SciRE-Solver: Efficient Sampling of Diffusion Probabilistic Models by Score-integrand Solver with Recursive Derivative Estimation

Diffusion probabilistic models (DPMs) are a powerful class of generative models known for their ability to generate high-fidelity image samples. A major challenge in the implementation of DPMs is the slow sampling process. In this work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a score-based exact solution paradigm for the diffusion ODEs corresponding to the sampling process of DPMs, which introduces a new perspective on developing numerical algorithms for solving diffusion ODEs. To achieve an efficient sampler, we propose a recursive derivative estimation (RDE) method to reduce the estimation error. With our proposed solution paradigm and RDE method, we propose the score-integrand solver with the convergence order guarantee as efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver attains state-of-the-art (SOTA) sampling performance with a limited number of score function evaluations (NFE) on both discrete-time and continuous-time DPMs in comparison to existing training-free sampling algorithms. Such as, we achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for continuous-time DPMs on CIFAR10, respectively. Different from other samplers, SciRE-Solver has the promising potential to surpass the FIDs achieved in the original papers of some pre-trained models with a small NFEs. For example, we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of $3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of $2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA 64$\times$64

Spatial Propagation in an Epidemic Model with Nonlocal Diffusion: the Influences of Initial Data and Dispersals

This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here the initial data stand for the spatial concentrations of infectious agent and infectious human population when the epidemic breaks out and the nonlocal dispersals mean their diffusion strategies. Two types of initial data decaying to zero exponentially or faster are considered. For the first type, we show that the spreading speeds are two constants whose signs change with the number of elements in some set. Moreover, we find an interesting phenomenon: the asymmetry of nonlocal dispersals can influence the propagating directions of solutions and the stability of steady states. For the second type, we show that the spreading speed is decreasing with respect to the exponentially decaying rate of initial data, and further, its minimum value coincides with the spreading speed for the first type. In addition, we give some results about the nonexistence of traveling wave solutions and the monotone property of solutions. Finally, some applications are presented to illustrate the theoretical results

Spatial Propagation in Nonlocal Dispersal Fisher-KPP Equations

In this paper we focus on three problems about the spreading speeds of nonlocal dispersal Fisher-KPP equations. First, we study the signs of spreading speeds and find that they are determined by the asymmetry level of the nonlocal dispersal and $f'(0)$, where $f$ is the reaction function. This indicates that asymmetric dispersal can influence the spatial dynamics in three aspects: it can determine the spatial propagation directions of solutions, influence the stability of equilibrium states, and affect the monotone property of solutions. Second, we give an improved proof of the spreading speed result by constructing new lower solutions and using the new "forward-backward spreading" method. Third, we establish the relationship between spreading speed and exponentially decaying initial data. Our result demonstrates that when dispersal is symmetric, spreading speed decreases along with the increase of the exponentially decaying rate. In addition, the results on the signs of spreading speeds are applied to two special cases where we present more details of the influence of asymmetric dispersal

Length–weight relationship and condition factor of giant tiger shrimp, Penaeus monodon (Fabricius, 1798) from four breeding families

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Background: Length–weight relationships and condition factors of giant tiger shrimp Penaeus monodon (Fabricius, 1798) from four breeding families (family S: South China seas family, family A: African family, family SA: ♂ South China seas family × ♀ Africa family, family AS: ♂ Africa family × ♀ South China seas family) were evaluated in this study. Findings and conclusion: Length–weight relationships can be expressed as W = 0.0239BL2.789 (R2 = 0.8977) in family S, W = 0.0206BL2.9107 (R2 = 0.9107) in family A, W = 0.0211BL2.831 (R2 = 0.8869) in family SA, and W = 0.0249BL2.781 (R2 = 0.9159) in family AS. The growth of P. monodon from four breeding families follows a negative allometric trend. Fulton’s body condition factor (K) was not significantly different in males, while in females, the highest K (3.07) was observed in family AS, and the lowest K was found in family A (1.88). Results from the present study indicate that the cross group family AS (♂ Africa family × ♀ South China seas family) has obvious heterosis in females. This may suggest that the direction of further breeding of P. monodon, should be conducted by using Africa family as male parent, and South China seas family as female parent. Results from the present study will provide valuable information on selective breeding in P. monodon. Methodology used in the present study can also be applied in other similar species

Complete mitochondrial genome of Metapenaeus affinis (H. Milne Edwards, 1837) and Metapenaeus ensis (De Haan, 1844)

Penaeid shrimp is one of the marine germplasm resources in tropical and subtropical regions. To better understand shrimp germplasm resources and develop cultured shrimp species, the complete mitochondrial genome of Metapenaeus affinis and Metapenaeus ensis was assembled. The length of M. affinis and M. ensis mitochondrial sequences is 15,957 and 15,943, respectively. Both mitochondrial sequences contain 13 protein coding, 22 tRNA, and two rRNA genes. The GC content of the genome was 34.23% and 34.12% in M. affinis and M. ensis, respectively. Phylogenetic analysis indicated that the M. affinis and M. ensis are closely related, and assigned to a branch of Metapenaeus. We assembled and published the mitochondrial genome sequences of these two species, which will provide important information for the research and utilization of shrimp germplasm resources

