Irregular Sequences Research Articles

Integer quantum Hall effect in graphene channel with p-n junction at domain wall in a strained ferroelectric film

We revealed that 180° domain walls in a strained ferroelectric film can induce p-n junctions in a graphene channel and lead to the nontrivial temperature and gate voltage dependences of the perpendicular modes of the integer quantum Hall effect (IQHE). In particular, the number of perpendicular modes v⊥, corresponding to the p-n junction across the graphene channel, varies with the gate voltage increase from small integers to higher non-integer numbers, e.g., v⊥ = 1.9, 2, …, 5.1, 6.875, …, 9.1, …, 23,…, 37.4, in the vicinity of the transition temperature from the ferroelectric to paraelectric phase. The non-integer numbers and their irregular sequence principally differ from the sequence of non-integer numbers ν = 3/2, 5/3, … reported earlier. The unusual v⊥-numbers originate from significantly different numbers of the edge modes, ν1 and ν2, corresponding to different concentrations of carriers in the left (n1) and right (n2) domains of the p-n junction boundary. The concentrations n1 and n2 are determined by the gate voltage and spontaneous polarization contributions, and so their difference originates from different directions of the spontaneous polarization in different domains of the strained ferroelectric film. The difference between n1 and n2 disappears with the vanishing of the film spontaneous polarization in a paraelectric phase. The temperature transition from the ferroelectric to paraelectric phase taking place in a strained ferroelectric film can be varied in a wide temperature range by an appropriate choice of misfit strain so that the first plateaus of the predicted IQHE effect can be observed even at room temperatures.

DETERMINISTIC IDENTIFICATION METHODS FOR NONLINEAR DYNAMICALSYSTEMS BASED ON THEVOLTERRA MODEL

The paper solves an important scientific and practical problem, which is to improve the accuracy and computational stability of the methods of deterministic identification of nonlinear dynamic systems in the form of Volterra model based on experimental data of observations ”input-output” taking. On the base of theoretical and experimental studies created effective instrumental algorithmic and software tools for estimating Volterra kernels in the time domain Into account measurement errors. Results of the further development of methods of deterministic identification of nonlinear dynamic systems based on Volterra models using irregular pulse sequences show. The methods are based on the use of the Tikhonov regularization procedure. The amplitude of test impulses is used as a regularization parameter. In the identification, procedure applies wavelet filtering for smooth the estimates of the Volterra kernels apply. This gives increase the accuracy and noise immunity of identification methods. The approximation method of identification of the nonlinear dynamic systems based on Volterra models is improved. Method is consists in the choice of amplitudes of test signals and of coefficients scaling of the partial components of responses a nonlinear system in procedure of processing of signals-responses. The improvement is reduced to minimizing the methodological error in the allocation of partial components from the response of the identification object and allows obtaining more accurate estimates of Volterra nuclei. To improve the computational stability of the developed identification algorithms and for noise reduction in the obtained estimates of multidimensional Volterra kernels the wavelet filtration is used. This allows obtaining smoothed solutions and decreases error of the identification by 1,5-2,5 times. A new robust method of deterministic identification of nonlinear dynamic systems based on Volterra models in the time domain is developed. In contrast to the interpolation method, where finite difference formulas with a predetermined number of experimental studies of the object of identification are used for numerical differentiation. It is proposed to solve the corresponding Volterra integral equations of the first kind, for the numerical implementation of which an unlimited number of experiments can be used. This makes it possible to increase the accuracy of the calculation of derivatives, and consequently, the accuracy of identification. Software tools on the system Matlab platform have been developed to implement the developed computational algorithms for deterministic identification of nonlinear dynamic systems in the form of Volterra kernels.

Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs.

