Characterizations of the Suzuki tower near polygons

In recent work, we constructed a new near octagon $\mathcal{G}$ from certain involutions of the finite simple group $G_2(4)$ and showed a correspondence between the Suzuki tower of finite simple groups, $L_3(2) < U_3(3) < J_2 < G_2(4) < Suz$, and the tower of near polygons, $\mathrm{H}(2,1) \subset \mathrm{H}(2)^D \subset \mathsf{HJ} \subset \mathcal{G}$. Here we characterize each of these near polygons (except for the first one) as the unique near polygon of the given order and diameter containing an isometrically embedded copy of the previous near polygon of the tower. In particular, our characterization of the Hall-Janko near octagon $\mathsf{HJ}$ is similar to an earlier characterization due to Cohen and Tits who proved that it is the unique regular near octagon with parameters $(2, 4; 0, 3)$, but instead of regularity we assume existence of an isometrically embedded dual split Cayley hexagon, $\mathrm{H}(2)^D$. We also give a complete classification of near hexagons of order $(2, 2)$ and use it to prove the uniqueness result for $\mathrm{H}(2)^D$.Comment: 20 pages; some revisions based on referee reports; added more references; added remarks 1.4 and 1.5; corrected typos; improved the overall expositio

A new near octagon and the Suzuki tower

We construct and study a new near octagon of order $(2,10)$ which has its full automorphism group isomorphic to the group $\mathrm{G}_2(4){:}2$ and which contains $416$ copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the $\mathrm{G}_2(4)$-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is $(2,4)$.Comment: 24 pages, revised version with added remarks and reference

On the valuations of the near polygon ℍn

We characterize the valuations of the near polygon that are induced by classical valuations of the dual polar space DW (2n - 1, 2) into which it is isometrically embeddable. An application to near 2n-gons that contain as a full subgeometry is given

The L₃(4) near octagon

In recent work we constructed two new near octagons, one related to the finite simple group and another one as a sub-near-octagon of the former. In the present paper, we give a direct construction of this sub-near-octagon using a split extension of the group . We derive several geometric properties of this near octagon, and determine its full automorphism group. We also prove that the near octagon is closely related to the second subconstituent of the distance-regular graph on 486 vertices discovered by Soicher (Eur J Combin 14:501-505, 1993)

Multi-scale Spatial Analysis of the Water-Food-Climate Nexus in the Nile Basin using Earth Observation Data

Securing enough water and food for everyone is a great challenge that the humanity faces today. This challenge is aggravated by many external drivers such as population growth, climate variability, and degradation of natural resources. Solutions for weak water and food securities require holistic knowledge of the different involved drivers through a nexus approach that looks at the interlinkages and the multi-directional synergies to be promoted and increased and trade-offs to be reduced or eliminated. In particular, the interlinkages between water, food, and climate, the so-called Water-Food-Climate Nexus (WFC Nexus) is critical for the given challenge in many regions around the world such as the Nile Basin (NB). Studying the WFC Nexus synergies and trade-offs might provide entry points for the required interventions that are potential to induce positive impacts on water and food securities. However, these synergies and trade-offs are not well known due to factors such as the complexity of the interactions which involve many dimensions within and across spatial and temporal domains and unavailability of reliable ground observations that could be used for such analysis. Therefore, multidisciplinary research that encompasses different methodologies and employs datasets with adequate spatial and temporal resolutions is required. The recent advancement in Earth Observation (EO) sensors and data processing algorithms have resulted in the accumulation of big data that are produced in rates faster than their usage in solving real challenges such as the one that is in the focus of the current research. The availability of public-domain datasets for several parameters with spatial and temporal coverage offers an excellent opportunity to discover the WFC Nexus interlinkages. To this end, the main goal of the current research is to employ EO data derived from public-domain datasets and supplemented with other primary and secondary data to identify WFC Nexus synergies and trade-offs in the NB region, taking the agricultural systems in Sudan as a central focus of this assessment. By concentrating mainly on the agricultural systems in Sudan, which are characterized by low performance and efficiency despite the huge potentials for food production, the current research provides a representative case study that could deliver helpful and transferrable knowledge to many areas within and outside the NB region. In the current research, multi-scale analysis of the WFC Nexus synergies and trade-offs was conducted. The assessment involved investigations on a country scale as a strategic level, and on river basin, agricultural scheme (both irrigated and rainfed systems) and field scales as operational levels. On a country scale, a general analysis of the vegetation’s Net Primary Productivity (NPP) and Water and Carbon Use Efficiencies (WUE and CUE, respectively) in different land cover types was carried out. A comparison between the land cover types in Sudan and Ethiopia was conducted to understand and compare the impact of inter-annual climate variability on the NPP, WUE and CUE indicators of these different land cover types under relatively different climate regimes. The results of this analysis indicate low magnitude of the three indicators in the land cover types that are in Sudan compared to their counterparts in Ethiopia. Moreover, the response of these indicators to climate variability varies widely among the land cover types. In addition, land cover types such as forests and woody savannah represent important natural sinks for the atmospheric CO2 that need to be protected. These observations suggest the need for effective policies that enhance crop productivity, especially in Sudan, and at the same time ensure preserving the land cover types that are important for climate change mitigation. On a river basin scale, which represented by the Blue Nile Basin (BNB), precipitation estimation is of utmost importance, as it is not only the main source of water in the basin but also because precipitation variability is controlling food production in the agricultural systems, especially in the rainfed schemes. The high spatial and temporal variation in precipitation within the BNB suggests the need for water storage and water harvesting be promoted and practiced. This would ensure water transfer spatially from wet to dry areas and temporally from wet to dry seasons. As a major staple cereal crop in Sudan, the performance of sorghum production in irrigated and rainfed schemes was investigated on agriculture schemes and field scales. A noticeable low and unstable sorghum yield is detected under both agricultural systems. This low performance represents a serious challenge, not only for food production but also for water availability. The current low performance was found to be controlled by many factors of physical, socio-economic and management nature. As many of these factors are closely linked, effectively addressing some of them might induce positive impacts on the other controlling factors. To conclude, the identified synergies and trade-offs of the WFC Nexus could be used as entry points to increase the efficiency of water use and bridge the crop yield gap. Even simple interventions in the field might induce positive effects to the total crop production of the agricultural schemes and water use efficiency. The increase of water availability in the river basin and improved production in the schemes would enhance the overall water and food security in the country and would minimize the need to convert land covers that are important for climate change mitigation into croplands. This paradigm shift needs to be done through a comprehensive sustainable intensification (SI) framework that is not only aimed at increasing crop yield but also targets promoting a healthy environment, improved livelihood, and a growing economy

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum