Some open problems related to creative telescoping

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research. This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

Supply chain performance for deteriorating items with cooperative advertising

To study the effect of cooperative advertising on the supply chain of deteriorating items, this paper establishes a Stackelberg game model for a two-echelon deteriorating items supply chain composed of one manufacturer and one retailer under a given support program with an exogenous participation rate. The manufacturer as the leader determines the wholesale price and production rate, and the retailer as the follower determines the retail price and advertising strategies. The strategies of the players under the decentralized scenario and the centralized scenario are respectively characterized. Numerical simulations and sensitivity analysis are conducted to gain some managerial insights. It is shown that the pricing, advertising and production strategies are negatively correlated to deteriorating coefficient, and both the profit and the channel efficiency decrease with deteriorating coefficient; The interaction between price, advertising investment and production rate results in a higher retail price of the centralized channel compared to that of the decentralized channel; Implementing the cooperative advertising program does improve the performance of the supply chain in some cases and the participation rate roughly at 0.5 is most preferable, but it is also possible to distort incentive and damage the channel performance when the participation rate reaches a relatively high level.     

Advance selling in the presence of product diffusion effect

Product diffusion refers to the phenomenon that the later demand is dependent on the early sales. To investigate how a firm’s advance selling strategy is affected by the effect of product diffusion, we consider a monopolist seller who sells a fashionable product in a market that comprises of myopic and strategic consumers over two periods (i.e., the advance selling season and the regular selling season). For a linear product diffusion effect we find that, when the effect of product diffusion is positive, the seller may set an extremely high advance selling price to induce the strategic consumers to purchase in the regular selling season, which is counter-intuitive. Moreover, the optimal procurement quantity for the seller may increase in the negative effect of product diffusion and decrease in the amount of strategic consumers. When we extend our model to consider a concave quadratic product diffusion effect, however, the optimal procurement quantity is concave in the amount of strategic consumers. Numerical studies are further presented to discuss the managerial insights.     

Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.     

Risk reduction in a project portfolio

The positive impacts of managing projects as a portfolio are quantified by comparing the value of the integrated risk of a project portfolio and the aggregation of single project risks implemented separately. Firstly, the integrated risk is defined by proposing risky events based on set theory. Secondly, as projects interact with each other in a project portfolio, the integrated risk is evaluated by using a Bayesian network structure learning algorithm to construct an interdependent network of risks. Finally, the integrated risk of a practical case is assessed using this method, and the results show that the proposed method is an effective tool for calculating the extent of risk reduction of implementing a project portfolio and identifying the most risky project, so as to assist companies in making comprehensive decisions in the phase of portfolio selection and portfolio controlling.     

Feature network-driven quadrant mapping for summarizing customer reviews

With the rapid growth of e-commerce, customers increasingly write online reviews of the product they purchase. These customer reviews are one of the most valuable sources of information affecting selection of products or services. Summarizing these customer reviews is becoming an interesting area of research, inspiring researchers to develop a more condensed, concise summarization for users. However, most of the current efforts at summarization are based on general product features without feature’s relationship. As a result, these summaries either ignore feedback from customers or do a poor job of reflecting the opinions expressed in customer reviews. To remedy this summarization shortcoming, we propose a feature network-driven quadrant mapping that captures and incorporates opinions from customer reviews. Our focus is on construction of a feature network, which is based on co-occurrence and sematic similarities, and a quadrant display showing the opinions polarity of feature groups. Moreover, the proposed approach involves clustering similar product features, and thus, it is different from standard text summarization based on abstraction and extraction. The summarized results can help customers better understand the overall opinions about a product.     

Optimal bundling and pricing decisions for complementary products in a two-layer supply chain

This article explores bundling and pricing decisions for two complementary products in a two-layer supply chain consisting of a multi-product manufacturer and a retailer. We establish four different pricing models under cases of decentralized decision, while considering different portfolio-bundling strategies of the manufacturer and the retailer. A game-theoretical method is used to characterize the corresponding equilibrium outcomes in each scenario. By further analyzing and comparing the maximum profits of all four possible scenarios, optimal bundling and pricing decisions for the manufacturer and the retailer are obtained, respectively. Model extensions and numerical examples are enriched to highlight the factors affecting optimal decision-making. Finally, valuable and interesting managerial insights are summarized. Results show that the upstream manufacturer always profits more when he sells complementary products separately. However, the optimal bundling decision of the downstream retailer is jointly determined by product complementarity (as a major factor) and the difference of product profitability (as a secondary factor). Market power cannot exert an influence on both optimal bundling decisions, but it can partly affect pricing decisions.     

Which is the use of systems theory in literature analysis?: The discovery of the place in La Mancha in Don Quixote

The use of systems theory to attempt to determine which ''place in La Mancha'' was the one whose name Cervantes could not quite recall in his universal novel, appears to be ordained to change certain attitudes towards science held in Cervantine literature. The reason: after four centuries of literary analysis, systemic methodology has proven able to identify the famous ''place'' with acceptable accuracy. Nonetheless, certain reasonable doubts persist around the suitability of a strictly scientific analysis of literature. In light of those doubts, the present article aims primarily to facilitate critique both of the systemic approach adopted and its outcome.