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Concept

Affine space

Related publications (28)

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Jan Sickmann Hesthaven, Junming Duan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

Academic Press Inc Elsevier Science2023

A New Analytical Approximation of the Fluid Antenna System Channel

Malek Khammassi

Fluid antenna systems (FAS) are an emerging technology that promises a significant diversity gain even in the smallest spaces. It consists of a freely moving antenna in a small linear space to pick up the strongest received signal. Previous works in the li ...

Ieee-Inst Electrical Electronics Engineers Inc2023

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Eva Bayer Fluckiger, Ting-Yu Lee

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Hebrew Univ Magnes Press2023

A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS

Sergej Monavari

Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...

Amer Mathematical Soc2023

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Haoqi Wang

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Ieee Computer Soc2023

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Finite Littlestone Dimension Implies Finite Information Complexity

Michael Christoph Gastpar, Ido Nachum, Aditya Pradeep

We prove that every online learnable class of functions of Littlestone dimension d admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of ...

2022

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Home, Spatial Familiarity And Routines In Mobility Behaviours

Marc-Edouard Baptiste Grégoire Schultheiss

This research explores the unreasoned influences of locational behaviour – i.e. locational habits – in Activity- Travel-Behaviour (ATB). In particular, the interrelations between Activity Space characteristics and mobility patterns. In a wider research eff ...

2021

Convex Combination of Diffusion Strategies Over Networks

Ali H. Sayed

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalize ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Affine Combination of Diffusion Strategies Over Networks

Ali H. Sayed

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strate ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

Streaming Principal Component Analysis From Incomplete Data

Armin Eftekhari

Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient algorithm for detecti ...

Microtome Publishing2019

Adversarial Analytics

Viet Anh Nguyen

Adversarial learning is an emergent technique that provides better security to machine learning systems by deliberately protecting them against specific vulnerabilities of the learning algorithms. Many adversarial learning problems can be cast equivalently ...

EPFL2019

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Michaël Unser, Daniel Andreas Schmitter

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose eleme ...

2018

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM Publications2018

Related publications (28)

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

MATHICSE2019