Dynamic variations in the peripheral blood lymphocyte subgroups of patients with 2009 pandemic H1N1 swine-origin influenza A virus infection

<p>Abstract</p> <p>Background</p> <p>Novel Influenza A (H1N1) is an acute respiratory infectious disease. Animal experiments indicated that when H1N1 virus infected early hosts, it showed strong CD4⁺, CD8⁺, and CD4⁺CD25⁺T cell reactions. The aim of this study was to investigate the dynamic fluctuations of the peripheral blood lymphocyte subgroups in patients infected with H1N1 swine-origin influenza A virus (S-OIV).</p> <p>Methods</p> <p>The frequency of T cells, B cells, natural killer (NK) cells, and regulatory T cells (Treg) in 36 severe H1N1 and 40 moderate H1N1 patients were detected at different periods by flow cytometry. In parallel, serum cytokines were detected by enzyme-linked immunosorbent assay and C-reactive protein (CRP) was analyzed through an image-type automatic biochemical analyzer. In addition, 20 healthy volunteers, who were not infected with 2009 H1N1 virus, were selected as controls.</p> <p>Results</p> <p>The frequency of NK cells were decreased in all cases and CD19⁺B cells were increased in severe cases than those of the controls. At 1-2d from onset, the frequency of CD4⁺and CD4⁺CD25⁺T cells in moderate cases was higher than in the severe cases. Serum cytokines, specifically IL-2, IL-4, IL-6, IL-10, and IFN-γ exhibited no significant change both in the moderate and the severe cases during the whole monitoring process. In the early stage of the disease, serum CRP levels in the severe and moderate groups were significantly higher than that in the control group.</p> <p>Conclusions</p> <p>Patients showed different lymphocyte subgroup distributions between mild and severe cases, which might affect the incidence and development of 2009 H1N1.</p

Association analysis of alpha-amylase (AMY) and cathepsin L (CTSL) SNPs with growth traits in giant tiger shrimp Penaeus monodon

Alpha-amylase (AMY) and cathepsin-L (CTSL) were selected as candidate genes for SNP discovery for growth traits of P. monodon. Six SNPs were found in AMY and three in CTSL in P. monodon. Association analyses for the candidate SNPs with important economic traits were performed in populations. That allele A at CTLS-213 SNP, AA, and GA, tended to be associated with increased body weight. Shrimps with genotype GG had significantly smaller CL, CW, and CH values than those with GT and TT genotypes (P < 0.05). While CTLS-820 SNP was found to be significantly associated with CH and FSL (P <0.05). These SNPs will be valid for marker-assisted selection breeding programs in P. monodon

Modified Limiting Equilibrium Method for Stability Analysis of Stratified Rock Slopes

The stratified rock of Jurassic strata is widely distributed in Three Gorges Reservoir Region. The limit equilibrium method is generally utilized in the stability analysis of rock slope with single failure plane. However, the stratified rock slope cannot be accurately estimated by this method because of different bedding planes and their variable shear strength parameters. Based on the idealized model of rock slope with bedding planes, a modified limiting equilibrium method is presented to determine the potential sliding surface and the factor of safety for the stratified rock slope. In this method, the S-curve model is established to define the spatial variations of the shear strength parameters c and  φ of bedding plane and the tensile strength of rock mass. This method was applied in the stability evaluation of typical stratified rock slope in Three Gorges Reservoir Region, China. The result shows that the factor of safety of the case study is 0.973, the critical sliding surface for the potential slip surface appears at bedding plane C, and the tension-controlled failure occurs at 10.5 m to the slope face

Paramagnetic behaviour of silver nanoparticles generated by decomposition of silver oxalate

Silver oxalate Ag2C2O4, was already proposed for soldering applications, due to the formation when it is decomposed by a heat treatment, of highly sinterable silver nanoparticles. When slowly decomposed at low temperature (125 °C), the oxalate leads however to silver nanoparticles isolated from each other. As soon as these nanoparticles are formed, the magnetic susceptibility at room temperature increases from -3.14 10-7 emu.Oe-1.g-1 (silver oxalate) up to -1.92 10-7 emu.Oe-1.g-1 (metallic silver). At the end of the oxalate decomposition, the conventional diamagnetic behaviour of bulk silver, is observed from room temperature to 80 K. A diamagnetic-paramagnetic transition is however revealed below 80 K leading at 2 K, to silver nanoparticles with a positive magnetic susceptibility. This original behaviour, compared to the one of bulk silver, can be ascribed to the nanometric size of the metallic particles