Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

A new accuracy measure based on bounded relative error for time series forecasting

Many accuracy measures have been proposed in the past for time series forecasting comparisons. However, many of these measures suffer from one or more issues such as poor resistance to outliers and scale dependence. In this paper, while summarising commonly used accuracy measures, a special review is made on the symmetric mean absolute percentage error. Moreover, a new accuracy measure called the Unscaled Mean Bounded Relative Absolute Error (UMBRAE), which combines the best features of various alternative measures, is proposed to address the common issues of existing measures. A comparative evaluation on the proposed and related measures has been made with both synthetic and real-world data. The results indicate that the proposed measure, with user selectable benchmark, performs as well as or better than other measures on selected criteria. Though it has been commonly accepted that there is no single best accuracy measure, we suggest that UMBRAE could be a good choice to evaluate forecasting methods, especially for cases where measures based on geometric mean of relative errors, such as the geometric mean relative absolute error, are preferred

Integrative analysis of extracellular and intracellular bladder cancer cell line proteome with transcriptome: improving coverage and validity of -omics findings

Characterization of disease-associated proteins improves our understanding of disease pathophysiology. Obtaining a comprehensive coverage of the proteome is challenging, mainly due to limited statistical power and an inability to verify hundreds of putative biomarkers. In an effort to address these issues, we investigated the value of parallel analysis of compartment-specific proteomes with an assessment of findings by cross-strategy and cross-omics (proteomics-transcriptomics) agreement. The validity of the individual datasets and of a “verified” dataset based on crossstrategy/omics agreement was defined following their comparison with published literature. The proteomic analysis of the cell extract, Endoplasmic Reticulum/Golgi apparatus and conditioned medium of T24 vs. its metastatic subclone T24M bladder cancer cells allowed the identification of 253, 217 and 256 significant changes, respectively. Integration of these findings with transcriptomics resulted in 253 “verified” proteins based on the agreement of at least 2 strategies. This approach revealed findings of higher validity, as supported by a higher level of agreement in the literature data than those of individual datasets. As an example, the coverage and shortlisting of targets in the IL-8 signalling pathway are discussed. Collectively, an integrative analysis appears a safer way to evaluate -omics datasets and ultimately generate models from valid observations

Extrapolation for Time-Series and Cross-Sectional Data

Extrapolation methods are reliable, objective, inexpensive, quick, and easily automated. As a result, they are widely used, especially for inventory and production forecasts, for operational planning for up to two years ahead, and for long-term forecasts in some situations, such as population forecasting. This paper provides principles for selecting and preparing data, making seasonal adjustments, extrapolating, assessing uncertainty, and identifying when to use extrapolation. The principles are based on received wisdom (i.e., experts’ commonly held opinions) and on empirical studies. Some of the more important principles are:• In selecting and preparing data, use all relevant data and adjust the data for important events that occurred in the past.• Make seasonal adjustments only when seasonal effects are expected and only if there is good evidence by which to measure them.• In extrapolating, use simple functional forms. Weight the most recent data heavily if there are small measurement errors, stable series, and short forecast horizons. Domain knowledge and forecasting expertise can help to select effective extrapolation procedures. When there is uncertainty, be conservative in forecasting trends. Update extrapolation models as new data are received.• To assess uncertainty, make empirical estimates to establish prediction intervals.• Use pure extrapolation when many forecasts are required, little is known about the situation, the situation is stable, and expert forecasts might be biased

AF-MSCs fate can be regulated by culture conditions

Human mesenchymal stem cells (hMSCs) represent a population of multipotent adherent cells able to differentiate into many lineages. In our previous studies, we isolated and expanded fetal MSCs from second-trimester amniotic fluid (AF) and characterized them based on their phenotype, pluripotency and proteomic profile. In the present study, we investigated the plasticity of these cells based on their differentiation, dedifferentiation and transdifferentiation potential in vitro. To this end, adipocyte-like cells (AL cells) derived from AF-MSCs can regain, under certain culture conditions, a more primitive phenotype through the process of dedifferentiation. Dedifferentiated AL cells derived from AF-MSCs (DAF-MSCs), gradually lost the expression of adipogenic markers and obtained similar morphology and differentiation potential to AF-MSCs, together with regaining the pluripotency marker expression. Moreover, a comparative proteomic analysis of AF-MSCs, AL cells and DAF-MSCs revealed 31 differentially expressed proteins among the three cell populations. Proteins, such as vimentin, galectin-1 and prohibitin that have a significant role in stem cell regulatory mechanisms, were expressed in higher levels in AF-MSCs and DAF-MSCs compared with AL cells. We next investigated whether AL cells could transdifferentiate into hepatocyte-like cells (HL cells) directly or through a dedifferentiation step. AL cells were cultured in hepatogenic medium and 4 days later they obtained a phenotype similar to AF-MSCs, and were termed as transdifferentiated AF-MSCs (TRAF-MSCs). This finding, together with the increase in pluripotency marker expression, indicated the adaption of a more primitive phenotype before transdifferentiation. Additionally, we observed that AF-, DAF- and TRAF-MSCs displayed similar clonogenic potential, secretome and proteome profile. Considering the easy access to this fetal cell source, the plasticity of AF-MSCs and their potential to dedifferentiate and transdifferentiate, AF may provide a valuable tool for cell therapy and tissue engineering applications

