Page
%P
-
Chapter
Correction to: Talking about Optimal Transport
-
Chapter
Talking about Optimal Transport
In this session, we have the pleasure of hosting Luigi Ambrosio, a professor at the Scuola Normale Superiore in Pisa, Italy, as our guest. Professor Ambrosio, who recently co-authored the new textbook, Lectures o...
-
Chapter
Optimal Transport, Fields Medals and beyond
Welcome to the Springer Math Podcast. This month, we’re delighted to host Alessio Figalli, the Director of the Institute for Mathematical Research at ETH Zurich, Switzerland. A distinguished academic, Professo...
-
Book
-
Article
Open AccessStem cell-derived small extracellular vesicles embedded into methacrylated hyaluronic acid wound dressings accelerate wound repair in a pressure model of diabetic ulcer
Over the past years, the development of innovative smart wound dressings is revolutionizing wound care management and research. Specifically, in the treatment of diabetic foot wounds, three-dimensional (3D) bi...
-
Article
Open AccessLinear inverse problems with Hessian–Schatten total variation
In this paper, we characterize the class of extremal points of the unit ball of the Hessian–Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer th...
-
Article
Open AccessFunctions with Bounded Hessian–Schatten Variation: Density, Variational, and Extremality Properties
In this paper we analyze in detail a few questions related to the theory of functions with bounded p-Hessian–Schatten total variation, which are relevant in connection with the theory of inverse problems and mach...
-
Article
Open AccessNanofibrous polypeptide hydrogels with collagen-like structure as biomimetic extracellular matrix
Supramolecular peptides exhibit obvious similarities with collagen fibers in terms of self-assembly characteristics, nanofibrous structure, and responsiveness to external stimuli. Here, a series of supramolecu...
-
Article
Open AccessMassive foreign body reaction and osteolysis following primary anterior cruciate ligament reconstruction with the ligament augmentation and reconstruction system (LARS): a case report with histopathological and physicochemical analysis
Autologous hamstrings and patellar tendon have historically been considered the gold standard grafts for anterior cruciate ligament reconstruction (ACLR). In the last decades, the utilization of synthetic graf...
-
Article
Open AccessOptimal \(C^\infty \) -approximation of functions with exponentially or sub-exponentially integrable derivative
We discuss Meyers-Serrin’s type results for smooth approximations of functions $$b=b(t,x): \mathbb {R}\times \mathbb {R}^n\rightarrow \mathbb ...
-
Chapter and Conference Paper
Introduction to the Notes of the School on Analysis and Geometry in Metric Spaces
The Schools on Analysis and Geometry in Metric Spaces have been meant to present different approaches to research topics in Geometric Measure Theory, Calculus of Variations, Partial Differential Equations, Differ...
-
Article
Open Access2D exfoliated black phosphorus influences healthy and cancer prostate cell behaviors
Nowadays, prostate cancer is the most widespread tumour in worldwide male population. Actually, brachytherapy is the most advanced radiotherapy strategy for the local treatment of prostate cancer. It consists ...
-
Chapter
Lecture 9: Analysis on Metric Spaces and the Dynamic Formulation of Optimal Transport
In this section we introduce basic notions and tools of analysis on metric spaces. We begin by defining the property of absolute continuity for curves γ : [a, b] → X, with (X, d) a metric space, and we prove stru...
-
Protocol
Synthesis of an UV-Curable Divinyl-Fumarate Poly-ε-Caprolactone for Stereolithography Applications
The limited number of commercially available photocrosslinkable resins for stereolithography has often been considered the main limitation of this technique. In this manuscript, a photocrosslinkable poly-ε-cap...
-
Chapter
Lecture 13: Examples of Gradient Flows in PDEs
Å
-
Chapter
Lecture 2: The Kantorovich Problem
We can now introduce Kantorovich’s formulation of the optimal transport problem. It involves the concept of transport plan (also called coupling in the Probability literature) between probability measures. In the...
-
Chapter
Lecture 4: Necessary and Sufficient Optimality Conditions
In this lecture we first extend the duality formula to lower semicontinuous costs (by monotone approximation with bounded and Lipschitz costs), then we consider necessary and sufficient optimality conditions a...
-
Chapter
Lecture 8: The Metric Side of Optimal Transport
In the first seven lectures we have introduced the optimal transport problem, starting from the classical Monge formulation, moving then to the general theory and to some applications. Now our goal is to show ...
-
Chapter
Lecture 1: Preliminary Notions and the Monge Problem
In this chapter we present basic notions and tools that will play a role in the rest of the book and we introduce the first formulation of the optimal transport problem, due to Monge.
-
Chapter
Lecture 18: An Introduction to Otto’s Calculus
In the seminal papers, Otto introduced a formal interpretation of the Wasserstein distance as a Riemannian distance in ...
