14 research outputs found
Hardness of linearly ordered 4-colouring of 3-colourable 3-uniform hypergraphs
A linearly ordered (LO) -colouring of a hypergraph is a colouring of its vertices with colours such that each edge contains a unique maximal colour. Deciding whether an input hypergraph admits LO -colouring with a fixed number of colours is NP-complete (and in the special case of graphs, LO colouring coincides with the usual graph colouring). Here, we investigate the complexity of approximating the `linearly ordered chromatic number' of a hypergraph. We prove that the following promise problem is NP-complete: Given a 3-uniform hypergraph, distinguish between the case that it is LO -colourable, and the case that it is not even LO -colourable. We prove this result by a combination of algebraic, topological, and combinatorial methods, building on and extending a topological approach for studying approximate graph colouring introduced by Krokhin, Opr\v{s}al, Wrochna, and \v{Z}ivn\'y (2023)
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
PASSIVE THERMAL CONTROL SYSTEMS FOR SPACE INSTRUMENTS MAKING – SCIENTIFIC BACKGROUND, QUALIFICATION, EXPLOITATION IN SPACE
Passive thermal control systems (TCS) are one of obligatory system of any space
mission, used as on large spacecraft and microsatellites Supporting of required temperature
range for space instruments is supported by rational design of TCS with optimal choice of
main thermal control components such as multilayer insulation, optical coatings, heat
conductive elements, heat insulation supports, thermal conductive gaskets, radiating surfaces
and other elements. New ideology in TCS design has come after appearance of new element
– heat pipe(s) which is a super heat conductive thermal conductor with constant or variable
thermal properties
New Directions for Contact Integrators
Contact integrators are a family of geometric numerical schemes which
guarantee the conservation of the contact structure. In this work we review the
construction of both the variational and Hamiltonian versions of these methods.
We illustrate some of the advantages of geometric integration in the
dissipative setting by focusing on models inspired by recent studies in
celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282
Quantum Gravity: From continuous to discrete
The consistent definition of a quantum gravity theory has to overcome several obstacles. Here we take important steps in the development of three approaches to quantum gravity. By utilising matter fields as mediators from ultraviolet to infrared energies, we study a coupling between asymptotically-safe quantum gravity and the hypercharge. The resulting symmetry enhancement allows for a possible ultraviolet completion of the joined system, predicting the infrared value of the hypercharge within estimated systematic errors, thereby increasing the predictive power of the model. Additionally, previous studies suggest that K ̈ahler-Dirac fermions on Euclidean dynamical triangulations do not spontaneously break chiral symmetry. Here we develop computational tools accounting for the back reaction of fermions on the lattice. If extended studies support the evidence that chiral symmetry remains intact, then the model passes an important observational viability test. Lastly, we provide procedures allowing for the extraction of geometrical and topological properties from a causal set. Specifically, we build a spatial distance function which can be used to construct dimensional estimators for the Hausdorff and spectral dimension. In agreement with other quantum-gravity approaches, the latter exhibits a form of dimensional reduction at high energies on account of the inherent non-localness of causal sets