A digital distance on the kisrhombille tiling.

The kisrhombille tiling is the dual tessellation of one of the semi-regular tessellations. It consists of right-angled triangle tiles with 12 different orientations. An adequate coordinate system for the tiles of the grid has been defined that allows a formal description of the grid. In this paper, two tiles are considered to be neighbors if they share at least one point in their boundary. Paths are sequences of tiles such that any two consecutive tiles are neighbors. The digital distance is defined as the minimum number of steps in a path between the tiles, and the distance formula is proven through constructing minimum paths. In fact, the distance between triangles is almost twice the hexagonal distance of their embedding hexagons.

Distances in the face-centered cubic crystalline structure applying operational research.

The f.c.c. (face-centered cubic) grid is the structure of many crystals and minerals. It consists of four cubic lattices. It is supposed that there are two types of steps between two grid points. It is possible to step to one of the nearest neighbors of the same cubic lattice (type 1) or to step to one of the nearest neighbors of another cubic lattice (type 2). Steps belonging to the same type have the same length (weight). However, the two types have different lengths and thus may have different weights. This paper discusses the minimal path between any two points of the f.c.c. grid. The minimal paths are explicitly given, i.e. to obtain a minimal path one is required to perform only O(1) computations. The mathematical problem can be the model of different spreading phenomena in crystals having the f.c.c. structure.

Vector Arithmetic in the Triangular Grid.

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [-1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Labelled regulatory elements are pervasive features of the macrophage genome and are dynamically utilized by classical and alternative polarization signals.

The concept of tissue-specific gene expression posits that lineage-determining transcription factors (LDTFs) determine the open chromatin profile of a cell via collaborative binding, providing molecular beacons to signal-dependent transcription factors (SDTFs). However, the guiding principles of LDTF binding, chromatin accessibility and enhancer activity have not yet been systematically evaluated. We sought to study these features of the macrophage genome by the combination of experimental (ChIP-seq, ATAC-seq and GRO-seq) and computational approaches. We show that Random Forest and Support Vector Regression machine learning methods can accurately predict chromatin accessibility using the binding patterns of the LDTF PU.1 and four other key TFs of macrophages (IRF8, JUNB, CEBPA and RUNX1). Any of these TFs alone were not sufficient to predict open chromatin, indicating that TF binding is widespread at closed or weakly opened chromatin regions. Analysis of the PU.1 cistrome revealed that two-thirds of PU.1 binding occurs at low accessible chromatin. We termed these sites labelled regulatory elements (LREs), which may represent a dormant state of a future enhancer and contribute to macrophage cellular plasticity. Collectively, our work demonstrates the existence of LREs occupied by various key TFs, regulating specific gene expression programs triggered by divergent macrophage polarizing stimuli.

Ultrafast multipulse damage threshold of femtosecond high reflectors.

Laser-induced damage threshold is a fundamental figure of merit of femtosecond optical components used in large-scale laser systems. We tested a series of ultrafast mirrors featuring high band-gap dielectric materials as well as improved design and coating techniques. In a broad range of the damage test pulse train involving between 10 and 100,000 pulses (40 fs, 800 nm), pure dielectric high reflectors exhibit around 1.5 J/cm2 and hybrid Ag-multilayer mirrors can exhibit well above 1.2 J/cm2 damage threshold. In addition, a reference antireflection coating exceeded 2 J/cm2. Damage threshold dependence on the number of pulses was similar for all optics involved.

A topological coordinate system for the diamond cubic grid.

Topological coordinate systems are used to address all cells of abstract cell complexes. In this paper, a topological coordinate system for cells in the diamond cubic grid is presented and some of its properties are detailed. Four dependent coordinates are used to address the voxels (triakis truncated tetrahedra), their faces (hexagons and triangles), their edges and the points at their corners. Boundary and co-boundary relations, as well as adjacency relations between the cells, can easily be captured by the coordinate values. Thus, this coordinate system is apt for implementation in various applications, such as visualizations, morphological and topological operations and shape analysis.

Femtosecond damage resistance of femtosecond multilayer and hybrid mirrors.

Improving the laser-induced damage threshold of optical components is a basic endeavor in femtosecond technology. By testing more than 30 different femtosecond mirrors with 42 fs laser pulses at 1 kHz repetition rate, we found that a combination of high-bandgap dielectric materials and improved design and coating techniques enable femtosecond multilayer damage thresholds exceeding 2 J/cm2 in some cases. A significant ×2.5 improvement in damage resistance can also be achieved for hybrid Ag-multilayer mirrors exhibiting more than 1 J/cm2 threshold with a clear anticorrelation between damage resistance and peak field strength in the stack. Slight dependence on femtosecond pulse length and substantial decrease for high (megahertz) repetition rates are also observed.

Wiener index on rows of unit cells of the face-centred cubic lattice.

The Wiener index of a connected graph, known as the `sum of distances', is the first topological index used in chemistry to sum the distances between all unordered pairs of vertices of a graph. The Wiener index, sometimes called the Wiener number, is one of the indices associated with a molecular graph that correlates physical and chemical properties of the molecule, and has been studied for various kinds of graphs. In this paper, the graphs of lines of unit cells of the face-centred cubic lattice are investigated. This lattice is one of the simplest, the most symmetric and the most usual, cubic crystal lattices. Its graphs contain face centres of the unit cells and other vertices, called cube vertices. Closed formulae are obtained to calculate the sum of shortest distances between pairs of cube vertices, between cube vertices and face centres and between pairs of face centres. Based on these formulae, their sum, the Wiener index of a face-centred cubic lattice with unit cells connected in a row graph, is computed.

Ultrafast Electron Emission from a Sharp Metal Nanotaper Driven by Adiabatic Nanofocusing of Surface Plasmons.

We report photoelectron emission from the apex of a sharp gold nanotaper illuminated via grating coupling at a distance of 50 µm from the emission site with few-cycle near-infrared laser pulses. We find a fifty-fold increase in electron yield over that for direct apex illumination. Spatial localization of the electron emission to a nanometer-sized region is demonstrated by point-projection microscopic imaging of a silver nanowire. Our results reveal negligible plasmon-induced electron emission from the taper shaft and thus efficient nanofocusing of few-cycle plasmon wavepackets. This novel, remotely driven emission scheme offers a particularly compact source of ultrashort electron pulses of immediate interest for miniaturized electron microscopy and diffraction schemes with ultrahigh time resolution.

Special multicolor illumination and numerical tilt correction in volumetric digital holographic microscopy.

We introduce a color imaging method in our digital holographic microscope system (DHM). This DHM can create color images of freely floating, or moving objects inside a large volume by simultaneously capturing three holograms using three different illumination wavelengths. In this DHM a new light source assembly is applied, where we use single mode fibers according to the corresponding wavelengths that are tightly and randomly arranged into a small array in a single FC/PC connector. This design has significant advantages over the earlier approaches, where all the used illuminations are coupled in the same fiber. It avoids the coupling losses and provides a cost effective, compact solution for multicolor coherent illumination. We explain how to determine and correct the different fiber end positions caused tilt aberration during the hologram reconstruction process. To demonstrate the performance of the device, color hologram reconstructions are presented that can achieve at least 1 µm lateral resolution.