57 research outputs found
Automatic 3D modeling by combining SBFEM and transfinite element shape functions
The scaled boundary finite element method (SBFEM) has recently been employed
as an efficient means to model three-dimensional structures, in particular when
the geometry is provided as a voxel-based image. To this end, an octree
decomposition of the computational domain is deployed and each cubic cell is
treated as an SBFEM subdomain. The surfaces of each subdomain are discretized
in the finite element sense. We improve on this idea by combining the
semi-analytical concept of the SBFEM with certain transition elements on the
subdomains' surfaces. Thus, we avoid the triangulation of surfaces employed in
previous works and consequently reduce the number of surface elements and
degrees of freedom. In addition, these discretizations allow coupling elements
of arbitrary order such that local p-refinement can be achieved
straightforwardly
Studies on nematodes of dune sands
Although nematodes abound in soils little has been discovered about their role in the biology of soils. Dune sands were selected for this study since if this "relatively simple" habitat could be understood it would provide a starting point to an understanding of the vastly more complex biology of agricultural soils. It was thought that the nematode fauna in sand dunes would be depauperate, that the environmental conditions might be simple enough to be understandable, if necessary duplicable, and that their variation might explain variation in the nematode fauna.
In an attempt to achieve some understanding of the nematode fauna the following points were considered:-
1. Taxonomic characterisation of the nematode fauna to species level. Although de Man (1880, 1884) described several species of nematodes from the coastal dunes of the Netherlands, the nematode fauna of this environment is poorly known. Clark (1960, 1963) and Killick (1964) have described new species from New Zealand dunes.
2. Examination of the population changes of the species in relation to season, depth and other environmental factors. The majority of population studies have concerned economically important species in agricultural soils.
3. Elucidation of trophic relationships. The trophic relationships of many nematodes are unknown or unsubstantiated. Goodey (1963) gives the essence of the knowledge of the bionomics of each genus.
4. General examination of the biology of "free living" nematodes, aided by comparison between conditions in vivo and in vitro. Because of the supposed simplicity of the biota, physics and chemistry of dune sands comparison of results obtained from cultures with those obtained in the field seem more acceptable than if species from a complex agricultural soil were used
Undecidability in number theory
These lecture notes cover classical undecidability results in number theory,
Hilbert's 10th problem and recent developments around it, also for rings other
than the integers. It also contains a sketch of the authors result that the
integers are universally definable in the rationals.Comment: 48 pages. arXiv admin note: text overlap with arXiv:1011.342
Relating different Polynomial-LWE problems
In this paper we focus on Polynomial Learning with Errors (PLWE). This problem is parametrized by a polynomial and we are interested in relating the hardness of the and problems for different polynomials and . More precisely, our main result shows that for a fixed monic polynomial , is at least as hard as , in both search and decision variants, for any monic polynomial . As a consequence, is harder than for a minimal polynomial of an algebraic integer from the cyclotomic field with specific properties. Moreover, we prove in decision variant that in the case of power-of-2 polynomials, is at least as hard as for a minimal polynomial of algebraic integers from the th cyclotomic field with weaker specifications than those from the previous result
A Subfield Lattice Attack on Overstretched NTRU Assumptions:Cryptanalysis of Some FHE and Graded Encoding Schemes
International audienc
On the Hardness of the Computational Ring-LWR Problem and its Applications
In this paper, we propose a new assumption, the Computational Learning With Rounding over rings, which is inspired by the computational Diffie-Hellman problem. Assuming the hardness of ring-LWE, we prove this problem is hard when the secret is small, uniform and invertible.
From a theoretical point of view, we give examples of a key exchange scheme and a public key encryption scheme, and prove the worst-case
hardness for both schemes with the help of a random oracle.
Our result improves both speed, as a result of not requiring Gaussian secret or noise, and size, as a result of rounding. In practice, our result suggests that decisional ring-LWR based schemes, such as Saber, Round2 and Lizard, which are among the most efficient solutions to the NIST post-quantum cryptography competition,stem from a provable secure design.
There are no hardness results on the decisional ring-LWR with polynomial modulus prior to this work, to the best of our knowledge
The European press and the question of Norwegian independence in 1814
The French Revolution, with its alternative legitimating principle of popular sovereignty, challenged and undermined the European old regimeâs foundation of dynastic-absolutist divine legitimacy. The constitutional fathers of Norway were inspired by the republican revolutions in France and America, and when the country was ceded from Denmark to Sweden according to the Treaty of Kiel in January 1814, they sought to secure Norwayâs independence through applying popular sovereignty as a legitimating principle. This qualitative study seeks to contribute to new insights in and understanding of how the dramatic political events of 1814 in Norway were perceived outside Scandinavia by examining historical newspapers from England, France, Prussia, Austria Russia, Saxony, Bavaria and Switzerland. Using discourse analytical tools this study attempts to shed light upon how the question of Norwegian sovereignty were perceived in 1814, whether Norwegian independence was conceptually possible in the eyes of people outside Scandinavia, and what the thinking about the possibility of a new independent state in 1814 looked like. The study establishes that there are to distinctly different discursive representations, or perceptions of reality, when it comes to the question of Norwegian independence in 1814: The Popular Sovereignty Representation and The Dynastic Sovereignty Representation. Furthermore, the study demonstrates that there is a palette of different varieties within these two main representations
Efficient modeling of 3D geometries using octreeâmeshes combined with SBFEM and transfinite elements
Three-Dimensional Image-Based Modeling by Combining SBFEM and Transfinite Element Shape Functions
Efficient modeling of 3D geometries using octree-meshes combined with SBFEM and transfinite elements
- âŠ