A robust and efficient implementation of LOBPCG

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. We also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed

Higgs mass from compositeness at a multi-TeV scale

Within composite Higgs models based on the top seesaw mechanism, we show that the Higgs field can arise as the pseudo Nambu-Goldstone boson of the broken U(3)_L chiral symmetry associated with a vector-like quark and the t-b doublet. As a result, the lightest CP-even neutral state of the composite scalar sector is lighter than the top quark, and can be identified as the newly discovered Higgs boson. Constraints on weak isospin violation push the chiral symmetry breaking scale above a few TeV, implying that other composite scalars are probably too heavy to be probed at the LHC, but may be within reach at a future hadron collider with center-of-mass energy of about 100 TeV.Comment: 30 pages. v2: discussion of T parameter expanded; references added. To be published in JHE

Enhancement of ferromagnetism by p-wave Cooper pairing in superconducting ferromagnets

In superconducting ferromagnets for which the Curie temperature $T_{m}$ exceeds the superconducting transition temperature $T_{c}$, it was suggested that ferromagnetic spin fluctuations could lead to superconductivity with p-wave spin triplet Cooper pairing. Using the Stoner model of itinerant ferromagnetism, we study the feedback effect of the p-wave superconductivity on the ferromagnetism. Below $T_{c}$, the ferromagnetism is enhanced by the p-wave superconductivity. At zero temperature, the critical Stoner value for itinerant ferromagnetism is reduced by the strength of the p-wave pairing potential, and the magnetization increases correspondingly. More important, our results suggest that once Stoner ferromagnetism is established, $T_m$ is unlikely to ever be below $T_c$. For strong and weak ferromagnetism, three and two peaks in the temperature dependence of the specific heat are respectively predicted, the upper peak in the latter case corresponding to a first-order transition.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Elliptic blowup equations for 6d SCFTs. Part II: Exceptional cases

The building blocks of 6d $(1,0)$ SCFTs include certain rank one theories with gauge group $G=SU(3),SO(8),F_4,E_{6,7,8}$. In this paper, we propose a universal recursion formula for the elliptic genera of all such theories. This formula is solved from the elliptic blowup equations introduced in our previous paper. We explicitly compute the elliptic genera and refined BPS invariants, which recover all previous results from topological string theory, modular bootstrap, Hilbert series, 2d quiver gauge theories and 4d $\mathcal{N}=2$ superconformal $H_{G}$ theories. We also observe an intriguing relation between the $k$-string elliptic genus and the Schur indices of rank $k$ $H_{G}$ SCFTs, as a generalization of Lockhart-Zotto's conjecture at the rank one cases. In a subsequent paper, we deal with all other non-Higgsable clusters with matters

Is the anisotropy of the upper critical field of Sr2_2RuO4_4 consistent with a helical pp-wave state?

We calculate the angular and temperature $T$ dependencies of the upper critical field $H_{c2}(\theta,\phi,T)$ for the $C_{4v}$ point group helical $p$-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting, and strong spin-orbit coupling that locks the spin-triplet $\vec{\bf d}$-vectors onto the layers. Good fits to the Sr$_2$RuO$_4$ $H_{c2,a}(\theta,T)$ data of Kittaka {\it et al.} [Phys. Rev. B {\bf 80}, 174514 (2009)] are obtained. Helical states with $\vec{\bf d}(\vec{\bf k})=k_x\vec{\bf x}-k_y\vec{\bf y}$ and $k_y\vec{\bf x}+k_x\vec{\bf y}$ (or $k_x\vec{\bf x}+k_y\vec{\bf y}$ and $k_y\vec{\bf x}-k_x\vec{\bf y}$) produce $H_{c2}(90^{\circ},\phi,T)$ that greatly exceed (or do not exhibit) the four-fold azimuthal anisotropy magnitudes observed in Sr$_2$RuO$_4$ by Kittaka {\it et al.} and by Mao {\it et al.} [Phys. Rev. Lett. {\bf 84}, 991 (2000)], respectively.Comment: 5+ pages, 4 figures, submitted as a Fast Track Communication to J. Phys. Condens. Matte

Multi-aspect, robust, and memory exclusive guest os fingerprinting

Precise fingerprinting of an operating system (OS) is critical to many security and forensics applications in the cloud, such as virtual machine (VM) introspection, penetration testing, guest OS administration, kernel dump analysis, and memory forensics. The existing OS fingerprinting techniques primarily inspect network packets or CPU states, and they all fall short in precision and usability. As the physical memory of a VM always exists in all these applications, in this article, we present OS-Sommelier+, a multi-aspect, memory exclusive approach for precise and robust guest OS fingerprinting in the cloud. It works as follows: given a physical memory dump of a guest OS, OS-Sommelier+ first uses a code hash based approach from kernel code aspect to determine the guest OS version. If code hash approach fails, OS-Sommelier+ then uses a kernel data signature based approach from kernel data aspect to determine the version. We have implemented a prototype system, and tested it with a number of Linux kernels. Our evaluation results show that the code hash approach is faster but can only fingerprint the known kernels, and data signature approach complements the code signature approach and can fingerprint even unknown kernels

Gearbox fault diagnosis under different operating conditions based on time synchronous average and ensemble empirical mode decomposition

In this paper, a new method is proposed by combining ensemble empirical mode decomposition (EEMD) with order tracking techniques to analyse the vibration signals from a two stage helical gearbox. The method improves EEMD results in that it overcomes the potential deficiencies and achieves better order spectrum representation for fault diagnosis. Based on the analysis, a diagnostic feature is designed based on the order spectra of extracted IFMs for detection and separation of gearbox faults. Experimental results show this feature is sensitive to different fault severities and robust to the influences from operating conditions and remote sensor locations