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Analysis of Variance for High-Dimensional Data : Applications in Life, Food, and Chemical Sciences
| Analysis of Variance for High-Dimensional Data : Applications in Life, Food, and Chemical Sciences |
| Autore | Smilde Age K |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2025 |
| Descrizione fisica | 1 online resource (339 pages) |
| Disciplina | 570.285 |
| Altri autori (Persone) |
MariniFederico
WesterhuisJohan A LilandKristian Hovde |
| Soggetto topico |
Life sciences - Data processing
Food science - Data processing Chemistry - Data processing Experimental design |
| ISBN |
1-394-21124-4
1-394-21122-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- About the Authors -- Foreword -- Preface -- Chapter 1 Introduction -- 1.1 Types of Data -- 1.2 Statistical Design of Experiments -- 1.3 High‐Dimensional Data -- 1.4 Examples -- 1.4.1 Metabolomics -- 1.4.2 Genomics -- 1.4.3 Microbiome -- 1.4.4 Proteomics -- 1.4.5 Food Science -- 1.4.6 Sensory Science -- 1.4.7 Chemistry -- 1.5 Complexities -- 1.5.1 Normalization -- 1.5.2 Different Measurement Scales -- 1.5.3 Different Distributions -- 1.5.4 Heteroscedastic Error -- 1.5.5 Comparability -- 1.5.6 Sparseness, Non‐detects, and Missing Values -- 1.5.7 Unbalancedness -- 1.6 Direct Versus Indirect Methods -- 1.7 Some History -- 1.A.1 Types of Measurements -- 1.A.2 Notation and Terminology -- 1.A.3 Some Definitions -- 1.A.4 Abbreviations -- Chapter 2 Basic Theory and Concepts -- 2.1 Mathematical Background -- 2.1.1 Vector Spaces and Subspaces -- 2.1.2 Matrix Decompositions -- 2.1.3 Inverses and Generalized Inverses -- 2.1.4 Distances and Projections -- 2.1.4.1 Formal Description of Distances -- 2.1.4.2 Projections -- 2.1.5 Principal Component Analysis -- 2.2 Statistical Background -- 2.2.1 Estimation Methods -- 2.2.1.1 Least Squares -- 2.2.1.2 Maximum Likelihood -- 2.2.2 Regression Methods -- 2.2.2.1 Multiple Linear Regression: Full Rank Case -- 2.2.2.2 Multiple Linear Regression Using Dummy Variables -- 2.2.2.3 Multiple Linear Regression: Rank Deficient Case -- 2.2.2.4 Penalized Regression -- 2.2.2.5 Principal Component Regression -- 2.2.2.6 Partial Least Squares -- 2.2.2.7 Redundancy Analysis -- 2.2.3 Significance Tests -- 2.2.3.1 Classical Tests -- 2.2.3.2 Permutation Tests -- 2.2.3.3 Likelihood Ratio Tests -- 2.3 Association Measures -- 2.3.1 Pearson and Spearman Correlation Coefficients -- 2.3.2 Problems with Correlations -- Chapter 3 Linear Models -- 3.1 Introduction -- 3.2 Simple ANOVA Models.
3.2.1 One‐Way ANOVA -- 3.2.2 Two‐Way ANOVA -- 3.2.2.1 Crossed Designs -- 3.2.2.2 Nested Designs -- 3.2.3 Unbalanced Designs -- 3.2.3.1 One‐Way ANOVA -- 3.2.3.2 Two‐Way ANOVA for Crossed Designs -- 3.2.3.3 Nested ANOVA -- 3.3 Regression Formulation, Estimability, and Contrasts -- 3.4 Coding Schemes -- 3.4.1 Codings for Balanced Designs -- 3.4.1.1 One‐Way Layout -- 3.4.1.2 Two‐Way Crossed Designs -- 3.4.1.3 Two‐Way Nested Designs -- 3.4.2 Codings for Unbalanced Designs -- 3.5 Advanced Models -- 3.5.1 Variance Component Models -- 3.5.2 Linear Mixed Models -- 3.5.2.1 General Idea -- 3.5.2.2 Estimation of Model Parameters -- 3.5.2.3 Repeated Measures ANOVA -- 3.5.2.4 Cross‐over Designs and Models -- 3.5.2.5 Longitudinal LMMs -- 3.6 Hasse Diagrams -- 3.6.1 Building a Hasse Diagram -- 3.7 Validation -- 3.7.1 Classical Tests Revisited -- 3.7.2 Expected Mean Squares from Hasse Diagrams -- 3.7.3 Permutation Tests -- 3.7.3.1 Exact Tests -- 3.7.3.2 Approximate Tests -- 3.8 Miscellaneous Models -- 3.8.1 Multivariate Analysis of Variance -- 3.8.1.1 Traditional Multivariate Analysis of Variance -- 3.8.1.2 Significance Testing in MANOVA -- 3.8.1.3 Regression Formulation of MANOVA -- 3.8.2 Multivariate LMMs -- 3.A.1 Proof -- 3.A.2 Relationships Between Codings -- 3.A.3 Practical Aspects of Codings -- Chapter 4 ASCA and Related Methods -- 4.1 ASCA -- 4.1.1 Basic Idea of ASCA -- 4.1.2 Properties of ASCA -- 4.1.3 Permutation Tests for ASCA -- 4.1.4 Back‐Projection -- 4.1.5 Scaling in ASCA -- 4.1.6 Group‐wise ASCA -- 4.1.7 Variable‐Selection ASCA -- 4.1.8 REP‐ASCA -- 4.1.9 ASCA as a Multivariate Multiple Regression Model -- 4.1.10 Geometry of ASCA -- 4.1.10.1 Geometry of ASCA in Row‐Space -- 4.1.10.2 Geometry of ASCA in Column‐Space -- 4.2 APCA -- 4.2.1 Basic Idea of APCA -- 4.2.2 Comparing APCA with ASCA -- 4.3 ASCA+ -- 4.3.1 Confidence Ellipsoids for ASCA. 4.3.2 ASCA and ASCA+ as RDA Models -- 4.4 Principal Response Curves -- 4.5 SMART -- 4.6 ASCA, PRC, and SMART Compared -- 4.7 MSCA -- 4.A.1 Proof of Equation -- 4.A.2 Proof of Equation -- Chapter 5 Alternative Methods -- 5.1 General Introduction -- 5.2 PLSR‐Based Methods -- 5.2.1 ANOVA‐TP -- 5.2.2 ANOVA Multiblock Orthogonal Partial Least Squares (AMOPLS) -- 5.3 LMM‐Based Methods -- 5.3.1 RM‐ASCA+ with Qualitative Time Models -- 5.3.2 Validation of the RM‐ASCA+ Model -- 5.3.2.1 Validation of RM‐ASCA+ Models with Nonparametric Bootstrap -- 5.3.2.2 Validation of RM‐ASCA+ Models with Permutation Testing -- 5.3.2.3 Visualization -- 5.3.2.4 RM‐ASCA+ with Quantitative Time Models -- 5.3.3 LiMM‐PCA -- 5.3.3.1 Validation -- 5.3.3.2 Visualization of Effects in LiMM‐PCA -- 5.4 Miscellaneous Methods -- 5.4.1 PC‐ANOVA -- 5.4.1.1 Basic Idea of PC‐ANOVA -- 5.4.1.2 Comparing PC‐ANOVA with ASCA -- 5.4.2 PARAFASCA -- 5.4.3 PE‐ASCA -- 5.4.4 rMANOVA -- 5.4.5 Fifty-Fifty MANOVA -- 5.4.6 AComDim -- 5.4.7 General Effect Modeling (GEM) -- Chapter 6 Distance‐based Methods -- 6.1 Introduction -- 6.1.1 Double Zeros -- 6.1.2 Horseshoe Effect -- 6.1.3 Compositionality -- 6.2 Methods -- 6.2.1 Principal Coordinate Analysis -- 6.2.2 PERMANOVA -- 6.2.2.1 PERMANOVA Calculated from the Gower Matrix -- 6.2.2.2 PERMANOVA of Non‐Euclidean Dissimilarity Matrices -- 6.2.3 Effect Sizes in PERMANOVA -- 6.2.4 Permutations in PERMANOVA -- 6.2.5 Assumptions for PERMANOVA -- 6.3 ANOSIM -- Chapter 7 Reviews and Reflections -- 7.1 Reviews -- 7.1.1 Metabolomics -- 7.1.1.1 Plant Science -- 7.1.1.2 Microbiology and Biotechnology -- 7.1.1.3 Animal Science -- 7.1.1.4 Human Science -- 7.1.2 Microbiome -- 7.1.3 Genomics -- 7.1.4 Proteomics -- 7.1.5 Food Science -- 7.1.6 Sensory Science -- 7.1.7 Chemistry -- 7.2 Reflections -- 7.2.1 Summary of Reviews -- 7.2.2 Overview of Methods. 7.2.3 Remaining Challenges -- 7.2.3.1 ASCA+ and Partial RDA -- 7.2.3.2 Permutations: Correlations and Unbalancedness -- 7.2.3.3 PERMANOVA and Effect Sizes -- 7.2.3.4 Back‐Projection Approach -- 7.2.3.5 Inferential Statistics -- 7.2.3.6 Advanced HD‐ANOVA Methods -- Chapter 8 Software -- 8.1 HD‐ANOVA Software -- 8.2 R Package HDANOVA -- 8.3 Installing and Starting the Package -- 8.4 Data Handling -- 8.4.1 Read from File -- 8.4.2 Data Pre‐processing -- 8.4.2.1 Re‐coding Categorical data -- 8.4.3 Data Structures for Analysis Including Blocks -- 8.4.3.1 Create List of Blocks -- 8.4.3.2 Create data.frame of Blocks -- 8.5 Analysis of Variance (ANOVA) -- 8.5.1 Simulated Data -- 8.5.2 Fixed Effect Models -- 8.5.2.1 One‐Way ANOVA -- 8.5.2.2 Two‐Way Crossed Effects ANOVA -- 8.5.2.3 Types of Sums of Squares -- 8.5.2.4 Coding Schemes -- 8.5.2.5 Fixed Effect Nested ANOVA -- 8.5.3 Linear Mixed Models -- 8.5.3.1 Least Squares − mixlm -- 8.5.3.2 Restrictions -- 8.5.3.3 Repeated Measures -- 8.5.3.4 REML -- 8.5.4 