Mixed Metrics Research Articles

Seeing past the Zero Sum Game in Environmental Policy Harder Than It Looks

In Nonzero: The Logic of Human Destiny, Robert Wright offers a sweeping view of human evolution that culminates in his argument that modern society has become so complex and interconnected that there are no true “zero sum” games to be played between people or institutions. Indeed, much of environmental policy rests on the promise of improving the greater good by leveraging the ubiquitous presence of nonzerosumness. But Wright’s thesis turns back on itself. There is no question that social-ecological systems (SES) are highly complex and interconnected, making true zero sum games hard to find. But the sheer complexity of massive SESs is what also makes it excruciatingly difficult to connect all the dots of the nonzero sum game within the SES. At a macro scale, nonzero sum rules; at the micro scale of the farmer seeing more water go by the farm in the river, it looks like zero sum. In this short essay I outline six reasons why seeing past these micro zero sum game is so difficult, particularly for those caught in them who consider themselves the losers: (1) mixed metrics; (2) multi-scalar nature of SESs; (3) temporal transitions; (4) distribution of costs and benefits; (5) imprecise valuation; and (6) polarizing effect of government intervention. The essay was written before the 2016 election. An Epilogue offers thoughts on its meaning.

Quantification of mixing in vesicle suspensions using numerical simulations in two dimensions.

We study mixing in Stokesian vesicle suspensions in two dimensions on a cylindrical Couette apparatus using numerical simulations. The vesicle flow simulation is done using a boundary integral method, and the advection-diffusion equation for the mixing of the solute is solved using a pseudo-spectral scheme. We study the effect of the area fraction, the viscosity contrast between the inside (the vesicles) and the outside (the bulk) fluid, the initial condition of the solute, and the mixing metric. We compare mixing in the suspension with mixing in the Couette apparatus without vesicles. On the one hand, the presence of vesicles in most cases slightly suppresses mixing. This is because the solute can be only diffused across the vesicle interface and not advected. On the other hand, there exist spatial distributions of the solute for which the unperturbed Couette flow completely fails to mix whereas the presence of vesicles enables mixing. We derive a simple condition that relates the velocity and solute and can be used to characterize the cases in which the presence of vesicles promotes mixing.

Water mass modification and mixing rates in a 1/12° simulation of the Canadian Arctic Archipelago

Strong spatial differences in diapycnal mixing across the Canadian Arctic Archipelago are diagnosed in a 1/12° basin-scale model. Changes in mass flux between water flowing into or out of several regions are analyzed using a volume-integrated advection–diffusion equation, and focus is given to denser water, the direct advective flux of which is mediated by sills. The unknown in the mass budget, mixing strength, is a quantity seldom explored in other studies of the Archipelago, which typically focus on fluxes. Regionally averaged diapycnal diffusivities and buoyancy fluxes are up to an order of magnitude larger in the eastern half of the Archipelago relative to those in the west. Much of the elevated mixing is concentrated near sills in Queens Channel and Barrow Strait, with stronger mixing particularly evident in the net shifts of the densest water to lower densities as it traverses these constrictions. Associated with these shifts are areally averaged buoyancy fluxes up to 10−8 m2 s−3 through the 1027 kg m−3 isopycnal surface, which lies at approximately 100 m depth. This value is similar in strength to the destabilizing buoyancy flux at the ocean surface during winter. Effective diffusivities estimated from the buoyancy fluxes can exceed 10−4 m2 s−1, but are often closer to 10−5 m2 s−1 across the Archipelago. Tidal forcing, known to modulate mixing in the Archipelago, is not included in the model. Nevertheless, mixing metrics derived from our simulation are of the same order of magnitude as the few comparable observations.

Criterion of the best approximant for multivariable functions in spaces $L_{1,p_2,...,p_n}$ and $L_{p_1,...,p_{n-1},1}$

The questions of the characterization of the best approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterions of the best approximant in spaces $L_{1,p_2,...,p_n}$ and $L_{p_1,...,p_{n-1},1}$ is obtained.

