Symmetries as Humean Metalaws

Symmetry principles are a central part of contemporary physics, yet there has been surprisingly little metaphysical work done on them. This paper develops the Wignerian treatment of symmetries as higher-order laws – metalaws – within a Humean framework of lawhood. Lange has raised two obstacles to Humean metalaws, and the paper shows that the account has the resources available to respond to both. It is argued that this framework for Humean metalaws stands as an example of naturalistic metaphysics, able to bring Humeanism into contact with the practice of actual science without giving up on the central denial of necessary connections.

Aperiodic crystals in biology

Biological systems display a broad palette of hierarchically ordered designs spanning over many orders of magnitude in size. Remarkably enough, periodic order, which profusely shows up in nonliving ordered compounds, plays a quite subsidiary role in most biological structures, which can be appropriately described in terms of the more general aperiodic crystal notion instead. In this Topical Review I shall illustrate this issue by considering several representative examples, including botanical phyllotaxis, the geometry of cell patterns in tissues, the morphology of sea urchins, or the symmetry principles underlying virus architectures. In doing so, we will realize that albeit the currently adopted quasicrystal notion is not general enough to properly account for the rich structural features one usually finds in biological arrangements of matter, several mathematical tools and fundamental notions belonging to the aperiodic crystals science toolkit can provide a useful modeling framework to this end.

Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

Rationalization of energy gaps of atomically precise AGNRs, “bulk” (ΔΕac) or “zigzag-end” (ΔΕzz), could be challenging and controversial concerning their magnitude, origin, substrate influence (ΔΕsb), and spin-polarization, among others. Hereby, a simple self-consistent and “economical” interpretation is presented, based on “appropriate” DFT (and TDDFT) calculations, general symmetry principles, and plausibility arguments, which is fully consistent with current experimental measurements for 5-, 7-, and 9-AGNRs within less than 1%, although at variance with some prevailing views or interpretations for ΔΕac, ΔΕzz, and ΔΕsb. Thus, an excellent agreement between experiment and theory emerges, provided some established stereotypes are reconsidered and/or abandoned. The primary source of discrepancies is the finite length of AGNRs together with inversion-symmetry conflict and topological end/edge states, which invariably mix with other “bulk” states making their unambiguous detection/distinction difficult. This can be further tested by eliminating end-states (and ΔΕzz), by eliminating empty (non-aromatic) end-rings

Torsional deformation of nonrelativistic string theory

Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first principles. In these notes, we focus on the bosonic closed string sector. In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory. We review previous proposals of such symmetry principles and propose a modified version that might be useful for supersymmetrizations. The appropriate target-space geometry determined by these local spacetime symmetries is string Newton-Cartan geometry. This geometry is equipped with a two-dimensional foliation structure that is restricted by torsional constraints. Breaking the symmetries that give rise to such torsional constraints in the target space will in general generate quantum corrections to a marginal deformation in the worldsheet quantum field theory. Such a deformation induces a renormalization group flow towards sigma models that describe relativistic strings.

Protein structure prediction by AlphaFold2: are attention and symmetries all you need?

The functions of most proteins result from their 3D structures, but determining their structures experimentally remains a challenge, despite steady advances in crystallography, NMR and single-particle cryoEM. Computationally predicting the structure of a protein from its primary sequence has long been a grand challenge in bioinformatics, intimately connected with understanding protein chemistry and dynamics. Recent advances in deep learning, combined with the availability of genomic data for inferring co-evolutionary patterns, provide a new approach to protein structure prediction that is complementary to longstanding physics-based approaches. The outstanding performance of AlphaFold2 in the recent Critical Assessment of protein Structure Prediction (CASP14) experiment demonstrates the remarkable power of deep learning in structure prediction. In this perspective, we focus on the key features of AlphaFold2, including its use of (i) attention mechanisms and Transformers to capture long-range dependencies, (ii) symmetry principles to facilitate reasoning over protein structures in three dimensions and (iii) end-to-end differentiability as a unifying framework for learning from protein data. The rules of protein folding are ultimately encoded in the physical principles that underpin it; to conclude, the implications of having a powerful computational model for structure prediction that does not explicitly rely on those principles are discussed.

