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Prediction of high-$T_{\rm{c}}$ superconductivity in hole-doped Li$_x$BC two decades ago has brought about an extensive effort to synthesize new materials with honeycomb B-C layers, but the thermodynamic stability of Li-B-C compounds remains largely unexplored. In this study, we use density functional theory to characterize well-established and recently reported Li-B-C phases. Our calculation of the Li chemical potential in Li$_x$BC helps estimate the ($T$,$P$) conditions required for delithiation of the LiBC parent material, while examination of B-C phases helps rationalize the observation of metastable BC$_3$ polymorphs with honeycomb and diamond-like morphologies. At the same time, we demonstrate that recently reported BC$_3$, LiBC$_3$, and Li$_2$B$_2$C phases with new crystal structures are both dynamically and thermodynamically unstable. With a combination of evolutionary optimization and rational design, we identify considerably more natural and favorable Li$_2$B$_2$C configurations that, nevertheless, remain above the thermodynamic stability threshold.

LiB, a predicted layered compound analogous to the MgB$_2$ superconductor, has been recently synthesized via cold compression and quenched to ambient pressure, yet its superconducting properties have not been measured. According to prior isotropic superconductivity calculations, the critical temperature ($T_{\rm{c}}$) was expected to be only 10$-$15 K. Using the anisotropic Migdal-Eliashberg formalism, we show that the $T_{\rm{c}}$ may actually exceed 32 K. Our analysis of the contribution from different electronic states helps explain the detrimental effect of pressure and doping on the compound's superconducting properties. In the search for related superconductors, we screened Li-Mg-B binary and ternary layered materials and found metastable phases with $T_{\rm{c}}$ close to or even 10$-$20% above the record 39 K value in MgB$_2$. Our reexamination of the Li-B binary phase stability reveals a possible route to synthesize the LiB superconductor at lower pressures readily achievable in multianvil cells.

Prescreening candidate structures with reliable classical potentials is an effective way to accelerate ab initio ground state searches. Given the growing popularity of machine learning force fields...

$\mathrm{Cu_2IrO_3}$ is among the newest layered honeycomb iridates and a promising candidate to harbor a Kitaev quantum spin liquid state. Here, we investigate the pressure and temperature dependence of its structure through a combination of powder x-ray diffraction and x-ray absorption fine structure measurements, as well as $ab$-$initio$ evolutionary structure search. At ambient pressure, we revise the previously proposed $C2/c$ solution with a related but notably more stable $P2_1/c$ structure. Pressures below 8 GPa drive the formation of Ir-Ir dimers at both ambient and low temperatures, similar to the case of $\mathrm{Li_2IrO_3}$. At higher pressures, the structural evolution dramatically depends on temperature. A large discontinuous reduction of the Ir honeycomb interplanar distance is observed around 15 GPa at room temperature, likely driven by a collapse of the O-Cu-O dumbbells. At 15 K, pressures beyond 20 GPa first lead to an intermediate phase featuring a continuous reduction of the interplanar distance, which then collapses at 30 GPa across yet another phase transition. However, the resulting structure around 40 GPa is not the same at room and low temperatures. Remarkably, the reduction in interplanar distance leads to an apparent healing of the stacking faults at room temperature, but not at 15 K. Possible implications on the evolution of electronic structure of $\mathrm{Cu_2IrO_3}$ with pressure are discussed., Comment: 11 pages, 7 figures, see ancillary file for Supplemental Material

We have combined a neural network formalism with metaheuristic structural global search algorithms to systematically screen the Mg-Ca binary system for new (meta)stable alloys. The combination of these methods allows for an efficient exploration of the potential energy surface beyond the possibility of the traditional searches based on ab initio energy evaluations. The identified pool of low-enthalpy structures was complemented with special quasirandom structures (SQS) at different stoichiometries. In addition to the only Mg-Ca phase known to form under standard synthesis conditions, C14-Mg2Ca, the search has uncovered several candidate materials that could be synthesized under elevated temperatures or pressures. We show that the vibrational entropy lowers the relative free energy of several phases with magnesium kagome layers: C15 and C36 Laves structures at the 2 : 1 composition and an orthorhombic oS36 structure at the 7 : 2 composition. The estimated phase transition temperatures close to the melting point leave open the possibility of synthesizing the predicted materials at high temperatures. At high pressures up to 10 GPa, two new phases at the 1 : 1 and 3 : 1 Mg : Ca stoichiometries become thermodynamically stable and should form in multi-anvil experiments.

