Probabilistic Arguments Research Articles

Does fine-tuning support the existence of a multiverse?

Abstract In the context of the probabilistic fine-tuning argument for the existence of a divine designer, appeals to the existence of a multiverse have often seemed ad hoc. The situation is rather different though if there is independent evidence from physics for a multiverse. This paper argues that the fate of the fine-tuning argument depends on open questions in fundamental physics and cosmology. It also argues that the many-worlds interpretation of quantum mechanics opens up new routes to undercutting the force of the fine-tuning argument.

Eta-Earth Revisited I: A Formula for Estimating the Maximum Number of Earth-Like Habitats.

In this hypothesis article, we discuss the basic requirements of planetary environments where aerobe organisms can grow and survive, including atmospheric limitations of millimeter-to-meter-sized biological animal life based on physical limits and O2, N2, and CO2 toxicity levels. By assuming that animal-like extraterrestrial organisms adhere to similar limits, we define Earth-like habitats (EH) as rocky exoplanets in the habitable zone for complex life that host N2-O2-dominated atmospheres with minor amounts of CO2, at which advanced animal-like life or potentially even extraterrestrial intelligent life can in principle evolve and exist. We then derive a new formula that can be used to estimate the maximum occurrence rate of such Earth-like habitats in the Galaxy. This contains realistic probabilistic arguments that can be fine-tuned and constrained by atmospheric characterization with future space and ground-based telescopes. As an example, we briefly discuss two specific requirements feeding into our new formula that, although not quantifiable at present, will become scientifically quantifiable in the upcoming decades due to future observations of exoplanets and their atmospheres. Key Words: Eta-Earth-Earth-like habitats-oxygenation time-nitrogen atmospheres-carbon dioxide-animal-like life. Astrobiology 24, 897-915.

Everettian quantum mechanics and the ghost of fission

Abstract Arguments from fission cases, most notably made by Parfit, have historically been utilized in discussions of Everettian quantum mechanics (EQM) in an attempt to illuminate details of familiar accounts in which an agent ‘splits’. Whilst such imagery is often seen as an innocuous depiction of Everett's theory, it is in fact a poisoned chalice. I argue firstly that the fission case analogy is responsible for the conceptual foundations of probability arguments in EQM and secondly, following a number of disanalogies between fission cases and Everettian branching, I argue that the analogy is unfounded. I conclude that much of the discussion of the probability problem over the past 20 years has been predicated on a problematic analogy and its effects are still apparent today.

On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems

We consider a class of time-inhomogeneous optimal stopping problems and we provide sufficient conditions on the data of the problem that guarantee monotonicity of the optimal stopping boundary. In our setting, time-inhomogeneity stems not only from the reward function but, in particular, from the time dependence of the drift coefficient of the one-dimensional stochastic differential equation (SDE) which drives the stopping problem. In order to obtain our results, we mostly employ probabilistic arguments: we use a comparison principle between solutions of the SDE computed at different starting times, and martingale methods of optimal stopping theory. We also show a variant of the main theorem, which weakens one of the assumptions and additionally relies on the renowned connection between optimal stopping and free-boundary problems.

Logarithmic correlation functions in 2D critical percolation

It is believed that the large-scale geometric properties of two-dimensional critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. We study several logarithmic correlation functions for critical percolation in the bulk and in the presence of a boundary, including the four-point function of the density (spin) field. Our analysis confirms previous findings, provides new explicit calculations and explains, in terms of lattice observables, the physical mechanism that leads to the logarithmic singularities we discover. Although we adopt conformal field theory (CFT) terminology to present our results, the core of our analysis relies on probabilistic arguments and recent rigorous results on the scaling limit of critical percolation and does not assume a priori the existence of a percolation CFT. As a consequence, our results provide strong support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of two-dimensional critical percolation.

Indexicality, Bayesian background and self‐location in fine‐tuning arguments for the multiverse

AbstractOur universe seems to be miraculously fine‐tuned for life. Multiverse theories have been proposed as an explanation for this on the basis of probabilistic arguments, but various authors have objected that we should consider our total evidence that this universe in particular has life in our inference, which would block the argument. The debate thus crucially hinges on how Bayesian background and evidence are distinguished and on how indexical or demonstrative terms are analysed. The aim of this article is to take a step back and examine these various aspects of Bayesian reasoning and how they affect the arguments. The upshot is that there are reasons to resist the fine‐tuning argument for the multiverse, but the “this‐universe‐objection” is not one of them.

