Discontinuous Circle Research Articles

A Roundness Detection Algorithm of Non-Standard Discontinuous Circle Based on the Curvature Change of Discrete Edge Points

In the practical application scene of image detection, it is of great significance to detect the circle in the image and judge the roundness of the circle. Because the edges of real objects are often discontinuous due to occlusion, roundness detection of discontinuous circles is a common task. Traditional circle detection algorithms mainly include voting/clustering algorithm based on edge points, optimization algorithm and arc segment-based algorithm. For discontinuous circles, because the integrity of the circle edges is different, the voting results of edge points are difficult to be used as the basis for roundness detection. When the algorithms based on optimization and arc segment detect nonstandard circles, a large number of overlapping misjudgments are easy to occur, and the overlapping of objects before and after will lead to maximum suppression, which is difficult to achieve good results. In this paper, the geometric properties of the circle itself are used to classify the edge points, so that the roundness of the discontinuous circle can be calculated and the size of the circle can be judged. In this paper, taking the photos of mutually blocked round fruits as an example, an algorithm is constructed to detect the roundness of non-standard discontinuous round objects. The results show that this algorithm has a good effect on roundness detection of non-standard discontinuous circles.

The effect of perceptual-motor continuity compatibility on the temporal control of continuous and discontinuous self-paced rhythmic movements.

One of the questions yet to be fully understood is to what extent the properties of the sensory and the movement information interact to facilitate sensorimotor integration. In this study, we examined the relative contribution of the continuity compatibility between motor goals and their sensory outcomes in timing variability. The variability of inter-response intervals was measured in a synchronization-continuation paradigm. Participants performed two repetitive movement tasks whereby they drew circles either using continuous or discontinuous self-paced movements while receiving discrete or continuous auditory feedback. The results demonstrated that the effect of perceptual-motor continuity compatibility may be limited in self-paced auditory-motor synchronization as timing variability was not significantly influenced by the continuity of the feedback or the continuity compatibility between feedback and the movement produced. In addition, results suggested that the presence of salient perceptual events marking the completion of the time intervals elicited a common timing process in both continuous and discontinuous circle drawing, regardless of the continuity of the auditory feedback. These findings open a new line of investigation into the role of the discriminability and reliability of the event-based information in determining the nature of the timing mechanisms engaged in continuous and discontinuous self-paced rhythmic movements.

RESEARCH OF DYNAMIC PHENOMENA OCCURRING DURING INTERMITTENT GRINDING

The purpose of scientific research is to determine the conditions for the creation in the elastic system of useful vibrations that promote self-sharpener the cutting microrelief of the intermittent circle, and the detection of the conditions for appearance the shock and parametric resonances. It was established that with the increase of the circumferential speed of the grinding discontinuous circle VKR, the amplitude of forced oscillations A decreases, and the regions of parametrical stability of the system of the grinding machine are shifted in the direction of decreasing the number of slots n on the working surface of the circle. It has been established that in the studied intervals of numbers of cutting protrusions 5≤n≤40 and the discontinuity factor 0,3≤N≤40, with the decrease of the limb depth of cutting tL, the range of variation of amplitudes of forced oscillations A is narrowed, and the boundaries of the regions of the parametric stability of the system of the machine are expanded. It has been established that in order to maintain the amplitude of the forced oscillations A at a constant level and to prevent the exit from the parametric stability zone of the elastic system, it is necessary, when H- increasing the factor of discontinious N to decrease the number of openings on the discontinious grinding tool. It is established that with the increase in the number of cutting protrusions n in a discontinuous circle, the amplitude of forced oscillations A is decreasing, and the boundaries of the stability regions are expanded. Conditions of discontinuous grinding are found, where in the elastic system of the grinding machine there is no shock and parametric resonance and there is the possibility of self-sharpening of the cutting microrelief of the working surface abrasive tool during its operation.

