Allende, H., Bravo, D., & Canessa, E. (2010). Robust design in multivariate systems using genetic algorithms. Qual. Quant., 44(2), 315–332.
Abstract: This paper presents a methodology based oil genetic algorithms, which finds feasible and reasonably adequate Solutions to problems of robust design in multivariate systems. We use a genetic algorithm to determine the appropriate control factor levels for simultaneously optimizing all of the responses of the system, considering the noise factors which affect it. The algorithm is guided by a desirability function which works with only one fitness function although the system May have many responses. We validated the methodology using data obtained from a real system and also from a process simulator, considering univariate and multivariate systems. In all cases, the methodology delivered feasible solutions, which accomplished the goals of robust design: obtain responses very close to the target values of each of them, and with minimum variability. Regarding the adjustment of the mean of each response to the target value, the algorithm performed very well. However, only in some of the multivariate cases, the algorithm was able to significantly reduce the variability of the responses.

Arbelaez, H., Bravo, V., Hernandez, R., Sierra, W., & Venegas, O. (2020). A new approach for the univalence of certain integral of harmonic mappings. Indag. Math.New Ser., 31(4), 525–535.
Abstract: The principal goal of this paper is to extend the classical problem of finding the values of alpha is an element of C for which either (f) over cap (alpha) (z) = integral(z)(0) (f (zeta)/zeta)(alpha) d zeta or f(alpha) (z) = integral(z)(0)(f' (zeta))(alpha)d zeta are univalent, whenever f belongs to some subclasses of univalent mappings in D, to the case of harmonic mappings, by considering the shear construction introduced by Clunie and SheilSmall in [4]. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

Arbelaez, H., Hernandez, R., & Sierra, W. (2019). Normal harmonic mappings. Mon.heft. Math., 190(3), 425–439.
Abstract: The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk D to the complex plane. In particular, we obtain necessary conditions for a function f to be normal.

Arbelaez, H., Hernandez, R., & Sierra, W. (2022). Lower and upper order of harmonic mappings. J. Math. Anal. Appl., 507(2), 125837.
Abstract: In this paper, we define both the upper and lower order of a sensepreserving harmonic mapping in D. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some consequences of a function having finite upper order. In addition, we improve a related result in the case when there is equality in a known distortion theorem for harmonic mappings with finite upper order. Some examples are provided to illustrate the developed theory. (C) 2021 Elsevier Inc. All rights reserved.

Arevalo, I., Hernandez, R., Martin, M. J., & Vukotic, D. (2018). On weighted compositions preserving the Caratheodory class. Mon.heft. Math., 187(3), 459–477.
Abstract: We characterize in various ways the weighted composition transformations which preserve the class P of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.

Aylwin, R., JerezHanckes, C., & Pinto, J. (2020). On the Properties of Quasiperiodic Boundary Integral Operators for the Helmholtz Equation. Integr. Equ. Oper. Theory, 92(2), 41 pp.
Abstract: We study the mapping properties of boundary integral operators arising when solving twodimensional, timeharmonic waves scattered by periodic domains. For domains assumed to be at least Lipschitz regular, we propose a novel explicit representation of Sobolev spaces for quasiperiodic functions that allows for an analysis analogous to that of Helmholtz scattering by bounded objects. Except for RayleighWood frequencies, continuity and coercivity results are derived to prove wellposedness of the associated first kind boundary integral equations.

Bachoc, F., Porcu, E., Bevilacqua, M., Furrer, R., & Faouzi, T. (2022). Asymptotically equivalent prediction in multivariate geostatistics. Bernoulli, 28(4), 2518–2545.
Abstract: Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the multivariate case has been elusive so far. The new challenges provided by modern spatial datasets, being typically multivariate, call for a deeper study of cokriging. In particular, we deal with the problem of misspecified cokriging prediction within the framework of fixed domain asymptotics. Specifically, we provide conditions for equivalence of measures associated with multivariate Gaussian random fields, with index set in a compact set of a ddimensional Euclidean space. Such conditions have been elusive for over about 50 years of spatial statistics. We then focus on the multivariate Matern and Generalized Wendland classes of matrix valued covariance functions, that have been very popular for having parameters that are crucial to spatial interpolation, and that control the mean square differentiability of the associated Gaussian process. We provide sufficient conditions, for equivalence of Gaussian measures, relying on the covariance parameters of these two classes. This enables to identify the parameters that are crucial to asymptotically equivalent interpolation in multivariate geostatistics. Our findings are then illustrated through simulation studies.

