Quick and accurate forecasts of incidence and mortality trends for the near future are particularly useful for the immediate allocation of available public health resources, as well as for understanding the long-term course of the pandemic. The surveillance data used for predictions, however, may come with some reporting delays. Consequently, auxiliary data sources that are available immediately can provide valuable additional information for recent time periods for which surveillance data have not yet become fully available. In this work, a set of Google search queries by individual users related to COVID-19 incidence and mortality is collected and analyzed. The information from these queries aims to improve quick forecasts. Initially, the identified search query keywords were ranked according to their predictive abilities with reported incidence and mortality. After that, the ARIMA, Prophet, and XGBoost models were fitted to generate forecasts using only the available reported incidence and mortality (baseline model) or together with combinations of searched keywords identified based on their predictive abilities (predictors model). In summary, the inclusion of top-ranked keywords as predictors significantly enhanced prediction accuracy for the majority of scenarios in the range from 50% to 90% across all considered models and is recommended for future use. The inclusion of low-ranked keywords did not provide such an improvement. In general, the ranking of predictors and the corresponding forecast improvements were more pronounced for incidence, while the results were less pronounced for mortality.

A finite point set in $\mathbb{R}^d$ is in general position if no $d + 1$ points lie on a common hyperplane. Let $\alpha _d(N)$ be the largest integer such that any set of $N$ points in $\mathbb{R}^d$, with no $d + 2$ members on a common hyperplane, contains a subset of size $\alpha _d(N)$ in general position. Using the method of hypergraph containers, Balogh and Solymosi showed that $\alpha _2(N) \lt N^{5/6 + o(1)}$. In this paper, we also use the container method to obtain new upper bounds for $\alpha _d(N)$ when $d \geq 3$. More precisely, we show that if $d$ is odd, then $\alpha _d(N) \lt N^{\frac {1}{2} + \frac {1}{2d} + o(1)}$, and if $d$ is even, we have $\alpha _d(N) \lt N^{\frac {1}{2} + \frac {1}{d-1} + o(1)}$. We also study the classical problem of determining $a(d,k,n)$, the maximum number of points selected from the grid $[n]^d$ such that no $k + 2$ members lie on a $k$-flat, and improve the previously best known bound for $a(d,k,n)$, due to Lefmann in 2008, by a polynomial factor when $k$ = 2 or 3 (mod 4).

Successful synthesis of a new design requires balancing of trade-offs that arise from multiple competing design objectives and constraints. Early-stage design synthesis typically does not consider detailed technical constraints; a task left to late-stage mathematical design optimisation to refine an already-determined configuration. The recently developed Multi-Objective Monotonicity Analysis (MOMA) has shown that design optimisation can be used successfully in configuration redesign. This article extends the MOMA approach to early-stage design. Synthesis of an aptly named ideal design is achieved by focusing on the avoidance or reduction of trade-offs and by managing active constraints across all stages of the design process. The ideal design meets a set of formal conditions, which provide the basis for a systematic collection of corresponding design principles that can be selectively combined to create new embodiments, avoiding overly restrictive trade-offs and constraints. These principles are consistent with the decision making of experienced mechanical designers, shown here in the industrial practice for designing drug delivery devices.

Generative artificial intelligence (GenAI) applications in job scheduling are expected to help schedulers embed their requirements into scheduling models in a more user-friendly way to generate customized scheduling results. However, there are still very few such applications, while using existing general-purpose GenAI services is inconvenient and prone to data leakage risks. To solve these problems, this study established a GenAI job scheduling system. By hosting the GenAI job scheduling system locally, schedulers can avoid the leakage of order- or recipe-related information that may occur when uploading to the cloud-based GenAI service. In the GenAI job scheduling system, a user interface is designed for users to enter queries in natural language. The user’s query is then analyzed to extract his/her requirements related to the scheduling task, thereby building an extended three-field notation (ETFN) of the scheduling problem. A customized genetic algorithm (GA) is generated to help solve the mathematical programming (MP) model corresponding to the ETFN, thereby updating invalid code or adding new code to the basic GA application. The effectiveness of the GenAI job scheduling system has been tested in a flexible job shop case.

A major challenge in laryngeal surgery today is the limited flexibility of surgical operations. To address the limitation, this paper proposes a novel continuum robot (CR) system with enhanced dexterity, a robust inverse kinematics algorithm, and a sensorless automatic calibration method. The proposed CR possesses 4 flexible degrees of freedom, allowing for control based on angles and end-effector position. Compared with traditional Jacobian-based methods, the proposed inverse kinematics algorithm effectively addresses the singularity issue arising from curvature hypotheses. Mitigating the singularity is crucial for ensuring continuous and stable motion planning. The calibration method enables automatic initialization without additional sensors, a capability not previously reported in the literature. The efficient and automatic calibration reduces preparation time for laryngeal surgery. Compared to the manual calibration, which requires approximately 210 s, the proposed method reduces the calibration time by 160 s, thereby achieving a 76.19 % improvement in efficiency. Taking the damped least squares method as the baseline, the inverse kinematics algorithm reduces the maximum solving error from 7.36 mm to just 0.05 mm. Furthermore, the CR is capable of dexterous motion within narrow and curved cavities. The phantom and animal experiment results demonstrate the practicality and reliability of the proposed CR system in laryngeal surgery.