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One of the possible approaches to decrease the demand for critical elements such as rare earths is to develop new sustainable magnets. Iron-based materials are suitable for gap magnets applications since iron is the most abundant ferromagnetic element on Earth. Fe$_5$SiB$_2$ is a candidate as gap magnet thanks to its high Curie temperature (T$_{\text{C}} \sim$ 800 K) and saturation magnetization (M$_{\text{S}}\sim$ 140 Am$^2$kg$^{-1}$). However its anisotropy field is too low for applications (H$_{\text{A}} \sim$ 0.8 T). In order to increase the anisotropy value, we synthesized a series of Ge, Re and Cr substituted Fe$_5$SiB$_2$ samples and studied their magnetic properties. They all crystallize in the Cr$_5$B$_3$-type tetragonal structure with the $I4/mcm$ space group. Curie temperature (T$_{\text{C}}$ = 803 K) and saturation magnetization (M$_{\text{S}}$ = 138 Am$^2$kg$^{-1}$) are slightly decreased by elemental substitution with Re having the largest effect. Despite being reduced, T$_{\text{C}}$ and M$_{\text{S}}$ still maintain significant values (T$_{\text{C}}>$ 750 K and M$_{\text{S}}$ = 118 Am$^2$kg$^{-1}$). The room temperature anisotropy field has been measured by Singular Point Detection (SPD) and increases by about 15% upon Re substitution, reaching 0.92 T for Fe$_{4.75}$Re$_{0.25}$SiB$_2$. We have also used Nuclear Magnetic Resonance and SPD measurements to study the spin reorientation transition which takes place at 172 K and we have found that it is partially suppressed by substitution of Ge from 172 K to 140 K and completely suppressed upon Cr and Re substitution., Comment: The paper consists of a main section and supplementary materials. The main section includes 15 pages, featuring 6 figures and 2 tables. The supplementary materials, appended at the end of the main section, span 4 pages and contain 6 figures

By means of single-crystal X-ray diffraction we have revealed the breaking of centrosymmetry when lowering the temperature under T$_s$ = 200 K concomitantly with the setting of a commensurate superstructure in the small A-site quadruple perovskite YMn$_3$Mn$_4$O$_{12}$. This results is in agreement with all data already reported for this compounds and solve the previous inconsistency about the Yttrium position. The superstructure is characterized by the appearing of satellite reflections in the single crystal pattern, consistent with an I-centered pseudo-orthorhombic commensurate supercell with $a \approx \sqrt{a_F} = 10.4352(7)$ \AA, $b \approx 2b_F = 14.6049(9)$ \AA, $c \approx \sqrt{c_F} = 10.6961(7)$ \AA and $\beta = 90.110(3)^\circ$, where F stands for the "fundamental" high-temperature cell ($a_F \approx c_F \approx 7.45$ \AA, $b_F \approx 7.34$ \AA, and $\beta \approx 90^\circ$). The space-group was unequivocally found to be Ia, which is non polar, thus allowing for a non-zero polarization in the material. We then have investigated in detail the pyrocurrent, transport, dielectric and the DC and AC magnetic properties of polycrystalline sample of YMn$_3$Mn$_4$O$_{12}$ over a wide temperature range. These measurements clearly highlight several critical temperatures in the material and correlation between the different orders: i) the centrosymmetry is broken at high temperature (T$_S$ = 200K), ii) then the long-range magnetic order of B-sites occurs at T$_{N,B}$ = 108 K and at this same temperature the compound enters in an insulating dielectric state. iii) Finally, a remnant polarization is stabilized concomitantly with a magnetic anomaly at T* = 70 K. We propose that YMn$_3$Mn$_4$O$_{12}$ is a peculiar magnetic ferroelectric in which the polar state is driven by short-range magnetic order.

When using Markov chain Monte Carlo (MCMC) algorithms to perform inference for Bayesian clustering models, such as mixture models, the output is typically a sample of clusterings (partitions) drawn from the posterior distribution. In practice, a key challenge is how to summarise this output. Here we build upon the notion of the posterior similarity matrix (PSM) in order to suggest new approaches for summarising the output of MCMC algorithms for Bayesian clustering models. A key contribution of our work is the observation that PSMs are positive semi-definite, and hence can be used to define probabilistically-motivated kernel matrices that capture the clustering structure present in the data. This observation enables us to employ a range of kernel methods to obtain summary clusterings, and otherwise exploit the information summarised by PSMs. For example, if we have multiple PSMs, each corresponding to a different dataset on a common set of statistical units, we may use standard methods for combining kernels in order to perform integrative clustering. We may moreover embed PSMs within predictive kernel models in order to perform outcome-guided data integration. We demonstrate the performances of the proposed methods through a range of simulation studies as well as two real data applications. R code is available at https://github.com/acabassi/combine-psms., Comment: Manuscript: 27 pages, 8 figures. Supplement: 62 pages, 68 figures. For associated R code, see https://github.com/acabassi/combine-psms

By means of magnetic, specific heat and pyroelectric measurements, we report on magnetic ferroelectricity in the quadruple perovskite \namno, characterized by a canted antiferromagnetic (AFM) CE structure. Surprisingly, ferroelectricity is concomitant to a dramatic broadening of the magnetic hysteresis loop, well below the AFM ordering temperature. This unconventional behavior shows that the formation of ferroelectric domains is induced by the symmetric exchange interaction in the local scale, e.g. at magnetic domain boundaries or defects. The value of electric polarization, $P = 0.027 \mu$C cm$^{-2}$, measured in polycrystalline samples is comparatively large as compared to other magnetic multiferroics, suggesting that the above scenario is promising indeed for the rational design of practical multiferroic materials., Comment: 5 pages, 4 figures

Building classification models that predict a binary class label on the basis of high dimensional multi-omics datasets poses several challenges, due to the typically widely differing characteristics of the data layers in terms of number of predictors, type of data, and levels of noise. Previous research has shown that applying classical logistic regression with elastic-net penalty to these datasets can lead to poor results (Liu et al., 2018). We implement a two-step approach to multi-omic logistic regression in which variable selection is performed on each layer separately and a predictive model is then built using the variables selected in the first step. Here, our approach is compared to other methods that have been developed for the same purpose, and we adapt existing software for multi-omic linear regression (Zhao and Zucknick, 2020) to the logistic regression setting. Extensive simulation studies show that our approach should be preferred if the goal is to select as many relevant predictors as possible, as well as achieving prediction performances comparable to those of the best competitors. Our motivating example is a cardiometabolic syndrome dataset comprising eight 'omic data types for 2 extreme phenotype groups (10 obese and 10 lipodystrophy individuals) and 185 blood donors. Our proposed approach allows us to identify features that characterise cardiometabolic syndrome at the molecular level. R code is available at https://github.com/acabassi/logistic-regression-for-multi-omic-data., Comment: Manuscript: 22 pages, 6 figures. Supplement: 24 pages, 20 figures. For associated R code, see https://github.com/acabassi/logistic-regression-for-multi-omic-data

Diverse applications - particularly in tumour subtyping - have demonstrated the importance of integrative clustering techniques for combining information from multiple data sources. Cluster-Of-Clusters Analysis (COCA) is one such approach that has been widely applied in the context of tumour subtyping. However, the properties of COCA have never been systematically explored, and its robustness to the inclusion of noisy datasets, or datasets that define conflicting clustering structures, is unclear. We rigorously benchmark COCA, and present Kernel Learning Integrative Clustering (KLIC) as an alternative strategy. KLIC frames the challenge of combining clustering structures as a multiple kernel learning problem, in which different datasets each provide a weighted contribution to the final clustering. This allows the contribution of noisy datasets to be down-weighted relative to more informative datasets. We compare the performances of KLIC and COCA in a variety of situations through simulation studies. We also present the output of KLIC and COCA in real data applications to cancer subtyping and transcriptional module discovery. R packages "klic" and "coca" are available on the Comprehensive R Archive Network., Comment: Manuscript: 18 pages, 6 figures. Supplement: 29 pages, 19 figures. This version contains additional simulation studies and comparisons to other methods. For associated R code, see https://CRAN.R-project.org/package=klic and https://github.com/acabassi/klic-pancancer-analysis

In this paper, we generalize the metric-based permutation test for the equality of covariance operators proposed by Pigoli et al. (2014) to the case of multiple samples of functional data. To this end, the non-parametric combination methodology of Pesarin and Salmaso (2010) is used to combine all the pairwise comparisons between samples into a global test. Different combining functions and permutation strategies are reviewed and analyzed in detail. The resulting test allows to make inference on the equality of the covariance operators of multiple groups and, if there is evidence to reject the null hypothesis, to identify the pairs of groups having different covariances. It is shown that, for some combining functions, step-down adjusting procedures are available to control for the multiple testing problem in this setting. The empirical power of this new test is then explored via simulations and compared with those of existing alternative approaches in different scenarios. Finally, the proposed methodology is applied to data from wheel running activity experiments, that used selective breeding to study the evolution of locomotor behavior in mice.

We report on the synthesis and characterization of BiFe0.5Mn0.5O3, a potential type-I multiferroic compound displaying temperature induced magnetization reversal. Bulk samples were obtained by means of solid state reaction carried out under the application of hydrostatic pressure at 6 GPa and 1100{\deg}C. The crystal structure is an highly distorted perovskite with no cation order on the B site, where, besides a complex scheme of tilt and rotations of the TM-O6 octahedra, large off-centering of the bismuth ions is detected. Below T1 = 420 K the compound undergoes a first weak ferromagnetic transition related to the ordering of iron rich clusters. At lower temperatures (just below RT) two distinct thermally activated mechanisms are superimposed, inducing at first an enhancement of the magnetization at T2 = 288 K, then a spontaneous reversal process centered at T3 = 250 K, finally giving rise to a negative response. The application of fields higher than 1500 Oe suppresses the process, yielding a ferromagnetic like behaviour. The complementary use of SQuID magnetometry and M\"ossbauer spectroscopy allowed the interpretation of the overall magnetic behaviour in terms of an uncompensated weak competitive coupling between non-equivalent clusters of interactions characterized by different critical temperatures and resultant magnetizations. PACS numbers: 75.85.+t, 75.60.Jk, 76.80.+y, 75.30.Et, 75.30.Kz, Comment: 30 pages, 13 figures

By means of neutron powder diffraction, we investigated the effect of the polar Bi$^{3+}$ ion on the magnetic ordering of the Mn$^{3+}$ ions in BiMn$_3$Mn$_4$O$_{12}$, the counterpart with \textit{quadruple} perovskite structure of the \textit{simple} perovskite BiMnO$_3$. The data are consistent with a \textit{noncentrosymmetric} spacegroup $Im$ which contrasts the \textit{centrosymmetric} one $I2/m$ previously reported for the isovalent and isomorphic compound LaMn$_3$Mn$_4$O$_{12}$, which gives evidence of a Bi$^{3+}$-induced polarization of the lattice. At low temperature, the two Mn$^{3+}$ sublattices of the $A'$ and $B$ sites order antiferromagnetically (AFM) in an independent manner at 25 and 55 K, similarly to the case of LaMn$_3$Mn$_4$O$_{12}$. However, both magnetic structures of BiMn$_3$Mn$_4$O$_{12}$ radically differ from those of LaMn$_3$Mn$_4$O$_{12}$. In BiMn$_3$Mn$_4$O$_{12}$ the moments $\textbf{M}_{A'}$ of the $A'$ sites form an anti-body AFM structure, whilst the moments \textbf{M}$_{B}$ of the $B$ sites result from a large and \textit{uniform} modulation $\pm \textbf{M}_{B,b}$ along the b-axis of the moments \textbf{M}$_{B,ac}$ in the $ac$-plane. The modulation is strikingly correlated with the displacements of the Mn$^{3+}$ ions induced by the Bi$^{3+}$ ions. Our analysis unveils a strong magnetoelastic coupling between the internal strain created by the Bi$^{3+}$ ions and the moment of the Mn$^{3+}$ ions in the $B$ sites. This is ascribed to the high symmetry of the oxygen sites and to the absence of oxygen defects, two characteristics of quadruple perovskites not found in simple ones, which prevent the release of the Bi$^{3+}$-induced strain through distortions or disorder. This demonstrates the possibility of a large magnetoelectric coupling in proper ferroelectrics and suggests a novel concept of internal strain engineering for multiferroics design., Comment: 9 pages, 7 figures, 5 tables

A first order structural Jahn-Teller transition at T_{JT} = 650 K has been recently reported for the quadruple perovskite LaMn7O12 . We have carried out magnetization and transport measurements below and above T_{JT} in order to investigate the effect of the transition. Electrical conduction turns out to be polaronic, changing from non-adiabatic to adiabatic through the transition. Magnetic behavior can be described by non-interacting Mn3+ ions below T_{JT}, while above T_{JT} it is of questionable interpretation. The effect of thermal cycling on as grown samples of different purity degree also allowed us to clarify the intrinsic magnetic response of LaMn7O12 at lower temperatures., Comment: 5 pages, 4 figures

We report on the high pressure synthesis of BiMn$_7$O$_{12}$, a manganite displaying a "quadruple perovskite" structure. Structural characterization of single crystal samples shows a distorted and asymmetrical coordination around the Bi atom, due to presence of the $6s^{2}$ lone pair, resulting in non-centrosymmetric space group Im, leading to a permanent electrical dipole moment and ferroelectric properties. On the other hand, magnetic characterization reveals antiferromagnetic transitions, in agreement with the isostructural compounds, thus evidencing two intrinsic properties that make BiMn$_7$O$_{12}$ a promising multiferroic material., Comment: 4 pages, 3 figures