On simple bounds for eigenvalues of symmetric tridiagonal matrices

How much can be said about the location of the eigenvalues of a symmetric tridiagonal matrix just by looking at its diagonal entries? We use classical results on the eigenvalues of symmetric matrices to show that the diagonal entries are bounds for some of the eigenvalues regardless of the size of the off-diagonal entries. Numerical examples are given to illustrate that our arithmetic-free technique delivers useful information on the location of the eigenvalues.

The bounds of education in the human brain connectome

Inter-individual heterogeneity is evident in aging; education level is known to contribute for this heterogeneity. Using a cross-sectional study design and network inference applied to resting-state fMRI data, we show that aging was associated with decreased functional connectivity in a large cortical network. On the other hand, education level, as measured by years of formal education, produced an opposite effect on the long-term. These results demonstrate the increased brain efficiency in individuals with higher education level that may mitigate the impact of age on brain functional connectivity.

Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.

Search for long-lived, weakly interacting particles that decay to displaced hadronic jets in proton--proton collisions at s√=8 TeV with the ATLAS detector

A search for the decay of neutral, weakly interacting, long-lived particles using data collected by the ATLAS detector at the LHC is presented. This analysis uses the full dataset recorded in 2012: 20.3 fb−1 of proton--proton collision data at s√=8 TeV. The search employs techniques for reconstructing decay vertices of long-lived particles decaying to jets in the inner tracking detector and muon spectrometer. Signal events require at least two reconstructed vertices. No significant excess of events over the expected background is found, and limits as a function of proper lifetime are reported for the decay of the Higgs boson and other scalar bosons to long-lived particles and for Hidden Valley Z′ and Stealth SUSY benchmark models. The first search results for displaced decays in Z′ and Stealth SUSY models are presented. The upper bounds of the excluded proper lifetimes are the most stringent to date.

Search for production of vector-like quark pairs and of four top quarks in the lepton-plus-jets final state in pp collisions at root 8=8 TeV with the ATLAS detector

A search for pair production of vector-like quarks, both up-type (T) and down-type (B), as well as for four-top-quark production, is presented. The search is based on pp collisions at s√=8 TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and corresponding to an integrated luminosity of 20.3 fb−1. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon with high transverse momentum, large missing transverse momentum and multiple jets. Dedicated analyses are performed targeting three cases: a T quark with significant branching ratio to a W boson and a b-quark (TT¯→Wb+X), and both a T quark and a B quark with significant branching ratio to a Higgs boson and a third-generation quark (TT¯→Ht+X and BB¯→Hb+X respectively). No significant excess of events above the Standard Model expectation is observed, and 95% CL lower limits are derived on the masses of the vector-like T and B quarks under several branching ratio hypotheses assuming contributions from T→Wb, Zt, Ht and B→Wt, Zb, Hb decays. The 95% CL observed lower limits on the T quark mass range between 715 GeV and 950 GeV for all possible values of the branching ratios into the three decay modes, and are the most stringent constraints to date. Additionally, the most restrictive upper bounds on four-top-quark production are set in a number of new physics scenarios.

Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

Whether at the zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we explicitly compute the stiffness at m = 0 and find strong evidence that it vanishes. In particular, we derive an upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m that is proportional to m2L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature, which implies the absence of ballistic transport for T > 0 for m = 0. Although our method relies in part on the thermodynamic Bethe ansatz (TBA), it does not evaluate the stiffness through the second derivative of the TBA energy eigenvalues relative to a uniform vector potential. Moreover, we provide strong evidence that in the thermodynamic limit the upper bounds on the spin current and stiffness used in our derivation remain valid under string deviations. Our results also provide strong evidence that in the thermodynamic limit the TBA method used by X. Zotos [Phys. Rev. Lett. 82, 1764 (1999)] leads to the exact stiffness values at finite temperature T > 0 for models whose stiffness is finite at T = 0, similar to the spin stiffness of the spin-1/2 Heisenberg chain but unlike the charge stiffness of the half-filled 1D Hubbard model.

Search for flavour-changing neutral current top quark decays t → Hq in pp collisions at √s=8 TeV with the ATLAS detector

A search for flavour-changing neutral current decays of a top quark to an uptype quark (q = u, c) and the Standard Model Higgs boson, where the Higgs boson decays to bb¯¯, is presented. The analysis searches for top quark pair events in which one top quark decays to Wb, with the W boson decaying leptonically, and the other top quark decays to Hq. The search is based on pp collisions at s√=8 TeV recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider and uses an integrated luminosity of 20.3 fb−1. Data are analysed in the lepton-plus-jets final state, characterised by an isolated electron or muon and at least four jets. The search exploits the high multiplicity of b-quark jets characteristic of signal events, and employs a likelihood discriminant that uses the kinematic differences between the signal and the background, which is dominated by tt¯→WbWb decays. No significant excess of events above the background expectation is found, and observed (expected) 95% CL upper limits of 0.56% (0.42%) and 0.61% (0.64%) are derived for the t → Hc and t → Hu branching ratios respectively. The combination of this search with other ATLAS searches in the H → γγ and H → WW *, ττ decay modes significantly improves the sensitivity, yielding observed (expected) 95% CL upper limits on the t → Hc and t → Hu branching ratios of 0.46% (0.25%) and 0.45% (0.29%) respectively. The corresponding combined observed (expected) upper limits on the |λ tcH | and |λ tuH | couplings are 0.13 (0.10) and 0.13 (0.10) respectively. These are the most restrictive direct bounds on tqH interactions measured so far.

Search for new light gauge bosons in Higgs boson decays to four-lepton final states in pp collisions at s√=8TeV with the ATLAS detector at the LHC

This paper presents a search for Higgs bosons decaying to four leptons, either electrons or muons, via one or two light exotic gauge bosons Zd, H→ZZd→4ℓ or H→ZdZd→4ℓ. The search was performed using pp collision data corresponding to an integrated luminosity of about 20 fb−1 at the center-of-mass energy of s√=8TeV recorded with the ATLAS detector at the Large Hadron Collider. The observed data are well described by the Standard Model prediction. Upper bounds on the branching ratio of H→ZZd→4ℓ and on the kinetic mixing parameter between the Zd and the Standard Model hypercharge gauge boson are set in the range (1--9)×10−5 and (4--17)×10−2 respectively, at 95% confidence level assuming the Standard Model branching ratio of H→ZZ∗→4ℓ, for Zd masses between 15 and 55 GeV. Upper bounds on the effective mass mixing parameter between the Z and the Zd are also set using the branching ratio limits in the H→ZZd→4ℓ search, and are in the range (1.5--8.7)×10−4 for 15bounds on the branching ratio of H→ZdZd→4ℓ and on Higgs portal coupling parameter, controlling the strength of the coupling of the Higgs boson to dark vector bosons, are set in the range (2--3)×10−5 and (1--10)×10−4 respectively, at 95 % confidence level assuming the Standard Model Higgs boson production cross sections, for Zd masses between 15 and 60 GeV.