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We study degree-theoretic properties of reals that are not random with respect to any continuous probability measure (NCR). To this end, we introduce a family of generalized Hausdorff measures based on the iterates of the "dissipation" function of a continuous measure and study the effective nullsets given by the corresponding Solovay tests. We introduce two constructions that preserve non-randomness with respect to a given continuous measure. This enables us to prove the existence of NCR reals in a number of Turing degrees. In particular, we show that every Δ 2 0 -degree contains an NCR element. [ABSTRACT FROM AUTHOR]

To protect network security, this paper develops a large-scale network anomalous traffic identification algorithm that utilizes the linear discriminant analysis method to intercept network anomalous traffic. Firstly, the classification of large-scale network anomalous traffic is explored, and the SSAE algorithm is combined with the feature selection of large-scale network traffic on the basis of network flow feature extraction. Secondly, data dimensionality reduction of network anomalous traffic using linear discriminant analysis and feature selection of large-scale network traffic based on SSAE to identify network anomalous traffic. Finally, the CICIDS2017 dataset and the NSL-KDD dataset are used to experimentally analyze the effect and performance of feature selection and anomaly identification algorithms. The results show that the classification accuracy of the feature selection algorithm is 0.989, the 10-dimensional optimal features selected are (12,6,5,38,29,3,33,35,36,40), and the recognition result is 0.803 for normal network traffic and 0.197 for anomalous traffic, with an overall recognition error of 0.003, and a performance of more than 0.988.

The Tusi system was the main means of border minority rule in the Ming Dynasty, and analyzing the beginning and end of the Tusi rebellion and its pacification is an effective perspective to analyze the governance of the system. The paper builds an algorithmic criticism paradigm for the historical study of the Shizhou Rebellion in the early Ming Dynasty, proposes a framework extraction algorithm to realize the automatic acquisition of historical knowledge, identifies the consistency of the knowledge framework based on the conceptual lattice, and corrects the inconsistency by combining with the unity algorithm. After using an iterative algorithm to fuse the multi-source knowledge framework, constraints are added to the conditional random field to improve the extraction of event elements. The semantic reasoning of event features is completed by establishing a semantic knowledge association network of historical events through the association of elements. Based on the results of knowledge association, it is found that the knowledge flow between the topic pair “Tusi→Shizhouwei” is most likely to occur in the future with an association probability of 0.631. “kampong→Education” The probability of association between the theme pairs “kampong→Education”, “Shizhou→Appliance”, “Lanyu→Military”, and “Crackdown→Politics” is 0.631. The same possibility of knowledge flow in the future exists between theme pairs such as “Shizhou→Appliance”, “Lanyu→Military” and “Crackdown→Politics”, with association probabilities greater than 0.550, which suggests that the core contradiction between the Shizhou Tusi Rebellion and governance lies in the contradiction between the Tusi and the leadership rights and interests of the Shizhou Guards. The dissection of the Shi Zhou Tusi rebellion declares the profound influence of the Tusi system on the frontier governance of the Ming Dynasty and reveals the fundamental problems of local governance in the ancient Chinese Great Unification Dynasty.

This paper applies the combinatorial genetic algorithm to the design of industrial product forms to achieve the effect of industrial product form design innovation. The standard genetic algorithm is applied to industrial product design, and the optimal order of genetic optimization is constructed through continuous population genetics, combined with the minimum value of the objective function to construct the constraints of the innovative design of industrial products. Using the method of combinatorial optimization to integrate different elements in industrial product design, a coding method based on rows and columns is proposed for the set coverage problem of design elements. Analyzing the user’s preference for industrial product form design allows us to explore the demand direction of industrial product innovation design and formulate a suitable innovation design scheme. The results show that the consensus satisfaction of hair dryer form design in genetic optimization 2nd and 9th are higher than 0.8. When users are stimulated by like and dislike sample pictures, there is no significant difference in the average response time, p=0.337>0.05, and the difference in the average response time of the users is more significant p=0.020

