Continuous Circle Research Articles

Arbitrary pattern formation on a continuous circle by oblivious robot swarm

In the field of distributed systems, the Arbitrary Pattern Formation (APF) problem is an extensively studied problem. The purpose of APF is to design an algorithm to move a swarm of robots to a particular position in an environment (discrete or continuous) such that the swarm can form a specific but arbitrary pattern given previously to every robot as an input. In this paper, the solvability of the APF problem on a continuous circle is discussed for a swarm of oblivious and silent robots without chirality under a semi-synchronous scheduler. Firstly a class of configurations (the initial placements of the robots on the circle) called Formable Configuration (FC) has been provided which is necessary to solve the APF problem on a continuous circle. Then considering the initial configuration to be an FC, a deterministic and distributed algorithm has been provided that solves the APF problem for n robots on a continuous circle of fixed radius within O(n) epochs without collision, where an epoch is considered to be a time interval in which all robots are activated at least once.

Are generic dynamical properties stable under composition with rotations?

In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving continuous circle maps that are composed with independent rotations on each of the sides. In particular, we analyze the stability of the locally eventually onto and measure-theoretic mixing properties.

The future of Black Theology of Liberation: Narrative as epistemological resource

The death of Black Theology of Liberation (BTL) has been announced, and many were invited to the funeral. This article rejects vehemently such a death as a myth, and provides two reasons why such a theology would have a place to address theologising in the world. It firstly argues that BTL attributes its birth through stories. These stories are captured in history; embodied stories that are told. Secondly, it is found in a broader epistemology than that provided by the Enlightenment paradigm. Therefore, it is not only found in conceptual, argumentative discourses, but other forms of knowledge systems, including stories, poetry, and personal storytelling. However, this has still not been equally appreciated and explored. Taking the above two reasons into account, the death of BTL cannot be announced by academics, since they were never the sole custodians thereof, only recipients of the tradition of an oppressed people.Intradisciplinary and/or interdisciplinary implications: The article has implications for how theology is being done in all theology-related disciplines, moving from context, to scripture, to context in a continuous hermeneutical circle. It addresses the way in which all theological disciplines have been functioning within the Enlightenment paradigm, and how black theology itself has lent itself to it, but is continually reforming, because of its nature to be narrative in its approach.

Visual Feedback Decoding During Bimanual Circle Drawing.

The between-hand interference during bimanual tasks is a consequence of the connection between the neural controllers of movement. Previous studies showed the existence of an asymmetric between-hand interference (caused by neural crosstalk) when different kinematics plans were to be executed by each hand or when only one was visually guided and received perturbed visual feedback. Here, in continuous bimanual circle drawing tasks, we investigated if the central nervous system (CNS) can benefit from visual composite feedback, i.e., a weighted sum of hands' positions presented for the visually-guided hand, to control the non-visible hand. Our results demonstrated improvement in the non-visible non-dominant hand (NDH) performance in the presence of the composite feedback. When NDH was visually guided, the dominant hand's (DH) performance during asymmetric drawing deteriorated, while its performance during symmetric drawing improved. This indicates that the CNS's ability to leverage composite feedback, which can be the result of decoding the non-visible hand positional information from the composite feedback, is task-dependent and can be asymmetric. Also, the non-visible hand's performance degraded when DH or NDH was visually guided with amplified error feedback. The results of the amplified feedback condition do not strongly support the asymmetry of the interference during asymmetric circle drawing. Comparing muscle activations in the asymmetric experiment, we concluded that the observed kinematic differences were not due to alternation in muscle co-contractions.

In-plane crushing response and energy absorption of two different arranged circular honeycombs

