Minimum and maximum entropy distributions for binary systems with known means and pairwise correlations

Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with these constraints has not been explored. We provide upper and lower bounds on the entropy for the {\em minimum} entropy distribution over arbitrarily large collections of binary units with any fixed set of mean values and pairwise correlations. We also construct specific low-entropy distributions for several relevant cases. Surprisingly, the minimum entropy solution has entropy scaling logarithmically with system size for any set of first- and second-order statistics consistent with arbitrarily large systems. We further demonstrate that some sets of these low-order statistics can only be realized by small systems. Our results show how only small amounts of randomness are needed to mimic low-order statistical properties of highly entropic distributions, and we discuss some applications for engineered and biological information transmission systems.Comment: 34 pages, 7 figure

Understanding soil fertility in organically farmed systems (OF0164)

This is the final report of the Defra project OF0164. Organic farming aims to create an economically and environmentally sustainable agriculture, with the emphasis placed on self-sustaining biological systems rather than external inputs. Building soil fertility is central to this ethos. ‘Soil fertility’ can be considered as a measure of the soil’s ability to sustain satisfactory crop growth, both in the short- and longer-term. It is determined by a set of interactions between the soil’s physical environment, chemical environment and biological activity. The aim of this project was, therefore, to provide a better scientific understanding of soil fertility under organic farming. The approach was to undertake a comprehensive literature review at the start of the project to assess and synthesise available information. Studies were then designed to address specific questions identified from the literature review. The literature review was written during the first year of the project. In addition to submitting written copies to DEFRA, the chapters were posted on a project website: www.adas.co.uk/soilfertility. The Review was based around key questions: • What are the soil organic matter characteristics and the roles of different fractions of the soil organic matter? • Do organically managed soils have higher levels of organic matter (SOM), with a resultant improvement in soil properties? • Is the soil biology different in organically managed soils, in terms of size, biodiversity and activity? • Do organically managed soils have a greater inherent capacity to supply plant nutrients? • What are the nutrient pools and their sizes? • What are the processes and rates of nutrient transfer in relation to nutrient demand? • What are the environmental consequences of organic management? The project also included a large amount of practical work. This necessarily covered a wide range of topics, which were examined in a series of separate studies: • Soil microbiology: a series of measurements focusing on two sites, undertaken by University of Wales Bangor (UWB) • Field campaigns in autumn 1999 and spring/summer 2000: separate field sampling campaigns focusing especially on nutrient pools, undertaken by HDRA, ADAS and IGER • Incubation studies: a series of three separate experiments to look in more detail at N dynamics, managed by ADAS, with support from IGER and HDRA From the literature review and the practical work, the following was concluded: Organic matter is linked intrinsically to soil fertility, because it is important in maintaining good soil physical conditions (e.g. soil structure, aeration and water holding capacity), which contribute to soil fertility. Organic matter also contains most of the soil reserve of N and large proportions of other nutrients such as P and sulphur. Field management data gathered from farmers showed, however, that organic matter returns are not necessarily larger in organic systems. Many non-organically farmed soils receive regular manure applications and the generally higher yielding crops on conventional farms may return larger crop residues. Conversely, many organic fields receive little or no manure, relying on the fertility building ley phase for organic matter input. This observation is important. Management practices within organic and non-organic systems are diverse, and all have consequences for soil fertility. The Executive Summary at the start of the main attached report has additional sections on Soil Structure, Soil Biology, and Nutrient Cycling with some greater detail on comparisons of organic and conventional management and the consequences for soil fertility

Inter-structural Space Effect of Fanya juu and Soil Bund Soil and Water Conservation Structures on Selected Soil Properties: In the Case of Habru District, North Ethiopia

