Mean-field Study of Charge, Spin, and Orbital Orderings in Triangular-lattice Compounds ANiO2 (A=Na, Li, Ag)

We present our theoretical results on the ground states in layered triangular-lattice compounds ANiO2 (A=Na, Li, Ag). To describe the interplay between charge, spin, orbital, and lattice degrees of freedom in these materials, we study a doubly-degenerate Hubbard model with electron-phonon couplings by the Hartree-Fock approximation combined with the adiabatic approximation. In a weakly-correlated region, we find a metallic state accompanied by \sqroot3x\sqroot3 charge ordering. On the other hand, we obtain an insulating phase with spin-ferro and orbital-ferro ordering in a wide range from intermediate to strong correlation. These phases share many characteristics with the low-temperature states of AgNiO2 and NaNiO2, respectively. The charge-ordered metallic phase is stabilized by a compromise between Coulomb repulsions and effective attractive interactions originating from the breathing-type electronphonon coupling as well as the Hund's-rule coupling. The spin-orbital-ordered insulating phase is stabilized by the cooperative effect of electron correlations and the Jahn-Teller coupling, while the Hund's-rule coupling also plays a role in the competition with other orbital-ordered phases. The results suggest a unified way of understanding a variety of low-temperature phases in ANiO2. We also discuss a keen competition among different spin-orbital-ordered phases in relation to a puzzling behavior observed in LiNiO2

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

Anisotropic phonon conduction and lattice distortions in CMR-type bilayer manganite (La1−z_{1-z}Prz_{z})1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7} (z=0,0.2,0.4 and 0.6) single crystals

We have undertaken a systematic study of thermal conductivity as a function of temperature and magnetic field of single crystals of the compound (La$_{1-z}$Pr$_{z}$)$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ for $z$(Pr) =0.2,0.4. and 0.6. The lattice distortion due to Pr-substitution and anisotropic thermal conductivity in bilayer manganites are discussed on the basis of different relaxation models of local lattice distortions in metal and insulating states proposed by Maderda et al. The giant magnetothermal effect is scaled as a function of magnetization and discussed on the basis of a systematic variation of the occupation of the $e_g$-electron orbital states due to Pr-substitution.Comment: 7 pages, 6 figures, in press in Phys.Rev.

Exchange coupling in CaMnO3_3 and LaMnO3_3: configuration interaction and the coupling mechanism

The equilibrium structure and exchange constants of CaMnO$_3$ and LaMnO$_3$ have been investigated using total energy unrestricted Hartree-Fock (UHF) and localised orbital configuration interaction (CI) calculations on the bulk compounds and Mn$_2$O$_{11}^{14-}$ and Mn$_2$O$_{11}^{16-}$ clusters. The predicted structure and exchange constants for CaMnO$_3$ are in reasonable agreement with estimates based on its N\'eel temperature. A series of calculations on LaMnO$_3$ in the cubic perovskite structure shows that a Hamiltonian with independent orbital ordering and exchange terms accounts for the total energies of cubic LaMnO$_3$ with various spin and orbital orderings. Computed exchange constants depend on orbital ordering. UHF calculations tend to underestimate exchange constants in LaMnO$_3$, but have the correct sign when compared with values obtained by neutron scattering; exchange constants obtained from CI calculations are in good agreement with neutron scattering data provided the Madelung potential of the cluster is appropriate. Cluster CI calculations reveal a strong dependence of exchange constants on Mn d e$_g$ orbital populations in both compounds. CI wave functions are analysed in order to determine which exchange processes are important in exchange coupling in CaMnO$_3$ and LaMnO$_3$.Comment: 25 pages and 9 postscript figure

Trends in support for research and development of cool season food legumes in the developing countries

In addition to their role in human nutrition, food legumes are an integral part of farming systems world wide in diversifying cropping systems and maintaining soil fertility. 1996 world production is around 57 million tonnes. The population in developing countries is expected to be 6.06 billion by 2010, and the demand for food legumes is expected to be around 110.65 million tonnes. This poses a challenge to scientists and policy makers to meet this demand. The growth trends during 1990-94 for area, production, and productivity globally were negative, with few exceptions. Many countries in Asia need to increase production by at least 50% by 2010, and double it by 2020, to meet the needs of the growing population. The current research and development (R&D) thrusts, in developing countries, are geared towards increased production, but with varied success. An increased reliance on plant breeding and extensive cultivation of legumes in marginal areas has led to over-exploitation of the limited genetic resources. Some national governments (eg Turkey and India) have programmes to increase production, but early successes have plateaued, and shifts in direction are needed. The major proportion (50-75%) of R&D funds in developing countries is allocated to staple cereals, and only a small portion of the remaining budget is available for legumes. The following strategies are suggested to strengthen support for food legume research: integrated cropping systems management (variety+agronomic practices+crop rotations) to bridge the yield gap in different agroclimatic conditions; strategic research to breach yield ceilings and develop cultivars that can produce high and stable yields in better-endowed environments and thus compete with cereals; strengthen research collaboration within and among national programmes and with the international agricultural research centres; increase the role of regional, networks and working groups to enhance technical cooperation among developing countries; increase the collaboration between public and private sectors and exploit their comparative advantages to achieve mutual goals; and create Food Legume Councils (that include farmers, traders, and exporters) which support R&D by levying taxes or cesses on commodities and value-added products

Trends in support for research and development of cool season food legumes in the developing countries

In addition to their role in human nutrition, food legumes are an integral part of farming systems world wide in diversifying cropping systems and maintaining soil fertility. 1996 world production is around 57 million tonnes. The population in developing countries is expected to be 6.06 billion by 2010, and the demand for food legumes is expected to be around 110.65 million tonnes. This poses a challenge to scientists and policy makers to meet this demand. The growth trends during 1990-94 for area, production, and productivity globally were negative, with few exceptions. Many countries in Asia need to increase production by at least 50% by 2010, and double it by 2020, to meet the needs of the growing population. The current research and development (R&D) thrusts, in developing countries, are geared towards increased production, but with varied success. An increased reliance on plant breeding and extensive cultivation of legumes in marginal areas has led to over-exploitation of the limited genetic resources. Some national governments (eg Turkey and India) have programmes to increase production, but early successes have plateaued, and shifts in direction are needed. The major proportion (50-75%) of R&D funds in developing countries is allocated to staple cereals, and only a small portion of the remaining budget is available for legumes. The following strategies are suggested to strengthen support for food legume research: integrated cropping systems management (variety+agronomic practices+crop rotations) to bridge the yield gap in different agroclimatic conditions; strategic research to breach yield ceilings and develop cultivars that can produce high and stable yields in better-endowed environments and thus compete with cereals; strengthen research collaboration within and among national programmes and with the international agricultural research centres; increase the role of regional, networks and working groups to enhance technical cooperation among developing countries; increase the collaboration between public and private sectors and exploit their comparative advantages to achieve mutual goals; and create Food Legume Councils (that include farmers, traders, and exporters) which support R&D by levying taxes or cesses on commodities and value-added products

Unsupervised machine learning on encrypted data

In the context of Fully Homomorphic Encryption, which allows computations on encrypted data, Machine Learning has been one of the most popular applications in the recent past. All of these works, however, have focused on supervised learning, where there is a labeled training set that is used to configure the model. In this work, we take the first step into the realm of unsupervised learning, which is an important area in Machine Learning and has many real-world applications, by addressing the clustering problem. To this end, we show how to implement the K-Means-Algorithm. This algorithm poses several challenges in the FHE context, including a division, which we tackle by using a natural encoding that allows division and may be of independent interest. While this theoretically solves the problem, performance in practice is not optimal, so we then propose some changes to the clustering algorithm to make it executable under more conventional encodings. We show that our new algorithm achieves a clustering accuracy comparable to the original K-Means-Algorithm, but has less than $5\%$ of its runtime

Towards a Practical Cluster Analysis over Encrypted Data

Cluster analysis is one of the most significant unsupervised machine learning tasks, and it is utilized in various fields associated with privacy issues including bioinformatics, finance and image processing. In this paper, we propose a practical solution for privacy-preserving cluster analysis based on homomorphic encryption~(HE). Our work is the first HE solution for the mean-shift clustering algorithm. To reduce the super-linear complexity of the original mean-shift algorithm, we adopt a novel random sampling method called dust sampling which perfectly fits in HE and achieves the linear complexity. We also substitute non-polynomial kernels by a new polynomial kernel so that it can be efficiently computed in HE. The HE implementation of our modified mean-shift clustering algorithm based on the approximate HE scheme HEAAN shows prominent performance in terms of speed and accuracy. It takes about $30$ minutes with $99\%$ accuracy over several public datasets with hundreds of data, and even for the dataset with $262,144$ data it takes only $82$ minutes applying SIMD operations in HEAAN. Our results outperform the previously best known result (SAC 2018) over $400$ times

Parabolic inequalities in L1 as limits of renormalized equations

The paper deals with the existence of solutions of some parabolic bilateral problems approximated by the renormalized solutions of some parabolic equations