Multivariate ANOVA (MANOVA) -- 8.6 Basic ASCA Family -- 8.6.1 Fit ASCA Model -- 8.6.1.1 Permutation Testing -- 8.6.1.2 Random Effects -- 8.6.1.3 Scores and Loadings -- 8.6.1.4 Data Ellipsoids and Confidence Ellipsoids -- 8.6.1.5 Combined Effects -- 8.6.1.6 Quantitative Effects -- 8.6.2 ANOVA‐PCA (APCA) -- 8.6.3 PC‐ANOVA -- 8.6.4 MSCA -- 8.6.5 LiMM‐PCA -- 8.6.6 Repeated Measures ASCA -- 8.7 Alternative Methods -- 8.7.1 Principal Response Curves (PRC) -- 8.7.2 Permutation‐Based MANOVA (PERMANOVA) -- 8.8 Software Packages -- 8.8.1 R Packages -- 8.8.2 MATLAB Toolboxes -- 8.8.3 Python -- References -- Index -- EULA. |
| Record Nr. | UNINA-9911020059203321 |
Smilde Age K
|
||
| Newark : , : John Wiley & Sons, Incorporated, , 2025 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina |
540.1519535
540.72 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-27462-X
9786610274628 0-470-01211-0 0-470-01210-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-way Analysis with Applications in the Chemical Sciences; CONTENTS; Foreword; Preface; Nomenclature and Conventions; 1 Introduction; 1.1 What is multi-way analysis?; 1.2 Conceptual aspects of multi-way data analysis; 1.3 Hierarchy of multivariate data structures in chemistry; 1.4 Principal component analysis and PARAFAC; 1.5 Summary; 2 Array definitions and properties; 2.1 Introduction; 2.2 Rows, columns and tubes; frontal, lateral and horizontal slices; 2.3 Elementary operations; 2.4 Linearity concepts; 2.5 Rank of two-way arrays; 2.6 Rank of three-way arrays
2.7 Algebra of multi-way analysis2.8 Summary; Appendix 2.A; 3 Two-way component and regression models; 3.1 Models for two-way one-block data analysis: component models; 3.2 Models for two-way two-block data analysis: regression models; 3.3 Summary; Appendix 3.A: some PCA results; Appendix 3.B: PLS algorithms; 4 Three-way component and regression models; 4.1 Historical introduction to multi-way models; 4.2 Models for three-way one-block data: three-way component models; 4.3 Models for three-way two-block data: three-way regression models; 4.4 Summary Appendix 4.A: alternative notation for the PARAFAC modelAppendix 4.B: alternative notations for the Tucker3 model; 5 Some properties of three-way component models; 5.1 Relationships between three-way component models; 5.2 Rotational freedom and uniqueness in three-way component models; 5.3 Properties of Tucker3 models; 5.4 Degeneracy problem in PARAFAC models; 5.5 Summary; 6 Algorithms; 6.1 Introduction; 6.2 Optimization techniques; 6.3 PARAFAC algorithms; 6.4 Tucker3 algorithms; 6.5 Tucker2 and Tucker1 algorithms; 6.6 Multi-linear partial least squares regression 6.7 Multi-way covariates regression models6.8 Core rotation in Tucker3 models; 6.9 Handling missing data; 6.10 Imposing non-negativity; 6.11 Summary; Appendix 6.A: closed-form solution for the PARAFAC model; Appendix 6.B: proof that the weights in trilinear PLS1 can be obtained from a singular value decomposition; 7 Validation and diagnostics; 7.1 What is validation?; 7.2 Test-set and cross-validation; 7.3 Selecting which model to use; 7.4 Selecting the number of components; 7.5 Residual and influence analysis; 7.6 Summary; 8 Visualization; 8.1 Introduction 8.2 History of plotting in three-way analysis8.3 History of plotting in chemical three-way analysis; 8.4 Scree plots; 8.5 Line plots; 8.6 Scatter plots; 8.7 Problems with scatter plots; 8.8 Image analysis; 8.9 Dendrograms; 8.10 Visualizing the Tucker core array; 8.11 Joint plots; 8.12 Residual plots; 8.13 Leverage plots; 8.14 Visualization of large data sets; 8.15 Summary; 9 Preprocessing; 9.1 Background; 9.2 Two-way centering; 9.3 Two-way scaling; 9.4 Simultaneous two-way centering and scaling; 9.5 Three-way preprocessing; 9.6 Summary; Appendix 9.A: other types of preprocessing Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9910143442703321 |
