scholarly journals On the Existence of Hamilton Cycles with a Periodic Pattern in a Random Digraph

10.37236/9376 ◽  
2020 ◽  
Vol 27 (4) ◽  
Author(s):  
Alan Frieze ◽  
Xavier Pérez-Giménez ◽  
Paweł Prałat
Keyword(s):  
Periodic Pattern ◽  
Hamilton Cycles

We consider Hamilton cycles in the random digraph $D_{n,m}$ where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in the same direction as we traverse the cycle. We show that if the orientation forms a periodic pattern, other than the trivial pattern, then approximately half the usual $n\log n$ edges are needed to guarantee the existence of such Hamilton cycles a.a.s.

Numerical analysis of trajectories in a Cassinian ion trap of second order with trap door ion inlet

2021 ◽  
Vol 27 (1) ◽  
pp. 3-12
Author(s):  
Bjoern Raupers ◽  
Hana Medhat ◽  
Juergen Grotemeyer ◽  
Frank Gunzer
Keyword(s):  
Ion Trap ◽  
Ion Traps ◽  
Second Order ◽  
Resolving Power ◽  
Periodic Pattern ◽  
Ion Motion ◽  
Trap Door ◽  
Mass Resolving Power ◽  
Long Time ◽  
The Fourier Transform

Ion traps like the Orbitrap are well known mass analyzers with very high resolving power. This resolving power is achieved with help of ions orbiting around an inner electrode for long time, in general up to a few seconds, since the mass signal is obtained by calculating the Fourier Transform of the induced signal caused by the ion motion. A similar principle is applied in the Cassinian Ion Trap of second order, where the ions move in a periodic pattern in-between two inner electrodes. The Cassinian ion trap has the potential to offer mass resolving power comparable to the Orbitrap with advantages regarding the experimental implementation. In this paper we have investigated the details of the ion motion analyzing experimental data and the results of different numerical methods, with focus on increasing the resolving power by increasing the oscillation frequency for ions in a high field ion trap. In this context the influence of the trap door, a tunnel through which the ions are injected into the trap, on the ion velocity becomes especially important.

scholarly journals Analysis of nocturnal desaturation waveforms using algorithms in patients with idiopathic pulmonary fibrosis

2021 ◽  
Author(s):  
Yuichiro Yasuda ◽  
Tatsuya Nagano ◽  
Shintaro Izumi ◽  
Mina Yasuda ◽  
Kosuke Tsuruno ◽  
...  
Keyword(s):  
Sleep Apnea ◽  
Idiopathic Pulmonary Fibrosis ◽  
Pulmonary Fibrosis ◽  
Diagnostic Algorithm ◽  
Sleep Time ◽  
Periodic Pattern ◽  
Apnea Hypopnea Index ◽  
Apnea Test ◽  
Eligibility Criteria ◽  
Obstructive Sleep

Abstract Purpose Sleep-disordered breathing is recognized as a comorbidity in patients with idiopathic pulmonary fibrosis (IPF). Among them, nocturnal hypoxemia has been reported to be associated with poor prognosis and disease progression. We developed a diagnostic algorithm to classify nocturnal desaturation from percutaneous oxygen saturation (SpO2) waveform patterns: sustained pattern, periodic pattern, and intermittent pattern. We then investigated the prevalence of nocturnal desaturation and the association between the waveform patterns of nocturnal desaturation and clinical findings of patients with IPF. Methods We prospectively enrolled patients with IPF from seven general hospitals between April 2017 and March 2020 and measured nocturnal SpO2 and nasal airflow by using a home sleep apnea test. An algorithm was used to classify the types of nocturnal desaturation. We evaluated the association between sleep or clinical parameters and each waveform pattern of nocturnal desaturation. Results Among 60 patients (47 men) who met the eligibility criteria, there were 3 cases with the sustained pattern, 49 cases with the periodic pattern, and 41 cases with the intermittent pattern. Lowest SpO2 during sleep and total sleep time spent with SpO2 < 90% were associated with the sustained pattern, and apnea–hypopnea index was associated with the intermittent pattern. Conclusion We demonstrated the prevalence of each waveform and association between each waveform and sleep parameters in patients with IPF. This classification algorithm may be useful to predict the degree of hypoxemia or the complication of obstructive sleep apnea.

scholarly journals Counting Hamilton cycles in Dirac hypergraphs

2020 ◽  
pp. 1-23
Author(s):  
Stefan Glock ◽  
Stephen Gould ◽  
Felix Joos ◽  
Daniela Kühn ◽  
Deryk Osthus
Keyword(s):  
Hamilton Cycle ◽  
Uniform Hypergraph ◽  
Similar Estimate ◽  
Hamilton Cycles

Abstract A tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge. Rödl, Ruciński and Szemerédi proved that for $k\ge 3$ , every k-graph on n vertices with minimum codegree at least $n/2+o(n)$ contains a tight Hamilton cycle. We show that the number of tight Hamilton cycles in such k-graphs is ${\exp(n\ln n-\Theta(n))}$ . As a corollary, we obtain a similar estimate on the number of Hamilton ${\ell}$ -cycles in such k-graphs for all ${\ell\in\{0,\ldots,k-1\}}$ , which makes progress on a question of Ferber, Krivelevich and Sudakov.

Collective periodic pattern discovery for understanding human mobility

2021 ◽  
Author(s):  
Tantan Shi ◽  
Genlin Ji ◽  
Zhaoyuan Yu ◽  
Bin Zhao
Keyword(s):  
Human Mobility ◽  
Pattern Discovery ◽  
Periodic Pattern

scholarly journals The primacy of rhythm: how discrete actions merge into a stable rhythmic pattern

2019 ◽  
Vol 121 (2) ◽  
pp. 574-587 ◽  
Author(s):  
Zhaoran Zhang ◽  
Dagmar Sternad
Keyword(s):  
Building Blocks ◽  
Periodic Pattern ◽  
Voluntary Movements ◽  
Rhythmic Pattern ◽  
Rhythmic Movements ◽  
Discrete Movements ◽  
Floquet Multipliers ◽  
Physiological Processes ◽  
Rhythmic Behavior ◽  
Virtual Target

This study examined how humans spontaneously merge a sequence of discrete actions into a rhythmic pattern, even when periodicity is not required. Two experiments used a virtual throwing task, in which subjects performed a long sequence of discrete throwing movements, aiming to hit a virtual target. In experiment 1, subjects performed the task for 11 sessions. Although there was no instruction to perform rhythmically, the variability of the interthrow intervals decreased to a level comparable to that of synchronizing with a metronome; furthermore, dwell times shortened or even disappeared with practice. Floquet multipliers and decreasing variability of the arm trajectories estimated in state space indicated an increasing degree of dynamic stability. Subjects who achieved a higher level of periodicity and stability also displayed higher accuracy in the throwing task. To directly test whether rhythmicity affected performance, experiment 2 disrupted the evolving continuity and periodicity by enforcing a pause between successive throws. This discrete group performed significantly worse and with higher variability in their arm trajectories than the self-paced group. These findings are discussed in the context of previous neuroimaging results showing that rhythmic movements involve significantly fewer cortical and subcortical activations than discrete movements and therefore may pose a computationally more parsimonious solution. Such emerging stable rhythms in neuromotor subsystems may serve as building blocks or dynamic primitives for complex actions. The tendency for humans to spontaneously fall into a rhythm in voluntary movements is consistent with the ubiquity of rhythms at all levels of the physiological system. NEW & NOTEWORTHY When performing a series of throws to hit a target, humans spontaneously merged successive actions into a continuous approximately periodic pattern. The degree of rhythmicity and stability correlated with hitting accuracy. Enforcing irregular pauses between throws to disrupt the rhythm deteriorated performance. Stable rhythmic patterns may simplify control of movement and serve as dynamic primitives for more complex actions. This observation reveals that biological systems tend to exhibit rhythmic behavior consistent with a plethora of physiological processes.

scholarly journals Tuning Deposition of Magnetic Metallic Nanoparticles from Periodic Pattern to Thin Film Entrainment by Dip Coating Method

Langmuir ◽  
2014 ◽  
Vol 30 (30) ◽  
pp. 9028-9035 ◽  
Author(s):  
J. Dugay ◽  
R. P. Tan ◽  
A. Loubat ◽  
L.-M. Lacroix ◽  
J. Carrey ◽  
...  
Keyword(s):  
Thin Film ◽  
Metallic Nanoparticles ◽  
Dip Coating ◽  
Periodic Pattern ◽  
Coating Method ◽  
Dip Coating Method

Improved Melting and Solidification in Thermal Energy Storage Through Topology Optimization of Highly Conductive Fins

2017 ◽  
Author(s):  
Alberto Pizzolato ◽  
Adriano Sciacovelli ◽  
Vittorio Verda
Keyword(s):  
Topology Optimization ◽  
Energy Storage ◽  
Phase Change ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Phase Change Materials ◽  
Optimization Method ◽  
Periodic Pattern ◽  
Melting Time ◽  
Bottom Part

Thermal energy storage units based on phase change materials (PCMs) need a fine design of highly conductive fins to improve the average heat transfer rate. In this paper, we seek the optimal distribution of a highly conductive material embedded in a PCM through a density-based topology optimization method. The phase change problem is solved through an enthalpy-porosity model, which accounts for natural convection in the fluid. Results show fundamental differences in the optimized layout between the solidification and the melting case. Fins optimized for solidification show a quasi-periodic pattern along the angular direction. On the other hand, fins optimized for melting elongate mostly in the bottom part of the unit leaving only two short baffles at the top. In both cases, the optimized structures show non-intuitive details which could not be obtained neglecting fluid flow. These additional features reduce the solidification and melting time by 11 % and 27 % respectively compared to a structure optimized for diffusion.

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