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

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

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

On the automatic identification of unobserved components models

Automatic identi cation of time series models is a necessity once the big data era has come and is staying among us. This has become obvious for many companies and public entities that has passed from a crafted analysis of each individual problem to handle a tsunami of information that has to be processed e ciently, online and in record time. Automatic identi cation tools has never been tried out on Unobserved Components models (UC). This chapter shows how information criteria, such as Akaike's or Schwarz's, are rather useful for model selection within the UC family. The di culty lies, however, on choosing an appropriate and as general as possible set of models to search in. A set too narrow would render poor forecast accuracy, while a set too wide would be highly time consuming. The forecasting results suggest that UC models are powerful potential forecasting competitors to other well-known methods. Though there are several pieces of software available for UC modeling, this is the rst implementation of an automatic algorithm for this class of models, to the best of the authors knowledge

On the formal foundations of cash management systems

[EN] Cash management aims to find a balance between what is held in cash and what is allocated in other investments in exchange for a given return. Dealing with cash management systems with multiple accounts and different links between them is a complex task. Current cash management models provide analytic solutions without exploring the underlying structure of accounts and its main properties. There is a need for a formal definition of cash management systems. In this work, we introduce a formal approach to manage cash with multiple accounts based on graph theory. Our approach allows a formal reasoning on the relation between accounts in cash management systems. A critical part of this formal reasoning is the characterization of desirable and non-desirable cash management policies. Novel theoretical results guide cash managers in the analysis of complex cash management systems.This work is partially funded by projects Logistar (H2020-769142), AI4EU (H2020-825619) and 2017 SGR 172.Salas-Molina, F.; Rodriguez-Aguilar, JA.; Pla Santamaría, D.; Garcia-Bernabeu, A. (2021). On the formal foundations of cash management systems. Operational Research. 21(2):1081-1095. https://doi.org/10.1007/s12351-019-00464-6S10811095212Baccarin S (2009) Optimal impulse control for a multidimensional cash management system with generalized cost functions. Eur J Oper Res 196(1):198–206Bollobás B (2013) Modern graph theory, vol 184. Springer, BerlinBondy JA, Murty USR (1976) Graph theory with applications, vol 290. Macmillan, LondonChartrand G, Oellermann OR (1993) Applied and algorithmic graph theory, vol 993. McGraw-Hill, New YorkConstantinides GM, Richard SF (1978) Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time. Oper Res 26(4):620–636da Costa Moraes MB, Nagano MS, Sobreiro VA (2015) Stochastic cash flow management models: a literature review since the 1980s. In: Guarnieri P (ed) Decision models in engineering and management. Springer, Berlin, pp 11–28de Avila Pacheco JV, Morabito R (2011) Application of network flow models for the cash management of an agribusiness company. Comput Ind Eng 61(3):848–857Golden B, Liberatore M, Lieberman C (1979) Models and solution techniques for cash flow management. Comput Oper Res 6(1):13–20Gormley FM, Meade N (2007) The utility of cash flow forecasts in the management of corporate cash balances. Eur J Oper Res 182(2):923–935Gregory G (1976) Cash flow models: a review. Omega 4(6):643–656Makridakis S, Wheelwright SC, Hyndman RJ (2008) Forecasting methods and applications. Wiley, New YorkRighetto GM, Morabito R, Alem D (2016) A robust optimization approach for cash flow management in stationery companies. Comput Ind Eng 99:137–152Salas-Molina F (2017) Risk-sensitive control of cash management systems. Oper Res. https://doi.org/10.1007/s12351-017-0371-0Salas-Molina F, Pla-Santamaria D, Rodriguez-Aguilar JA (2018) A multi-objective approach to the cash management problem. Ann Oper Res 267(1):515–529Srinivasan V, Kim YH (1986) Deterministic cash flow management: state of the art and research directions. Omega 14(2):145–166Valiente G (2013) Algorithms on trees and graphs. Springer, Berli