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Concept

Kakutani fixed-point theorem

Related publications (30)

Building Duration / El Portico de los Huespedes

Patricia Guaita, Raffael Baur

El Portico de los Huéspedes is a pedagogical, design-research project that tests the possibility of an open-ended architecture, where duration links between past and future. It is a work of architecture as becoming: ‘work’ meaning the structure, rhythms an ...

Association of Collegiate Schools of Architecture2019

Inverse Problems and Optimal Power Flow in Active Distribution Networks

Cong Wang

During the last decade, distribution networks have experienced essential changes driven by the integration of renewable-energy sources, batteries, electric-vehicle charging stations, etc. This results in not only opportunities, but also operational problem ...

EPFL2019

Displacement Convexity in Spatially Coupled Scalar Recursions

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential function. We show, under mild conditions, that the potential fu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Training DNNs with Hybrid Block Floating Point

Babak Falsafi, Martin Jaggi, Tao Lin, Mario Paulo Drumond Lages De Oliveira

The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full-precision floating-point arithmetic t ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Walking, weak first-order transitions, and complex CFTs

Bernardo Zan, Victor Gorbenko

We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both impl ...

Springer Nature2018

Code Generation in Computational Neuroscience: A Review of Tools and Techniques

Pramod Shivaji Kumbhar

Advances in experimental techniques and computational power allowing researchers to gather anatomical and electrophysiological data at unprecedented levels of detail have fostered the development of increasingly complex models in computational neuroscience ...

2018

Dispatching Stochastic Heterogeneous Resources Accounting for Grid and Battery Losses

Mario Paolone, Jean-Yves Le Boudec, Fabrizio Sossan, Lorenzo Enrique Reyes Chamorro, Eleni Stai

We compute an optimal day-ahead dispatch plan for distribution networks with stochastic resources and batteries, while accounting for grid and battery losses. We formulate and solve a scenario-based AC Optimal Power Flow (OPF), which is by construction non ...

2018

Closed-loop electrical neurostimulation: Challenges and opportunities

José del Rocio Millán Ruiz, Inaki Asier Iturrate Gil, Michael Eric Anthony Pereira

Non-invasive and invasive electrical neurostimulation are promising tools to better understand brain function and ultimately treat its malfunction. In current open-loop approaches, a clinician chooses a fixed set of stimulation parameters, informed by obse ...

2018

The size of the sync basin revisited

Philippe René Joseph Jacquod

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated t ...

American Institute of Physics2017

Fixed Points For Bounded Orbits In Hilbert Spaces

Nicolas Monod, Maxime Gheysens

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...

2017