Full Shift Research Articles

Concentration inequalities and rates of convergence of the ergodic theorem for countable shifts with Gibbs measures

In this paper we obtain an exponential concentration inequality for a countable Markov shift with a Gibbs measure associated to a Hölder continuous potential ϕ. We apply concentration inequalities to obtain bounds on the rate of convergence of the ergodic theorem for Lipschitz observables and for the wider class of bounded and -a.e. continuous observables.

Broadband transparent terahertz vortex beam generator based on thermally tunable geometric metasurface

Metasurfaces have been successfully employed for realization of orbital angular momentum (OAM) waves, however, current available vortex beam generators suffer from low efficiency and limited bandwidth. In this study, we propose a transparent geometric metasurface composed of InSb cylindroid to generate vortex beams in terahertz region. The operating frequency can achieve broadband coverage from 1.8 THz to 4.5 THz, with a fractional bandwidth of 85.7%, by changing the temperature of the InSb cylindroid from 220K to 340K. Based on geometric phase principle, the full 2π phase shift can be obtained at the operating frequency by rotating the cylindroid. Vortex beam generators with topological charges of +1 and −2 are designed over a broadband range by employing the InSb cylindroid with different temperature. The results indicate that the generated vortex beams have high mode purity at different frequencies. The proposed vortex beam generators can reconstruct the operating frequency by directly changing the external temperature without altering the size of device, which show tremendous potential in wireless communication system. • A reconfigurable InSb metasurface is proposed to generate vortex beams in terahertz region. • The operating frequency of InSb metasurface can be reconstructed by changing the external temperature. • Generated vortex beams have high mode purity over a broadband.

Local $${\mathcal {P}}$$ entropy and stabilized automorphism groups of subshifts

For a homeomorphism \(T :X \rightarrow X\) of a compact metric space X, the stabilized automorphism group \({\text {Aut}}^{(\infty )}(T)\) consists of all self-homeomorphisms of X which commute with some power of T. Motivated by the study of these groups in the context of shifts of finite type, we introduce a certain entropy for groups called local \({\mathcal {P}}\) entropy. We show that when (X, T) is a non-trivial mixing shift of finite type, the local \({\mathcal {P}}\) entropy of the group \({\text {Aut}}^{(\infty )}(T)\) is determined by the topological entropy of (X, T). We use this to give a complete classification of the isomorphism type of the stabilized automorphism groups of full shifts.

Delayed Renewal Process with Uncertain Random Inter-Arrival Times

An uncertain random variable is a tool used to research indeterminacy quantities involving randomness and uncertainty. The concepts of an ’uncertain random process’ and an ’uncertain random renewal process’ have been proposed in order to model the evolution of an uncertain random phenomena. This paper designs a new uncertain random process, called the uncertain random delayed renewal process. It is a special type of uncertain random renewal process, in which the first arrival interval is different from the subsequent arrival interval. We discuss the chance distribution of the uncertain random delayed renewal process. Furthermore, an uncertain random delay renewal theorem is derived, and the chance distribution limit of long-term expected renewal rate of the uncertain random delay renewal system is proved. Then its average uncertain random delay renewal rate is obtained, and it is proved that it is convergent in the chance distribution. Finally, we provide several examples to illustrate the consistency with the existing conclusions.

On the Perron root and eigenvectors associated with a subshift of finite type

In this paper, we describe the relationship between the Perron root and eigenvectors of an irreducible subshift of finite type with the correlation between the forbidden words in the subshift. In particular, we derive an expression for the Perron eigenvectors of the associated adjacency matrix. As an application, we obtain the Perron eigenvectors for irreducible (0,1) matrices which are adjacency matrices for directed graphs. Moreover, we derive an alternate definition of the Parry measure in ergodic theory on an irreducible subshift of finite type.

