Large-scale Multiple Testing: Fundamental Limits of False Discovery Rate Control and Compound Oracle

The false discovery rate (FDR) and the false non-discovery rate (FNR), defined as the expected false discovery proportion (FDP) and the false non-discovery proportion (FNP), are the most popular benchmarks for multiple testing. Despite the theoretical and algorithmic advances in recent years, the optimal tradeoff between the FDR and the FNR has been largely unknown except for certain restricted class of decision rules, e.g., separable rules, or for other performance metrics, e.g., the marginal FDR and the marginal FNR (mFDR and mFNR). In this paper we determine the asymptotically optimal FDR-FNR tradeoff under the two-group random mixture model when the number of hypotheses tends to infinity. Distinct from the optimal mFDR-mFNR tradeoff, which is achieved by separable decision rules, the optimal FDR-FNR tradeoff requires compound rules and randomization even in the large-sample limit. A data-driven version of the oracle rule is proposed and shown to outperform existing methodologies on simulated data for models as simple as the normal mean model. Finally, to address the limitation of the FDR and FNR which only control the expectations but not the fluctuations of the FDP and FNP, we also determine the optimal tradeoff when the FDP and FNP are controlled with high probability and show it coincides with that of the mFDR and the mFNR.Comment: 39 page

Knowledge Condensation Distillation

Knowledge Distillation (KD) transfers the knowledge from a high-capacity teacher network to strengthen a smaller student. Existing methods focus on excavating the knowledge hints and transferring the whole knowledge to the student. However, the knowledge redundancy arises since the knowledge shows different values to the student at different learning stages. In this paper, we propose Knowledge Condensation Distillation (KCD). Specifically, the knowledge value on each sample is dynamically estimated, based on which an Expectation-Maximization (EM) framework is forged to iteratively condense a compact knowledge set from the teacher to guide the student learning. Our approach is easy to build on top of the off-the-shelf KD methods, with no extra training parameters and negligible computation overhead. Thus, it presents one new perspective for KD, in which the student that actively identifies teacher's knowledge in line with its aptitude can learn to learn more effectively and efficiently. Experiments on standard benchmarks manifest that the proposed KCD can well boost the performance of student model with even higher distillation efficiency. Code is available at https://github.com/dzy3/KCD.Comment: ECCV202

Impact of dyslipidemia on the severity of symptomatic lumbar spine degeneration: A retrospective clinical study

BackgroundLumbar intervertebral disc degeneration (IVDD) is an important cause of low back pain or sciatica, and metabolic factors play an important role. However, little is known about the relationship of dyslipidemia to the risk of intervertebral disc degeneration (IVDD). This study aimed to assess the impact of serum lipid levels on the severity of lumbar disc degeneration and to investigate its association with endplate inflammation.MethodsWe conducted a case retrospective study in which a total of 302 hospitalized Chinese patients were recruited, of whom 188 (112 males and 76 females; mean age: 51.66 years) were without underlying disease, while the remaining 114 patients (51 males and 63 females; mean age: 62.75 years) had underlying diseases. We examined fasting serum lipid levels for total cholesterol (TC), triglycerides (TG), low-density lipoprotein cholesterol (LDL-C), and high-density lipoprotein cholesterol (HDL-C). Magnetic resonance imaging (MRI) was used to determine endplate inflammation. Pfirrmann grading and Weishaupt grading were used to evaluate the severity of intervertebral disc degeneration and facet joint degeneration, respectively.ResultsThere was no difference in age, gender, and general BMI between the two groups (P > 0.05), but there were significantly high levels in TC, LDL-C, and LDL-C/HDL-C (P = 0.04, P = 0.013, P = 0.01, respectively). TG and HDL-C showed no significant difference (P = 0.064, P = 0.336, respectively). The multivariate logistic regression model showed that age was a risk factor for the occurrence of endplate inflammation. In the group without underlying diseases, age, but not other indicators, was a risk factor for the occurrence of endplate inflammation (P < 0.01), In the group with underlying diseases, none of the patient indicators was directly related to the occurrence of endplate inflammation (P > 0.05). A nonlinear machine learning model was used to measure the contribution of each factor to the disease outcome and to analyze the effect between the top three contributing factors and the outcome variables. In patients without underlying diseases, the top three factors contributing to the severity grading of intervertebral disc degeneration were age (32.9%), high-density lipoproteins (20.7%), and triglycerides (11.8%). For the severity grading of facet joint degeneration, the top three contributing factors were age (27.7%), high-density lipoproteins (19.4%), and triglycerides (14.6%). For patients with underlying diseases, the top three factors contributing to intervertebral disc degeneration were age (25.4%), BMI (15.3%), and low-density lipoprotein/high-density lipoprotein ratio (13.9%). In terms of degree classification for facet joint degeneration, the top three contributing factors were age (17.5%), BMI (17.2%), and total cholesterol (16.7%).ConclusionThis study shows that age, high-density lipoprotein, and triglycerides affect the degree of degeneration in patients with symptomatic lumbar degeneration without underlying diseases. Age and BMI are two major factors affecting the severity of degeneration in patients with underlying diseases, and dyslipidemia is a secondary factor. However, there is no clear association between dyslipidemia and the occurrence of endplate inflammation in either group