Since 1997 a considerable effort has been spent on the study of the swap (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and Sfragara published a breakthrough paper about irregular normal and directed degree sequences for which rapid mixing of the swap Markov chain is proved. In this paper we present two groups of results. An example from the first group is the following theorem: let be a directed degree sequence on n vertices. Denote by Δ the maximum value among all in- and out-degrees and denote by the number of edges in the realization. Assume furthermore that . Then the swap Markov chain on the realizations of is rapidly mixing. This result is a slight improvement on one of the results of Greenhill and Sfragara. An example from the second group is the following: let d be a bipartite degree sequence on the vertex set U ⊎ V, and let 0 < c1 ≤ c2 < |U| and 0 < d1 ≤ d2 < |V| be integers, where c1 ≤ d(v) ≤ c2: ∀v ∈ V and d1 ≤ d(u) ≤ d2: ∀u ∈ U. Furthermore assume that (c2 − c1 − 1)(d2 − d1 − 1) < max{c1(|V| − d2), d1(|U| − c2)}. Then the swap Markov chain on the realizations of d is rapidly mixing. A straightforward application of this latter result shows that when a random bipartite or directed graph is generated under the Erdős—Rényi G(n, p) model with mild assumptions on n and p then the degree sequence of the generated graph has, with high probability, a rapidly mixing swap Markov chain on its realizations.

New evidence of a rhythmic priming effect that enhances grammaticality judgments in children

Musical rhythm and the grammatical structure of language share a surprising number of characteristics that may be intrinsically related in child development. The current study aimed to understand the potential influence of musical rhythmic priming on subsequent spoken grammar task performance in children with typical development who were native speakers of English. Participants (ages 5–8 years) listened to rhythmically regular and irregular musical sequences (within-participants design) followed by blocks of grammatically correct and incorrect sentences upon which they were asked to perform a grammaticality judgment task. Rhythmically regular musical sequences improved performance in grammaticality judgment compared with rhythmically irregular musical sequences. No such effect of rhythmic priming was found in two nonlinguistic control tasks, suggesting a neural overlap between rhythm processing and mechanisms recruited during grammar processing. These findings build on previous research investigating the effect of rhythmic priming by extending the paradigm to a different language, testing a younger population, and employing nonlanguage control tasks. These findings of an immediate influence of rhythm on grammar states (temporarily augmented grammaticality judgment performance) also converge with previous findings of associations between rhythm and grammar traits (stable generalized grammar abilities) in children. Taken together, the results of this study provide additional evidence for shared neural processing for language and music and warrant future investigations of potentially beneficial effects of innovative musical material on language processing.

Thermal Conductivity Reduction at Inorganic–Organic Interfaces: From Regular Superlattices to Irregular Gradient Layer Sequences

AbstractNanoscale superlattice structures are known to significantly suppress the thermal conductivity in thin films due to phonon scattering at the interfaces of the mutually different layers. Here it is demonstrated that in addition to the number of interfaces, their spacing within the film can lead to a reduction in thermal conductivity. The proof‐of‐concept data are for ZnO/benzene thin films fabricated through sequential gas‐surface reactions in atomic/molecular layer precision using the atomic/molecular layer deposition technique. In comparison to similarly constructed regular superlattice thin films, thermal conductivity values that are of the same magnitude, or even lower, are achieved for hybrid ZnO/benzene thin films in which the inorganic and organic layers are arranged in a more irregular manner to form various gradient patterns.

The effects of regularity of simulated ship motions on the behaviour and physiology of sheep

Floor movement influences sheep responses to transport, but the importance of movement regularity and interactions between sheep are unknown. To test this, sheep were restrained in pairs in a crate mounted on a moveable, programmable platform for 60 min periods, changing treatments over 12 consecutive days. In an initial experiment a repeated speed of movement and change in angle (regular movement) was compared to variable angles and speeds (irregular movement) of roll, pitch or combined movements, for sheep behaviour, heart rate and feed and water intake responses. Feed intake was increased by irregular roll+pitch motion (P = 0.04). During irregular sequences sheep affiliated more, with their heads one above the other (P = 0.001) and supported themselves against the crate (P < 0.001) or kneeling (P = 0.03). Irregular sequences and combined roll and pitch synergistically increased stepping behaviour, indicating loss of balance, and heart rate, possibly indicating stress (P < 0.001). Heat rate data demonstrated that the RMSSD band was reduced during irregular movement (P = 0.04), and LF/HF ratio increased during irregular sequences of roll+pitch (P = 0.007), suggesting less parasympathetic nervous system activity. In a second experiment, we investigated the effects of these floor motion patterns with and without a barrier to separate the sheep. With no barrier or irregular motion, sheep stepped more to avoid loss of balance (P < 0.001) and were again more affiliative. During irregular motion they supported themselves more against the crate (P < 0.001). With no barrier there was more agonistic behaviour (body pushing (P = 0.02), butting (P = 0.02) and evading the other sheep (P = 0.001) and less rumination (P = 0.02), which together with a reduction in RMSSD and NN50 suggested that sheep welfare was reduced by the close proximity of the other sheep. The ratio of low to high frequency beats was highest (P = 0.005) and the RMSSD and NN50 were lowest (P < 0.001) during irregular motion and no barrier. Evidence is provided that sheep were both more stressed in this combination of treatments and also exercising more, through stepping behaviour. Thus irregular sequences and combined roll and pitch caused stress and increased activity to correct loss of balance, as well as increased affiliative behaviour. Separating sheep during irregular motion reduced body instability and stress, suggesting that close stocking is detrimental to their welfare.

