Extremal solutions of periodic boundary value problems for first order integro-differential equations of mixed type

AbstractThis paper investigates the maximal and minimal solutions of periodic boundary value problems for first order nonlinear integro-differential equations of mixed type by establishing a comparison result and using the monotone iterative technique

Fair Supervised Learning with A Simple Random Sampler of Sensitive Attributes

As the data-driven decision process becomes dominating for industrial applications, fairness-aware machine learning arouses great attention in various areas. This work proposes fairness penalties learned by neural networks with a simple random sampler of sensitive attributes for non-discriminatory supervised learning. In contrast to many existing works that critically rely on the discreteness of sensitive attributes and response variables, the proposed penalty is able to handle versatile formats of the sensitive attributes, so it is more extensively applicable in practice than many existing algorithms. This penalty enables us to build a computationally efficient group-level in-processing fairness-aware training framework. Empirical evidence shows that our framework enjoys better utility and fairness measures on popular benchmark data sets than competing methods. We also theoretically characterize estimation errors and loss of utility of the proposed neural-penalized risk minimization problem

Effects of Low-Level Laser Therapy and Eccentric Exercises in the Treatment of Patellar Tendinopathy

The study aims to investigate if low-level laser therapy (LLLT) combined with eccentric exercises could more effectively treat patellar tendinopathy than LLLT alone and eccentric exercises alone. Twenty-one patients with patellar tendinopathy were randomized to three groups: laser alone, exercise alone, or laser plus exercise, with seven in each group. Laser irradiations were administered at the inferior pole of the patella and the two acupoints of Extra 36 (Xiyan) with the intensity of 1592 mW/cm2. Eccentric training program consisted of three sets of 15 repetitions of unilateral squat on level ground. All patients received six treatments per week for four weeks. Knee pain and function and quadriceps muscle strength and endurance were evaluated at baseline and the end of treatment. After the 4-week intervention, all groups showed significant improvements in all the outcomes (P<0.01). The laser + exercise group had significantly greater improvements in all the outcomes than the other two groups (P<0.05), except nonsignificant difference in pain relief between the laser + exercise group and the laser group. In conclusion, LLLT combined with eccentric exercises is superior to LLLT alone and eccentric exercises alone to reduce pain and improve function in patients with patellar tendinopathy

Unified tensor network theory for frustrated classical spin models in two dimensions

Frustration is a ubiquitous phenomenon in many-body physics that influences the nature of the system in a profound way with exotic emergent behavior. Despite its long research history, the analytical or numerical investigations on frustrated spin models remain a formidable challenge due to their extensive ground state degeneracy. In this work, we propose a unified tensor network theory to numerically solve the frustrated classical spin models on various two-dimensional (2D) lattice geometry with high efficiency. We show that the appropriate encoding of emergent degrees of freedom in each local tensor is of crucial importance in the construction of the infinite tensor network representation of the partition function. The frustrations are thus relieved through the effective interactions between emergent local degrees of freedom. Then the partition function is written as a product of a one-dimensional (1D) transfer operator, whose eigen-equation can be solved by the standard algorithm of matrix product states rigorously, and various phase transitions can be accurately determined from the singularities of the entanglement entropy of the 1D quantum correspondence. We demonstrated the power of our unified theory by numerically solving 2D fully frustrated XY spin models on the kagome, square and triangular lattices, giving rise to a variety of thermal phase transitions from infinite-order Brezinskii-Kosterlitz-Thouless transitions, second-order transitions, to first-order phase transitions. Our approach holds the potential application to other types of frustrated classical systems like Heisenberg spin antiferromagnets.Comment: 20 pages, 19 figure

SOHLHs Might Be Gametogenesis-Specific bHLH Transcriptional Regulation Factors in Crassostrea gigas

The self-renewal and differentiation of germ cells are essential for gametogenesis and reproduction. In mammals, the transcription factors SOHLH1 and SOHLH2, two members of the bHLH family, are specifically expressed in the gonads, and play an important role in spermatocyte and oocyte differentiation. In our previous study, we performed a phylogenetic analysis of the Lophotrochozoa bHLH genes, and two Sohlh were identified in the Pacific oyster Crassostrea gigas. Based on the genomes of other species that have complete genomic information, we further analyzed the phylogenetics of the Sohlh in this study. The results indicate that the Sohlh are ancient genes that were lost in many species during evolution, including in some invertebrates, and lower vertebrates. The phylogenetic tree shows that Sohlh1 and Sohlh2 are located in different scaffolds and that they have low similarity, suggesting early separation in invertebrates. We used RNA-seq and RT-PCR to examine the mRNA expression of the Sohlh in C. gigas (termed Cg-Sohlh), we found that Cg-Sohlh1, and Cg-Sohlh2 are specifically expressed in the gonads. During gonadal development, the mRNA expression levels of both genes increased from the proliferative stage and reached the highest level at the growth stage (P &lt; 0.05). Then, the expression level decreased until the resting stage. In addition, immunohistochemistry was used to determine that the Cg-SOHLH1 protein was specifically expressed in the spermatogonia and spermatocytes. Cg-Sohlh2 mRNA was expressed in both the male and female gonads, while Cg-Sohlh1 mRNA was highly expressed in the female gonads at all developmental stages except for the resting stage. These data indicate that Cg-SOHLH might be gonad-specific regulatory factors, similar to mammalian SOHLH, and that Cg-SOHLH1 might be involved in spermatogonial differentiation. This study lays the foundation to further determine the functional role of SOHLH in mollusk gametogenesis and provides a foundation to better understand the regulatory mechanism of gametogenesis in invertebrates

Experimental Equilibrium Moisture Content of Wood Under Vacuum

Wood equilibrium moisture content (EMC) was measured under vacuum by an electronic method. A wafer was used to measure EMC using an in-house designed vacuum instrument. EMC at 4 to 100 kPa and temperature from 30 to 90°C were measured. The relationships among temperature, pressure, and EMC were determined, and a diagram of wood EMC was produced. The results showed there are obvious differences between experimental EMC values obtained and theoretical EMC values of other researchers. It is suggested that corrections should be introduced into theoretical models or a new model for the vacuum condition developed

Theoretical Prediction and Experimental Determination of Heating Time During High-Temperature Heat Treatment of Wood

Theoretical prediction provides basic understanding and guidance to correctly implement a certaintechnology in the production process. The present study uses a differential equation to predict the heattransfer time between the surface and core layer of wood during the heat treatment, with applicability inestimating the duration of heat treatments at high temperatures. The obtained prediction was compared withthe result of an experimental study performed on Chinese poplar wood with various thicknesses (20, 40 and60mm). During this experiment, the time necessary for the core of wood to reach a temperature of 100°C,130°C and finally 180°C was monitored and the recorded values were compared with the predicted ones.The result of this comparison proved that the experimental values matched the theoretically predicted times,validating thus the applicability of the proposed equation as prediction tool

2-(4-Methyl­benzo­yl)benzoic acid monohydrate

In the title compound, C15H12O3·H2O, the two rings are oriented at a dihedral angle of 69.12 (3)°. In the crystal structure, intermolecular O—H⋯O hydrogen bonds link the mol­ecules into a three-dimensional framework