Density Estimation

Density is an important property of ionic liquids (ILs) that is required for process and product design. A recent article by Gardas and Coutinho (2008) reports the extended density correlation of ILs in wide ranges of temperature and pressure. However, they validated the density correlation only for ILs based on the following cations: imidazolium, pyridinium, pyrrolidinium, and phosphonium. The objective

... a function that is assumed to have two continuous derivatives, adding the side condition guarantees positivity and produces, uniquely, the Epanechnikov kernel. ... It will be clear from the previous paragraphs that, in the problem of noise-free density estimation, the side constraints ...

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.

This paper introduces a new stochastic process, a collection of U-statis-tics indexed by a family of symmetric kemels. Conditions are found for the uniform almost-sure convergence of a sequence of such processes. Rates of convergence are obtained. An application to cross-validation ...

With the rapid development of automated visual analysis, visual analysis systems have become a popular research topic in the field of computer vision and automated analysis. Visual analysis systems can assist humans to detect anomalous events (e.g., fighting, walking alone on the grass, etc). In general, the existing methods for visual anomaly detection are usually based on an autoencoder architecture, i.e., reconstructing the current frame or predicting the future frame. Then, the reconstruction error is adopted as the evaluation metric to identify whether an input is abnormal or not. The flaws of the existing methods are that abnormal samples can also be reconstructed well. In this paper, inspired by the human memory ability, we propose a novel deep neural network (DNN) based model termed cognitive memory-augmented network (CMAN) for the visual anomaly detection problem. The proposed CMAN model assumes that the visual analysis system imitates humans to remember normal samples and then distinguishes abnormal events from the collected videos. Specifically, in the proposed CMAN model, we introduce a memory module that is able to simulate the memory capacity of humans and a density estimation network that can learn the data distribution. The reconstruction errors and the novelty scores are used to distinguish abnormal events from videos. In addition, we develop a two-step scheme to train the proposed model so that the proposed memory module and the density estimation network can cooperate to improve performance. Comprehensive experiments evaluated on various popular benchmarks show the superiority and effectiveness of the proposed CMAN model for visual anomaly detection comparing with the state-of-the-arts methods. The implementation code of our CMAN method can be accessed at https://github.com/CMAN-code/CMAN_pytorch.

Aim: Reliable estimates of population density are fundamental to wildlife conservation and management. Although the leopard cat is the most common and widespread wild felid in China, little is known about the ecology and population biology of this species in the country. Using spatially explicit capture-recapture (SERC) modelling derived from extensive camera-trapping data, we estimated the population density and activity patterns of leopard cats in a well-protected private nature reserve in southern China.

Methods: Between June 2020 and May 2021, we conducted a camera-trap survey across a pre-determined grid system in Kadoorie Farm and Botanic Garden (KFBG), Hong Kong. KFBG was established on a barren hillside following sustained anthropogenic disturbances. After six decades of protection, secondary forest currently covers approximately 80% of the site. We deployed a total of 19 camera trap stations across our small 1.5 km2 study area, with two opposite-facing cameras at each station to obtain images of both flanks of leopard cats. The consecutive 12-month survey yielded 113 independent capture events of the leopard cat, of which 61 events were clear enough to facilitate individual identification. Based on closed population assumptions for capture-recapture models, we also divided the 12-month survey into six two-month sampling periods, and estimated the population density for each sampling period using Maximum Likelihood SECR modelling. We also examined activity kernel densities to estimate the difference in diel activity patterns between wet and dry seasons.

Results: Our analyses revealed that results from two sampling periods were robust and precise enough (i.e., low standard error and narrow 95% confidence intervals) to estimate leopard cat density. We estimated leopard density between June-July 2020 as D = 0.64 ± 0.31 (0.26–1.55) individuals/km2, and between February-March 2021 as D = 0.87 ± 0.48 (0.31–2.40) individuals/km2, which are among the highest density estimates for this species reported in any region. We also found that the diel activity pattern of leopard cats in the study site is arrhythmic during the wet season, but became more nocturnal-crepuscular during the dry season, though they also exhibited some diurnal activity. Kernel density analyses however suggested no significant differences in diel activity patterns occurred between wet and dry seasons. 

