On secret-key agreement as source coding with side information

openThe key reconciliation stage in the secret key generation process may leak partial information to the eavesdropper through the public channel. In this thesis, two metrics, based on rate-distortion and entropy are considered to gauge the secrecy achievable with a channel scheme with side information at the receivers. Two theorems that provide bounds on the performance in this scenario according to different metrics are considered, and the resulting performance in terms of secret key rate is assessed.The key reconciliation stage in the secret key generation process may leak partial information to the eavesdropper through the public channel. In this thesis, two metrics, based on rate-distortion and entropy are considered to gauge the secrecy achievable with a channel scheme with side information at the receivers. Two theorems that provide bounds on the performance in this scenario according to different metrics are considered, and the resulting performance in terms of secret key rate is assessed

A Result about Selectors in non-Archimedean Spaces

A sort of strong completeness property for subsets of a non-Archimedean space is defi{}ned. On the subsets which satisfy this property there exists a Vietoris continuous selector. The set of discrete closed subsets of $\mathbb{R}$ has a continuous selector when it is equipped with the Vietoris topology induced by the Michael line. Some properties of the tree of a non-Archimedean space are used

Integration-by-parts identities and differential equations for parametrised Feynman integrals

Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a different viewpoint on these important tools by working in Feynman-parameter space, and using its projective geometry. Our work is based upon little-known results pre-dating the modern era of loop calculations: we adapt and generalise these results, deriving a very general expression for sets of IBP identities in parameter space, associated with a generic Feynman diagram, and valid to any loop order, relying on the characterisation of Feynman-parameter integrands as projective forms. We validate our method by deriving and solving systems of differential equations for several simple diagrams at one and two loops, providing a unified perspective on a number of existing results.Comment: 22 pages + appendices, 4 figure

Integrated use of sewage sludge and basalt mine waste as soil substitute for environmental restoration

If not managed properly, mining waste can be detrimental to the environment. In addition, sewage treatment plants produce sludge, a biowaste rich in organic matter which is often sent to landfills. The present study evaluated the use of sewage sludge as an amendment for mine waste from a basalt quarry as an alternative to the use of soil from borrow areas during environmental restoration. An ex situ experiment was developed at the Federal University of Rio Grande do Sul – UFRGS. The experimental delineation compared the addition of two sources of organic matter (sewage sludge – SS and cover soil from that same region - CS) to basalt waste rock (BWR) against the sole use of cover soil, which a current restoration technique. The graminoid Avena strigosa (black oats) and soil fertility tests were used as indicators of soil conditions. Amending BWR with SS led to the best physical and chemical conditions and the highest production of dry matter in comparison to the use of CS as amendment or its single use as cover soil. These results show that mixing SS to BWR can be used as a substitute for cover soil during the environmental restoration of basalt quarries, further contributing to the final disposal of these materials

On the existence of kings in continuous tournaments

The classical result of Landau on the existence of kings in finite tournaments (=finite directed complete graphs) is extended to continuous tournaments for which the set X of players is a compact Hausdorff space. The following partial converse is proved as well. Let X be a Tychonoff space which is either zero-dimensional or locally connected or pseudocompact or linearly ordered. If X admits at least one continuous tournament and each continuous tournament on X has a king, then X must be compact. We show that a complete reversal of our theorem is impossible, by giving an example of a dense connected subspace Y of the unit square admitting precisely two continuous tournaments both of which have a king, yet Y is not even analytic (much less compact).Comment: The proof of item (iii) of Theorem 3.5 was rectified. Minor inconsistencies and typos were corrected. One reference was adde