On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums

In this work we continue the investigation about the interplay between hypergeometric functions and Fourier-Legendre ($\textrm{FL}$) series expansions. In the section "Hypergeometric series related to $\pi,\pi^2$ and the lemniscate constant", through the FL-expansion of $\left[x(1-x)\right]^\mu$ (with $\mu+1\in\frac{1}{4}\mathbb{N}$) we prove that all the hypergeometric series $$\sum_{n\geq 0}\frac{(-1)^n(4n+1)}{p(n)}\left[\frac{1}{4^n}\binom{2n}{n}\right]^3,\quad \sum_{n\geq 0}\frac{(4n+1)}{p(n)}\left[\frac{1}{4^n}\binom{2n}{n}\right]^4,$$ $$\quad \sum_{n\geq 0}\frac{(4n+1)}{p(n)^2}\left[\frac{1}{4^n}\binom{2n}{n}\right]^4,\; \sum_{n\geq 0}\frac{1}{p(n)}\left[\frac{1}{4^n}\binom{2n}{n}\right]^3,\; \sum_{n\geq 0}\frac{1}{p(n)}\left[\frac{1}{4^n}\binom{2n}{n}\right]^2$$ return rational multiples of $\frac{1}{\pi},\frac{1}{\pi^2}$ or the lemniscate constant, as soon as $p(x)$ is a polynomial fulfilling suitable symmetry constraints. Additionally, by computing the FL-expansions of $\frac{\log x}{\sqrt{x}}$ and related functions, we show that in many cases the hypergeometric $\phantom{}_{p+1} F_{p}(\ldots , z)$ function evaluated at $z=\pm 1$ can be converted into a combination of Euler sums. In particular we perform an explicit evaluation of $$\sum_{n\geq 0}\frac{1}{(2n+1)^2}\left[\frac{1}{4^n}\binom{2n}{n}\right]^2,\quad \sum_{n\geq 0}\frac{1}{(2n+1)^3}\left[\frac{1}{4^n}\binom{2n}{n}\right]^2.$$ In the section "Twisted hypergeometric series" we show that the conversion of some $\phantom{}_{p+1} F_{p}(\ldots,\pm 1)$ values into combinations of Euler sums, driven by FL-expansions, applies equally well to some twisted hypergeometric series, i.e. series of the form $\sum_{n\geq 0} a_n b_n$ where $a_n$ is a Stirling number of the first kind and $\sum_{n\geq 0}b_n z^n = \phantom{}_{p+1} F_{p}(\ldots;z)$

Investment forecasting with business survey data

Business investment is a very important variable for short- and medium-term economic analysis, but it is volatile and difficult to predict. Qualitative business survey data are widely used to provide indicators of economic activity ahead of the publication of official data. Traditional indicators exploit only aggregate survey information, namely the proportions of respondents who report “up” and “down”. As a consequence, neither the heterogeneity of individual responses nor the panel dimension of microdata is used. We illustrate the use of a disaggregate panel-based indicator that exploits all information coming from two yearly industrial surveys carried out on the same sample of Italian manufacturing firms. Using the same sample allows us to match exactly investment plans and investment realisations for each firm and so estimate a panel data model linking individual investment realisations to investment intentions. The model generates a one-year-ahead forecast of investment variation that follows the aggregate dynamics with a limited bias.investment plans, dynamic panel data model, forecasting

A neural network architecture for data editing in the Bank of ItalyÂ’s business surveys

This paper presents an application of neural network models to predictive classification for data quality control. Our aim is to identify data affected by measurement error in the Bank of ItalyÂ’s business surveys. We build an architecture consisting of three feed-forward networks for variables related to employment, sales and investment respectively: the networks are trained on input matrices extracted from the error-free final survey database for the 2003 wave, and subjected to stochastic transformations reproducing known error patterns. A binary indicator of unit perturbation is used as the output variable. The networks are trained with the Resilient Propagation learning algorithm. On the training and validation sets, correct predictions occur in about 90 per cent of the records for employment, 94 per cent for sales, and 75 per cent for investment. On independent test sets, the respective quotas average 92, 80 and 70 per cent. On our data, neural networks perform much better as classifiers than logistic regression, one of the most popular competing methods, on our data. They appear to provide a valid means of improving the efficiency of the quality control process and, ultimately, the reliability of survey data.data quality, data editing, binary classification, neural networks, measurement error

