Periodic Points Research Articles

Accelerating material property prediction using generically complete isometry invariants

Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these algorithms is the representation used for a periodic crystal. While similar objects like molecules and proteins have a finite number of atoms and their representation can be built based upon a finite point cloud interpretation, periodic crystals are unbounded in size, making their representation more challenging. In the present work, we adapt the Pointwise Distance Distribution (PDD), a continuous and generically complete isometry invariant for periodic point sets, as a representation for our learning algorithm. The PDD distinguished all (more than 660 thousand) periodic crystals in the Cambridge Structural Database as purely periodic sets of points without atomic types. We develop a transformer model with a modified self-attention mechanism that combines PDD with compositional information via a spatial encoding method. This model is tested on the crystals of the Materials Project and Jarvis-DFT databases and shown to produce accuracy on par with state-of-the-art methods while being several times faster in both training and prediction time.

Intersection control based on Fine-grained Phases for connected and automated vehicles

Traditional traffic signal control is one of the most widely used urban traffic control methods, due to its high efficiency, robustness, and simplicity. However, in the era of connected and automated vehicles (CAVs), it is prospective to enhance traffic control precision and achieve vehicle coordination in a more efficient manner. Focusing on an isolated intersection, this study proposes an innovative concept of Fine-grained Phase (FP) for CAV-enabled traffic control, which realizes more refined right-of-way allocation than traditional signal phases while preserving the simplicity and scalability. The development of FP jointly optimizes traffic control strategy and intersection layout design to fully utilize time-space resources, and multiple forms of FP could be generated in response to various traffic demands; meanwhile, vehicle coordination is achieved in an offline–online manner to balance solution quality and efficiency. Under the FP-based control, each lane is assigned with periodical entry time points using FP design results, then vehicles are supposed to catch up with the appropriate time points to fulfill their trips. Theoretical analyses are conducted under stationary vehicle arrival patterns, where the average delay and the intersection capacity associated with different forms of FP can be analytically acquired. For the implementation of FP-based control, we construct a general offline–online framework, consisting of an offline model that optimizes the geometry of the conflict zone at intersections and the control strategy of vehicles simultaneously, which is formulated as a mixed-integer linear programming problem, and an online FP adoption mechanism that can adapt to varying demand patterns. Under the framework, limited online computation is required, facilitating its practical real-time implementation. Simulation studies under a variety of demand settings show that FP-based control is advantageous over benchmark methods in reducing vehicle delay and also improving intersection capacity in most cases; even for cases with extremely imbalanced demands, FP-based control can admit comparable throughput, while the average delay is much smaller. In addition, results of computation time reveal that FP-based control could realize real-time implementation with negligible computation burden.

Poissonian pair correlation for directions in multi-dimensional affine lattices and escape of mass estimates for embedded horospheres

Abstract We prove the convergence of moments of the number of directions of affine lattice vectors that fall into a small disc, under natural Diophantine conditions on the shift. Furthermore, we show that the pair correlation function is Poissonian for any irrational shift in dimension 3 and higher, including well-approximable vectors. Convergence in distribution was already proved in the work of Strömbergsson and the second author [The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems. Ann. of Math. (2)172 (2010), 1949–2033], and the principal step in the extension to convergence of moments is an escape of mass estimate for averages over embedded $\operatorname {SL}(d,\mathbb {R})$ -horospheres in the space of affine lattices.

Computing parametrised large intersection sets of 1D invariant manifolds: a tool for blender detection

