text:
\section{Introduction}
Correlated electronic systems with spinel structure have seen a surge in interest of late, due inherently to rich physics involving frustrated magnetism, orbital ordering, charge ordering, etc. Fascinating physical phenomena emerge from the coupling between various degrees of freedom like spin, orbital and lattice, in the presence of both geometric frustration and Coulomb correlation~\cite{TokuraSc, LeeJPS, RadaNJP, KhomPRL, KatoPRL, TsunePRB}. The competition among different degrees of freedom manifests itself in several structural and magnetic transitions accompanied by orbital ordering in these systems~\cite{DebPRB, LeePRL, MacPRB, GarleaPRL}. These compounds, having generic formula AB$_2$O$_4$, consist of two distinct cation sites: A site is tetrahedrally coordinated with neighboring O sites while B site is octahedrally coordinated with O ligands~\cite{NiiPRB}, as shown schematically in Fig.~\ref{Fig1}(a). Geometrically frustrated magnetic spinels provide a fertile playground for exploration of interplay between these degrees of freedom~\cite{TchernyPRL, MatteoPRB}.

MnV$_2$O$_4$ is a member of AB$_2$O$_4$ family, which has the A-site (Mn$^{+2}$, S=5/2) magnetic but not orbitally active, while the B-site (V$^{+3}$, S=1) is both magnetic and orbitally active. The combined effect of magnetic and orbital degrees brings in rich and complex physics. This compound undergoes a magnetic transition from paramagnetic (PM) to collinear ferrimagnetic (FiM) phase at T$_{N1}$= 57K; followed by a structural transition (cubic$\rightarrow$ tetragonal) together with a second magnetic transition at T$_{N2}$= 54K where non collinear FiM spin ordering sets in~\cite{GarleaPRL,SuzukiPRL,AdachiPRL}.

Earlier, the controversies mostly centered around the ordering of orbitals of V, and stimulated an upsurge of research in this system~\cite{GarleaPRL, AdachiPRL, SarkarPRL}. Various possible scenarios were proposed for the orbital order based on the symmetry of the tetragonal phase and the type of dominant interactions~\cite{GarleaPRL, AdachiPRL}. In a recent theoretical study~\cite{DeyPRB}, A-type antiferro-orbital ordering has been observed at the V sites where one t$_{2g}$ electron occupies the d$_{xy}$ orbital at every V site and other electron occupies d$_{xz}$ and d$_{yz}$ orbitals alternately along c direction. These findings are in good agreement with the experimental measurements in MnV$_2$O$_4$~\cite{GarleaPRL}.

Though much attention has been given to the electronic properties, the phonon-related phenomena and their coupling with other degrees of freedom remained unexplored. However, few fascinating experiments performed in the recent past indicate that phonons play an important role at the microscopic level. Takubo {\it et al.}~\cite{TakuboPRB}, investigated Raman scattering of MnV$_2$O$_4$ and observed that several peaks evolve in the Raman spectra below T$_{N2}$. They showed a peculiar polarization-dependence of B$_g$ modes, and tried to explain it with Mott excitation phenomena. However, the appearance of experimental intensity peak with XY polarization was not supported by their analysis. Their mode-assignment of the Raman-active peaks in the tetragonal phase was based on the I4$_1$/amd space group, whereas the space group symmetry of MnV$_2$O$_4$ is I4$_1$/a~\cite{GarleaPRL}. Later, an inelastic light scattering study of the temperature and magnetic field dependences of one-and two-magnon excitations in MnV$_2$O$_4$ revealed that spin-lattice coupling is indeed significant in its low-temperature phase~\cite{GleasonPRB}. Additionally, anomalous temperature-dependence of the peak intensity was observed which was attributed to a strong coupling between magnetic and vibrational excitations in MnV$_2$O$_4$.

In view of the significant effects of phonons in this system, we have investigated the spin-phonon coupling across the Brillouin zone (BZ), along with Raman scattering to understand the polarization-dependence of B$_g$ modes from density functional theory (DFT) calculations. The paper is organized as follows. In Sec.~\ref{meth}, we briefly discuss the methodology used to calculate phonons and related properties. In Sec.~\ref{res}, first, we discuss the structural properties in detail and calculate phonon modes at $\Gamma$ point of the BZ. Next we present analysis Raman scattering intensities of the B$_g$ mode. Later, we study the effects of spin-phonon coupling and calculate the coupling term at different high symmetry points of the BZ and compare our results with experimental data. Finally, we give a brief summary and outlook in Sec.~\ref{conc}.

\section{Methods}
\label{meth}
Our first-principles calculations based on the density functional theory~\cite{KohnShamPR, HohenKohnPR} have been performed using plane-wave basis, as implemented in the Vienna {\it ab-initio} simulation package VASP~\cite{KresseVASP1, KresseVASP2}. We have used projector-augmented wave (PAW)~\cite{BlochPAW, KressePAW} potentials in our calculations and the wave functions were expanded in the plane-wave basis with a kinetic energy cutoff of 500 eV. We used a generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE)~\cite{GGAPBE} parametrization for the exchange-correlation energy functional. Total energies were converged to less than 10$^{-8}$ eV to achieve self-consistency and Brillouin zone integration was sampled on a $\Gamma$ centered k-mesh of 6 $\times$ 6 $\times$ 6. Electron correlation effects beyond GGA were incorporated for 3$d$-electrons of Mn, and V ions within GGA+U~\cite{DudarevPRB} approximation where U is the on-site Coulomb correlation~\cite{Hubbard} (U = 5 eV for both the transition metals), and Hund's coupling strengths (J) were set at J = 1 eV. In structural relaxation, positions of the ions were relaxed towards the equilibrium using conjugate gradient algorithm, until the Hellman-Feynman forces became less than 10$^{-3}$ eV/\AA.

Dynamical matrix and phonons were calculated from a frozen-phonon method with atomic displacements of $\pm$ 0.03\AA, as driven by the PHONOPY code~\cite{Phonopy} and Raman scattering intensity peaks were obtained from PHONON software~\cite{PHONON} interfacing with DFT as implemented in the VASP code. Spin-phonon couplings were determined based on the scheme~\cite{RayPRB} used by Ray {\it et al.}.

\section{Results and Discussion}
\label{res}
\subsection{Structural properties}
The MnV$_2$O$_4$ compound, in its low-temperature phase, has a tetragonal structure with I4$_1$/a space group symmetry. A network of edge-shared VO$_6$ octahedra with interstitial MnO$_4$ tetrahedra form a geometrically frustrated lattice in which the mirror or glide plane perpendicular to the ab plane is absent. The tetragonal unit cell of MnV$_2$O$_4$ is shown in Fig.~\ref{Fig1}(a).
\begin{figure}[ht]
\begin{center}
\includegraphics[width=9.0cm]{Fig1.pdf}
\caption{(Color online) (a) Crystallographic unit cell and (b) primitive cell of MnV$_2$O$_4$ compound. Oxygen octahedra (tetrahedra) around V (Mn) ions are shown in grey (cyan-blue).}
\label{Fig1}
\end{center}
\end{figure}

The lattice constants and the atomic positions are optimized within GGA and GGA+U approximations to achieve the minimum energy structure. However, the phonon calculations with the GGA-optimized structure show modes with imaginary frequencies in the phonon density of states (DOS) (Fig.~\ref{Fig2}(a)), which may arise due to the inaccuracy in calculating forces within GGA approximation. As the compound MnV$_2$O$_4$ is known to be a Mott insulator, strong correlation physics is incorporated in the calculations within GGA+U approximation. The calculations have been performed for U$_{eff}$ ($=U-J$, where U is the on-site Coulomb interaction and J is the Hund's exchange interaction) ranging from 3 eV to 5 eV at the Mn and V sites. For U$_{eff}$ $\geqslant$ 4 eV we observe no imaginary modes in the DOS (Fig.~\ref{Fig2}(b)). We would like to note that, our calculations do not change significantly for U$_{eff}$ above that value. Therefore, we present the results obtained for U$_{eff}=$4 eV at both sites. In addition, we have considered collinear ferrimagnetic (FiM) ordering of spins in our calculations where V spin moments are aligned opposite to Mn spin moments. Within the FiM spin configuration, the crystal structure preserves the symmetry of the experimental structure. It is evident from Fig.~\ref{Fig3}(a) that, the electronic band structure of MnV$_2$O$_4$ shows zero band gap within GGA calculations. On the other hand, GGA+U calculated electronic band structure (Fig.~\ref{Fig3}(b)) correctly represents the insulating state. We have also shown the atom projected electronic DOS (Fig.~\ref{Fig4}(a), (b)) for FiM and ferromagnetic (FM) spin states within GGA+U approximation.  In both cases, the DOS shows the insulating state.
\begin{figure}
\begin{center}
\includegraphics[width=7.2cm]{Fig2.pdf}
\caption{\label{Fig2}(Color online) Total phonon-DOS is shown for (a) GGA, and (b) GGA+U calculations in FiM configuration. Unstable modes with imaginary frequencies (given as -ve) are observed only in GGA calculations. Projected DOS of Mn, V and O atoms within GGA+U calculations in (c) FiM, and (d) FM states.}
\end{center}
\end{figure}

\begin{table*}
\centering
\begin{tabular}{p{2.0cm}|p{3.5cm}|p{3.5cm}|p{3.5cm}|p{3.5cm}}
 \hline
  & \centering Experimental & \centering GGA & \centering GGA+U & ~~~~~~~~~~ GGA+U \\
  & & \centering (FiM) & \centering (FiM) & ~~~~~~~~~~~~ (FM)\\
 \hline
 \hline
Lattice Const. & \centering a=6.05\AA & \centering a=6.00\AA & \centering a=6.19\AA &~~~~~~~~~~ a=6.20\AA \\
  & \centering c=8.46\AA & \centering c=8.48\AA & \centering c=8.60\AA &~~~~~~~~~~ c=8.61\AA \\
 \hline
\centering Mn & \centering 0.000~~ 0.750~~ 0.875 & \centering 0.000~~ 0.750~~ 0.875  & \centering 0.000~~ 0.750~~ 0.875  & ~~~ 0.000~~ 0.750~~ 0.875 \\