We consider a hyperbolic automorphism A:T3→T3 of the three-torus whose two-dimensional unstable distribution splits into weak and strong unstable subbundles. We unfold A into two one-parame...

The atomic-scale reduction mechanism of α-Fe2O3 nanowires by H2 was followed using transmission electron microscopy to reveal the evolution of atomic structures and the associated transformation pathways for different iron oxides. The reduction commences with the generation of oxygen vacancies that order onto every 10th (3030) plane. This vacancy ordering is followed by an allotropic transformation of α-Fe2O3 → γ-Fe2O3 along with the formation of Fe3O4 nanoparticles on the surface of the γ-Fe2O3 nanowire by a topotactic transformation process, which shows 3D correspondence between the structures of the product and its host. These observations demonstrate that the partial reduction of α-Fe2O3 nanowires results in the formation of a unique hierarchical structure of hybrid oxides consisting of the parent oxide phase, γ-Fe2O3, as the one-dimensional wire and the Fe3O4 in the form of nanoparticles decorated on the parent oxide skeleton. We show that the proposed mechanism is consistent with previously publish...

The hyper-kagome lattice iridate ${\mathrm{Na}}_{3}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$, closely related to spin liquid candidate ${\mathrm{Na}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$, is unusual in that spin-orbit interactions acting on the 1/3-filled ${J}_{\mathrm{eff}}=1/2$ state lead to a semimetallic ground state, in contrast to the conventional insulating Mott state stabilized by S-O interactions in the 1/2-filled ${J}_{\mathrm{eff}}=1/2$ state of other iridates including ${\mathrm{Na}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$. We have studied the evolution of crystal structure, electronic structure, and transport in ${\mathrm{Na}}_{3}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$ under high pressure using x-ray diffraction, x-ray absorption near edge structure, and electrical resistance measurements in a diamond anvil cell. The study was augmented by the use of ab initio calculations, which provided insight into pressure-induced changes in crystal and electronic structure. We found that ${\mathrm{Na}}_{3}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$ transforms from a semimetal to an insulator under pressure, with an estimated energy gap that increases to about 130 meV at $P\ensuremath{\sim}$ 9 GPa. At approximately 10 GPa, a cubic-to-monoclinic structural transition takes place between two insulating phases. This structural transition features a sizable volume collapse and a high-pressure phase characterized by apparent dimerization of Ir-Ir distances, wide dispersion of Ir-O-Ir bond angles, and an increase in the occupation of $5d$ states. Although the energy gap is reduced in the high-pressure phase, insulating behavior remains to the highest pressures $\ensuremath{\sim}1$ Mbar. The strongly pressure-dependent insulating gap shows a positive correlation with the expectation value of the angular part of the S-O interaction, $\ensuremath{\langle}\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}\ensuremath{\rangle}$, which may indicate an active role of S-O interactions in stabilizing the insulating state that emerges in the compressed ${\mathrm{Na}}_{3}{\mathrm{Ir}}_{3}{\mathrm{O}}_{8}$ structure.

The traditional paradigm for materials discovery has been recently expanded to incorporate substantial data-driven research. With the intent to accelerate the development and the deployment of new technologies, the AFLOW Fleet for computational materials design automates high-throughput first-principles calculations and provides tools for data verification and dissemination for a broad community of users. AFLOW incorporates different computational mod- ules to robustly determine thermodynamic stability, electronic band structures, vibrational dispersions, thermomechanical properties, and more. The AFLOW data repository is publicly accessible online at aflow.org, with more than 1.8 million materials entries and a panoply of queryable computed properties. Tools to programmatically search and process the data, as well as to perform online machine learning predictions, are also available.

BaSn$_2$ has been shown to form as layers of buckled stanene intercalated by barium ions~\cite{Kim_2008}. However, despite an apparently straightforward synthesis and significant interest in stanene as a topological material, BaSn$_2$ has been left largely unexplored, and has only recently been recognized as a potential topological insulator. Belonging to neither the lead nor bismuth chalcogenide families, it would represent a unique manifestation of the topological insulating phase. Here we present a detailed investigation of BaSn$_2$, using both {\it ab initio} and experimental methods. First-principles calculations demonstrate that this overlooked material is a indeed strong topological insulator with a bulk band gap of 360meV, among the largest observed for topological insulators. We characterize the surface state dependence on termination chemistry, providing guidance for experimental efforts to measure and manipulate its topological properties. Additionally, through {\it ab initio} modeling and synthesis experiments we explore the stability and accessibility of this phase, revealing a complicated phase diagram that indicates a challenging path to obtaining single crystals.

Using in situ transmission electron microscopy observations of the thermally induced reduction of CuO nanowires sheathed by a carbon shell, we show that a confined nanoscale geometry leads to changes in the oxide reduction mechanism from a surface dominated process to the bulk dominated process. It is shown that the reduction of carbon-confined CuO nanowires occurs via oxygen vacancy clustering in the bulk that results in the nanowire fragmentation into Cu2O segments encapsulated by the carbon shell while the reduction of un-confined CuO nanowires proceeds via the nucleation and growth of Cu2O islands on the nanowire surface. The comparative in situ TEM observations demonstrate that the surface coating layer reduces the thermal stability of the oxide nanowires, which is in contrast to the commonly anticipated effect of enhancing the nanostructure stability by developing a surface protective coating layer. Our density functional theory analyses reveal that the effects of oxygen vacancy ordering at the surface and in the bulk of CuO are comparable in energy, which support the alternative reduction process observed in the bulk of the sheathed CuO nanowires.

The contributions of atomic size and electronic factors to the structural stability of transition metal carbides and topologically close-packed (TCP) phases are investigated. The hard-sphere model that has been used by Cottrell to rationalize the occurrence of the octahedral and trigonal local coordination polyhedra within the transition metal carbides is shown to have limitations in TiC since density functional theory (DFT) predicts that the second most metastable phase closest to the B1 (NaCl) ground state takes the B (BN) structure type with 5-atom local coordination polyhedra with very short Ti–C bond lengths. The importance of electronic factors in the TCP phases is demonstrated by DFT predictions that the A15, and phases are stabilized between groups VI and VII of the elemental transition metals, whereas the and Laves phases are destabilized. The origin of this difference is related to the bimodal shape parameter of the electronic density of states by using the bond-order potential expansion...

The atomic-scale reduction mechanism of α-Fe2O3 nanowires by H2 was followed using transmission electron microscopy to reveal the evolution of atomic structures and the associated transformation pathways for different iron oxides. The reduction commences with the generation of oxygen vacancies that order onto every 10th (303¯0) plane. This vacancy ordering is followed by an allotropic transformation of α-Fe2O3 → γ-Fe2O3 along with the formation of Fe3O4 nanoparticles on the surface of the γ-Fe2O3 nanowire by a topotactic transformation process, which shows 3D correspondence between the structures of the product and its host. These observations demonstrate that the partial reduction of α-Fe2O3 nanowires results in the formation of a unique hierarchical structure of hybrid oxides consisting of the parent oxide phase, γ-Fe2O3, as the one-dimensional wire and the Fe3O4 in the form of nanoparticles decorated on the parent oxide skeleton. We show that the proposed mechanism is consistent with previously published and our density functional theory results on the thermodynamics of surface termination and oxygen vacancy formation in α-Fe2O3. Compared to previous reports of α-Fe2O3 directly transformed to Fe3O4, our work provides a more in-depth understanding with substeps of reduction, i.e., the whole reduction process follows: α-Fe2O3 → α-Fe2O3 superlattice → γ-Fe2O3 + Fe3O4→ Fe3O4.

Two-dimensional (2D) ${\mathrm{BNSi}}_{2}$ has been recently proposed to be a viable candidate material with a graphenelike structure. We have carried out ab initio evolutionary ground state searches and uncovered a number of 2D structures in the $(\mathrm{BN}){}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ pseudobinary system with considerably lower energies. Nevertheless, our formation energy analysis shows that none of these or previously proposed polymorphs are stable with respect to phase separation into 2D Si and BN. Examination of the related CSi, ${\mathrm{BNC}}_{2}$, and ${\mathrm{BNSi}}_{2}$ 2D compounds indicates that the lack of miscibility in the last two systems is due to limited involvement of nitrogen electronic states in the covalent bonding.

The group-IV tin has been hypothesized to possess intriguing electronic properties in an atom-thick hexagonal form. An attractive pathway of producing sizable 2D crystallites of tin is based on deintercalation of bulk compounds with suitable tin frameworks. Here, we have identified a new synthesizable metal distannide, NaSn2, with a 3D stacking of flat hexagonal layers and examined a known compound, BaSn2, with buckled hexagonal layers. Our ab initio results illustrate that despite being an exception to the 8-electron rule, NaSn2 should form under pressures easily achievable in multi-anvil cells and remain (meta)stable under ambient conditions. Based on calculated Z2 invariants, the predicted NaSn2 may display topologically non-trivial behavior and the known BaSn2 could be a strong topological insulator.

Recent application of neural networks (NNs) to modeling interatomic interactions has shown the learning machines' encouragingly accurate performance for select elemental and multicomponent systems. In this study, we explore the possibility of building a library of NN-based models by introducing a hierarchical NN training. In such a stratified procedure NNs for multicomponent systems are obtained by sequential training from the bottom up: first unaries, then binaries, and so on. Advantages of constructing NN sets with shared parameters include acceleration of the training process and intact description of the constituent systems. We use an automated generation of diverse structure sets for NN training on density functional theory-level reference energies. In the test case of Cu, Pd, Ag, Cu-Pd, Cu-Ag, Pd-Ag, and Cu-Pd-Ag systems, NNs trained in the traditional and stratified fashions are found to have essentially identical accuracy for defect energies, phonon dispersions, formation energies, etc. The models' robustness is further illustrated via unconstrained evolutionary structure searches in which the NN is used for the local optimization of crystal unit cells.

Silicon nitride is a bulk and a coating material exhibiting excellent mechanical properties. We present a transferable reduced tight-binding (TB) model for the silicon nitride system, developed within the framework of coarse graining the electronic structure from density-functional theory (DFT) to tight binding (TB) to bond-order potentials (BOPs). The TB bond integrals are obtained directly from mixed-basis DFT projections of wave functions onto a minimal basis of atom-centered orbitals. This approach reduces the number of overall parameters to be fitted. Furthermore, applying the reduced TB approximation automatically leads to a single $\ensuremath{\sigma}$ bond order that contributes to the bond energy. DFT binding energies of ground state and metastable crystal structures are used as the benchmark to which the TB repulsive parameters are fitted. The quality of the TB models is demonstrated by comparing their predictions for the binding energies, heats of formation, elastic constants, and defect energies with DFT and experimental values.

Kolmogorov's article "Contemporary Debates on the Nature of Mathematics" was published in 1929 in Nauchnoe slovo journal (no. 6, pp. 41---54) and has not been republished since then. At the end of the 19th and at the beginning of the 20th century, abstractions of a very high order appeared and were rooted in mathematics, so that their correlation with reality became a crucial question. A number of great mathematicians of the time were interested in this question, and Kolmogorov's article was quite up to date. The goal of the republication of this article, which is currently difficult to access, is not only to acquaint the reader with a scarcely known article of the great scientist but to invite him to observe the process of scientific progress. It should be noted that, only a year after the publication of the article, some astonishing results of Godel appeared that gave answers to a number of questions in Kolmogorov's article and brought mathematical strictness in the very formulation of these questions. Therefore, the article is accompanied by external comments in order to give an insight into the current state of the art. In the text the comments are indicated by numbers in brackets, from [1] to [21].1 As for the rest, Kolmogorov's text is published in the same way as it was published in Nauchnoe slovo, without any alterations of the sense. Accompanying comments given to the article by the editors of Nauchnoe slovo (footnotes and introduction to the article) are omitted.

Prediction and characterization of crystal structures of alloys are a key problem in materials research. Using high-throughput ab initio calculations we explore the low-temperature phase diagrams for the following systems: Bi–In, Bi–Mg, Bi–Sb, In–Mg, In–Sb, and Mg–Sb. For the experimentally observed phases in these systems we provide information about their stability at low temperatures.

The paper is published without modifications. Kolmogorov's manuscript was apparently prepared during his participation in one of expeditions of the ship "D. Mendeleev" to the Atlantic Ocean (1969) or in a circumnavigation of the world (1971) organized by the Institute for Oceanology led at the time by A.S. Monin. As Kolmogorov himself wrote, the choice of the topic was stimulated by observations concerning "...meanders with horizontal sizes of hundreds of kilometers on a flow involving a layer of hundreds of meters, with subsequent disintegration of these meanders into vortices gradually decreasing in size to several kilometers." In modern terminology, the paper is devoted to the problem of intensive mixing in pycnoclines, that is, thin layers of stratified fluid, caused by internal waves whose frequencies are less than the Brent-Vaisala frequency. Here I would like to note two circumstances. The first is the scientific insight characteristic for Kolmogorov; this very approach was later reflected in numerous publications (see, for instance, the monograph by V.S. Modevich, V.I. Nikulin, and A.G. Stetsenko "Dynamics of internal mixing in a stratified medium," Institute for Hydromechanics, Academy of Sciences of Ukraine, Naukova Dumka, Kiev 1988). The second, the more significant in my opinion, is the genuine intellectual curiosity and breadth of thought of this great thinker, who studied not only the most abstract mathematical constructions but also got his head out of the clouds with great interest to solve concrete applied problems.

The paper was apparently written at the end of the 1950s. The text is in its final form, but the list of references was not worked out in detail. Ya.G.?Sinai added some comments to the text and included in the list of references some items related to the content of the paper.

The note that is published here was written by A. N. Kolmogorov more than 40 years ago (the author dates it April 1962). At that time I was a graduate student of Andrei Nikolaevich [Kolmogorov] and was investigating the possibility of generalizing and amplifying the wellknown Chebyshev inequality. Some of my results I presented at Kolmogorov’s seminar at the Moscow State University. In 1962, on Bernstein’s request, I wrote a commentary on his work “On some modifications of the Chebyshev inequality” (this paper can be found in the fourth volume of Bernstein’s collected works). Andrei Nikolaevich approached my work (which was published by the MphTI press the same year) with interest. During my next visit to Komarovka, when I was reporting the work in progress on my doctoral thesis, he gave me a short manuscript and asked me to read it. The idea of that note was close to the one contained in my published work and in my commentary on Bernstein’s work. After some time I asked Andrei Nikolaevich whether he planned to prepare that note for publication. He said that he did not plan to do so in the near future. The manuscript remained in my archive. This note does not contain a fundamental result, as was usually the case with most of Kolmogorov’s other works. However, it presents an opportunity of learning what this great scientist thought and worked on during a fruitful period of his career. In this respect, this short work is certainly valuable to both experts and new practitioners in the field of probability theory. The manuscript contains formula (9), where e > 0 and p ∈ (0, 1) and μn denotes the number of successes in n Bernoulli trials with the probability of success p. For p = 1 2 the manuscript contains the more precise inequality (8). It should be mentioned that similar inequalities appear in several textbooks published at later dates: A. A. Borovkov, Probability Theory, Gordon and Breach, United Kingdom, 1998; A. N. Shiryaev, Probability, Springer-Verlag, Berlin, New York, 1984. In particular, the first textbook gives the following inequalities

The well-defined geometry and extreme structural anisotropy of a multiwalled carbon nanotube can bring qualitatively new features to its nanometer-scale tribology. Efficient cancellation of registration-dependent interactions in incommensurate tubes (and also, surprisingly, certain axial commensurate tubes) can induce extremely small and nonextensive shear strengths.

he following paper was originally obtained from V. V. Ivanov, along with some other materials also pertaining to Russian verse research, which Andrei Nikolaevich Kolmogorov studied actively and with inspiration together with a group of his younger colleagues while Chair of Probability Theory at Moscow University. The typewritten copy of the manuscript contained nine pages, had no date, and, as far as I know, was never submittedfor publication. One can only make guesses as to why this manuscript was not published: could it be that Kolmogorov considered it unfinished, or that his last check revealed regrettable inaccuracies that had crept into it and he put off publication? Now, 35 years later (the paper was probably written in 1962), the editors of Theory of Probability and Its Applications, sharing the finally formed conviction that everything Kolmogorov ever wrote should come out, has decided to publish this manuscript. A. B. Sossinsky, with whom Andrei Nikolaevich discussed these matters quite frequentl...

