Directed spatial permutations on asymmetric tori

It is time-consuming and expensive to take high-quality or high-resolution electron microscopy (EM) and fluorescence microscopy (FM) images. Taking these images could be even invasive to samples and may damage certain subtleties in the samples after long or intense exposures, often necessary for achieving high-quality or high-resolution in the first place. Advances in deep learning enable us to perform various types of microscopy image-to-image transformation tasks such as image denoising, super-resolution, and segmentation that computationally produce high-quality images from the physically acquired low-quality ones. When training image-to-image transformation models on pairs of experimentally acquired microscopy images, prior models suffer from performance loss due to their inability to capture inter-image dependencies and common features shared among images. Existing methods that take advantage of shared features in image classification tasks cannot be properly applied to image transformation tasks because they fail to preserve the equivariance property under spatial permutations, something essential in image-to-image transformation. To address these limitations, we propose the augmented equivariant attention networks (AEANets) with better capability to capture inter-image dependencies, while preserving the equivariance property. The proposed AEANets captures inter-image dependencies and shared features via two augmentations on the attention mechanism, which are the shared references and the batch-aware attention during training. We theoretically derive the equivariance property of the proposed augmented attention model and experimentally demonstrate its consistent superiority in both quantitative and visual results over the baseline methods.

We consider a family of distributions on spatial random partitions that provide a coupling between different models of interest: the ideal Bose gas; the zero-range process; particle clustering; and spatial permutations. These distributions are invariant for a "chain of Chinese restaurants" stochastic process. We obtain results for the distribution of the size of the largest component.

Interesting qualitative consequences can arise from the quantum mechanical identity among strongly correlated particles that carry spin. This is demonstrated for properties connected with the low energy excitations in molecular and electronic systems. Spatial permutations among the identical particles are used as the key features.The particular behaviour of rotational tunneling molecules or molecular parts under the influence of dissipation are discussed together with the consequences arising for conversion transitions. The relationship between the thermal shifting of the tunneling line and the conversion rate at low and at elevated temperatures is explicated. The valuable information, that can be extracted from the conversion behaviour after isotopical substitution, is explained in detail. At low temperatures qualitative changes are predicted for the conversion rate by deuteration. Weakly hindered rotors show, also experimentally, drastic isotopic effects.The second part is devoted to finite systems of strongly interacting electrons that appear in semi‐conductor nano‐structures. The lowest excitation energies are strongly influenced by the interaction. They can be understood and determined starting from the limit of crystallized electrons by introducing localized many particle ‘pocket states’. The energy levels show multiplet structure, in agreement with numerical results. The total electron spin, associated with the low energy excitations, is crucially important for the nonlinear transport properties through quantum dots. It allows for instance to explain the appearance of negative differential conductances.

Radical rest and recreation and their spatial permutations

Green infrastructure (GI) is increasingly being used in urban areas to supplement the function of conventional drainage infrastructure. GI relies on the “natural” hydrological processes of infiltration and evapotranspiration to treat surface runoff close to where it is generated, alleviating loading on the conventional infrastructure systems. This research addresses growing interest in identification and quantification of uncertainties with distributed, infiltration-based stormwater control measures, retrofitted on private and public properties and in right-of-ways in existing urban areas. We identify four major sources of variability and uncertainty in cumulative performance of systems that rely on extensive implementation of distributed GI: non-additive effects of individual best management practices (BMPs) at the catchment scale; the spatial configuration of fine-scale land use and land cover changes; performance changes due to climate change; and noise levels present in urban flow monitoring programs. Using a three-dimensional coupled surface-subsurface hydrological model of a residential sewershed in Washington DC, we find that prolonged, large-magnitude rain events affect various spatial configurations of GI networks differently. Runoff peaks and volumes can both be influenced by the spatial permutations of infiltration opportunities in addition to the absolute magnitude of treated area. However, the magnitude of the last source of uncertainty—noise levels in urban flow monitoring programs—may be larger than sources of variability associated with spatial changes in fine-scale land use and land cover. Changes associated with climate change-- more frequent and larger rainfall events-- will likely intensify performance differences between spatial configurations of GI but also increase noise levels in urban flow monitoring programs.

Grouping has been commonly used in deep metric learning for computing diverse features. To improve the performance and interpretability, we propose an improved and interpretable grouping method to be integrated flexibly with any metric learning framework. Specifically, our method is based on the attention mechanism with a learnable query for each group. The query is fully trainable and can capture group-specific information when combined with the diversity loss. An appealing property of our method is that it naturally lends itself interpretability. The attention scores between the learnable query and each spatial position can be interpreted as the importance of that position. We formally show that our proposed grouping method is invariant to spatial permutations of features. When used as a module in convolutional neural networks, our method leads to translational invariance. We conduct comprehensive experiments to evaluate our method. Our quantitative results indicate that the proposed method outperforms prior methods consistently and significantly across different datasets, evaluation metrics, base models, and loss functions. For the first time to the best of our knowledge, our interpretation results clearly demonstrate that the proposed method enables the learning of diverse and stable semantic features across groups.

