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We present a polarization-resolved and temperature-dependent Raman scattering study of AFe2As2 (A = Ca, Eu). In the spin-density-wave (SDW) phase, spectral weight redistribution is observed in the fully symmetric and non-symmetric scattering channels at different energies. An anisotropic Raman response is observed in the fully symmetric channel in spontaneously detwinned CaFe2As2 samples. We calculate the orbital-resolved electronic structures using a combination of density functional theory and dynamical mean field theory (DFT+DMFT). We identify the electronic transitions corresponding to these two spectral features and find that the anisotropic Raman response originates from the lifted degeneracy of the dxz/yz orbitals in the broken symmetry phase., Comment: 7 pages, 5 figures

Superconducting MgB$\_2$ shows an E$\_{2g}$ zone center phonon, as measured by Raman spectroscopy, that is very broad in energy and temperature dependent. The Raman shift and lifetime show large differences with the values elsewhere in the Brillouin Zone measured by Inelastic X-ray Scattering (IXS), where its dispersion can be accounted for by standard harmonic phonon theory, adding only a moderate electron-phonon coupling. Here we show that the effects rapidly disappear when electron-phonon coupling is switched off by Al substitution on the Mg sites. Moreover, using IXS with very high wave-vector resolution in MgB$\_2$, we can follow the dispersion connecting the Raman and the IXS signal, in agreement with a theory using only electron-phonon coupling but without strong anharmonic terms. The observation is important in order to understand the effects of electron-phonon coupling on zone center phonons modes in MgB$\_2$, but also in all metals characterized by a small Fermi velocity in a particular direction, typical for layered compounds.

$\delta$-hyperbolic graphs, originally conceived by Gromov in 1987, occur often in many network applications; for fixed $\delta$, such graphs are simply called hyperbolic graphs and include non-trivial interesting classes of "non-expander" graphs. The main motivation of this paper is to investigate the effect of the hyperbolicity measure $\delta$ on expansion and cut-size bounds on graphs (here $\delta$ need not be a constant), and the asymptotic ranges of $\delta$ for which these results may provide improved approximation algorithms for related combinatorial problems. To this effect, we provide constructive bounds on node expansions for $\delta$-hyperbolic graphs as a function of $\delta$, and show that many witnesses (subsets of nodes) for such expansions can be computed efficiently even if the witnesses are required to be nested or sufficiently distinct from each other. To the best of our knowledge, these are the first such constructive bounds proven. We also show how to find a large family of s-t cuts with relatively small number of cut-edges when s and t are sufficiently far apart. We then provide algorithmic consequences of these bounds and their related proof techniques for two problems for $\delta$-hyperbolic graphs (where $\delta$ is a function $f$ of the number of nodes, the exact nature of growth of $f$ being dependent on the particular problem considered)., Comment: Final corrected author version, to appear in the journal Algorithmica

A key ingredient in emerging quantum-enhanced technologies is the ability to coherently manipulate and detect superpositions of basis states. In integrated optics implementations, transverse spatial modes supported by multimode structures offer an attractive carrier of quantum superpositions. Here we propose an integrated dynamic mode converter based on the electro-optic effect in nonlinear channel waveguides for deterministic transformations between mutually non-orthogonal bases of spatial modes. We theoretically show its capability to demonstrate a violation of a Bell-type Clauser-Horne-Shimony-Holt inequality by measuring spatially mode-entangled photon pairs generated by an integrated photon pair source. The proposed configuration, numerically studied for the potassium titanyl phosphate (KTP) material, can be easily implemented using standard integrated optical fabrication technology.

It has recently been established that the high temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order and quenched disorder arising from dopants and strain. This complex, multiscale phase separation invites the development of theories of high temperature superconductivity that include complexity. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mescoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both the charge-density-wave puddles (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4+y, the single layer cuprate with the highest Tc, 95 kelvin. We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usual assumed random, uncorrelated distribution. The interstitials-oxygen-rich domains are spatially anti-correlated with the charge-density-wave domains, leading to a complex emergent geometry of the spatial landscape for superconductivity., Comment: 11 pages, 3 figures

In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can be achieved for certain ranges of the power law exponent $\beta$. For the value of power law exponent $\beta=1.5$ we obtain an approximation ratio of $1.34$ for Graphic TSP. Moreover we study the $(1,2)$-TSP with the underlying graph of $1$-edges being a PLG. We show improved approximation ratios in the case of underlying deterministic PLGs for $\beta$ greater than $1.666$. For underlying random PLGs we further improve the analysis and show even better expected approximation ratio for the range of $\beta$ between $1$ and $3.5$. On the other hand we prove the first explicit inapproximability bounds for $(1,2)$-TSP for an underlying power law graph.

