Multivariate Approach of End-Member Contributions to Streamflow in the Critical Zone. Case Study: Valles Caldera, New Mexico

Multivariable End-member Mixing Analysis (EMMA) that incorporates principal component analysis (PCA) is a widely utilized tool to identify the sources of water that generate streamflow in catchment hydrology. In this study, we investigated how different combinations of principal components (PC) allow assessing the importance that potential end-members have to surface waters. We evaluated mixing spaces of different dimensions in order to justify the number of end-members needed to generate streamflow. Furthermore, this multidimensional approach provided further evidence of the hydrologic processes that dominate in the headwaters at the Jemez River Basin Critical Zone Observatory (JRB-CZO). Our results showed that the U-mixing spaces of three dimensions of the La Jara and Upper Jaramillo catchments highlight the contributions of deep groundwater that the two-dimensional mixing space neglected. Conversely, in the History Grove catchment, a two-dimensional U-mixing space was enough to explain streamflow generation. Groundwater, snowmelt, rainfall and soil water are the end-members identified in each catchment. The geomorphology (e.g. aspect, topography, and geology) of each watershed and climate variability, however, influence the contribution of these source waters in each system. Groundwater contributions dominate streamflow generation in the JRB-CZO. Moreover, increments of snowmelt, rainfall and soil water contributions are observed specifically during base-flow conditions. We argue that the contributions of these end-members do not correspond specifically to overland flow, but rather contributions of shallow groundwater and subsurface lateral flow that possess the chemical signature of these source waters

Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes

In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the $\ell^1$ norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predictors and (3) moment conditions on the noise appearing in the linear representation. Two kinds of aggregations are considered giving rise to different moment conditions on the noise and more or less sharp oracle inequalities. We apply this approach for deriving an adaptive predictor for locally stationary time varying autoregressive (TVAR) processes. It is obtained by aggregating a finite number of well chosen predictors, each of them enjoying an optimal minimax convergence rate under specific smoothness conditions on the TVAR coefficients. We show that the obtained aggregated predictor achieves a minimax rate while adapting to the unknown smoothness. To prove this result, a lower bound is established for the minimax rate of the prediction risk for the TVAR process. Numerical experiments complete this study. An important feature of this approach is that the aggregated predictor can be computed recursively and is thus applicable in an online prediction context.Comment: Published at http://dx.doi.org/10.1214/15-AOS1345 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

My Sets Are My Foundation

You might be wondering, what the hell does set theory have to do with writing? I’ll tell you a secret:\ everything is built on sets. Sets are things of beauty. They are great ways to conceptualize, compartmentalize, and classify the world and everything it encompasses. And now I know I’ve danced around the question of what sets have to do with my writing. So, here is my answer: I use set theory as the foundation for all of my writing

Economic Polarization Through Trade: Trade Liberalization and Regional Growth in Mexico

economic growth, regional disparities, trade, integration, polarization, Mexico

My Sets and Sexuality

It was only with the application of set theory to my own personal life that I discovered my true identity and sexuality. In this exploratory, personal essay, I detail my own discovery of my sexuality through mathematics and how this math has become a lens through which I view the world. And, with new knowledge of literary criticism in hand, I can now retroactively describe the thoughts I had in this discovery process

Can explicit processes support implicit category learning?: The effect of relevant rule-oriented selective attention on implicit learning

Categorization is a crucial component of human cognition. Multiple systems theories suggest categories can be learned by explicit or implicit processes/systems depending on the type of category (e.g., Ashby & Valentin, 2017). Research examining the interaction between these systems found that explicit learning impairs implicit performance (Ashby & Crossley, 2010; Crossley & Ashby, 2015; Sanchez et al., 2020). The nature of this impairment remains unclear. The current study examined the effect of selective attention to rule dimensions that were either relevant or irrelevant to a later implicit categorization task to better understand how this impairment occurs. The results suggested that attention to relevant dimensions is crucial for implicit learning. Both systems can learn in parallel as long as the relevant category information is attended. This suggests the primary mechanism of implicit impairment by the explicit system may be drawing attention away from relevant information rather than rule-based strategy perseveration

Scouting Knots Are Not the Same Knots When Knotted

Knots are used everyday by all people, mathematicians and non-mathematicians alike. There are certain subsets of people that use knots more frequently than others such as sailors or members of the Scouting Movement. A mathematical knot is a subset of 3-space that is homeomorphic to the unit circle. A knot used in non-mathematical circles is generally considered when two strings, etc. are wrapped around each other, with the ends potentially hanging. We introduce and explain through examples 1) how mathematical knots differ from general knots; 2) how mathematical knots differ from other mathematical knots via methods of deformation, colorability, and polynomials; 3) apply mathematical methods of knot determinations to practical knots to see how practical knots might behave as mathematical knots

Experimental study of electrostatic aerosol filtration at moderate filter face velocity

Electrostatic filtration media (electret) has been used in many applications due to its ability to efficiently collect submicron particles while maintaining a low pressure drop. Filter face velocities have ranged from 0.01-0.5 m/s in previous studies. However, in this study, measurements were conducted from 0.5-2.5 m/s, a region where Reynolds numbers range from 0.05-0.24. Within this regime, commonly used filtration theory is incomplete and does not predict performance of electret media, therefore data must be measured. Experimental measurements were conducted in various combinations of charge and neutralized filter media with aerosolized particles possessing the Boltzmann charge distribution or zero charge. Collection efficiency of the charged FiltreteTM media was significantly higher than the FiltreteTM which had been charged neutralized. As filter face velocity increased, however, collection efficiency decreased in the electret media. As filter face velocity increased for the neutralized media, collection efficiency increased due to inertial impaction. Particle bounce was assumed to occur with particles of aerodynamic diameter 65 400 nm. Electrostatic attraction, i.e. Coulombic, polarization and image forces were analyzed based on experimental data. The Coulombic force had the greatest effect on efficiency at all three filter face velocities, followed by the polarization force. The effect of image forces was negligible for all three filter face velocities. This study provides unique empirical data outside of the viscous filter flow regime, data which is useful in the design of, and performance prediction of, high volume commercial and industrial applications, such as HVAC (heating, ventilation, and air conditioning) systems. The data presented can be used to validate\u27 numerical models for filtration at moderate Reynolds numbers where data is scarce for electrostatically charged filtration.\u2