With the increasing degree of vehicle intelligence, unmanned vehicles have been widely used in civilian and military fields, which is of research value. In this paper, considering the vehicle dynamics constraints and the efficiency of the algorithm calculation to improve the DWA algorithm for the path of the self-driving vehicle, taking the intelligent vehicle node as the center of the circle and the sensor detection distance as the radius to extract the local map, combining the improved A* algorithm to fuse the DWA algorithm to carry out the local path planning at the key points, and through the design of the simulation experiments in the static and dynamic environments, the results show that, in the static environment of the simulation experiments The results show that in the static environment, the changes of the swing angle of the three vehicles fluctuate between -3 and 4, and the changes of the lateral speed of the vehicles fluctuate between -0.06 and 0.08, which are within a reasonable range of changes and satisfy the safety requirements. In the dynamic environment simulation experiments, the curve amplitude of the curvature similarity evaluation function in the improved algorithm is 40% less than that in the traditional algorithm, the number of iterations is 240 times less, and the car can reach the end point faster. This research can improve path planning accuracy, dynamic obstacle avoidance ability, and better path planning effect, which can be applied in the field of intelligent vehicles.

In recent years, the physical fitness of college students has been declining year by year, which has become the focus of national concern. In this paper, firstly, the human body motion tracking based on a multi-objective optimization algorithm is applied in the auxiliary training of college students’ sports to provide data support for the formulation of sports plans, and the Chebyshev function evolution calculation is used to obtain the Pareto optimal solution for sports training. Secondly, the similarity function between the two-dimensional projection of the skeleton and the silhouette of the image is established in the constructed human body model so as to calculate the multi-objective optimization function. The optimized training plan was specifically analyzed after analyzing the sports assessment of college students in X school. The results show that compared with the conventional training plan, the optimized training plan has more sports load intensity indexes distributed between 1.5 and 2.0, indicating that the plan is more scientific and effective. The research presented in this paper can be a valuable resource for the creation of sports programs for college students.

In the actual teaching of English translation, problems such as the disconnection of theory and practice and the insufficient perfection of the teaching system have emerged, which greatly affect the development of practical activities of English translation teaching in colleges and universities. This paper establishes the English translation teaching system based on the CIPP evaluation model, and to ensure the objectivity of the weights of evaluation indexes, the weights of the evaluation indexes are solved by cluster search algorithm, and the process of solving the index weights is optimized by using genetic algorithm. Taking ten universities in the university city of S province as the object of investigation, the corresponding questionnaires are designed to obtain the evaluation data, and the quality of English translation teaching is graded comprehensively evaluated, and analyzed through the fuzzy comprehensive evaluation model. The results show that: in the process of constructing the English translation teaching system in colleges and universities, the weight value of the teaching objectives reaches 0.2747, and the weight value of the implementation of the teaching links in the teaching process is the highest at 0.0493, and the use of the fuzzy comprehensive evaluation model can carry out a comprehensive evaluation of the quality of English translation teaching. The English translation teaching system of colleges and universities constructed based on CIPP evaluation model can help colleges and universities to find out the problems of English translation teaching and carry out innovative reforms in a targeted way, to improve the practical power of English translation teaching.

China’s modern cultural industry faces difficulties in tax collection and high pressure on expenditure; in order to solve such problems, this paper constructs a modern cultural industry tax model based on Lasso regression algorithm to promote the development of modern cultural industry. In order to further study the relationship between economic factors and the tax revenue of the modern culture industry, the relevant data on China’s tax revenue between 2000 and 2021 are selected, and 12 economic factors affecting the tax revenue of the modern culture industry are screened by combining the least squares method, Lasso regression algorithm and linear regression model. After the screening of indicator variables, according to the linear regression theory, the relationship between the key economic factors screened out by Lasso regression algorithm and the fiscal revenues is estimated by fitting and tested for normality, and the modern culture industry tax revenue model based on Lasso regression algorithm is constructed. Based on the tax revenue of the modern cultural industry between 2000 and 2021, the Lasso regression algorithm is used to analyze the modern cultural industry tax revenue. Examples are used to analyze the results. The results show that the tax revenue of the culture industry in 2020 is obtained as 208, 988, 838.42 billion yuan, and the tax revenue of the culture industry in a province in 2021 is 221, 794, 675 billion yuan, and its growth rate is 6.13%, which indicates that the Lasso regression algorithm is able to extract the information contained in the tax revenue of the modern culture industry well, and the coefficients of the parameter part are also in line with the actual tax situation coincides with the actual tax situation. Through the innovation of tax management structures and theoretical optimization, this study aims to promote the healthy and rapid development of modern cultural industries.