1231 A Full-Cycle Audit Of ‘Safe’ Surgical Handovers in A Tertiary Centre

Abstract Aim 1. Assess performance in surgical handovers at Southampton General Hospital (SGH) against RCS ‘Safe Handover’ guidelines Identify any areas for improvement to ensure safe and effective handover of surgical patients Method 10 evening surgical handovers were anonymously audited In October 2019 against RCS ‘safe handover’ guidelines. The results were subsequently analysed and circulated amongst the surgical department. Handovers were then led consistently by surgical registrars and advanced nurse practitioners (ANPs). A prompt including the RCS handover guidelines was made and distributed to all members of the surgical team and included in departmental inductions. Following this, a further 10 evening handovers were anonymously audited between July and August 2020. Results Many aspects of handover performance descriptors described by the RCS in the re-audit improved following the circulation of our prompt including RCS handover guidelines and examples of minimum or good standards of practice for handover. Specifically, handover timeliness, the briefings provided (100% from 70%), the audibility of a single speaker (70% from 30%), the number of educational discussions held during handovers (100% from 50%) and awareness of the on-call overnight consultant (100% from 80%) all vastly improved. Conclusions Emphasis on undertaking effective handovers needs to continue as ‘safe' handovers between shifts can protect both patient and doctor safety. This is especially true following the implementation of the European Working Time Directive (EWTD) and a move to full shift working. Handovers are also proposed as opportunities for training which may be helpful especially in an era of reduced hours of surgical training.

Endotoxin in Aerosol Particles from Metalworking Fluids Measured with a Sioutas Cascade Impactor.

The aim of this study was to characterize personal occupational exposure to endotoxin in size-separated airborne particles of MWF aerosol, using a Sioutas cascade impactor (SCI). Exposure to inhalable fractions of MWF aerosol and endotoxin was measured by personal sampling of 52 individuals over an 8-h work shift using a PAS-6 sampler in parallel with a SCI (<0.25, 0.25-0.5, 0.5-1.0, 1.0-2.5, and 2.5-10 µm). Aerosol mass concentration was measured for each worker with a real-time instrument (DataRAM) during a full shift. Samples of MWF were collected from the machines and central tanks during the work shift. A total of 117 measurements of inhalable MWF aerosols were made among 52 workers. The geometric mean of inhalable MWF aerosol was 0.16 mg m-3 air. The geometric mean of endotoxin concentration on the inhalable sampler was 0.15 EU m-3. Airborne endotoxin was found on all size fractions from the impactor, with the major part seen in the fraction (2.5-10 µm). There was a correlation between the inhalable fraction of endotoxin measured by the PAS-6 sampler and on the SCI sampler (2.5-10 µm), estimated to be 0.51 for all samples (P < 0.0001). The concentration of endotoxin varied between the MWFs, as did the proportion of Gram-negative bacteria among the culturable bacteria (>80% in one MWF and <1.5% in the other three). The personal exposure to inhalable fractions of endotoxin contained in the MWF aerosol were low, where most of the endotoxin were found in fraction (2.5-10 µm), measured by SCI. There are differences between factories and MWF systems regarding the distribution of endotoxin and so results from one context should not be generalized to other plants and systems. Compressed air was used for less than 10 min shift-1. The mixed-effect model showed that working with open machines and grinding as cutting task were important determinants of exposure to inhalable aerosol. It is important to keep occupational exposure to aerosols low with the help of good ventilation systems, enclosed machines, and organization of work.

Single-Pixel Imaging Using Carrier-Depletion Optical Phased Array With Reduced Phase Shift Requirement

The optical-phased array (OPA) has gained special interest in recent years as a high-speed and compact imaging device. While large-scale OPAs have been demonstrated in single-pixel imaging, the complexity of the driver circuit is becoming a crucial problem as the number of phase shifters increases. Here, we investigate the phase shift requirement of OPA for single-pixel imaging and demonstrate, for the first time, that full 2π phase shifts are not mandatory to generate a set of illumination patterns with a sufficient degree of randomness required to reconstruct the image. Using a silicon photonic OPA chip with 128 carrier-depletion-based phase shifters, we experimentally confirm this property by successfully retrieving an image under a maximum phase shift of only ∼1.5π without affecting the quality of the image. Consequently, the input voltage can be reduced significantly. Since the carrier-depletion phase shifters generally require high driving voltages, this finding paves the way to high-speed OPA-based imaging with a minimum device requirement.