Circular honeycombs have been widely used in many fields due to their excellent mechanical properties recently, however, circular honeycombs with different arrangements have been rarely studied. In this paper, two circular honeycombs with different arrangements were designed and fabricated using a 3D printer. Both honeycombs were investigated by experiment and finite element (FE) analysis to compare their performance. It is worth noting that both honeycombs possess the same relative density. The accuracy of the FE models was validated by comparing them with experimental results and relevant reports. Subsequently, a series of numerical studies were conducted to analyse the in-plane dynamic crushing behaviour and energy absorption characteristics at different impact velocities. Based on different experiment deformation modes were identified from the observation of results respectively. Additionally, continuous circle honeycomb (CCH) exhibits a higher reaction force but is prone to fracture. On the other hand, spacing circle honeycomb (SCH) possesses a lower reaction force but offers greater stability due to its ability to flex and release force. As a result, SCH can effectively absorb energy and demonstrates superior crushing capacity compared to CCH. To investigate and compare the plateau stress and energy absorption of these honeycombs, the FE method was used, which also involved a detailed analysis of the impact velocity and relative density of the honeycomb. It was observed that the crushing stress and energy absorption of SCH were higher than those of CCH with the same impact velocity and relative density. According to the one dimensional shock wave theory, empirical formulas for two circular honeycombs to predict the plateau stress are given respectively with the maximum error lower than 12%. This paper aims to offer valuable insights for the design of different configurations, with the goal of improving the crashworthiness and energy absorption capacity of a specific honeycomb structure.

Artificial Intelligence: From Talos to da Vinci

Artificial Intelligence: From Talos to da Vinci

Topological entropy of induced circle maps on hyperspaces

In this paper, we show on some aspects of the structures of ω-limit sets of the set-valued extensions of continuous circle maps. Next, we prove that topological entropies of every circle map and its set-valued extension agree.

Generalizing the German Tank Problem

The German Tank Problem dates back to World War II when the Allies used a statistical approach to estimate the number of enemy tanks produced or on the field from observed serial numbers after battles. Assuming that the tanks are labeled consecutively starting from 1, if we observe k tanks from a total of N tanks with the maximum observed tank being m, then the best estimate for N is m(1 + 1/k) - 1. We refer to an estimate as "best" when the estimate is closest to the actual number of tanks. We explore many generalizations; first, we looked at the discrete and continuous one-dimensional case. We attempted to improve the original formula by using different estimators such as the second largest and Lth largest tank, and applied motivation from portfolio theory by seeing if a weighted average of different estimators would produce less variance; however, the original formula, using the largest tank proved to be the best; the continuous case was similar. Then, we looked at the discrete and continuous square and circle variants where we pick pairs instead of points, which were more complex as we dealt with problems in geometry and number theory, such as dealing with curvature issues in the circle, and the problem that not every number is representable as a sum of two squares. In some cases, when we could not derive precise formulas, we derived approximate formulas. For the discrete and continuous square, we tested various statistics, but found that the largest observed component of our pairs is the best statistic to look at; the scaling factor for both cases is (2k+1)/2k. For the circle we used motivation from the equation of a circle; for the continuous case, we looked at the square root of X2+Y2 and for the discrete case, we looked at X2+Y2 and took a square root at the end to estimate for r. Interestingly, the scaling factors, a number, generally a little greater than 1, that we multiplied to scale up to get our estimation, were different for the cases. Lastly, we generalized the problem into L-dimensional squares and circles. The discrete and continuous square proved to be similar to the two-dimensional square problem. However, for the Lth dimensional circle, we had to use formulas for the volume of the L-ball, and had to approximate the number of lattice points inside it. The discrete circle formula was particularly interesting, as there was no L dependence in the formula.

Luzin’s Problem on Fourier Convergence and Homeomorphisms

We show that for every continuous function $$f$$ there exists an absolutely continuous circle homeomorphism $$\phi$$ such that the Fourier series of $$f\circ\phi$$ converges uniformly. This resolves a problem posed by N. N. Luzin.

Development of Microstrip Decimeter Antennas with Circular Polarization

Modern design variants of microstrip antennas with circular polarization are considered, in which circular polarization is created using single-point and two-point power supply. To manufacture the studied antenna model with circular polarization, the simplest form of the antenna was chosen; the one with a radiator in the form of a continuous circle, which is powered by a two-point scheme. With regard to use in intra-object telemetry systems, the frequency of operation range of 640 ... 650 MHz was chosen. Two options for a two-point power supply of such an antenna were studied - with the help of a symmetrical and asymmetric square strip bridge. Calculation, coordination and tuning simulation of power divider variants were performed. As a result, the manufactured layout of the first antenna design turned out to be three-layered, the second - two-layered. The technique for creating antennas includes an estimated calculation of geometric dimensions, which was further refined using computer simulation in the CST Microwave Studio program. Frequency tuning of the completed antenna layouts is carried out using adjusting teeth along the contour of the round radiator. The study of the created antenna layouts showed better manufacturability and stability of the characteristics of a two-layer structure compared to a three-layer one. Therefore, a two-layer round antenna with a point-to-point power supply was chosen for production. It is designed for telemetric radio channels inside enclosed spaces. The measurements performed showed that the manufactured antenna operates in right-hand circular polarization with an ellipticity factor of 1.2 dB. The standing wave ratio in the operating frequency band of 640…650 MHz did not exceed 1.32, the gain was at least 5 dBi, the width of the radiation patterns in two planes was 95 and 93 angular degrees, respectively. The antenna provides for an operation mode as a transceiver, since the decoupling of the receiving and transmitting paths is carried out due to different polarization, for which it is necessary to connect the second input of the power divider instead of a balanced resistor to the receiving device.