Bravo, V., Hernandez, R., & Venegas, O. (2017). On the univalence of certain integral for harmonic mappings. J. Math. Anal. Appl., 455(1), 381–388.
Abstract: We generalize the problem of univalence of the integral of f'(z)(alpha) when f is univalent to the complex harmonic mappings. To do this, we extend the univalence criterion by Ahlfors in [1] to those mappings. (C) 2017 Elsevier Inc. All rights reserved.

Canessa, E., Droop, C., & Allende, H. (2012). An improved genetic algorithm for robust design in multivariate systems. Qual. Quant., 46(2), 665–678.
Abstract: In a previous article, we presented a genetic algorithm (GA), which finds solutions to problems of robust design in multivariate systems. Based on that GA, we developed a new GA that uses a new desirability function, based on the aggregation of the observed variance of the responses and the squared deviation between the mean of each response and its corresponding target value. Additionally, we also changed the crossover operator from a onepoint to a uniform one. We used three different case studies to evaluate the performance of the new GA and also to compare it with the original one. The first case study involved using data from a univariate real system, and the other two employed data obtained from multivariate process simulators. In each of the case studies, the new GA delivered good solutions, which simultaneously adjusted the mean of each response to its corresponding target value. This performance was similar to the one of the original GA. Regarding variability reduction, the new GA worked much better than the original one. In all the case studies, the new GA delivered solutions that simultaneously decreased the standard deviation of each response to almost the minimum possible value. Thus, we conclude that the new GA performs better than the original one, especially regarding variance reduction, which was the main problem exhibited by the original GA.

Chaigneau, S. E., Puebla, G., & Canessa, E. C. (2016). Why the designer's intended function is central for proper function assignment and artifact conceptualization: Essentialist and normative accounts. Dev. Rev., 41, 38–50.
Abstract: People tend to think that the function intended by an artifact's designer is its real or proper function. Relatedly, people tend to classify artifacts according to their designer's intended function (DIF), as opposed to an alternative opportunistic function. This centrality of DIF has been shown in children from 6 years of age to adults, and it is not restricted to Western societies. We review four different explanations for the centrality of DIF, integrating developmental and adult data. Two of these explanations are essentialist accounts (causal and intentional essentialism). Two of them are normative accounts (conventional function and idea ownership). Though essentialist accounts have been very influential, we review evidence that shows their limitations. Normative accounts have been less predominant. We review evidence to support them, and discuss how they account for the data. In particular, we review evidence suggesting that the centrality of DIF can be explained as a case of idea ownership. This theory makes sense of a great deal of the existing data on the subject, reconciles contradictory results, links this line of work to other literatures, and offers an account of the observed developmental trend. (C) 2016 Elsevier Inc. All rights reserved.

ColiniBaldeschi, R., Cominetti, R., & Scarsini, M. (2019). Price of Anarchy for Highly Congested Routing Games in Parallel Networks. Theor. Comput. Syst., 63(1), 90–113.
Abstract: We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.

Cominetti, R., Dose, V., & Scarsini, M. (2022). The price of anarchy in routing games as a function of the demand. Math. Program., Early Access.
Abstract: The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worstcase bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.