Investigation of morphological and anatomical underground parts structure of genus Primula L. Cultivated species

Investigation of morphological and anatomical underground parts structure of genus Primula L. Cultivated species

Heat transfer and pressure drop performance of printed circuit heat exchanger with different fin structures

With the development of compact electronic system, the cooling problem with high heat flux in the electronic system has attached much more attention. The high-efficiency cooling devices with micro-channels are investigated and widely used in order to stabilize the surface of the component under the safe temperature. In recent years, a new type of cooler called printed circuit heat exchanger (PCHE), which has characteristics of high heat transfer ability and high compactness, is applied to act the heat sink of devices with high heat flux. The plates of the PCHE are fabricated by photochemical etching method, which can easily process the complex flow channels at low cost. Then, the plates can be stacked and brazed with the diffusion bonding technique in the vacuum circumstance. In this paper, the electronic device with the heat flux of 6.05×105 W/m2 is cooling by water at 25°C and 0.2 MPa. The geometric dimension is 143.2 mm×30 mm and the material is copper. Meanwhile, the heat is original generated from the bottom of the device and the PCHE is fixed on the top of the model to transfer heat. The hydrodynamic and heat transfer performances of PCHEs with different structures of fins are analyzed by numerical method. The models of PCHE with continuous straight fins and discontinuous fins, including the circle fins, ellipse fins, airfoil fins and modified airfoil fins, are constructed. It is worth to point out that the straight model and the circle model are compared in the same cross section area and the other three discontinuous models are compared in the same fin perimeters. Furthermore, the symmetry boundary condition is used in the width direction and the edge effect is neglected according to previous research. The SST k - ω turbulence model assembled in the commercial CFX 12.1 software is validated reasonably to solve the problem in our cases. The result shows that the discontinuous circle fins have better heat transfer performance than the continuous straight fins, which because the fluid can break the boundary layer more effectively with the velocity variation in flow direction. However, the pressure drop also increases in the discontinuous model due to the separated blocks. On the other hand, it can be seen that the Nusselt number increases with the increase of Reynolds number and the gradient become slow, which indicated that it is limited to enhance the heat transfer by increasing the mass flow rate. However, the pressure drop increase exponentially at high Reynolds number. The average Nusselt number of the PCHE with circle fins, ellipse fins, airfoil fins increases 70.2%, 45.5% and 29.1% and the pressure drop also increases 340%, 114% and 40.9%, respectively, comparing with the continuous straight fins. Furthermore, it is found that the PCHE cooler with modified airfoil fins has better comprehensive heat transfer performance, which is based on the heat transfer rate and pressure loss per unit length, especially under the high mass flow rate condition. Comparing with the continuous straight fins, it can be seen that the average Nusselt number increases by 20.2%, and the pump power only increase by 5.6%. It can be concluded that the reduction of pressure loss is the major point for the optimization of the PCHE with discontinuous fins.

Wild oscillations in a nonlinear neuron model with resets: (Ⅱ) Mixed-mode oscillations

This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by which these are generated relies fundamentally on the hybrid structure of the flow: invariant manifolds of the continuous dynamics govern small oscillations, while discrete resets govern the emission of spikes or bursts, contrasting with classical MMO mechanisms in ordinary differential equations involving more than three dimensions and generally relying on a timescale separation. The decomposition of mechanisms reveals the geometrical origin of MMOs, allowing a relatively simple classification of points on the reset manifold associated to specific numbers of small oscillations. We show that the MMO pattern can be described through the study of orbits of a discrete adaptation map, which is singular as it features discrete discontinuities with unbounded left-and right-derivatives. We study orbits of the map via rotation theory for discontinuous circle maps and elucidate in detail complex behaviors arising in the case where MMOs display at most one small oscillation between each consecutive pair of spikes.

Shared Inputs, Entrainment, and Desynchrony in Elliptic Bursters: From Slow Passage to Discontinuous Circle Maps

What input signals will lead to synchrony versus desynchrony in a group of biological oscillators? This question connects with both classical dynamical systems analyses of entrainment and phase locking and with emerging studies of stimulation patterns for controlling neural network activity. Here, we focus on the response of a population of uncoupled, elliptically bursting neurons to a common pulsatile input. We extend a phase reduction from the literature to capture inputs of varied strength, leading to a circle map with discontinuities of various orders. In a combined analytical and numerical approach, we apply our results to both a normal form model for elliptic bursting and to a biophysically based neuron model from the basal ganglia. We find that, depending on the period and amplitude of inputs, the response can appear either chaotic (with provably positive Lyapunov exponent for the associated circle maps) or periodic with a broad range of phase-locked periods. Throughout, we discuss the critical und...

Study on the crystal morphology and melting behavior of isothermally crystallized composites of short carbon fiber and poly(trimethylene terephthalate)

The spherulites of the short carbon fiber(SCF)/poly (trimethylene terephthalate) (PTT) composites formed in limited space at designed temperatures, and their melting behaviors were studied by the polarized optical microscopy, atomic force microscopy (AFM), and scanning electron microscopy (SEM), respectively. The results suggest that SCF content, isothermal crystallization temperatures, and the film thicknesses influence the crystal morphology of the composites. The dimension of the spherulites is decreased with increasing SCF content, but whether banded or nonbanded spherulites will form in the composites is not dependent on SCF content. However, the crystal morphology of the composites depends strongly on the temperature. When the isothermal crystallization temperatures increase from 180°C to 230°C, the crystal morphology of SCF/PTT composites continuously changes in the following order: nonbanded → banded → nonbanded spherulites. Discontinuous circle lines form in the film when the film thickness increases from 30 to 60 μm. Basing on the SEM observation, it is found that these circle lines are cracks formed due to the constriction difference of the different parts of the spherulites. These cracks are formed when the film is cooled from the isothermal crystallization temperature to the room temperature at a slow cooling rate; while they will disappear gradually at different temperatures in the heating process. The crack will appear/disappear first around the center of the spherulite when the film was cooled/heated. The nontwisted or slightly twisted lamellas will reorganize to form highly twisted lamellas inducing apparent banded texture of the spherulites.

Temporal variability in continuous versus discontinuous drawing for children with Developmental Coordination Disorder

Children with Developmental Coordination Disorder (DCD) are reported to have high temporal variability in tasks requiring precise timing. The current study examined whether this timing deficit was due to the cerebellar ‘explicit timing’ process in the discontinuous, but not the continuous movement. Ten children with DCD and 31 typically developing children performed continuous, discontinuous circle and line drawing tasks. Results showed that both children with DCD and their age-matched controls had higher temporal variability in the discontinuous than that in the continuous movements. Individual comparisons between each child with DCD and the performance of typically developing children revealed that 2 out of 10 children with DCD showed limited timing deficit in both types of discontinuous drawing (lines and circles). Additionally, three different children with DCD had timing problems with only discontinuous line drawing. Thus, the possibility of a compromised cerebellar function may exist in a subgroup of children with DCD. This work raises a critical issue with respect to the functional heterogeneity of this population and emphasizes the importance of an individualized analysis in this movement disorder.

Multiple Devil's staircase in a discontinuous circle map

The multiple Devil's staircase, which describes phase-locking behavior, is observed in a discontinuous nonlinear circle map. Phase-locked steps form many towers with similar structure in winding number(W)-parameter(k) space. Each step belongs to a certain period-adding sequence that exists in a smooth curve. The Collision modes that determine steps and the sequence of mode transformations create a variety of tower structures and their particular characteristics. Numerical results suggest a scaling law for the width of phase-locked steps in the period-adding (W=n/(n+i), n,i∈int) sequences, that is, Δk(n)∝n-τ (τ>0). And the study indicates that the multiple Devil's staircase may be common in a class of discontinuous circle maps.

DISSONANCE OF MULTIPLE DEVIL'S STAIRCASES

The multiple Devil's staircase reported by Qu, Wu and He in 1997 was composed of many tower-like structures. Each of which include two branches of the conventional complete Devil's staircases that connect the "single-exit" top and bottom steps. Their analytic conclusion show that all the conventional Devil's staircases are confined by two smooth curves with similar function forms W ∝ 1/ln ∊. These may be addressed as a kind of consonance. Our recent study found that it happens only in a few cases. Actually, in their system, 16 different kinds of tower branches exist in most parts of the parameter space. A lot of the steps lose the consonant property which are the so-called dissonant structures. The number of types of the corresponding dissonant branches is employed to describe the dissonance of the staircase. When the number of the discontinuous regions n, in the system develops, the dissonance of the staircase increases with 2n3- n rule. The numerical result shows that the conclusion is valid for a general discontinuous circle map.

Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps

We extend a few well-known results about orientation preserving homeomorphisms of the circle to orientation preserving circle maps, allowing even an infinite number of discontinuities. We define a set-valued map associated to the lift by filling the gaps in the graph, that shares many properties with continuous functions. Using elementary set-valued analysis, we prove existence and uniqueness of the rotation number, periodic limit orbit in the case when the latter is rational, and Cantor structure of the unique limit set when the rotation number is irrational. Moreover, the rotation number is found to be continuous with respect to the set-valued extension if we endow the space of such maps with the Haussdorff topology on the graph. For increasing continuous families of such maps, the set of parameter values where the rotation number is irrational is a Cantor set (up to a countable number of points).

Neuronal populations with reciprocal inhibition and rebound currents: Effects of synaptic and threshold noise.

The analysis of networks of time-summating binary neural networks is relevant to the study of coherent oscillatory behavior in neuronal populations. A class of networks based on a discrete-time version of leaky integrator networks has recently been extended to include the effects of hyperpolarization-activated inward currents [S. Coombes and S. H. Doole, Dyn. Stability Syst. 11, 193, (1996)]. Suchrebound currents are important for central pattern generation in neuronal circuits with reciprocal inhibition. In this paper, we incorporate models of intrinsic synaptic and threshold noise into the above neural system. The macroscopic behavior of time-summating networks with rebound currents and random thresholds is analyzed in the thermodynamic limit. Mean field equations are derived for the average network activity in a homogeneous network with inhibitory synaptic connections. Periodic and chaotic solutions are shown to exist, together with hysteretic transitions between periodic orbits. This hysteresis is observed between particular periodic orbit branches, as well as more globally with respect to variations in external input or threshold noise. Moreover, rebound currents are shown to suppress chaotic network response to external input, in favor of low order periodic responses, which in turn define well ordered coherent macroscopic oscillatory states for the system. The response characteristic of a single neuron in the presence of synaptic multiplicative noise is also considered and compared to its zero noise limit. In this latter case, the dynamics is reduced to a piecewise linear discontinuous circle map, while the former is expressed in terms of a random iterated function system. \textcopyright{} 1996 The American Physical Society.

Escaping from Strange Sets in Discontinuous Circle Map

The leakage of iterations from chaotic attractor near crisis due to dynamical interaction between discontinuity and noninvertibility has been studied. The scaling law of the mean life time is derived analytically. The numerical result shows very good agreement.

Neuronal population dynamics with post inhibitory rebound:A reduction to piecewise linear discontinuous circle maps

Post inhibitory rebound (PIR) is a nonlinear phenomenon present in a variety of nerve cells. It is an important mechanism underlying central pattern generation for heartbeat, swimming and other motor patterns in many neuronal systems. In this paper, we propose an extension of the binary threshold neuron model to incorporate the effects of PIR. For a single neuron, the dynamics can be described by a piecewise linear circle map with two discontinuities. Both frequency-locking and chaos can occur. The Liapunov exponent of the map is evaluated and used to define transitions between these two distinct types of asymptotic behaviour. Hysteresis between periodic orbits is also observed. A small network of these model neurons, with reciprocal inhibition, is shown to exhibit 'self-sustained' anti-phase oscillations, making PIR a plausible mechanism for central pattern generation in neuronal systems. Unlike coupled oscillator theories, network oscillations emerge naturally as a consequence of the biological description from which the neuronal dynamics is derived. The simplicity of the dynamical model allows for the possibility of large population studies in contrast to other classical models of single neuron dynamics that incorporate active processes

Dynamic interaction between discontinuity and noninvertibility: An analytical study.

A discontinuous and noninvertible circle map is introduced to describe modulated relaxation oscillators. The boundaries of the parameter regions are calculated where images of the jumping gap completely cover the noninvertible region so that the dynamics of the system are abruptly changed. We show that a kind of structure called a ''hole'' may appear due to the interaction between these two competing characteristics and may lead to some dynamic features. The influence of the holes on the boundaries of Arnold tongues is also discussed.