|
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences [[electronic resource] /] / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina |
540.1519535
540.72 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| ISBN |
1-280-27462-X
9786610274628 0-470-01211-0 0-470-01210-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-way Analysis with Applications in the Chemical Sciences; CONTENTS; Foreword; Preface; Nomenclature and Conventions; 1 Introduction; 1.1 What is multi-way analysis?; 1.2 Conceptual aspects of multi-way data analysis; 1.3 Hierarchy of multivariate data structures in chemistry; 1.4 Principal component analysis and PARAFAC; 1.5 Summary; 2 Array definitions and properties; 2.1 Introduction; 2.2 Rows, columns and tubes; frontal, lateral and horizontal slices; 2.3 Elementary operations; 2.4 Linearity concepts; 2.5 Rank of two-way arrays; 2.6 Rank of three-way arrays
2.7 Algebra of multi-way analysis2.8 Summary; Appendix 2.A; 3 Two-way component and regression models; 3.1 Models for two-way one-block data analysis: component models; 3.2 Models for two-way two-block data analysis: regression models; 3.3 Summary; Appendix 3.A: some PCA results; Appendix 3.B: PLS algorithms; 4 Three-way component and regression models; 4.1 Historical introduction to multi-way models; 4.2 Models for three-way one-block data: three-way component models; 4.3 Models for three-way two-block data: three-way regression models; 4.4 Summary Appendix 4.A: alternative notation for the PARAFAC modelAppendix 4.B: alternative notations for the Tucker3 model; 5 Some properties of three-way component models; 5.1 Relationships between three-way component models; 5.2 Rotational freedom and uniqueness in three-way component models; 5.3 Properties of Tucker3 models; 5.4 Degeneracy problem in PARAFAC models; 5.5 Summary; 6 Algorithms; 6.1 Introduction; 6.2 Optimization techniques; 6.3 PARAFAC algorithms; 6.4 Tucker3 algorithms; 6.5 Tucker2 and Tucker1 algorithms; 6.6 Multi-linear partial least squares regression 6.7 Multi-way covariates regression models6.8 Core rotation in Tucker3 models; 6.9 Handling missing data; 6.10 Imposing non-negativity; 6.11 Summary; Appendix 6.A: closed-form solution for the PARAFAC model; Appendix 6.B: proof that the weights in trilinear PLS1 can be obtained from a singular value decomposition; 7 Validation and diagnostics; 7.1 What is validation?; 7.2 Test-set and cross-validation; 7.3 Selecting which model to use; 7.4 Selecting the number of components; 7.5 Residual and influence analysis; 7.6 Summary; 8 Visualization; 8.1 Introduction 8.2 History of plotting in three-way analysis8.3 History of plotting in chemical three-way analysis; 8.4 Scree plots; 8.5 Line plots; 8.6 Scatter plots; 8.7 Problems with scatter plots; 8.8 Image analysis; 8.9 Dendrograms; 8.10 Visualizing the Tucker core array; 8.11 Joint plots; 8.12 Residual plots; 8.13 Leverage plots; 8.14 Visualization of large data sets; 8.15 Summary; 9 Preprocessing; 9.1 Background; 9.2 Two-way centering; 9.3 Two-way scaling; 9.4 Simultaneous two-way centering and scaling; 9.5 Three-way preprocessing; 9.6 Summary; Appendix 9.A: other types of preprocessing Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9910830068003321 |
|
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Multi-way analysis with applications in the chemical sciences / / Age Smilde, Rasmus Bro, and Paul Geladi