Approximation of functions from Korobov spaces by shallow neural networks

In this paper, we consider the problem of approximating functions from a Korobov space on [−1,1]d by ReLU shallow neural networks and present a rate O(m−25(1+2d)log⁡m) of uniform approximation by networks of m hidden neurons. This is achieved by combining a novel Fourier analysis approach and a probability argument. We apply our approximation theory to a learning algorithm for regression based on ReLU shallow neural networks and derive learning rates of order O(N−4(d+2)9d+8log⁡N) for the excess generalization error with the sample size N when the regression function lies in the Korobov space.

Optimal exercise of American options under time-dependent Ornstein–Uhlenbeck processes

We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein–Uhlenbeck process, a diffusion often adopted by practitioners to model commodity prices and interest rates. By framing the optimal exercise of the American option as a problem of optimal stopping and relying on probabilistic arguments, we provide a non-linear Volterra-type integral equation characterizing the exercise boundary, develop a novel comparison argument to derive upper and lower bounds for such a boundary, and prove its Lipschitz continuity in any closed interval that excludes the expiration date and, thus, its differentiability almost everywhere. We implement a Picard iteration algorithm to solve the Volterra integral equation and show illustrative examples that shed light on the boundary's dependence on the process's drift and volatility.

Density and Correlation in a Random Sequential Adsorption Model

We consider the random sequential adsorption process on the one- dimensional lattice with nearest-neighbor exclusion. In this model, each site s 2 Z starts empty and a particle will be deposited in it at time ts, where (ts)s2Z is a sequence of independent random variables uniformly distributed on the interval [0; 1]. The site will be occupied if both of its neighbors are vacant. Analytical expressions for the density of occupied sites and the pair correlation function, for all time t, are well-established and have been obtained through methods such as generating functions and differential equations. In this study, we present a method based on probabilistic arguments for the calculation of these expressions.

Research repertoires and boundary work in the search for extra-terrestrial intelligence (SETI)

ABSTRACT The idea of scouting the sky in search of extra-terrestrial signals (SETI) was first proposed in the late 1950s; soon afterwards, its scope was formalised in the so-called Drake Equation, a probabilistic argument to gauge the number of ‘civilisations’ capable of radio communication on the basis of astronomical, biological and cultural factors. Since then, radio telescopes around the world have been searching for an artificial signal from elsewhere in the universe, a sign of extraterrestrial communication. How have SETI practitioners claimed scientific legitimacy and epistemic authority over the search for extra-terrestrial life, a matter often regarded to be at the very periphery of science? And how have they succeeded (or failed) in maintaining them over time? The historical trajectory of SETI offers the opportunity to investigate how, over time, an interdisciplinary community coalesced around a research repertoire and navigated ebbs and flows of interest by rearticulating the methods and scope of their research. The ‘probability repertoire’ around which the SETI community coalesced is an evolving entity, entailing significant boundary work. As with every successful repertoire, it is a flexible but always entailing a recognisable alignment of material, social and epistemic components instrumental for a research community in gaining recognition and negotiating its epistemic positioning within the always shifting boundaries of science.

An individual-level probabilistic model and solution for control of infectious diseases

<p>We present an individual-level probabilistic model to evaluate the effectiveness of two traditional control measures for infectious diseases: the isolation of symptomatic individuals and contact tracing (plus subsequent quarantine). The model allows us to calculate the reproduction number and the generation-time distribution under the two control measures. The model is related to the work of Fraser et al. on the same topic <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. In particular, we are able to provide more precise results for a disease that has two classes of infected individuals – the individuals who will remain asymptomatic throughout and the individuals who will eventually become symptomatic. Using the properties of integral operators with positive kernels, we also resolve the important theoretical issue as to why the density function of the steady-state generation time is the eigenfunction associated with the largest eigenvalue of the underlying integral operator. Moreover, the same theoretical result shows why the simple algorithm of repeated integration can find numerical solutions for virtually all initial conditions. We discuss the model's implications, especially how it enhances our understanding about the impact of asymptomatic individuals. For instance, in the special case where the infectiousness of the two classes is proportional to each other, the effects of the asymptomatic individuals can be understood by supposing that all individuals will be symptomatic but with modified infectiousness and modified efficacy of the isolation measure. The numerical results show that, out of the two measures, isolation is the more decisive one, at least for the COVID-19 parameters used in the numerical experiments.</p>

