On the Compressive Power of Boolean Threshold Autoencoders.

An autoencoder is a layered neural network whose structure can be viewed as consisting of an encoder, which compresses an input vector to a lower dimensional vector, and a decoder, which transforms the low-dimensional vector back to the original input vector (or one that is very similar). In this article, we explore the compressive power of autoencoders that are Boolean threshold networks by studying the numbers of nodes and layers that are required to ensure that each vector in a given set of distinct input binary vectors is transformed back to its original. We show that for any set of n distinct vectors there exists a seven-layer autoencoder with the optimal compression ratio, (i.e., the size of the middle layer is logarithmic in n ), but that there is a set of n vectors for which there is no three-layer autoencoder with a middle layer of logarithmic size. In addition, we present a kind of tradeoff: if the compression ratio is allowed to be considerably larger than the optimal, then there is a five-layer autoencoder. We also study the numbers of nodes and layers required only for encoding, and the results suggest that the decoding part is the bottleneck of autoencoding. For example, there always is a three-layer Boolean threshold encoder that compresses n vectors into a dimension that is twice the logarithm of n .

On the Distribution of Successor States in Boolean Threshold Networks.

We study the distribution of successor states in Boolean networks (BNs). The state vector y is called a successor of x if y = F(x) holds, where x, y ∈ {0,1}n are state vectors and F is an ordered set of Boolean functions describing the state transitions. This problem is motivated by analyzing how information propagates via hidden layers in Boolean threshold networks (discrete model of neural networks) and is kept or lost during time evolution in BNs. In this article, we measure the distribution via entropy and study how entropy changes via the transition from x to y , assuming that x is given uniformly at random. We focus on BNs consisting of exclusive OR (XOR) functions, canalyzing functions, and threshold functions. As a main result, we show that there exists a BN consisting of d -ary XOR functions, which preserves the entropy if d is odd and , whereas there does not exist such a BN if d is even. We also show that there exists a specific BN consisting of d -ary threshold functions, which preserves the entropy if [Formula: see text]. Furthermore, we theoretically analyze the upper and lower bounds of the entropy for BNs consisting of canalyzing functions and perform computational experiments using BN models of real biological networks.

Floxuridine-chlorambucil conjugate nanodrugs for ovarian cancer combination chemotherapy.

Due to no specific symptoms and lack of early diagnosis for ovarian cancer, most diagnosed patients are often in the terminal stage resulting that tumor tissue is unable to be resected completely by operation. So postoperative chemotherapy has become an important and indispensable treatment procedure for them. Up to date, it remains a challenge to treat ovarian cancer by an effective chemotherapy strategy. Recently, the strategy of ADDC has been regarded as a highly effective chemotherapy strategy to treat various cancers without any drug carriers. Here a novel ADDC is synthesized by linking a water-soluble antitumor drug floxuridine (Fud) and a water-insoluble antitumor drug chlorambucil (Cb) through the esterification. Then the Fud-Cb conjugate can form stable nanodrugs in water with an average size around 103.0 nm through molecular self-assembly. After internalization of cells, the ester bonds in nanodrugs can be degraded to release free Fud and Cb at a fixed ratio under the intracellular acid conditions, which exhibits the high synergistic effect on ovarian cancer cells. The cytotoxicity test results show that Fud-Cb nanodrugs can efficiently inhibit the growth of ovarian cancer cells. The apoptosis data exhibit that the cell necrotic and apoptotic rate treated with Fud-Cb nanodrugs is about 73.7 % and 18.76 % within 24 h. These results suggest that Fud-Cb nanodrugs based on ADDC strategy can effectively enhance synergistic anticancer efficacy to ovarian cancer.