arXiv subjects

Daniel Campos

Publications and source records attributed to Daniel Campos.

72 records · Page 4Linked to original sources

arXiv2019

Experiments in Inferring Social Networks of Diffusion

Information diffusion is a fundamental process that takes place over networks. While it is rarely realistic to observe the individual transmissions of the information diffusion process, it is typically possible to observe when individuals first publish the information. We look specifically at previously published algorithm NETINF that probabilistically identifies the optimal network that best explains the observed infection times. We explore how the algorithm could perform on a range of intrinsically different social and information network topologies, from news blogs and websites to Twitter to Reddit.

cs.SI↗

arXiv2019

Reconstruction of the magnetic field for a Schrödinger operator in a cylindrical setting

In this thesis we consider a magnetic Schrödinger inverse problem over a compact domain contained in an infinite cylindrical manifold. We show that, under certain conditions on the electromagnetic potentials, we can recover the magnetic field from boundary measurements in a constructive way. A fundamental tool for this procedure is a global Carleman estimate for the magnetic Schrödinger operator. We prove this by conjugating the magnetic operator essentially into the Laplacian, and using the Carleman estimates for it proven by Kenig-Salo-Uhlmann in the anisotropic setting, see [KSU11a]. The conjugation is achieved through pseudodifferential operators over the cylinder, for which we develop the necessary results. The main motivations to attempt this question are the following results concerning the magnetic Schrödinger operator: first, the solution to the uniqueness problem in the cylindrical setting in [DSFKSU09], and, second, the reconstruction algorithm in the Euclidean setting from [Sal06]. We will also borrow ideas from the reconstruction of the electric potential in the cylindrical setting from [KSU11b]. These two new results answer partially the Carleman estimate problem (Question 4.3.) proposed in [Sal13] and the reconstruction for the magnetic Schrödinger operator mentioned in the introduction of [KSU11b]. To our knowledge, these are the first global Carleman estimates and reconstruction procedure for the magnetic Schrödinger operator available in the cylindrical setting.

math.AP↗

arXiv2019

Recurrence time correlations in random walks with preferential relocation to visited places

Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and subsequent recurrence times through a site; typically, a preference for revisiting sites is expected to result in a positive correlation between consecutive recurrence times. Here we derive a continuous-time generalization of the random walk model with preferential relocation to visited sites proposed in [Phys. Rev. Lett. 112, 240601] to explore this effect, together with the main transport properties induced by the long-range memory. Despite the highly non-Markovian character of the process, our analytical treatment allows us to (i) observe the existence of an asymptotic logarithmic (ultraslow) growth for the mean square displacement, in accordance to the results found for the original discrete-time model, and (ii) confirm the existence of positive correlations between first-passage and subsequent recurrence times. This analysis is completed with a comprehensive numerical study which reveals, among other results, that these correlations between first-passage and recurrence times also exhibit clear signatures of the ultraslow dynamics present in the process.

cond-mat.stat-mech↗

arXiv2019

Transport properties and first arrival statistics of random searches with stochastic reset times

Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to a given position $x$, may reach it in a finite time when they reset their position. In this work we study these emerging phenomena from a unified perspective. On one hand we study the existence of a finite equilibrium MSD when resets are applied to random motion with $\langle x^2(t)\rangle _m\sim t^p$ for $0<p\leq2$. For exponentially distributed reset times, a compact formula is derived for the equilibrium MSD of the overall process in terms of the mean reset time and the motion MSD. On the other hand, we also test the robustness of the finiteness of the MFAT for different motion dynamics which are subject to stochastic resets. Finally, we study a biased Brownian oscillator with resets with the general formulas derived in this work, finding its equilibrium first moment and MSD, and its MFAT to the minimum of the harmonic potential.

cond-mat.stat-mech↗

arXiv2019

Demographic stochasticity and extinction in populations with Allee effect

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.

cond-mat.stat-mech↗

arXiv2018

Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics

In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an expression for the mean square displacement of the overall process and study its dependence with the statistical properties of the resets, the residence and the movement. From this general formula, we see that the inclusion of the residence after the resets is able to induce super-diffusive to sub-diffusive (or diffusive) regimes and it can also make a sub-diffusive walker reach a constant MSD or even collapse. Second, we study how the reset-and-residence mechanism affects the first arrival time of different search processes to a given position, showing that the long time behavior of the reset and residence time distributions determine the existence of the mean first arrival time.

cond-mat.stat-mech↗

arXiv2018

MS MARCO: A Human Generated MAchine Reading COmprehension Dataset

We introduce a large scale MAchine Reading COmprehension dataset, which we name MS MARCO. The dataset comprises of 1,010,916 anonymized questions---sampled from Bing's search query logs---each with a human generated answer and 182,669 completely human rewritten generated answers. In addition, the dataset contains 8,841,823 passages---extracted from 3,563,535 web documents retrieved by Bing---that provide the information necessary for curating the natural language answers. A question in the MS MARCO dataset may have multiple answers or no answers at all. Using this dataset, we propose three different tasks with varying levels of difficulty: (i) predict if a question is answerable given a set of context passages, and extract and synthesize the answer as a human would (ii) generate a well-formed answer (if possible) based on the context passages that can be understood with the question and passage context, and finally (iii) rank a set of retrieved passages given a question. The size of the dataset and the fact that the questions are derived from real user search queries distinguishes MS MARCO from other well-known publicly available datasets for machine reading comprehension and question-answering. We believe that the scale and the real-world nature of this dataset makes it attractive for benchmarking machine reading comprehension and question-answering models.

cs.CL↗

arXiv2017

Stochastic foundations in nonlinear density-regulation growth

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for population extinction and calculate the mean time to extinction. If the population does not become extinct, we obtain analytical expressions for the population abundance distribution. Our theoretical results are based on WKB theory and the probability generating function formalism and are verified by numerical simulations.

q-bio.PE↗

arXiv2017

Langevin dynamics for ramified structures

We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. The mean square displacement (MSD) along the backbone characterizes the transport through the ramified structure. We derive a general analytical expression for this observable in terms of the probability distribution function of the motion along the secondary branches. We apply our result to various types of motion along the secondary branches of finite or infinite length, such as subdiffusion, superdiffusion, and Langevin dynamics with colored Gaussian noise and with non-Gaussian white noise. Monte Carlo simulations show excellent agreement with the analytical results. The MSD for the case of Gaussian noise is shown to be independent of the noise color. We conclude by generalizing our analytical expression for the MSD to the case where each secondary branch is $n$ dimensional.

cond-mat.stat-mech↗

arXiv2015

Phase transitions in optimal search times: how random walkers should combine resetting and flight scales

Recent works have explored the properties of Lévy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT) through the origin [Phys. Rev. Lett. 113, 220602 (2014)]. Here we show how actually an interesting dynamics, including also phase transitions for the minimization of the MFPT, can also be obtained without invoking the use of Lévy statistics but for the simpler case of random walks with exponentially distributed flights of constant speed. We explore this dynamics both in the case of finite and infinite domains, and for different implementations of the resetting mechanism to show that different ways to introduce resetting consistently lead to a quite similar dynamics. The use of exponential flights has the strong advantage that exact solutions can be obtained easily for the MFPT through the origin, so a complete analytical characterization of the system dynamics can be provided. Furthermore, we discuss in detail how the phase transitions observed in random walks with resetting are closely related to several ideas recurrently used in the field of random search theory, in particular to other mechanisms proposed to understand random search in space as mortal random-walks or multi-scale random-walks. As a whole we corroborate that one of the essential ingredients behind MFPT minimization lies in the combination of multiple movement scales (whatever its origin).

cond-mat.stat-mech↗

arXiv2015

Mesoscopic description of random walks on combs

Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches.

cond-mat.stat-mech↗

arXiv2015

First-passage times in multi-scale random walks: the impact of movement scales on search efficiency

An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets, which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about targets distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

cond-mat.stat-mech↗

arXiv2015

Stochastic dynamics and logistic population growth

The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic parameters. In addition, we derive the conditions for extinction or persistence of the population by employing either the "momentum-space" spectral theory or the "real-space" Wentzel-Kramers-Brillouin (WKB) approximation to determine the probability distribution function and the mean time to extinction of the population. Our analytical results agree well with numerical simulations.