A Continuous-Time Urn Model for a System of Activated Particles

We study a system of M particles with jump dynamics on a network of N sites. The particles can exist in two states, active or inactive. Only the former can jump. The state of each particle depends on its position. A given particle is inactive when it is at a given site, and active when it moves to a change site. Indeed, each sleeping particle activates at a rate λ>0, leaves its initial site, and moves for an exponential random time of parameter μ>0 before uniformly landing at a site and immediately returning to sleep. The behavior of each particle is independent of that of the others. These dynamics conserve the total number of particles; there is no limit on the number of particles at a given site. This system can be represented by a continuous-time Pólya urn with M balls where the colors are the sites, with an additional color to account for particles on the move at a given time t. First, using this Pólya interpretation for fixed M and N, we obtain the average number of particles at each site over time and, therefore, those on the move due to mass conservation. Secondly, we consider a large system in which the number of particles M and the number of sites N grow at the same rate, so that the M/N ratio tends to a scaling constant α>0. Using the moment-generating function technique added to some probabilistic arguments, we obtain the long-term distribution of the number of particles at each site.

An Alternative View of Familial Alzheimer's Disease Genetics.

Probabilistic and parsimony-based arguments regarding available genetics data are used to propose that Hardy and Higgin's amyloid cascade hypothesis is valid but is commonly interpreted too narrowly to support, incorrectly, the primacy of the amyloid-β peptide (Aβ) in driving Alzheimer's disease pathogenesis. Instead, increased activity of the βCTF (C99) fragment of AβPP is the critical pathogenic determinant altered by mutations in the APP gene. This model is consistent with the regulation of APP mRNA translation via its 5' iron responsive element. Similar arguments support that the pathological effects of familial Alzheimer's disease mutations in the genes PSEN1 and PSEN2 are not exerted directly via changes in AβPP cleavage to produce different ratios of Aβ length. Rather, these mutations likely act through effects on presenilin holoprotein conformation and function, and possibly the formation and stability of multimers of presenilin holoprotein and/or of the γ-secretase complex. All fAD mutations in APP, PSEN1, and PSEN2 likely find unity of pathological mechanism in their actions on endolysosomal acidification and mitochondrial function, with detrimental effects on iron homeostasis and promotion of "pseudo-hypoxia" being of central importance. Aβ production is enhanced and distorted by oxidative stress and accumulates due to decreased lysosomal function. It may act as a disease-associated molecular pattern enhancing oxidative stress-driven neuroinflammation during the cognitive phase of the disease.

Beyond classical theories: An integrative mathematical model of mating dynamics and parental care.

Classical theories, such as Bateman's principle and Trivers' parental investment theory, attempted to explain the coevolution of sexual selection and parental care through simple verbal arguments. Since then, quantitative models have demonstrated that it is rarely that simple because many non-intuitive structures and non-linear relationships are actually at play. In this study, we propose a new standard for models of mating dynamics and parental care, emphasizing the clarity and use of mathematical and probabilistic arguments, the meaning of consistency conditions, and the key role of spatial densities and the law of mass action. We used adaptive dynamics to calculate the evolutionary trajectory of the total care duration. Our results clearly show how the outcomes of parental care evolution can be diverse, depending on the quantitative balance between a set of dynamical forces arising from relevant differences and conditions in the male and female populations. The intensity of sexual selection, synergy of care, care quality, and relative mortality rates during mating interactions and caring activities act as forces driving evolutionary transitions between uniparental and biparental care. Sexual selection reduces the care duration of the selected sex, uniparental care evolves in the sex that offers the higher care quality, higher mortality during mating interactions of one sex leads to more care by that sex, and higher mortality during caring activities of one sex favours the evolution of uniparental care in the other sex. Both synergy and higher overall mortality during mating interactions can stabilize biparental care when sexual selection reduces the care duration of the selected sex. We discuss how the interaction between these forces influences the evolution of care patterns, and how sex ratios can vary and be interpreted in these contexts. We also propose new directions for future developments of our integrative model, creating new comparable analyses that share the same underlying assumptions and dynamical frameworks.

Stability of polydisc slicing

AbstractWe prove a dimension‐free stability result for polydisc slicing due to Oleszkiewicz and Pełczyński. Intriguingly, compared to the real case, there is an additional asymptotic maximizer. In addition to Fourier‐analytic bounds, we crucially rely on a self‐improving feature of polydisc slicing, established via probabilistic arguments.

The Distribution of the Number of Automorphisms of Random Trees

We study the size of the automorphism group of two different types of random trees: Galton–Watson trees and rooted Pólya trees. In both cases, we prove that it asymptotically follows a log-normal distribution and provide asymptotic formulas for the mean and variance of the logarithm of the size of the automorphism group. While the proof for Galton–Watson trees mainly relies on probabilistic arguments and a general result on additive tree functionals, generating functions are used in the case of rooted Pólya trees. We also show how to extend the results to some classes of unrooted trees.

