Yu Liang

Strong Turing Determinacy, or ${\mathrm {sTD}}$, is the statement that for every set A of reals, if $\forall x\exists y\geq _T x (y\in A)$, then there is a pointed set $P\subseteq A$. We prove the following consequences of Turing Determinacy ( ${\mathrm {TD}}$ ) and ${\mathrm {sTD}}$ over ${\mathrm {ZF}}$ —the Zermelo–Fraenkel axiomatic set theory without the Axiom of Choice: (1) ${\mathrm {ZF}}+{\mathrm {TD}}$ implies $\mathrm {wDC}_{\mathbb {R}}$ —a weaker version of $\mathrm {DC}_{\mathbb {R}}$.(2) ${\mathrm {ZF}}+{\mathrm {sTD}}$ implies that every set of reals is measurable and has Baire property.(3) ${\mathrm {ZF}}+{\mathrm {sTD}}$ implies that every uncountable set of reals has a perfect subset.(4) ${\mathrm {ZF}}+{\mathrm {sTD}}$ implies that for every set of reals A and every $\epsilon>0$ :(a)There is a closed set $F\subseteq A$ such that $\mathrm {Dim_H}(F)\geq \mathrm {Dim_H}(A)-\epsilon $, where $\mathrm {Dim_H}$ is the Hausdorff dimension.(b)There is a closed set $F\subseteq A$ such that $\mathrm {Dim_P}(F)\geq \mathrm {Dim_P}(A)-\epsilon $, where $\mathrm {Dim_P}$ is the packing dimension.

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.

A novel data-driven model-free adaptive control approach is first proposed by combining the advantages of model-free adaptive control and data-driven optimal iterative learning control, and then its stability and convergence analysis is given to prove algorithm stability and asymptotical convergence of tracking error. Besides, the parameters of presented approach are adaptively adjusted with fuzzy logic to determine the occupied proportions of MFAC and DDOILC according to their different control performances in different control stages. Lastly, the proposed fuzzy DDMFAC approach is applied to the control of particle quality in drug development phase of spray fluidized-bed granulation process, and its control effect is compared with MFAC and DDOILC and their fuzzy forms, in which the parameters of MFAC and DDOILC are adaptively adjusted with fuzzy logic. The effectiveness of the presented FDDMFAC approach is verified by a series of simulations.

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.

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.

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.

Facial expressions influence our experience and perception of emotions—they not only tell other people what we are feeling but also might tell us what to feel via sensory feedback. We conducted three experiments to investigate the interaction between facial feedback phenomena and different environmental stimuli, by asking participants to remember emotional autobiographical memories. Moreover, we examined how people with schizotypal traits would be affected by their experience of emotional facial simulations. We found that using a directed approach (gripping a pencil with teeth/lips) while remembering a specific autobiographical memory could successfully evoke participants’ positive (e.g. happy and excited)/negative (e.g. angry and sad) emotions (i.e. Experiment 1). When using indirective environmental stimuli (e.g. teardrop glasses), the results of our experiments (i.e. Experiments 2 and 3) investigating facial feedback and the effect of teardrop glasses showed that participants who scored low in schizotypy reported little effect from wearing teardrop glasses, while those with high schizotypy reported a much greater effect in both between- and within-subject conditions. The results are discussed from the perspective of sense of ownership, which people with schizophrenia are believed to have deficits in.

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.