The weak Smale horseshoe and mean hyperbolicity

The paper concerns the mean hyperbolicity of the skew-product flows induced by the perturbation equations driven by varieties of non-periodic forcings. The weakly averaged horseshoe can be constructed as a mean hyperbolic invariant set in the Poincare section for high dimensional phase space. Due to the non-periodic property, the Poincare return map restricted to the weakly averaged horseshoe region can semi-conjugate to the full Bernoulli shift on infinite symbols, which implies the infinitely many independent choices on the length of return time. As a direct application of mean hyperbolicity, we extend the shadowing lemma due to Liao to the general nonautonomous dynamical systems.

Chaotic behavior of the p-adic Potts–Bethe mapping II

AbstractThe renormalization group method has been developed to investigate p-adic q-state Potts models on the Cayley tree of order k. This method is closely related to the examination of dynamical behavior of the p-adic Potts–Bethe mapping which depends on the parameters q, k. In Mukhamedov and Khakimov [Chaotic behavior of the p-adic Potts–Behte mapping. Discrete Contin. Dyn. Syst.38 (2018), 231–245], we have considered the case when q is not divisible by p and, under some conditions, it was established that the mapping is conjugate to the full shift on $\kappa _p$ symbols (here $\kappa _p$ is the greatest common factor of k and $p-1$ ). The present paper is a continuation of the forementioned paper, but here we investigate the case when q is divisible by p and k is arbitrary. We are able to fully describe the dynamical behavior of the p-adic Potts–Bethe mapping by means of a Markov partition. Moreover, the existence of a Julia set is established, over which the mapping exhibits a chaotic behavior. We point out that a similar result is not known in the case of real numbers (with rigorous proofs).

Highly irregular orbits for subshifts of finite type: large intersections and emergence

In their recent paper (2019 arXiv:1904.03424), the first author, Kiriki and Soma introduced a concept of pointwise emergence to measure the complexity of irregular orbits. They constructed a residual subset of the full shift with high pointwise emergence. In this paper we consider the set of points with high pointwise emergence for topologically mixing subshifts of finite type. We show that this set has full topological entropy, full Hausdorff dimension, and full topological pressure for any Hölder continuous potential. Furthermore, we show that this set belongs to a certain class of sets with large intersection property. This is a natural generalization of Färm and Persson (2011 Nonlinearity 24 1291–1309) to pointwise emergence and Carathéodory dimension.

Universal gates with wires in a row

We give some optimal size generating sets for the group generated by shifts and local permutations on the binary full shift. We show that a single generator, namely the fully asynchronous application of the elementary cellular automaton 57 (or, by symmetry, ECA 99), suffices in addition to the shift. In the terminology of logical gates, we have a single reversible gate whose shifts generate all (finitary) reversible gates on infinitely many binary-valued wires that lie in a row and cannot (a priori) be rearranged. We classify pairs of words u, v such that the gate swapping these two words, together with the shift and the bit flip, generates all local permutations. As a corollary, we obtain analogous results in the case where the wires are arranged on a cycle, confirming a conjecture of Macauley-McCammond-Mortveit and Vielhaber.

Extremely thin reflective metasurface for low-frequency underwater acoustic waves: Sharp focusing, self-bending, and carpet cloaking

An extremely thin metasurface is proposed for manipulating underwater reflected waves. Each metasurface unit is only 1/61.7 of the target wavelength in thickness and comprises an air cavity capped with a thin vibration plate held in place by rubber spacers on steel supports. The unit-cell design is thin, simple, and can be adjusted to obtain a full 2π phase shift in water waves that are reflected from the metasurface. It also provides this phase shift for a broad frequency range of 20–800 Hz for incident waves. The effectiveness of the design and the resolution of the expected effect is demonstrated for sharp focusing, self-bending, and directional carpet cloaking, which are applications with great potential in energy harvesting, underwater communication, and submarine stealth and antidetection.