AbstractA dynamical system given by a diffeomorphism with a three-dimensional phase space may have a blender, which is a hyperbolic set $$\Lambda $$ Λ with, say, a one-dimensional stable invariant manifold that behaves like a surface. This means that the stable manifold of any fixed or periodic point in $$\Lambda $$ Λ weaves back and forth as a curve in phase space such that it is dense in some projection; we refer to this as the carpet property. We present a method for computing very long pieces of such a one-dimensional manifold so efficiently and accurately that a very large number of intersection points with a specified section can reliably be identified. We demonstrate this with the example of a family of Hénon-like maps $$\mathcal {H}$$ H on $$\mathbb {R}^3$$ R 3 , which is the only known, explicit example of a diffeomorphism with proven existence of a blender. The code for this example is available as a Matlab script as supplemental material. In contrast to earlier work, our method allows us to determine a very large number of intersection points of the respective one-dimensional stable manifold with a chosen planar section and render each as individual curves when a parameter is changed. With suitable accuracy settings, we not only compute these parametrised curves for the fixed points of $$\mathcal {H}$$ H over the relevant parameter interval, but we also compute the corresponding parametrised curves of the stable manifolds of a period-two orbit (with negative eigenvalues) and of a period-three orbit (with positive eigenvalues). In this way, we demonstrate that our algorithm can handle large expansion rates generated by (up to) the fourth iterate of $$\mathcal {H}$$ H .

Fixed point and periodic point theorems

Fixed point and periodic point theorems

Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns

Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns

Implementation and effectiveness outcomes of Community Health Advocacy Teams to improve long-lasting insecticide net distribution and use in six districts in Ghana: A one-group pre-post-test study.

Malaria remains a leading cause of illness and death especially among children and pregnant women in Ghana. Despite the efforts made by the National Malaria Elimination Programme (NMEP), including distribution of Long-Lasting Insecticide Nets (LLINs) to households through periodic Point Mass Distribution (PMD) campaigns and continuous channels (antenatal, schools and postnatal), there is a gap between access and use of LLINs in Ghana. An effective and functional community-based group that would seek to improve the effectiveness of LLIN distribution before, during, after PMD Campaigns and continuous distribution at the community level could help address this gap. This paper assesses the implementation outcomes and short-term effectiveness of the pilot implementation of co-created community health advocacy teams (CHAT) intervention in Ghanaian communities to plan and implement campaigns to increase LLIN use. The study employed a one-group pre-post study design and measured implementation outcomes (acceptability, appropriateness, and feasibility) and effectiveness outcomes (LLIN awareness, LLIN access, willingness to purchase LLIN, and LLIN use) among 800 community households. The CHAT intervention was implemented for four months across six districts in the Eastern and Volta regions of Ghana. The data were downloaded directly from REDCap and analyzed statistically (descriptive and McNemar test of association) using SPSS 22 software. After the implementation period, the majority of respondents in all six districts indicated that the CHAT intervention was acceptable (89.8%), appropriate (89.5%), and feasible (90%). Also, there was a significant association between baseline and end-line assessment on all four effectiveness outcome measures. Household members' awareness of, access to, willingness to purchase, and use of LLINs increased significantly over the four-month period that the CHAT intervention was implemented. The study concludes that CHAT is an acceptable, appropriate, and feasible intervention for supporting the National Malaria Programme in LLIN PMD and for engaging in Social and Behaviour Change Communication activities through the continuous channels of distribution. Additionally, the CHAT demonstrates short-term effectiveness outcomes in terms of creating LLIN awareness, providing access to LLIN, and encouraging Ghanaian community members to be willing to purchase and use LLINs. Although the activities of CHAT members were largely voluntary, integration into the existing primary health care system will make it sustainable.

Sources of Social Support and Trauma Recovery: Evidence for Bidirectional Associations from a Recently Trauma-Exposed Community Sample.

Although the association between post-traumatic stress disorder (PTSD) and social support is well documented, few studies have tested the causal pathways explaining this association at several points in the acute post-trauma recovery period or examined whether the association varies for different sources of social support. To address these gaps, 151 community individuals (mean age = 37.20 years, 69.5% women) exposed to trauma within the previous 6 months were recruited to complete measures of PTSD and social support from intimate partners, friends, and relatives four times in 1 year. In line with recent recommendations for research on social support and PTSD symptoms, random intercept cross-lagged panel modeling (RI-CLPM) was used to examine dynamic changes between PTSD severity and social support over time. The pattern of RI-CLPM cross-lagged coefficients indicated that positive deviations from one's expected stable level of total social support (across all sources) sped up the recovery of PTSD symptoms at the end of the post-trauma year, and more severe PTSD symptoms than expected based on one's expected stable level of PTSD started eroding social support midway through the assessment year. When specific sources of social support were analyzed separately, the association between within-person increases in social support from friends at any given time point accelerated the recovery from PTSD across the entire year. Among participants with intimate partners (n = 53), intimate partner support did not predict PTSD symptoms, but more severe PTSD symptoms at any given time point predicted less support at the following time point. Results from this longitudinal study provide additional support for the bidirectional relationship between PTSD and social support over time and suggest that perceived social support from friends may be especially helpful during trauma recovery.

