SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.

Worldwide, about one in eight people live in slums. Empirical studies based on satellite data have identified that the size distributions of this type of settlement are similar in different cities of the Global South. Based on these results, we developed a model describing the formation of slums with a Turing mechanism, in which patterns are created by diffusion-driven instability and the inherent characteristic length of the system is independent of boundary conditions. We examine the model in this paper by critically reflecting its assumptions, comparing them with recent empirical observations and discussing possible adjustments and future extensions based on new methods of identifying pattern formation mechanisms.

In this paper, I propose a test for machine self-awareness inspired by the Turing test. While my test is plain and simple, it offers a much-needed alternative to ungrounded speculation while still capturing the essence of self-awareness. I discuss how to apply the test to Large Language Models and conduct experiments on GPT-3.5 that suggest it is not self-aware. I discuss the implications of machine self-awareness and relate it to questions about meaning and understanding. Finally, I present some next steps for studying self-awareness in machines.

With the rapid development of network science, Turing pattern on complex networks has attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator-prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing pattern is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing pattern. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing pattern is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing pattern, which is not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing pattern and spatiotemporal pattern. We believe that these findings contribute to a better understanding of self-organization on complex networks.

Knowledge processing is an important feature of intelligence in general and artificial intelligence in particular. To develop computing systems working with knowledge, it is necessary to elaborate means of working with knowledge representations (as opposed to data) because knowledge is an abstract structure. There are different forms of knowledge representations derived from data. One of the basic forms is called a schema. The goal of this paper is the development of theoretical and practical tools for processing schemas. To achieve this goal, we use schema representations elaborated in the mathematical theory of schemas and use structural machine as a powerful theoretical tool for modeling parallel and concurrent computational processes. We describe the schema of autopoietic machines as physical realizations of structural machines. An autopoietic Machine is a technical system capable of regenerating, reproducing and maintaining itself by production, transformation and destruction of its components and the networks of processes downstream contained in them. We present the theory and practice of designing and implementing autopoietic machines as information processing structures integrating both symbolic computing and neural networks. Autopoietic machines use knowledge structures containing the behavioral evolution of the system and its interactions with the environment to maintain stability by counteracting fluctuations.

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in the small-sized sample or highly heterogeneous assemblage. Estimating species richness in a large-scale region typically involves an integrated data set consisting of subsamples collected independently from different subregions. However, the pooled sample of integrated data is no longer a random sample from the entire region, and the use of different sampling schemes results in variations in data formats. Consequently, employing a single sampling distribution to model the pooled sample becomes impractical, rendering existing richness estimators inadequate. This study theoretically explains the applicability of Chao's lower bound estimators in estimating species richness for large-scale areas using the pooled sample. Additionally, a new nonparametric estimator is introduced, which adjusts the bias of Chao's lower bound estimator by leveraging the Good-Turing frequency formula. This proposed estimator only utilizes the pooled sample's singleton, doubleton, and tripleton richness. Simulated data sets across various models are employed to demonstrate the statistical performance of the estimator, showcasing its ability to reduce bias and provide accurate 95% confidence intervals. Real data sets are also utilized to illustrate the practical application of the proposed approach.

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

This paper presents a concise exploration of the synthetic biology currently to artificially 1 create life, juxtaposed against natural life’s emergence over Earth’s 4.5-billion-year history. It explores 2 the complexities of life’s origins, sustaining factors, and the consequences of synthetic life creation, 3 addressing key scientific milestones such as the Urey-Miller experiment and Jacques Monod’s pro- 4 posals. The narrative navigates through the roles of energy, Maxwell’s demons, bifurcations, and 5 genetic information in the emergence and evolution of complex biological systems. Despite significant 6 strides in genetic engineering, the challenge of creating life from scratch persists, necessitating a deep 7 understanding of diverse scientific disciplines. While synthetic biology holds promise for medicine 8 and biotechnology, the creation of truly autonomous synthetic life forms raises ethical concerns. The 9 paper also stresses the imperative for careful ethical evaluation of the societal and environmental 10 implications arising from these advancements.

