A Hypothetical Approach to Cosmic Inflation Incorporating Binary Entropy

The current paper presents an alternative hypothesis for the termination of cosmic inflation based on Huang’s model of spacetime involving the movement of a superfluid through a random resistor network. Using this model, we previously derived a mathematical relationship between the velocity of a reference frame and the probability that a random bond is intact. As an extension of this finding, the permutations of open and closed bonds are now shown to represent potential microstates, thus providing a means of relating motion within the network to binary entropy. Applying this concept to cosmic inflation, termination of this process is an expected consequence of the changes in binary entropy associated with the increasing velocity of expansion.

Binarized Neural Networks for Resource-Efficient Hashing with Minimizing Quantization Loss

In order to solve the problem of memory consumption and computational requirements, this paper proposes a novel learning binary neural network framework to achieve a resource-efficient deep hashing. In contrast to floating-point (32-bit) full-precision networks, the proposed method achieves a 32x model compression rate. At the same time, computational burden in convolution is greatly reduced due to efficient Boolean operations. To this end, in our framework, a new quantization loss defined between the binary weights and the learned real values is minimized to reduce the model distortion, while, by minimizing a binary entropy function, the discrete optimization is successfully avoided and the stochastic gradient descend method can be used smoothly. More importantly, we provide two theories to demonstrate the necessity and effectiveness of minimizing the quantization losses for both weights and activations. Numerous experiments show that the proposed method can achieve fast code generation without sacrificing accuracy.

A Novel Index Based on Binary Entropy to Confirm the Spatial Expansion Degree of Urban Sprawl

The phenomenon of urban sprawl has received much attention. Accurately confirming the spatial expansion degree of urban sprawl (SEDUS) is a prerequisite to controlling urban sprawl. However, there is no reliable metric to accurately measure SEDUS. In this paper, based on binary entropy, we propose a new index named the spatial expansion degree index (SEDI), to overcome this difficulty. The study shows that the new index can accurately determine SEDUS and, compared with other commonly used measures, the new index has an obvious advantage in measuring SEDUS. The new index belongs to the second-order metrics of point pattern analysis, and greatly extends the concept of entropy. The new index can also be applied to other spatial differentiation research from a broader perspective. Although the new index is influenced by the scaling problem, because of small differences between different scales, given that the partition scheme in the research process is the same, the new index is a quite robust method for measuring SEDUS.

Perfect Graphs of Fixed Density: Counting and Homogeneous Sets

For c ∈ (0,1) let n(c) denote the set of n-vertex perfect graphs with density c and let n(c) denote the set of n-vertex graphs without induced C5 and with density c.We show that with otherwise, where H is the binary entropy function.Further, we use this result to deduce that almost all graphs in n(c) have homogeneous sets of linear size. This answers a question raised by Loebl and co-workers.