Shadowing for nonuniformly hyperbolic maps in Hilbert spaces

We prove a shadowing lemma for nonuniformly hyperbolic maps in Hilbert spaces. As applications, we firstly prove that the positive Lyapunov exponents of a hyperbolic ergodic measure µ can be approximated by positive Lyapunov exponents of atomic measures on hyperbolic periodic orbits; secondly, give an upper estimation of metric entropy by using the exponential growth rate of the number of such periodic points that their atomic measures approximate µ and their positive Lyapunov exponents approximate the positive Lyapunov exponents of µ.

Effectiveness of erector spinae plane block in children with pectus excavatum deformity during minimally invasive thoracoplasty with osteosynthesis of the sternocostal complex: a prospective randomized comparative study

BACKGROUND: Despite the widespread use of regional blocks in children, ensuring adequate perioperative pain control during minimally invasive thoracoplasty with osteosynthesis of the sternocostal complex remains a problem. The introduction of ultrasound navigation has allowed specialists to increasingly give preference to peripheral blockades; paravertebral anesthesia has proven to be effective in thoracic surgery. However, safer interfascial blocks, including erector spinae plane block, are rarely used in pediatrics, and there is no evidence base for the effectiveness of the method.
 OBJECTIVE: Our aim was to compare the effectiveness of erector spinae plane block with paravertebral blockade during minimally invasive thoracoplasty with osteosynthesis of the sternocostal complex in children.
 MATERIALS AND METHODS: A prospective randomized comparative study of children who underwent minimally invasive thoracoplasty with osteosynthesis of the sternocostal complex was conducted from September 2022 to April 2023. According to the inclusion criteria, the selected 39 children were divided into groups: I — paravertebral blockade, and II — erector spinae plane block. The mean arterial pressure, heart rate during the perioperative period stages, postanesthesia recovery by Aldrete scale and pain intensity by the Wong–Baker scale, and stress response markers (cortisol and lactate) were assessed.
 RESULTS: No significant differences were observed in the study groups when comparing mean arterial pressure and heart rate at any of the measurement points of the perioperative period (p 0.05). Further, no significant differences were noted between the groups when comparing cortisol and lactate levels (p 0.05). The awakening level was characterized by a short recovery period and did not differ between the groups (p 0.05). The intensity of pain during the observation period did not exceed 5 points on the verbal rating scale in both groups, and the severity of pain was significantly higher in the group with blockade of the erector spinae plane block only 2 hours after surgery (p 0.05).Postoperative nausea and vomiting were more common in children with erector spinae plane block (p 0.05). No other adverse events were recorded.
 CONCLUSION: Erector spinae plane block is an effective and simple method of regional anesthesia for minimally invasive thoracoplasty with osteosynthesis of the sternocostal complex and can be used as an alternative to paravertebral blockade in children.

Synchronizing dynamical systems: Their groupoids and 𝐶*-algebras

Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic C ∗ C^\ast -algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various C ∗ C^\ast -algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space.

