Whitney tower concordance of classical links

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the entire preprint "Geometric Filtrations of Classical Link Concordance" (arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint "Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2 [math.GT]

Hybrid computer Monte-Carlo techniques

Hybrid analog-digital computer systems for Monte Carlo method application

Reclaiming human machine nature

Extending and modifying his domain of life by artifact production is one of the main characteristics of humankind. From the first hominid, who used a wood stick or a stone for extending his upper limbs and augmenting his gesture strength, to current systems engineers who used technologies for augmenting human cognition, perception and action, extending human body capabilities remains a big issue. From more than fifty years cybernetics, computer and cognitive sciences have imposed only one reductionist model of human machine systems: cognitive systems. Inspired by philosophy, behaviorist psychology and the information treatment metaphor, the cognitive system paradigm requires a function view and a functional analysis in human systems design process. According that design approach, human have been reduced to his metaphysical and functional properties in a new dualism. Human body requirements have been left to physical ergonomics or "physiology". With multidisciplinary convergence, the issues of "human-machine" systems and "human artifacts" evolve. The loss of biological and social boundaries between human organisms and interactive and informational physical artifact questions the current engineering methods and ergonomic design of cognitive systems. New developpment of human machine systems for intensive care, human space activities or bio-engineering sytems requires grounding human systems design on a renewed epistemological framework for future human systems model and evidence based "bio-engineering". In that context, reclaiming human factors, augmented human and human machine nature is a necessityComment: Published in HCI International 2014, Heraklion : Greece (2014

A super-analogue of Kontsevich's theorem on graph homology

In this paper we will prove a super-analogue of a well-known result by Kontsevich which states that the homology of a certain complex which is generated by isomorphism classes of oriented graphs can be calculated as the Lie algebra homology of an infinite-dimensional Lie algebra of symplectic vector fields.Comment: 15 page

Natural climate solutions

Our thanks for inputs by L. Almond, A. Baccini, A. Bowman, S. CookPatton, J. Evans, K. Holl, R. Lalasz, A. Nassikas, M. Spalding, M. Wolosin, and expert elicitation respondents. Our thanks for datasets developed by the Hansen lab and the NESCent grasslands working group (C. Lehmann, D. Griffith, T. M. Anderson, D. J. Beerling, W. Bond, E. Denton, E. Edwards, E. Forrestel, D. Fox, W. Hoffmann, R. Hyde, T. Kluyver, L. Mucina, B. Passey, S. Pau, J. Ratnam, N. Salamin, B. Santini, K. Simpson, M. Smith, B. Spriggs, C. Still, C. Strömberg, and C. P. Osborne). This study was made possible by funding from the Doris Duke Charitable Foundation. Woodbury was supported in part by USDA-NIFA Project 2011-67003-30205 Data deposition: A global spatial dataset of reforestation opportunities has been deposited on Zenodo (https://zenodo.org/record/883444). This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710465114/-/DCSupplemental.Peer reviewedPublisher PD