Full Dimensional Sets of Reals Whose Sums of Partial Quotients Increase in Certain Speed

For a real x∈(0,1)∖Q, let x=[a1(x),a2(x),⋯] be its continued fraction expansion. Let sn(x)=∑j=1naj(x). The Hausdorff dimensions of the level setsEφ(n),α:={x∈(0,1):limn→∞⁡sn(x)φ(n)=α} for α≥0 and a non-decreasing sequence {φ(n)}n=1∞ have been studied by E. Cesaratto, B. Vallée, J. Wu, J. Xu, G. Iommi, T. Jordan, L. Liao, M. Rams et al. In this work we carry out a kind of inverse project of their work, that is, we consider the conditions on φ(n) under which one can expect a 1-dimensional set Eφ(n),α. We give certain upper and lower bounds on the increasing speed of φ(n) when Eφ(n),α is of Hausdorff dimension 1 and a new class of sequences {φ(n)}n=1∞ such that Eφ(n),α is of full dimension. For an irregular sequence {φ(n)}n=1∞, a full dimensional set Eφ(n),α is impossible.

Detection of repetitive and irregular hypercall attacks from guest virtual machines to Xen hypervisor

Virtualization is critical to the infrastructure of cloud computing environment and other online services. Hypercall interface is provided by hypervisor to offer privileged requests by the guest domains. Attackers may use this interface to send malicious hypercalls. In the reported work, repetitive hypercall attacks and sending hypercalls within irregular sequences to Xen hypervisor were analyzed, and finally, an intrusion detection system (IDS) is proposed to detect these attacks. The proposed system is placed in the host domain (Dom0). Monitoring hypercalls traffic the system operates based on the identification of irregular behaviors in hypercalls sent from guest domains to hypervisor. Later on, the association rule algorithm is applied on the collected data within a fixed time window, and a set of thresholds for maximum number of all types of the hypercalls is extracted. The results from the implementation of the proposed system show 91% true positive rate.

The Role of Place Cues in Voluntary Stream Segregation for Cochlear Implant Users.

Sequential stream segregation by cochlear implant (CI) listeners was investigated using a temporal delay detection task composed of a sequence of regularly presented bursts of pulses on a single electrode (B) interleaved with an irregular sequence (A) presented on a different electrode. In half of the trials, a delay was added to the last burst of the regular B sequence, and the listeners were asked to detect this delay. As a jitter was added to the period between consecutive A bursts, time judgments between the A and B sequences provided an unreliable cue to perform the task. Thus, the segregation of the A and B sequences should improve performance. In Experiment 1, the electrode separation and the sequence duration were varied to clarify whether place cues help CI listeners to voluntarily segregate sounds and whether a two-stream percept needs time to build up. Results suggested that place cues can facilitate the segregation of sequential sounds if enough time is provided to build up a two-stream percept. In Experiment 2, the duration of the sequence was fixed, and only the electrode separation was varied to estimate the fission boundary. Most listeners were able to segregate the sounds for separations of three or more electrodes, and some listeners could segregate sounds coming from adjacent electrodes.