\centering V & \centering 0.250~~ 0.250~~ 0.750 & \centering 0.250~~ 0.250~~ 0.750 &  \centering 0.250~~ 0.250~~ 0.750 & ~~~ 0.250~~ 0.250~~ 0.750 \\

\centering O & \centering 0.997~~ 0.474~~ 0.737 & \centering 0.999~~ 0.478~~ 0.739 & \centering 0.993~~ 0.474~~ 0.739 & ~~~ 0.993~~ 0.474~~ 0.739\\
 \hline
 \hline
\end{tabular}
\caption{Energy-minimized structural parameters of MnV$_2$O$_4$ in the FiM and FM states within GGA and GGA+U approximation. Experimental structural parameters are given for comparison\cite{NiiPRB}.}
\label{Tab1}
\end{table*}

In Table~\ref{Tab1} we compare the structural parameters of the GGA- and GGA+U-optimized structures for different spin configurations with the experimental one. We can see that the lattice constants, c/a ratio and the atomic positions of the optimized structures are comparable.
\begin{figure}
\begin{center}
\includegraphics[width=9.2cm]{Fig3.pdf}
\caption{\label{Fig3}(Color online) Electronic band structure of MnV$_2$O$_4$ in FiM state within (a) GGA and (b) GGA+U calculations.}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=7.5cm]{Fig4.pdf}
\caption{\label{Fig4}(Color online) Total and projected electronic DOS of Mn, V and O atoms of MnV$_2$O$_4$ in (a) FiM, and (b) FM states within GGA+U calculations. DOS in the positive Y-axis represent up-spin states, while DOS in the negative Y-axis represent down-spin states}
\end{center}
\end{figure}
The MnV$_2$O$_4$ compound in the tetragonal phase has C$_{4h}$ point group symmetry and its primitive unit cell (See Fig.~\ref{Fig1}(b)) contains six magnetic ions (two Mn and four V) and eight non-magnetic O ions. Phonons at the $\Gamma$ point can be classified according to the irreducible representations of the C$_{4h}$ point group of MnV$_2$O$_4$ as $\Gamma$ = 6E$_u$ + 6A$_u$ + 6B$_u$ + 4B$_g$ + 4E$_g$ + 3A$_g$, where the acoustic modes are omitted. Among them, the B$_g$, E$_g$, and A$_g$ modes are Raman active, while the E$_u$ and A$_u$ modes are IR active.

\subsection{Raman activity} In this section, we calculate the Raman spectra from density functional theory. The irreducible representation of Raman-active modes at $\Gamma$ point are listed in Table~\ref{Tab2} along with the calculated phonon frequencies. Calculated Raman allowed phonon modes are in good agreement with the experiments~\cite{TakuboPRB}.
\begin{table}[ht]
\begin{center}
\begin{tabular}{p{1.5cm} |p{1.5cm} |p{1.5cm} |p{1.5cm} |p{1.5cm}}
 \hline
\centering Modes & \centering Expt. (T=5K) & \centering FiM (GGA+U) & \centering FM (GGA+U) & ~~$\Delta_{rel}$(\%)\\
  \hline
  \hline
\centering  4B$_g$ & \centering $-$ & \centering 181 & \centering 184 & ~~ -1.7 \\
\centering   & \centering $-$ & \centering 367 & \centering 374 & ~~ -1.9 \\
\centering   & \centering 479 & \centering 440 & \centering 438 & ~~~ 0.4\\
\centering   & \centering 585 & \centering 539 & \centering 538 & ~~~ 0.2\\
  \hline
\centering  4E$_g$ & \centering $-$ & \centering 185 & \centering 187 & ~~ -1.1 \\
\centering  & \centering $-$ & \centering 257 & \centering 248 & ~~~ 3.5 \\
\centering  & \centering $-$ & \centering 451 & \centering 449 & ~~~ 0.4 \\
\centering  & \centering 570 & \centering 549 & \centering 550 & ~~ -0.2 \\
  \hline
\centering  3A$_g$ & \centering $-$ & \centering 319 & \centering 322 & ~~ -0.9 \\
\centering  & \centering $-$ & \centering 378 & \centering 377 & ~~~ 0.3 \\
\centering  & \centering 673 & \centering 633 & \centering 623 & ~~~ 1.6 \\
  \hline
  \hline
\end{tabular}
\caption{Irreducible representations of the Raman-active modes, calculated phonon frequencies (in cm$^{-1}$) for FiM and FM spin configurations in comparison with the Raman-active modes observed experimentally. The dashes in the second column imply that the intensity of the corresponding peak was too weak to observe experimentally~\cite{TakuboPRB}. Relative angular frequency shift ($\Delta_{rel}$=$\frac{\omega_{FiM}-\omega_{FM}}{\omega_{FiM}}\times$100\%) due to change in magnetic ordering of the Raman-active modes are given in the fifth column.}
\label{Tab2}
\end{center}
\end{table}

In a Raman scattering process, an incident photon of frequency $\omega_{l}$ and polarization versor {\textbf{g}}$_{l}$ either creates (Stokes process) or annihilates (anti-Stokes process) a phonon of frequency $\omega_{j}$ and scatters to an outgoing photon of frequency $\omega_{s}$ and polarization versor {\textbf{g}}$_{s}$.
From the principle of energy conservation, we can write $\omega_{s}$ = $\omega_{l}$ $\pm$ $\omega_{j}$, where the (plus) minus sign ascribe to the (anti-) Stokes process. The differential cross section for Raman scattering in non-resonant conditions of the Stokes process involving a phonon of eigenmode $j$ is given by the following equation (for a unit volume of the sample)~\cite{Cardona, Bru}:
\begin{equation}
\frac{\mathrm{d}^2 \sigma}{\mathrm{d} \Omega \mathrm{d} \omega}=\sum\limits_{j}\frac{\omega_{s}^{4}}{c^4}\lvert \mathrm{\textbf{g}}_{s}.\overline{R}^{j}.\mathrm{\textbf{g}}_{l} \rvert^2[n_{b}(\omega)+1]\delta(\omega-\omega_{j})
\label{eq1}
\end{equation}
In this expression $n_{b}(\omega)$ is the Bose occupation factor, and c is the velocity of light in vacuum. The second rank tensor $\overline{R}^{j}$ in Eq.~\ref{eq1} is known as the Raman tensor associated with the phonon eigenmode $j$ which is given by the following equation:
\begin{equation}
R_{\alpha\beta}^{j}=\sqrt{\frac{V\hslash}{2\omega_{j}}}\sum\limits_{\kappa=1}^{N}\frac{\partial \chi_{\alpha\beta}}{\partial \mathrm{\textbf{r}}(\kappa)}.\frac{\mathrm{\textbf{e}}(j,\kappa)}{\sqrt{M_{\kappa}}} ; (\alpha,\beta = 1, 2, 3)
\label{eq2}
\end{equation}
Here, $V$ is the unit cell volume. $\textbf{r}(\kappa)$ and $M_{\kappa}$ are the position and mass of the $\kappa^{th}$ atom respectively and the summation runs over all the $N$ atoms in the unit cell. The eigenstates and eigenvalues of the dynamical matrix at the $\Gamma$ point are denoted by $\textbf{e}(j,\kappa)$, and ${\omega_{j}}$ respectively. In Eq.~\ref{eq2}, the electric polarizability tensor $\chi_{\alpha\beta}$ is defined as: $\chi_{\alpha\beta}=\frac{1}{4\pi}(\epsilon_{\alpha\beta}-\delta_{\alpha\beta})$, where $\epsilon_{\alpha\beta}$ is the dielectric tensor. The tensor $\overline{R}^{j}$ is computed from the electric polarizability tensor within finite difference approach by moving the atoms of different symmetry with a displacement of 0.03\AA~\cite{UmariPRB,CeriottiPRB}.
\begin{figure}
\begin{center}
\includegraphics[width=9.0cm]{Fig5.pdf}
\caption{\label{Fig5}(Color online) Calculated Raman spectrum for light
in the X$^{\prime}$Y$^{\prime}$ and XY polarization. Raman peaks with red (blue) color are observed in X$^{\prime}$Y$^{\prime}$ (XY) polarization.}
\end{center}
\end{figure}

In order to compare our theoretical results with the available experimental data, we have computed the intensity of the Raman spectra of a single-crystal sample from differential scattering cross-section as implemented in the PHONON software~\cite{PHONON} at various polarization configurations of the incident and scattered light (same as the experimental ones~\cite{TakuboPRB}). In our calculations, we have considered linear polarization along [100], [010], [110], and [1$\overline{1}$0] direction which is ascribed as X, Y, X$^{\prime}$, and Y$^{\prime}$ respectively. Temperature-dependence of the Raman spectra within the XY (polarization direction of the incident and scattered light respectively) and X$'$Y$'$ polarization configurations has been reported experimentally, and by analyzing the intensity peaks of certain modes, the nature of the orbital ordering in this compound was established\cite{TakuboPRB}. However, the phonon frequencies were calculated by assuming short-range force constants for the nearest- neighbor bonds and the modes were assigned (irreducible representation) based on the I4$_1$/amd space group, while the space group symmetry of the parent compound is actually I4$_1$/a.

