Geometry and the onset of rigidity in a disordered network

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture - the number of nodes and the number of bonds between them - this rigidity transition must have a geometric origin. Naive, degree-of-freedom based mechanical analyses such as the Maxwell-Calladine count or the pebble game algorithm overlook such geometric rigidity transitions and offer no means of predicting or characterizing them. We apply tools that were developed for the topological analysis of zero modes and states of self-stress on regular lattices to two-dimensional random spring networks, and demonstrate that the onset of rigidity, at a finite simple shear strain $\gamma^\star$, coincides with the appearance of a single state of self stress, accompanied by a single floppy mode. The process conserves the topologically invariant difference between the number of zero modes and the number of states of self stress, but imparts a finite shear modulus to the spring network. Beyond the critical shear, we confirm previously reported critical scaling of the modulus. In the sub-critical regime, a singular value decomposition of the network's compatibility matrix foreshadows the onset of rigidity by way of a continuously vanishing singular value corresponding to nascent state of self stress.Comment: 6 pages, 6 figue

The slippery slope to State capture: cadre deployment as an enabler of corruption and a contributor to blurred party–State lines

Drawing on both legal and political sources, this article scrutinises the policy of cadre deployment that the African National Congress (ANC), the ruling party in South Africa, has implemented, and continues to apply. The analysis begins by recalling and commenting on the only reported judgment in South African jurisprudence that dealt with the political influencing of municipalities’ exercise of their public power to make appointments, namely, Mlokoti v Amathole District Municipality & another 2009 (6) SA 354 (ECD). What the Mlokoti case has confirmed is that the legal foundation for the exercise of public power is found in the Constitution and its enabling legislation, and not in party political policy, such as the ongoing practice of cadre deployment. In an investigation of cadre deployment, the article then demonstrates that this ANC policy, particularly judging by its stated purpose, is incompatible with the constitutional State and, instead, enables the rise of the shadow State. Unsurprisingly, therefore, political commentators increasingly observe that, apart from the revelations at the Zondo Commission of Inquiry, State capture in South Africa in fact commenced when the ANC assumed political power in pursuit of the National Democratic Revolution. It is argued that the pursuit of a National Democratic Revolution in South Africa is directly at odds with the vision and goals of the 1994 constitutional pact. Convening a bipartisan national convention on philosophical and other approaches to the fight against corruption may offer a solution. Here, a starting point would be to reconsider the country’s anti-corruption strategies to pay proper attention to the ethical causes of this scourge

Multi-modal dictionary learning for image separation with application in art investigation

In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. In this problem, the X-ray signals to be separated have similar morphological characteristics, which brings previous source separation methods to their limits. Our solution is to use photographs taken from the front and back-side of the panel to drive the separation process. The crux of our approach relies on the coupling of the two imaging modalities (photographs and X-rays) using a novel coupled dictionary learning framework able to capture both common and disparate features across the modalities using parsimonious representations; the common component models features shared by the multi-modal images, whereas the innovation component captures modality-specific information. As such, our model enables the formulation of appropriately regularized convex optimization procedures that lead to the accurate separation of the X-rays. Our dictionary learning framework can be tailored both to a single- and a multi-scale framework, with the latter leading to a significant performance improvement. Moreover, to improve further on the visual quality of the separated images, we propose to train coupled dictionaries that ignore certain parts of the painting corresponding to craquelure. Experimentation on synthetic and real data - taken from digital acquisition of the Ghent Altarpiece (1432) - confirms the superiority of our method against the state-of-the-art morphological component analysis technique that uses either fixed or trained dictionaries to perform image separation.Comment: submitted to IEEE Transactions on Images Processin

X-ray image separation via coupled dictionary learning

In support of art investigation, we propose a new source sepa- ration method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation meth- ods, which are based on statistical or structural incoherence of the sources, we use visual images taken from the front- and back-side of the panel to drive the separation process. The coupling of the two imaging modalities is achieved via a new multi-scale dictionary learning method. Experimental results demonstrate that our method succeeds in the discrimination of the sources, while state-of-the-art methods fail to do so.Comment: To be presented at the IEEE International Conference on Image Processing (ICIP), 201

Modelling water-harvesting systems in the arid south of Tunisia using SWAT

In many arid countries, runoff water-harvesting systems support the livelihood of the rural population. Little is known, however, about the effect of these systems on the water balance components of arid watersheds. The objective of this study was to adapt and evaluate the GIS-based watershed model SWAT (Soil Water Assessment Tool) for simulating the main hydrologic processes in arid environments. The model was applied to the 270-km(2) watershed of wadi Koutine in southeast Tunisia, which receives about 200 mm annual rain. The main adjustment for adapting the model to this dry Mediterranean environment was the inclusion of water-harvesting systems, which capture and use surface runoff for crop production in upstream subbasins, and a modification of the crop growth processes. The adjusted version of the model was named SWAT-WH. Model evaluation was performed based on 38 runoff events recorded at the Koutine station between 1973 and 1985. The model predicted that the average annual watershed rainfall of the 12-year evaluation period (209 mm) was split into ET (72%), groundwater recharge (22%) and outflow (6%). The evaluation coefficients for calibration and validation were, respectively, R-2 (coefficient of determination) 0.77 and 0.44; E (Nash-Sutcliffe coefficient) 0.73 and 0.43; and MAE (Mean Absolute Error) 2.6 mm and 3.0 mm, indicating that the model could reproduce the observed events reasonably well. However, the runoff record was dominated by two extreme events, which had a strong effect on the evaluation criteria. Discrepancies remained mainly due to uncertainties in the observed daily rainfall and runoff data. Recommendations for future research include the installation of additional rainfall and runoff gauges with continuous data logging and the collection of more field data to represent the soils and land use. In addition, crop growth and yield monitoring is needed for a proper evaluation of crop production, to allow an economic assessment of the different water uses in the watershed