Minimal Gaps Research Articles

Difference Sets and the Metric Theory of Small Gaps

Abstract Let $(a_n)_{n \geq 1}$ be a sequence of distinct positive integers. In a recent paper, Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n \alpha \mod 1, ~1 \leq n \leq N\}$ as $N \to \infty $, valid for Lebesgue-almost all $\alpha $ and formulated in terms of the additive energy of $\{a_1, \dots , a_N\}$. In the present paper, we argue that the metric theory of minimal gaps of such sequences is not controlled by the additive energy, but rather by the cardinality of the difference set of $\{a_1, \dots , a_N\}$. We establish a (complicated) sharp convergence/divergence test for the typical asymptotic order of the minimal gap and prove (slightly weaker) general upper and lower bounds that allow for a direct application. A major input for these results comes from the recent proof of the Duffin–Schaeffer conjecture by Koukoulopoulos and Maynard. We show that our methods give very precise results for slowly growing sequences whose difference set has relatively high density, such as the primes or the squares. Furthermore, we improve a metric result of Blomer, Bourgain, Rudnick, and Radziwiłł on the order of the minimal gap in the eigenvalue spectrum of a rectangular billiard.

ML-TOMCAT: machine-learning-based satellite-corrected global stratospheric ozone profile data set from a chemical transport model

Abstract. High-quality stratospheric ozone profile data sets are a key requirement for accurate quantification and attribution of long-term ozone changes. Satellite instruments provide stratospheric ozone profile measurements over typical mission durations of 5–15 years. Various methodologies have then been applied to merge and homogenise the different satellite data in order to create long-term observation-based ozone profile data sets with minimal data gaps. However, individual satellite instruments use different measurement methods, sampling patterns and retrieval algorithms which complicate the merging of these different data sets. In contrast, atmospheric chemical models can produce chemically consistent long-term ozone simulations based on specified changes in external forcings, but they are subject to the deficiencies associated with incomplete understanding of complex atmospheric processes and uncertain photochemical parameters. Here, we use chemically self-consistent output from the TOMCAT 3-D chemical transport model (CTM) and a random-forest (RF) ensemble learning method to create a merged 42-year (1979–2020) stratospheric ozone profile data set (ML-TOMCAT V1.0). The underlying CTM simulation was forced by meteorological reanalyses, specified trends in long-lived source gases, solar flux and aerosol variations. The RF is trained using the Stratospheric Water and OzOne Satellite Homogenized (SWOOSH) data set over the time periods of the Microwave Limb Sounder (MLS) from the Upper Atmosphere Research Satellite (UARS) (1991–1998) and Aura (2005–2016) missions. We find that ML-TOMCAT shows excellent agreement with available independent satellite-based data sets which use pressure as a vertical coordinate (e.g. GOZCARDS, SWOOSH for non-MLS periods) but weaker agreement with the data sets which are altitude-based (e.g. SAGE-CCI-OMPS, SCIAMACHY-OMPS). We find that at almost all stratospheric levels ML-TOMCAT ozone concentrations are well within uncertainties of the observational data sets. The ML-TOMCAT (V1.0) data set is ideally suited for the evaluation of chemical model ozone profiles from the tropopause to 0.1 hPa and is freely available via https://doi.org/10.5281/zenodo.5651194 (Dhomse et al., 2021).

Responding to rural allied health workforce challenges in the public health system: Evaluation of the Allied Health Rural Generalist Pathway pilot in western New South Wales.

The Allied Health Rural Generalist Pathway pilot aimed to improve consistent access to physiotherapy services in rural communities using the "grow own" workforce strategy and existing resources. A summative evaluation of the quality improvement project used to implement the Allied Health Rural Generalist Pathway was completed. A mixed method design was used and included focus groups and a framework analysis. The temporary redesign of specific workforce resources created "development" positions. A shared same-discipline supervisor resource supported five early-career physiotherapists, the participants. The project was undertaken in rural New South Wales in the public health system. The main outcome measures included a number of chronically vacant physiotherapy positions and stakeholder satisfaction. Targeted vacancies were filled, services sustained with minimal service gaps and mean retention rate of 2.9years. A statistically significant increase in service activity to patients in rural locations occurred as a result of the intervention (R-squared 29%, P<.05). Four out of five early career physiotherapists fulfilled terms of their contract and secured senior positions within the region. Whilst participants developed professionally, they did not complete the tertiary education component. The Allied Health Rural Generalist multi-factorial approach supported recruitment, retention and capacity building within the targeted discipline of the allied health workforce. Patient need was met. The rural pipeline capacity was developed. The pathway was complementary of existing NSW Health systems. Systemic change is needed to overcome inefficiencies experienced during implementation and to ensure sustainability. Further research to develop discipline-specific clinical training guidance through the stages of a rural allied health professionals' career may be helpful.

Solar Cycle Evolution of Filaments over a Century: Investigations with the Meudon and McIntosh Hand-drawn Archives

Abstract Hand-drawn synoptic maps from the Meudon Observatory (1919 onwards) and the McIntosh archive (1967 onwards) are two important sources of long-term, manually recorded filament observations. In this study, we calibrate the Meudon maps and subsequently identify filaments through an automated method. We extract physical parameters from this filament database and perform a comparative study of their long-term evolution focusing on the cotemporal period of the McIntosh and Meudon observations. The spatiotemporal evolution of filaments manifests in the form of a filament butterfly diagram, further indicating that they are intimately related to the large-scale solar cycle. Physical descriptors such as the number and length of filaments, which are tracers of the solar surface magnetic field, have cycles which are phase locked with the ∼11 yr sunspot cycle. The tilt-angle distribution of filaments—both near to or distant from active region locations—indicates that their origin is due to either large-scale surface magnetic field or inter-active-region field evolution. This study paves the way for constructing a composite series of hand-drawn filament data with minimal gaps stretching over the time span of solar filament observations up to a century. On the one hand, this would serve as a useful constraint for models of magnetic field emergence and evolution on the Sun’s surface over multiple solar cycles, and on the other hand, this filament database may be used to guide the reconstruction of filament/prominence associated eruptive events before the space age.

Development of Patient Specific Conformal 3D-Printed Devices for Dose Verification in Radiotherapy

In radiation therapy, a bolus is used to improve dose distribution in superficial tumors; however, commercial boluses lack conformity to patient surface leading to the formation of an air gap between the bolus and patient surface and suboptimal tumor control. The aim of this study was to explore 3D-printing technology for the development of patient-specific conformal 3D-printed devices, which can be used for the radiation treatment of superficial head and neck cancer (HNC). Two 3D boluses (0.5 and 1.0 cm thick) for surface dose build-up and patient-specific 3D phantom were printed based on reconstruction of computed tomography (CT) images of a patient with HNC. The 3D-printed patient-specific phantom indicated good tissue equivalency (HU = −32) and geometric accuracy (DSC = 0.957). Both boluses indicated high conformity to the irregular skin surface with minimal air gaps (0.4–2.1 mm for 0.5 cm bolus and 0.6–2.2 mm for 1.0 cm bolus). The performed dose assessment showed that boluses of both thicknesses have comparable effectiveness, increasing the dose that covers 99% of the target volume by 52% and 26% for single field and intensity modulated fields, respectively, when compared with no bolus case. The performed investigation showed the potential of 3D printing in development of cost effective, patient specific and patient friendly conformal devices for dose verification in radiotherapy.

Planning when to say: Dissociating cue use in utterance initiation using cross-validation.

In conversation, turns follow each other with minimal gaps. To achieve this, speakers must launch their utterances shortly before the predicted end of the partner's turn. We examined the relative importance of cues to partner utterance content and partner utterance length for launching coordinated speech. In three experiments, Dutch adult participants had to produce prepared utterances (e.g., vier, "four") immediately after a recording of a confederate's utterance (zeven, "seven"). To assess the role of corepresenting content versus attending to speech cues in launching coordinated utterances, we varied whether the participant could see the stimulus being named by the confederate, the confederate prompt's length, and whether within a block of trials, the confederate prompt's length was predictable. We measured how these factors affected the gap between turns and the participants' allocation of visual attention while preparing to speak. Using a machine-learning technique, model selection by k-fold cross-validation, we found that gaps were most strongly predicted by cues from the confederate speech signal, though some benefit was also conferred by seeing the confederate's stimulus. This shows that, at least in a simple laboratory task, speakers rely more on cues in the partner's speech than corepresentation of their utterance content. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

EXaSkin: A novel high-density bolus for 6MV X-rays radiotherapy.

To evaluate eXaSkin, a novel high-density bolus alternative to commercial tissue-equivalent Superflab, for 6MV photon-beam radiotherapy. We delivered a 10×10cm2 open field at 90° and head-and-neck clinical plan, generated with the volumetric modulated arc therapy (VMAT) technique, to an anthropomorphic phantom in three scenarios: with no bolus on the phantom's surface, with Superflab, and with eXaSkin. In each scenario, we measured dose to a central planning target volume (PTV) in the nasopharynx region with an ionization chamber, and we measured dose to the skin, at three different positions within the vicinity of a neck lymph node PTV, with MOSkin™, a semiconductor dosimeter. Measurements were compared against calculations with the treatment planning system (TPS). For the static field, MOSkin results underneath the eXaSkin were in agreement with calculations to within 1.22%; for VMAT, to within 5.68%. Underneath Superflab, those values were 3.36% and 11.66%. The inferior agreement can be explained by suboptimal adherence of Superflab to the phantom's surface as well as difficulties in accurately reproducing its placement between imaging and treatment session. In all scenarios, dose measured at the central target agreed to within 1% with calculations. eXaSkin was shown to have superior adaptation to the phantom's surface, producing minimal air gaps between the skin surface and bolus, allowing for accurate positioning and reproducibility of set-up conditions. eXaSkin with its high density material provides sufficient build-up to achieve full skin dose with less material thickness than Superflab.

Large-Area 2D-MXene Nanosheet Assemblies Using Langmuir-Schaefer Technique: Wrinkle formation.

The formation of uniform sheets of exfoliated MXene over a large area is important for improving their performance in practical applications. In this study, the Langmuir-Schaefer technique was employed to deposit uniform MXene sheets on a solid substrate and control the morphological structure over a large area. At the liquid-gas interface, MXene flakes were densely compressed into nanosheets with minimal gaps between them at 20 mN/m. Through further compression, the wrinkle morphologies of MXene sheets tend to be perpendicularly aligned to the compression direction. These wrinkle structures were also exhibited when MXene sheets were mixed in equal proportions with graphene oxide sheets. Owing to the close correlation of the morphologies of MXene films with the performance of MXene-based materials, the technique employed in this study can provide a route for applications requiring wrinkled MXene, ranging from nanoelectronic devices to energy storage materials, such as supercapacitors and battery electrodes.

Scalp and Cranium Radiation Therapy Using Modulation (SCRUM) and Bolus

PurposeA bolus is usually required to ensure radiation dose coverage of extensive superficial tumors of the scalp or skull. Oftentimes, these boluses are challenging to make and are nonreproducible, so an easier method was sought. Methods and MaterialsThermoplastic sheets are widely available in radiation oncology clinics and can serve as bolus. Two template cutouts were designed for anterior and posterior halves to encompass the cranium of children and adults. ResultsThe created bolus was imaged using computed tomography, which demonstrated good conformity and minimal air gaps. ConclusionsAlthough making a bolus for treating superficial tumors of the scalp or head and neck is challenging, the presented technique enables thermoplastic to be used as a bolus and is quick, easy, and reproducible.

Concentration Versus Diversification: A Spatial Deployment Approach to Improve the Economics of Wind Power

Previous studies on the economics of onshore wind parks in Germany found that geographic diversifi-cation results in no significant system costs savings. Furthermore, such diversification does not neces-sarily result in higher market values (Eising et al., 2020) or better merchant profitability (Klie and Madlener, 2020). Therefore, the question arises whether an alternative allocation (i.e. a concentration) rather than diversification of the German wind park fleet is more economical. In this paper, we compare the future (2030) market values, subsidy needs and total system costs of a more concentrated versus a more diversified allocation of onshore wind turbines in Germany. The results show that a concentration of turbines, in areas where the gap between market values and levelized costs of electricity is smallest (i.e. in the North of Germany), is more beneficial in terms of subsidy need and system costs. The analysis further shows that these areas are also more beneficial in terms of market values, when using system-friendly turbine configurations selected based on the same approach. To incentivize such a selection of areas and turbine configurations based on minimal gaps between market values and levelized costs an alternative renewables support scheme is presented, which favors such minimal gaps in its auctioning process.

The upgraded Polaris powder diffractometer at the ISIS neutron source.

This paper describes the design and operation of the Polaris time-of-flight powder neutron diffractometer at the ISIS pulsed spallation neutron source, Rutherford Appleton Laboratory, UK. Following a major upgrade to the diffractometer in 2010-2011, its detector provision now comprises five large ZnS scintillator-based banks, covering an angular range of 6° ≤ 2θ ≤ 168°, with only minimal gaps between each bank. These detectors have a substantially increased solid angle coverage (Ω ∼ 5.67 sr) compared to the previous instrument (Ω ∼ 0.82 sr), resulting in increases in count rate of between 2× and 10×, depending on 2θ angle. The benefits arising from the high count rates achieved are illustrated using selected examples of experiments studying small sample volumes and performing rapid, time-resolved investigations. In addition, the enhanced capabilities of the diffractometer in the areas of in situ studies (which are facilitated by the installation of a novel design of radial collimator around the sample position and by a complementary programme of advanced sample environment developments) and in total scattering studies (to probe the nature of short-range atomic correlations within disordered crystalline solids) are demonstrated.

