Research Articles (Mathematical Sciences)
Permanent URI for this collection
Browse
Recent Submissions
Now showing 1 - 5 of 108
- ItemOn the minimal Hamming weight of a multi-base representation(Elsevier, 2020) Krenn, Daniel; Suppakitpaisarn, Vorapong; Wagner, StephanGiven a finite set of bases b1, b2, ..., br (integers greater than 1), a multi-base representation of an integer n is a sum with summands dbα1 1 b α2 2 ··· bαr r , where the αj are nonnegative integers and the digits d are taken from a fixed finite set. We consider multi-base representations with at least two bases that are multiplicatively independent. Our main result states that the order of magnitude of the minimal Hamming weight of an integer n, i.e., the minimal number of nonzero summands in a representation of n, is log n/(log log n). This is independent of the number of bases, the bases themselves, and the digit set. For the proof, the existing upper bound for prime bases is generalized to multiplicatively independent bases; for the required analysis of the natural greedy algorithm, an auxiliary result in Diophantine approximation is derived. The lower bound follows by a counting argument and alternatively by using communication complexity; thereby improving the existing bounds and closing the gap in the order of magnitude.
- ItemSome combinatorial matrices and their LU-decomposition(De Gruyter, 2020-02) Prodinger, HelmutThree combinatorial matrices were considered and their LU-decompositions were found. This is typically done by (creative) guessing, and the proofs are more or less routine calculations.
- ItemA conceptual map of invasion biology : integrating hypotheses into a consensus network(Wiley, 2020-03-25) Enders, Martin; Havemann, Frank; Ruland, Florian; Bernard-Verdier, Maud; Catford, Jane A.; Gomez-Aparicio, Lorena; Haider, Sylvia; Heger, Tina; Kueffer, Christoph; Kuh, Ingolf; Meyerson, Laura A.; Musseau, Camille; Novoa, Ana; Ricciardi, Anthony; Sagouis, Alban; Schittko, Conrad; Strayer, David L.; Vilà, Montserrat; Essl, Franz; Hulme, Philip E.; Van Kleunen, Mark; Kumschick, Sabrina; Lockwood, Julie L.; Mabey, Abigail L.; McGeoch, Melodie A.; Estibaliz, Palma; Pysek, Petr; Saul, Wolf-Christian; Yannelli, Florencia A.; Jeschke, Jonathan M.Background and aims: Since its emergence in the mid-20th century, invasion biology has matured into a productive research field addressing questions of fundamental and applied importance. Not only has the number of empirical studies increased through time, but also has the number of competing, overlapping and, in some cases, contradictory hypotheses about biological invasions. To make these contradictions and redundancies explicit, and to gain insight into the field’s current theoretical structure, we developed and applied a Delphi approach to create a consensus network of 39 existing invasion hypotheses. Results: The resulting network was analysed with a link-clustering algorithm that revealed five concept clusters (resource availability, biotic interaction, propagule, trait and Darwin’s clusters) representing complementary areas in the theory of invasion biology. The network also displays hypotheses that link two or more clusters, called connecting hypotheses, which are important in determining network structure. The network indicates hypotheses that are logically linked either positively (77 connections of support) or negatively (that is, they contradict each other; 6 connections). Significance: The network visually synthesizes how invasion biology’s predominant hypotheses are conceptually related to each other, and thus, reveals an emergent structure – a conceptual map – that can serve as a navigation tool for scholars, practitioners and students, both inside and outside of the field of invasion biology, and guide the development of a more coherent foundation of theory. Additionally, the outlined approach can be more widely applied to create a conceptual map for the larger fields of ecology and biogeography.
- ItemA wide class of Combinatorial matrices related with Reciprocal Pascal and Super Catalan matrices(2019) Kilic, Emrah; Prodinger, HelmutAbstract. In this paper, we present a number of combinatorial matrices that are generalizations or variants of the super Catalan matrix and the reciprocal Pascal matrix. We present explicit formul for LUdecompositions of all the matrices and their inverses. Alternative derivations using hypergeometric functions are also given.
- ItemMAVSCOT : a fuzzy logic-based HIV diagnostic system with indigenous multi-lingual interfaces for rural Africa(Public Library of Science, 2020-11-06) Oluwagbemi, Olugbenga Oluseun; Oluwagbem, Folakemi Etseoghena; Jatto, Abdulwahab; Hui, Cang; Department of Mathematical SciencesHIV still constitutes a major public health problem in Africa, where the highest incidence and prevalence of the disease can be found in many rural areas, with multiple indigenous languages being used for communication by locals. In many rural areas of the KwaZulu-Natal (KZN) in South Africa, for instance, the most widely used languages include Zulu and Xhosa, with only limited comprehension in English and Afrikaans. Health care practitioners for HIV diagnosis and treatment, often, cannot communicate efficiently with their indigenous ethnic patients. An informatics tool is urgently needed to facilitate these health care professionals for better communication with their patients during HIV diagnosis. Here, we apply fuzzy logic and speech technology and develop a fuzzy logic HIV diagnostic system with indigenous multi-lingual interfaces, named Multi-linguAl HIV indigenouS fuzzy logiC-based diagnOstic sysTem (MAVSCOT). This HIV multilingual informatics software can facilitate the diagnosis in underprivileged rural African communities. We provide examples on how MAVSCOT can be applied towards HIV diagnosis by using existing data from the literature. Compared to other similar tools, MAVSCOT can perform better due to its implementation of the fuzzy logic. We hope MAVSCOT would help health care practitioners working in indigenous communities of many African countries, to efficiently diagnose HIV and ultimately control its transmission.