The overlap operator as a continued fraction

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. This is of significant importance when dynamical overlap fermions are simulated.Comment: 3 pages, 1 figure, talk presented by U. Wenger at Lattice2001(chiral

The triviality bound on the Higgs mass; its value and what it means

Older lattice work exploring the Higgs mass triviality bound is briefly reviewed. It indicates that a strongly interacting scalar sector in the minimal standard model cannot exist; on the other hand low energy QCD phenomenology might be interpreted as an indication that it could. We attack this puzzle using the $1/N$ expansion and discover a simple criterion for selecting a lattice action that is more likely to produce a heavy Higgs particle. Depending on the precise form of the limitation put on the cutoff effects, our large $N$ calculations, when combined with old numerical data, suggest that the Higgs mass bound might be around 750 $GeV$, which is higher than the $\sim 650~GeV$ previously obtained. Preliminary numerical work indicates that an increase of at least 19\% takes place at $N=4$ on the $F_4$ lattice when the old simple action is replaced with a new action (still containing only nearest neighbor interactions) if one uses the lattice spacing as the physical cutoff for both actions. It appears that, while a QCD like theory could produce $M_H / F ~ \sim 6$, a meaningful ``minimal elementary Higgs'' theory cannot have M_H/ F~ \gtapprox 3. Still, even at 750 $GeV$, the Higgs particle is so wide ($\sim 290~$GeV), that one cannot argue any more that the scalar sector is weakly coupled.Comment: 8 pages. Latex file with 4 ps figures included. Preprint RU-92-22, SCRI-92-11

Noncompact chiral U(1) gauge theories on the lattice

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in PR

Quenched divergences in the deconfined phase of SU(2) gauge theory

The spectrum of the overlap Dirac operator in the deconfined phase of quenched gauge theory is known to have three parts: exact zeros arising from topology, small nonzero eigenvalues that result in a non-zero chiral condensate, and the dense bulk of the spectrum, which is separated from the small eigenvalues by a gap. In this paper, we focus on the small nonzero eigenvalues in an SU(2) gauge field background at $\beta=2.4$ and $N_T=4$. This low-lying spectrum is computed on four different spatial lattices ($12^3$, $14^3$, $16^3$, and $18^3$). As the volume increases, the small eigenvalues become increasingly concentrated near zero in such a way as to strongly suggest that the infinite volume condensate diverges.Comment: 12 pages, 3 figures, version to appear in Physical Review

Accuracy and Prognostic Role of NCCT-ASPECTS Depend on Time from Acute Stroke Symptom-onset for both Human and Machine-learning Based Evaluation.

PURPOSE We hypothesize that the detectability of early ischemic changes on non-contrast computed tomography (NCCT) is limited in hyperacute stroke for both human and machine-learning based evaluation. In short onset-time-to-imaging (OTI), the CT angiography collateral status may identify fast stroke progressors better than early ischemic changes quantified by ASPECTS. METHODS In this retrospective, monocenter study, CT angiography collaterals (Tan score) and ASPECTS on acute and follow-up NCCT were evaluated by two raters. Additionally, a machine-learning algorithm evaluated the ASPECTS scale on the NCCT (e-ASPECTS). In this study 136 patients from 03/2015 to 12/2019 with occlusion of the main segment of the middle cerebral artery, with a defined symptom-onset-time and successful mechanical thrombectomy (MT) (modified treatment in cerebral infarction score mTICI = 2c or 3) were evaluated. RESULTS Agreement between acute and follow-up ASPECTS were found to depend on OTI for both human (Intraclass correlation coefficient, ICC = 0.43 for OTI < 100 min, ICC = 0.57 for OTI 100-200 min, ICC = 0.81 for OTI ≥ 200 min) and machine-learning based ASPECTS evaluation (ICC = 0.24 for OTI < 100 min, ICC = 0.61 for OTI 100-200 min, ICC = 0.63 for OTI ≥ 200 min). The same applied to the interrater reliability. Collaterals were predictors of a favorable clinical outcome especially in hyperacute stroke with OTI < 100 min (collaterals: OR = 5.67 CI = 2.38-17.8, p < 0.001; ASPECTS: OR = 1.44, CI = 0.91-2.65, p = 0.15) while ASPECTS was in prolonged OTI ≥ 200 min (collaterals OR = 4.21,CI = 1.36-21.9, p = 0.03; ASPECTS: OR = 2.85, CI = 1.46-7.46, p = 0.01). CONCLUSION The accuracy and reliability of NCCT-ASPECTS are time dependent for both human and machine-learning based evaluation, indicating reduced detectability of fast stroke progressors by NCCT. In hyperacute stroke, collateral status from CT-angiography may help for a better prognosis on clinical outcome and explain the occurrence of futile recanalization

Correction to: Accuracy and Prognostic Role of NCCT-ASPECTS Depend on Time from Acute Stroke Symptom-onset for both Human and Machine-learning Based Evaluation.