BIFURCATIONS IN A DISCONTINUOUS CIRCLE MAP: A THEORY FOR A CHAOTIC CARDIAC ARRHYTHMIA

The dynamics of discontinuous circle maps are investigated in the context of modulated parasystole, a cardiac arrhythmia in which there is an interaction between normal (sinus) and abnormal (ectopic) pacemaking sites in the heart. A class of noninvertible discontinuous circle maps with slope greater than 1 displays banded chaos under certain conditions. Banded chaos in these maps is characterized by a zero rotation interval width in the presence of a positive Lyapunov exponent. The bifurcations of a simple piecewise linear circle map are investigated. Parameters that result in banded chaos are organized into discrete, nonoverlapping zones in the parameter space. We apply these results to analyze a circle map that models modulated parasystole. Analysis of the model is complicated by the fact that the map has slope less than 1 for part of its domain. However, numerical simulations indicate that the modulated parasystole map displays banded chaos over a wide range of parameters. Banded chaos in this map produces rhythms with a relatively constant sinus-ectopic coupling interval, long trains of uninterrupted sinus beats, and patterns of successive sinus beats between ectopic beats characteristic of those found clinically.

Periodically kicked hard oscillators.

A model of a hard oscillator with analytic solution is presented. Its behavior under periodic kicking, for which a closed form stroboscopic map can be obtained, is studied. It is shown that the general structure of such an oscillator includes four distinct regions; the outer two regions correspond to very small or very large amplitude of the external force and match the corresponding regions in soft oscillators (invertible degree one and degree zero circle maps, respectively). There are two new regions for intermediate amplitude of the forcing. Region 3 corresponds to moderate high forcing, and is intrinsic to hard oscillators; it is characterized by discontinuous circle maps with a flat segment. Region 2 (low moderate forcing) has a certain resemblance to a similar region in soft oscillators (noninvertible degree one circle maps); however, the limit set of the dynamics in this region is not a circle, but a branched manifold, obtained as the tangent union of a circle and an interval; the topological structure of this object is generated by the finite size of the repelling set, and is therefore also intrinsic to hard oscillators.

Neuronal dynamics based on discontinuous circle maps

An analysis is given of the dynamics of binary threshold neurons with extended time-summation and nonlinear threshold activity. It is shown that the dynamics is either trivial or described by circle maps with a single discontinuity. In the latter case both frequency-locking and chaos can occur.

Further studies on the morphology, distribution and ecology ofStephanoscyphus planulophorus (Scyphozoa, Coronata)

The solitary scyphopolypStephanoscyphus planulophorus Werner, 1971 was detected in the submarine caves of the French Mediterranean coast near Marseille, and on the Sorrent Peninsula as well as near the Isle of Ischia (Italy). It was rare at the French sites studied but in the Italian caves of the upper sublittoral it proved fairly abundant. Its life history is unique because (a) the medusa generation is reduced to a transitional embryonic stage, and (b) no germ cells could be traced in any phase. The polyps reared in the laboratory gave rise to several continuous generations. Thus, previous observations on their morphology, distribution and ecology could be completed. Growth and size (defined as length of the peridermal tube) are analyzed, and calculations of the form quotient D/L (D = upper diameter, L = length of tube) are given. Observations on the structure of peridermal teeth which mark the inner wall of the tube in its basal parts indicate that (a) shape is a characteristic of diagnostic value and (b) number and symmetrical arrangement can be described by the formula 4 P + 4 I + 8 A (B; 5–7). A discontinuous circle of whitish pigment spots restricted to the endodermal cells of tentacle bases is another mark of diagnostic value confined to the soft body.S. planulophorus has a bicnidom of holotriches isorhizas and heterotrich microbasic euryteles. Size and distribution of nematocysts are listed for the life-cycle phases. The difference in distribution and population density between the sites near Marseille and Naples can be explained by local differences of water temperature and the thermal requirements of the polyp, the strobilation phase of which is temperature-sensitive. According to the present state of knowledge,S. planulophorus is one of the few true cave-living scyphopolyps. Considering the evolutionary consequences, the particulars of its life cycle can be interpreted as an adaptation to the special habitat conditions. The evolutionary progress of medusa reduction as well as the disadvantage of apogamous propagation are discussed briefly. A diagnosis is given based on the new morphological observations.