q-bio.PE↗

arXiv2012

Depths and Cohen-Macaulay Properties of Path Ideals

Given a tree T on n vertices, there is an associated ideal I of a polynomial ring in n variables over a field, generated by all paths of a fixed length of T. We show that such an ideal always satisfies the Konig property and classify all trees for which R/I is Cohen-Macaulay. More generally, we show that an ideal I whose generators correspond to any collection of subtrees of T satisfies the Konig property. Since the edge ideal of a simplicial tree has this form, this generalizes a result of Faridi. Moreover, every square-free monomial ideal can be represented (non-uniquely) as a subtree ideal of a graph, so this construction provides a new combinatorial tool for studying square-free monomial ideals. For a special class of trees, namely trees that are themselves a path, a precise formula for the depth is given and it is shown that the proof extends to provide a lower bound on the Stanley depth of these ideals. Combining these results gives a new class of ideals for which the Stanley Conjecture holds.

math.AC↗

arXiv2008

The effects of distributed life cycles on the dynamics of viral infections

We explore the role of cellular life cycles for viruses and host cells in an infection process. For this purpose, we derive a generalized version of the basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population dynamics of immune responses to persistent viruses. Science 272, 74-79) from a mesoscopic description. In its final form the model can be written as a set of Volterra integrodifferential equations. We consider the role of age-distributed delays for death times and the intracellular (eclipse) phase. These processes are implemented by means of probability distribution functions. The basic reproductive ratio $R_0$ of the infection is properly defined in terms of such distributions by using an analysis of the equilibrium states and their stability. It is concluded that the introduction of distributed delays can strongly modify both the value of $R_0$ and the predictions for the virus loads, so the effects on the infection dynamics are of major importance. We also show how the model presented here can be applied to some simple situations where direct comparison with experiments is possible. Specifically, phage-bacteria interactions are analysed. The dynamics of the eclipse phase for phages is characterized analytically, which allows us to compare the performance of three different fittings proposed before for the one-step growth curve.

q-bio.PE↗

arXiv2008

Limited resources and evolutionary learning may help to understand the mistimed reproduction in birds caused by climate change

We present an agent-based model inspired by the Evolutionary Minority Game (EMG), albeit strongly adapted to the case of competition for limited resources in ecology. The agents in this game become able, after some time, to predict the a priori best option as a result of an evolution-driven learning process. We show that a self-segregated social structure can emerge from this process, i.e., extreme learning strategies are always favoured while intermediate learning strategies tend to die out. This result may contribute to understanding some levels of organization and cooperative behaviour in ecological and social systems. We use the ideas and results reported here to discuss an issue of current interest in ecology: the mistimings in egg laying observed for some species of bird as a consequence of their slower rate of adaptation to climate change in comparison with that shown by their prey. Our model supports the hypothesis that habitat-specific constraints could explain why different populations are adapting differently to this situation, in agreement with recent experiments.

q-bio.PE↗

arXiv2008

The growth of human settlements during the Neolithic, clustering and food crisis

We present a stochastic two-population model that describes the migration and growth of semi-sedentary foragers and sedentary farmers along a river valley during the Neolithic transition. The main idea of this paper is that random migration and transition from sedentary to foraging way of life and backward is strongly coupled with the local crop production and the associated degradation of land. We derive a non-linear integral equation for the population density coupled with the equations for the density of soil nutrients and crop production. Our model provides an explanation for the formation of human settlements along a river valley. The numerical results show that the individual farmers have a tendency for aggregation and clustering. We show that the large-scale pattern is a transient phenomenon which eventually disappears due to land degradation.

nlin.AO↗

arXiv2008

Anomalous reaction-transport processes: the dynamics beyond the Mass Action Law

In this paper we reconsider the Mass Action Law (MAL) for the anomalous reversible reaction $A\rightleftarrows B$ with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states $A$ and $B$ are governed by anomalous (heavy-tailed) waiting-time distributions. We derive the set of mesoscopic integro-differential equations for the mean densities of reacting and diffusing particles in both states. We show that the effective reaction rate memory kernels in these equations and the uniform asymptotic states depend on transport characteristics such as jumping rates. This is in contradiction with the classical picture of MAL. We find that transport can even induce an extinction of the particles such that the density of particles $A$ or $B$ tends asymptotically to zero. We verify analytical results by Monte Carlo simulations and show that the mesoscopic densities exhibit a transient growth before decay.

cond-mat.stat-mech↗