International students are a bridge between Chinese and foreign cultures, but they still face multiple dilemmas in Chinese cultural communication due to different cultural backgrounds and values. In this paper, we utilize the subsumption sorting algorithm to sort the amount of cultural communication of international students’ exchanges, which is dynamically switched by a combination of two methods: back-block forward interpolation and header exchange. The D-S monopolistic competition model is used to construct the theoretical model of international student exchange that affects China’s international cultural communication power. The CES utility function is used to construct China’s international cultural communication network, which calculates the total amount of communication culture of cross-cultural exchanges between international students. In the end, an analysis of 85 international student samples revealed a correlation between international student exchanges and China’s international cultural communication. The results show that the correlation coefficient between international student exchanges and China’s international cultural communication is 0.305 p > 0.05, indicating that international student exchanges have a positive promotion effect on China’s international cultural communication. This study examines the general law of international cultural communication, which is crucial in promoting Chinese culture worldwide.

This paper applies the emotion extraction method based on emotion lexicon to the group emotion analysis of the information system, combines the vector space model to process the text emotion in the information system, expresses the emotion in the form of vectors, and divides the different types of emotion according to the distance between the emotion vectors for identification. The five-level index system in fuzzy mathematics is chosen to measure the value of emotional intensity, and by analyzing the emotional state of the group in the information leakage incident, a decision in line with the user’s emotion is made based on the emotion of the information system security. Accordingly, the security defense index of the information system is improved according to the information security risk index. The results show that in identifying the emotions of the information system security events, the group’s emotions are mainly biased towards the negative. The proportion of negative emotions is the largest of 98%, which indicates that attention should be paid to the confidentiality of the user group’s information in the security of the information system. The maximum security event risk value in the evaluation in the information system is in the T8 period, with a value of 0.819, indicating that the security defense of the information system should be strengthened in the T8 period.

We initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence of the ergodic averages for integrable functions can be arbitrarily slow (Krengel Monatshefte Für Mathematik 86, 3–6 1978). In contrast, we show that for a class of PSPACE L1 functions, and a class of PSPACE computable measure-preserving ergodic transformations, the ergodic average exists and is equal to the space average on every EXP random. We establish a partial converse that PSPACE non-randomness can be characterized as non-convergence of ergodic averages. Further, we prove that there is a class of resource-bounded randoms, viz. SUBEXP-space randoms, on which the corresponding ergodic theorem has an exact converse - a point x is SUBEXP-space random if and only if the corresponding effective ergodic theorem holds for x. [ABSTRACT FROM AUTHOR]

We apply Context-free Grammars (CFG) to measure the structural information content of a symbolic music string. CFGs are appropriate to this domain because they highlight hierarchical patterns, and their dictionary of rules can be used for compression. We adapt this approach to estimate the conditional Kolmogorov complexity of a string with a concise CFG of another string. Thus, a related string may be compressed with the production rules for the first string. We then define an information distance between two symbolic music strings, and show that this measure can separate genres, composers and musical styles. Next, we adapt our approach to a model-selection problem, expressing the model as a CFG with restricted size, generated from a set of representative strings. We show that a well-generated CFG for a composer identifies characteristic patterns that can significantly compress other pieces from the same composer, while not being useful on pieces from different composers. We identify further opportunities of this approach, including using CFGs for generating new music in the style of a composer. [ABSTRACT FROM AUTHOR]