South Africa’s transition to democracy coincided and interlinked with massive global shifts, including the fall of communism and the rise of western capitalist triumphalism. Late capitalism operates through paradoxical global-local dynamics, both universalising identities and expanding local particularities. The erstwhile hegemonic identity of apartheid, ‘the Afrikaner’, was a product of Afrikaner nationalism. Like other identities, it was spatially organised, with Afrikaner nationalism projecting its imagined community (‘the volk’) onto a national territory (‘white South Africa’). The study traces the neo-nationalist spatial permutations of ‘the Afrikaner’, following Massey’s (2005) understanding of space as (1) political, (2) produced through interrelations ranging from the global to micro intimacies, (3) potentially a sphere for heterogeneous co-existence, and (4) continuously created. Research is presented that shows a neo-nationalist revival of ethnic privileges in a defensive version of Hall’s ‘return to the local’ (1997a). Although Afrikaner nationalism’s territorial claims to a nation state were defeated, neo-nationalist remnants reclaim a purchase on white Afrikaans identities, albeit in shrunken territories. This phenomenon is, here, called Afrikaner enclave nationalism. Drawing on a global revamping of race as a category of social subjugation, a strategy is deployed that is here called ‘inward migration’. These dynamics produce a privatised micro-apartheid in sites ranging from homes, to commercial and religious enterprises, to suburbs. Virtual white spaces in the form of Afrikaans media products serve as extensions of these whitened locales. The lynchpin holding it all together is the heteronormative, middle-class family, with consumption the primary mode of the generation of its white comfort zones.

We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and it should be exact to lowest order in the scattering length of the particle interactions. We find that the change in the critical temperature is proportional to a rho^{1/3} with constant c = -2.33; this contradicts the current consensus among physicists.

The model of spatial permutations is related to the Feynman-Kac representation of the Bose gas. The transition to infinite cycles corresponds to Bose-Einstein condensation. We review the general setting and some results, and we derive a multi-body interaction between permutation jumps, that is due to the original interactions between quantum particles.

We study random spatial permutations on Z^3 where each jump x -> \pi(x) is penalized by a factor exp(-T ||x-\pi(x)||^2). The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to Poisson-Dirichlet. This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported by numerical data.

We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a Poisson-Dirichlet law.

A phylloid ground state of reverted floral specimens of Psophocarpus tetragonolobus (L.) DC (Fabaceae): Cancelled floral meristem and continued floral organ identity

We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.

South Africa’s transition to democracy coincided and interlinked with massive global shifts, including the fall of communism and the rise of western capitalist triumphalism. Late capitalism operates through paradoxical global-local dynamics, both universalising identities and expanding local particularities. The erstwhile hegemonic identity of apartheid, ‘the Afrikaner’, was a product of Afrikaner nationalism. Like other identities, it was spatially organised, with Afrikaner nationalism projecting its imagined community (‘the volk’) onto a national territory (‘white South Africa’). The study traces the neo-nationalist spatial permutations of ‘the Afrikaner’, following Massey’s (2005) understanding of space as (1) political, (2) produced through interrelations ranging from the global to micro intimacies, (3) potentially a sphere for heterogeneous co-existence, and (4) continuously created. Research is presented that shows a neo-nationalist revival of ethnic privileges in a defensive version of Hall’s ‘return to the local’ (1997a). Although Afrikaner nationalism’s territorial claims to a nation state were defeated, neo-nationalist remnants reclaim a purchase on white Afrikaans identities, albeit in shrunken territories. This phenomenon is, here, called Afrikaner enclave nationalism. Drawing on a global revamping of race as a category of social subjugation, a strategy is deployed that is here called ‘inward migration’. These dynamics produce a privatised micro-apartheid in sites ranging from homes, to commercial and religious enterprises, to suburbs. Virtual white spaces in the form of Afrikaans media products serve as extensions of these whitened locales. The lynchpin holding it all together is the heteronormative, middle-class family, with consumption the primary mode of the generation of its white comfort zones.

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter $\alpha$. For weak interactions, the shift in critical temperature is expected to be linear in $\alpha$ with constant of linearity $c$. Using Markov chain Monte Carlo methods and finite-size scaling, we find $c = 0.618 \pm 0.086$. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations.