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An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger alphabet. As a corollary we obtain embeddings of systems of partial mutually orthogonal Latin cubes and $n$-ary quasigroups., Comment: 7 pages

We study a model of programmable matter systems consisting of $n$ devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line $L$ where for all nodes $u$ in $S$ either $u \in L$ or $u$ is connected to $L$ by a line of nodes perpendicular to $L$. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of $n$ nodes to be transformed into a nice shape of $n-1$ nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size $n$ into any other nice shape of size $n$ in $O(n^2)$ time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes., Comment: 22 pages, 10 figures

We consider a discrete system of $n$ simple indistinguishable devices, called \emph{agents}, forming a \emph{connected} shape $S_I$ on a two-dimensional square grid. Agents are equipped with a linear-strength mechanism, called a \emph{line move}, by which an agent can push a whole line of consecutive agents in one of the four directions in a single time-step. We study the problem of transforming an initial shape $S_I$ into a given target shape $S_F$ via a finite sequence of line moves in a distributed model, where each agent can observe the states of nearby agents in a Moore neighbourhood. Our main contribution is the first distributed connectivity-preserving transformation that exploits line moves within a total of $O(n \log_2 n)$ moves, which is asymptotically equivalent to that of the best-known centralised transformations. The algorithm solves the \emph{line formation problem} that allows agents to form a final straight line $S_L$, starting from any shape $ S_I $, whose \emph{associated graph} contains a Hamiltonian path., Comment: 31 pages, 18 figures

The solid-state reaction C + H$_2$O $\rightarrow$ H$_2$CO was studied experimentally following the codeposition of C atoms and H$_2$O molecules at low temperatures. In spite of the reaction barrier and absence of energetic triggering, the reaction proceeds fast on the experimental timescale pointing to its quantum tunneling mechanism. This route to formaldehyde shows a new "non-energetic" pathway to complex organic and prebiotic molecules in astrophysical environments. Energetic processing of the produced ice by UV irradiation leads mainly to the destruction of H$_2$CO and the formation of CO$_2$ challenging the role of energetic processing in the synthesis of complex organic molecules under astrophysically relevant conditions., Comment: to appear in APJ

A necklace is an equivalence class of words of length $n$ over an alphabet under the cyclic shift (rotation) operation. As a classical object, there have been many algorithmic results for key operations on necklaces, including counting, generating, ranking, and unranking. This paper generalises the concept of necklaces to the multidimensional setting. We define multidimensional necklaces as an equivalence classes over multidimensional words under the multidimensional cyclic shift operation. Alongside this definition, we generalise several problems from the one dimensional setting to the multidimensional setting for multidimensional necklaces with size $(n_1,n_2,...,n_d)$ over an alphabet of size $q$ including: providing closed form equations for counting the number of necklaces; an $O(n_1 \cdot n_2 \cdot ... \cdot n_d)$ time algorithm for transforming some necklace $w$ to the next necklace in the ordering; an $O((n_1 \cdot n_2 \cdot ... \cdot n_d)^5)$ time algorithm to rank necklaces (determine the number of necklaces smaller than $w$ in the set of necklaces); an $O((n_1\cdot n_2 \cdot ... \cdot n_d)^{6(d + 1)} \cdot \log^d(q))$ time algorithm to unrank multidimensional necklace (determine the $i^{th}$ necklace in the set of necklaces). Our results on counting, ranking, and unranking are further extended to the fixed content setting, where every necklace has the same Parikh vector, in other words every necklace shares the same number of occurrences of each symbol. Finally, we study the $k$-centre problem for necklaces both in the single and multidimensional settings. We provide strong approximation algorithms for solving this problem in both the one dimensional and multidimensional settings.

The number of $n$-ary bent functions is less than $2^{3\cdot2^{n-3}(1+o(1))}$ as $n$ is even and $n\rightarrow\infty$. Keywords: Boolean function, bent function, upper bound

We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors from codes with weight $1$ grows to infinity. We find an example of a sequence of linear codes such that the dimension of the code is the half of the codelength but it has not a uniform weight spectrum. This example generates eigenfunctions of the Fourier transform with minimal support and partial covering sets. Moreover, we generalize some MacWilliams-type identity. Keywords: weight distribution of code, dual code, MacWilliams identity, Fourier transform, partial covering array

Two-dimensional random metal networks possess unique electrical and optical properties, such as almost total optical transparency and low sheet resistance, which are closely related to their disordered structure. Here we present a detailed experimental and theoretical investigation of their plasmonic properties, revealing Anderson (disorder-driven) localized surface plasmon (LSP) resonances of very large quality factors and spatial localization close to the theoretical maximum, which couple to electromagnetic waves. Moreover, they disappear above a geometry-dependent threshold at ca. 1.7 eV in the investigated Au networks, explaining their large transparencies in the optical spectrum.

