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Record Nr. |
UNINA9910915676103321 |
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Autore |
Ledrappier François |
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Titolo |
The Regularity of the Linear Drift in Negatively Curved Spaces |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2023 |
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©2023 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (164 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.281 |
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Classificazione |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Geodesic flows |
Stochastic analysis |
Brownian motion processes |
Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Cover -- Title page -- Chapter 1. Introduction and statement of results -- Main notations and conventions -- Chapter 2. Preliminaries -- 2.1. Jacobi fields and the geodesic flow -- 2.2. Anosov flow and invariant manifolds -- 2.3. Harmonic measure for the stable foliation -- 2.4. Busemann function and the linear drift -- Chapter 3. Regularity of the linear drift -- 3.1. Regularity of the leafwise divergence term ^{ }\overline{ } -- 3.2. Regularity of the harmonic measure -- 3.3. Differentials of the linear drift -- Chapter 4. Brownian motion and stochastic flows -- 4.1. Parallelism and the Brownian motion -- 4.2. A stochastic analogue of the geodesic flow -- 4.3. Growth of the stochastic tangent maps in time -- 4.4. Brownian bridge and conditional estimations -- 4.5. Regularity of the stochastic analogue of the geodesic flow -- Chapter 5. The first differential of the heat kernels in metrics -- 5.1. Strategy -- 5.2. A description of _{ }^{ } -- 5.3. The |
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existence of ^{ }_{ } -- 5.4. Quasi-invariance property of _{ }^{ } -- 5.5. The extended map ^{ } -- 5.6. The differential of \mapsto ^{ }( , ,⋅) -- Chapter 6. Higher order regularity of the heat kernels in metrics -- 6.1. A sketch of the proof for Theorem 1.3 with ≥2 -- 6.2. Proofs of the properties concerning ^{ }_{ } -- Chapter 7. Regularity of the stochastic entropy -- Acknowledgments -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is Ck-2 differentiable along any Ck curve in the manifold of Ck Riemannian metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C1 differentiable along any C3 curve of C3 Riemannian metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show they are critical at locally symmetric metrics"-- |
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2. |
Record Nr. |
UNINA9911039315103321 |
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Autore |
Kaushikk Rajaniesh |
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Titolo |
The Data Lakehouse Revolution : Harnessing the Power of Databricks for Generative AI and Machine Learning / / by Rajaniesh Kaushikk |
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Pubbl/distr/stampa |
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Berkeley, CA : , : Apress : , : Imprint : Apress, , 2025 |
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ISBN |
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9798868817212 |
9798868817205 |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (345 pages) |
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Collana |
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Professional and Applied Computing Series |
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Disciplina |
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Soggetti |
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Microsoft Azure (Computing platform) |
Machine learning |
Artificial intelligence |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Chapter 1: Getting Started with Databricks -- Chapter 2: Introduction to Machine Learning and Data Lakehouses -- Chapter 3: Data Preparation and Management -- Chapter 4: Building Machine Learning |
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Models -- Chapter 5: AutoML and Model Optimization -- Chapter 6: Deploying Machine Learning Models -- Chapter 7: Advanced Topics in Machine Learning -- Chapter 8: Lakehouse AI and Retrieval-Augmented Generation (RAG) -- Chapter 9: Conclusion and Next Steps. |
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Sommario/riassunto |
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We are racing toward a new kind of AI—faster, smarter, and more connected than ever. At the heart of it is the Data Lakehouse, and Databricks is the engine powering the transformation. Whether you're a data scientist training models, an engineer scaling pipelines, or an architect modernizing your stack, this book gives you what you need to stay ahead. Inside, you'll understand how to unlock the full potential of Machine Learning and Generative AI (GenAI) using Databricks—no fluff, just real tools, real strategies, and real results. From MLFlow and AutoML to Unity Catalog, Retrieval Augment Generation (RAG), and Vector Search, you'll get a complete blueprint for building intelligent systems that actually work in production. With step-by-step labs, industry case studies, and expert tips from someone who's lived through the entire evolution of enterprise AI, this book is your guide to mastering what's next. If you're serious regarding building AI that matters, this is where your journey begins. What You'll Learn Build full-stack ML and GenAI solutions on Databricks Train and track models with MLFlow, AutoML, and tuning strategies Secure and govern data with Unity Catalog Apply explainable, ethical AI techniques Deploy and monitor ML models in real-world pipelines Use RAG and vector search to power GenAI applications Gain confidence with hands-on labs and real enterprise use cases. |
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