The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

In classical density functional theory (DFT) the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function $g(x)$ and structure factor $S(k)$ of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.Comment: 9 pages, 3 figure

Inductive logic programming at 30

Inductive logic programming (ILP) is a form of logic-based machine learning. The goal of ILP is to induce a hypothesis (a logic program) that generalises given training examples and background knowledge. As ILP turns 30, we survey recent work in the field. In this survey, we focus on (i) new meta-level search methods, (ii) techniques for learning recursive programs that generalise from few examples, (iii) new approaches for predicate invention, and (iv) the use of different technologies, notably answer set programming and neural networks. We conclude by discussing some of the current limitations of ILP and discuss directions for future research.Comment: Extension of IJCAI20 survey paper. arXiv admin note: substantial text overlap with arXiv:2002.11002, arXiv:2008.0791

Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method

The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons of the introduction of the so-called ``electrodynamics dualism concept" (simultaneous coexistence of instantaneous Newton long-range and Faraday-Maxwell short-range interactions) have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a self-consistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.Comment: ReVTeX file, 24pp. Small corrections which do not have influence results of the paper. Journal reference is adde

Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.Comment: 10 pages, 1 figure, to be submitted to Journal of Physics A: Mathematical and Genera

Lineage and fate of each blastomere of the eight-cell sea urchin embryo

A fluoresceinated lineage tracer was injected into individual blastomeres of eight-cell sea urchin (Strongylocentrotus purpuratus) embryos, and the location of the progeny of each blastomere was determined in the fully developed pluteus. Each blastomere gives rise to a unique portion of the advanced embryo. We confirm many of the classical assignments of cell fate along the animal-vegetal axis of the cleavage-stage embryo, and demonstrate that one blastomere of the animal quartet at the eight-cell stage lies nearest the future oral pole and the opposite one nearest the future aboral pole of the embryo. Clones of cells deriving from ectodermal founder cells always remain contiguous, while clones of cells descendant from the vegetal plate (i.e., gut, secondary mesenchyme) do not. The locations of ectodermal clones contributed by specific blastomeres require that the larval plane of bilateral symmetry lie approximately equidistant (i.e., at a 45 degree angle) from each of the first two cleavage planes. These results underscore the conclusion that many of the early spatial patterns of differential gene expression observed at the molecular level are specified in a clonal manner early in embryonic sea urchin development, and are each confined to cell lineages established during cleavage

Advancing Precambrian palaeomagnetism with the PALEOMAGIA and PINT(_QPI) databases.

State-of-the-art measurements of the direction and intensity of Earth's ancient magnetic field have made important contributions to our understanding of the geology and palaeogeography of Precambrian Earth. The PALEOMAGIA and PINT(QPI) databases provide thorough public collections of important palaeomagnetic data of this kind. They comprise more than 4,100 observations in total and have been essential in supporting our international collaborative efforts to understand Earth's magnetic history on a timescale far longer than that of the present Phanerozoic Eon. Here, we provide an overview of the technical structure and applications of both databases, paying particular attention to recent improvements and discoveries

Millimeter-wave defected ground structure-based MIMO antenna for 6G wireless applications

In this paper, a 2×2 multiple-input-multiple-output (MIMO) assembly of an elliptical-shaped millimeter-wave (mm-wave) antenna with defected-ground structures (DGS) is presented. The antenna is integrated with ring slot-shaped cut-outs as DGS on the bottom ground to generate multiple resonances combined in a wide bandwidth of 25.0-29.7 GHz. The simulated results show an efficiency above 75% and realized gain above 4.5 dBi in the entire range with a peak gain of 7.64 dBi at 27 GHz. The proposed MIMO antenna is well-suited for the 6 th Generation (6G) wireless applications

Smooth Bosonization as a Quantum Canonical Transformation

We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonization proposed by Damgaard et al. as well as an example of a quantum canonical transformation for a quantum field theory.Comment: 20 pages, revte