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 $\sum_{n\geq 0}b_n z^n = \phantom{}_{p+1} F_{p}(\ldots;z)$

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

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

Finite element fracture risk assessment of metastatic femur using deep-learning lesion segmentation

LAUREA MAGISTRALEL’obbiettivo di questo studio è sia quello di determinare se l’utilizzo della tecnica degli elementi finiti combinata con segmentazioni delle lesioni (derivate sia da un algoritmo di deep learning sia manualmente) sia migliore nel determinare l’indice di rischio per metastasi ossee litiche nel femore rispetto all’utilizzo della sola tecnica agli elementi finiti, sia di trovare un modo per implementare le proprietà meccaniche delle metastasi blastiche nel modello ad elementi finiti. 8 pazienti litici e 6 blastici sono stati analizzati con 5 segmentazioni ed una segmentazione rispettivamente. Il modello ad elementi finiti specifico per ogni paziente è stato costruito partendo dalle immagini CT. Nei pazienti litici si è analizzato il coefficiente di Dice, il BOS score (il carico di fallimento normalizzato per il peso corporeo) e la classifica dei carichi di fallimento. Dato che i BOS score ottenuti dalla segmentazioni manuale erano positivi, si è deciso di allargare lo studio a 33 pazienti. Su di essi, si sono calcolati i valori di sensitività, specificità e di valore predittivo positivo e negativo. Per le metastasi blastiche, si è cercata una relazione tra la riduzione del modulo di Young delle metastasi e la differenza tra i carichi di fallimenti tra il modello standard e quello modificato con la segmentazione. Per i pazienti litici, la segmentazione automatica più simile alla segmentazione manuale ha ottenuto un coefficiente di Dice pari a 64,43%. La segmentazione manuale ha una classifica dei carichi di fallimento molto diversa dalle segmentazioni automatiche e dal modello standard. Le segmentazioni automatiche hanno una classifica molto simile tra loro e al modello standard. I valori di sensitività, specificità, valore predittivo positivo e negativo dei 33 pazienti sono pari rispettivamente a 100%, 93%, 78% e 100%, mentre i valori ottenuti utilizzando solamente la tecnica ad elementi finiti sono pari rispettivamente a 100%, 74%, 39% e 100%. Anche le segmentazioni automatiche hanno mostrato un miglioramento nella predizione del fattore di rischio ma non così buona come quella ottenuta con la segmentazione manuale. Per le metastasi blastiche, solo due pazienti su sei hanno mostrato l’andamento previsto. Entrambi i pazienti hanno in comune di avere lesioni molto diffuse sul femore, mentre gli altri quattro pazienti le lesioni risultano essere molto ridotte. La tecnica ad elementi finiti combinata con la segmentazione manuale migliora la predizione del fattore di rischio delle metastasi ossee litiche nel femore, rispetto all’utilizzo della sola tecnica ad elementi finiti, invece per ottenere risultati simili con il deep learning, l’algoritmo deve essere migliorato. Nelle metastasi blastiche, la riduzione delle proprietà meccaniche nel modello ad elementi finiti influenza la forza di reazione solo in presenza di lesioni diffuse.The purpose of this work is to determine if patient-specific finite element models (FEM) with adapted material properties in the lesions segmented by a deep learning metastatic or a manual segmentation are better at assessing fracture risk for femoral bone metastasis compared to the original patient-specific FEMs. Additionally, we aimed to find a way to adapt the material properties of the blastic metastasis in the FEMs to diminish the overestimation of the strength in these femurs. Material properties of eight lytic patients and six blastic patients were adapted based on five segmentations and one manual segmentation respectively. Patient-specific FEMs were constructed based on the geometry and the bone density obtained from the baseline CT scans used for radiotherapy planning. The analysis of the lytic patients consisted in the calculation of the Dice coefficients (DC), the BOne strength (BOS) score (the reaction force (RF) normalized by body weights) and the ranking of the RFs. Since the BOS scores obtained by the FEMs modified with the manual segmentation were very promising, a larger number of patients (33) was tested and the diagnostic accuracy values (sensitivity, specificity and positive (PPV) and negative predictive values (NPV)) were calculated. For the blastic metastasis, the relation between the reduction in Young’s modulus and the difference in RF between the standard and the modified model was determined, expecting a progressive decreasing of the reaction force of the femurs. The automatic segmentation that the most like the manual segmentation had a DC equal to 64.43%. The manual segmentation had a completely different ranking in comparison to the standard FEM, whereas the ranking of all the automatic segmentations were very similar to the standard FEM. The automatic segmentations showed an improvement on the assessment on the fracture risk but not as good as the manual segmentations. The sensitivity, the specificity, the PPV and the NPV obtained studying 33 patients were respectively 100%, 93%, 78% and 100%, whereas the values obtained by using the standard FEM were respectively 100%, 74%, 39% and 100%. For the blastic metastasis only two out of six patients showed the expected trend. This can be explained by the fact that these two patients had large lesions spread throughout the femurs, whereas in the other four femurs the metastatic lesions were small and had less effect on the strength of the femur. The patient-specific FEMs combine with the manual segmentation improved the fracture risk assessments of femoral bone metastasis in cancer patients compared to the original patient-specific FEM. However, to reach the same goal with the automatic segmentations the algorithm must be improved. In the blastic metastasis, decreasing the material properties in the FEM only influenced the RF if the patient had larger metastatic lesions