Recently, a connection has been established between two branches of computability theory, namely between algorithmic randomness and algorithmic learning theory. Learning-theoretical characterizations of several notions of randomness were discovered. We study such characterizations based on the asymptotic density of positive answers. In particular, this note provides a new learning-theoretic definition of weak 2-randomness, solving the problem posed by (Zaffora Blando, Rev. Symb. Log. 2019). The note also highlights the close connection between these characterizations and the problem of convergence on random sequences. [ABSTRACT FROM AUTHOR]

Numerous learning tasks can be described as the process of extrapolating patterns from observed data. One of the driving intuitions behind the theory of algorithmic randomness is that randomness amounts to the absence of any effectively detectable patterns: it is thus natural to regard randomness as antithetical to inductive learning. Osherson and Weinstein [11] draw upon the identification of randomness with unlearnability to introduce a learning-theoretic framework (in the spirit of formal learning theory) for modelling algorithmic randomness. They define two success criteria—specifying under what conditions a pattern may be said to have been detected by a computable learning function—and prove that the collections of data sequences on which these criteria cannot be satisfied correspond to the set of weak 1-randoms and the set of weak 2-randoms, respectively. This learning-theoretic approach affords an intuitive perspective on algorithmic randomness, and it invites the question of whether restricting attention to learning-theoretic success criteria comes at an expressivity cost. In other words, is the framework expressive enough to capture most core algorithmic randomness notions and, in particular, Martin-Löf randomness—arguably, the most prominent algorithmic randomness notion in the literature? In this article, we answer the latter question in the affirmative by providing a learning-theoretic characterisation of Martin-Löf randomness. We then show that Schnorr randomness, another central algorithmic randomness notion, also admits a learning-theoretic characterisation in this setting. [ABSTRACT FROM AUTHOR]

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({Xn} \right)} $ 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 $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left(X \right)\,{\rm{d}}X$ 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 ${\rm{\hat{\Omega }}}\left(X \right) \oplus X{ \ge _T}\emptyset \prime$ 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 $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left(X \right)$ ; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left(X \right)$ is rational. [ABSTRACT FROM AUTHOR]

We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$ -random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C -incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal. [ABSTRACT FROM AUTHOR]

We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α , while ensuring that the sequences that inductively witness R 's rank are all Martin-Löf random with respect to a single countably supported and computable measure. This is a strengthening for random degrees of a recent result of Downey, Wu, and Yang, and can be understood as a randomized version of it. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The proofs of Kleene, Chaitin and Boolos for Gödel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incompleteness theorem has the Rosser property when the independence of the true but unprovable sentence can be shown by assuming only the (simple) consistency of the theory. It is known that Gödel's own proof for his incompleteness theorem does not have the Rosser property, and we show that neither do Kleene's or Boolos' proofs. However, we show that a variant of Chaitin's proof can have the Rosser property. The proofs of Gödel, Rosser and Kleene are constructive in the sense that they explicitly construct, by algorithmic ways, the independent sentence(s) from the theory. We show that the proofs of Chaitin and Boolos are not constructive, and they prove only the mere existence of the independent sentences. [ABSTRACT FROM AUTHOR]

The article discusses randomness via infinite computation and effective descriptive set theory. It discusses a study on randomness beyond Π11-randomness and its Martin-Löf type variant. It focuses on a class strictly between Π1 1 and Σ1 2 that is given by the infinite time Turing machines (ITTMs). Results include mutual randoms not sharing information and that a version of van Lambalgen's theorem holds, and an analogue to a theorem of Sacks.

The article discusses avoiding effective packing dimension 1 below arraynoncomputable computably enumerable (c.e.) degrees. It discusses research work showing that there is a Turing degree with nonzero effective packing dimension, but which does not contain any set of effective packing dimension 1. It shows the existence of such a degree below every c.e. array noncomputable degree, and hence that they occur below precisely those of the c.e. degrees which are array noncomputable.

We call a subset of an ordinal λ recognizable if it is the unique subset x of λ for which some Turing machine with ordinal time and tape and an ordinal parameter, that halts for all subsets of λ as input, halts with the final state 0. Equivalently, such a set is the unique subset x which satisfies a given Σ 1 formula in L [ x ] . We further define the recognizable closure for subsets of λ by closing under relative recognizability for subsets of λ . We prove several results about recognizable sets and their variants for other types of machines. Notably, we show the following results from large cardinals. • Recognizable sets of ordinals appear in the hierarchy of inner models at least up to the level Woodin cardinals, while computable sets are elements of L. • A subset of a countable ordinal λ is in the recognizable closure for subsets of countable ordinals if and only if it is an element of the inner model M ∞ , which is obtained by iterating the least measure of the least fine structural inner model M 1 with a Woodin cardinal through the ordinals. [ABSTRACT FROM AUTHOR]

We generalize the classical theorem by Jarnik and Besicovitch on the irrationality exponents of real numbers and Hausdorff dimension and show that the two notions are independent. For any real number a greater than or equal to 2 and any non-negative real b be less than or equal to 2 / a, we show that there is a Cantor-like set with Hausdorff dimension equal to b such that, with respect to its uniform measure, almost all real numbers have irrationality exponent equal to a. We give an analogous result relating the irrationality exponent and the effective Hausdorff dimension of individual real numbers. We prove that there is a Cantor-like set such that, with respect to its uniform measure, almost all elements in the set have effective Hausdorff dimension equal to b and irrationality exponent equal to a. In each case, we obtain the desired set as a distinguished path in a tree of Cantor sets. [ABSTRACT FROM AUTHOR]

In this paper, we prove that if a c.e. Turing degree d is non-low, then there are two left-c.e. reals β , β in d, such that, if β is wtt-reducible to a left-c.e. real α, then β is not computable Lipschitz (cl-) reducible to α. As a corollary, d contains a left-c.e. real which is not cl-reducible to any complex (wtt-complete) left-c.e. real. [ABSTRACT FROM AUTHOR]

A set A is coarsely computable with density r ∈ [ 0 , 1 ] if there is an algorithm for deciding membership in A which always gives a (possibly incorrect) answer, and which gives a correct answer with density at least r . To any Turing degree a we can assign a value Γ T ( a ) : the minimum, over all sets A in a , of the highest density at which A is coarsely computable. The closer Γ T ( a ) is to 1, the closer a is to being computable. Andrews, Cai, Diamondstone, Jockusch, and Lempp noted that Γ T can take on the values 0, 1/2, and 1, but not any values in strictly between 1/2 and 1. They asked whether the value of Γ T can be strictly between 0 and 1/2. This is the Gamma question. Replacing Turing degrees by many-one degrees, we get an analogous question, and the same arguments show that Γ m can take on the values 0, 1/2, and 1, but not any values strictly between 1/2 and 1. We will show that for any r ∈ [ 0 , 1 / 2 ] , there is an m -degree a with Γ m ( a ) = r . Thus the range of Γ m is [ 0 , 1 / 2 ] ∪ { 1 } . Benoit Monin has recently announced a solution to the Gamma question for Turing degrees. Interestingly, his solution gives the opposite answer: the only possible values of Γ T are 0, 1/2, and 1. [ABSTRACT FROM AUTHOR]

We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on 2 ω , the so-called proper sequences. Our main results are as follows: (1) We show that the initial segment complexity of a proper sequence X is bounded from below by a computable function (that is, X is complex) if and only if X is random with respect to some computable, continuous measure. (2) We prove that a uniform version of the previous result fails to hold: there is a family of complex sequences that are random with respect to a single computable measure such that for every computable, continuous measure μ , some sequence in this family fails to be random with respect to μ . (3) We show that there are proper sequences with extremely slow-growing initial segment complexity, that is, there is a proper sequence the initial segment complexity of which is infinitely often below every computable function, and even a proper sequence the initial segment complexity of which is dominated by all computable functions. (4) We prove various facts about the Turing degrees of such sequences and show that they are useful in the study of certain classes of pathological measures on 2 ω , namely diminutive measures and trivial measures. [ABSTRACT FROM AUTHOR]