Minimum-weight triangulation is NP-hard

A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum-weight triangulation (MWT) problem, we are looking for a triangulation of a given point set that minimizes the sum of the edge lengths. We prove that the decision version of this problem is NP-hard. We use a reduction from PLANAR-1-IN-3-SAT. The correct working of the gadgets is established with computer assistance, using dynamic programming on polygonal faces, as well as the beta-skeleton heuristic to certify that certain edges belong to the minimum-weight triangulation.Comment: 45 pages (including a technical appendix of 13 pages), 28 figures. This revision contains a few improvements in the expositio

Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump

The small size (58 residues) and simple structure of the B domain of staphylococcal protein A (BdpA) have led to this domain being a paradigm for theoretical studies of folding. Experimental studies of the folding of BdpA have been limited by the rapidity of its folding kinetics. We report the folding kinetics of a fluorescent mutant of BdpA (G29A F13W), named F13W*, using nanosecond laser-induced temperature jump experiments. Automation of the apparatus has permitted large data sets to be acquired that provide excellent signal-to-noise ratio over a wide range of experimental conditions. By measuring the temperature and denaturant dependence of equilibrium and kinetic data for F13W*, we show that thermodynamic modeling of multidimensional equilibrium and kinetic surfaces is a robust method that allows reliable extrapolation of rate constants to regions of the folding landscape not directly accessible experimentally. The results reveal that F13W* is the fastest-folding protein of its size studied to date, with a maximum folding rate constant at 0 M guanidinium chloride and 45°C of 249,000 (s-1). Assuming the single-exponential kinetics represent barrier-limited folding, these data limit the value for the preexponential factor for folding of this protein to at least ≈2 x 10(6) s(-1)

Experimental evaluation of 3D printed spiral phase plates for enabling an orbital angular momentum multiplexed radio system

This paper evaluates the performance of three-dimensionally (3D) printed spiral phase plates (SPPs) for enabling an orbital angular momentum (OAM) multiplexed radio system. The design and realization of the SPPs by means of additive manufacturing exploiting a high-permittivity material is described. Modes 1 and 2 SPPs are then evaluated at 15 GHz in terms of 3D complex radiation pattern, mode purity and beam collimation by means of a 3D printed dielectric lens. The results with the lens yield a crosstalk of −8 dB for between modes 1 and −1, and −11.4 dB for between modes 2 and −2. We suggest a mode multiplexer architecture that is expected to further reduce the crosstalk for each mode. An additional loss of 4.2 dB is incurred with the SPPs inserted into the communication link, which is undesirable for obtaining reliable LTE-based communications. Thus, we suggest: using lower loss materials, seeking ways to reduce material interface reflections or alternative ways of OAM multiplexing to realize a viable OAM multiplexed radio system

Random walk through fractal environments

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is less than 2, there is though always a finite rate of unaffected escape. Random walks through fractal sets with D less or equal 2 can thus be considered as defective Levy walks. The distribution of jump increments for D > 2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk-increments. It is shown that the particles undergo anomalous, enhanced diffusion for D_F < 2, the diffusion is dominated by the finite escape rate. Diffusion for D_F > 2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality (SOC) models give rise to enhanced diffusion. The analytical results are illustrated by Monte-Carlo simulations.Comment: 22 pages, 16 figures; in press at Phys. Rev. E, 200

Modern microwave methods in solid state inorganic materials chemistry: from fundamentals to manufacturing

No abstract available

Partitioning of Mg, Sr, Ba and U into a subaqueous calcite speleothem

The trace-element geochemistry of speleothems is becoming increasingly used for reconstructing palaeoclimate, with a particular emphasis on elements whose concentrations vary according to hydrological conditions at the cave site (e.g. Mg, Sr, Ba and U). An important step in interpreting trace-element abundances is understanding the underlying processes of their incorporation. This includes quantifying the fractionation between the solution and speleothem carbonate via partition coefficients (where the partitioning (D) of element X (DX) is the molar ratio [X/Ca] in the calcite divided by the molar ratio [X/Ca] in the parent water) and evaluating the degree of spatial variability across time-constant speleothem layers. Previous studies of how these elements are incorporated into speleothems have focused primarily on stalagmites and their source waters in natural cave settings, or have used synthetic solutions under cave-analogue laboratory conditions to produce similar dripstones. However, dripstones are not the only speleothem types capable of yielding useful palaeoclimate information. In this study, we investigate the incorporation of Mg, Sr, Ba and U into a subaqueous calcite speleothem (CD3) growing in a natural cave pool in Italy. Pool-water measurements extending back 15 years reveal a remarkably stable geochemical environment owing to the deep cave setting, enabling the calculation of precise solution [X/Ca]. We determine the trace element variability of ‘modern’ subaqueous calcite from a drill core taken through CD3 to derive DMg, DSr, DBa and DU then compare these with published cave, cave-analogue and seawater-analogue studies. The DMg for CD3 is anomalously high (0.042 ± 0.002) compared to previous estimates at similar temperatures (∼8 °C). The DSr (0.100 ± 0.007) is similar to previously reported values, but data from this study as well as those from Tremaine and Froelich (2013) and Day and Henderson (2013) suggest that [Na/Sr] might play an important role in Sr incorporation through the potential for Na to outcompete Sr for calcite non-lattice sites. DBa in CD3 (0.086 ± 0.008) is similar to values derived by Day and Henderson (2013) under cave-analogue conditions, whilst DU (0.013 ± 0.002) is almost an order of magnitude lower, possibly due to the unusually slow speleothem growth rates (&lt;1 μm a−1), which could expose the crystal surfaces to leaching of uranyl carbonate. Finally, laser-ablation ICP-MS analysis of the upper 7 μm of CD3, regarded as ‘modern’ for the purposes of this study, reveals considerable heterogeneity, particularly for Sr, Ba and U, which is potentially indicative of compositional zoning. This reinforces the need to conduct 2D mapping and/or multiple laser passes to capture the range of time-equivalent elemental variations prior to palaeoclimate interpretation

Single-cell immune profiling reveals markers of emergency myelopoiesis that distinguish severe from mild respiratory syncytial virus disease in infants

Whereas most infants infected with respiratory syncytial virus (RSV) show no or only mild symptoms, an estimated 3 million children under five are hospitalized annually due to RSV disease. This study aimed to investigate biological mechanisms and associated biomarkers underlying RSV disease heterogeneity in young infants, enabling the potential to objectively categorize RSV-infected infants according to their medical needs. Immunophenotypic and functional profiling demonstrated the emergence of immature and progenitor-like neutrophils, proliferative monocytes (HLA-DRLow, Ki67+), impaired antigen-presenting function, downregulation of T cell response and low abundance of HLA-DRLow B cells in severe RSV disease. HLA-DRLow monocytes were found as a hallmark of RSV-infected infants requiring hospitalization. Complementary transcriptomics identified genes associated with disease severity and pointed to the emergency myelopoiesis response. These results shed new light on mechanisms underlying the pathogenesis and development of severe RSV disease and identified potential new candidate biomarkers for patient stratification