Visual encoder-based angle measurement method in low-frequency angular vibration calibration.

Angular vibration calibration is required to determine the sensitivity of sensors such as dynamic inclinometers, gyroscopes, and angular accelerometers, which are used for angular motion measurement in engineering applications. Additionally, the calibration performance depends on the accuracy of the angle measurement by laser interferometry or a circular grating (CG) method that is commonly used in vibration calibration. However, these methods usually own a complex and high-cost system or limited frequency and amplitude ranges. In this study, a novel, to the best of our knowledge, angle measurement method that combines a special visual encoder and an accurate angular position detection method is investigated; the method requires only a simple and flexible telecentric vision measurement system. Comparison experiments with the CG method demonstrate that the investigated method has the maximum measurement deviation of 0.0014° and 0.0138° for static angle measurement in the small-angle range and continuous full circle, respectively. The relative deviation of the angular vibration measurement in the range of 0.1-8 Hz with amplitudes 0-100° is less than 0.173%. Additionally, the relative deviation of calibrated sensitivity of a gyroscope by the investigated and CG methods is less than 0.096%.

Sufi turning and the spirituality of sacred space

ABSTRACT Sufism, the mystical dimension of Islam, has long included in its sema/sama – the worship ceremony – animated practices and performances, notably the use of sound and movement to express spiritual states, which is not favored by more traditional/conventional denominations of Islam. Sufis encourage song and chant, dance and movement, and other demonstrative exhibitions of faith, as palpable demonstrations of ecstatic love and spiritual joy in communion with the Divine. One of the most notable Sufis in the history of Islam is Jalaluddin Rumi (CE 1207–1273) – or, simply, Rumi – who founded a Sufi order known popularly as the Whirling Dervishes. The dervishes adhere to a meditative practice that Rumi encouraged as part of the sema/sama, the ‘dance’ of whirling, or turning. Sufi turning is a devotional expression of dhikr, the remembrance and contemplation of God. This essay discusses how the entranced spinning of the deliberately structured Sufi body (head, hands, arms, torso) can transform a secular/profane place into a space of mystical encounter with the Divine as the dervish whirls in continuous circles around the invisible axis that binds the Sufi to Allah. The essay will draw on the poetry and prose of Rumi to illustrate the transformation of indeterminate place to sanctified space.

Traumatic intraocular lens ectopia from a nonadhesive capsule

Introduction: This study describes a case of traumatic intraocular lens (IOL) ectopia with retention in the pupil that occurred 2 years after cataract surgery. Patient and Clinical Findings: A 55-year-old man, who underwent cataract surgery 2 years ago, sustained an ocular injury while slapping a bug on the left eyelid, following which he had decreased vision. His IOL shifted out of the capsule and was retained in the pupil. Diagnosis, Intervention, and Outcomes: The patient was diagnosed with IOL ectopia with retention in the pupil. An IOL reposition operation was performed successfully. The IOL was completely returned into the capsule, and postoperatively, his uncorrected distance visual acuity immediately improved to 0.097 logMAR. Conclusions: An IOL could slide out of the nonadhesive capsule under external force even if the capsulorhexis is performed perfectly with a continuous curvilinear circle at the center and the anterior capsule covers the IOL optical surface.

ρ-bounded orbits and Arnold tongues for quasiperiodically forced circle maps* *Supported by the National Natural Science Foundation of China (11771316, 11790274 and 12171347).

For quasiperiodically forced (qpf) continuous circle maps with degree one, the set of fibred rotation numbers is a closed interval or a singleton. We show in this paper that if a number ρ is in the interior of this interval, then there exist ρ-bounded orbits. We also discuss extensions of the structure of Arnold tongues for qpf circle homeomorphisms to qpf continuous circle maps with degree one.

Inflammation in Asthma Pathogenesis: Role of T Cells, Macrophages, Epithelial Cells and Type 2 Inflammation.

Asthma is a chronic disease with abnormal inflammatory and immunological responses. The disease initiates by antigens in subjects with genetic susceptibility. However, environmental factors play a role in the initiation and exacerbation of asthma attack. Asthma is a T-helper 2 (Th2)-cell-mediated disease. Recent studies indicate that asthma is not a single disease entity, but it occurs with multiple phenotypes and endotypes. The pathophysiological changes in asthma include a series of continuous vicious circles of cellular activation contributing to the induction of chemokines and cytokines that potentiate inflammation. The heterogeneity of asthma influences the treatment response. The asthma pathogenesis is driven by varied sets of cells, such as eosinophils, basophils, neutrophils, macrophages, epithelial cells, and T cells. Macrophages induce a set of mediators that are involved in asthma pathogenesis and include MIF, Prostaglandin, CXCR3L, IL-12, IL-1ß, TSLP, IL-18, IL-33, LTC4, MMP-2, TNF-α, IL-17, IL-10, TGF-ß and IL-27. While, T-cells mediators effect in asthma is induced via TNF-α, IL-17, IL-10, TGF-ß, IL-27, Tim, GM-CSF, IL-2, IL-4, IL-13, INF- γ, and PPAR γ. However, the epithelial cells induced mediators potentiate proinflammatory effects, increase the number of Th2 cells, activate dendritic cells, increase the number of mast cells, and recruit eosinophils, basophils, neutrophils, T-cells, monocytes and dendritic cells. In this review, the role of T cells, macrophages, and epithelial cells is discussed.

S-limit shadowing is generic for continuous Lebesgue measure-preserving circle maps

AbstractIn this paper we show that generic continuous Lebesgue measure-preserving circle maps have the s-limit shadowing property. In addition, we obtain that s-limit shadowing is a generic property also for continuous circle maps. In particular, this implies that classical shadowing, periodic shadowing and limit shadowing are generic in these two settings as well.

Radiofrequency pulmonary vein isolation using catheter dragging technique guided by grid annotation vs. point-by-point technique guided by Ablation Index: a randomized controlled trial

Abstract Background Pulmonary vein isolation (PVI) with radiofrequency (RF) ablation is an important treatment option in symptomatic atrial fibrillation (AF) patients. Ablation Index (AI) has recently attracted considerable interest as a guide for PVI procedures and combines contact force, RF application time and ablation power into a single metric. A limitation of ablation strategies guided by AI is the impossibility to use a catheter dragging technique. Although comparative studies are sparse, ablation using a catheter dragging technique may shorten procedural duration and improve PVI durability by creating uninterrupted linear ablation lesions. These ablation lesions can be visualized by a grid (grid annotation), which may provide valuable information on both lesion depth and lesion contiguity. We compared an AF ablation approach guided by grid annotation, with a point-by-point AI annotation approach in a single-center randomized study. Methods Eighty-eight patients with paroxysmal or persistent AF were randomized 1:1 to undergo RF-PVI guided by either grid annotation or AI annotation. In the grid annotation arm, ablation was visualized using automatic generation of 1mm3 grid points projected on the electroanatomic map, with grid points coloring red after 15 seconds of ablation while meeting predefined stability and contact force criteria. Ablation was performed aiming for a continuous circle of red grid points. In the AI annotation arm, ablation was visualized using automatically generated lesion tags with a diameter of 3 mm. AI target values were set at 380 and 500 for posterior/inferior and anterior/roof segments, respectively. Ablation lesions were created in a point-by-point fashion, aiming for a maximum interlesion distance of 6 mm. All study participants were followed up for 12 months after PVI using out-patient clinic visits, ECGs, 24-hour Holter monitoring and a mobile-based one-lead ECG device to assess heart rhythm when symptoms suggestive of an arrhythmia occurred. Results The primary endpoint of procedure time was not different between the two randomization arms (grid annotation 71±19 min, AI annotation 72±26 min, p=0.765, Figure 1A). RF time was significantly longer in the grid annotation arm compared with the AI annotation arm (49±8 min vs. 37±8 min, respectively, p<0.001). Neither fluoroscopy time or radiation dose were different between the randomization arms. All patients completed 12 months of follow-up and recurrent atrial tachyarrhythmias were observed in 29 patients (33%). Recurrence of any atrial tachyarrhythmia was documented in 10 patients (23%) in the grid annotation arm compared with 19 patients (42%) in the AI annotation arm, which did not reach statistical significance by log-rank test (p=0.074, Figure 1B). Conclusions Findings from this randomized controlled study suggest that grid annotation may provide an alternative approach for RF-PVI using AI, allowing for ablation with the catheter dragging technique. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Biosense Webster, Inc. Figure 1

