A Goal-Driven Tree-Structured Neural Model for Math Word Problems

Most existing neural models for math word problems exploit Seq2Seq model to generate solution expressions sequentially from left to right, whose results are far from satisfactory due to the lack of goal-driven mechanism commonly seen in human problem solving. This paper proposes a tree-structured neural model to generate expression tree in a goal-driven manner. Given a math word problem, the model first identifies and encodes its goal to achieve, and then the goal gets decomposed into sub-goals combined by an operator in a top-down recursive way. The whole process is repeated until the goal is simple enough to be realized by a known quantity as leaf node. During the process, two-layer gated-feedforward networks are designed to implement each step of goal decomposition, and a recursive neural network is used to encode fulfilled subtrees into subtree embeddings, which provides a better representation of subtrees than the simple goals of subtrees. Experimental results on the dataset Math23K have shown that our tree-structured model outperforms significantly several state-of-the-art models.

Interactions Between Citrus Viroids Affect Symptom Expression and Field Performance of Clementine Trees Grafted on Trifoliate Orange

Citrus exocortis viroid (CEVd), Citrus bent leaf viroid (CBLVd), a noncachexia variant of Hop stunt viroid (HSVd), Citrus viroid III (CVd-III), and Citrus viroid IV (CVd-IV) were co-inoculated as two-, three-, four-, and five-viroid mixtures to Clementine trees grafted on trifoliate orange to evaluate their effect on symptom expression, tree growth, and fruit yield. Most trees infected with CEVd-containing viroid mixtures developed exocortis scaling symptoms, as did CEVd alone, whereas most trees infected with HSVd- or CVd-IV-containing mixtures developed bark-cracking symptoms. Trees infected with mixtures containing both CEVd and CVd-IV revealed the existence of antagonism between these two viroids in terms of the expected bark-scaling and cracking symptoms. Synergistic interactions also were identified in trees infected with certain viroid combinations that, in spite of lacking CEVd, expressed exocortis-like scaling symptoms. Viroid interactions also affected the expected response of trees in terms of vegetative growth and fruit yield. Trees infected with viroid combinations containing CEVd or CVd-III were smaller and produced less fruit than trees infected with mixtures not containing these viroids. Viroid interactions on scion circumference and cumulative fruit yield, in terms of additivity of their effects, were statistically confirmed using a factorial analysis of variance model with two mean estimation approaches. In single-viroid infections, CEVd, CVd-III, and, to a lesser extent, CBLVd consistently and significantly reduced tree size and fruit yield. Conversely, HSVd and CVd-IV slightly increased fruit yield and reduced scion circumference. Rare and not consistent significant interactions were detected with the five-, four-, and three-viroid combinations. Antagonistic interactions between CEVd and CVd-III or CBLVd and CVd-III were revealed over the years with consistent significance. The antagonistic interaction between CEVd and CVd-IV was highly significant over the years when additional viroids were present; however, this antagonism appeared much later in the case of an exclusive interaction. HSVd and CVd-IV showed a consistent and significant synergistic interaction on yield only when both viroids were exclusively present. These results demonstrate antagonistic or synergistic relationships between citrus viroids depending on the viroid mixtures present in the host.