Estabilidad de las obras civiles en la corona del Malecón Costanera, Distrito San Miguel - Lima

This study indicates the causes that determined the prematural deterioration of the civil work, located on the waterfront of the Malecón La Costanera section Av. Universidad Av. Rafael Escardo San Miguel LIMA, confirms the work did not meet its useful period guaranteed by the Constructor consortium , part of it was made on an uncontrolled landfill, verified with pits, geological mapping and the erosion caused by the marine dynamics, add the calculations made by using the numerical results of the tests and analyzes carried out in the UNI. Application of the Terzaghi formula and the Monobe Okabe method. Support of the recommendations given in the responsibilities matrix.The work in 80% was built on a surface obtained on uncontrolled landfill (dump, formed by solid waste from civil works made in the Lima megalopolis), the difference is on a surface of a natural soil, formed by silts, sands, gravels , pebbles and peat of irregular sequence given by layer on layer with little cementing material (clays), process occurred in hundreds of years, has good packaging. Load resistance&gt; 3 kg / cm2.The layers of soil in fan is the result of different cumulative stages given in the dump from the expansion, modernization and urban vertical growth of Lima. Decade 1980 - 203 (constructive boon). This soil has low packing, carrying capacity qa = 1.7 kgs / cm2. [Terzaghi] Indicator that will rise if it is dosed with clayey soil, affirmed, cultivation soil, or grout oxide of cement or lime is injected, which will give optimum compression behavior (roller), thus stabilize the uncontrolled filling, the cementing material will be in a ratio of 2 / 10m3, process that will form a floor folder with loan material, which will be 2m thick in the five failed sectors [fault plane], the use of excess water in the crown of the embankment slope accelerates the local circular faults.To be installed on the stable or stepped stable slope 62% = 28º, xerophilous vegetation, crossula sp, cacti, grasses variety ray grass poaceae, schinus molle, shrubs and trees, the civil works will fulfill their useful period. It is indicated that the edge of the beach in this sector requires protection by constructing two groynes or perimetric collar based on silicified andesite rocks.

Auditory-motor coupling affects phonetic encoding

Recent studies have shown that moving in synchrony with auditory stimuli boosts attention allocation and verbal learning. Furthermore rhythmic tones are processed more efficiently than temporally random tones ('timing effect'), and this effect is increased when participants actively synchronize their motor performance with the rhythm of the tones, resulting in auditory-motor synchronization.Here, we investigated whether this applies also to sequences of linguistic stimuli (syllables). We compared temporally irregular syllable sequences with two temporally regular conditions where either the interval between syllable onsets (stimulus onset asynchrony, SOA) or the interval between the syllables’ vowel onsets was kept constant. Entrainment to the stimulus presentation frequency (1 Hz) and event-related potentials were assessed in 24 adults who were instructed to detect pre-defined deviant syllables while they either pedaled or sat still on a stationary exercise bike.We found larger 1 Hz entrainment and P300 amplitudes for the SOA presentation during motor activity. Furthermore, the magnitude of the P300 component correlated with the motor variability in the SOA condition and 1 Hz entrainment, while in turn 1 Hz entrainment correlated with auditory-motor synchronization performance. These findings demonstrate that acute auditory-motor coupling facilitates phonetic encoding.

New Classes of Degree Sequences with Fast Mixing Swap Markov Chain Sampling

In network modelling of complex systems one is often required to sample random realizations of networks that obey a given set of constraints, usually in the form of graph measures. A much studied class of problems targets uniform sampling of simple graphs with given degree sequence or also with given degree correlations expressed in the form of a Joint Degree Matrix. One approach is to use Markov chains based on edge switches (swaps) that preserve the constraints, are irreducible (ergodic) and fast mixing. In 1999, Kannan, Tetali and Vempala (KTV) proposed a simple swap Markov chain for sampling graphs with given degree sequence, and conjectured that it mixes rapidly (in polynomial time) for arbitrary degree sequences. Although the conjecture is still open, it has been proved for special degree sequences, in particular for those of undirected and directed regular simple graphs, half-regular bipartite graphs, and graphs with certain bounded maximum degrees. Here we prove the fast mixing KTV conjecture for novel, exponentially large classes of irregular degree sequences. Our method is based on a canonical decomposition of degree sequences into split graph degree sequences, a structural theorem for the space of graph realizations and on a factorization theorem for Markov chains. After introducing bipartite ‘splitted’ degree sequences, we also generalize the canonical split graph decomposition for bipartite and directed graphs.