Marxism in Zakia Mashhadi's Death of an Insect

Poverty is the root cause of exploitation of the poor at the hands of the rich in the root structure of the society that leads the poor towards the state of self-pity. This study is an interlink between the domains of World Englishes, Freudo-Marxist Literature, Trauma Literature and Postcolonial Literature. The postcolonial context of the subcontinent amidst language appropriation is the major theme that witnesses the phenomenon of exploitation and poverty through the canvas of Freudo-Marxist Literature. The current study attempts to find Marxist themes, predominantly exploitation and poverty, from a short story Death of an Insect by Zakia Mashhadi. The textual qualitative method of analysis proceeds under the operational theoretical lens of Edgar W. Schneider and Karl Marx. The former deals with textual analysis through language appropriation, while the latter deals with thematic analysis through the behaviour of the bourgeoisie towards the proletariat, respectively. The study has found that the upper class, for their vested interests, even for the satisfaction of their ego, brutally exploit the poor working class, who have to suffer and bear all inhuman behaviour without any resistance. Thus, this continuous Vicious Circle of exploitation and poverty cause difficulties and hardships for the poor class.

Impact of domestic violence against pregnant women in Minia governorate, Egypt: a cross sectional study

BackgroundDomestic violence is a common problem that is related to many serious short-term and long-term health hazards around the world.MethodsDuring obtaining the medical history from the participants, the questions used to assess the abuse were derived from the widely used Abuse Assessment Screen (AAS). Potential risk factors including a variety of socio-demographic and reproductive health-relation indicators were assessed. The influence of violence on the pregnancy outcome was determined by the continuous follow-up till giving birth.Results513 pregnant women were included. The prevalence of violence among them was 50.8%. The prevalence of physical, sexual, verbal, and emotional abuse was 30.2, 20, 41.7, and 45.4% respectively. Exposure to violence during pregnancy had significant effects on the women and their pregnancy outcome in the form of development of vaginal infection (P-value =0.036), vaginal bleeding (P-value = 0.008), preterm labour (P-value = 0.003), premature rupture of membrane (P-value = 0.001).ConclusionViolence against pregnant women in Minia Governorate, Egypt is common especially emotional violence and it has many adverse effects on the women and their pregnancy outcome. One of the most important risk factors is the fear of the husband which makes violence a continuous vicious circle.

Continuous crop circles drawn by Riemann's zeta function

Let η(s)=∑n=1∞(−1)n+1n−s be the alternating zeta function. For a real number τ we define certain complex numbers bM,m(τ) and consider finite Dirichlet series υM(τ,s)=∑m=1MbM,m(τ)m−s and ηN(τ,s)=∑M=1NυM(τ,s). Computations demonstrate some remarkable properties of these finite Dirichlet series, but nothing was supported by a proof so far.First, numerical data show that ηN(τ,s) approximates η(s) with high accuracy for s in the vicinity of 1/2+iτ; this allows one to surmise that(*)η(s)=∑M=1∞υM(τ,s). Moreover, it looks thatlimM→∞⁡mυM(τ,1−σ+it)‾mυM(τ,σ+it)=η(σ+it)mη(1−σ+it)‾m; in other words, the individual summands in expected expansion (⁎) satisfy with an increasing accuracy a counterpart of the classical functional equation.Let ϒM(τ,σ+it)=υM(τ,σ+it)/η(σ+it). When M, τ, and either σ or t are fixed, and the fourth parameter varies, the plot of ϒM(τ,σ+it) on the complex plane contains numerous almost ideally circular arcs with geometrical parameters closely related to the non-trivial zeros of the zeta function.