In this note we give a new effective proof method for the equivalence of the notions of testability and nondeterministic testability for uniform hypergraph parameters. We provide the first effective upper bound on the sample complexity of any nondeterministically testable $r$-uniform hypergraph parameter as a function of the sample complexity of its witness parameter for arbitrary $r$. The dependence is of the form of an exponential tower function with the height linear in $r$. Our argument depends crucially on the new upper bounds for the $r$-cut norm of sampled $r$-uniform hypergraphs. We employ also our approach for some other restricted classes of hypergraph parameters, and present some applications., Comment: 26 pages

In this work we present a new chemical route to synthesize Tm2Mn2O7 pyrochlore, a compound which is thermodynamically unstable at ambient pressure. Differently from the reported in the past high pressure synthesis of the same compound applying oxides as starting materials, we have obtained a pure phase Tm2Mn2O7 by a converting TmMnO3 at 1100 C and 1300 bar oxygen pressure. The studies of Tm2Mn2O7 performed by a high resolution neutron powder diffraction have shown, that a pure pyrochlore cubic phase Tm2Mn2O7 (space group Fd-3m) have been obtained. On cooling below 25K there is a transition to a ferromagnetically (FM) ordered phase observed with an additional antiferromagnetic (AFM) canting suggesting a lowering of the initial cubic crystal symmetry. The magnetic transition is accompanied by small but well visible magnetostrsiction effect. Using symmetry analysis we have found a solution for the AFM structure in the maximal Shubnikov subgroup I41/am'd'., Comment: 20 pages, 9 figures

The degradation of signal in silicon sensors is studied under conditions expected at the CERN High-Luminosity LHC. 200 $\mu$m thick n-type silicon sensors are irradiated with protons of different energies to fluences of up to $3 \cdot 10^{15}$ neq/cm$^2$. Pulsed red laser light with a wavelength of 672 nm is used to generate electron-hole pairs in the sensors. The induced signals are used to determine the charge collection efficiencies separately for electrons and holes drifting through the sensor. The effective trapping rates are extracted by comparing the results to simulation. The electric field is simulated using Synopsys device simulation assuming two effective defects. The generation and drift of charge carriers are simulated in an independent simulation based on PixelAV. The effective trapping rates are determined from the measured charge collection efficiencies and the simulated and measured time-resolved current pulses are compared. The effective trapping rates determined for both electrons and holes are about 50% smaller than those obtained using standard extrapolations of studies at low fluences and suggests an improved tracker performance over initial expectations.

The paper proves the equivalence of the notions of nondeterministic and deterministic parameter testing for uniform dense hypergraphs of arbitrary order. It generalizes the result previously known only for the case of simple graphs. By a similar method we establish also the equivalence between nondeterministic and deterministic hypergraph property testing, answering the open problem in the area. We introduce a new notion of a cut norm for hypergraphs of higher order, and employ regularity techniques combined with the ultralimit method., Comment: 33 pages

In this paper, we propose a method for the generation of higher dimensional modal entanglement through type II spontaneous parametric down conversion process using a three waveguide directional coupler in a periodically poled lithium niobate substrate. We show that by a proper design, it is possible to achieve an output state of two photons occupying three different spatial modes. The advantage of using such waveguide structure is its flexibility and the design space availability to achieve desired characteristics of the photon pairs generated in the down conversion process, Comment: 11 pages,21 figures

We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form $n^{\epsilon}$ in the case when the power law exponent satisfies $\beta <1$. In the case when $\beta =1$, the lower bound is of the form $\log (n)^{\epsilon}$. The embedding technique used in the proof could also be of independent interest., Comment: 16 pages, 2 figures

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs., Comment: 19 pages, 4 figures

