Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $\omega-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Uniqueness Method (HUM) among all the admissible ones. Finally, we illustrate our results by an interesting example.Comment: 16 page

Experimental design-aided systematic pathway optimization of glucose uptake and deoxyxylulose phosphate pathway for improved amorphadiene production

Artemisinin is a potent antimalarial drug; however, it suffers from unstable and insufficient supply from plant source. Here, we established a novel multivariate-modular approach based on experimental design for systematic pathway optimization that succeeded in improving the production of amorphadiene (AD), the precursor of artemisinin, in Escherichia coli. It was initially found that the AD production was limited by the imbalance of glyceraldehyde 3-phosphate (GAP) and pyruvate (PYR), the two precursors of the 1-deoxy-d-xylulose-5-phosphate (DXP) pathway. Furthermore, it was identified that GAP and PYR could be balanced by replacing the phosphoenolpyruvate (PEP)-dependent phosphotransferase system (PTS) with the ATP-dependent galactose permease and glucose kinase system (GGS) and this resulted in fivefold increase in AD titer (11 to 60 mg/L). Subsequently, the experimental design-aided systematic pathway optimization (EDASPO) method was applied to systematically optimize the transcriptional expressions of eight critical genes in the glucose uptake and the DXP and AD synthesis pathways. These genes were classified into four modules and simultaneously controlled by T7 promoter or its variants. A regression model was generated using the four-module experimental data and predicted the optimal expression ratios among these modules, resulting in another threefold increase in AD titer (60 to 201 mg/L). This EDASPO method may be useful for the optimization of other pathways and products beyond the scope of this study.Singapore-MIT Alliance for Research and Technology (SMART

Learning Purified Feature Representations from Task-irrelevant Labels

Learning an empirically effective model with generalization using limited data is a challenging task for deep neural networks. In this paper, we propose a novel learning framework called PurifiedLearning to exploit task-irrelevant features extracted from task-irrelevant labels when training models on small-scale datasets. Particularly, we purify feature representations by using the expression of task-irrelevant information, thus facilitating the learning process of classification. Our work is built on solid theoretical analysis and extensive experiments, which demonstrate the effectiveness of PurifiedLearning. According to the theory we proved, PurifiedLearning is model-agnostic and doesn't have any restrictions on the model needed, so it can be combined with any existing deep neural networks with ease to achieve better performance. The source code of this paper will be available in the future for reproducibility.Comment: arXiv admin note: substantial text overlap with arXiv:2011.0847

The Dawn After the Dark: An Empirical Study on Factuality Hallucination in Large Language Models

In the era of large language models (LLMs), hallucination (i.e., the tendency to generate factually incorrect content) poses great challenge to trustworthy and reliable deployment of LLMs in real-world applications. To tackle the LLM hallucination, three key questions should be well studied: how to detect hallucinations (detection), why do LLMs hallucinate (source), and what can be done to mitigate them (mitigation). To address these challenges, this work presents a systematic empirical study on LLM hallucination, focused on the the three aspects of hallucination detection, source and mitigation. Specially, we construct a new hallucination benchmark HaluEval 2.0, and designs a simple yet effective detection method for LLM hallucination. Furthermore, we zoom into the different training or utilization stages of LLMs and extensively analyze the potential factors that lead to the LLM hallucination. Finally, we implement and examine a series of widely used techniques to mitigate the hallucinations in LLMs. Our work has led to several important findings to understand the hallucination origin and mitigate the hallucinations in LLMs. Our code and data can be accessed at https://github.com/RUCAIBox/HaluEval-2.0.Comment: 24 pages, 8 figures, 13 table

A vector spectrum analyzer of 55.1 THz spectral bandwidth and 99 kHz frequency resolution

The analysis of optical spectra - emission or absorption - has been arguably the most powerful approach for discovering and understanding matters. The invention and development of many kinds of spectrometers have equipped us with versatile yet ultra-sensitive diagnostic tools for trace gas detection, isotope analysis, and resolving hyperfine structures of atoms and molecules. With proliferating data and information, urgent and demanding requirements have been placed today on spectrum analysis with ever-increasing spectral bandwidth and frequency resolution. These requirements are especially stringent for broadband laser sources that carry massive information, and for dispersive devices used in information processing systems. In addition, spectrum analyzers are expected to probe the device's phase response where extra information is encoded. Here we demonstrate a novel vector spectrum analyzer (VSA) that is capable to characterize passive devices and active laser sources in one setup. Such a dual-mode VSA can measure loss, phase response and dispersion property of passive devices. It also can coherently map a broadband laser spectrum into the RF domain. The VSA features a bandwidth of 55.1 THz (1260 to 1640 nm), frequency resolution of 99 kHz, and dynamic range of 56 dB. Meanwhile, our fiber-based VSA is compact and robust. It requires neither high-speed modulators and photodetectors, nor any active feedback control. Finally, we successfully employ our VSA for applications including characterization of integrated dispersive waveguides, mapping frequency comb spectra, and coherent light detection and ranging (LiDAR). Our VSA presents an innovative approach for device analysis and laser spectroscopy, and can play a critical role in future photonic systems and applications for sensing, communication, imaging, and quantum information processing

An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave

Background: The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022–February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province. Methods: A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters. Results: The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R0 of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R0k (age group k to age group k), the values of R0k (an infected of age group k to the total population) and the values of R^0k (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship R0k>R0k>R^0k was valid. Then, the fluctuating tendencies of effective reproduction number Rt were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19. Conclusions: This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited