Large Degree Research Articles

Heffter spaces

The notion of a Heffter array, which received much attention in the last decade, is equivalent to a pair of orthogonal Heffter systems. In this paper we study the existence problem of a set of r mutually orthogonal Heffter systems for any r. Such a set is equivalent to a resolvable partial linear space of degree r whose parallel classes are Heffter systems: this is a new combinatorial design that we call a Heffter space. We present a series of direct constructions of Heffter spaces with odd block size and arbitrarily large degree r obtained with the crucial use of finite fields. Among the applications we establish, in particular, that if q=2kw+1 is a prime power with kw odd and k≥3, then there are at least ⌈w4k4⌉ mutually orthogonal k-cycle systems of order q.

Targeted immunization thresholds for the contact process on power-law trees

Scale-free configuration models are intimately connected to power law Galton–Watson trees. It is known that contact process epidemics can propagate on these trees and therefore these networks with arbitrarily small infection rate, and this continues to be true after uniformly immunizing a small positive proportion of vertices. So, we instead immunize those with largest degree: above a threshold for the maximum permitted degree, we discover the epidemic with immunization has survival probability similar to without, by duality corresponding to comparable metastable density. With maximal degree below a threshold on the same order, this survival probability is severely reduced or zero.

Autologous bone grafting in combination with autologous chondrocyte implantation yields favourable outcomes in the treatment of osteochondral defects of the knee: A systematic literature review.

This study addresses the gap in the current literature by evaluating the combined treatment of autologous bone grafting and autologous chondrocyte implantation (ABCI) for osteochondral defects of the knee. It aims to evaluate clinical outcomes against methodological quality and to summarize histological results and surgical techniques. A thorough search was conducted across Pubmed, Cochrane and Embase databases. Studies reporting clinical outcomes of ABCI for osteochondral defects of the knee were included. Patient-reported outcome measures (PROMs), failure rates, methodological quality and potential conflicts of interest were evaluated. Histological results and surgical techniques were summarized. Eighteen studies with 344 analyzed patients met the eligibility criteria for inclusion. All studies showed a significant improvement (p < 0.05) across different PROMs (subjective International Knee Documentation Committee score, Cincinnati Knee Rating System, Visual Analogue Scale, Lysholm Score, Tegner Activity Scale, Knee injury and Osteoarthritis Outcome Score and Knee Society Score) compared to the preoperative status. Failure rates ranged from 0% to 17.6%, with a mean follow-up of 73.2 months (range: 9.0-143.6 months). Methodological quality was low to medium, including only one comparative study. Six studies reviewed reported a potential conflict of interest. The histological assessment showed effective bonding between autologous chondrocytesand bone graft. A large degree of variability was observed in the operative technique used. The current literature suggests that ABCI yields good clinical outcomes at mid- to long-term follow-up with favourable histological results for osteochondral defects of the knee. However, future research should focus on high-quality comparative studies to better guide treatment choices. Introducing ABCI as the standard abbreviation may enhance clarity in future research. Level IV.

Energy transfer and a novel SBR thermometry of SrY2O4:Sm3+/Eu3+ phosphor based on redshift of charge transfer band edge

In this study, a solid-state reaction was employed to synthesize SrY2O4: Sm3+, SrY2O4: Eu3+ and SrY2O4: Sm3+/Eu3+ phosphors. An intriguing redshift phenomenon from charge transfer band (CTB) edge was investigated for single-band ratiometric (SBR) thermometry applications. The phosphors synthesized exhibited an orthogonal CaFe2O4 structure with Pnam (62) space group. The Y3+ sites from host lattice were most likely to be replaced by Sm3+/Eu3+ ions. The sample of SrY2O4: 0.03 Sm3+/0.3Eu3+ showed a large degree of agglomeration with elongated particles, having an average size of approximately 4 μm. The energy bandgap decreased due to increased surface imperfections, resulting in enhanced defect level concentration. The dipole-dipole interaction could be used to explain energy transfer (ET) of Sm3+-Sm3+ and Sm3+-Eu3+. Furthermore, the energy transfer (ET) efficiency of Sm3+→Eu3+ in Sr2YO4 reached 77.7 %. The sample exhibited a good thermal stability (90.956 %@423 K) with Ea of 0.31 eV, which was an important parameter for broadening thermometry range. A thermometry strategy utilized this redshift phenomenon from CTB edge with anti-thermal quenching behavior and other peaks or bands with thermal quenching was therefore proposed. The high Sr value of 1.533 % K−1@298 K provides a great potential for optical thermometry application, contributing significantly to the advancement of single band ratiometric thermometry technologies.

Improving the Representation of Moisture and Convective Instability in Baroclinic-Wave Channel Simulations

Abstract We present an improved approach to generating moist baroclinically unstable background states for f-plane-channel simulations via potential vorticity (PV) inversion. Previous studies specified PV distributions with constant values in the troposphere and the stratosphere, but this produces unrealistic static-stability profiles that decrease sharply with height in the troposphere. Adding moisture to such environments can yield unrealistically large values of convective available potential energy (CAPE) even for reasonable relative humidity (RH) distributions. In our modified approach, we specify a PV distribution that increases with height in the troposphere and the stratosphere, yielding background states with more realistic values of static stability and CAPE. This modification produces environments that are better suited for representing moist processes, namely, deep convection, in idealized extratropical-cyclone simulations. Also, we present a method for introducing moisture that preserves a specified RH distribution while maintaining hydrostatic balance. Our approach allows for a large degree of control over the initial conditions, as background states with different jet strengths and shapes, average temperatures, moisture contents, or horizontal shears can easily be obtained without changing the underlying PV formula and inadvertently producing unreasonable values of static stability or CAPE. We demonstrate the characteristics of idealized extratropical cyclones developing in our background states by adding localized perturbations that represent an upper-level trough passing over a low-level frontal zone. In particular, we illustrate the impacts of horizontal shear, moisture, and grid spacing on baroclinic-wave development.

Terminal Hydride Complex of High-Spin Mn.

The iron-molybdenum cofactor of nitrogenase (FeMoco) catalyzes fixation of N2 via Fe hydride intermediates. Our understanding of these species has relied heavily on the characterization of well-defined 3d metal hydride complexes, which serve as putative spectroscopic models. Although the Fe ions in FeMoco, a weak-field cluster, are expected to adopt locally high-spin Fe2+/3+ configurations, synthetically accessible hydride complexes featuring d5 or d6 electron counts are almost exclusively low-spin. We report herein the isolation of a terminal hydride complex of four-coordinate, high-spin (d5; S = 5/2) Mn2+. Electron paramagnetic resonance and electron-nuclear double resonance studies reveal an unusually large degree of spin density on the hydrido ligand. In light of the isoelectronic relationship between Mn2+ and Fe3+, our results are expected to inform our understanding of the valence electronic structures of reactive hydride intermediates derived from FeMoco.

The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph W8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_8$$\\end{document}

The Ramsey numbers R(Tn,W8)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(T_n,W_8)$$\\end{document} are determined for each tree graph Tn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_n$$\\end{document} of order n≥7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge 7$$\\end{document} and maximum degree Δ(Tn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta (T_n)$$\\end{document} equal to either n-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n-4$$\\end{document} or n-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n-5$$\\end{document}. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to Hafidh and Baskoro, that R(Tn,Wm)=2n-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R(T_n,W_m) = 2n-1$$\\end{document} for each tree graph Tn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_n$$\\end{document} of order n≥m-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\ge m-1$$\\end{document} with Δ(Tn)≤n-m+2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta (T_n)\\le n-m+2$$\\end{document} when m≥4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\\ge 4$$\\end{document} is even.

Nonlocal fermions with local interactions and the SYK model

One of the most promising routes to non-fermi liquids and strange metals has been through SYK models (Sachdev 2010 Phys. Rev. Lett. 105 151602) which necessarily involve large flavor degrees of freedom and interactions with imposed disorder. We introduce an interacting model of nonlocal spinless fermions in which large flavor and effective disorder emerge spontaneously in the extreme nonlocal limit. This model may be thought of as an expansion in a dimensionless ‘locality scale,’ α, with the limit α→0 recovering a conventional local action. For finite α, the resulting interacting nonlocal action exhibits a large number of low-energy degrees of freedom—proportional to α—and the structure factor mediating the local interactions between these fermions is effectively random for large α. In one dimension, with finite α, we show that interactions are marginal to the one loop level (as they are in the conventional local case), preserving a gapless phase. At large α the interaction strength becomes comparable to the bandwidth and we analyze this large flavor limit in a manner similar to the diagrammatic approach to SYK. As α is increased we argue that the gapless phase established by conventional RG possibly crosses over to a gapless SYK phase, although the ‘melon’ diagrams are not exclusively dominant. We speculate on how this model might arise physically from an S-matrix connecting pure excited states—rather than the vacuum—to access finite temperature interacting fermions.

Squatting biomechanics following physiotherapist-led care or hip arthroscopy for femoroacetabular impingement syndrome: a secondary analysis from a randomised controlled trial.

Femoroacetabular impingement syndrome (FAIS) can cause hip pain and chondrolabral damage that may be managed non-operatively or surgically. Squatting motions require large degrees of hip flexion and underpin many daily and sporting tasks but may cause hip impingement and provoke pain. Differential effects of physiotherapist-led care and arthroscopy on biomechanics during squatting have not been examined previously. This study explored differences in 12-month changes in kinematics and moments during squatting between patients with FAIS treated with a physiotherapist-led intervention (Personalised Hip Therapy, PHT) and arthroscopy. A subsample (n = 36) of participants with FAIS enrolled in a multi-centre, pragmatic, two-arm superiority randomised controlled trial underwent three-dimensional motion analysis during squatting at baseline and 12-months following random allocation to PHT (n = 17) or arthroscopy (n = 19). Changes in time-series and peak trunk, pelvis, and hip biomechanics, and squat velocity and maximum depth were explored between treatment groups. No significant differences in 12-month changes were detected between PHT and arthroscopy groups. Compared to baseline, the arthroscopy group squatted slower at follow-up (descent: mean difference -0.04 m∙s-1 (95%CI [-0.09 to 0.01]); ascent: -0.05 m∙s-1 [-0.11 to 0.01]%). No differences in squat depth were detected between or within groups. After adjusting for speed, trunk flexion was greater in both treatment groups at follow-up compared to baseline (descent: PHT 7.50° [-14.02 to -0.98]%; ascent: PHT 7.29° [-14.69 to 0.12]%, arthroscopy 16.32° [-32.95 to 0.30]%). Compared to baseline, both treatment groups exhibited reduced anterior pelvic tilt (descent: PHT 8.30° [0.21-16.39]%, arthroscopy -10.95° [-5.54 to 16.34]%; ascent: PHT -7.98° [-0.38 to 16.35]%, arthroscopy -10.82° [3.82-17.81]%), hip flexion (descent: PHT -11.86° [1.67-22.05]%, arthroscopy -16.78° [8.55-22.01]%; ascent: PHT -12.86° [1.30-24.42]%, arthroscopy -16.53° [6.72-26.35]%), and knee flexion (descent: PHT -6.62° [0.56- 12.67]%; ascent: PHT -8.24° [2.38-14.10]%, arthroscopy -8.00° [-0.02 to 16.03]%). Compared to baseline, the PHT group exhibited more plantarflexion during squat ascent at follow-up (-3.58° [-0.12 to 7.29]%). Compared to baseline, both groups exhibited lower external hip flexion moments at follow-up (descent: PHT -0.55 N∙m/BW∙HT[%] [0.05-1.05]%, arthroscopy -0.84 N∙m/BW∙HT[%] [0.06-1.61]%; ascent: PHT -0.464 N∙m/BW∙HT[%] [-0.002 to 0.93]%, arthroscopy -0.90 N∙m/BW∙HT[%] [0.13-1.67]%). Exploratory data suggest at 12-months follow-up, neither PHT or hip arthroscopy are superior at eliciting changes in trunk, pelvis, or lower-limb biomechanics. Both treatments may induce changes in kinematics and moments, however the implications of these changes are unknown. Australia New Zealand Clinical Trials Registry reference: ACTRN12615001177549. Trial registered 2/11/2015.

Rheological aspects of solid-to-liquid phase transitions in paraffin wax/bitumen blends for thermal energy storage applications

This paper correlates the evolution of the rheological and thermal properties with microstructure during the phase change of a blend of bitumen with a selected paraffin wax, having a melting point centred around 60 °C, for the development of bituminous based membranes for thermal energy storage applications. For this purpose, temperature sweep tests within the linear viscoelastic range, stationary state flow curves, Differential Scanning Calorimetry (DSC), polarised optical microscopy observations and solar irradiation tests were performed. The reported rheological results clearly point out a gel-like behaviour for both paraffin and paraffin/bitumen blend that is preserved almost up to the end of the phase change interval. This is consequence of the development of a network of interconnected crystals of paraffin wax which progressively disappear as temperature increases. Interestingly, a weak gel structure is kept even at low crystallinity levels since only a few junctions among structures are necessary to build a spanning network. Finally, the large degree of crystallinity of paraffin wax retained in the bitumen/paraffin wax is behind its thermoregulation ability, as was corroborated by solar irradiation tests. Therefore, results indicated the great potential of these formulations for thermal energy storage and related applications.