Conclusions: Our study provides important early data on the population density of leopard cats in southern mainland China, the results of which allow for comparisons with other studies elsewhere using capture-recapture modelling approaches. We further demonstrate the utility of SECR methods for estimating population density over short and long sampling periods across necessarily small sampling areas. We further provide practical recommendations for conducting camera trap surveys to enhance the success rates of individual identification and “recapture” of leopard cats. In accordance with the conclusion of other studies, our results show that leopard cats are highly adaptable, exhibit great plasticity in daily activity, and thrive well in human-modified landscapes.

Excel spreadsheet FYSCONST#2.0.xls calculates the physical food properties Density, Thermal Conductivity, Specific Heat, and Thermal Diffusivity, of an unfrozen or a (partly) frozen food.
Required input: the food product composition in mass% of protein, mass% of fat, mass% of carbohydrates, mass% of fiber, mass% of ash, mass% of unfrozen water and mass% of ice; also the actual food temperature has to be supplied.
For (partly) frozen foods, a separate spreadsheet section calculates the mass% of both ice and unfrozen water, based on composition and initial freezing point, by applying the TCHIGEOV equation. For many foods, table 3 lists this initial freezing point, together with the mass% of the main food components.
All equations used in FYSCONST#2.0.xls, and their sources, are presented.
On validation, the physical food properties, calculated by FYSCONST#2.0.xls, were (almost) exactly equal to those of food products, reported by Ibarz & Barbosa-Cánovas (2005: 319-320), by R. Paul Singh in Heldman & Lund (1992: 253), and by ASHRAE (2006: 9-6).
6 extensively worked examples explain how to use both the spreadsheets FYSCONS#2.0.xls, and the  Tchigeov equation.

(EN ESPAÑOL): En este trabajo detallamos el procedimiento metodológico para la realización de mapas que nos permitan analizar la evolución de la densidad del poblamiento antiguo en un territorio. Nos centraremos concretamente en el cálculo basado en la estimación de la densidad de núcleo (KDE). En este tipo de análisis es muy importante seleccionar un ancho de banda (h) óptimo, para cuyo cálculo existen dos estrategias: una que baraja criterios cualitativos y otra centrada en procedimientos cuantitativos. Tras valorar los pros y los contras de cada una de estas estrategias, proponemos una tercera opción que consiste en combinar ambos criterios. Para ejemplificar esta propuesta metodológica hemos tomado como caso de estudio varias zonas del Bajo Guadalquivir (SO de
España) en las que se han documentado yacimientos arqueológicos datados entre los siglos II y IV d.C.

(IN ENGLISH): In this paper we reflect on the different concepts and issues required to make density maps that allow the ancient settlements in a territory to be studied. We will focus on the kernel density estimation (KDE). In this
type of analysis, it is important to select an optimum bandwidth (h) and there are two strategies for this purpose: one that considers qualitative criteria and another that focuses on quantitative criteria. After evaluating each of these strategies, we propose a third option that consists of combining both criteria. Following a series of statistical calculations, a minimum and maximum value can be determined for the bandwidth, using this interval as a qualitative testing range. To exemplify this methodological proposal with a practical case, a series of density maps have been drawn up based on the known Roman sites in the Lower Guadalquivir Basin (SW Spain) between the 2nd and 4th centuries AD.

The aim of this thesis is to investigate the applicability of a novel image synthesis technique based on Monte Carlo particle transport to daylight simulation. Many materials used in daylight simulation are specifically designed to redirect light, and as such give rise to complex effects such as caustics. The photon map technique was chosen for its efficent handling of these effects. To assess its ability to produce physically correct results which can be applied to lighting simulation, a validation was carried out based on analytical case studies and on simple experimental setups. As prerequisite to validation, the photon map´s inherent bias/noise tradeoff is investigated. This tradeoff depends on the density estimate bandwidth used in the reconstruction of the illumination. The error analysis leads to the development of a bias compensating operator which adapts the bandwidth according to the estimated bias in the reconstructed illumination.

We formulate conditions for convergence of Laws of Large Numbers and show its links with of parts mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of Law of Large Numbers such as Stochastic Approximation, Density and Regression Estimation, Identification.