From Earthquake Geophysical Measures to Insurance Premium: A Generalised Method for the Evaluation of Seismic Risk, with Application to Italy’s Housing Stock

Following the increasing necessity of quantitative measures for the impact of natural catastrophes, this paper proposes a new technique for a probabilistic assessment of seismic risk by using publicly available data on the earthquakes that have occurred in Italy. We implement an insurance-oriented methodology to produce a new map of the seismic risk and to evaluate, under various hypotheses, the costs of insuring all the Italian housing units against it. The model is compared with two main privately developed models, well known in the reinsurance industry, providing fairly similar results

Discovering miRNA Regulatory Networks in Holt–Oram Syndrome Using a Zebrafish Model

MicroRNAs (miRNAs) are small non-coding RNAs that play an important role in the post-transcriptional regulation of gene expression. miRNAs are involved in the regulation of many biological processes such as differentiation, apoptosis, and cell proliferation. miRNAs are expressed in embryonic, postnatal, and adult hearts, and they have a key role in the regulation of gene expression during cardiovascular development and disease. Aberrant expression of miRNAs is associated with abnormal cardiac cell differentiation and dysfunction. Tbx5 is a member of the T-box gene family, which acts as transcription factor involved in the vertebrate heart development. Alteration of Tbx5 level affects the expression of hundreds of genes. Haploinsufficiency and gene duplication of Tbx5 are at the basis of the cardiac abnormalities associated with Holt-Oram syndrome (HOS). Recent data indicate that miRNAs might be an important part of the regulatory circuit through which Tbx5 controls heart development. Using high-throughput technologies, we characterized genome-widely the miRNA and mRNA expression profiles in WT- and Tbx5-depleted zebrafish embryos at two crucial developmental time points, 24 and 48 h post fertilization (hpf). We found that several miRNAs, which are potential effectors of Tbx5, are differentially expressed; some of them are already known to be involved in cardiac development and functions, such as miR-30, miR-34, miR-190, and miR-21. We performed an integrated analysis of miRNA expression data with gene expression profiles to refine computational target prediction approaches by means of the inversely correlation of miRNA-mRNA expressions, and we highlighted targets, which have roles in cardiac contractility, cardiomyocyte proliferation/apoptosis, and morphogenesis, crucial functions regulated by Tbx5. This approach allowed to discover complex regulatory circuits involving novel miRNAs and protein coding genes not considered before in the HOS such as miR-34a and miR-30 and their targets.</p