Control of cortical oscillatory frequency by a closed-loop system

BackgroundWe present a closed-loop system able to control the frequency of slow oscillations (SO) spontaneously generated by the cortical network in vitro. The frequency of SO can be controlled by direct current (DC) electric fields within a certain range. Here we set out to design a system that would be able to autonomously bring the emergent oscillatory activity to a target frequency determined by the experimenter.MethodsThe cortical activity was recorded through an electrode and was analyzed online. Once a target frequency was set, the frequency of the slow oscillation was steered through the injection of DC of variable intensity that generated electric fields of proportional amplitudes in the brain slice. To achieve such closed-loop control, we designed a custom programmable stimulator ensuring low noise and accurate tuning over low current levels. For data recording and analysis, we relied on commercial acquisition and software tools.ResultsThe result is a flexible and reliable system that ensures control over SO frequency in vitro. The system guarantees artifact removal, minimal gaps in data acquisition and robustness in spite of slice heterogeneity.ConclusionsOur tool opens new possibilities for the investigation of dynamics of cortical slow oscillations—an activity pattern that is associated with cognitive processes such as memory consolidation, and that is altered in several neurological conditions—and also for potential applications of this technology.

Longest increasing paths with gaps

We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal gaps between abscissae and ordinates of successive points of the path. For both cases (continuous and discrete) our approach rely on couplings with well-studied models: respectively the classical Ulam-Hammersley problem and last-passage percolation with geometric weights. Thanks to these couplings we obtain explicit limiting shapes in both settings. We also establish that, as in the classical Ulam-Hammersley problem, the fluctuations around the mean are given by the Tracy-Widom distribution.

Intensification of Fast Chemical Processes at Interfaces of Two-Component Liquid Media in Tubular Turbulent Reactors

The possibility of intensifying fast chemical processes at the interface of two-component liquid medium in a tubular turbulent reactor has been considered. A new application of the turbulent reactor for processes occurring at interfaces in two-component liquid systems has been found. It has been observed that the chemical reaction time abruptly decreases, and the physics of the process affects the direction of and conversion in the chemical reaction at a high (up to 100%) yield of desired products. The geometric characteristics of the reactor have been analyzed, and it has been shown that the dispersion of drops in the emulsion is most efficient at large angles of inclination of an obstruction to the flow and at minimal gaps in the convergent-divergent channel of the reactor. It has been demonstrated that the average perimeter of drops of the dispersion oscillates with time, which causes elongation and breakup of drops. In its turn, the latter influences the contact surface area of the emulsion and, significantly, the chemical reaction rate.

Modular assembly of plasmonic core-satellite structures as highly brilliant SERS-encoded nanoparticles.

Herein, we present a fabrication approach that produces homogeneous core–satellite SERS encoded particles with minimal interparticle gaps (<2–3 nm) and maximum particle loading, while positioning the encoding agents at the gaps. Integration of plasmonic building blocks of different sizes, shapes, compositions, surface chemistries or encoding agents is achieved in a modular fashion with minimal modification of the general synthetic protocol. These materials present an outstanding optical performance with homogeneous enhancement factors over 4 orders of magnitude as compared with classical SERS encoded particles, which allows their use as single particle labels.

Engineering non-equilibrium quantum phase transitions via causally gapped Hamiltonians

We introduce a phenomenological theory for many-body control of critical phenomena by engineering causally-induced gaps for quantum Hamiltonian systems. The core mechanisms are controlling information flow within and/or between clusters that are created near a quantum critical point. To this end, we construct inhomogeneous quantum phase transitions via designing spatiotemporal quantum fluctuations. We show how non-equilibrium evolution of disordered quantum systems can create new effective correlation length scales and effective dynamical critical exponents. In particular, we construct a class of causally-induced non-adiabatic quantum annealing transitions for strongly disordered quantum Ising chains leading to exponential suppression of topological defects beyond standard Kibble–Zurek predictions. Using exact numerical techniques for 1D quantum Hamiltonian systems, we demonstrate that our approach exponentially outperforms adiabatic quantum computing. Using strong-disorder renormalization group (SDRG), we demonstrate the universality of inhomogeneous quantum critical dynamics and exhibit the reconstructions of causal zones during SDRG flow. We derive a scaling relation for minimal causal gaps showing they narrow more slowly than any polynomial with increasing size of system, in contrast to stretched exponential scaling in standard adiabatic evolution. Furthermore, we demonstrate similar scaling behavior for random cluster-Ising Hamiltonians with higher order interactions.

Public Support for Gun Violence Prevention Policies Among Gun Owners and Non-Gun Owners in 2017.

To compare public support for 24 different gun policies between gun owners and non-gun owners in 2017. We fielded a national public opinion survey in January 2017 using an online panel to measure US adults' support for 24 gun policies. We compared support among gun owners and non-gun owners. For 23 of the 24 policies examined, most respondents supported restricting or regulating gun ownership. Only 8 of 24 policies had greater than a 10-point support gap between gun owners and non-gun owners. Policies with high public support and minimal support gaps by gun ownership status included universal background checks, greater accountability for licensed gun dealers unable to account for their inventory, higher safety training standards for concealed carry permit holders, improved reporting of records related to mental illness for background checks, gun prohibitions for persons subject to temporary domestic violence restraining orders, and gun violence restraining orders. Public Health Implications. Although there are important areas where Americans disagree on guns, large majorities of both gun owners and non-gun owners strongly support measures to strengthen US gun laws.

Bacterial leakage and micro-computed tomography evaluation in round-shaped canals obturated with bioceramic cone and sealer using matched single cone technique.

ObjectivesTo evaluate sealing ability of root canals obturated with bioceramic-impregnated gutta percha cone (BCC) or gutta percha (GP), with bioceramic sealer (BCS) or AH Plus (AH; Dentsply-Maillefer), in roundly-prepared canals using matched single-cone technique, based on bacterial leakage test, and to analyze obturation quality using micro-computed tomography (CT) analysis.Materials and MethodsNinety-two distobuccal roots of maxillary molars were prepared using nickel-titanium files to apical size 40/0.06. The roots were divided into 4 groups (n = 20) that were obturated with a master cone and sealer: GP/AH, BCC/AH, GP/BCS, and BCC/BCS. Bacterial leakage model using Enterococcus faecalis was used to evaluate sealing ability for 60-day period. Obturated samples from each group (n = 4) were analyzed using micro-CT.ResultsAll groups showed bacterial leakage at 20%–45% of samples with mean leakage times of 42–52 days. There were no significant differences in bacterial leakage among the groups. Micro-CT showed minimal gaps and voids in all groups at less than 1%.ConclusionsIn roundly-prepared canals, the single cone obturation with BCC/BCS was comparable to GP/AH for bacterial leakage at 60 days.

Comparative Performance and Model Agreement of Three Common Photovoltaic Array Configurations.

Three grid-connected monocrystalline silicon arrays on the National Institute of Standards and Technology (NIST) campus in Gaithersburg, MD have been instrumented and monitored for 1 yr, with only minimal gaps in the data sets. These arrays range from 73 kW to 271 kW, and all use the same module, but have different tilts, orientations, and configurations. One array is installed facing east and west over a parking lot, one in an open field, and one on a flat roof. Various measured relationships and calculated standard metrics have been used to compare the relative performance of these arrays in their different configurations. Comprehensive performance models have also been created in the modeling software pvsyst for each array, and its predictions using measured on-site weather data are compared to the arrays' measured outputs. The comparisons show that all three arrays typically have monthly performance ratios (PRs) above 0.75, but differ significantly in their relative output, strongly correlating to their operating temperature and to a lesser extent their orientation. The model predictions are within 5% of the monthly delivered energy values except during the winter months, when there was intermittent snow on the arrays, and during maintenance and other outages.

Experimental study on heat transfer through a few layers of multilayer insulation from 300 K to 4.2 K

The final focusing magnet system at the SuperKEKB interaction region has been designed under stringent space constraints and consists of 8 main Superconducting (SC) quadrupole magnets, 4 compensation SC solenoids, and 43 SC correction coils. SC correction coils are directly wound on the inner containment tubes of liquid helium (LHe) vessels, which serve as support bobbins for SC cables. Beam pipes, which are kept at room temperature (∼300 K), are inserted into the cold bores of the vessel inner tubes. Between them, the minimal radial gaps are only 3.5 mm. Heat transfer from the warm beam pipes causes the raised operation temperatures of SC cables and increases heat leaks into cryostats. Multilayer insulation (MLI) is adopted to reduce heat flux in the narrow gaps. MLI performance as a function of the layer number was studied with a vertical anti-cryostat of dedicated design. The measurements were carried out by a calorimeter of thermal conduction and a modified LHe boil-off method. This paper presents the cryogenic measurement system and discusses the experimental results for the cryostats of the SuperKEKB final focusing SC magnets.