PURPOSE: We hypothesize that the detectability of early ischemic changes on non-contrast computed tomography (NCCT) is limited in hyperacute stroke for both human and machine-learning based evaluation. In short onset-time-to-imaging (OTI), the CT angiography collateral status may identify fast stroke progressors better than early ischemic changes quantified by ASPECTS. METHODS: In this retrospective, monocenter study, CT angiography collaterals (Tan score) and ASPECTS on acute and follow-up NCCT were evaluated by two raters. Additionally, a machine-learning algorithm evaluated the ASPECTS scale on the NCCT (e-ASPECTS). In this study 136 patients from 03/2015 to 12/2019 with occlusion of the main segment of the middle cerebral artery, with a defined symptom-onset-time and successful mechanical thrombectomy (MT) (modified treatment in cerebral infarction score mTICI = 2c or 3) were evaluated. RESULTS: Agreement between acute and follow-up ASPECTS were found to depend on OTI for both human (Intraclass correlation coefficient, ICC = 0.43 for OTI < 100 min, ICC = 0.57 for OTI 100–200 min, ICC = 0.81 for OTI ≥ 200 min) and machine-learning based ASPECTS evaluation (ICC = 0.24 for OTI < 100 min, ICC = 0.61 for OTI 100–200 min, ICC = 0.63 for OTI ≥ 200 min). The same applied to the interrater reliability. Collaterals were predictors of a favorable clinical outcome especially in hyperacute stroke with OTI < 100 min (collaterals: OR = 5.67 CI = 2.38–17.8, p < 0.001; ASPECTS: OR = 1.44, CI = 0.91–2.65, p = 0.15) while ASPECTS was in prolonged OTI ≥ 200 min (collaterals OR = 4.21,CI = 1.36–21.9, p = 0.03; ASPECTS: OR = 2.85, CI = 1.46–7.46, p = 0.01). CONCLUSION: The accuracy and reliability of NCCT-ASPECTS are time dependent for both human and machine-learning based evaluation, indicating reduced detectability of fast stroke progressors by NCCT. In hyperacute stroke, collateral status from CT-angiography may help for a better prognosis on clinical outcome and explain the occurrence of futile recanalization. SUPPLEMENTARY INFORMATION: The online version of this article (10.1007/s00062-021-01110-5) contains supplementary material, which is available to authorized users

Comparison of metal-based nanoparticles and nanowires: Solubility, reactivity, bioavailability and cellular toxicity

While the toxicity of metal-based nanoparticles (NP) has been investigated in an increasing number of studies, little is known about metal-based fibrous materials, so-called nanowires (NWs). Within the present study, the physico-chemical properties of particulate and fibrous nanomaterials based on Cu, CuO, Ni, and Ag as well as TiO$_{2}$ and CeO$_{2}$ NP were characterized and compared with respect to abiotic metal ion release in different physiologically relevant media as well as acellular reactivity. While none of the materials was soluble at neutral pH in artificial alveolar fluid (AAF), Cu, CuO, and Ni-based materials displayed distinct dissolution under the acidic conditions found in artificial lysosomal fluids (ALF and PSF). Subsequently, four different cell lines were applied to compare cytotoxicity as well as intracellular metal ion release in the cytoplasm and nucleus. Both cytotoxicity and bioavailability reflected the acellular dissolution rates in physiological lysosomal media (pH 4.5); only Ag-based materials showed no or very low acellular solubility, but pronounced intracellular bioavailability and cytotoxicity, leading to particularly high concentrations in the nucleus. In conclusion, in spite of some quantitative differences, the intracellular bioavailability as well as toxicity is mostly driven by the respective metal and is less modulated by the shape of the respective NP or NW

On the spectral density from instantons in quenched QCD

We investigate the contribution of instantons to the eigenvalue spectrum of the Dirac operator in quenched QCD. The instanton configurations that we use have been derived, elsewhere, from cooled SU(3) lattice gauge fields and, for comparison, we also analyse a random `gas' of instantons. Using a set of simplifying approximations, we find a non-zero chiral condensate. However we also find that the spectral density diverges for small eigenvalues, so that the chiral condensate, at zero quark mass, diverges in quenched QCD. The degree of divergence decreases with the instanton density, so that it is negligible for the smallest number of cooling sweeps but becomes substantial for larger number of cools. We show that the spectral density scales, that finite volume corrections are small and we see evidence for the screening of topological charges. However we also find that the spectral density and chiral condensate vary rapidly with the number of cooling sweeps -- unlike, for example, the topological susceptibility. Whether the problem lies with the cooling or with the identification of the topological charges is an open question. This problem needs to be resolved before one can determine how important is the divergence we have found for quenched QCD.Comment: 33 pages, 16 figures (RevTex), substantial revisions; to appear in Phys.Rev.