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

Data Unfolding with Wiener-SVD Method

Data unfolding is a common analysis technique used in HEP data analysis. Inspired by the deconvolution technique in the digital signal processing, a new unfolding technique based on the SVD technique and the well-known Wiener filter is introduced. The Wiener-SVD unfolding approach achieves the unfolding by maximizing the signal to noise ratios in the effective frequency domain given expectations of signal and noise and is free from regularization parameter. Through a couple examples, the pros and cons of the Wiener-SVD approach as well as the nature of the unfolded results are discussed.Comment: 26 pages, 12 figures, match the accepted version by JINS

Nodeless superconductivity in Ca3Ir4Sn13: evidence from quasiparticle heat transport

We report resistivity $\rho$ and thermal conductivity $\kappa$ measurements on Ca$_3$Ir$_4$Sn$_{13}$ single crystals, in which superconductivity with $T_c \approx 7$ K was claimed to coexist with ferromagnetic spin-fluctuations. Among three crystals, only one crystal shows a small hump in resistivity near 20 K, which was previously attributed to the ferromagnetic spin-fluctuations. Other two crystals show the $\rho \sim T^2$ Fermi-liquid behavior at low temperature. For both single crystals with and without the resistivity anomaly, the residual linear term $\kappa_0/T$ is negligible in zero magnetic field. In low fields, $\kappa_0(H)/T$ shows a slow field dependence. These results demonstrate that the superconducting gap of Ca$_3$Ir$_4$Sn$_{13}$ is nodeless, thus rule out nodal gap caused by ferromagnetic spin-fluctuations.Comment: 5 pages, 4 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