Trends in air toxics cancer risk in Southern California, 1998-2018

Air toxics are an important category of air pollutants that are known to cause adverse health effects, including increased cancer risk. Regulatory efforts at federal, state, and local levels have aimed to decrease air toxics emissions over the past several decades. This study evaluated trends in air toxics cancer risks in Southern California using data from 1998 to 2018. We estimated air toxics cancer risk for each of four iterations of the South Coast Air Quality Management District’s Multiple Air Toxics Exposure Study, which included at least one year of measurements at 10 stations and air toxics modeling for each iteration. Cancer risks were calculated using the measured and modeled air toxics concentrations averaged over a one to two year period and multiplied by the corresponding cancer potency factor and combined exposure factor that accounted for multiple exposure pathways and children’s increased sensitivity to the health effects of air pollution. We examined temporal trends in overall air toxics cancer risks and evaluated changes in the air toxics species that contributed most to cancer risk in the region. Both measurement and modeling results show that air toxics cancer risk in Southern California decreased by more than 80% between 1998 and 2018, including a decrease of about 50% from 2012 to 2018. Diesel particulate matter was the main risk driver, followed by benzene, 1,3-butadiene, and formaldehyde. We found that more densely populated communities showed larger decreases than sparsely populated areas. The substantial decrease in air toxics levels over this 20-year period points to the success of air pollution policies aimed at addressing air toxics emissions and can inform future policy efforts to further reduce air toxics health impacts.

Positively ep-expansive dynamical systems

In this paper we investigate the basic properties of those dynamical systems which are positively expansive on a dense set containing all eventually periodic points and show how the dynamical behavior of these systems fits within the theoretical framework of usual (positive) expansiveness.

Control of chaos in Darcy–Bénard axisymmetric convection in a cylindrical enclosure using a uniform vertical cross-flow

The linear and weakly nonlinear stability analyses of Darcy–Bénard convection of a Newtonian fluid experiencing a uniform vertical cross-flow is investigated in the paper for various aspect ratios. Making use of the Maclaurin series representation, an expression for axial eigenfunctions is obtained with the radial eigenfunction being a Bessel function of first kind. These eigenfunctions are influenced by the Peclet number, Pe, the non-dimensional number that signifies the rate of vertical cross-flow. The modified-Vadasz-Lorenz model obtained in this paper has newly defined non-dimensional parameters that capture the influence of vertical cross-flow. From the linear stability analysis, it is found that the effect of introducing vertical cross-flow is to stabilize the system. Using a weakly nonlinear stability analysis, the closed-form expression of the Hopf-Rayleigh number as a function of Pe is obtained. Furthermore, the behavior of the modified-Vadasz–Lorenz model is analyzed using the largest Lyapunov exponent and the bifurcation diagram. This gives information about the intensity of chaos and occurrence of the periodic motion. We observe that the influence of vertical cross-flow is to increase the value of the Hopf–Rayleigh number and thereby to delay the onset of chaos. Furthermore, the appearance of the first periodic point is preponed due to the vertical cross-flow. As the rate of vertical cross-flow increases, the intensity of chaos decreases, thereby indicating that the effect of introducing vertical cross-flow is to suppress chaos.

Comparison of hemodynamic and analgesic effects of interscalene block with bupivacaine versus bupivacaine-dexmedetomidine combination for shoulder arthroscopy under general anesthesia

Background: The interscalene block in shoulder arthroscopy is a well-established procedure. Many drugs have been used as adjuvants to local anesthetics to increase the quality of block in regional anesthesia, with variable results. Aims and Objectives: The present study was designed to evaluate the effect of dexmedetomidine as an adjuvant to bupivacaine during interscalene block in terms of intraoperative hemodynamic changes and postoperative analgesia. Materials and Methods: Thirty patients, aged 20–55 years of either sex, American Society of Anesthesiologists physical status I-II, scheduled for shoulder arthroscopic surgery for <2 h, were allocated into two equal groups to receive inj. bupivacaine (0.25%) with inj. dexmedetomidine 1 μg/kg (Group BD, n=15) or inj. bupivacaine (0.25%) with 1 mL normal saline (Group BS, n=15), total volume 20 mL in each case. After settlement of the interscalene block, both groups received general anesthesia as per standard protocol. Hemodynamic parameters (heart rate [HR] and systolic blood pressure [SBP]) were assessed in the intraoperative period, and postoperative pain was assessed using a visual analog scale score in the postoperative period at stipulated time points. Results: The mean values of HR and SBP were considerably low at all observed time points in the intraoperative period (i.e., at 10 min, 30 min, 60 min, 90 min, and120 min), in comparison with the saline group (P<0.0001). VAS scores between the two groups were considerably lower only at 8, 12, and 18 h in patients receiving dexmedetomidine (P<0.001). Conclusion: Dexmedetomidine as an adjuvant with bupivacaine can achieve a better hemodynamic profile (lower HR and SBP) in the intraoperative period. Also, the use of dexmedetomidine provides better postoperative analgesia profiles in the later part of the postoperative period (8–18 h), and the effect usually wanes by 24 h.