Electronic, magnetic and structural properties of CoFeVAl and CoFeV0.5Mn0.5Al

In this study, we present results of a comprehensive computational and experimental study of CoFeVAl and CoFeV0.5Mn0.5Al Heusler alloys. It is shown that while CoFeVAl exhibits a fairly large degree of spin polarization, this material is not half-metallic due to the presence of the vanadium spin-down states at the Fermi level. However, replacing 50% of vanadium with manganese results in a nearly half-metallic transition, largely due to the shift of the Fermi level towards occupied states. Moreover, the half-metallicity of CoFeV0.5Mn0.5Al is rather robust in a wide range of considered mechanical strain and under experimentally observed B2-type atomic disorder, thus making this alloy potentially suitable for practical spintronic applications. Both considered alloys exhibit ferromagnetic alignment at larger lattice constants, aside from a relatively small magnetic moment of vanadium which is anti-aligned with the magnetic moments of Co, Fe and Mn. We have synthesized both CoFeVAl and CoFeV0.5Mn0.5Al alloys in cubic structure with some structural disorder using arc melting and annealing. The structural and magnetic properties of the synthesized CoFeV0.5Mn0.5Al alloy are in good agreement with the theoretical calculations but vary slightly from the parent compound.

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge of the quantum order by disorder effect of the S=1/2 system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of subextensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Among all possible configurations, we focus on the stripe (up and down spins aligning straightly) and kinked (up and down spins forming zigzag spin chains) patterns. Adopting the the real space perturbation theory, we estimate the leading order energy correction when the nearest-neighbor spin exchange coupling, J, is considered, and the overall model becomes an effective XXZ model with a spatial anisotropy. Our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When J becomes larger, we adopt the infinite projected entangled-pair state (iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for two-dimensional quantum simulators. Published by the American Physical Society 2024

Approximate and Randomized Algorithms for Computing a Second Hamiltonian Cycle

In this paper we consider the following problem: Given a Hamiltonian graph G, and a Hamiltonian cycle C of G, can we compute a second Hamiltonian cycle C′≠C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{\\prime } \ e C$$\\end{document} of G, and if yes, how quickly? If the input graph G satisfies certain conditions (e.g. if every vertex of G is odd, or if the minimum degree is large enough), it is known that such a second Hamiltonian cycle always exists. Despite substantial efforts, no subexponential-time algorithm is known for this problem. In this paper we relax the problem of computing a second Hamiltonian cycle in two ways. First, we consider approximating the length of a second longest cycle on n-vertex graphs with minimum degree δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} and maximum degree Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}. We provide a linear-time algorithm for computing a cycle C′≠C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{\\prime } \ e C$$\\end{document} of length at least n-4α(n+2α)+8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n-4\\alpha (\\sqrt{n}+2\\alpha )+8$$\\end{document}, where α=Δ-2δ-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha = \\frac{\\Delta -2}{\\delta -2}$$\\end{document}. This results provides a constructive proof of a recent result by Girão, Kittipassorn, and Narayanan in the regime of Δδ=o(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\Delta }{\\delta } = o(\\sqrt{n})$$\\end{document}. Our second relaxation of the problem is probabilistic. We propose a randomized algorithm which computes a second Hamiltonian cycle with high probability, given that the input graph G has a large enough minimum degree. More specifically, we prove that for every 0<p≤0.02\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<p\\le 0.02$$\\end{document}, if the minimum degree of G is at least 8plog8n+4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{8}{p} \\log \\sqrt{8}n + 4$$\\end{document}, then a second Hamiltonian cycle can be computed with probability at least 1-1n50p4+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 - \\frac{1}{n}\\left( \\frac{50}{p^4} + 1 \\right) $$\\end{document} in poly(n)·24pn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$poly(n) \\cdot 2^{4pn}$$\\end{document} time. This result implies that, when the minimum degree δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} is sufficiently large, we can compute with high probability a second Hamiltonian cycle faster than any known deterministic algorithm. In particular, when δ=ω(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta = \\omega (\\log n)$$\\end{document}, our probabilistic algorithm works in 2o(n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{o(n)}$$\\end{document} time.

Acromegaly management in the Nordic countries:A Delphi consensus survey.

Acromegaly is associated with increased morbidity and mortality if left untreated. The therapeutic options include surgery, medical treatment, and radiotherapy. Several guidelines and recommendations on treatment algorithms and follow-up exist. However, not all recommendations are strictly evidence-based. To evaluate consensus on the treatment and follow-up of patients with acromegaly in the Nordic countries. A Delphi process was used to map the landscape of acromegaly management in Denmark, Sweden, Norway, Finland, and Iceland. An expert panel developed 37 statements on the treatment and follow-up of patients with acromegaly. Dedicated endocrinologists (n = 47) from the Nordic countries were invited to rate their extent of agreement with the statements, using a Likert-type scale (1-7). Consensus was defined as ≥80% of panelists rating their agreement as ≥5 or ≤3 on the Likert-type scale. Consensus was reached in 41% (15/37) of the statements. Panelists agreed that pituitary surgery remains first line treatment. There was general agreement to recommend first-generation somatostatin analog (SSA) treatment after failed surgery and to consider repeat surgery. In addition, there was agreement to recommend combination therapy with first-generation SSA and pegvisomant as second- or third-line treatment. In more than 50% of the statements, consensus was not achieved. Considerable disagreement existed regarding pegvisomant monotherapy, and treatment with pasireotide and dopamine agonists. This consensus exploration study on the management of patients with acromegaly in the Nordic countries revealed a relatively large degree of disagreement among experts, which mirrors the complexity of the disease and the shortage of evidence-based data.

Spatiotemporal variability of surface ozone and associated meteorological conditions over the Arabian Peninsula

This study investigates the spatiotemporal variability of surface ozone (O3) over the Arabian Peninsula (AP) between 2005 and 2019, focusing on the Arabian Gulf (AG). The analysis explores the relationship between surface O3 data from the Copernicus Atmosphere Monitoring Service (CAMS) with boundary layer height (BLH), 2 m temperature (T2M), downward ultraviolet radiation at the surface (UVB), and 10 m wind speed (WS) and direction from the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA5). Also, the study considers Carbon Monoxide (CO) and Nitrogen Oxides (NOx) surface emissions from the Tropospheric Chemical Reanalysis version 2 (TCR-2). Furthermore, it investigates the impact of El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) on surface O3 variations on a seasonal scale. Surface O3 observations from 15 ground-based stations across the AP were used to evaluate CAMS-O3, showing a good agreement between CAMS and the observations. The analysis of mean diurnal variations of CAMS-O3 and ERA5 reveals that surface O3 is highest over the eastern parts of the AP, mainly the AG, peaking during summer, followed by spring, fall, and winter. This seasonal cycle is also observed, to a large degree, in BLH, T2M, UVB, and WS. The results also reveal insignificant correlation between surface O3 and ENSO, but stronger correlation with IOD, especially over the AG during summer and fall. The analysis indicates that elevated T2M and UVB during daytime and elevated BLH during nighttime are significant contributors to increased levels of O3 over the AG.

Double-Cabin Galvanic Cell-Synthesizing Nanoporous, Flower-like, Pb-Containing Pd-Au Nanoparticles for Nonenzymatic Formaldehyde Sensor.

In this work, a novel formaldehyde sensor was constructed based on nanoporous, flower-like, Pb-containing Pd-Au nanoparticles deposited on the cathode in a double-cabin galvanic cell (DCGC) with a Cu plate as the anode, a multiwalled carbon nanotube-modified glassy carbon electrode as the cathode, a 0.1 M HClO4 aqueous solution as the anolyte, and a 3.0 mM PdCl2 + 1.0 mM HAuCl4 + 5.0 mM Pb(ClO4)2 + 0.1 M HClO4 aqueous solution as the catholyte, respectively. Electrochemical studies reveal that the stripping of bulk Cu can induce underpotential deposition (UPD) of Pb during the galvanic replacement reaction (GRR) process, which affects the composition and morphology of Pb-containing Pd-Au nanoparticles. The electrocatalytic activity of Pb-containing nanoparticles toward formaldehyde oxidation was examined in an alkaline solution, and the experimental results showed that formaldehyde mainly caused direct oxidation on the surface of Pb-containing Pd-Au nanoparticles while inhibiting the formation of CO poison to a large degree. The proposed formaldehyde sensor exhibits a linear amperometric response to formaldehyde concentrations from 0.01 mM to 5.0 mM, with a sensitivity of 666 μA mM-1 cm-2, a limit of detection (LOD) of 0.89 μM at triple signal-to-noise, rapid response, high anti-interference ability, and good repeatability.