Testing the cosmological principle with CatWISE quasars: a bayesian analysis of the number-count dipole

ABSTRACT The Cosmological Principle, that the Universe is homogeneous and isotropic on sufficiently large scales, underpins the standard model of cosmology. However, a recent analysis of 1.36 million infrared-selected quasars has identified a significant tension in the amplitude of the number-count dipole compared to that derived from the cosmic microwave background (CMB), thus challenging the Cosmological Principle. Here, we present a Bayesian analysis of the same quasar sample, testing various hypotheses using the Bayesian evidence. We find unambiguous evidence for the presence of a dipole in the distribution of quasars with a direction that is consistent with the dipole identified in the CMB. However, the amplitude of the dipole is found to be 2.7 times larger than that expected from the conventional kinematic explanation of the CMB dipole, with a statistical significance of 5.7σ. To compare these results with theoretical expectations, we sharpen the ΛCDM predictions for the probability distribution of the amplitude, taking into account a number of observational and theoretical systematics. In particular, we show that the presence of the Galactic plane mask causes a considerable loss of dipole signal due to a leakage of power into higher multipoles, exacerbating the discrepancy in the amplitude. By contrast, we show using probabilistic arguments that the source evolution of quasars improves the discrepancy, but only mildly so. These results support the original findings of an anomalously large quasar dipole, independent of the statistical methodology used.

“Quod possibile est non esse quandoque non est”. Aquinas’ Third Way in the light of Hintikka’s Principle of Plenitude

According to both Jaakko Hintikka and Simo Knuuttila, Aquinas’ third way to demonstrate that God exists presupposes the acceptance of the principle of plenitude, i.e., of the claim that all possibilities are realized at some time. Aquinas, however, maintained elsewhere that not all possibilities are always realized, and the coherence of his philosophical project may be called into question if one were to accept Hintikka’s and Knuuttila’s reading of the third way. In this paper, I argue that it is difficult to present the third way without invoking the principle of plenitude in Hintikka’s formulation. The corollary of this claim is that third way cannot be a demonstration within the philosophical system outlined by Aquinas, despite his claim to the contrary. Against the backdrop of this exegetical discussion, it is possible to rephrase Aquinas’ third way as a probabilistic argument that shows that God’s existence is highly likely, although not necessarily proven.

Murphy's Anselmian theism and the problem of evil

Abstract Mark Murphy has recently defended a novel account of divine agency on which God would have very minimal requiring reasons and a wide range of merely justified reasons. This account grounds his response to the problem of evil. If God would not have requiring reasons to promote the well-being of creatures, Murphy argues, then the evil we observe would not count as evidence against theism. I argue that Murphy's conclusion, if successful in undermining the problem of evil, also undermines probabilistic arguments for theism. However, there is good reason to resist his conclusion. Even if God does not have requiring reasons, but merely has justifying reasons, to promote creaturely well-being, God may nevertheless have most motivating reason to do so, and this would be enough to predict divine action, at least given Murphy's further assumption that God is perfectly free. It does not follow from the rational permissibility of God's Φ-ing that it is possible for God to Φ.

Mapinsights: deep exploration of quality issues and error profiles in high-throughput sequence data.

High-throughput sequencing (HTS) has revolutionized science by enabling super-fast detection of genomic variants at base-pair resolution. Consequently, it poses the challenging problem of identification of technical artifacts, i.e. hidden non-random error patterns. Understanding the properties of sequencing artifacts holds the key in separating true variants from false positives. Here, we develop Mapinsights, a toolkit that performs quality control (QC) analysis of sequence alignment files, capable of detecting outliers based on sequencing artifacts of HTS data at a deeper resolution compared with existing methods. Mapinsights performs a cluster analysis based on novel and existing QC features derived from the sequence alignment for outlier detection. We applied Mapinsights on community standard open-source datasets and identified various quality issues including technical errors related to sequencing cycles, sequencing chemistry, sequencing libraries and across various orthogonal sequencing platforms. Mapinsights also enables identification of anomalies related to sequencing depth. A logistic regression-based model built on the features of Mapinsights shows high accuracy in detecting 'low-confidence' variant sites. Quantitative estimates and probabilistic arguments provided by Mapinsights can be utilized in identifying errors, bias and outlier samples, and also aid in improving the authenticity of variant calls.