The gravitational field of a global monopole

We present an exact solution to the non-linear equation which describes a global monopole in the flat space. We re-examine the metric and the geodesics outside the global monopole. We will see that a global monopole produces a repulsive gravitational field outside the core in addition to a solid angular deficit. The lensing property of the global monopole and the global monopole-antimonopole annihilation mechanism are studied.Comment: 8 pages, no figure

Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic

Combinatorial analysis of interacting RNA molecules

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.Comment: 22 pages, 15 figure

Aberrant posterior cingulate connectivity classify first-episode schizophrenia from controls: A machine learning study

Background Posterior cingulate cortex (PCC) is a key aspect of the default mode network (DMN). Aberrant PCC functional connectivity (FC) is implicated in schizophrenia, but the potential for PCC related changes as biological classifier of schizophrenia has not yet been evaluated. Methods We conducted a data-driven approach using resting-state functional MRI data to explore differences in PCC-based region- and voxel-wise FC patterns, to distinguish between patients with first-episode schizophrenia (FES) and demographically matched healthy controls (HC). Discriminative PCC FCs were selected via false discovery rate estimation. A gradient boosting classifier was trained and validated based on 100 FES vs. 93 HC. Subsequently, classification models were tested in an independent dataset of 87 FES patients and 80 HC using resting-state data acquired on a different MRI scanner. Results Patients with FES had reduced connectivity between PCC and frontal areas, left parahippocampal regions, left anterior cingulate cortex, and right inferior parietal lobule, but hyperconnectivity with left lateral temporal regions. Predictive voxel-wise clusters were similar to region-wise selected brain areas functionally connected with PCC in relation to discriminating FES from HC subject categories. Region-wise analysis of FCs yielded a relatively high predictive level for schizophrenia, with an average accuracy of 72.28% in the independent samples, while selected voxel-wise connectivity yielded an accuracy of 68.72%. Conclusion FES exhibited a pattern of both increased and decreased PCC-based connectivity, but was related to predominant hypoconnectivity between PCC and brain areas associated with DMN, that may be a useful differential feature revealing underpinnings of neuropathophysiology for schizophrenia

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states

We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure n-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families