Calculated frequencies of the four Raman-allowed B$_g$ modes within I4$_1$/a space group symmetry are at 181cm$^{-1}$(B$_{g}$(1)), 367cm$^{-1}$(B$_{g}$(2)), 440cm$^{-1}$(B$_{g}$(3)), and 539cm$^{-1}$(B$_{g}$(4)). From our Raman scattering calculations, we found finite intensity peaks in the X$'$Y$'$ polarization (Fig.~\ref{Fig5}) at two higher frequency B$_{g}$ modes (B$_{g}$(3) and B$_{g}$(4)), while the lower modes (B$_{g}$(1) and B$_{g}$(2)) are absent. This result agrees well with the experimental findings~\cite{TakuboPRB}. Interestingly, an intensity peak appears in XY polarization at 367 cm$^{-1}$ (see Fig.~\ref{Fig5}) associated with the B$_{g}$(2) mode. This mode is also observed experimentally at 370 cm$^{-1}$ in the XY spectrum, while earlier theoretical calculations based on the Franck-Condon formalism predicted the absence of intensity peaks in the same polarization~\cite{TakuboPRB}. According to their theory, the Mott excitations along the in-plane V-V bond are allowed in the XY configuration, and due to the symmetric nature of the d$_{xy}$ orbital, Mott transitions to the forward and backward direction cancel the intensity~\cite{TakuboPRB}.
\begin{figure}
\begin{center}
\includegraphics[width=9.0cm]{Fig6.pdf}
\caption{\label{Fig6}(Color online) Atomic displacements of B$_{g}$ phonons responsible for the Raman peaks associated with the four B$_{g}$ modes at (a) 181cm$^{-1}$(B$_{g}$(1)), (b) 367cm$^{-1}$(B$_{g}$(2)), (c) 440cm$^{-1}$(B$_{g}$(3)), and (d) 539cm$^{-1}$(B$_{g}$(4)).}
\end{center}
\end{figure}

We discuss the Raman peaks of the specific phonon modes of MnV$_2$O$_4$ in its tetragonal phase, and understand the displacement patterns of the lattice vibrations obtained from {\it ab-initio} phonon calculations. Among the four B$_{g}$ modes, only three B$_g$ modes show the finite intensity of the Raman peaks, while the first one (B$_g$(1)) does not contribute to the Raman scattering process. In Fig.~\ref{Fig6}, we have shown the displacement patterns of these modes. B$_g$(1) mode corresponds to the stretching of the Mn ions along the c-direction (Fig.~\ref{Fig6}(a)), the O ions barely move in this mode. We can see in Fig.~\ref{Fig2}(c),(d) phonons associated with the vibration of Mn ions contribute more to the DOS around that frequency range. The B$_g$(2) (Fig.~\ref{Fig6}(b)) mode, responsible for the Raman peak at 367cm$^{-1}$ comes from the displacements of the O ions along a and b axes while the atomic vibrations of Mn ions are negligibly small. The mode B$_g$(3) and B$_g$(4), responsible for the Raman peaks at 440cm$^{-1}$ and 539cm$^{-1}$ respectively, correspond to the displacements of O atoms as shown in Fig.~\ref{Fig6}(c), and Fig.~\ref{Fig6}(d). We have clearly shown here that the lowest frequency B$_g$ mode emerges due to the phonons associated with Mn ions, and high-frequency B$_g$ modes originate from the atomic vibrations of O ions mainly. However, in all cases, V ions do not move.

\subsection{Spin-phonon coupling}
To understand the interplay between magnetic ordering and phonons, we determine phonons at the zone center and zone boundaries with FiM and FM ordering which gives a measure of spin-phonon coupling. While any spin configuration instead of FM would have been also useful for this purpose, the space group symmetry remains the same in these spin configurations. In Fig.~\ref{Fig7}, we show phonon spectra along high symmetry directions in the Brillouin zone for the FiM and FM spin-ordered states in the tetragonal phase of MnV$_2$O$_4$. In the absence of spin-phonon coupling, hardly any change in phonon spectra is expected in the different magnetic configurations. A strong spin-phonon coupling along the zone center and zone boundary points is  however observed as the phonon frequencies change  with changing magnetic order. In the phonon dispersion (Fig.~\ref{Fig7}), no unstable modes appear at any point in the BZ for either magnetic order.
\begin{figure}
\begin{center}
\includegraphics[width=9.0cm]{Fig7.pdf}
\caption{\label{Fig7}(Color online) Phonon dispersion of FiM (red solid lines) and FM (black dotted linens) states of MnV$_2$O$_4$ in its tetragonal phase.}
\end{center}
\end{figure}

Heisenberg spin Hamiltonian for MnV$_2$O$_4$ can be written as:
\begin{equation}
H=\frac{1}{2}\sum\limits_{<ij>}J_{ij}\vec{S_i}\cdot\vec{\sigma_j}-\frac{1}{2}\sum\limits_{<kl>}J_{kl}^{'}\vec{\sigma_k}\cdot\vec{\sigma_l}
\label{eq3}
\end{equation}
$J_{ij}$ is the AFM exchange interaction between $\vec{S_i}$ (Mn spins) and $\vec{\sigma_j}$ (V spins) giving an FiM state, whereas $J_{kl}$ is the FM exchange interaction between V spins.
Changes in the exchange interactions due to the spin-phonon coupling can be obtained by a Taylor series expansion of $J$ with respect to the amplitude of atomic displacements~\cite{GranadoPRB,KumarPRB},
\begin{equation}
J(\vec{u}_{\nu}^\lambda) = J_0+\vec{u}_{\nu}^\lambda (\nabla_{u_{\nu}}J)+\frac{1}{2}\vec{u}_{\nu}^\lambda (\nabla^2_{u_{\nu\nu'}}J)\vec{u}_{\nu'}^\lambda
\label{eq4}
\end{equation}
\begin{figure}
\begin{center}
\includegraphics[width=7.0cm]{Fig8.pdf}
\caption{\label{Fig8}(Color online) The Hellman-Feynman forces on the Oxygen ions in the FM configuration of the relaxed FiM configuration (crystallographic unit cell). The forces are drawn with golden arrows and give the lowest order spin-phonon coupling.}
\end{center}
\end{figure}
Here, $\vec{u}_\nu^\lambda$ is the displacement vector from the equilibrium position of the $\nu^{th}$ ion for the $\lambda$th phonon mode. $J_0$ is the bare spin-spin exchange coupling term, and $\nabla_{u}J$ relates to the forces on atoms arising from the change in magnetic configuration (w.r.t its ground state magnetic order). This term, which is linear in atomic displacements, gives the lowest order coupling between spins and phonons. As seen in Fig.~\ref{Fig8}, these forces are equal and opposite for the pairs of Oxygen atoms, and also have the full symmetry (A$_g$) of the lattice. This could lead to the magneto-elastic anomaly at T$_N$. Shift in the phonon frequency $\Delta_\lambda$ of the $\lambda$th phonon mode due to the change in the magnetic order is related to $\nabla^2_{u}J$~\cite{GranadoPRB} (second-order coupling) by the following expression (the reduced mass and the frequency of the $\lambda$th phonon mode are denoted by $\mu_\lambda$ and $\omega_\lambda$ respectively, and $\hat{u}_{\nu}^\lambda = \vec{u}_{\nu}^\lambda/|\vec{u}_{\nu}^\lambda|$):
\begin{equation}
\Delta_\lambda = \frac{1}{2\mu_\lambda \omega_\lambda}\sum\limits_{\nu}{\hat{u}}_{\nu}^\lambda(\nabla^2_{u_{\nu}}J){\hat{u}}_{\nu}^\lambda = \frac{J''_\lambda}{2\mu_\lambda \omega_\lambda}
\label{eq5}
\end{equation}
This quantity gives an estimate of second-order spin-phonon coupling ($J''_\lambda = \sum\limits_{\nu}{\hat{u}}_{\nu}^\lambda(\nabla^2_{u_{\nu}}J){\hat{u}}_{\nu}^\lambda$~\cite{KumarA}), and hence, large values of $\Delta$ imply strong spin-phonon coupling. Relative change in phonon frequency ($\Delta_{rel}^\lambda$ = $\frac{\omega_{FiM}^\lambda-\omega_{FM}^\lambda}{\omega_{FiM}^\lambda}\times$100\%)~\cite{PaulPRB} due to change in the magnetic order for the $\Gamma$ ({\bf{q}}=$0,0,0$) phonons, as well as for the zone boundary phonons at N ($1/2,0,0$), X ($0,0,1/2$), and Z ($1/2,1/2,-1/2$) points of the BZ are presented in Fig.~\ref{Fig9} (a)-(d).
\begin{figure}
\begin{center}
\includegraphics[width=9.2cm]{Fig9.pdf}
\caption{\label{Fig9}(Color online) Relative change in phonon frequency ($\Delta_{rel}$ = $\frac{\omega_{FiM}-\omega_{FM}}{\omega_{FiM}}\times$100\%) calculated at the zone center (a) $\Gamma$, and zone boundary points (b) N, (c) X, (d) Z.}
\end{center}
\end{figure}

In Fig.~\ref{Fig9}(a), two low-frequency (181 cm$^{-1}$, 367 cm$^{-1}$) B$_g$ modes (all B$_g$ modes are marked in red circles) show softening of frequency due to change in spin configuration from FM to FiM. However, two high-frequency B$_g$ modes at 440 cm$^{-1}$ and 549 cm$^{-1}$ show very weak spin-phonon coupling compared to the others. Among all the $\Gamma$ phonons, B$_u$ mode at 178 cm$^{-1}$ (marked by sky-blue circles) shows maximum relative softening ($\sim-4$\%), while 257 cm$^{-1}$ E$_g$ mode (marked by green circles) shows maximum relative hardening due to spin-phonon interaction. Among the zone boundary phonons, 70 cm$^{-1}$ phonon mode (pink circles) (Fig.~\ref{Fig9}(b)) at the N point of the BZ ($1/2,0,0$) shows more than 10\% hardening of frequency due to change in magnetic order from FM to FiM and exhibits strongest spin-phonon coupling across BZ.