Hybrid metallic nanoparticles encapsulated in oxide shells are currently intensely studied for plasmonic applications in sensing, medicine, catalysis, and photovoltaics. Here, we introduce a method for the synthesis of Au@Ag@SiO$_2$ cubes with a uniform silica shell of variable and adjustable thickness in the nanometer range; and we demonstrate their excellent, highly reproducible, and tunable optical response. Varying the silica shell thickness, we could tune the excitation energies of the single nanoparticle plasmon modes in a broad spectral range between 2.55 and 3.25\,eV. Most importantly, we reveal a strong coherent coupling of the surface plasmons at the silver-silica interface with the whispering gallery resonance at the silica-vacuum interface leading to a significant field enhancement at the encapsulated nanoparticle surface in the range of 100\,\% at shell thicknesses $t\,$$\simeq\,$20\,nm. Consequently, the synthesis method and the field enhancement open pathways to a widespread use of silver nanoparticles in plasmonic applications including photonic crystals and may be transferred to other non-precious metals.

The heterostructure consisting of the Mott insulator LaVO$_3$ and the band insulator SrTiO$_3$ is considered a promising candidate for future photovoltaic applications. Not only does the (direct) excitation gap of LaVO$_3$ match well the solar spectrum, but its correlated nature and predicted built-in potential, owing to the non-polar/polar interface when integrated with SrTiO$_3$, also offer remarkable advantages over conventional solar cells. However, experimental data beyond the observation of a thickness-dependent metal-insulator transition is scarce and a profound, microscopic understanding of the electronic properties is still lacking. By means of soft and hard X-ray photoemission spectroscopy as well as resistivity and Hall effect measurements we study the electrical properties, band bending, and band alignment of LaVO$_3$/SrTiO$_3$ heterostructures. We find a critical LaVO$_3$ thickness of five unit cells, confinement of the conducting electrons to exclusively Ti 3$d$ states at the interface, and a potential gradient in the film. From these findings we conclude on electronic reconstruction as the driving mechanism for the formation of the metallic interface in LaVO$_3$/SrTiO$_3$., Comment: 13 pages, 12 figures

This article addresses extraction of physically meaningful information from STEM EELS and EDX spectrum-images using methods of Multivariate Statistical Analysis. The problem is interpreted in terms of data distribution in a multi-dimensional factor space, which allows for a straightforward and intuitively clear comparison of various approaches. A new computationally efficient and robust method for finding physically meaningful endmembers in spectrum-image datasets is presented. The method combines the geometrical approach of Vertex Component Analysis with the statistical approach of Bayesian inference. The algorithm is described in detail at an example of EELS spectrum-imaging of a multi-compound CMOS transistor.

This work relates to the field of ultra-low-frequency (ULF) spectroscopy of near-Earth plasma. Our attention is focused on the Alfv\'en ionospheric resonator (IAR), the spectrum of which is a series of discrete lines. The aim of the study is to experimentally verify a well-defined theoretical prediction. Within the framework of an idealized resonator model, a hypothesis about the relationship between the frequencies of spectral lines has been formulated. To test the hypothesis, observations of ULF oscillations at the mid-latitude Mondy observatory were used. The result of the analysis confirmed the hypothesis that odd harmonics of the IAR discrete spectrum are observed on the Earth's surface. Key words: electromagnetic oscillations, Alfv\'en waves, ionospheric Alfv\'en resonator, ultra-low-frequency spectroscopy., Comment: 13 pages, 2 figures

Dust grains play a central role in the physics and chemistry of cosmic environments. They influence the optical and thermal properties of the medium due to their interaction with stellar radiation; provide surfaces for the chemical reactions that are responsible for the synthesis of a significant fraction of key astronomical molecules; and they are building blocks of pebbles, comets, asteroids, planetesimals, and planets. In this paper, we review experimental studies of physical and chemical processes, such as adsorption, desorption, diffusion, and reactions forming molecules, on the surface of reliable cosmic dust grain analogues as related to processes in diffuse, translucent, and dense interstellar clouds, protostellar envelopes, planet-forming disks, and planetary atmospheres. The information that such experiments reveal should be flexible enough to be used in many different environments. In addition, we provide a forward look discussing new ideas, experimental approaches, and research directions., Comment: Accepted for publication in International Reviews in Physical Chemistry

The main result of the paper is the first polynomial-time algorithm for ranking bracelets. The time-complexity of the algorithm is O(k^2 n^4), where k is the size of the alphabet and n is the length of the considered bracelets. The key part of the algorithm is to compute the rank of any word with respect to the set of bracelets by finding three other ranks: the rank over all necklaces, the rank over palindromic necklaces, and the rank over enclosing apalindromic necklaces. The last two concepts are introduced in this paper. These ranks are key components to our algorithm in order to decompose the problem into parts. Additionally, this ranking procedure is used to build a polynomial-time unranking algorithm.

Analyzing paradoxes is interesting and instructive. Sometimes the analysis leads to non-trivial results. This methodological note sets out a paradox arising in the theory of propagation of electromagnetic waves in moving plasmas. The paradox is interesting in itself, and, generally speaking, it should be taken into account when analyzing geoelectromagnetic waves. The paradox is as follows: contrary to expectations, the group velocity of the waves is the same in the comoving and laboratory frames of reference. The condition for the appearance of the paradox is the quadratic dependence of the frequency on the wave number. A paradoxical property manifests itself in the theory of the propagation of radio waves (in particular, whistling atmospherics), Langmuir waves and Alfv\'en waves. From a cognitive point of view, it is interesting that the paradox can be traced in relation to de Broglie waves. An explanation of the paradox is proposed. Keywords: group velocity, moving plasma, Doppler Effect, dispersion, longitudinal waves, transverse waves., Comment: 9 pages