Transverse jet mixing characteristics

This experimental study explores and quantifies mixing characteristics associated with a gaseous round jet injected perpendicularly into cross-flow for a range of flow and injection conditions. The study utilizes acetone planar laser-induced fluorescence imaging to determine mixing metrics in both centreplane and cross-sectional planes of the jet, for a range of jet-to-cross-flow momentum flux ratios ($2\leqslant J\leqslant 41$), density ratios ($0.35\leqslant S\leqslant 1.0$) and injector configurations (flush nozzle, flush pipe and elevated nozzle), all at a fixed jet Reynolds number of 1900. For the majority of conditions explored, there is a direct correspondence between the nature of the jet’s upstream shear layer instabilities and structure, as documented in detail in Getsingeret al.(J. Fluid Mech., vol. 760, 2014, pp. 342–367), and the jet’s mixing characteristics, consistent with diffusion-dominated processes, but with a few notable exceptions. When quantified as a function of distance along the jet trajectory, mixing metrics for jets in cross-flow with an absolutely unstable upstream shear layer and relatively symmetric counter-rotating vortex pair cross-sectional structure tend to show better local molecular mixing than for jets with convectively unstable upstream shear layers and generally asymmetric cross-sectional structures. Yet the spatial evolution of mixing with downstream distance can be greater for a few specific convectively unstable conditions, apparently associated with the initiation and nature of shear layer rollup as a trigger for improved mixing. A notable exception to these trends concerns conditions where the equidensity jet in cross-flow has an upstream shear layer that is already absolutely unstable, and the jet density is then reduced in comparison with that of the cross-flow. Here, density ratios below unity tend to mix less well than for equidensity conditions, demonstrated to result from differences in the nature of higher-density cross-flow entrainment into lower-density shear layer vortices.

Chemical imaging of ambient aerosol particles: Observational constraints on mixing state parameterization

AbstractA new parameterization for quantifying the mixing state of aerosol populations has been applied for the first time to samples of ambient particles analyzed using spectro‐microscopy techniques. Scanning transmission X‐ray microscopy/near edge X‐ray absorption fine structure (STXM/NEXAFS) and computer‐controlled scanning electron microscopy/energy dispersive X‐ray spectroscopy (CCSEM/EDX) were used to probe the composition of the organic and inorganic fraction of individual particles collected on 27 and 28 June during the 2010 Carbonaceous Aerosols and Radiative Effects study in the Central Valley, California. The first field site, T0, was located in downtown Sacramento, while T1 was located near the Sierra Nevada Mountains. Mass estimates of the aerosol particle components were used to calculate mixing state metrics, such as the particle‐specific diversity, bulk population diversity, and mixing state index, for each sample. The STXM data showed evidence of changes in the mixing state associated with a buildup of organic matter confirmed by collocated measurements, and the largest impact on the mixing state was due to an increase in soot dominant particles during this buildup. The mixing state from STXM was similar between T0 and T1, indicating that the increased organic fraction at T1 had a small effect on the mixing state of the population. The CCSEM/EDX analysis showed the presence of two types of particle populations: the first was dominated by aged sea‐salt particles and had a higher mixing state index (indicating a more homogeneous population); the second was dominated by carbonaceous particles and had a lower mixing state index.

Criterion of the best non-symmetric approximant for multivariable functions in spaces $L_{p_1,...,p_n}$

The questions of the characterization of the best nonsymmetric approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterion of best nonsymmetric approximant in these spaces is obtained.

Contesting Mexico City’s alleged polycentric condition through a centrality-mixed land-use composite index

We examine Mexico City’s urban structure through a composite index by combining two previously existing metrics: one derived from the Urban Network Analysis tool (UNA), recently published by MIT researchers, and the other, using an Entropy Index, which in essence, represents the mixed land-use degree. The proposed composite index embodies a different approach from previous methods reported in the literature because it uses disaggregated data at the unit level, performs weighted cluster calculations through a network data set, and incorporates a mixed land-use metric. This method was developed in order to test if the urban arrangement showed signs of a polycentric condition under a particular centrality standpoint. We observed that Mexico City has a relatively weak polycentric urban condition.

Evaluation of poly-disperse solid particles mixing in a slant cone mixer using discrete element method

There is a lack of sufficient knowledge regarding mixing of poly-disperse particles. Thus, the main objective of this study was to investigate the mixing of the bi-disperse, tri-disperse, and poly-disperse particles in the slant cone using the discrete element method. DEM results were validated using experimental data obtained from both sampling and image analysis techniques. The effects of initial loading scenarios, particle size, drum and agitator speeds on the mixing efficiency were explored. The mixing metric was utilized to measure the mixing quality for the different mixtures. The mixing index increased to a maximum value and decreased slightly before reaching a plateau for bi-disperse particles for different loading methods and 15rpm drum speed as a direct result of the trajectory segregation of the particles with different sizes. The highest mixing index for bi-disperse particles was achieved for top–bottom smaller-to-larger initial loading and 45rpm drum speed. The mixing quality of the bi-disperse particles was improved by the rotation of the agitator compared to that achieved with the stationary agitator at the fill level of 100%. The highest mixing indices were achieved for the tri-disperse and poly-disperse particles under the top–bottom smaller-to-larger loading method at the drum speed of 15 and 55rpm, respectively.