Remote processing of firm microdata at the Bank of Italy

Providing the possibility to run personalised econometric/statistical analyses on the appropriate data sets by remote processing allows greater flexibility in the production of economic information. Binding confidentiality requirements are required with business survey data. The Bank of Italy's infrastructure allows its business survey data to be exploited, while preserving anonymity of individual data. The system is based on the LISSY platform and has been already adopted by the Luxembourg Income Study (LIS) and other research centres. Firms' privacy is safeguarded by forbidding potentially confidentiality-breaking programme statements and by denying the visualisation of individual data. Data confidentiality is protected by removing key identifiers from the database and by trimming data in the right tail of the distribution. The platform provides its services through plain-text e-mails. The authorised user sends an e-mail containing an identifying header followed by a statistical programme to a predetermined address. The system checks the validity of the header, strips out the code and submits it in a batch to one of the econometric/statistical packages available (SAS and Stata). The outputs are mailed back to the user after passing an array of automatic and manual checks.microdata, confidentiality, remote access

On the Correlation Between Tactile Stimulation and Pleasantness

: several studies in the affective haptics research field showed the potential of using haptic technology to convey emotions in remote communications. In this context, it is of interest to simplify the haptic feedback without altering the informative content of the stimulus, with a two-fold advantage. on one side, it would allow the development of affective haptic devices whose technological complexity is limited, hence more compatible with wearability and portability requirements. On the other side, having a simplified set of stimuli would decrease the amount of data to be transmitted, thus improving the overall quality of remote haptic interactions. In this work, we investigated the correlation between the parameters regulating a caress-like stimulation and the perceived pleasantness. This was done by means of two experiments, in which we asked subjects to adjust the temperature and the motion velocity of a set of stimuli in order to find the most pleasant combination. results indicated that subjects preferred different values of temperature and velocity of the stimulus depending on the proposed tactile stimulation. a small difference in the pleasantness ratings was observed between caresses provided with linear movements and those given as discrete sequences of taps. In particular, participants preferred linear movements set at 34.5 °C and 3.4 cms-1. As regards caress-like stimuli provided with discrete sequences of taps, the preferred temperature and velocity were 33.2 °C and 2.9 cms-1, respectively. the presence of vibration had a little effect on the perceived pleasantness

Free thyroxine measurement in clinical practice: how to optimize indications, analytical procedures, and interpretation criteria while waiting for global standardization

Thyroid dysfunctions are among the most common endocrine disorders and accurate biochemical testing is needed to confirm or rule out a diagnosis. Notably, true hyperthyroidism and hypothyroidism in the setting of a normal thyroid-stimulating hormone level are highly unlikely, making the assessment of free thyroxine (FT4) inappropriate in most new cases. However, FT4 measurement is integral in both the diagnosis and management of relevant central dysfunctions (central hypothyroidism and central hyperthyroidism) as well as for monitoring therapy in hyperthyroid patients treated with anti-thyroid drugs or radioiodine. In such settings, accurate FT4 quantification is required. Global standardization will improve the comparability of the results across laboratories and allow the development of common clinical decision limits in evidence-based guidelines. The International Federation of Clinical Chemistry and Laboratory Medicine Committee for Standardization of Thyroid Function Tests has undertaken FT4 immunoassay method comparison and recalibration studies and developed a reference measurement procedure that is currently being validated. However, technical and implementation challenges, including the establishment of different clinical decision limits for distinct patient groups, still remain. Accordingly, different assays and reference values cannot be interchanged. Two-way communication between the laboratory and clinical specialists is pivotal to properly select a reliable FT4 assay, establish reference intervals, investigate discordant results, and monitor the analytical and clinical performance of the method over time