Non-negative integral matrices with given spectral radius and controlled dimension

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

One-sided topological conjugacy of normal subshifts and gauge actions on the associated C*-algebras

The class of normal subshifts includes irreducible nontrivial topological Markov shifts, irreducible nontrivial sofic shifts, synchronized systems, Dyck shifts, β-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated -algebras and its gauge actions with potentials. In particular, the one-sided topological conjugacy class of irreducible nontrivial sofic shifts are characterized in terms of the simple purely infinite Cuntz-Krieger algebras associated with the matrices of its left Fischer cover graphs and gauge actions with potentials. This generalizes the author's previous result for irreducible nontrivial topological Markov shifts and Cuntz-Krieger algebras with gauge actions.

Characterization and topological behavior of homomorphism tree-shifts

The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.

Strongly aperiodic subshifts of finite type on hyperbolic groups

AbstractWe prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end.

Subshifts and colorings on ascending HNN-extensions of finitely generated abelian groups

AbstractFor an ascending HNN-extension$G*_{\psi }$of a finitely generated abelian groupG, we study how a synchronization between the geometry of the group and weak periodicity of a configuration in$\mathcal {A}^{G*_{\psi }}$forces global constraints on it, as well as in subshifts containing it. A particular case are Baumslag–Solitar groups$\mathrm {BS}(1,N)$,$N\ge 2$, for which our results imply that a$\mathrm {BS}(1,N)$-subshift of finite type which contains a configuration with period$a^{N^\ell }\!, \ell \ge 0$, must contain a strongly periodic configuration with monochromatic$\mathbb {Z}$-sections. Then we study propern-colorings,$n\ge 3$, of the (right) Cayley graph of$\mathrm {BS}(1,N)$, estimating the entropy of the associated subshift together with its mixing properties. We prove that$\mathrm {BS}(1,N)$admits a frozenn-coloring if and only if$n=3$. We finally suggest generalizations of the latter results ton-colorings of ascending HNN-extensions of finitely generated abelian groups.

Manufacturing worker perceptions of using wearable inertial sensors for multiple work shifts

Wearable inertial sensors may be used to objectively quantify exposure to some physical risk factors associated with musculoskeletal disorders. However, concerns regarding their potential negative effects on user safety and satisfaction remain. This study characterized the self-reported daily discomfort, distraction, and burden associated with wearing inertial sensors on the upper arms, trunk, and dominant wrist of 31 manufacturing workers collected over 15 full work shifts. Results indicated that the workers considered the devices as generally comfortable to wear, not distracting, and not burdensome to use. Exposure to non-neutral postures (discomfort, right arm, beta = 0.02; trunk, beta = −0.01), non-cyclic tasks (distraction, beta = -0.26), and higher body mass indices (discomfort, beta = 0.05; distraction, beta = 0.02) contributed to statistically significant (p < 0.05), albeit practically small increases in undesirable ratings. For instance, for each additional percentage of time working with the right arm elevated ≥60°, self-reported discomfort ratings increased 0.02 cm on a standard 10 cm visual analog scale. Female workers reported less discomfort and distraction while wearing the sensors at work than males (discomfort, beta = −0.93; distraction, beta = −0.3). In general, the low ratings of discomfort, distraction, and burden associated with wearing the devices during work suggests that inertial sensors may be suitable for extended use among manufacturing workers.

A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson. Extending those tilings to the Heisenberg group by exploiting the group’s structure and posing additional local rules to prune out remaining periodic behavior, we maintain a rich projective subdynamics on Z2 cosets. In addition, the obtained subshift factors onto a strongly aperiodic, minimal sofic shift via a map that is invertible on a dense set of configurations.