Integrative analysis of extracellular and intracellular bladder cancer cell line proteome with transcriptome: improving coverage and validity of –omics findings

Characterization of disease-associated proteins improves our understanding of disease pathophysiology. Obtaining a comprehensive coverage of the proteome is challenging, mainly due to limited statistical power and an inability to verify hundreds of putative biomarkers. In an effort to address these issues, we investigated the value of parallel analysis of compartment-specific proteomes with an assessment of findings by cross-strategy and cross-omics (proteomics-transcriptomics) agreement. The validity of the individual datasets and of a “verified” dataset based on cross-strategy/omics agreement was defined following their comparison with published literature. The proteomic analysis of the cell extract, Endoplasmic Reticulum/Golgi apparatus and conditioned medium of T24 vs. its metastatic subclone T24M bladder cancer cells allowed the identification of 253, 217 and 256 significant changes, respectively. Integration of these findings with transcriptomics resulted in 253 “verified” proteins based on the agreement of at least 2 strategies. This approach revealed findings of higher validity, as supported by a higher level of agreement in the literature data than those of individual datasets. As an example, the coverage and shortlisting of targets in the IL-8 signalling pathway are discussed. Collectively, an integrative analysis appears a safer way to evaluate -omics datasets and ultimately generate models from valid observations

Forecasting Player Behavioral Data and Simulating in-Game Events

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors

Forecasting the price of gold

This article seeks to evaluate the appropriateness of a variety of existing forecasting techniques (17 methods) at providing accurate and statistically significant forecasts for gold price. We report the results from the nine most competitive techniques. Special consideration is given to the ability of these techniques to provide forecasts which outperforms the random walk (RW) as we noticed that certain multivariate models (which included prices of silver, platinum, palladium and rhodium, besides gold) were also unable to outperform the RW in this case. Interestingly, the results show that none of the forecasting techniques are able to outperform the RW at horizons of 1 and 9 steps ahead, and on average, the exponential smoothing model is seen providing the best forecasts in terms of the lowest root mean squared error over the 24-month forecasting horizons. Moreover, we find that the univariate models used in this article are able to outperform the Bayesian autoregression and Bayesian vector autoregressive models, with exponential smoothing reporting statistically significant results in comparison with the former models, and classical autoregressive and the vector autoregressive models in most cases

Demand forecasting: a case study in the food industry

The use of forecasting methods is nowadays regarded as a business ally since it supports both the operational and the strategic decision-making processes. This paper is based on a research project aiming the development of demand forecasting models for a company (designated here by PR) that operates in the food business, more specifically in the delicatessen segment. In particular, we focused on demand forecasting models that can serve as a tool to support production planning and inventory management at the company. The analysis of the company’s operations led to the development of a new demand forecasting tool based on a combination of forecasts, which is now being used and tested by the company.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the Project Scope: UID/CEC/00319/201

Rule-Based Forecasting: Using Judgment in Time-Series Extrapolation

Rule-Based Forecasting (RBF) is an expert system that uses judgment to develop and apply rules for combining extrapolations. The judgment comes from two sources, forecasting expertise and domain knowledge. Forecasting expertise is based on more than a half century of research. Domain knowledge is obtained in a structured way; one example of domain knowledge is managers= expectations about trends, which we call “causal forces.” Time series are described in terms of 28 conditions, which are used to assign weights to extrapolations. Empirical results on multiple sets of time series show that RBF produces more accurate forecasts than those from traditional extrapolation methods or equal-weights combined extrapolations. RBF is most useful when it is based on good domain knowledge, the domain knowledge is important, the series is well behaved (such that patterns can be identified), there is a strong trend in the data, and the forecast horizon is long. Under ideal conditions, the error for RBF’s forecasts were one-third less than those for equal-weights combining. When these conditions are absent, RBF neither improves nor harms forecast accuracy. Some of RBF’s rules can be used with traditional extrapolation procedures. In a series of studies, rules based on causal forces improved the selection of forecasting methods, the structuring of time series, and the assessment of prediction intervals