A widely accepted tenet of evolutionary biology is that spontaneous mutations occur randomly with regard to their fitness effect. However, since the mutation rate varies along a genome and this variation can be subject to selection, organisms might evolve lower mutation rates at loci where mutations are most deleterious or increased rates where mutations are most needed. In fact, mechanisms of targeted hypermutation are known in organisms ranging from bacteria to humans. Here we review the main forces driving the evolution (...) of local mutation rates and identify the main limiting factors. Both targeted hyper‐ and hypomutation can evolve, although the former is restricted to loci under very frequent positive selection and the latter is severely limited by genetic drift. Nevertheless, we show how an association of repair with transcription or chromatin‐associated proteins could overcome the drift limit and lead to non‐random hypomutation along the genome in most organisms.Editor's suggested further reading in BioEssays Stress‐induced mutation via DNA breaks in Escherichia coli: A molecular mechanism with implications for evolution and medicine Abstract. (shrink)

Although we use randomness when we don’t know any better, a principle of indifference cannot be used to explain anything interesting or fundamental. For example, in thermodynamics it can be shown that the real explanatory work is being done by the Second Law, not the equal a priori probability postulate. But to explain the interesting Second Law, many physicists try to retreat to a “random explanation,” which fails. Looking at this problem from a different perspective reveals a natural solution: (...) boundary-based explanations that arguably should be viewed as no less fundamental than other physical laws. (shrink)

Infants use statistical information in their environment, as well as others’ emotional communication, to understand the intentions of social partners. However, rarely do researchers consider these two sources of social information in tandem. This study assessed 2-year-olds’ attributions of intentionality from non-random sampling events and subsequent discrete emotion reactions. Infants observed an experimenter remove five objects from either the non-random minority (18%) or random majority (82%) of a sample and express either joy, disgust, or sadness after each selection. Two-year-olds inferred (...) the experimenter’s intentionality by giving her the object that she had previously selected when she expressed joy or disgust after non-random sampling events, but not when she expressed sadness or sampled at random. These findings demonstrate that infants use both statistical regularities and discrete emotion communication to infer an agent’s intentions. In particular, the present findings show that 2-year-olds infer that an agent can intentionally select a preferred or an undesired object from a sample as a function of the discrete emotion. Implications for the development of inferring intentionality from statistical sampling events and discrete emotion communication are discussed. (shrink)

We present a model for genome evolution, comprising biologically plausible events such as transpositions inside the genome and insertions of exogenous sequences. This model attempts to formulate a minimal proposition accounting for key statistical properties of genomes, avoiding, as far as possible, unsupportable hypotheses for the remote evolutionary past. The statistical properties that are observed in genomic sequences and are reproduced by the proposed model are: (i) deviations from randomness at different length scales, measured by suitable algorithms, (ii) a (...) special form of size distribution (power law distribution) characterising different levels of genome organisation in the non‐coding, and (iii) extensive resemblance in the alternation of coding and non‐coding regions at several length scales (self‐similarity) in long genomic sequences of higher eukaryotes. BioEssays 23:647–656, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

We show a number of improvements in the use of Hidden Conditional Random Fields for phone classification on the TIMIT and Switchboard corpora. We first show that the use of regularization effectively prevents overfitting, improving over other methods such as early stopping. We then show that HCRFs are able to make use of non-independent features in phone classification, at least with small numbers of mixture components, while HMMs degrade due to their strong independence assumptions. Finally, we successfully apply Maximum a (...) Posteriori adaptation to HCRFs, decreasing the phone classification error rate in the Switchboard corpus by around 1% – 5% given only small amounts of adaptation data. (shrink)

Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanicism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems (...) is usually provided in terms of their mathematical properties, and not in mechanistic terms. They have intensively studied the explanation of the properties of ecosystems that behave following the rules of a non-random network. However, no attention has been devoted to the study of the nature of the explanation in those that form a random network. In this paper, we cover that gap by analysing the explanation of the stability behaviour of the microbiome recently elaborated by Coyte and colleagues, to determine whether it fits with the model of explanation suggested by the new-mechanist or by the defenders of mathematical explanation. Our analysis of this case study supports three theses: (1) that the explanation is not given solely in terms of mechanisms, as the new-mechanists understand the concept; (2) that the mathematical properties that describe the system play an essential explanatory role, but they do not exhaust the explanation; (3) that a non-previously identified appeal to the type of interactions that the entities in the network can exhibit, as well as their abundance, is also necessary for Coyte and colleagues’ account to be fully explanatory. From the combination of these three theses we argue for the necessity of an integrative pluralist view of the nature of behaviour explanation when this is given by appealing to the existence of a random network. (shrink)

This research note challenges the idea that Random Somatic Mutations are entirely random, highlighting their non-equiprobable nature and their influence on evolution, involution, or indeterminacy. It recalls the Neutrosophic Theory of Evolution, extending Darwin’s theory, and emphasizes the importance of distinguishing between different senses of ‘random mutation’ in evolutionary theory.

We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated (...) solutions to issues in the Humean best-system account. On both notions, we have a much tighter connection between probabilistic laws and their corresponding sets of possible worlds. Certain histories permitted by traditional probabilistic laws are ruled out as physically impossible. As a result, such laws avoid one variety of empirical underdetermination, but the approach reveals other varieties of underdetermination that are typically overlooked. (shrink)

Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr random but not Martin-Löf (...) random, and provide a new characterization of Schnorr random real numbers in terms of prefix-free machines. We prove that unlike Martin-Löf random c.e. reals, not all Schnorr random c.e. reals are Turing complete, though all are in high Turing degrees. We use the machine characterization to define a notion of "Schnorr reducibility" which allows us to calibrate the Schnorr complexity of reals. We define the class of "Schnorr trivial" reals, which are ones whose initial segment complexity is identical with the computable reals, and demonstrate that this class has non-computable members. (shrink)

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...) and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

Introduction: Falls are the leading cause of fatal and nonfatal injuries among older adults. Studies showed that older adults can reduce the risk of falls after participation in an unexpected perturbation-based balance training, a relatively novel approach that challenged reactive balance control. This study aims to investigate the effect of the practice schedule on reactive balance function and its transfer to proactive balance function. Our primary hypothesis is that improvements in reactive balance control following block PBBT will be not inferior (...) to the improvements following random PBBT.Methods and Analysis: This is a double-blind randomized controlled trial. Fifty community-dwelling older adults will be recruited and randomly allocated to a random PBBT group or a block PBBT group. The random PBBT group will receive eight training sessions over 4 weeks that include unexpected machine-induced perturbations of balance during hands-free treadmill walking. The block PBBT group will be trained by the same perturbation treadmill system, but only one direction will be trained in each training session, and the direction of the external perturbations will be announced. Both PBBT groups will receive a similar perturbation intensity during training, the same training period, and the same concurrent cognitive tasks during training. The generalization and transfer of learning effects will be measured by assessing the reactive and proactive balance control during standing and walking before and after 1 month of PBBT, for example, step and multiple steps and fall thresholds, Berg balance test, and fear of falls. The dependent variable will be rank transformed prior to conducting the analysis of covariance to allow for nonparametric analysis.Discussion: This research will explore which of the balance retraining paradigms is more effective to improve reactive balance and proactive balance control in older adults over 1 month. The research will address key issues concerning balance retraining: older adults’ neuromotor capacities to optimize training responses and their applicability to real-life challenges.Clinical Trial Registration: Helsinki research ethics approval has been received. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

We explore the ability to distinguish random from non-random events. Randomness is defined in terms of radioactive decay whereas non-randomness is quantified by excess repetitions (“repeat”) or alternations (“switch”) between successive bits. In the first four experiments no mention was made of randomness, probability, or related concepts in task instructions. We found superior performance in distinguishing random stimuli from repeat stimuli compared to switch stimuli. The last three experiments explicitly evoked the concept of randomness, thus allowing (...) comparison of perceptual and conceptual performance. The ability to identify random events from switch distracters was inferior to the ability to discriminate random from switch stimuli. In contrast, for repeat stimuli the concept of randomness appears to roughly coincide with perceptual discriminability. Finally, the ability to identify or produce stimuli as random did not co-vary with the ability to discriminate random from non-random stimuli. (shrink)

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is (...) always positive (non zero).A “functional” formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers. (shrink)

This essay explores quantum physics and theology to propose that ontological randomness does not exist, but divine Providence does. Some interpretations of quantum physics that involve mathematical formalism and observational phenomenology are deterministic (de Broglie-Bohm, many-worlds, cosmological, time-symmetric, many-minds), while others are non-deterministic (Copenhagen, stochastic, objective collapse, transactional). Yet, quantum events are merely epistemically indeterminable by us, but actually do have a fundamental cause. Compatibilism best describes the teaching of the Bible. Humans possess free agency, and are determined by (...) their desires and values. Hence, they can be said to have “free will,” because they do what they want. The fundamental cause, as understood by Compatibilism, is God’s Providence, defined as God’s continual involvement with creation through keeping it existing, cooperating with creation in every action, and directing it to fulfill His purposes. The interaction between quantum physics and Providence suggests methodological parallels between science and theology in a quest for synthesis. (shrink)

We compare various notions of algorithmic randomness. First we consider relativized randomness. A set is n-random if it is Martin-Löf random relative to ∅. We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C ≥ |x|-c. The ‘only if' direction was obtained independently by Joseph Miller. This characterization can be extended to the case of time-bounded C-complexity. Next we prove (...) some results on lowness. Among other things, we characterize the 2-random sets as those 1-random sets that are low for Chaitin's Ω. Also, 2-random sets form minimal pairs with 2-generic sets. The r.e. low for Ω sets coincide with the r.e. K-trivial ones. Finally we show that the notions of Martin-Löf randomness, recursive randomness, and Schnorr randomness can be separated in every high degree while the same notions coincide in every non-high degree. We make some remarks about hyperimmune-free and PA-complete degrees. (shrink)

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 \(\Delta ^0_2\) -degree contains an NCR element. (shrink)

Demuth tests generalize Martin-Löf tests in that one can exchange the m-th component a computably bounded number of times. A set fails a Demuth test if Z is in infinitely many final versions of the Gm. If we only allow Demuth tests such that GmGm+1 for each m, we have weak Demuth randomness.We show that a weakly Demuth random set can be high and , yet not superhigh. Next, any c.e. set Turing below a Demuth random set is strongly (...) jump-traceable.We also prove a basis theorem for non-empty classes P. It extends the Jockusch–Soare basis theorem that some member of P is computably dominated. We use the result to show that some weakly 2-random set does not compute a 2-fixed point free function. (shrink)

We investigate the question “To what extent can random reals be used as a tool to establish number theoretic facts?” Let $\text{2-\textit{RAN\/}}$ be the principle that for every real $X$ there is a real $R$ which is 2-random relative to $X$. In Section 2, we observe that the arguments of Csima and Mileti [3] can be implemented in the base theory $\text{\textit{RCA}}_0$ and so $\text{\textit{RCA}}_0+\text{2-\textit{RAN\/}}$ implies the Rainbow Ramsey Theorem. In Section 3, we show that the Rainbow Ramsey Theorem is (...) not conservative over $\text{\textit{RCA}}_0$ for arithmetic sentences. Thus, from the Csima—Mileti fact that the existence of random reals has infinitary-combinatorial consequences we can conclude that $\text{2-\textit{RAN\/}}$ has non-trivial arithmetic consequences. In Section 4, we show that $\text{2-\textit{RAN\/}}$ is conservative over $\text{\textit{RCA}}_0+\text{\textit{B\/}$\,\Sigma$}_2$ for $\Pi^1_1$-sentences. Thus, the set of first-order consequences of $\text{2-\textit{RAN\/}}$ is strictly stronger than $P^-+I\Sigma_1$ and no stronger than $P^-+\text{\textit{B\/}$\,\Sigma$}_2$. (shrink)

In this paper, we examine the pioneering research on electronic noise—the current fluctuations in electronic circuit devices due to their intrinsic physical characteristics rather than their defects—in Germany and the U.S. during the 1910s–1920s. Such research was not just another demonstration of the general randomness of the physical world Einstein’s work on Brownian motion had revealed. In contrast, we stress the importance of a particular engineering context to electronic noise studies: the motivation to design and improve high-gain thermionic-tube amplifiers (...) for radio and wired communications. Engineering scientists’ endeavors to understand electronic noise started in 1918, when Walter Schottky at Siemens formulated a theory of “shot noise,” current fluctuations owing to the random emissions of discrete electrons in a tube. Schottky’s theory was revised and experimentally tested at Siemens, General Electric, and AT&T during the 1920s, leading to the discoveries of several other types of noise and an increasing interest in the thermal fluctuations in electronic circuits. In 1925–1928, J.B. Johnson and Harry Nyquist at Bell Labs developed a theory of thermal noise for any electrical resistor at a non-zero temperature. Although these studies were initiated to chart the fundamental performance limit of electronic technology, they ended up assisting the empirical determination of individual electronic components’ characteristics. (shrink)

By pitting John Cage against Andy Warhol, Arthur Danto shows how the arts themselves were gripped by a progressive logic that aimed at only one goal: to overcome the gap between art and life. The non‐tautological reading preserves a fundamental, philosophical difference between commonplace and art objects. The semantical space accounts for the aboutness of the work and is thus the necessary condition for something to be an artwork. Together with other Pop artists, Rauschenberg transformed the Artworld, while Cage aimed (...) at a re‐enfranchisement of the commonplace. Danto writes that his Buddhist phase came to an end when he, as a philosopher, felt the need for theories. The works of Fluxus and Cage, in the end, accepted asylum within the sanctuary of the Artworld, where they became less radical, and perhaps less radical than Pop. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...) Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

According to the free energy principle, life is an “inevitable and emergent property of any random dynamical system at non-equilibrium steady state that possesses a Markov blanket” :20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly any attention. (...) Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets. (shrink)

This essay concerns Heidegger’s assertion that the biography of the poet is unimportant when interpreting great works of poetry. I approach the question in three ways. First, I consider its merits as a principle of literary interpretation and contrast Heidegger’s view with those of other Trakl interpreters. This allows me to clarify his view as a unique variety of non-formalistic interpretation and raise some potential worries about his approach. Second, I consider Heidegger’s view in the context of his broader philosophical (...) project. Viewed this way, Heidegger’s decision to neglect the poet’s biography seems quite reasonable and consistent with his inquiry into the being of language. Finally, I consider Heidegger’s suggestion that Trakl is a kind of mad genius. I recast this paradigmatic figure in terms of what I call the ‘wretched prophet’ and consider some ways in which its appeal sheds light on the crisis of modernity and the aestheticization of politics. (shrink)

We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish non-isomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? Random Structures and Algorithms 26 119–145] of (...) D)=log1/pn+O. (shrink)

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these claims are unjustified, illustrating this on the issues of (non)existence of joint distributions, probabilities of ordered events, and additivity of probabilities. The specific focus of this note is on showing that the mistakes underlying these claims can be precluded by labeling all random variables involved contextually. Moreover, contextual (...) labeling also enables a valuable additional way of analyzing probabilistic aspects of empirical situations: determining whether the random variables involved form a contextual system, in the sense generalized from quantum mechanics. Thus, to the extent the Wang-Busemeyer QQ equality for the question order effect holds, the system describing them is noncontextual. The double-slit experiment and its behavioral analogues also turn out to form a noncontextual system, having the same probabilistic format (cyclic system of rank 4) as the one describing spins of two entangled electrons. (shrink)

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL- (...) class='Hi'>randomness. Our first main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

There are two intriguing paradoxes in molecular biology-the inconsistent relationship between organismal complexity and (1) cellular DNA content and (2) the number of protein-coding genes-referred to as the C-value and G-value paradoxes, respectively. The C-value paradox may be largely explained by varying ploidy. The G-value paradox is more problematic, as the extent of protein coding sequence remains relatively static over a wide range of developmental complexity. We show by analysis of sequenced genomes that the relative amount of non-protein-coding sequence increases (...) consistently with complexity. We also show that the distribution of introns in complex organisms is non-random. Genes composed of large amounts of intronic sequence are significantly overrepresented amongst genes that are highly expressed in the nervous system, and amongst genes downregulated in embryonic stem cells and cancers. We suggest that the informational paradox in complex organisms may be explained by the expansion of cis-acting regulatory elements and genes specifying trans-acting non-protein-coding RNAs. (shrink)

The probability ranking conclusion is an extension of the absolute form evaluation conclusion. Firstly, the random simulation evaluation model is introduced; then, the general idea of converting the traditional evaluation method to the random simulation evaluation model is analyzed; on this basis, based on the rule of “further ensuring the stability of the ranking chain on the basis of increasing the possibility of the ranking chain,” two methods of solving the probability ranking conclusion are given. Based on the rule of (...) “further guaranteeing the stability of the ranking chain on the basis of improving the likelihood of the ranking chain,” two methods are given to solve the likelihood conclusion. This paper argues that this absolute form of conclusion hinders the approximation of the theory to the essence of the actual problem and is an important reason for the problem of “non-consistency of multi-evaluation conclusions.” To address this problem, a stochastic simulation-based comprehensive evaluation solution algorithm based on the idea of “Monte Carlo simulation” is proposed, and the corresponding ranking method is investigated, which is characterized by generating evaluation conclusions with probability information, and thus has more advantages than the absolute conclusion form in terms of problem interpretability. The method is characterized by the generation of evaluation conclusions with probabilistic information and thus has more advantages than the absolute conclusion form in terms of problem interpretation. Because of the independence of the stochastic simulation solution method, it is applied to the “bottom-up” evaluation model as an example, and a novel autonomous evaluation method is constructed. Finally, the application of the stochastic simulation evaluation model is illustrated by an example and compared with the absolute form evaluation. The evaluation model is an extension of the traditional evaluation model, which can further broaden the practical application of comprehensive evaluation theory. (shrink)

We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr random (...) reals. We show that Low(ML, Kurtz) coincides with the non-DNR degrees, while both Low(CR, Kurtz) and Low(Schnorr, Kurtz) are exactly the non-high, non-DNR degrees. (shrink)

Let f be a computable function from finite sequences of 0ʼs and 1ʼs to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also prove: if X is strongly f-random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f-random relative to Z. In addition, we prove analogous propagation results for other notions of partial randomness, including non-K-triviality and autocomplexity. We prove that f- (...) class='Hi'>randomness relative to a PA-degree implies strong f-randomness, hence f-randomness does not imply f-randomness relative to a PA-degree. (shrink)

This essay concerns Heidegger’s assertion that the biography of the poet is unimportant when interpreting great works of poetry. I approach the question in three ways. First, I consider its merits as a principle of literary interpretation and contrast Heidegger’s view with those of other Trakl interpreters. This allows me to clarify his view as a unique variety of non-formalistic interpretation and raise some potential worries about his approach. Second, I consider Heidegger’s view in the context of his broader philosophical (...) project. Viewed this way, Heidegger’s decision to neglect the poet’s biography seems quite reasonable and consistent with his inquiry into the being of language. Finally, I consider Heidegger’s suggestion that Trakl is a kind of mad genius. I recast this paradigmatic figure in terms of what I call the ‘wretched prophet’ and consider some ways in which its appeal sheds light on the crisis of modernity and the aestheticization of politics. (shrink)

There are two fundamental computably enumerable sets associated with any Kolmogorov complexity measure. These are the set of non-random strings and the overgraph. This paper investigates the computational power of these sets. It follows work done by Kummer, Muchnik and Positselsky, and Allender and co-authors. Muchnik and Positselsky asked whether there exists an optimal monotone machine whose overgraph is not tt-complete. This paper answers this question in the negative by proving that the overgraph of any optimal monotone machine, or any (...) optimal process machine, is tt-complete. The monotone results are shown for both descriptional complexity Km and KM, the complexity measure derived from algorithmic probability. A distinction is drawn between two definitions of process machines that exist in the literature. For one class of process machines, designated strict process machines, it is shown that there is a universal machine whose set of non-random strings is not tt-complete. (shrink)

We show that for random bit strings, Up, with probability, image, the first order quantifier depth D) needed to distinguish non-isomorphic structures is Θ, with high probability. Further, we show that, with high probability, for random ordered graphs, G≤,p with edge probability image, D)=Θ, contrasting with the results for random graphs, Gp, given by Kim et al. [J.H. Kim, O. Pikhurko, J. Spencer, O. Verbitsky, How complex are random graphs in first order logic? Random Structures and Algorithms 26 119–145] of (...) D)=log1/pn+O. (shrink)

The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables. In this paper we present general principles that justify the use of dichotomizations and determine their choice. The main idea in choosing dichotomizations is that if the set of possible values of a random variable is endowed with a pre-topology (V-space), then the allowable dichotomizations split the space (...) of possible values into two linked subsets (“linkedness” being a weak form of pre-topological connectedness). We primarily focus on two types of random variables most often encountered in practice: categorical and real-valued ones (including continuous random variables, greatly underrepresented in the contextuality literature). A categorical variable (one with a finite number of unordered values) is represented by all of its possible dichotomizations. If the values of a random variable are real numbers, then they are dichotomized by intervals above and below a variable cut point. (shrink)

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle . The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in λ . While the Hippocratic approach is in general much more restrictive, there (...) are cases where the two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Löf randomness and the measure λ is a Bernoulli measure, classical randomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity. (shrink)

We consider tautologies formed form a pseudo-random number generator, defined in Krajicek [11] and in Alekhnovich et al. [2]. We explain a strategy of proving their hardness for Extended Frege systems via a conjecture about bounded arithmetic formulated in Krajicek [11]. Further we give a purely finitary statement, in the form of a hardness condition imposed on a function, equivalent to the conjecture. This is accompanied by a brief explanation, aimed at non-specialists, of the relation between prepositional proof complexity and (...) bounded arithmetic. (shrink)