We consider the problem of recovering (that is, interpolating) and identity testing of a "hidden" monic polynomial $f$, given an oracle access to $f(x)^e$ for $x\in{\mathbb F_q}$ (extension fields access is not permitted). The naive interpolation algorithm needs $O(e\, \mathrm{deg}\, f)$ queries and thus requires $e\, \mathrm{deg}\, f

Selection comparator networks have been studied for many years. Recently, they have been successfully applied to encode cardinality constraints for SAT-solvers. To decrease the size of generated formula there is a need for constructions of selection networks that can be efficiently generated and produce networks of small sizes for the practical range of their two parameters: n - the number of inputs (boolean variables) and k - the number of selected items (a cardinality bound). In this paper we give and analyze a new construction of smaller selection networks that are based on the pairwise selection networks introduced by Codish and Zanon-Ivry. We prove also that standard encodings of cardinality constraints with selection networks preserve arc-consistency., Comment: Extended version of the paper sent to CP2015

Among the widely studied superconducting iron-pnictide compounds belonging to the Ln1111 family (with Ln a lanthanide), a systematic investigation of the crossover region between the superconducting and the antiferromagnetic phase for the Ln = Nd case has been missing. We fill this gap by focusing on the intermediate doping regime of NdFeAsO(1-x)F(x) by means of dc-magnetometry and muon-spin spectroscopy measurements. The long-range order we detect at low fluorine doping is replaced by short-range magnetic interactions at x = 0.08, where also superconductivity appears. In this case, longitudinal-field muon-spin spectroscopy experiments show clear evidence of slow magnetic fluctuations that disappear at low temperatures. This fluctuating component is ascribed to the glassy-like character of the magnetically ordered phase of NdFeAsO at intermediate fluorine doping.

We demonstrate that images of flux vortices in a superconductor taken with a transmission electron microscope can be used to measure the penetration depth and coherence length in all directions at the same temperature and magnetic field. This is particularly useful for MgB$_2$, where these quantities vary with the applied magnetic field and values are difficult to obtain at low field or in the $c$-direction. We obtained images of flux vortices from an MgB$_2$ single crystal cut in the $ac$ plane by focussed ion beam milling and tilted to $45^\circ$ with respect to the electron beam about its $a$ axis. A new method was developed to simulate these images which accounted for vortices with a non-zero core in a thin, anisotropic superconductor and a simplex algorithm was used to make a quantitative comparison between the images and simulations to measure the penetration depths and coherence lengths. This gave penetration depths $\Lambda_{ab}=100\pm 35$ nm and $\Lambda_c=120\pm 15$ nm at 10.8 K in a field of 4.8 mT. The large error in $\Lambda_{ab}$ is a consequence of tilting the sample about $a$ and had it been tilted about $c$, the errors would be reversed. Thus, obtaining the most precise values requires taking images of the flux lattice with the sample tilted in more than one direction. In a previous paper, we obtained a more precise value using a sample cut in the $ab$ plane. Using this value gives $\Lambda_{ab}=107\pm 8$ nm, $\Lambda_c=120\pm 15$ nm, $\xi_{ab}=39\pm 11$ nm and $\xi_c=35\pm 10$ nm which agree well with measurements made using other techniques. The experiment required two days to conduct and does not require large-scale facilities. It was performed on a very small sample: $30\times 15$ microns and 200 nm thick so this method could prove useful for characterising new superconductors where only small single crystals are available., Comment: 12 pages, 6 figures. Typos corrected and titles added to references. Accepted for publication in Physical Review B

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast. Julia questions notions generally held as "laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment, and 3. There are parts of a system for the programmer, and other parts best left untouched as they are built by the experts. We introduce the Julia programming language and its design --- a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can have machine performance without sacrificing human convenience., Comment: 37 pages

The number of triangulations of a planar n point set is known to be $c^n$, where the base $c$ lies between $2.43$ and $30.$ The fastest known algorithm for counting triangulations of a planar n point set runs in $O^*(2^n)$ time. The fastest known arbitrarily close approximation algorithm for the base of the number of triangulations of a planar n point set runs in time subexponential in $n.$ We present the first quasi-polynomial approximation scheme for the base of the number of triangulations of a planar point set.

