Search Results for « HSW distance »

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that affine distance gives us a new concept of distance in Robertson-Walker space-times, according to Hubble law.

Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is the average of transportation cost between one-dimensional representations (projections) of original measures that are obtained by Radon Transform (RT). Despite its efficiency in the number of supports, estimating the sliced Wasserstein requires a relatively large number of projections in high-dimensional settings. Therefore, for applications where the number of supports is relatively small compared with the dimension, e.g., several deep learning applications where the mini-batch approaches are utilized, the complexities from matrix multiplication of Radon Transform become the main computational bottleneck. To address this issue, we propose to derive projections by linearly and randomly combining a smaller number of projections which are named bottleneck projections. We explain the usage of these projections by introducing Hierarchical Radon Transform (HRT) which is constructed by applying Radon Transform variants recursively. We then formulate the approach into a new metric between measures, named Hierarchical Sliced Wasserstein (HSW) distance. By proving the injectivity of HRT, we derive the metricity of HSW. Moreover, we investigate the theoretical properties of HSW including its connection to SW variants and its computational and sample complexities. Finally, we compare the computational cost and generative quality of HSW with the conventional SW on the task of deep generative modeling using various benchmark datasets including CIFAR10, CelebA, and Tiny ImageNet.

It is well known that the quadratic Wasserstein distance $W_2 (\mathord{\boldsymbol{\cdot}}, \mathord{\boldsymbol{\cdot}})$ is formally equivalent, for infinitesimally small perturbations, to some weighted $H^{-1}$ homogeneous Sobolev norm. In this article I show that this equivalence can be integrated to get non-asymptotic comparison results between these distances. Then I give an application of these results to prove that the $W_2$ distance exhibits some localisation phenomenon: if $μ$ and $ν$ are measures on $\mathbf{R}^n$ and $\varphi \colon \mathbf{R}^n \to \mathbf{R}_+$ is some bump function with compact support, then under mild hypotheses, you can bound above the Wasserstein distance between $\varphi \cdot μ$ and $\varphi \cdot ν$ by an explicit multiple of $W_2 (μ, ν)$.

Though the Suzhou government has provided household solid waste (HSW) source separation since 2000, the program remains largely ineffective. Between January and March 2014, the authors conducted an intercept survey in five different community groups in Suzhou, and 505 valid surveys were completed. Based on the survey, the authors used an ordered probit regression to study residents’ HSW source separation activities for both Suzhou and for the five community groups. Results showed that 43% of the respondents in Suzhou thought they knew how to source separate HSW, and 29% of them have source separated HSW accurately. The results also found that the current HSW source separation pilot program in Suzhou is valid, as HSW source separation facilities and residents’ separation behavior both became better and better along with the program implementation. The main determinants of residents’ HSW source separation behavior are residents’ age, HSW source separation facilities and government preferential policies. The accessibility to waste management service is particularly important. Attitudes and willingness do not have significant impacts on residents’ HSW source separation behavior.

Certain plant growth promoting bacteria can protect associated plants from harmful effects of salinity. We report the isolation and characterization of 1-aminocyclopropane-1-carboxylic acid (ACC) deaminase bacterium Bacillus licheniformis HSW-16 capable of ameliorating salt (NaCl) stress in wheat plants. The bacterium was isolated from water of Sambhar salt lake, Rajasthan, India. The presence of ACC deaminase activity was confirmed by enzyme assay and analysis of AcdS gene, a structural gene for ACC deaminase. Inoculation of B. licheniformis HSW-16 protected wheat plants from growth inhibition caused by NaCl and increased plant growth (6-38%) in terms of root length, shoot length, fresh weight, and dry weight. Ionic analysis of plant samples showed that the bacterial inoculation decreased accumulation of Na+ content (51%), and increased K+ (68%), and Ca2+ content (32%) in plants at different concentration of NaCl. It suggested that bacterial inoculation protected plants from the effect of NaCl by decreasing level of Na+ in plants. Production of exopolysaccharide by the B. licheniformis HSW-16 can also protect from Na+ by binding this ion. Moreover, application of test isolate resulted in an increase in certain osmolytes such as total soluble sugar, total protein content and a decrease in malondialdehyde content, illustrating their role in the protection of plants. The ability of B. licheniformis HSW-16 to colonize plant root surface was examined by staining the bacterium with acridine orange followed by fluorescence microscopy and polymerase chain reaction (PCR)-based DNA fingerprinting analysis. These results suggested that B. licheniformis HSW-16 could be used as a bioinoculant to improve the productivity of plants growing under salt stress.

The commuting variety of matrices over a given field is a well-studied object in linear algebra and algebraic geometry. As a set, it consists of all pairs of square matrices with entries in that field that commute with one another. In this paper we generalise the commuting variety by using the commuting distance of matrices. We show that over an algebraically closed field, each of our sets does indeed form a variety. We compute the dimension of the distance-$2$ commuting variety and characterize its irreducible components. We also work over other fields, showing that the distance-$2$ commuting set is a variety but that the higher distance commuting sets may or may not be varieties, depending on the field and on the size of the matrices.

This study analyses responses to an open-ended survey question and directs attention to discourse around research knowledge utilisation in health social work (HSW) in Sweden. The central finding is the projection of three subject positions: a research-oriented HSW, a research-distanced HSW and a patient-centred HSW. A research-oriented HSW is analysed as an ideal that is not realised. By analysing depictions of actions not being taken to increase research knowledge utilisation – questioning the trustworthiness of research, as well as HSWs ability to use it – the go-to subject position becomes a research-distanced HSW. A third subject position emerges creating a dichotomy between daily work and research knowledge, a patient-centred HSW. Very few respondents challenged this dichotomy, describing actions that had been taken to enhance research knowledge utilisation, underpinning the potential gain to the professional identity as well as to the benefit of patients.

Given $p$ node pairs in an $n$-node graph, a distance preserver is a sparse subgraph that agrees with the original graph on all of the given pairwise distances. We prove the following bounds on the number of edges needed for a distance preserver: - Any $p$ node pairs in a directed weighted graph have a distance preserver on $O(n + n^{2/3} p)$ edges. - Any $p = Ω\left(\frac{n^2}{rs(n)}\right)$ node pairs in an undirected unweighted graph have a distance preserver on $O(p)$ edges, where $rs(n)$ is the Ruzsa-Szemerédi function from combinatorial graph theory. - As a lower bound, there are examples where one needs $ω(σ^2)$ edges to preserve all pairwise distances within a subset of $σ= o(n^{2/3})$ nodes in an undirected weighted graph. If we additionally require that the graph is unweighted, then the range of this lower bound falls slightly to $σ\le n^{2/3 - o(1)}$.