Effects of Long-Range Interactions on Magnetic Excitations and Phase Transition on a Magnetically Frustrated Square Lattice

We investigate the effects of long-range interaction on the magnetic excitations and the competition between magnetic phases on a frustrated square lattice. Applying the spin wave theory and assisted with symmetry analysis, we obtain analytical expression for spin wave spectrum of competing Neel and (pi, 0) stripe states of systems containing any-order long-range interactions. In the specific case of long-range interactions with power-law decay, we found surprisingly that staggered long-range interaction suppresses quantum fluctuation and enlarges the ordered moment, especially in the Neel state, and thus extends its phase boundary to the stripe state. Our findings only illustrate the rich possibilities of the roles of long-range interactions, and advocate future investigations in other magnetic systems with different structures of interactions.Comment: 9 pages, 9 figure

N′-(5-Chloro-2-hy­droxy­benzyl­idene)-4-meth­oxy­benzohydrazide

The asymmetric unit of the title compound, C15H13ClN2O3, contains two independent hydrazone mol­ecules. Each mol­ecule adopts an E configuration with respect to the methyl­idene unit and forms an intra­molecular O—H⋯N hydrogen bond. The principal difference between the two unique mol­ecules is the relative orientation of the two benzene rings, the dihedral angles between them being 4.0 (3) and 65.9 (3)°, respectively. In the crystal, mol­ecules are linked through N—H⋯O hydrogen bonds, forming chains running along the c axis

Comparison of ontology alignment systems across single matching task via the McNemar's test

Ontology alignment is widely-used to find the correspondences between different ontologies in diverse fields.After discovering the alignments,several performance scores are available to evaluate them.The scores typically require the identified alignment and a reference containing the underlying actual correspondences of the given ontologies.The current trend in the alignment evaluation is to put forward a new score(e.g., precision, weighted precision, etc.)and to compare various alignments by juxtaposing the obtained scores. However,it is substantially provocative to select one measure among others for comparison.On top of that, claiming if one system has a better performance than one another cannot be substantiated solely by comparing two scalars.In this paper,we propose the statistical procedures which enable us to theoretically favor one system over one another.The McNemar's test is the statistical means by which the comparison of two ontology alignment systems over one matching task is drawn.The test applies to a 2x2 contingency table which can be constructed in two different ways based on the alignments,each of which has their own merits/pitfalls.The ways of the contingency table construction and various apposite statistics from the McNemar's test are elaborated in minute detail.In the case of having more than two alignment systems for comparison, the family-wise error rate is expected to happen. Thus, the ways of preventing such an error are also discussed.A directed graph visualizes the outcome of the McNemar's test in the presence of multiple alignment systems.From this graph, it is readily understood if one system is better than one another or if their differences are imperceptible.The proposed statistical methodologies are applied to the systems participated in the OAEI 2016 anatomy track, and also compares several well-known similarity metrics for the same matching problem

ATTITUDES AND ACHIEVEMENT ORIENTATIONS OF STUDENTS TOWARDS LEARNING OF SCIENCE AND MATHEMATICS IN ENGLISH

This study examines the policy of teaching science and mathematics in English in the Malaysian educational system by focusing on the attitudes and achievement orientations of secondary school students towards the learning of these two subjects. Attitudes and achievement are two important outcomes of learning that will determine the effectiveness of an education policy. This study is based on a sample of 400 secondary school students selected from four non-premier schools. It looks into the students’ general attitudes and achievement orientations towards learning of science and mathematics as well as their variations according to four background variables, i.e., gender, ethnicity, types of feeder school and English achievement grades. It also examines the inter-correlations between the students’ attitudes and achievement orientations. Findings from statistical analyses of collected data were supplemented by more in-depth interviews. This study shows that the students’ general attitudes and achievement orientations towards learning of science and mathematics in English do not indicate that the policy has achieved its objective. However, their attitudes and achievement motivations vary according to the four background variables. The significant and positive inter-correlations between attitudes and achievement orientations towards learning of science and mathematics further confirm the causal relationship between these two important dimensions of learning

Curvature-based sparse rule base generation for fuzzy rule interpolation

Fuzzy logic has been successfully widely utilised in many real-world applications. The most common application of fuzzy logic is the rule-based fuzzy inference system, which is composed of mainly two parts including an inference engine and a fuzzy rule base. Conventional fuzzy inference systems always require a rule base that fully covers the entire problem domain (i.e., a dense rule base). Fuzzy rule interpolation (FRI) makes inference possible with sparse rule bases which may not cover some parts of the problem domain (i.e., a sparse rule base). In addition to extending the applicability of fuzzy inference systems, fuzzy interpolation can also be used to reduce system complexity for over-complex fuzzy inference systems. There are typically two methods to generate fuzzy rule bases, i.e., the knowledge driven and data-driven approaches. Almost all of these approaches only target dense rule bases for conventional fuzzy inference systems. The knowledge-driven methods may be negatively affected by the limited availability of expert knowledge and expert knowledge may be subjective, whilst redundancy often exists in fuzzy rule-based models that are acquired from numerical data. Note that various rule base reduction approaches have been proposed, but they are all based on certain similarity measures and are likely to cause performance deterioration along with the size reduction. This project, for the first time, innovatively applies curvature values to distinguish important features and instances in a dataset, to support the construction of a neat and concise sparse rule base for fuzzy rule interpolation. In addition to working in a three-dimensional problem space, the work also extends the natural three-dimensional curvature calculation to problems with high dimensions, which greatly broadens the applicability of the proposed approach. As a result, the proposed approach alleviates the ‘curse of dimensionality’ and helps to reduce the computational cost for fuzzy inference systems. The proposed approach has been validated and evaluated by three real-world applications. The experimental results demonstrate that the proposed approach is able to generate sparse rule bases with less rules but resulting in better performance, which confirms the power of the proposed system. In addition to fuzzy rule interpolation, the proposed curvature-based approach can also be readily used as a general feature selection tool to work with other machine learning approaches, such as classifiers

Rate distortion functions of countably infinite alphabet memoryless sources

The Shannon lower bound approach to the evaluation of rate distortion functions R(D) for countably infinite alphabet memoryless sources is considered. Sufficient conditions based on the Contraction Mapping Theorem for the existence of the Shannon lower bound RL(D) to R(D) in a region of distortion [0, D1], D1 > 0 are obtained. Sufficient conditions based on the Schauder Fixed Point Theorem for the existence of a Dc > 0 such that R(D) = RL(D) for all D ε [0, Dc] are derived. Explicit evaluation of R(D) is considered for a class of column balanced distortion measures. Other results for distortion measures with no symmetry conditions are also discussed