Sign switch of Gaussian bending modulus for microemulsions; a self-consistent field analysis exploring scale invariant curvature energies

Bending rigidities of tensionless balanced liquid-liquid interfaces as occurring in microemulsions are predicted using self-consistent field theory for molecularly inhomogeneous systems. Considering geometries with scale invariant curvature energies gives unambiguous bending rigidities for systems with fixed chemical potentials: The minimal surface Im3m cubic phase is used to find the Gaussian bending rigidity, $\bar{\kappa}$, and a torus with Willmore energy $W=2 \pi^2$ allows for direct evaluation of the mean bending modulus, $\kappa$. Consistent with this, the spherical droplet gives access to $2 \kappa + \bar{\kappa}$. We observe that $\bar{\kappa}$ tends to be negative for strong segregation and positive for weak segregation; a finding which is instrumental for understanding phase transitions from a lamellar to a sponge-like microemulsion. Invariably, $\kappa$ remains positive and increases with increasing strength of segregation.Comment: 7 pages, 5 figure

Multiorder neurons for evolutionary higher-order clustering and growth

This letter proposes to use multiorder neurons for clustering irregularly shaped data arrangements. Multiorder neurons are an evolutionary extension of the use of higher-order neurons in clustering. Higher-order neurons parametrically model complex neuron shapes by replacing the classic synaptic weight by higher-order tensors. The multiorder neuron goes one step further and eliminates two problems associated with higher-order neurons. First, it uses evolutionary algorithms to select the best neuron order for a given problem. Second, it obtains more information about the underlying data distribution by identifying the correct order for a given cluster of patterns. Empirically we observed that when the correlation of clusters found with ground truth information is used in measuring clustering accuracy, the proposed evolutionary multiorder neurons method can be shown to outperform other related clustering methods. The simulation results from the Iris, Wine, and Glass data sets show significant improvement when compared to the results obtained using self-organizing maps and higher-order neurons. The letter also proposes an intuitive model by which multiorder neurons can be grown, thereby determining the number of clusters in data

Yang-Mills equation for stable Higgs sheaves

We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group

Concentration in Knowledge Output:A Case of Economics Journals

Journals moderate knowledge activity in economics. The activity of publishing article in professional journal forms significant part of knowledge output. Output of economics articles has been growing over the time. We examine an important question: Is there any case of institutional or location concentration in knowledge production? This paper analyses concentration indicators specific to economics journals and explores link between publication process and concentration. The analysis of various concentration measures present evidence for institutional-geographic-area-author concentration in Knowledge production in Economics. High concentration levels indicate possibility of institutional lock-in. The literature provides evidence for myopic refereeing, editorial favouritism and the presence of ‘lock-in’ effect. The achievement in journal publication is influenced by factors like institutional affiliation, propitious circumstances etc. Discussion carried out in this paper hints the possibility of causal link between unfair process and unfair outcome.Knowledge,Lotka's Law,Fourier Series

Schubert varieties are arithmetically Cohen-Macaulay

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On Simulating Liouvillian Flow From Quantum Mechanics Via Wigner Functions

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer- Duffin beta-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard `trace' techniques. The results are compared with a recent derivation due to Bosanac.Comment: 9 pages, Latex; email: [email protected]