An O(m² + mn²) algorithm for the bi-objective location problem on a network with mixed metrics

In this paper, we formulate the Euclidean maximin with the network minisum bi-objective location model for a semi-obnoxious facility on a transportation network that is embedded into the Euclidean plane. The Euclidean distance metric is used in modelling the undesirable characteristics of the facility, using the maximin objective, while the network shortest path distance metric is used for modelling the transportation cost to these facilities using the minisum objective. After identifying the problem properties, we develop an O(m2 + mn2) algorithm for generating the efficient set and implement this algorithm in a realistic example involving the location of a semi-obnoxious facility in the province of Bursa in Turkey.

Properties of the sample estimators used for statistical normalization of feature vectors

Normalization of feature vectors is often used as a step of data preprocessing for clustering. A unified statistical approach to feature vector normalization has been proposed recently by the authors. After the proposed normalization, the contributions of both numerical and categorical attributes to a specified objective function are statistically the same. In spite of the importance for estimators to be consistent, the consistency of the sample estimators used for normalization, has never been considered. A mathematical justification of the statistical normalization procedure is given here. The sample estimators proposed for normalization of attributes of feature vectors are proven to have desirable properties, namely they are consistent and unbiased. Some other mathematical questions related to clustering have got here a rigorous treatment. In particular, the statistical normalization procedure is discussed in detail in the cases of the objective functions being based on the Chebyshev, attribute mismatch categorical and Minkowski mixed p-metrics. As an application of the normalization procedure, clustering of several benchmark datasets is performed with non-normalized and introduced normalized mixed metrics using either the $$k$$k-prototypes (for $$p=2$$p=2) or another algorithm (for $$p\not = 2$$p?2).

General form of linear continuous functional and criterion of the best approximant in spaces with mixed integral metric

The questions of the characterization of the best approximant in spaces with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of best approximant in these spaces are obtained.

Electrical Noise in Heterojunction Interband Tunnel FETs

We present an analysis of electrical noise in III-V heterojunction TFET (HTFET). Using numerical simulations, random telegraph noise (RTN) amplitude induced by a single charge trap is investigated with regard to trap location, electron band-to-band-generation rate, bias, and transistor size. It is found that HTFET RTN amplitude does not scale inversely with gate length and is governed by tunneling distance of carriers at source-channel junction. HTFET exhibits 40% less relative RTN amplitude at 0.3 V at gate lengths around 20 nm, over subthreshold Si-FinFET. RTN of HTFET at VGS=0 V is higher for a trap location at source-channel tunnel junction. To analyze flicker, shot, and thermal noise, we created transistor level Verilog-A-based electrical noise models. The results indicate HTFETs competitive noise performance in megahertz frequency range, over Si-FinFET. In the range 10 GHz or more with operating voltages exceeding 0.3 V, HTFET input noise is worse due to the dominance of shot noise. A differential amplifier with active load is used to examine the electrical noise performance at circuit level. We emphasize that high intrinsic gain, drive current, and output resistance of HTFET can be used to achieve superior mixed signal performance metrics in HTFET design over Si-FinFET design, at an improved electrical noise performance.

Quantifying aerosol mixing state with entropy and diversity measures

Abstract. This paper presents the first quantitative metric for aerosol population mixing state, defined as the distribution of per-particle chemical species composition. This new metric, the mixing state index χ, is an affine ratio of the average per-particle species diversity Dα and the bulk population species diversity Dγ, both of which are based on information-theoretic entropy measures. The mixing state index χ enables the first rigorous definition of the spectrum of mixing states from so-called external mixture to internal mixture, which is significant for aerosol climate impacts, including aerosol optical properties and cloud condensation nuclei activity. We illustrate the usefulness of this new mixing state framework with model results from the stochastic particle-resolved model PartMC-MOSAIC. These results demonstrate how the mixing state metrics evolve with time for several archetypal cases, each of which isolates a specific process such as coagulation, emission, or condensation. Further, we present an analysis of the mixing state evolution for a complex urban plume case, for which these processes occur simultaneously. We additionally derive theoretical properties of the mixing state index and present a family of generalized mixing state indexes that vary in the importance assigned to low-mass-fraction species.

