Boosting-based Construction of BDDs for Linear Threshold Functions and Its Application to Verification of Neural Networks

Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply verification techniques for characteristics of interest. This approach is promising since rich results of verification techniques for circuits and other Boolean expressions can be readily applied. The bottleneck is the time complexity of the transformation. More precisely, (i) each neuron of the network, i.e., a linear threshold function, is converted to a Binary Decision Diagram (BDD), and (ii) they are further combined into some final form, such as Boolean circuits. For a linear threshold function with $n$ variables, an existing method takes $O(n2^{\frac{n}{2}})$ time to construct an ordered BDD of size $O(2^{\frac{n}{2}})$ consistent with some variable ordering. However, it is non-trivial to choose a variable ordering producing a small BDD among $n!$ candidates. We propose a method to convert a linear threshold function to a specific form of a BDD based on the boosting approach in the machine learning literature. Our method takes $O(2^n \text{poly}(1/\rho))$ time and outputs BDD of size $O(\frac{n^2}{\rho^4}\ln{\frac{1}{\rho}})$, where $\rho$ is the margin of some consistent linear threshold function. Our method does not need to search for good variable orderings and produces a smaller expression when the margin of the linear threshold function is large. More precisely, our method is based on our new boosting algorithm, which is of independent interest. We also propose a method to combine them into the final Boolean expression representing the neural network

Whole blueberry protects pancreatic beta-cells in diet-induced obese mouse

Background Blueberry is rich in bioactive substances and possesses powerful antioxidant potential, which can protect against oxidant-induced and inflammatory cell damage and cytotoxicity. The aim of this study was to determine how blueberry affects glucose metabolism and pancreatic β-cell proliferation in high fat diet (HFD)-induced obese mice. Methods Wild type male mice at age of 4 weeks received two different kinds of diets: high-fat diet (HFD) containing 60% fat or modified HFD supplemented with 4% (wt:wt) freeze-dried whole blueberry powder (HFD + B) for 14 weeks. A separate experiment was performed in mice fed with low-fat diet (LFD) containing 10% fat or modified LFD + B supplemented with 4% (wt:wt) freeze-dried whole blueberry powder. The metabolic parameters including blood glucose and insulin levels, glucose and insulin tolerances were measured. Results Blueberry-supplemented diet significantly increased insulin sensitivity and glucose tolerance in HFD + B mice compared to HFD mice. However, no difference was observed in blood glucose and insulin sensitivity between LFD + B and LFD mice. In addition, blueberry increased β-cell survival and prevented HFD-induced β-cell expansion. The most important finding was the observation of presence of small scattered islets in blueberry treated obese mice, which may reflect a potential role of blueberry in regenerating pancreatic β-cells. Conclusions Blueberry-supplemented diet can prevent obesity-induced insulin resistance by improving insulin sensitivity and protecting pancreatic β-cells. Blueberry supplementation has the potential to protect and improve health conditions for both type 1 and type 2 diabetes patients

Chinese Dairy Farm Performance and Policy Implications in the New Millennium

China has significantly expanded its dairy cow numbers and increased its dairy processing capacity over the last five year in an attempt to meet increased demand for dairy products. China’s net imports of dairy products, however, has expanded at a growth rate in excess of 30% during the same period. To consider why China is still struggling to meet rising dairy product demand in China in the new millennium, this paper employs a new set of farm-level survey data and stochastic input distance functions to empirically estimate Total factor Productivity (TFP) on China’s dairy farms. The results show that the TFP growth has been positive on and this rise in productivity has been mostly driven by technological change. However, the new results show that on average, the same farms have been behind the advancing technical frontier. We also find one of the drivers of the dairy farms’ productivity advances is the relatively robust rate of technological change. The results suggest that efforts to achieve increased adoption of new technologies and better advice on how to use the technologies and manage production and marketing within the dairy farm sector, will likely further increase TFP growth in China.Distance Function; Total Factor Productivity; Technical Inefficiency; Dairy Farms

Microscopic changing-mass model of PVA hydrogel under unidirectional compression

PVA (Polyvinyl Alcohol) hydrogel is a kind of soft materials, with nontoxic and good biocompatibility. This kind of hydrogel shows strong nonlinearity in the static compression tests because of the high water content (~60‑90%), and the water is squeezed out when the PVA hydrogel is compressed. It means that the PVA hydrogel losts the mass during compression. Aiming at the changing mass mechanism and constitution in the compression of PVA hydrogel, we established a simplified microscopic model which is a single layer frame composite structure consisting of PVA fibers, water, and virtual membrane, in which the membrane wraps outside surfaces of the cubic cells and has no mass, but its membrane force has same properties with the surface tension of water. In the model, the deformation of PVA fibers and the compressive water sustains the external stress when the PVA hydrogel is compressed. In addition, by considering the limitation of the maximum membrane force induced by compressive water, the squeezed water will be calculated in each compressive step and the mechanism of the changing mass is determined quantitatively; in the meantime, the constitution of the PVA hydrogel may be deduced

Numerical analysis of yield properties of closed-cell aluminum foam under multiaxial loads by 3D voronoi model

Metallic foam is a typical porous material whose yield surface is related to not only von Mises equivalent stress but also the hydrostatic pressure. It is essential to study the yield properties of closed-cell aluminum foam under complex loading conditions. However, because the current experimental technique may support only a few proportions of multiaxial loading, it is hard to learn the yield surface well especially for the tensile hydrostatic pressure. In this article, we explored a numerical method to learn the yield properties of aluminum foam, in which the meso structures of aluminum foam were simulated by 3D Voronoi method. In addition, the yield surface of aluminum foam was drawn successfully with the numerical method. The main works included: (1) In our numerical simulation, we tested the calculating parameters such as mass scaling, elements number, and loading velocity on simulation results and verified the homogeneity of the 3D Voronoi model firstly. Furthermore, the optimized calculating parameters were determined by considering both reliability and feasibility of the calculation. Homogeneity of 3D Voronoi model was checked by the compression behaviors of aluminum in different directions. (2) In order to overcome the difficulty to determine critical yield state of metallic foams under complex loads, we recommended criterion by setting a dimensionless plastic dissipation value to determine the onset yield state of the foam under multiaxial loads. The critical value of dimensionless plastic dissipation was deduced from the common criterion—0.2% plastic strain in uniaxial loading, and the effect of relative densities on critical values was analyzed. (3) Three normal stresses were applied on cubic aluminum foam proportionally to implement the proportional loading. The different loading proportional factors of the three normal stresses were set widely to insure the yield surface including enough data, such as the hydrostatic loads cover from minimum negative to maximum positive values; each proportion has three loading proportional factors. Further, effects of the relative density on yield surface were investigated