We have studied the angular dependent de Haas-van Alphen oscillations of LaRu$_2$P$_2$ using magnetic torque in pulsed magnetic fields up to 60T. The observed oscillation frequencies are in excellent agreement with the geometry of the calculated Fermi surface. The temperature dependence of the oscillation amplitudes reveals effective masses m*($\alpha$)=0.71 and m*($\beta$)=0.99 m$_e$, which are enhanced over the calculated band mass by $\lambda^{cyc}$ of 0.8. We find a similar enhancement $\lambda^{\gamma} \approx 1$ in comparing the measured electronic specific heat ($\gamma = 11.5$ mJ/mol K$^2$) with the total DOS from band structure calculations. Remarkably, very similar mass enhancements have been reported in other pnictides LaFe$_2$P$_2$, LaFePO ($T_c \approx 4K$), and LaRuPO, independent of whether they are superconducting or not. This is contrary to the common perceptions that the normal state quasi-particle renormalizations reflect the strength of the superconducting paring mechanism and leads to new questions about pairing in isostructural and isoelectronic Ru- and Fe-pnictide superconductors., Comment: 4 pages, 4 figures

In layered superconductors the order parameter may be modulated within the unit cell, leading to non-trivial modifications of the vortex core if the interlayer coherence length $\xi_c(T)$ is comparable to the interlayer distance. In the iron-pnictide SmFeAs(O,F) ($T_c \approx 50$K) this occurs below a cross-over temperature $T^\star \approx 41$K, which separates two regimes of vortices: anisotropic Abrikosov-like at high and Josephson-like at low temperatures. Yet in the transition region around $T^\star$, hybrid vortices between these two characteristics appear. Only in this region around $T^\star$ and for magnetic fields well aligned with the FeAs layers, we observe oscillations of the c-axis critical current $j_c(H)$ periodic in $\frac{1}{\sqrt{H}}$ due to a delicate balance of intervortex forces and interaction with the layered potential. $j_c(H)$ shows pronounced maxima when a hexagonal vortex lattice is commensurate with the crystal structure. The narrow temperature window in which oscillations are observed suggests a significant suppression of the order parameter between the superconducting layers in SmFeAs(O,F), despite its low coherence length anisotropy ($\gamma_\xi \approx 3-5$)., Comment: accepted for PRL

Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock-state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entanglement of the two output modes. A conditional projective measurement onto a single photon at one output mode heralds the success of the process. This operation, which implements a measurement-induced nonlinearity, is capable of suppressing particular photon-number probability amplitudes of an arbitrary quantum state. We employ coherent-state process tomography to determine the precise operation realized in our experiment. To identify the key sources of experimental imperfection, we develop a model of the process and identify three main contributions that significantly hamper its efficacy. The reconstructed tensor is compared with a model of the process taking into account sources of experimental imperfection with fidelity better than 0.95. This enables us to identify three key challenges to overcome in realizing a filter with high fidelity - namely the single-photon nature of the auxiliary state, high-mode overlap, and the need for number resolving detection when heralding. The results show that the filter does indeed exhibit a nonlinear response as a function of input photon number and preserves the phase relation between Fock layers of the output state, providing promise for future applications.

We study the sample complexity of nondeterministically testable graph parameters and improve existing bounds on it by several orders of magnitude. The technique used would be also of independent interest. We also discuss the special case of weak nondeterministic testing for uniform hypergraphs of arbitrary order., Comment: 27 pages

In this paper we study a problem of vertex two-coloring of undirected graph such that there is no monochromatic cycle of given length. We show that this problem is hard to solve. We give a proof by presenting a reduction from variation of satisfiability (SAT) problem. We show nice properties of coloring cliques with two colors which plays pivotal role in the reduction construction.

Arrays are such a rich and fundamental data type that they tend to be built into a language, either in the compiler or in a large low-level library. Defining this functionality at the user level instead provides greater flexibility for application domains not envisioned by the language designer. Only a few languages, such as C++ and Haskell, provide the necessary power to define $n$-dimensional arrays, but these systems rely on compile-time abstraction, sacrificing some flexibility. In contrast, dynamic languages make it straightforward for the user to define any behavior they might want, but at the possible expense of performance. As part of the Julia language project, we have developed an approach that yields a novel trade-off between flexibility and compile-time analysis. The core abstraction we use is multiple dispatch. We have come to believe that while multiple dispatch has not been especially popular in most kinds of programming, technical computing is its killer application. By expressing key functions such as array indexing using multi-method signatures, a surprising range of behaviors can be obtained, in a way that is both relatively easy to write and amenable to compiler analysis. The compact factoring of concerns provided by these methods makes it easier for user-defined types to behave consistently with types in the standard library., Comment: 6 pages, 2 figures, workshop paper for the ARRAY '14 workshop, June 11, 2014, Edinburgh, United Kingdom

Iron-based compounds (IBS) display a surprising variety of superconducting properties that seems to arise from the strong sensitivity of these systems to tiny details of the lattice structure. In this respect, systems that become superconducting under pressure, like CaFe$_2$As$_2$, are of particular interest. Here we report on the first directional point-contact Andreev-reflection spectroscopy (PCARS) measurements on CaFe$_2$As$_2$ crystals under quasi-hydrostatic pressure, and on the interpretation of the results using a 3D model for Andreev reflection combined with ab-initio calculations of the Fermi surface (within the density functional theory) and of the order parameter symmetry (within a random-phase-approximation approach in a ten-orbital model). The almost perfect agreement between PCARS results at different pressures and theoretical predictions highlights the intimate connection between the changes in the lattice structure, a topological transition in the hole-like Fermi surface sheet, and the emergence on the same sheet of an order parameter with a horizontal node line., Comment: 13 pages, 8 color figures. This is an author-created, un-copyedited version of an article published in Scientific Reports. The published version is available online, together with Supplementary Information, at http://www.nature.com/articles/srep26394

We present a unified framework on the limits of constraint satisfaction problems (CSPs) and efficient parameter testing which depends only on array exchangeability and the method of cut decomposition without recourse to the weakly regular partitions. In particular, we formulate and prove a representation theorem for compact colored $r$-uniform directed hypergraph ($r$-graph) limits, and apply this to $r$CSP limits. We investigate the sample complexity of testable $r$-graph parameters, we discuss the generalized ground state energies and demonstrate that they are efficiently testable., Comment: 58 pages

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite $(3,3)$-hypergraphs. The proof technique of this paper uses the general correlation decay technique and a new combinatorial analysis of the underlying structures of the intersection graphs. The proof method could be also of independent interest., Comment: We thank Michael Simkin who pointed out and fixed an error (cf. Lemma 3 and the proof of Claim 7) in an earlier version of this paper

The goal of this paper is to propose and test a new memetic algorithm for the capacitated vehicle routing problem in parallel computing environment. In this paper we consider simple variation of vehicle routing problem in which the only parameter is the capacity of the vehicle and each client only needs one package. We present simple reduction to prove the existence of polynomial-time algorithm for capacity 2. We analyze the efficiency of the algorithm using hierarchical Parallel Random Access Machine (PRAM) model and run experiments with code written in CUDA (for capacities larger than 2)., Comment: This paper has been withdrawn by the author due to crucial error in the experimental evaluation

We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization entanglement in the Shih-Alley configuration, yielding visibilities consistently above 90%., Comment: 9 pages, 6 figures

Imaging of flux vortices in high quality MgB$_2$ single crystals has been successfully performed in a commercial Field Emission Gun-based Transmission Electron Microscope. In Cryo-Lorentz Microscopy, the sample quality and the vortex lattice can be monitored simultaneously, allowing one to relate microscopically the surface quality and the vortex dynamics. Such a vortex motion ultimately determines the flow resistivity, $\rho_{f}$, the knowledge of which is indispensable for practical applications such as superconducting magnets or wires for Magnetic Resonance Imaging. The observed patterns have been analyzed and compared with other studies by Cryo-Lorentz Microscopy or Bitter decoration. We find that the vortex lattice arrangement depends strongly on the surface quality obtained during the specimen preparation, and tends to form an hexagonal Abrikosov lattice at a relatively low magnetic field. Stripes or gossamer-like patterns, recently suggested as potential signatures of an unconventional behavior of MgB$_2$, were not observed.