Evidence for Complex Fixed Points in Pandemic Data

Mathematical models used in epidemiology to describe the diffusion of infectious diseases often fail to reproduce the recurrent appearance of exponential growth in the number of infections (waves). This feature requires a time-modulation of some parameters of the model. Moreover, epidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is neatly encoded via complex fixed points in the epidemic Renormalization Group approach. As a result, we obtain the first consistent mathematical description of multiple wave dynamics and its inter-wave strolling regime. Our results are tested and calibrated against the COVID-19 pandemic data. Because of the simplicity of our approach that is organized around symmetry principles, our discovery amounts to a paradigm shift in the way epidemiological data are mathematically modelled. We show that the strolling period is crucial in controlling the emergence of the next wave, thus encouraging the maintenance of (non)pharmaceutical measures during the period following a wave.

A Class of Novel Mann-Type Subgradient Extragradient Algorithms for Solving Quasimonotone Variational Inequalities

Symmetries play an important role in the dynamics of physical systems. As an example, quantum physics and microworld are the basis of symmetry principles. These problems are reduced to solving inequalities in general. That is why in this article, we study the numerical approximation of solutions to variational inequality problems involving quasimonotone operators in an infinite-dimensional real Hilbert space. We prove that the iterative sequences generated by the proposed iterative schemes for solving variational inequalities with quasimonotone mapping converge strongly to some solution. The main advantage of the proposed iterative schemes is that they use a monotone and non-monotone step size rule based on operator knowledge rather than a Lipschitz constant or some line search method. We present a number of numerical experiments for the proposed algorithms.

Is Reproducibility Always Important or Even Possible for a Scientific Experiment?

This article provides an extended commentary on three books by R. Laymon and A. Franklin about the methodology and epistemology of the scientific experi­ment, as well as their article on the issue of reproducibility of experiments. The reproducibility of scientific results has historically been considered one of the methodological standards of science, and it is associated with ideas about the truth and intersubjective nature of scientific knowledge. The problem of re­producibility has received particular attention in recent decades because special­ized studies have revealed that more than half of the results from the social sci­entific studies cannot be reproduced; many cases of fraud in biomedical sciences have been uncovered; and the collective nature of subjectivity in elementary par­ticle physics has accentuated the instability of the knowledge obtained by large collaborations. In reconstructing discussions about reproducibility in the philo­sophical literature, we distinguish between replicating an experiment by repeat­ing it in a way that is as close as possible to the original and actually reproducing it by re-obtaining a previously observed phenomenon in a significantly modified instrumental-theoretical setting. We also introduce the concept of replication-2 as an intermediate form between replication and reproducing. These kinds of re­search repetitions perform different functions in experimental practice. We show that a variety of kinds of replication and reproduction are at the heart of a set of epistemic strategies: experimental methodological standards identified by Franklin based on decades of research in scientific practice. We analyze a num­ber of experiments in which a single measurement, in the absence of epistemic strategies, was sufficient for the community to accept a new theory. In these cases, we argue, a theory based on high-value symmetry principles turned out to be the dominant lens of the community, while the experiment played a role only as a demonstration. Such examples, in our opinion, indicate that the experiment’s role in a situation of shifting scientific paradigms is different from its role in nor­mal science: the requirements for reproducibility and epistemic strategies are significantly alleviated in the former in comparison to the latter.

METAPHYSICAL ASPECTS OF THE STANDARD MODEL OF THE ELEMENTARY PARTICLES PHYSICS AND THE HISTORY OF ITS CREATION

Metaphysical aspects of the standard model (SM) of the modern elementary particles theory are considered. This article briefly views a history of the formation of the SM (from fundamental paper of C. Yang and R. Mills (1954) to the completion of electroweak theory and quantum chromodynamics in the early 1970s). Three groups of the interrelated metaphysical aspects are discussed: local gauge symmetry’s structure of the theory, problem of the truth and reality and the role of the metaphysical factors in the construction of the theory. Scientific-realistic nature of the SM creator’s metaphysical views are emphasized. A. Einstein’s model of the theory’s construction (with “Einstein’s arc”), E. Wigner’s three layer scheme of the structure and the development of the scientific knowledge (with the symmetry principles as a main layer) and S.I. Vavilov’s “mistakability” сonception of the scientific knowledge development are proposed for the study of the metaphysical factors and their role in the formation of the SM.