The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation

We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94 (1999) 807-823, Ann. Statist. 28 (2000) 408-428) for the detection of shape parameters of densities on the real line to the case of circular data. It turns out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz semi-group satisfying "circular" causality, that is, not introducing possibly artificial modes with increasing levels of smoothing. Some notable differences between Euclidean and circular scale space theory are highlighted. Based on this, we provide an asymptotic theory to make inference about the persistence of shape features. The resulting circular mode persistence diagram is applied to the analysis of early mechanically-induced differentiation in adult human stem cells from their actin-myosin filament structure. As a consequence, the circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the verification at a controlled error level of the observation reported by Zemel et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation, polarizations of stem cells exhibit preferred directions in three different micro-environments.Comment: Published at http://dx.doi.org/10.3150/15-BEJ722 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Poverty and aspirations failure

We develop a model of internal constraints to show that a greater degree of initial disadvantage results in a higher likelihood of low aspirations and low achievement. Our model and results are supported by evidence from anthropology, sociology and social psychology. Our analysis suggests that internal constraints are a key ingredient in perpetuating poverty traps. We show that a poor person will choose to restrict her cognitive window (the set of other individuals who are her role models) and study the conditions under which a role model could alter her aspirations and achievement. We show how enodgenously chosen cognitive windows interact with the inital distribution of status to determine whether or not a society is connected, and hence the transmission of aspirations across individuals in that society. Our work provides a normative justification for programs that aim at empowering disadvantaged individuals by directly shocking their aspirations

Achieving sustainable irrigation water withdrawals: global impacts on food security and land use

Unsustainable water use challenges the capacity of water resources to ensure food security and continued growth of the economy. Adaptation policies targeting future water security can easily overlook its interaction with other sustainability metrics and unanticipated local responses to the larger-scale policy interventions. Using a global partial equilibrium grid-resolving model SIMPLE-G, and coupling it with the global Water Balance Model, we simulate the consequences of reducing unsustainable irrigation for food security, land use change, and terrestrial carbon. A variety of future (2050) scenarios are considered that interact irrigation productivity with two policy interventions— inter-basin water transfers and international commodity market integration. We find that pursuing sustainable irrigation may erode other development and environmental goals due to higher food prices and cropland expansion. This results in over 800 000 more undernourished people and 0.87 GtC additional emissions. Faster total factor productivity growth in irrigated sectors will encourage more aggressive irrigation water use in the basins where irrigation vulnerability is expected to be reduced by inter-basin water transfer. By allowing for a systematic comparison of these alternative adaptations to future irrigation vulnerability, the global gridded modeling approach offers unique insights into the multiscale nature of the water scarcity challenge

Topology-Aware Focal Loss for 3D Image Segmentation

The efficacy of segmentation algorithms is frequently compromised by topological errors like overlapping regions, disrupted connections, and voids. To tackle this problem, we introduce a novel loss function, namely Topology-Aware Focal Loss (TAFL), that incorporates the conventional Focal Loss with a topological constraint term based on the Wasserstein distance between the ground truth and predicted segmentation masks' persistence diagrams. By enforcing identical topology as the ground truth, the topological constraint can effectively resolve topological errors, while Focal Loss tackles class imbalance. We begin by constructing persistence diagrams from filtered cubical complexes of the ground truth and predicted segmentation masks. We subsequently utilize the Sinkhorn-Knopp algorithm to determine the optimal transport plan between the two persistence diagrams. The resultant transport plan minimizes the cost of transporting mass from one distribution to the other and provides a mapping between the points in the two persistence diagrams. We then compute the Wasserstein distance based on this travel plan to measure the topological dissimilarity between the ground truth and predicted masks. We evaluate our approach by training a 3D U-Net with the MICCAI Brain Tumor Segmentation (BraTS) challenge validation dataset, which requires accurate segmentation of 3D MRI scans that integrate various modalities for the precise identification and tracking of malignant brain tumors. Then, we demonstrate that the quality of segmentation performance is enhanced by regularizing the focal loss through the addition of a topological constraint as a penalty term

A Primer on the Tools and Concepts of Computable Economics

Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society

Poverty and Aspirations Failure

This paper models the role of internal constraints in causing aspirations failure at the individual level. It shows how initial disadvantage increases the likelihood of binding internal constraints and hence aspirations failure, thus suggesting a new behavioral explanation for poverty traps. In examining common approaches to relaxing such internal constraints, it describe how an individual’s endogenous choice of a "cognitive window" (i.e. a set of relevant "similar" individuals)can limit the e¤ectiveness of role models. Further, we consider how the distribution of initial status determines the degree of connectedness in a society and hence the individual perception of these constraints. Our work provides a normative justification for programs that aim to empower participants through a direct positive shock to their aspirations.