Scientists are gradually becoming aware of the challenges in the understanding of the very root mechanisms of massively parallel computations that are observed in literally all scientific disciplines ranging from cosmology, physics, across chemistry, biochemistry, and ending in biology. This leads us to the main motivation and simultaneously to the central thesis of this review: “Can we design artificial, massively-parallel, self-organized, emergent, error-resilient, computational environments?” A large number of simulations along with examples and counter-examples, finalized by a list of the future directions, are giving hints and partial answers to the main thesis. This all together is opening the crucial question whether there is existing a deeper, beyond the Turing machine theoretical description of massively-parallel computing. Important information dealing with this topic is reviewed along with highly expressive animations generated by the open-source, Python software GoL-N24. The perspective, future directions including applications in robotics and biology of this research are discussed in the light of known information.

Inferring algorithmic structure in data is essential for discovering causal generative models. In this research, we present a quantum computing framework using the circuit model, for estimating algorithmic information metrics. The canonical computation model of the Turing machine is restricted in time and space resources, to make the target metrics computable under realistic assumptions. The universal prior distribution for the automata is obtained as a quantum superposition, which is further conditioned to estimate the metrics. Specific cases are explored where the quantum implementation offers polynomial advantage, in contrast to an indispensable exhaustive enumeration in the corresponding classical case. The unstructured output data and the computational irreducibility of Turing machines make this algorithm impossible to approximate using heuristics. Thus, exploring the space of program-output relations is one of the most promising problems for demonstrating quantum supremacy using Grover search that cannot be dequantized. Experimental use cases for quantum acceleration are developed for self-replicating programs and algorithmic complexity of short strings. With quantum computing hardware rapidly attaining technological maturity, we discuss how this framework will have significant advantage for various genomics applications in meta-biology, phylogenetic tree analysis, protein-protein interaction mapping and synthetic biology. This is the first time experimental algorithmic information theory is implemented using quantum computation. Our implementation on the Qiskit quantum programming platform is copy-left and can be found on https://github.com/Advanced-Research-Centre/QPULBA

We define computable functions $g,h:$ $\mathbb N$ $\setminus \{0\} \to$ $\mathbb N$ $\setminus \{0\}$. For an integer $n \geqslant 3$, let $\Psi_n$ denote the following statement: if a system ${\mathcal S} \subseteq \Bigl\{x_i!=x_k: (i,k \in \{1,\ldots,n\}) \wedge (i \neq k)\Bigr\} \cup \Bigl\{x_i \cdot x_j=x_k: i,j,k \in \{1,\ldots,n\}\Bigr\}$ has only finitely many solutions in positive integers $x_1,\ldots,x_n$, then each such solution $(x_1,\ldots,x_n)$ satisfies $x_1,\ldots,x_n \leqslant g(n)$. For a positive integer $n$, let $\Gamma_n$ denote the following statement: if a system $S \subseteq \Bigl\{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\Bigr\} \cup \Bigl\{2^{\textstyle 2^{\textstyle x_i}}=x_k:~i,k \in \{1,\ldots,n\}\Bigr\}$ has only finitely many solutions in positive integers $x_1,\ldots,x_n$, then each such solution $(x_1,\ldots,x_n)$ satisfies $x_1,\ldots,x_n \leqslant h(n)$. We prove: (1) if the equation $x!+1=y^2$ has only finitely many solutions in positive integers, then the statement $\Psi_6$ guarantees that each such solution $(x,y)$ belongs to the set $\{(4,5),(5,11),(7,71)\}$, (2) the statement $\Psi_9$ proves the following implication: if there exists a positive integer $x$ such that $x^2+1$ is prime and $x^2+1>g(7)$, then there are infinitely many primes of the form $n^2+1$, (3) the statement $\Psi_9$ proves the following implication: if there exists an integer $x \geqslant g(6)$ such that $x!+1$ is prime, then there are infinitely many primes of the form $n!+1$, (4) the statement $\Psi_{16}$ proves the following implication: if there exists a twin prime greater than $g(14)$, then there are infinitely many twin primes, {\bf (5)}~the statement $\Gamma_{13}$ proves the following implication: if $n \in$ $\mathbb N$ $\setminus \{0\}$ and $2^{\textstyle 2^{\textstyle n}}+1$ is composite and greater than $h(12)$, then $2^{\textstyle 2^{\textstyle n}}+1$ is composite for infinitely many positive integers $n$.