Data-driven discovery of invariant measures

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and stochastic dynamics in either continuous or discrete time. We provide convergence results and illustrate the performance of our method on data from the logistic map and a stochastic double-well system, for which invariant measures can be found by other means. We then use our method to approximate the physical measure of the chaotic attractor of the Rössler system, and we extract unstable periodic orbits embedded in this attractor by identifying discrete-time periodic points of a suitably defined Poincaré map. This final example is truly data-driven and shows that our method can significantly outperform previous approaches based on model identification.

A dynamical analogue of a question of Fermat

Given a quadratic polynomial with rational coefficients, we investigate the existence of consecutive squares in the orbit of a rational point under the iteration of the polynomial. We display three different constructions of $1$-parameter quadratic polynomials with orbits containing three consecutive squares. In addition, we show that there exists at least one polynomial of the form $x^2+c$ with a rational point whose orbit under this map contains four consecutive squares. This can be viewed as a dynamical analogue of a question of Fermat on rational squares in arithmetic progression. Finally, assuming a standard conjecture on exact periods of periodic points of quadratic polynomials over the rational field, we give necessary and sufficient conditions under which the orbit of a periodic point contains only rational squares.

Results in Cone Metric Spaces and Related Fixed Point Theorems for Contractive Type Mappings With Application

In this article, we prove some new fixed point theorems for contractive type mappings in the setting of complete cone metric spaces and provide examples to illustrate the concepts and results developed in the article. We consider some consequences of our results to establish fixed point theorems in the context of cone metric spaces. As an application of our results, periodic point results for the contractive type mappings are proved.

Transcriptome analysis of the harmful alga Heterosigma akashiwo under a 24-hour light-dark cycle

The photoperiod, which is defined as the period of time within a 24-hour time frame that light is available, is an important environmental regulator of several physiological processes in phytoplankton, including harmful bloom-forming phytoplankton. The ichthyotoxic raphidophyte Heterosigma akashiwo is a globally distributed bloom-forming phytoplankton. Despite extensive studies on the ecological impact of H. akashiwo, the influence of the photoperiod on crucial biological processes of this species remains unclear. In this study, gene expression in H. akashiwo was analyzed over a 24-hour light-dark (14:10) treatment period. Approximately 36 % of unigenes in H. akashiwo were differentially expressed during this 24-hour treatment period, which is indicative of their involvement in the response to light-dark variation. Notably, the number of differentially expressed genes exhibited an initial increase followed by a subsequent decrease as the sampling time progressed (T0 vs. other time points). Unigenes associated with photosynthesis and photoprotection reached their peak expression levels after 2–4 h of illumination (T12-T14). In contrast, the expression of unigenes associated with DNA replication peaked at the starting point of the dark period (T0). Furthermore, although several unigenes annotated to photoreceptors displayed potential diel periodicity, genes from various photoreceptor families (such as phytochrome and cryptochrome) showed unique expression patterns. Collectively, our findings offer novel perspectives on the response of H. akashiwo to the light-dark cycle, serving as a valuable resource for investigating the physiology and ecology of this species.

Approximating fixed points of weak enriched contractions using Kirk’s iteration scheme of higher order

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{F}$\\end{document}-contraction, weak enriched F′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{F^{\\prime}}$\\end{document}-contraction, and k-fold averaged mapping based on Kirk’s iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk’s iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature.