kolmogorov complexity
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2022 ◽  
Vol 8 ◽  
Author(s):  
Bin Wang ◽  
Xiong Han ◽  
Zongya Zhao ◽  
Na Wang ◽  
Pan Zhao ◽  
...  

Objective: Antiseizure medicine (ASM) is the first choice for patients with epilepsy. The choice of ASM is determined by the type of epilepsy or epileptic syndrome, which may not be suitable for certain patients. This initial choice of a particular drug affects the long-term prognosis of patients, so it is critical to select the appropriate ASMs based on the individual characteristics of a patient at the early stage of the disease. The purpose of this study is to develop a personalized prediction model to predict the probability of achieving seizure control in patients with focal epilepsy, which will help in providing a more precise initial medication to patients.Methods: Based on response to oxcarbazepine (OXC), enrolled patients were divided into two groups: seizure-free (52 patients), not seizure-free (NSF) (22 patients). We created models to predict patients' response to OXC monotherapy by combining Electroencephalogram (EEG) complexities and 15 clinical features. The prediction models were gradient boosting decision tree-Kolmogorov complexity (GBDT-KC) and gradient boosting decision tree-Lempel-Ziv complexity (GBDT-LZC). We also constructed two additional prediction models, support vector machine-Kolmogorov complexity (SVM-KC) and SVM-LZC, and these two models were compared with the GBDT models. The performance of the models was evaluated by calculating the accuracy, precision, recall, F1-score, sensitivity, specificity, and area under the curve (AUC) of these models.Results: The mean accuracy, precision, recall, F1-score, sensitivity, specificity, AUC of GBDT-LZC model after five-fold cross-validation were 81%, 84%, 91%, 87%, 91%, 64%, 81%, respectively. The average accuracy, precision, recall, F1-score, sensitivity, specificity, AUC of GBDT-KC model with five-fold cross-validation were 82%, 84%, 92%, 88%, 83%, 92%, 83%, respectively. We used the rank of absolute weights to separately calculate the features that have the most significant impact on the classification of the two models.Conclusion: (1) The GBDT-KC model has the potential to be used in the clinic to predict seizure-free with OXC monotherapy. (2). Electroencephalogram complexity, especially Kolmogorov complexity (KC) may be a potential biomarker in predicting the treatment efficacy of OXC in newly diagnosed patients with focal epilepsy.


2021 ◽  
Vol 52 (4) ◽  
pp. 31-54
Author(s):  
Andrei Romashchenko ◽  
Alexander Shen ◽  
Marius Zimand

This formula can be informally read as follows: the ith messagemi brings us log(1=pi) "bits of information" (whatever this means), and appears with frequency pi, so H is the expected amount of information provided by one random message (one sample of the random variable). Moreover, we can construct an optimal uniquely decodable code that requires about H (at most H + 1, to be exact) bits per message on average, and it encodes the ith message by approximately log(1=pi) bits, following the natural idea to use short codewords for frequent messages. This fits well the informal reading of the formula given above, and it is tempting to say that the ith message "contains log(1=pi) bits of information." Shannon himself succumbed to this temptation [46, p. 399] when he wrote about entropy estimates and considers Basic English and James Joyces's book "Finnegan's Wake" as two extreme examples of high and low redundancy in English texts. But, strictly speaking, one can speak only of entropies of random variables, not of their individual values, and "Finnegan's Wake" is not a random variable, just a specific string. Can we define the amount of information in individual objects?


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1654
Author(s):  
Tiasa Mondol ◽  
Daniel G. Brown

We build an analysis based on the Algorithmic Information Theory of computational creativity and extend it to revisit computational aesthetics, thereby, improving on the existing efforts of its formulation. We discuss Kolmogorov complexity, models and randomness deficiency (which is a measure of how much a model falls short of capturing the regularities in an artifact) and show that the notions of typicality and novelty of a creative artifact follow naturally from such definitions. Other exciting formalizations of aesthetic measures include logical depth and sophistication with which we can define, respectively, the value and creator’s artistry present in a creative work. We then look at some related research that combines information theory and creativity and analyze them with the algorithmic tools that we develop throughout the paper. Finally, we assemble the ideas and their algorithmic counterparts to complete an algorithmic information theoretic recipe for computational creativity and aesthetics.


Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 334
Author(s):  
Marius Zimand

It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. However, is it possible to construct a few strings, no longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that takes as input a string x of length n and returns a list with O(n2) strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n−loglogn−O(1). We also present an algorithm that obtains a list of quasi-polynomial size in which each element can be produced in polynomial time.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1604
Author(s):  
Amirmohammad Farzaneh ◽  
Justin P. Coon ◽  
Mihai-Alin Badiu

Throughout the years, measuring the complexity of networks and graphs has been of great interest to scientists. The Kolmogorov complexity is known as one of the most important tools to measure the complexity of an object. We formalized a method to calculate an upper bound for the Kolmogorov complexity of graphs and networks. Firstly, the most simple graphs possible, those with O(1) Kolmogorov complexity, were identified. These graphs were then used to develop a method to estimate the complexity of a given graph. The proposed method utilizes the simple structures within a graph to capture its non-randomness. This method is able to capture features that make a network closer to the more non-random end of the spectrum. The resulting algorithm takes a graph as an input and outputs an upper bound to its Kolmogorov complexity. This could be applicable in, for example evaluating the performances of graph compression methods.


2021 ◽  
Vol 12 ◽  
Author(s):  
András Kornai

Neither linguistics nor psychology offers a single, unified notion of simplicity, and therefore the simplest “core” layer of vocabulary is hard to define in theory and hard to pinpoint in practice. In section 1 we briefly survey the main approaches, and distinguish two that are highly relevant to lexicography: we will call these common and basic. In sections 2 and 3 we compare these approaches, and in section 4 we point the reader to Kolmogorov complexity, unfamiliar as it may be to most working psychologists, lexicographers, and educators, as the best formal means to deal with core vocabulary.


Author(s):  
Songsong Dai

In this paper, we give a definition for quantum information distance. In the classical setting, information distance between two classical strings is developed based on classical Kolmogorov complexity. It is defined as the length of a shortest transition program between these two strings in a universal Turing machine. We define the quantum information distance based on Berthiaume et al.’s quantum Kolmogorov complexity. The quantum information distance between qubit strings is defined as the length of the shortest quantum transition program between these two qubit strings in a universal quantum Turing machine. We show that our definition of quantum information distance is invariant under the choice of the underlying quantum Turing machine.


Computability ◽  
2021 ◽  
pp. 1-28
Author(s):  
Neil Lutz ◽  
D.M. Stull

This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp ( L ) is the set of all effective Hausdorff dimensions of individual points on L. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff dimension dim ( a , b ) is equal to the effective packing dimension Dim ( a , b ), then sp ( L ) contains a unit interval. We also show that, if the dimension dim ( a , b ) is at least one, then sp ( L ) is infinite. Together with previous work, this implies that the dimension spectrum of any line is infinite.


2021 ◽  
Vol 13 (3) ◽  
pp. 1-15
Author(s):  
Neil Lutz

Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that two prominent, fundamental results about the dimension of Borel or analytic sets also hold for arbitrary sets.


10.53733/148 ◽  
2021 ◽  
Vol 52 ◽  
pp. 585-604
Author(s):  
Eric Allender

We survey recent developments related to the Minimum Circuit Size Problem and time-bounded Kolmogorov Complexity.


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