Y. U. Liang

Arbuscular mycorrhizal fungi are considered as a potential biotechnological tool for improving phytostabilization efficiency and plant tolerance to heavy metal-contaminated soils. However, the mechanisms through which AMF help to alleviate metal toxicity in plants are still poorly understood. A greenhouse experiment was conducted to evaluate the effects of two AMF species on the growth, Pb accumulation, photosynthesis and antioxidant enzyme activities of a leguminous tree at Pb addition levels of 0, 500, 1000 and 2000 mg kg-1 soil. AMF symbiosis decreased Pb concentrations in the leaves and promoted the accumulation of biomass as well as photosynthetic pigment contents. Mycorrhizal plants had higher gas exchange capacity, non-photochemistry efficiency, and photochemistry efficiency compared with non-mycorrhizal plants. The enzymatic activities of superoxide dismutase, ascorbate peroxidases and glutathione peroxidase were enhanced, and hydrogen peroxide and malondialdehyde contents were reduced in mycorrhizal plants. These findings suggested that AMF symbiosis could protect plants by alleviating cellular oxidative damage in response to Pb stress. Furthermore, mycorrhizal dependency on plants increased with increasing Pb stress levels, indicating that AMF inoculation likely played a more important role in plant Pb tolerance in heavily contaminated soils. Overall, both F. mosseae and R. intraradices were able to maintain efficient symbiosis with R. pseudoacacia in Pb polluted soils. AMF symbiosis can improve photosynthesis and reactive oxygen species scavenging capabilities and decrease Pb concentrations in leaves to alleviate Pb toxicity in R. pseudoacacia. Our results suggest that the application of the two AMF species associated with R. pseudoacacia could be a promising strategy for enhancing the phytostabilization efficiency of Pb contaminated soils.

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness.

Objective: Patients with hypochondriasis hold unexplainable beliefs and a fear of having a lethal disease, with poor compliances and treatment response to psychotropic drugs. Although several studies have demonstrated that patients with hypochondriasis demonstrate abnormalities in brain structure and function, gray matter volume and functional connectivity in hypochondriasis still remain unclear.Methods: The present study collected T1-weighted and resting-state functional magnetic resonance images from 21 hypochondriasis patients and 22 well-matched healthy controls. We first analyzed the difference in the GMV between the two groups. We then used the regions showing a difference in GMV between two groups as seeds to perform functional connectivity analysis. Finally, a support vector machine was applied to the imaging data to distinguish hypochondriasis patients from HCs.Results: Compared with the HCs, the hypochondriasis group showed decreased GMV in the left precuneus, and increased GMV in the left medial frontal gyrus. FC analyses revealed decreased FC between the left medial frontal gyrus and cuneus, and between the left precuneus and cuneus. A combination of both GMV and FC in the left precuneus, medial frontal gyrus, and cuneus was able to discriminate the hypochondriasis patients from HCs with a sensitivity of 0.98, specificity of 0.93, and accuracy of 0.95.Conclusion: Our study suggests that smaller left precuneus volumes and decreased FC between the left precuneus and cuneus seem to play an important role of hypochondriasis. Future studies are needed to confirm whether this finding is generalizable to patients with hypochondriasis.

Machine learning algorithms now sweep the world to train machines to learn and make decisions similar to a human. These algorithms provide recommendations and sometimes make judgments on a human’s behalf. However, machine learning creates a disconnect between the intention of human beings and the results of machine learning algorithms, which is defined as the alignment problem. This chapter aims to establish what is required for future leaders to address the alignment problem and the related ethical challenges. It also provides the details of an experiment Duke Kunshan University is conducting in China in undergraduate education to illustrate how the institution prepares responsible leaders for the digital future with innovative educational practices.

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness.

We prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left$ is rational.

We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+"There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+"There exists an inaccessible cardinal"; 2. For all a ∈ 2ω.(ω₁)L[a] = ω₁ if and only if there exists a $\Pi _{1}^{1}[a]$ maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) $\utilde{\Pi}{}_{1}^{1}$ maximal chain of Turing degrees"

This paper investigates the Hausdorff dimension properties of chains and antichains in Turing degrees and hyperarithmetic degrees. Our main contributions are threefold: First, for antichains in hyperarithmetic degrees, we prove that every maximal antichain necessarily attains Hausdorff dimension 1. Second, regarding chains in Turing degrees, we establish the existence of a maximal chain with Hausdorff dimension 0. Furthermore, under the assumption that $$\omega _1=(\omega _1)^L$$, we demonstrate the existence of such maximal chains with $$\Pi ^1_1$$ complexity. Third, we extend our investigation to maximal antichains of Turing degrees by analyzing both the packing dimension and effective Hausdorff dimension.

Maschinelles Lernen Algorithmen durchziehen nun die Welt, um Maschinen zu trainieren und Entscheidungen ähnlich wie ein Mensch zu treffen. Diese Algorithmen liefern Empfehlungen und treffen manchmal Urteile im Namen eines Menschen. Maschinelles Lernen schafft jedoch eine Diskrepanz zwischen der Absicht des Menschen und den Ergebnissen der Algorithmen für maschinelles Lernen, die als das Ausrichtungsproblem definiert wird. Dieses Kapitel zielt darauf ab, festzustellen, was zukünftige Führungskräfte benötigen, um das Ausrichtungsproblem und die damit verbundenen ethischen Herausforderungen anzugehen. Es liefert auch die Details eines Experiments, das die Duke Kunshan Universität in China in der universitären Ausbildung durchführt, um zu veranschaulichen, wie die Institution verantwortungsbewusste Führungskräfte für die digitale Zukunft mit innovativen Bildungspraktiken vorbereitet.

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.

We investigate the initial segment complexity of random reals. Let K denote prefix-free Kolmogorov complexity. A natural measure of the relative randomness of two reals α and β is to compare complexity K and K. It is well-known that a real α is 1-random iff there is a constant c such that for all n, Kn−c. We ask the question, what else can be said about the initial segment complexity of random reals. Thus, we study the fine behaviour of K for random α. Following work of Downey, Hirschfeldt and LaForte, we say that αK β iff there is a constant such that for all n, . We call the equivalence classes under this measure of relative randomness K-degrees. We give proofs that there is a random real α so that lim supn K−K=∞ where Ω is Chaitin's random real. One is based upon work of Solovay, and the other exploits a new idea. Further, based on this new idea, we prove there are uncountably many K-degrees of random reals by proving that μ=0. As a corollary to the proof we can prove there is no largest K-degree. Finally we prove that if n ≠ m then the initial segment complexities of the natural n- and m-random sets and Ω︀) are different. The techniques introduced in this paper have already found a number of other applications