Da Silva, C., Astals, S., Peces, M., Campos, J. L., & Guerrero, L. (2018). Biochemical methane potential (BMP) tests: Reducing test time by early parameter estimation. Waste Manage., 71, 19–24.
Abstract: Biochemical methane potential (BMP) test is a key analytical technique to assess the implementation and optimisation of anaerobic biotechnologies. However, this technique is characterised by long testing times (from 20 to > 100 days), which is not suitable for waste utilities, consulting companies or plants operators whose decisionmaking processes cannot be held for such a long time. This study develops a statistically robust mathematical strategy using sensitivity functions for early prediction of BMP firstorder model parameters, i.e. methane yield (B0) and kinetic constant rate (k). The minimum testing time for early parameter estimation showed a potential correlation with the k value, where (i) slowly biodegradable substrates (k <= 0.1 d(1)) have a minimum testing times of >= 15 days, (ii) moderately biodegradable substrates (0.1 < k < 0.2 d(1)) have a minimum testing times between 8 and 15 days, and (iii) rapidly biodegradable substrates (k > 0.2 d(1)) have testing times lower than 7 days. (C) 2017 Elsevier Ltd. All rights reserved.

Efraimidis, I., Gaona, J., Hernandez, R., & Venegas, O. (2017). On harmonic Blochtype mappings. Complex Var. Elliptic Equ., 62(8), 1081–1092.
Abstract: Let f be a complexvalued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Blochtype function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the wellknown analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent.

Eyheramendy, S., Saa, P. A., Undurraga, E. A., Valencia, C., Lopez, C., Mendez, L., et al. (2021). Screening of COVID19 cases through a Bayesian network symptoms model and psychophysical olfactory test. iScience, 24(12), 103419.
Abstract: The sudden loss of smell is among the earliest and most prevalent symptoms of COVID19 when measured with a clinical psychophysical test. Research has shown the potential impact of frequent screening for olfactory dysfunction, but existing tests are expensive and time consuming. We developed a lowcost ($0.50/test) rapid psychophysical olfactory test (KOR) for frequent testing and a modelbased COVID19 screening framework using a Bayes Network symptoms model. We trained and validated the model on two samples: suspected COVID19 cases in five healthcare centers (n = 926; 33% prevalence, 309 RTPCR confirmed) and healthy miners (n = 1,365; 1.1% prevalence, 15 RTPCR confirmed). The model predicted COVID19 status with 76% and 96% accuracy in the healthcare and miners samples, respectively (healthcare: AUC = 0.79 [0.750.82], sensitivity: 59%, specificity: 87%; miners: AUC = 0.71 [0.630.79], sensitivity: 40%, specificity: 97%, at 0.50 infection probability threshold). Our results highlight the potential for lowcost, frequent, accessible, routine COVID19 testing to support society's reopening.

Galanopoulos, P., Girela, D., & Hernandez, R. (2011). Univalent Functions, VMOA and Related Spaces. J. Geom. Anal., 21(3), 665–682.
Abstract: This paper is concerned mainly with the logarithmic Bloch space B(log) which consists of those functions f which are analytic in the unit disc D and satisfy sup(z<1)(1z) log 1/1z f' (z)<infinity, and the analytic Besov spaces Bp, 1 <= p < infinity. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We give explicit examples of: A bounded univalent function in U(p>1) B(P) Bp but not in the logarithmic Bloch space. A bounded univalent function in B(log) but not in any of the Besov spaces B(p) with p < 2. We also prove that the situation changes for certain subclasses of univalent functions. Namely, we prove that the convex univalent functions in D which belong to any of the spaces B(0), VMOA, B(p) (1 <= p <= infinity), Blog, or some other related spaces are the same, the bounded ones. We also consider the question of when the logarithm of the derivative, log g', of a univalent function g belongs to Besov spaces. We prove that no condition on the growth of the Schwarzian derivative Sg of g guarantees log g' is an element of B(p). On the other hand, we prove that the condition integral(D) (1z(2))(2p2) Sg(z)(p) d A(z)<infinity implies that log g' is an element of B(p) and that this condition is sharp. We also study the question of finding geometric conditions on the image domain g(D) which imply that log g' lies in Bp. First, we observe that the condition of g( D) being a convex Jordan domain does not imply this. On the other hand, we extend results of Pommerenke and Warschawski, obtaining for every p is an element of (1, infinity), a sharp condition on the smoothness of a Jordan curve Gamma which implies that if g is a conformal mapping from D onto the inner domain of Gamma, then log g' is an element of B(p).