Effect of Ultrasonic Treatment on Vitis vinifera L. Cell Wall Pectin Components

In order to clarify the content and structural changes of different pectin fractions in grape cell walls under ultrasonic treatment, the grapes were treated with different ultrasonic time and ultrasonic power in this study, and the content of pectin fractions, composition of monosaccharides and structural changes of grape cell walls were analyzed by means of carbazole sulfuric acid method, PMP pre-column derivatization, high-performance liquid gel chromatography , scanning electron microscopy, Fourier transform infrared spectroscopy and circular dichroism. Results showed that the highest and the lowest contents in fresh grape cell walls were alkali-soluble pectin (NSP) and chelate pectin (CSP), respectively, and they were 27.41 mg/g AIR and 8.25 mg/g AIR. The total pectin decreased after ultrasonic treatments, in which the water-soluble pectin (WSP) increased and the CSP and NSP decreased. A total of six monosaccharides were detected in three pectins, and the monosaccharides of different pectin were not the same. The galactose and arabinose were high in WSP, the glucuronic acid was the most abundant of CSP and the rhamnose were the highest in NSP. After ultrasonic treatment, the contents of monosaccharides decreased, while the composition did not change, and the main chain structure of pectin was no change, but the linear structure and the degree of branch chain were changed. With the increase of ultrasonic times and powers, the molecular weight of different pectins declined gradually. And in the microstructure showed a more loose morphology. In addition, ultrasonic treatment had an effect on the structure and chain conformation of CSP and NSP, which made their maximum response values shift, and the effect of ultrasonic power was more significant. In conclusion, ultrasonic treatment could reduce the pectin and monosaccharide contents in grape cell walls, and affect the molecular linear structure and molecular chain conformation of pectin. These results can provide theoretical basis for the quality change of grape products under ultrasonic treatment

Asymptotic Spreading Speed for the Weak Competition System with a Free Boundary

This paper is concerned with a diffusive Lotka-Volterra type competition system with a free boundary in one space dimension. Such a system may be used to describe the invasion of a new species into the habitat of a native competitor, and its long-time dynamical behavior can be described by a spreading-vanishing dichotomy. The main purpose of this paper is to determine the asymptotic spreading speed of the invading species when its spreading is successful, which involves two systems of traveling wave type equations

Spreading speed for a West Nile virus model with free boundary

The purpose of this paper is to determine the precise asymptotic spreading speed of the virus for a West Nile virus model with free boundary, introduced recently in Lin and Zhu (J Math Biol 75:1381–1409, 2017), based on a model of Lewis et al. (Bull Math Biol 68:3–23, 2006).We show that this speed is uniquely defined by a semiwave solution associated with theWest Nile virus model. To find such a semiwave solution, we firstly consider a general cooperative system over the half-line [0,∞), and prove the existence of amonotone solution by an upper and lower solution approach; we then establish the existence and uniqueness of the desired semiwave solution by applying this method together with some other techniques including the sliding method. Our result indicates that the asymptotic spreading speed of theWest Nile virus model with free boundary is strictly less than that of the corresponding model in Lewis et al. (2006)

Spreading of two competing species governed by a free boundary model in a shifting environment

We investigate the long-time spreading behavior of two competing species in a shifting environment. The evolution of the population densities of the species is governed by a one space dimension diffusive Lotka-Volterra competition system with two different free boundaries, describing a dynamical process of two competitors invading into the new habitat in the same direction. It is assumed that the unfavourable region of the environment moves into the otherwise favourable homogeneous environment with a given speed c>0 in the spreading direction of the species. By close examination of certain simple cases, we show that such a shifting environment could reverse the fates of the species. A complete classification of the long-time dynamical behavior of the system is obtained for such cases