New species of the xenophyophore genus Aschemonella (Rhizaria: Foraminifera) from areas of the abyssal eastern Pacific licensed for polymetallic nodule exploration

We describe Aschemonella monile Gooday and Holzmann sp. nov. from the Clarion-Clipperton Zone (CCZ, abyssal eastern equatorial Pacific), a region characterized by commercially significant concentrations of polymetallic nodules. The new species is the most abundant xenophyophore (giant agglutinated foraminifera) in our main sampling area (12-14°N; 116°30′-117°26′W). Additional specimens originate from the central CCZ, and from a third area, ∼900 km NW of the main area, where A. monile numerically dominates the megabenthos in photographic surveys of the seafloor (average densities 1.54 individuals/m 2; peak densities > 3 individuals/m 2). Aschemonella monile is much larger (≥ 7 cm in length) than previously described species of the genus, with a test comprising an irregular sequence of self-contained, partly overlapping 'segments', creating a multichambered structure. A similar, much rarer species from the main study area, described here as Aschemonella aspera Gooday and Holzmann sp. nov., has an unsegmented test with a very rough, coarsely agglutinated wall. Genetic data suggest that A. monile is distinct from A. aspera and most closely related to a group comprising Rhizammina algaeformis and Aschemonella ramuliformis. Both new species have delicate tests that are often attached to nodule surfaces, making them particularly vulnerable to seafloor disturbances.

The mre11 A470 alleles influence the hereditability and the segregation of telosomes in Saccharomyces cerevisiae.

Telomeres, the nucleoprotein complexes at the termini of linear chromosomes, are essential for the processes of end replication, end protection, and chromatin segregation. The Mre11 complex is involved in multiple cellular roles in DNA repair and structure in the regulation and function of telomere size homeostasis. In this study, we characterize yeast telomere chromatin structure, phenotypic heritability, and chromatin segregation in both wild-type [MRE11] and A470 motif alleles. MRE11 strains confer a telomere size of 300 base pairs of G+T irregular simple sequence repeats. This DNA and a portion of subtelomeric DNA is embedded in a telosome: a MNase-resistant non-nucleosomal particle. Chromatin immunoprecipitation shows a three to four-fold lower occupancy of Mre11A470T proteins than wild-type proteins in telosomes. Telosomes containing the Mre11A470T protein confer a greater resistance to MNase digestion than wild-type telosomes. The integration of a wild-type MRE11 allele into an ectopic locus in the genome of an mre11A470T mutant and the introduction of an mre11A470T allele at an ectopic site in a wild-type strain lead to unexpectedly differing results. In each case, the replicated sister chromatids inherit telosomes containing only the protein encoded by the genomic mre11 locus, even in the presence of protein encoded by the opposing ectopic allele. We hypothesize that the telosome segregates by a conservative mechanism. These data support a mechanism for the linkage between sister chromatid replication and maintenance of either identical mutant or identical wild-type telosomes after replication of sister chromatids. These data suggest the presence of an active mechanism for chromatin segregation in yeast.

Turn-taking ceremonies in a colonial seabird: Does behavioral variation signal individual condition?

ABSTRACT In species with biparental care, pairs share a cooperative interest in offspring survival but may be in conflict over their relative investments, as reported in recent turn-taking studies of chick-provisioning birds. Turn-taking in Common Murres (Uria aalge) involves the foraging bird returning to the colony to provision the chick and the brooding parent departing. We examined whether Common Murres in poor condition had slower or more irregular turn-taking behavior, as has been documented in Common Murres equipped with geologgers. Irregularities include the brooding bird not trading parental roles with its returning mate or a bird returning to the colony without a fish. Irregular turn-taking sequences generally took longer than normal turn-taking sequences and differed in the rate and synchrony of allopreening, the main interactive behavior between mates. There was a delayed onset of allopreening when nest reliefs were protracted, whereas returners that did not bring a fish started allopreening s...

A Comparison of Implicit and Explicit Motor Sequence Learning in Patients with Relapsing-Remitting Multiple Sclerosis.

This study tends to assess implicit and explicit types of motor learning in patients with Multiple Sclerosis (MS) and normal peers by means of a serial reaction time. Sample size was 15 for each group and Samples included 30 patients with MS and 30 normal peers and were assigned to implicit and explicit learning groups. A repeated measures ANOVA was used for measuring reaction time and response error, and a paired samples t-test was used to compare regular and irregular sequence data in each group. Comparison of these two types of learning in speed (response time) and accuracy (number of errors) showed the number of errors (P = 0.012) and response time (P = 0.012) in the implicit motor learning group of MS patients and the number of errors (P = 0.096) and response time (P = 0.954) in the explicit motor learning group of MS patients. Moreover, comparison showed the number of errors (P = 0.008) and response time (P = 0.05) in the implicit group of normal peers and the number of errors (P = 0.011) and response time (P = 0.442) in the explicit group of normal peers. The results showed that explaining and describing the task is less effective at training the motor sequence of MS patients and that these patients benefit more from implicit learning.