Goles, E., & Montealegre, P. (2014). Computational complexity of threshold automata networks under different updating schemes. Theor. Comput. Sci., 559, 3–19.
Abstract: Given a threshold automata network, as well as an updating scheme over its vertices, we study the computational complexity associated with the prediction of the future state of a vertex. More precisely, we analyze two classes of local functions: the majority and the ANDOR rule (vertices take the AND or the OR logic functions over the state of its neighborhoods). Depending on the updating scheme, we determine the complexity class (NC, P, NP, PSPACE) where the prediction problem belongs. (C) 2014 Elsevier B.V. All rights reserved.

Goles, E., Montealegre, P., & Vera, J. (2016). Naming Game Automata Networks. J. Cell. Autom., 11(56), 497–521.
Abstract: In this paper we introduce automata networks to model some features of the emergence of a vocabulary related with the naming game model. We study the dynamical behaviour (attractors and convergence) of extremal and majority local functions.

Jimenez, D., Barrera, J., & Cancela, H. (2023). Communication Network Reliability Under Geographically Correlated Failures Using Probabilistic Seismic Hazard Analysis. IEEE Access, 11, 31341–31354.
Abstract: The research community's attention has been attracted to the reliability of networks exposed to largescale disasters and this has become a critical concern in network studies during the last decade. Earthquakes are high on the list of those showing the most significant impacts on communication networks, and simultaneously, they are the least predictable events. This study uses the Probabilistic Seismic Hazard Analysis method to estimate the network element state after an earthquake. The approach considers a seismic source model and ground prediction equations to assess the intensity measure for each element according to its location. In the simulation, nodes fail according to the building's fragility curves. Similarly, links fail according to a failure rate depending on the intensity measure and the cable's characteristics. We use the sourceterminal, and the diameter constrained reliability metrics. The approach goes beyond the graph representation of the network and incorporates the terrain characteristics and the component's robustness into the network performance analysis at an affordable computational cost. We study the method on a network in a seismic region with almost 9000 km of optical fiber. We observed that for sourceterminal that are less than 500 km apart the improvements are marginals while for those that are more than 1000 km apart, reliability improves near a 30% in the enhanced designs. We also showed that these results depend heavily on the robustness/fragility of the infrastructure, showing that performance measures based only the network topology are not enough to evaluate new designs.

Ko, Y., Peng, E. W., Cote, P., Ferrarese, L., Liu, C. Z., Longobardi, A., et al. (2022). The Next Generation Virgo Cluster Survey. XXXIII. Stellar Population Gradients in the Virgo Cluster Core Globular Cluster System. Astrophys. J., 931(2), 120.
Abstract: We present a study of the stellar populations of globular clusters (GCs) in the Virgo Cluster core with a homogeneous spectroscopic catalog of 692 GCs within a majoraxis distance R (maj) = 840 kpc from M87. We investigate radial and azimuthal variations in the mean age, total metallicity, [Fe/H], and alphaelement abundance of blue (metalpoor) and red (metalrich) GCs using their coadded spectra. We find that the blue GCs have a steep radial gradient in [Z/H] within R (maj) = 165 kpc, with roughly equal contributions from [Fe/H] and [alpha/Fe], and flat gradients beyond. By contrast, the red GCs show a much shallower gradient in [Z/H], which is entirely driven by [Fe/H]. We use GCtagged Illustris simulations to demonstrate an accretion scenario where more massive satellites (with more metal and alpharich GCs) sink further into the central galaxy than less massive ones, and where the gradient flattening occurs because of the low GC occupation fraction of lowmass dwarfs disrupted at larger distances. The dense environment around M87 may also cause the steep [alpha/Fe] gradient of the blue GCs, mirroring what is seen in the dwarf galaxy population. The progenitors of red GCs have a narrower mass range than those of blue GCs, which makes their gradients shallower. We also explore spatial inhomogeneity in GC abundances, finding that the red GCs to the northwest of M87 are slightly more metalrich. Future observations of GC stellar population gradients will be useful diagnostics of halo merger histories.