Let an oracle be called low for prefix-free complexity on a set in case access to the oracle improves the prefix-free complexities of the members of the set at most by an additive constant. Let an oracle be called weakly low for prefix-free complexity on a set in case the oracle is low for prefix-free complexity on an infinite subset of the given set. Furthermore, let an oracle be called low and weakly for prefix-free complexity along a sequence in case the oracle is low and weakly low, respectively, for prefix-free complexity on the set of initial segments of the sequence. Our two main results are the following characterizations. An oracle is low for prefix-free complexity if and only if it is low for prefix-free complexity along some sequences if and only if it is low for prefix-free complexity along all sequences. An oracle is weakly low for prefix-free complexity if and only if it is weakly low for prefix-free complexity along some sequence if and only if it is weakly low for prefix-free complexity along almost all sequences. As a tool for proving these results, we show that prefix-free complexity differs from its expected value with respect to an oracle chosen uniformly at random at most by an additive constant, and that similar results hold for related notions such as a priori probability. Furthermore, we demonstrate that on every infinite set almost all oracles are weakly low but are not low for prefix-free complexity, while by Shoenfield absoluteness there is an infinite set on which uncountably many oracles are low for prefix-free complexity. Finally, we obtain no-gap results, introduce weakly low reducibility, or WLK-reducibility for short, and show that all its degrees except the greatest one are countable.

This is among the last turn of the century one of the central figure in French culture: Bergson philosophy of life perspective, to interpret the same period of modern painting as part of research projects. The initial study was the author of "father of modern painting" plugs yet and the real comparative study between Bergson; then have follow-up, respectively, In order to explore the art of movement: Fauvism , stereo doctrine , Yun legal doctrine and the future doctrine theory of representative artists and creative裡in the philosophy of Bergson quality. This adjourned its regardless aims to metaphysics裡"appearance with the really" and the knowledge regardless裡"intuition and management wisdom" of the analysis into the road, explore the stereo doctrine offshoot Ophelia doctrine of the representative artists: De Los inside of the "Bergson style." Hope this closely-related research before and after, can be further described regardless of modern painting and Bergson philosophy, culture and meaning in the same system of interaction and development of the situation; and interpretation in this framework, multi-arts style of modern painting; as distinct from the present work are generally more focused on the analysis of form or out regardless. Henri Bergson's philosophy shares great importance in the late 19 and early 20 centuries in French. This is the point of departure I will take in this article, which constitutes the third part of my modern painting research. The first part of the research started from the issue regarding Cézanne and Bergson. While the second part regarding representatives of Cézanne's successors: Fauvism, Cubism and Rhythmism was also probed. On these grounds and under the same direction, this article moves forward for further research. Namely, I will take the similar approach to interpret Robert Delaunay of Orphism . With these I will show the multiple styles of modern art with Bergsonian viewpoints. Consequently, a principal characteristic of early 20 century European painting could better be interpreted as the multiple formal expressions and innovative developments of "Bergsonian style", or the crystallization of Bergsonian spiritual-positivism

This article is based on Bergson philosophy of life point of view, to interpret the same period of modern painting as part of research projects. The initial study was the author of "father of modern painting," Cézanne and the real comparative study between Bergson; then, have been discussed separately subsequent art movements: Fauvism, Cubism, rhythm, Futurism and the doctrine of representativeness of Ophelia in theory and creative artists in the philosophy of Bergson quality. This adjourned its theta to metaphysics in "appearance and it is" and the theory of knowledge in "intuition and reason" analysis into the road, explore the important artists: Duchamp of the "Bergson style." Hope this is closely related to before and after the study is further discussed in contemporary painting and Bergson philosophy, culture and meaning in the same system of interaction and development of the situation; and interpretation in this framework, multi-arts style of modern painting; as distinct from the present work are generally more focused on the analysis or discussion of the form. Henri Bergson's philosophy shares great importance in the late 19 and early 20 centuries in French. This is the point of departure I will take in this article, which constitutes the third part of my modern painting research. The first part of the research started from the issue regarding Cézanne and Bergson. While the second part regarding representatives of Cézanne's successors: Fauvism, Cubism, Rhythmism, Futurism and Orphism were also probed. On these grounds and under the same direction, this article moves forward for further research. Namely, Ⅰ will take the similar approach to interpret Marcel Duchamp's art. With these Ⅰ will show the multiple styles of modern art with Bergsonian viewpoints. Consequently, a principal characteristic of early 20 century European painting could better be interpreted as the multiple formal expressions and innovative developments of "Bergsonian style", or the crystallization of Bergsonian spiritual-positivism

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