| Multi-way analysis with applications in the chemical sciences / / Age Smilde, Rasmus Bro, and Paul Geladi |
| Autore | Smilde Age K |
| Pubbl/distr/stampa | Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 |
| Descrizione fisica | 1 online resource (397 p.) |
| Disciplina | 540/.72 |
| Altri autori (Persone) |
BroRasmus
GeladiPaul |
| Soggetto topico |
Chemistry - Statistical methods
Multivariate analysis |
| ISBN |
9786610274628
9781280274626 128027462X 9780470012116 0470012110 9780470012109 0470012102 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Multi-way Analysis with Applications in the Chemical Sciences; CONTENTS; Foreword; Preface; Nomenclature and Conventions; 1 Introduction; 1.1 What is multi-way analysis?; 1.2 Conceptual aspects of multi-way data analysis; 1.3 Hierarchy of multivariate data structures in chemistry; 1.4 Principal component analysis and PARAFAC; 1.5 Summary; 2 Array definitions and properties; 2.1 Introduction; 2.2 Rows, columns and tubes; frontal, lateral and horizontal slices; 2.3 Elementary operations; 2.4 Linearity concepts; 2.5 Rank of two-way arrays; 2.6 Rank of three-way arrays
2.7 Algebra of multi-way analysis2.8 Summary; Appendix 2.A; 3 Two-way component and regression models; 3.1 Models for two-way one-block data analysis: component models; 3.2 Models for two-way two-block data analysis: regression models; 3.3 Summary; Appendix 3.A: some PCA results; Appendix 3.B: PLS algorithms; 4 Three-way component and regression models; 4.1 Historical introduction to multi-way models; 4.2 Models for three-way one-block data: three-way component models; 4.3 Models for three-way two-block data: three-way regression models; 4.4 Summary Appendix 4.A: alternative notation for the PARAFAC modelAppendix 4.B: alternative notations for the Tucker3 model; 5 Some properties of three-way component models; 5.1 Relationships between three-way component models; 5.2 Rotational freedom and uniqueness in three-way component models; 5.3 Properties of Tucker3 models; 5.4 Degeneracy problem in PARAFAC models; 5.5 Summary; 6 Algorithms; 6.1 Introduction; 6.2 Optimization techniques; 6.3 PARAFAC algorithms; 6.4 Tucker3 algorithms; 6.5 Tucker2 and Tucker1 algorithms; 6.6 Multi-linear partial least squares regression 6.7 Multi-way covariates regression models6.8 Core rotation in Tucker3 models; 6.9 Handling missing data; 6.10 Imposing non-negativity; 6.11 Summary; Appendix 6.A: closed-form solution for the PARAFAC model; Appendix 6.B: proof that the weights in trilinear PLS1 can be obtained from a singular value decomposition; 7 Validation and diagnostics; 7.1 What is validation?; 7.2 Test-set and cross-validation; 7.3 Selecting which model to use; 7.4 Selecting the number of components; 7.5 Residual and influence analysis; 7.6 Summary; 8 Visualization; 8.1 Introduction 8.2 History of plotting in three-way analysis8.3 History of plotting in chemical three-way analysis; 8.4 Scree plots; 8.5 Line plots; 8.6 Scatter plots; 8.7 Problems with scatter plots; 8.8 Image analysis; 8.9 Dendrograms; 8.10 Visualizing the Tucker core array; 8.11 Joint plots; 8.12 Residual plots; 8.13 Leverage plots; 8.14 Visualization of large data sets; 8.15 Summary; 9 Preprocessing; 9.1 Background; 9.2 Two-way centering; 9.3 Two-way scaling; 9.4 Simultaneous two-way centering and scaling; 9.5 Three-way preprocessing; 9.6 Summary; Appendix 9.A: other types of preprocessing Appendix 9.B: geometric view of centering |
| Record Nr. | UNINA-9911019379303321 |
|
Smilde Age K
|
||
| Chichester, West Sussex, England ; ; Hoboken, NJ, : J. Wiley, c2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||