To connect our results with experiments~\cite{GleasonPRB} and to understand the observed temperature-dependence of phonon frequencies, we use Ginzburg-Landau (GL) theory. The free-energy of our spin-phonon coupled system can be written as
\begin{equation}
F = F_0 + a~m^2 + b~m^4 + \sum\limits_{\lambda}(J''_\lambda m^2 v_\lambda^2 + \frac{1}{2} \mu_\lambda {\omega_0}_\lambda^2 v_\lambda^2)
\label{eq6}
\end{equation}
Here, $a$ and $b$ are usual GL parameters, $m$ is the FiM order parameter, $v_\lambda$ is the amplitude of the $\lambda$th phonon mode, and $\omega_{0\lambda}$ is the high temperature ($T \geq T_N$) phonon frequency. The temperature-dependence of FiM order parameter $m$ is assumed to be $\propto (1-T/T_N)^{\beta}$ for $T<T_N$. It is evident that in the presence of spin-phonon coupling, the phonon frequency will change below $T_N$ as the FiM ordering sets in. The modified phonon frequency is

\begin{equation}
\omega_\lambda = 2 \Delta_\lambda m^2 \pm \sqrt{{\omega_0}_\lambda^2 + 4\Delta_\lambda^2 m^4}
\label{eq7}
\end{equation}
Here, the positive solution has been considered, as the other solution gives negative values of $\omega_\lambda$. We have estimated $\Delta_\lambda$ from our DFT calculations and then used it in Eq.~\ref{eq7} to find the temperature-dependence of relevant phonon frequencies (Fig.~\ref{Fig10}) in the tetragonal phase of MnV$_2$O$_4$. We have taken the critical exponent value $\beta=0.5$ (mean-field theory) and $\beta=0.365$ (3D-Heisenberg model) respectively. Zhang {\it et al.}\cite{ZhangEPL} showed that the 3D-Heisenberg model is the best model to describe the critical properties of ferromagnet spinel CdCr$_2$Se$_4$. We have also found that $\beta=0.365$ gives a better temperature-dependence than the mean-field behavior.
\begin{figure}
\begin{center}
\includegraphics[width=7.0cm]{Fig10.pdf}
\caption{\label{Fig10}(Color online) Temperature-dependence of (a) 178 cm$^{-1}$ phonon mode ($\Delta_\lambda=-6$ cm$^{-1}$), and (b) 70 cm$^{-1}$ phonon mode ($\Delta_\lambda=7$ cm$^{-1}$) as obtained from the GL theory. We have considered the critical exponet value~\cite{ZhangEPL} $\beta=0.5$ (mean-field theory) and $\beta=0.365$ (3D-Heisenberg model) respectively in our calculations.}
\end{center}
\end{figure}

In Fig.~\ref{Fig10}(a), we see the phonon frequency decreases with decreasing temperature below T$_N$, which is associated with the softening of a phonon mode ($\Delta_\lambda<0$) due to spin-phonon coupling. Interestingly, in the Raman scattering experiments~\cite{TakuboPRB, GleasonPRB}, modes near 178 cm$^{-1}$ show anomalous temperature-dependence as the frequency decreases with decreasing temperature below $T_N$. However, in Fig.~\ref{Fig10}(b) the phonon frequency increases with decreasing temperature below $T_N$ and this is associated with the hardening of a phonon mode ($\Delta_\lambda>0$) due to coupling between spins and phonons. Experimentally, the temperature-dependence of Raman intensity peak near 80 cm$^{-1}$ shows a similar behavior below the FiM transition temperature. Our results agree qualitatively with the experimental observations, and also corroborate the experimental prediction of strong spin-lattice coupling across the BZ in this material.

\section{Conclusions}
\label{conc}
Our first-principles study of phonon dispersions  in two different magnetic orders (FiM and FM) in MnV$_2$O$_4$ show notable spin-phonon coupling. We also find that in the low-temperature tetragonal structure of MnV$_2$O$_4$, correlations are necessary to eliminate unstable modes. Raman intensities for XY and X$'$Y$'$ polarization reveal finite-intensity peaks in the X$'$Y$'$ polarization at two higher frequency B$_g$ modes (B$_g$(3) and B$_g$(4)) and a peak in XY polarization at 367 cm$^{-1}$ which is associated with B$_g$(2) mode. The lowest frequency B$_g$ mode is found to emerge from phonons associated with Mn ions, while high frequency B$_g$ modes originate from O ion vibration. Landau theory analysis reveals the mechanism governing the low-temperature Raman anomalies of MnV$_2$O$_4$. Our results agree qualitatively with recent experiments~\cite{TakuboPRB,GleasonPRB} and reveal that a strong interplay between the lattice and magnetic degrees of freedom is important for understanding the underlying physics of MnV$_2$O$_4$.

\section{Acknowledgments}
D.D. acknowledges Department of Science and Technology (DST), India for an INSPIRE research fellowship. U.V.W. acknowledges support from a J.C. Bose National Fellowship and a Sheikh Saqr Fellowship. A.T. acknowledges research funding from CSIR (India) through the grant number: 03(1373)/16/EMR-II.

redpajama_set_name: RedPajamaArXiv


Exploring a virtual Christmas world with many surprises at home in the warmth of a living room. Our customers were able to experience this with our xmasAR app.
Besides new hardware Apple presented quite some innovations on the software side. Yves, our Head of Innovation & Technology, was there.
What tech trends shaped the past year and what will move the mobile world the most in 2017? Our consultants, engineers and project managers put their heads together.
What's moving the «mobile world» in 2016?
How has the mobile market evolved in the past year? And what trends are emerging in relation to mobile technologies and what opportunities do they bring to suppliers and consumers?


Win your very own FreshBed at Somnex: The Sleep Show!
Somnex: The Sleep Show is the first ever exhibition dedicated entirely to sleep-health. Over three packed days, leading experts in the field of sleep will gather to share news, practical information, tips and workshops about all things sleep.
…and so much more! Check out the full agenda here.
Q&A with leading hospitality experts who will share how they are helping their guests sleep better and what impact that has had on their brand, customer experience and retention.
See the full Trade Day agenda here.
FreshBed is happy to be taking part in the first ever Somnex, and for a really special treat: visitors who stop by our booth will have a chance to win their very own FreshBed*!
This is our first ever FreshBed giveaway, and we can't wait to give one lucky winner the gift of a FreshBed for their very own home. The winner will be announced on Sunday, the last day of the exhibition.
Furthermore, we will be unveiling and demonstrating a very special sleep enhancement product: the Zeez Sleep Pebble. The Zeez Sleep Pebble is a spectacular device used to improve sleep by reducing the impact of stress. It prompts your brain to slow down, relax, fall asleep, and experience wonderful deep sleep. And it also helps overcome jet lag! Nearly 80% of Zeez Sleep Pebble users tell us that they sleep better and have more energy, so FreshBed is proud to be the official Zeez Sleep Pebble partner, and we'd love to show you how it works at The Sleep Show next month.
So join us in London October 12th to 14th for what is sure to be a fun, informative, and memorable three days.
Purchase your exhibition pass here.
Friends of FreshBed will receive a 40% discount by using the promo code EXH40.
Note: Buyers, purchasers, or procurement managers wishing to attend Somnex can apply for a free Trade Day pass here.


Experience the Realtime implementation of Ranorex projects by exploring different features of report customization, and coding with the Ranorex API, Ranorex Studio and etc. Learn techniques for fully exploiting the capabilities of the RanoreXPath query language. And also You will learn the finer nuances of creating automation tests such as adding validation steps, creating modular tests from reusable components, and using external data sources to form iterative, data-driven tests.
Avg. Salary for Ranorex Automation Engineer $66,859 PA.
Ranorex has a market share of about 1.12%.
Used by top industries across various business Verticals. Ex: Sonsoft Inc, BAE Systems, Capgemini etc.
This event is organized by MindMajix Technologies Inc..
See more from MindMajix Technologies Inc.


text:
Q: In Gradle, can one get the calling project or task from a Groovy method? // method in a library or in an "ext" property

void aMethod(Object arg) {

    // in some way determine the "self" "this" etc of the **caller** and determine if
    // the caller is a project or task within a project and get the project or task.

    // I assume this would use some sort of Groovy capability in the Gradle context

    File argFile = callingProject.file(arg) // expand file paths relative to callingProject
}

redpajama_set_name: RedPajamaStackExchange


text:
Vol. 8 (2019): Proceedings of the conference "Building Bridges for English Language Centers" /
Promoting Your Department and Practice with Twitter
Crystal Bock Thiessen
Intensive English Programs (IEPs) constantly find themselves in an ongoing battle for their legitimacy and relevancy throughout many university campuses in the United States. The often overlooked professional development demands and multicultural endeavors in which ESL instructors partake, coupled with our current social and political climate, makes it imperative that IEPs and English language instructors take on the promotion of their important work on campus and with our international English language learners themselves. Fortunately, with the prevalence of social media, Twitter in particular, it is easier and more accessible for English language professionals and departments to demonstrate that what they do extends greatly beyond teaching.
Vol. 8 (2019): Proceedings of the conference "Building Bridges for English Language Centers"
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution Non-Commercial 4.0 International License that allows non-commercial uses of the work with an acknowledgement of the work's authorship and initial publication in this journal.

redpajama_set_name: RedPajamaCommonCrawl


text:
Ohio State football's Justin Fields makes Heisman Trophy bid as the nation's toughest quarterback
Updated: Nov. 30, 2019, 8:04 p.m. |
Published: Nov. 30, 2019, 7:01 p.m.
Ohio State's Justin Fields tosses 4 TD passes against Michigan
ANN ARBOR, Mich. -- Ohio State quarterback Justin Fields leaned against the railing of the stairs leading to the interview dais, the ice pack on his left knee bulging beneath his sweat pants.
A few minutes later, Fields confirmed what many suspected in the week leading up to the Buckeyes' game at Michigan on Saturday. The sophomore was playing hurt, after suffering what he called a "sprained MCL" late in the previous week's victory over Penn State.
In addition to applying the appropriate treatment, Ohio State's medical personnel wanted Fields wear a brace against the Wolverines. He agreed to a small one. Halfway through the third quarter — after Fields clutched his left knee in pain and limped off the field into a medical tent — they insisted on an upgrade.
What happened next — Fields returning to the field seven plays later to throw a touchdown pass on his first snap that propelled Ohio State to a 56-27 victory — will replay in preview footage of future installments of "The Game" for years to come.
Ohio State coach Ryan called it first, "a magical moment," then, "a Heisman moment."
Fields' chances of challenging LSU quarterback Joe Burrow for the Heisman Trophy seemed long entering the week. His best statistical case relied on efficiency, not eye-popping accumulation. His running prowess impacted the game most as the diversion creating openings for running back J.K. Dobbins.
Yet by strapping on that bigger brace and limping back to the field at Michigan Stadium on Saturday, Fields made perhaps his best possible case for the award. He is not the most prolific quarterback in college football, and considering what Burrow has meant in reviving LSU, his story may not be the most inspirational.
Fields, however, may be the nation's toughest quarterback, and the effect on the rest of the Buckeyes is palpable.
"Coach (Ryan) Day emphasizes toughness, so I wanted to show the team I was tough," Fields said. "I just got out there and played the game."
Ohio State took possession with 8:28 remaining in the third quarter, leading 35-16. Fields ran for a 9-yard gain on first down, then completed a 15-yard pass to Austin Mack on the sideline on second down. Those following the path of the ball did not see tight end Luke Farrell get blocked back into Fields at the end of the play, rolling up onto that left knee.
Fields immediately clutched the knee and remained on the field while athletic trainers attended to him. He eventually stood and limped off the field directly to the medical tent on Ohio State's sideline. Fields said the athletic trainers performed standard tests to check for more significant knee damage and, presumably after finding none, affixed the larger, more cumbersome brace.
"It's all metal like a lineman," Fields said later, laughing. "I'm not trying to be out there acting like an O lineman."
Meanwhile, backup Chris Chugonov kept the Buckeyes driving. He completed a third-and-5 pass to K.J. Hill for 11 yards to move the chains. Master Teague, giving Dobbins a break, reached for the six feet necessary to convert a third-and-2.
Around this time, Fields emerged from the tent with his helmet. On second-and-10 at the Michigan 30, he put it on and trotted back onto the field.
On the first play, Michigan's pass rush breached the pocket, immediately testing Fields' mobility. He rolled out to his left, keeping his eyes downfield. Then he planted a lofted a strike into the back of the end zone, where only freshman Garrett Wilson could catch it in stride for a touchdown and a 42-16 lead with 3:46 left in the third quarter.
"For him to ad lib, make a play and then make that throw going to his left — that's about as good a throw as I've seen in a long time," Day said. "He put it right in the back of the end zone. And that just goes to show you what's inside of him. His heart, his character, and his competitive toughness is as good as I've ever been around, and I can't say enough about the way he played today."
That entire sequence could have imploded in panic. The other Buckeyes knew Fields' injury could be serious. Left guard Jonah Jackson said he prayed before refocusing on the next play. Eight plays later, after the touchdown, Jackson went to congratulate his quarterback — or at least the player he thought was his quarterback.
"When the touchdown happened I was like, 'Where's Chuggs at?'" Jackson said. "I didn't even realize Justin threw it. But that was awesome, just to see his toughness and perseverance in the game and his ability to come back in and do what he did."
Fields finished the game, completing 14 of 25 passes for 302 yards and four touchdowns. He took only one sack — on the first drive of the game — and rushed for 29 yards on his other five carries.
He also improved to 12-0 as Ohio State's starting quarterback. Would any of the other candidates for the job following Dwayne Haskins' decision to enter the NFL Draft be able to stay the same? Perhaps, considering the dominance of the Buckeyes' defense, but not likely.
Day, in an almost impossible position, has avoided picking a favorite in his team's three-way race to reach the Heisman Trophy presentation in New York City later this month.
Should it be Fields, the multi-talented field general? How about Dobbins, whose production has been stifled only by how seldom he plays in the second half in the name of prudent usage and sportsmanship. What about defensive end Chase Young, who has made as strong a push as any defensive player in years for consideration?
"I'll say this: All three of them played great today," Day said. "And I will say that all three of them deserve to be in New York and I'll let everybody make the decision on who they think."
You can measure a quarterback in any number of ways. After his second consecutive 300-yard passing game, Fields has thrown 37 touchdown passes against one interception. He should end the regular season as one of the five most efficient passers in the nation.
He is also 12-0 and his team sits atop the Big Ten Conference and the College Football Playoff rankings. The yards may not be piling up, but the intangibles are. You can ask the other Heisman candidate whose volcanic intensity inspires the Ohio State defense.
"I feel like he's the best quarterback I the country," Young said. "You can definitely see his toughness. I love Justin, and he's definitely leading us right now."
Get Buckeyes Insider texts in your phone from Doug Lesmerises: Cut through the clutter of social media and communicate directly with the award-winning OSU football reporter, just like you would with your friends. It's just $3.99 a month, which works out to about 13 cents a day. Learn more and sign up here.
More OSU coverage
Ohio State storms past Michigan 56-27 to extend winning streak in The Game to eight
OSU makes Michigan play a perfect game, and under Harbaugh, the Wolverines can't do it: Doug Lesmerises
Eight plays that defined the game
The OSU-Michigan rivalry: Transfusing passion from Buckeyes fans to coaches and players new to it
Ohio State fans recall shocking 1969 loss at Michigan: 'One of the worst days of my life.'
9 things you might not know about the 1969 game and college football 50 years ago
Ohio State vs. Michigan 1969: Read the story from the loss that broke Buckeyes' hearts
Who are some of the recruits Ohio State is battling for with Michigan?
Ohio State-Michigan betting line history
Buy Buckeyes tickets: StubHub, SeatGeek, Ticketmaster


2) Wear Gold shirt , navy shorts, and navy socks to tomorrows game.
3) Bring all shirts and if you don't have training kits yet please bring a gold and a navy shirt.
4) Arrive 45 minutes prior to kickoff and expect traffic. Going to Mason at rush hour = sitting in traffic if you don't leave early!
5) Please communicate with your coach after a game if you are going to miss the next coming games even if you have already as we have a lot of players to look after.
6) Be sure to hydrate a lot tomorrow/ all weekend and eat healthy as it will help your recovery and performance on the field.
7) Taking stretching seriously as we want to avoid injury while increasing our stamina and flexibility this weekend.
p.s. Thanks to Bill Wolf for all the spirit wear and constant communication. Also if anyone has a tent and the forecast on Saturday/ Sunday is extremely hot, we could use it!


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UNLEASH brought more than 1,000 global talents to Denmark to search for innovative solutions to the Sustainable Development Goals. The water track took some of the talents to Bjerringbro and Grundfos. We have met a couple them during their days in our backyard.
innovation lab in Denmark. Each SDG represented a track, and Grundfos hosted and sponsored the water track, which brought more than 120 of the future stars to Bjerringbro.
Here they worked hard on finding innovative solutions to their water cases, and they got the opportunity to get acquainted with Grundfos-technology, -business models and -ambitions.
"The involvement of Grundfos in linked markets, as opposed to the core business of pumps, I found that very progressive," says Matthew Davey from South Africa, who was one of the participants in the UNLEASH Innovation Lab 2017.
The event concluded in Aarhus on Monday 21 August, where the very best cases from each track were awarded.


We don't know exactly when Shakespeare started writing plays, but they were probably being performed in London by 1592, and he's likely to have written his final plays just a couple of years before his death in 1616.
It is believed that he wrote around 38 plays, including collaborations with other writers. here's a chronological list of Shakespeare's plays by decade.


text:
Methodology Article
A semi-automated, KNIME-based workflow for biofilm assays
Katrin Leinweber1,2,4,
Silke Müller3 &
Peter G. Kroth4
BMC Microbiology volume 16, Article number: 61 (2016) Cite this article
A current focus of biofilm research is the chemical interaction between microorganisms within the biofilms. Prerequisites for this research are bioassay systems which integrate reliable tools for the planning of experiments with robot-assisted measurements and with rapid data processing. Here, data structures that are both human- and machine readable may be particularly useful.
In this report, we present several simplification and robotisation options for an assay of bacteria-induced biofilm formation by the freshwater diatom Achnanthidium minutissimum. We also tested several proof-of-concept robotisation methods for pipetting, as well as for measuring the biofilm absorbance directly in the multi-well plates. Furthermore, we exemplify the implementation of an improved data processing workflow for this assay using the Konstanz Information Miner (KNIME), a free and open source data analysis environment. The workflow integrates experiment planning files and absorbance read-out data, towards their automated processing for analysis.
Our workflow lead to a substantial reduction of the measurement and data processing workload, while still reproducing previously obtained results in the A. minutissimum biofilm assay. The methods, scripts and files we designed are described here, offering adaptable options for other medium-throughput biofilm screenings.
Diatoms (Bacillariophyceae) are a group of highly productive unicellular photoautotrophs and responsible for roughly one fifth of Earth's primary production [1, 2]. Many diatoms produce and secrete extracellular polymeric substances (EPS) which are a major component of their extracellular polymeric matrices, and which convey motility and substrate adherence [3, 4]. Such aggregates of microbes that are embedded in a matrix of secreted EPS form so called biofilms [5]. Biofouling, the colonisation of man-made structures like e.g. ship hulls or underwater constructions by diatoms and other aquatic organisms may causes considerable maintenance costs [6, 7].
Achnanthidium minutissimum is a benthic pennate diatom that appears cosmopolitically in freshwater habitats which may form biofilms on substrata [8]. Carbohydrate secretion and biofilm formation by A. minutissimum can be induced by certain bacteria, but also in the presence of substances secreted by the bacteria, indicating that the bacteria induce or even may control biofilm formation by the diatom [9, 10]. In order to quantify biofilm formation as well as to purify and identify bacterial signal substances, a bioassay based on these effects has been established in our laboratory previously [11]. This biofilm assay relies on the staining of diatom cells with crystal violet (CV). This compound is also used for staining of Gram-positive bacteria. It is binding to organic polymers such as polysaccharides and peptidoglycans ([12], Table 2). Subsequently, the stain can be extracted with ethanol (EtOH), and quantified photometrically. However, this protocol is not automated, and thus proved to be difficult to apply to medium-throughput screenings, e.g. for biofilm-inducing, bacterial infochemicals or biofilm-relevant mutants.
Inspired by other biofilm assay approaches which include automated steps [13, 14], we aimed to improve the A. minutissimum bioassay described above with semi-automated pipetting and absorbance read-out methods. Additionally, we wanted to improve the preparation of sample metadata and biofilm measurement data for analysis, adopting an already widely used tool in nucleotide sequencing and biochemical screening: the Konstanz Information Miner (https://www.knime.org/) (KNIME; [15, 16]). The program is an interactive, visual, modular environment and open platform for the design and execution of data analysis workflows [17]. To the best of our knowledge, no diatom- or biofilm-focussed approach so far is based on KNIME-supported data analyses or shares such workflows. Therefore, the objective of this study is to explain the above-mentioned automation options, and to present compelling evidence for their improvement potential using several examples from a laborious diatom biofilm assay.
Cultivation conditions
Xenic cultures of Achnanthidium minutissimum (Kützing) [18] were isolated from epilithic biofilms from the littoral zone of Lake Constance, and axenified as described previously [19]. Both xenic and axenic A. minutissimum stocks were cultivated in modified BM (Bacillariophycean medium) in ventilated tissue culture flasks (Sarstedt, Newton, NC, USA). These were stored in a climatised culture room at 16 °C, 50 % humidity and in a day-night cycle of 12 h at 20–50 \(\frac {\mu \text {mol~photons}}{\mathrm {m}^{2} \cdot \mathrm {s}}\) and 12 h of darkness. Cultures were subcultivated monthly by scraping cells off the flask bases and transferring 1 mL of the resulting suspension into fresh flasks with ca. 40 mL BM.
Bacteroidetes strain 32 (S32) was cultivated on agar plates prepared from 50 % (v/v) LB [20]. Between monthly transfers to fresh plates, S32 was grown for 5 days at 22 °C in darkness, and was then stored at 4–8 °C. Liquid S32 cultures were prepared by inoculating 50 % LB and shaking at 22 °C and 120 rpm for 3–5 days.
Human- and machine-readable plate layout worksheets
The first optimisable step of the biofilm assay experiments was the planning of sample layouts in the multi-well plates before their inoculation. Our proposed plate layout scheme is based on Microsoft's Office Open XML format (.xlsx files), of which we used the worksheets to represent the multi-well plates (Fig. 1 a and Additional file 1). These worksheets are both human- and machine-readable. In each sheet, the sample metadata was contained in several plate-congruent coordinate systems which are titles with the metadata type (e.g. culture, treatment, identifiers, etc.). Because our workflow produces data files which are compatible with the R environment for statistical computing, in the terminology of R the table titles are factors and the contents are levels.
Overview of semi-automated biofilm assay from metadata tables (a) to measurement workflow (c). Hexagonal boxes indicate manual steps of biofilm assay procedure. Rounded boxes represent robotised steps. Dashed, grey-lined boxes represent main sections of the biofilm assay protocol. a Metadata tables in .xlsx worksheet are used to plan the layout of samples on the multi-well plate (see Additional file 1). Table headings represent factors (cell_culture & treatment), whose levels (respectively, ax, co & xen, as well as NA for controls & S32 for co-cultures) fill the plate-congruent coordinate systems of the tables. Grey cells indicates bases for formulas, which help to rapidly fill repetitive tables with for example technical replicates or dilution calculations. b Photo of incubated plate, ready for removal of non-adherent cells and absorbance measurement. c Robotised measurement preparation (see Table 1), absorbance read-out and data processing from biofilm assay plates (see Additional files 3, 4, 5 and 6)
Table 1 Overview of electronic pipetting scripts executed by the Viaflo ASSIST robot (http://www. integra-biosciences.com/sites/viaflo\_assist.html)
The KNIME workflow is agnostic towards the number of wells per plate and the number of factors and levels. Therefore, all plate-congruent tables can be adjusted congruently to other multi-well formats by adding or removing rows and columns. More such tables can be added to the worksheets in order to add more metadata to the samples, which can be used later in the data analyses and visualisations. Adding more plates to an experiment was mirrored by adding more worksheets to the same .xlsx file. Spreading the worksheets across different .xlsx files is possible, but may cause more work later when preparing the KNIME workflow.
KNIME workflow for data processing
Due to the incubation time of the diatom biofilms, about two weeks usually passed between preparing the plate layout worksheets and obtaining the measurement results as described in sections Bioassay experiments and Absorbance read-outs of stained and unstained biofilm assays. In order to link planning documents of an experiment with the final data analyses and results visualisations, we designed a data processing workflow that unifies multiple files for further analysis (Fig. 2 and Additional file 5). The workflow was implemented in the Konstanz Information Miner (KNIME) (https://www.knime.org/knime) v3.1.1 [17] using freely available functions and nodes, particularly the HCS-Tools (https://github.com/knime-mpicbg/HCS-Tools) extension [21].
KNIME workflow example for the integration of sample metadata and measurement results for analysis & visualisation. The green indicator below each node indicates that the entire workflow has been successfully executed. See Additional file 5 for an importable copy of this workflow, which serves as an interactive tutorial for the methodology presented in this article
Before execution of this workflow, three manual adjustments have to be made. Firstly, file path and name of the layout worksheets in .xlsx format (see Fig. 1 a and Additional file 1) were selected for each plate through the respective Load Layout nodes. Secondly, once the corresponding absorbance data files were obtained, they were selected through the respective File Reader nodes. Lastly, the machine-readable export target file has to be defined in CSV Writer.
More plates can be accommodated by inserting more groups of Load Layout, File Reader, Expand Well Position, Joiner and Concatenate nodes into an existing connection between a Joiner and a Concatenate node by copying, pasting and reconnecting the relevant nodes. Thus, the researcher can quickly expand the provided minimal example (see Fig. 2) to the desired number of plates, accommodating any number of biological or technical replicates at a time and/or experiment repetitions over time, as long as the tree-like scheme is preserved.
Based on the exported .csv, downstream analysis and visualisation of the KNIME-processed data (Figs. 3, 4 and 5) was conducted in a separate work step in RStudio v0.99 Desktop Open Source Edition (http://www.rstudio.com/products/rstudio/) with the ggplot2 (http://ggplot2.org/) package v2.0.0 (https://github.com/hadley/ggplot2/releases/tag/v2.0.0) [22] and R v3.2.3 [23] (see Additional file 6).
Comparison of photometer- and plate-reader-based absorbance measurements of CV-stained A. minutissimum biofilms. Biofilms stained with CV were first measured in the wells with a plate reader (left facet). Afterwards CV was extracted with EtOH, transferred into photometric cuvettes and re-measured in a spectrophotometer (right facet). Axenic (ax) and xenic (xen) wells represent the negative and positive controls in this bioassay (non-adherent and adherent cells, respectively; N = 36). Boxes represent the first and third quartiles. Whiskers extend to the lowest and highest value that lies within 1.5-fold of the inter-quartile range (IQR). Black dots are extreme values that lie outside the IQR. Black center lines represent medians. Notches indicated the range of \(1.58 \cdot IQR / \sqrt {N}\) (ca. 95 % confidence interval) around the medians. For a more detailed explanation of box-and-whisker plots and their variants, we recommend reading [40]. See also Additional file 7 for R code and data used to plot this and the following figures
Detection of A. minutissimum biofilms with a plate reader before and after staining with CV. Absorbance was measured at wavelengths 630, 650 and 750 nm before staining the biofilms with crystal violet (CV), and at 580 nm after the staining. Negative, axenic controls; biofilm-positive, xenic controls; co-culture of axenic A. minutissimum and Bacteroidetes strain 32; N = 48 to 64 wells per culture type, spread across 4 plates, across 2 independent experiments
Detection of differently strong A. minutissimum biofilms before and after staining with CV. Bacteroidetes strain 32 supernatant was centrifuged and sterile-filtered from three 7 d old glcBM liquid cultures with OD600 of 0.25. Biofilm induction was highest around 25–50 % spent bacterial medium (v/v) as shown in Figure 3A of [11]
Bioassay experiments
Bioassays were prepared in 48-well plates (#677180, Cellstar (https://shop.gbo.com/de/germany/articles/catalogue/article/0110_0040_0110_0010_0010/13533/); Greiner Bio-One, Frickenhausen, Germany) by scraping both axenic and xenic A. minutissimum cultures off the flask bottoms and washing the cells once with fresh BM to remove residues of the spent cultivation medium (see Additional file 2). Axenic cells in this stock suspension were counted in a Thoma chamber in order to calculate the cell concentrations. After extracting chlorophyll in 5 % MeOH and 95 % acetone according to Jeffrey & Humphrey [24] from both diatom cultures, their washed suspensions were independently adjusted to \(10^{6} \frac {\text {cells}}{\text {mL}}\). For that purpose, both cultures were assumed to contain equal amounts of chlorophyll per cell. This stock suspension of 50 μL (containing 5·104 washed cells) was transferred into each well, as pre-recorded in the worksheets discussed in section Human- and machine-readable plate layout worksheets .
Treatments were administered within minutes of pipetting the diatom cultures into the multi-well plates. For co-culture experiments of the axenic diatom with S32, suspensions of the bacterial cells were prepared by centrifuging the LB liquid cultures at 5−10·103 g for 5–10 min and washing them with BM supplemented with 10 mM glucose (glcBM). The washed bacterial cells were resuspended in BM to an OD of 0.1 and 5 μL of that suspension was added to the wells with the axenic A. minutissimum cultures. For supernatant experiments, different volumes of sterile-filtered bacterial supernatant were added to the wells. This supernatant was harvested from S32 cultures in glcBM and filtered through 0.2 μm pores (Sarstedt AG, Nürmbrecht, Germany). In either case, each well was filled with fresh BM to a final volume of 500 μL. Negative control wells contained untreated axenic A. minutissimum, while xenic cultures served as biofilm-positive controls. Bioassay plates were sealed with Parafilm (Bemis, Neenah, WI, USA) and cultivated for 10–12 d as described for the stock cultures in section Cultivation conditions .
Robotised biofilm quantification
We evaluated the utility of robotised pipetting for the removal of non-adherent cells and medium, as well as for the staining of the remaining biofilms with crystal violet (CV) as visualised in Fig. 1 c. VIALINK Pipette Management Software (http://www.integra-biosciences.com/sites/vialink.html) was used to program custom scripts. Repeat Dispense scripts were programmed on a 1250 μL Viaflo Electronic Pipette (http://www.integra-biosciences.com/sites/viaflo_pipettes.html). The latter was used with six 1250 μL pipette tips for all pipetting steps, along the long axis of the 48-well plate. We tested using eight tips and pipetting along the short axis of the plate, but found that they did not reliably align with the wells. Both script types (see Table 1) were executed with the pipette connected to the Viaflo ASSIST (http://www.integra-biosciences.com/sites/viaflo_assist.html) robot (INTEGRA Biosciences AG, Switzerland).
The crucial, optimisable step for removing non-adherent cells is the mixing step. For our A. minutissimum cultures, mixing was optimised in terms of immersion depth (54.5 mm; see Table 1), mixing volume (400 μL), speed (7) and cycles (7) at room temperature, so that axenic cultures were resuspended while the xenic biofilms were not disturbed. These settings have to be adjusted for other organisms, in order to accommodate different biofilm thicknesses, strengths of adherence, etc.
The plate reader device Tecan Infinite F500 (http://lifesciences.tecan.com/products/reader_and_washer/microplate_readers/infinite_f500) (Tecan Group Ltd., Switzerland) was used at room temperature to measure biofilm absorbances. For that purpose, a custom method (see Additional file 4) was implemented in the Magellan (http://lifesciences.tecan.com/products/software/magellan_data_analysis_software) dataa analysis software v7.1. It took absorbance measurements at 16 evenly spread points in a filled circle with a 1.7 mm distance to the well edge. The absorbances of unstained biofilms were read out at 630, 650 and 750 nm. These wavelengths were chosen according to Jeffrey & Humphrey [24] for the chlorophyll c absorbance maximum (630 nm), for a compromise between the chl a maximum and an available filter (650 nm), as well as for the light scattering due to cells (750 nm). After measuring the absorbances of the unstained biofilms, they were incubated for 1 min with 200 μL of a 1:100 dilution of the crystal violet (CV) staining reagent described previously [25]. The CV solution was removed by pipetting as described above. Afterwards, sterile-filtered tap water was added to the wells for washing, and removed after 1 min. The plate-reader was used again to measure the absorbance at 580 nm. Finally, the Magellan method ensured the data export into machine-readable .asc files for subsequent input into the KNIME workflow.
For comparison of the above described robotised biofilm quantification with the manual protocol established previously [11], CV was extracted from the wells after plate-reading. This was done by pipetting 1 mL EtOH up and down several times and the resulting CV solution was transferred into a quartz cuvette. The absorbance was measured at 580 nm in an Ultrospec 2100 pro (http://www.thomassci.com/Instruments/Spectrophotometers/_/0A56FFDB-A8B9-473E-99CF-960599F301B7) UV/visible spectrophotometer (Biochrom Ltd. Cambridge, UK (http://www.biochrom.co.uk/contact/)).