Silvery fullerene in Ag102 nanosaucer.

Despite the discovery of a series of fullerenes and a handful of noncarbon clusters with the typical topology of I h-C60, the smallest fullerene with a large degree of curvature, C20, and its other-element counterparts are difficult to isolate experimentally. In coinage metal nanoclusters (NCs), the first all-gold fullerene, Au32, was discovered after a long-lasting pursuit, but the isolation of similar silvery fullerene structures is still challenging. Herein, we report a flying saucer-shaped 102-nuclei silver NC (Ag102) with a silvery fullerene kernel of Ag32, which is embraced by a robust cyclic anionic passivation layer of (KPO4)10. This Ag32 kernel can be viewed as a non-centered icosahedron Ag12 encaged into a dodecahedron Ag20, forming the silvery fullerene of Ag12@Ag20. The anionic layer (KPO4)10 is located at the interlayer between the Ag32 kernel and Ag70 shell, passivating the Ag32 silvery fullerene and templating the Ag70 shell. The t BuPhS- and CF3COO- ligands on the silver shell show a regioselective arrangement with the 60 t BuPhS- ligands as expanders covering the upper and lower of the flying saucer and 10 CF3COO- as terminators neatly encircling the edges of the structure. In addition, Ag102 shows excellent photothermal conversion efficiency (η) from the visible to near-infrared region (η=67.1%±0.9% at 450nm, 60.9%±0.9% at 660nm and 50.2%±0.5% at 808nm), rendering it a promising material for photothermal converters and potential application in remote laser ignition. This work not only captures silver kernels with the topology of the smallest fullerene C20, but also provides a pathway for incorporating alkali metal (M) into coinage metal NCs via M-oxoanions.

Visuo-dynamic self-modelling of soft robotic systems.

Soft robots exhibit complex nonlinear dynamics with large degrees of freedom, making their modelling and control challenging. Typically, reduced-order models in time or space are used in addressing these challenges, but the resulting simplification limits soft robot control accuracy and restricts their range of motion. In this work, we introduce an end-to-end learning-based approach for fully dynamic modelling of any general robotic system that does not rely on predefined structures, learning dynamic models of the robot directly in the visual space. The generated models possess identical dimensionality to the observation space, resulting in models whose complexity is determined by the sensory system without explicitly decomposing the problem. To validate the effectiveness of our proposed method, we apply it to a fully soft robotic manipulator, and we demonstrate its applicability in controller development through an open-loop optimization-based controller. We achieve a wide range of dynamic control tasks including shape control, trajectory tracking and obstacle avoidance using a model derived from just 90 min of real-world data. Our work thus far provides the most comprehensive strategy for controlling a general soft robotic system, without constraints on the shape, properties, or dimensionality of the system.

We need to change how we compute RMSEA for nested model comparisons in structural equation modeling.

Comparison of nested models is common in applications of structural equation modeling (SEM). When two models are nested, model comparison can be done via a chi-square difference test or by comparing indices of approximate fit. The advantage of fit indices is that they permit some amount of misspecification in the additional constraints imposed on the model, which is a more realistic scenario. The most popular index of approximate fit is the root mean square error of approximation (RMSEA). In this article, we argue that the dominant way of comparing RMSEA values for two nested models, which is simply taking their difference, is problematic and will often mask misfit, particularly in model comparisons with large initial degrees of freedom. We instead advocate computing the RMSEA associated with the chi-square difference test, which we call RMSEAD. We are not the first to propose this index, and we review numerous methodological articles that have suggested it. Nonetheless, these articles appear to have had little impact on actual practice. The modification of current practice that we call for may be particularly needed in the context of measurement invariance assessment. We illustrate the difference between the current approach and our advocated approach on three examples, where two involve multiple-group and longitudinal measurement invariance assessment and the third involves comparisons of models with different numbers of factors. We conclude with a discussion of recommendations and future research directions. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Local dominance unveils clusters in networks

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data.