Land degradation is one of the most serious environmental problems in Ethiopia. To halt the problem, large scale soil and water conservation (SWC) practices such as; fanya juu, soil bund and other physical structures were implemented in the different parts of the country including Habru district. However, development of fertility gradient between the two successive SWC structures makes debatable to use the implemented structures in the sustainable manner. The study aimed at evaluating the spatial variability in soil properties between inter-structural-terrace area. Representative Kutaye catchment was deliberately selected based on the availability of fanya juu and soil bund. Then the catchment was sub-divided into two sub-watersheds, cropland treated with fanya juu and cropland treated with soil bund based on the structural dominance. Inter-structure-terrace plots were independently selected and systematically replicated (second, fourth and sixth) between two SWC structures for the purpose of soil sampling. In order to evaluate selected soil property variation, the soil samples were taken following the contour between the two successive structures. Additionally, undisturbed core samples were collected for the bulk density analysis. The samples were analyzed following standard laboratory procedure and parameters like; soil texture, bulk density (Bd), soil reaction (pH), organic carbon (OC), total nitrogen (TotN) available phosphorus (AvP), cation exchange capacity (CEC), exchangeable potassium (K+) and electrical conductivity (EC) were determined. Statistical analysis was performed using SPSS v.20 software. Parameter relative distance was created for allowing comparison; because the distance between the successive SWC structures were highly variable. One-way ANOVA was used; selected soil properties as dependent and relative distance (inter-structure area) as independent variables. Tukey (HSD test) was used for mean separation between relative distance at p < 0.05. The result revealed that soil properties percentage of sand and clay significantly influenced by inter-structure-spaces plots treated with fanya juu at p < 0.05. In both SWC structures, cation exchange capacity (CEC), exchangeable potassium (K+) and bulk density (Bd) were significantly (p < 0.05) affected with inter-structure space. In order to manage variation in some soil properties between the successive SWC inter-structures-space area; optimizing its’ inter-structural terrace space and application of site-specific soil management practices were suggested with appropriate contour ploughing. Keywords: Fanya juu, Inter-structural space, Land degradation, Soil bund, Soil property, Soil and water conservation, Soil and Water Conservation practices DOI: 10.7176/JEES/10-3-01 Publication date:March 31st 202

Effect of Eucalyptus Plantations on Soil Proporties: The Case of Entoto Area, Northern Addis Ababa, Ethiopia

Eucalyptus species are blamed for negatively affecting the soil and inhibiting growth of other plants though it is extensively planted in Ethiopia. This study investigated the effect of Eucalyptus plantations on selected soil physical and chemical properties at Entoto Mountain, in the Northern part of the capital, Addis Ababa. Three land-uses/covers (monoculture Eucalyptus plantations, cropland, and natural forests) with a plot size of 100x100m (1ha) each were used for comparison. Each experimental plot was sub-divided into three sub-plots of 100x33m for soil sampling. Sampling was done to 30cm depth with soil auger. A study of people’s perception on impacts of Eucalyptus was also undertaken to supplement the soil investigation. The soil samples were dried and analyzed while following standard procedures. One way ANOVA test result indicated that Eucalyptus plantations have significantly different effect on soil parameters such as texture (sand 35 %, silt 29 % and clay 27.11 %), soil bulk density (1.43gcm-3), pH level(5.32), total nitrogen (2.36 %), organic carbon (4.07 %), Available potassium (127.23 ppm) and phosphors (8.23 ppm) from the other land-uses/covers. However, the three land uses/covers did not significantly differ from each other in influencing the soil exchangeable Mg, Ca, Na and C/N ratio. The people in the study area perceived that Eucalyptus plantations have negative effects on crop yield and soil moisture; this perception correlated with and supported by the results of this study on soil texture and bulk density where Eucalyptus plantations increased the bulk density of the soil which in turn indicates compactness and low moisture holding capacity. Keywords: Eucalyptus species, Monoculture, Experimental plot DOI: 10.7176/JEES/9-6-05 Publication date:June 30th 2019

Setting an integrated soil monitoring system for Malta : strategy, feasibility and recommendations

Chapter 6Since 2010, MEPA has embarked on a project (which attracted co-funded ERDF assistance) (1) to develop a multi-thematic environment strategy that would lead to updating of its data/ information monitoring capabilities for a number of environmental sectors. The monitoring and continuous evaluation of soil properties is one important sector within this project. Essentially, a multi-criterion assessment of existing available information has been carried out with a view to objectively chart the most appropriate process to carry out a pilot field sampling by testing a pre-agreed set of indicators. The latter were established after taking into consideration all degradation pressures threatening the continued sustainability of this resource. Multi-criterion analysis was carried out by means of a limited set of soil-related datasets published in past editions of Malta’s State of the Environment Report in order to support a number of objectives stipulated within the Project’s ambitious Terms of Reference. Information was derived from earlier attempts to establish a soil information system for Malta. All soil degradation threats, officially determined by the European Commission’s Technical Working Groups, have been taken into consideration within the aforementioned project and its research methodology with a view of establishing a shared GIS environment in accordance with state-of-the-art information dissemination standards.peer-reviewe