Feasibility of In-Vivo Simulation of Acute Hemodynamics in Human Atrial Fibrillation.

This study evaluated hemodynamic feasibility and reproducibility of a new method for in vivo simulation of human atrial fibrillation (AF). The method was tested during sinus rhythm in 10 patients undergoing catheter ablation for AF. A simple electronic device was assembled that allowed triggering a cardiac stimulator by predefined series of RR intervals. Irregular RR interval sequences with a mean heart rate of 90/min and 130/min were obtained from ECG recordings of another patients with AF. Simultaneous atrioventricular pacing was delivered by catheters placed inside the coronary sinus and at the His bundle region. Hemodynamic effect of the simulated AF was assessed by invasive measurement of the left ventricular (LV) pressure, dP/dt, and Tau. Compared to regular pacing at the same mean heart rate, the simulated AF significantly impaired the LV both systolic and diastolic function. Repeated AF pacing in the same patients generated similar LV hemodynamics. The proposed method provides a realistic and reproducible in-vivo model of AF. It can be exploited for investigation of the hemodynamic consequences of AF in various patient populations.

Examining the Round Trip Time and Packet Length Effect on Window Size by Using the Cuckoo Search Algorithm

Irregular sequences of inter-arrival times of packet(s) and packet lengths in a network session determine effective traffic performance. Crucial to this is the width of the sliding window. This study utilized raw data from network traffic and built a Neural Network (NN) model trained with the Cuckoo Search (CS) algorithm. Round trip time (RTT) and packet length were captured over several network sessions. They were used as input and their effects were evaluated on window size as the output. Experimental analysis was carried out in order to test the model with various partitioning levels of training and test data. The results of the experiments show that the proposed NN model trained with CS successfully converged without any form of oscillation; the minimum MSE was observed shortly after 100 cycles. The predicted window size and target window size fitted each other. This signifies that the training was successful based on the fitted values of the window size. Thus the proposed model trained with the CS algorithm provides a high convergence rate to the true global minimum and a better optimal solution. Therefore, the combination of CS and NN (CSNN) contributed to decision making on the allocation of window size in determining network flow problems and congestion control.

Tracing the neural basis of auditory entrainment

Neurons in the auditory cortex synchronize their responses to temporal regularities in sound input. This coupling or “entrainment” is thought to facilitate beat extraction and rhythm perception in temporally structured sounds, such as music. As a consequence of such entrainment, the auditory cortex responds to an omitted (silent) sound in a regular sequence. Although previous studies suggest that the auditory brainstem frequency-following response (FFR) exhibits some of the beat-related effects found in the cortex, it is unknown whether omissions of sounds evoke a brainstem response. We simultaneously recorded cortical and brainstem responses to isochronous and irregular sequences of consonant–vowel syllable /da/ that contained sporadic omissions. The auditory cortex responded strongly to omissions, but we found no evidence of evoked responses to omitted stimuli from the auditory brainstem. However, auditory brainstem responses in the isochronous sound sequence were more consistent across trials than in the irregular sequence. These results indicate that the auditory brainstem faithfully encodes short-term acoustic properties of a stimulus and is sensitive to sequence regularity, but does not entrain to isochronous sequences sufficiently to generate overt omission responses, even for sequences that evoke such responses in the cortex. These findings add to our understanding of the processing of sound regularities, which is an important aspect of human cognitive abilities like rhythm, music and speech perception.

Rotation sets and almost periodic sequences

We study the rotational behaviour on minimal sets of torus homeomorphisms and show that the associated rotation sets can be any type of line segment as well as non-convex and even plane-separating continua. This shows that the restriction which hold for rotation sets on the whole torus are not valid on minimal sets. The proof uses a construction of rotational horseshoes by Kwapisz to transfer the problem to a symbolic level, where the desired rotational behaviour is implemented by means of suitable irregular Toeplitz sequences.