Human- and machine-readable data processing
Regarding our use of the plate layout worksheets and KNIME, we found that using such software for managing experimental workflows is advantageous [26, 27]. This results from the data processing being reviewable independently [28], reproduced by other researchers, as well as prepared and tested with example data or initial measurement data. We also found KNIME useful for tracking the progress of experiments because all nodes indicate their status (traffic light symbols in Fig. 2). This becomes particularly useful for complex experiments during which replicate data is obtained at different times and/or after long incubation times (e.g. seasonal repetitions [29]).
Preparing plate layouts in .xlsx-compatible programs enabled the calculation and planning of dilution series, and even randomisations. However, the potential benefit of randomised sample placement should be evaluated on a case-by-case basis against the increased workload and the risk of pipetting errors during manual inoculation. This risk can be mitigated by keeping dilution series in their inherent order, but pipetting them in alternating directions across the plate (pseudo-randomisation). The worksheets should obviously be prepared before the inoculation, in order to be useful as pipetting guides at the bench. However, they can be updated at any time to reflect pipetting errors, changes of the experimental plan, or the sample sets, etc.
The KNIME workflow may be improved by integrating such scripts, so that data analysis and visualisation can be started immediately with the first absorbance data file. Because inputting the paths of the corresponding layout worksheets and absorbance data files into the nodes is repetitive, it may be desirable to automate the detection and pairing of corresponding files in large numbers. Such an automation may be possible using KNIME's Read XLS Sheet Names, StringManipulation, flow-variables and loops (personal communication, Patrick Winter).
Regarding the robotised liquid removal steps, we found that they could not be conducted reliably at this immersion depth, because notable residue volumes remained in the wells. Immersing the pipette tips further risked scratching the biofilms, so we instead used the electronic pipettes manually, tilting the tips into the well edges. Despite this manual removal of liquids, the time requirement and work intensity per plate could be reduced considerably from ca. 30–45 min of intense manual pipetting [11] to ca. 10–15 min of intermittent electronic pipetting and device operations.
A read-out of the EtOH-filled wells after CV extraction was possible, but similarly to a report by Rasmussen & Østgaard [30] (Discussion | Experimental Systems), the meniscus of the solution distorted the measurements in a ring-shaped area around to the well edges. As smaller well sizes may exacerbate this problem, we refrained from using 96-well plates. Manual removal of residual liquid with finer pipette tips, or a separate drying step might alleviate this risk, but would extend the time for measurements.
Our workflow can be adopted easily to other organisms and biofilm assays by adjusting the plate-reading method (Additional file 3; particularly the number of the measurements, as well as the chosen wavelengths) in Tecan's Magellan software. One potential improvement is the randomisation of the measurement positions in the wells [31], but this was not yet available in our Magellan version.
The bottleneck of this workflow is the number of samples and plates that can reasonably be inoculated manually. Dispensing Bacillariophyceaen medium (BM) and A. minutissimum with a stepper or multi-channel pipette requires only a few minutes per 48-well plate, but the application of different treatments (e.g. S32 co-cultivation or its supernatant extracts, or compounds at different dilutions, etc.) easily multiplied that time per plate. To remove this bottleneck, further robotisation protocols similar to those reported previously [32] are required. For that purpose it will be necessary to either add control cultures for that protocol's semi-sterile nature, or to optimise it towards fully sterile conditions. As a next step, a robotised A. minutissimum and S32 co-cultivation system could be connected to high-resolution mass spectrometry in order to elucidate the nature of biofilm-inducing substance [11, 32].
Absorbance read-outs of stained and unstained biofilm assays
The initial proof-of-concept of the above-described measurement protocol was conducted with non-adherent, axenic (ax) and biofilm-forming, xenic (xen) A. minutissimum cultures (Fig. 3). Using the plate reader resulted in lower absolute absorbances for both culture types. The spread of data read-outs from axenic replicates was about half of those from the EtOH- and photometer-based measurements. For xenic biofilms, the spread was only 25 % smaller, but the plate reader measured lower absorbances. Nevertheless, the absorbance read-outs still were clearly distinct between axenic and xenic samples.
The EtOH- and photometer-based method [11] resolved the differences of biofilm intensities better. However, xenic replicates with strong deviation below the median absorbance could result from drying of the biofilms before staining or before the extraction of the stain with EtOH. Axenic replicates with strong deviation above the median absorbance could readily result from small crystal violet residues getting carried into the EtOH extraction. Therefore, the EtOH- and photometer-based method risks false measurements in both controls. This previous method is only feasible for the quantification of small sample sets. The faster plate-reading was less error-prone and more reproducible. It still allows the EtOH- and photometer-based method to be appended in case additional verification of unclear read-outs is required.
The next step of our proof-of-concept deals with the detection of unstained biofilms at 630, 650 and 750 nm (Fig. 4). Median absorbances were significantly distinct between the axenic, non-adherent control and the biofilm-forming co- and xenic cultures in any case. The total spreads of data from the axenic controls overlapped only slightly with those of the two biofilm-positives sample types (co- and xenic culture). The median absorbances after staining with CV were more distinct, and the data spreads did not overlap, although those of the biofilm samples were larger. In summary, the medians and spreads of data show that the distinctiveness of unstained biofilm-free and -containing wells was reflected by the absorbances on three different wavelengths as well as by the CV-specific wavelength.
The similarity of biofilm absorbances read-outs at 630, 650 and 750 nm confirms other biofilm measurements conducted at wavelengths of 680 nm [33] and 600 nm [14]. The latter study also involved staining with CV of bacterial biofilms in multi-well plates, in order to test combinatorially produced surface coatings for anti-fouling capabilities. The similarity of technical set-ups suggests that our KNIME-based workflow can be applied beyond diatom biofilm research. In another photometric approach [13] monitored biofilm formation of the diatom Planothidium sp. in a sterile incubator. They detected the growth of unstained biofilms by attenuation of the visible light spectrum around a peak of 600 nm in real-time. The common result of those cited with our study is that diatom and bacterial biofilms can be detected between 580 and 680 nm. This suggest that any wavelengths within this range is suitable. Moreover, the cited biofilm assays were conducted with less than ten replicates. Our workflow helps to handle more biological and/or technical replicates at a time, experiment repetitions over time, and/or repetitions by different researchers. All these are key to the statistical power of studies and help to reduce the risk of false research findings [34], but increase the workload considerably. Our workflow decouples the number of replicates and repetitions from the data processing and analysis workload.
The lower absolute absorbances of unstained biofilms at 630, 650 and 750 nm (Fig. 4) can be explained by the detection of only adherent cells. CV stains EPS structures like stalks and capsules in addition to the cellular polymeric structures [12], and thus contributes to the high absolute absorbances at 580 nm. EPS are important for the surface attachment of microbes and are a logical requirement for biofilm formation [3, 4]. Our protocol supports the staining where necessary, but the elimination of CV staining from workflows does not prohibit the biofilm detection. CV-free workflows can be desirable, because the stain may increase the risk of false-positives, and is classified as toxic to aquatic life [35].
As a final assessment of our proof-of-concept, we tested the biofilm induction in axenic A. minutissimum by addition of sterile-filtered S32 supernatant. We used the same measurement set-up as described for Fig. 4. All absorbance curves peak between 10–50 % (v/v) supernatant (Fig. 5). Absorbances of unstained biofilms measured by plate-reader at 630, 650 and 750 nm had lower absolute differences. At those wavelengths, the unstained biofilms had the absorbance maxima at 25 % supernatant. After staining with CV and measurement at 580 nm, the maximum shifted to the range of 25–50 %.
The shapes of all biofilm-induction curves (Fig. 5 agree with analogous curves determined previously with the EtOH-extraction protocol ([11], Fig. 3A therein). This demonstrates that the less time-consuming protocol proposed in the present study is able to detect differently strong, unstained biofilms, as already discussed for the light-attenuation-based evidence reported previously [13]. In addition to the faster, non-invasive biofilm detection, our workflow leaves two opportunities to increase the absorbance resolution for unclear samples: (1) Read-out of stained biofilms can easily be integrated; (2) EtOH extraction of the stain and photometric measurement can be appended as well.
To summarise, the three proof-of-concept steps confirmed the results of previous studies and highlighted several simplification and automation options. These options are applicable for biofilm assays in general, and specifically enhance the utility of A. minutissimum in environmental monitoring. This is relevant, because this diatom has been used previously as a bioindicator of heavy metal pollution [36, 37]. That application relied on the detection of frustule deformations – an approach that has been questioned by Lavoie et al. [38] who observed the valves often settling in girdle view, which hindered the quantification of frustule deformations in this diatom species. Using A. minutissimum as an example, we present the simpler, robotised proxy measurement of the presence or absence of cells as a means to detect biofilms. Thus, we demonstrate here an improved in vitro variant of in situ "stable platforms", which Amin et al. [39] recommended for the study of diatom-bacteria interactions.
Because we show in several examples that staining with crystal violet is not strictly required for the detection of Achnanthidium minutissimum biofilms, our workflow may enable a broad range of existing plate-reading set-ups to be used for biofilm assays, while reducing chemical waste. By demonstrating the successful implementation of human- and machine-readable data structures and processing workflows in the free and open source software KNIME, we offer generally useful options for the standardisation, up-scaling and replication of biofilm assays that utilise diatoms, bacteria or other microbes. Particularly the A. minutissimum bioassay, but also other laborious assays, may thus become applicable for use in medium-throughput screening of chemicals or mutant strains for biofilm-inducing or -inhibiting effects, due to the considerable reduction of measurement and data processing workload. This will stimulate the use of biofilm assays in environmental and anti-biofouling research. Moreover, since the KNIME workflow is agnostic to the type of measurement and sample preparation, its basic concept of integrating planning documents and measurement results is applicable to any other experiment with multi-well plates.
The dataset supporting the conclusions of this article is included as Additional file 7. Other additional files pertain to the methodology described in this article. Please note that TAR files need to be unpacked (e.g. with 7-Zip (http://7-zip.org) before import into the respective programs.
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We thank the Young Scholar Fund of the Zukunftskolleg (https://www.zukunftskolleg.uni-konstanz.de/home/) at the University of Konstanz and the Konstanz Research School Chemical Biology (www.chembiol.uni-konstanz.de/home.html) for funding this research. Our gratitude also belongs to Patrick Winter for advice about KNIME, and Lachlan Dow for proof-reading the manuscript.
Zukunftskolleg, Universitätsstraße 10, Postbox 216, Konstanz, 78457, Germany
Katrin Leinweber
Konstanz Research School Chemical Biology (KoRS-CB), Universitätsstraße 10, Postbox 630, Konstanz, 78457, Germany
Screening Center Konstanz, Universitätsstraße 10, Screening Facility, Konstanz, 78457, Germany
Silke Müller
Department of Biology, University of Konstanz, Universitätsstraße 10, Postbox 611, Konstanz, 78457, Germany
& Peter G. Kroth
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Correspondence to Katrin Leinweber.
KL has submitted observation notes regarding the application of Viaflo pipettes in the context of this biofilm assay to Integra Biosciences, and may co-author a testimonial or application note. Non-financial compensation may be received in the form of supplies for the Screening Center Konstanz (https://cms.uni-konstanz.de/screening-center/).
KL conceived and performed the experiments, analysed the data, wrote the manuscript, as well as prepared figures, tables and files for publication. SM designed pipetting scripts, the plate-reading method and KNIME workflow, and contributed the devices, as well as ideas to the experimental design. PGK contributed ideas and revisions to the manuscript. All authors read and approved the final manuscript.
Additional file 1
Plate layout template for recording sample placement in multi-well plates and merging metadata with measurements in KNIME. See Fig. 1 for illustration. (XLSX 24.4 kb)
Detailed instructions for the manual preparation of the Achnanthidium minutissimum bioassays, based on the protocol by Windler et al. [11]. (PNG 991 kb)
Viaflo (http://www.integra-biosciences.com/sites/viaflo_pipettes.html) electronic pipetting scripts to successively remove cells, crystal violet staining solution and wash water after steps 1, 3 and 5 (Table 1). See Fig. 1 for experimental context and Vialink's (http://www.integra-biosciences.com/sites/vialink.html) built-in help for importing instructions. (TAR 35.5 kb)
Plate-reading method for Tecan's Magellan software. See section Robotised biofilm quantification for details. (MTH 15.6 kb)
Importable workflow for the KNIME Analytics Platform to demonstrate the merging of sample metadata (plate-layout-template.xlsx) and Magellan-measured absorbance data (.asc files). See Fig. 2 for illustration. Please note that importing will return an error initially, because the file paths can not match, and have to be corrected as described in section KNIME workflow for data processing . In case of the File Reader nodes, this correction should be conducted with the option Preserve user settings for new location activated. If forgotten, and if the data preview shows a column filled with question marks, please right-click on that column and activate the option DON'T include column in output table. Traffic light symbols below the nodes will indicate whether corrections are still necessary (red), or whether the nodes can be executed (yellow). Upon execution of this workflow, data files are read in and the Expand Well Position nodes ensure equal formatting of the sample metadata and measurement results according to the well coordinates (defined in the .xlsx file and present in the .asc files). Joiner combines these tables per row, discarding incongruencies between plate layouts and measurement data. Concatenate progressively merges two plates' data tables into one. Plate Heatmap Viewer provides a visual comparison of the data processing result with the visual impression of a plate. In particular, the expected locations of biofilm-negative and -positive controls are easily discernible. In the concatenated table, Plate Row Converter and Column Combiner regenerate the alphanumeric well coordinates so that the data and visual impression of individual wells can be compared. Column Filter and Column Resorter exclude obsolete coordinate metadata and pre-format the remaining table for export by CSV Writer. (TAR 65.0 kb)
R code to demonstrate the plotting of KNIME-processed data. Please note that due to a randomisation function in the plate layout .xlsx file, editing the latter and running the KNIME workflow and this script again may produce a plot with different assignments of data points to the levels X, Y and Z. (R 1.22 kb)
R code and data (.csv format) used to produce the plots in this article. (TAR 45.0 kb)
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Leinweber, K., Müller, S. & G. Kroth, P. A semi-automated, KNIME-based workflow for biofilm assays. BMC Microbiol 16, 61 (2016) doi:10.1186/s12866-016-0676-9
Achnanthidium minutissimum
Medium throughput
Diatom-bacteria interactions
Bioassay


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I used to use Staples and Kinkos for our printing. We would do a couple thousand color flyers a couple times a month, plus our business cards and stationery. I got a referral to Colorprint and what a difference. Way lower price, great service, free delivery, and I work with the same nice folks every time.
We do want the job done right and on time every time we make a promise to a client. I can tell you Colorprint is reliable and trustworthy no matter how big your business.
We are so thrilled with our relationship with the team at Colorprint! They are attentive to details, efficient, and really supportive. The turn around time on our projects is always extremely quick!
Using Colorprint as our printer, mailhouse, and designer has saved us money, a ton of time, and a lot of frustration. I highly recommend them!!
The team at Colorprint is courteous, knowledgeable and fast. They take responsibility for meeting deadlines and do the job right the first time.


The goal of each human is to look good in whatever they dress thus the saying "Look Good, Feel Good'. Sometimes we overlook the very pieces of cloth that will make us look stylish, keep us warm etc and shop for ones that won't be of much help during cold or hot seasons and also in the fashion world. But then they are always readily available and you can buy them anytime once you get to know how important they are.
1.Polo-necks are extremely important clothes that are a must have.
– They can be styled with nice necklaces of all kinds, scarfs, a throw on top piece of cloth etc.
– They give extremely adorable look when worn with a suit.
2. High-waist Trousers are the 2nd most important cloth you shouldn't miss in your closet.
Why? because in itself it seems to give a thousand and one reasons. I simply love high-waist trousers.
another key reason it's because one can never run out of styling options with a high-waist trouser.
Below is how I styled my polo-neck with a high-waist trouser and throw on top waterfall in a bid to keep myself warm.