The set theoretic axioms of the calculus of probability, in formulating which I had the opportunity of playing some part (Kolmogorov, 1950), had solved the majority of formal difficulties in the construction of a mathematical apparatus which is useful for a very large number of applications of probabilistic methods, so successfully that the problem of finding the basis of real applications of the results of the mathematical theory of probability became rather secondary to many investigators. I have already expressed the view [see Kolmogorov (1950), Chapter I] that the basis for the applicability of the results of the mathematical theory of probabi lity to real 'random phenomena' must depend on some form of the frequency concept of probability, the unavoidable nature of which has been established by von Mises in a spirited manner. However, for a long time I had the following views. (1) The frequency concept based on the notion of limiting frequency as the number of trials increases to infinity, does not contribute anything to substantiate the applicability of the results of probability theory to real practical problems where we have always to deal with a finite number of trials. (2) The frequency concept applied to a large but finite number of trials does not admit a rigorous formal exposition within the framework of pure mathematics. Accordingly I have sometimes put forward the frequency concept which involves the conscious use of certain not rigorously formal ideas about 'practical reliability', 'approximate stability of the frequency in a long series of trials', without the precise definition of the series which are-'sufficiently large' etc. [see Foundation^ of the Theory of Probability, Chapter I and for more details Great Soviet Encyclo paedia (section on Probability) and Mathematika iou metod i Znachenye (Chapter on Probability Theory)]. I still maintain the first of the two theses mentioned above. As regards the second, however, I have come to realise that the concept of random distribution of a property in a large finite population can have a strict formal mathematical exposition. In fact, we can show that in sufficiently large populations the distribution of the pro perty may be such that the frequency of its occurrence will be almost the same for all sufficiently large sub-populations, when the law of choosing these is sufficiently simple. Such a conception in its full development requires the introduction of a measure of the complexity of the algorithm. I propose to discuss this question in another article. In the present article, however, I shall use the fact that there cannot be a very large number of simple algorithms. 369 3

A multitude of observed boron-based materials have outstanding superconducting, mechanical, and refractory properties. Yet, the structure, the composition, and the very existence of some reported metal boride (M–B) compounds have been a subject of extensive debate. This density functional theory work seeks to set a baseline for current understanding of known metal boride phases as well as to identify new synthesizable candidates. We have generated a database of over 12,000 binary M–B entries for pressures of 0 and 30 GPa producing the largest scan of compositions and systems in this materials׳ class. The 175 selected crystal structures include both observed prototypes and the new ones found with our evolutionary ground state search. The metals considered are Al, Ag, Au, Ba, Be, Ca, Cd, Co, Cr, Cs, Cu, Fe, Hf, Hg, Ir, K, La, Li, Mg, Mn, Mo, Na, Nb, Ni, Os, Pd, Pt, Rb, Re, Rh, Ru, Sc, Sr, Ta, Tc, Ti, V, W, Y, Zn, and Zr. Based on the formation energy calculated at zero pressure and temperature 4 new M–B phases or structures have been predicted, while a number of previously reported compounds have been shown to be unstable. At 30 GPa, changes in the convex hulls are expected to occur in 18 out of 41 M–B systems, which is used to indicate regions of the periodic table (for metal borides) that require further investigation from the community. Analysis of the collected information has revealed a nearly linear relationship between the magnetic moment per atom and the metal content for all the Fe–B, Co–B, and Ni–B structures within 0.15 eV/atom of the stability tie line. Both GGA-PBE and LDA-PW functionals were used to provide an understanding of the systematic error introduced by the choice of the exchange-correlation functional.

In the search for MgB${}_{2}$-like phonon-mediated superconductors we have carried out a systematic density functional theory study of the Ca-B system, isoelectronic to Mg-B, at ambient and gigapascal pressures. A remarkable variety of candidate high-pressure ground states have been identified with an evolutionary crystal structure search, including a stable alkaline-earth monoboride oI8-CaB, a superconductor with an expected critical temperature (T${}_{c}$) of 5.5 K. We have extended our previous study of CaB${}_{6}$ [Phys. Rev. Lett. 108, 102501 (2012)] to nearby stoichiometries of CaB${}_{6+x}$, finding that extra boron further stabilizes the proposed B${}_{24}$ units. Here an explanation is given for the transformation of cP7-CaB${}_{6}$ into the more complex oS56 and tI56 polymorphs at high pressure. The stability of the known metallic tP20 phase of CaB${}_{4}$ at ambient pressure is explained from a crystal structure and chemical bonding point of view. The tP20 structure is shown to destabilize at 19 GPa relative to a semiconducting MgB${}_{4}$-like structure due to chemical pressure from the metal ion. The hypothetical AlB${}_{2}$-type structure of CaB${}_{2}$, previously shown to have favorable superconducting features, is demonstrated here to be unstable at all pressures; two new metallic CaB${}_{2}$ polymorphs with unusual boron networks stabilize at elevated pressures above 8 GPa but are found to have very low critical temperatures (T${}_{c}$ $\ensuremath{\sim}$ 1 K). The stability of all structures has been rationalized through comparison with alkaline-earth analogs, emphasizing the importance of the size of the metal ion for the stability of borides. Our study illustrates the inverse correlation between the thermodynamic stability and superconducting properties and the necessity to carefully examine both in the design of new synthesizable superconducting materials.

Single crystals of novel orthorhombic (space group Pnnm) iron tetraboride FeB4 were synthesised at pressures above 8 GPa and high temperatures. Magnetic susceptibility measurements demonstrated bulk superconductivity below 2.9 K. The putative isotope effect on the superconducting critical temperature indicates that FeB4 is likely a phonon-mediated superconductor, which is unexpected in the light of previous knowledge on Fe-based superconductors. The discovered iron tetraboride is highly incompressible and has the nanoindentation hardness of 65(5) GPa, thus, it opens a new class of highly desirable materials combining advanced mechanical properties and superconductivity., Comment: 7 pages

L'A. definit la completude unique de l'algebre de Boole metrique par analogie avec la notion de completude d'un espace metrique isomorphe. Cette definition, fondee sur la notion de volume d'une figure spatiale et sur la probabilite d'un evenement, sous-tend le developpement logique des mathematiques recentes dans le sens de la theorie de la mesure. L'algebre de Boole s'apparente donc a la theorie de la mesure d'un ensemble, en ce qui concerne son objet et son traitement formel

Neural Networks (NN's) involve an innovative method of simulating and analysing complex and constantly changing systems of relationships. Originally developed to mimic the neural architecture and functioning of the human brain, NN techniques have recently been applied to many different business fields and have demonstrated a capability to solve complex problems. This paper investigates the use of NN techniques as a tool for the modelling and prediction of corporate bankruptcy and other corporate outcomes. The within and out-of-sample accuracy of trained NNs are compared with those of standard logit and multilogit techniques. The results of the study suggest that, from a pure predictive point of view, NN simulation produces a higher predictive accuracy and is more robust than conventional logit and multilogit models.

By electron and x-ray diffractionwe establish that the CrB4 compound discovered over 40 years ago crystallizes in the oP 10 (Pnnm) structure, in disagreement with previous experiments but in agreement with a recent first-principles prediction. The 3D boron network in this structure is a distorted version of the rigid carbon sp(3) network proposed recently for the high-pressure C-4 allotrope. Our systematic density functional theory analysis of the electronic, structural, and elastic properties in ten related transition metal TMB4 tetraborides (TM = Ti, V, Cr, Mn, Fe and Y, Zr, Nb, Mo, Tc) identifies CrB4 as the prime candidate to be a superhard material. In particular, the compound's calculated weakest shear and tensile stresses exceed 50 GPa, and its Vickers hardness is estimated to be 48 GPa. We compare the reported and estimated Vickers hardness for notable (super) hard materials and find that the CrB4 calculated value is exceptionally high for a material synthesizable under standard ambient-pressure conditions.

We synthesized and solved an unexpectedly complex crystal structure of ${\mathrm{CaB}}_{6}$ under high pressures (up to 44 GPa) and temperatures. The only known crystal structure in the large family of metal hexaborides, a simple cubic $cP7$ type discovered over 80 years ago, is shown here to transform into a tetragonal $tI56$ configuration comprised of unfamiliar 24-atom boron units. The interpretation of the convoluted x-ray diffraction pattern was accomplished with an ab initio evolutionary search which identified the $tI56$ structure (28 atoms per primitive unit cell) without any parameter input. The exotic ${\mathrm{CaB}}_{6}$ phase was successfully quenched down to ambient pressure.

We report inelastic neutron scattering measurements on ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below ${T}_{N}=15.3\text{ }\text{ }\mathrm{K}$ is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90\ifmmode^\circ\else\textdegree\fi{} Ir-O-Ir bonds required for dominant Kitaev exchange.