein we extend the model to take into account the discreteness and finiteness of the population, which leads us to a stochastic description. We present a particular critical criterion for likely extinction, namely, that the standard deviation of the population be equal to the mean. According to this criterion, we find that while survival can no longer be guaranteed for any refuge size, for sufficiently weak competition one can make the refuge large enough (certainly larger than L_c) to cause extinction to be unlikely. However, beyond a certain value of the competition rate parameter it is no longer possible to escape a likelihood of extinction even in an infinite refuge. These unavoidable fluctuations therefore have a severe impact on refuge design issues.

cond-mat.stat-mech↗

arXiv2003

Outbreaks of Hantavirus induced by seasonality

Using a model for rodent population dynamics, we study outbreaks of Hantavirus infection induced by the alternation of seasons. Neither season by itself satisfies the environmental requirements for propagation of the disease. This result can be explained in terms of the seasonal interruption of the relaxation process of the mouse population toward equilibrium, and may shed light on the reported connection between climate variations and outbreaks of the dise ase.

cond-mat.stat-mech↗