Scheduling Algorithms for Primary LSPs with n-to-m Protection in MPLS Networks

The protection mechanism is very important in networks when working paths fall failure. In this paper, we propose a scheduling mechanism with n-to-m protection (n is the number of primary LSPs (Label Switching Path), m is the number of backup LSPs) in MPLS (Multi-Protocol Label Switching) networks. Two scheduling algorithms are proposed: the flrst algorithm is MMMSA (maximize mixing metric scheduling algorithm), aiming at maximize the mixing metrics of backup LSPs by calculating the proportion of each ∞ow that transferred from primary LSPs to backup LSPs with linear programming; the second algorithm is AHP-WSA (analytic hierarchy process-weight scheduling algorithm), considering multi-metrics (bandwidth, delay, package error rate) of backup LSPs separately and making pairwise comparison of the alternatives, then flnding out each backup LSP’s weight to a speciflc primary LSP and scheduling the ∞ows with theses weights. Simulation results show that these algorithms can achieve e‐cient and high performance scheduling.

Introducing semantic variables in mixed distance measures: Impact on hierarchical clustering

Today, it is well known that taking into account the semantic information available for categorical variables sensibly improves the meaningfulness of the final results of any analysis. The paper presents a generalization of mixed Gibert's metrics, which originally handled numerical and categorical variables, to include also semantic variables. Semantic variables are defined as categorical variables related to a reference ontology (ontologies are formal structures to model semantic relationships between the concepts of a certain domain). The superconcept-based distance (SCD) is introduced to compare semantic variables taking into account the information provided by the reference ontology. A benchmark shows the good performance of SCD with respect to other proposals, taken from the literature, to compare semantic features. Mixed Gibert's metrics is generalized incorporating SCD. Finally, two real applications based on touristic data show the impact of the generalized Gibert's metrics in clustering procedures and, in consequence, the impact of taking into account the reference ontology in clustering. The main conclusion is that the reference ontology, when available, can sensibly improve the meaningfulness of the final clusters.

Parametric Analysis of Pylon-Aided Fuel Injection in Scramjet Engines

The current study investigates means to increase the efficiency of fuel-air mixing into supersonic flow upstream of a flame holding cavity. Previous work has shown much promise in increasing the penetration and mixing of a fuel-air mixture into the freestream by injecting fuel behind small triangular pylons. The current paper examines 21 triangular pylons of varying widths, heights, and lengths with a computational fluid dynamics (CFD) performance analysis. Increasing the height of the pylons increased the penetration, flammable fuel plume area, and floor gap. Variations in pylon length had no discernible impact on the fuel-air mixing metrics. Aerodynamic loses were minimal for all pylon configurations and did not correlate to the absolute size of the pylons tested.

Mixed moduli of smoothness in mixed metrics

For a mixed modulus of smoothness of positive order, its relationship with the norms of partial sums of a Fourier series in a mixed metric is obtained. The relation between mixed moduli of smoothness of positive order in different mixed metrics is established.

Passive and reactive scalar measurements in a transient high-Schmidt-number Rayleigh–Taylor mixing layer

An experimental study of mixing induced by Rayleigh–Taylor (RT) instability at an Atwood number (A t ) ~7.5 × 10−4 and Schmidt number (Sc) ~1,000 has been performed. A new transient experimental facility developed on the working principles of the draw-tank facility at Cambridge (Dalziel et al. in J Fluid Mech, 399:1–48, 1999) has been established and enhanced to observe a higher (2×) Reynolds number regime. Water and brine were used to produce the RT density stratification. The evolution of the instability was studied using passive and reactive scalar techniques and quantified using optical diagnostic methods. The data were combined to estimate local and global mixing metrics representative of the mixing mechanism across the mixing layer. In comparison with parameters reported from analogous experiments, the mixing phenomenon at a high Sc shows a strong dependency on the initial conditions prevailing at the onset of the instability and the evidence of a delay in the mixing transition. Values of global and integral mixing parameters did not reach late-time asymptotic values that have been reported previously from steady-state experiments (Texas A&M Water Channel) and may be attributed to the effect of the barrier pull and the overturning mechanism that is thought to hinder the progress of the mixing layer.

Statistical approach to normalization of feature vectors and clustering of mixed datasets

Normalization of feature vectors of datasets is widely used in a number of fields of data mining, in particular in cluster analysis, where it is used to prevent features with large numerical values from dominating in distance-based objective functions. In this study, a unified statistical approach to normalization of all attributes of mixed databases, when different metrics are used for numerical and categorical data, is proposed. After the proposed normalization, the contributions of both numerical and categorical attributes to a specified objective function are statistically the same. Formulae for the statistically normalized Minkowski mixedp-metrics are given in an explicit way. It is shown that the classicz-score standardization and the min–max normalization are particular cases of the statistical normalization, when the objective function is, respectively, based on the Euclidean or the Tchebycheff (Chebyshev) metrics. Finally, clustering of several benchmark datasets is performed with non-normalized and introduced normalized mixed metrics using either thek-prototypes (forp=2) or another algorithm (forp≠2).