Full Shift Research Articles

中小學教師換證制度之研究：體系內涵、遭遇阻力與配套措施 License Renewal System for Elementary and Secondary School Teachers: Contents, Resistance, and Supporting Measures

中小學教師換證制度之研究：體系內涵、遭遇阻力與配套措施 License Renewal System for Elementary and Secondary School Teachers: Contents, Resistance, and Supporting Measures

The Number of Configurations in the Full Shift with a Given Least Period

For any group G and any set A, consider the shift action of G on the full shift \(A^G\). A configuration \(x \in A^G\) has least period \(H \le G\) if the stabiliser of x is precisely H. Among other things, the number of such configurations is interesting as it provides an upper bound for the size of the corresponding \(\mathrm {Aut}(A^G)\)-orbit. In this paper, we show that if G is finitely generated and H is of finite index, then the number of configurations in \(A^G\) with least period H may be computed by using the Möbius function of the lattice of subgroups of finite index in G. Moreover, when H is a normal subgroup, we classify all situations such that the number of G-orbits with least period H is at most 10.

The Stabilized Automorphism Group of a Subshift

AbstractFor a mixing shift of finite type, the associated automorphism group has a rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce a stabilization of the automorphism group, study its algebraic properties, and use them to distinguish many of the stabilized automorphism groups. We also show that for a full shift, the subgroup of the stabilized automorphism group generated by elements of finite order is simple and that the stabilized automorphism group is an extension of a free abelian group of finite rank by this simple group.

RFID Tag Data Encryption Using Triple DES and RSA Algorithms

With the future full shift to cashless and contactless toll fee collection in the Philippines, installation of radio frequency identification (RFID) readers at toll plazas and tags on all vehicles is the most practicable solution. The Department of Transportation recently implemented this initiative to help minimize the transmission of COVID-19. RFID tags in the forms of stickers contains the motorist’s account number which if hacked can be used to access other important details about the owner. With the weak security of these tags, possible instances that information from RFID tags could be accessed. Information derived from these can be easily retrieved if the attacker has access to the tags' data. The worst thing is that public access to the database that contains essential information concerning the holder's account. In this paper, the authors aim to provide more information about tag ID’s encryption that is limited to RFID usage in the Philippine expressways. An algorithm devised by the authors well secures the information contained in the RFID tags.

Longest common substring for random subshifts of finite type

Dans cet article, nous etudions le comportement de la plus longue sous-chaine commune pour des sous-shifts aleatoires de type fini (pour les dynamiciens) ou de la plus longue sous-chaine commune pour des suites aleatoires en milieux aleatoires (pour les probabilistes). Nous prouvons que, sous des hypotheses de melange exponentiel, ce comportement est lie a l’entropie de Renyi de la mesure stationnaire. Nous soulignons que ce que nous etablissons est un resultat de type «quenched».

On the entropies of subshifts of finite type on countable amenable groups

Let G,H be two countable amenable groups. We introduce the notion of group charts, which gives us a tool to embed an arbitrary H -subshift into a G -subshift. Using an entropy addition formula derived from this formalism we prove that whenever H is finitely presented and admits a subshift of finite type (SFT) on which H acts freely, then the set of real numbers attained as topological entropies of H -SFTs is contained in the set of topological entropies of G -SFTs modulo an arbitrarily small additive constant for any finitely generated group G which admits a translation-like action of H . In particular, we show that the set of topological entropies of G -SFTs on any such group which has decidable word problem and admits a translation-like action of \mathbb{Z}^2 coincides with the set of non-negative upper semi-computable real numbers. We use this result to give a complete characterization of the entropies of SFTs in several classes of groups.

Stiffness tuning of a functional-switchable active coding elastic metasurface

Recently, a new type of metasurface namely coding metasurface has emerged as a new technology in manipulating waves. Based on its R-bit, a coding metasurface utilizes 2R of coding units to achieve real-time wave controls which makes the operation of a metasurface easier. Although coding metasurfaces have simpler configurations than conventional metasurfaces, it is yet unavoidable to have structural reconfiguration of metasurface in order to perform different functionalities in single or different frequencies. To overcome this drawback, a functionally switchable 3-bit active coding elastic metasurface comprised of stacked piezoelectric patches shunted with negative capacitance circuit is proposed to manipulate elastic longitudinal waves. By tuning the negative capacitance in the circuitry element, arbitrary tuning of stiffness can be attained which leads to the coverage of full 2π phase range without modifying the structure of metasurface. In addition, analytical model and numerical simulations are developed to verify capability of the proposed coding metasurface for covering full 2π phase shift besides having high transmission at the same time. By utilizing the 8 fundamental coding units with different phase response, the proposed metasurface is designed and simulated based on a finite element approach to illustrate switchable functionalities such as arbitrary refraction and wave focusing, which can be realized through proper tuning of the negative capacitance, in broadband frequencies.

Verification of mixing properties in two-dimensional shifts of finite type

This work introduces constructive and systematic methods for verifying the topological mixing and strong specification (or strong irreducibility) of two-dimensional shifts of finite type. First, we define transition matrices on infinite strips of width n for all n ≥ 2. To determine the primitivity of the transition matrices, we introduce the connecting operators that reduce the high-order transition matrices to lower-order transition matrices. Then, two sufficient conditions for primitivity are provided; they are invariant diagonal cycles and primitive commutative cycles of connecting operators. Then, the primitivity, corner-extendability, and crisscross-extendability are used to demonstrate the topological mixing. Finally, we show that the hole-filling condition yields the strong specification property. The application of all the above-mentioned conditions can be verified in a finite number of steps.

Plasma Rich in Growth Factors Promotes Autophagy in ARPE19 Cells in Response to Oxidative Stress Induced by Blue Light.

Age-related macular degeneration (AMD) causes the degeneration of photoreceptors and retinal cells leading to vision loss in older subjects. Among possible exogenous risk factors, it has been recently proposed that long-term exposure to blue light could aggravate the course of AMD. In the search for therapeutic options, plasma rich in growth factors (PRGF) has been shown to enhance cell antioxidant pathways and protect photoreceptors against the harm produced by blue light, although its mechanism of action remains unknown. One possible mechanism, autophagy, is one of the most conservative cell renewal systems used in eukaryotes to destroy cellular components that have been damaged by some kind of insult. The oxidative stress of exposure to blue light is known to induce cell autophagy. In this study, we examined the combined effects on autophagy of blue light and PRGF in a retinal cell line, ARPE19. In response to treatment with both PRGF and blue light, we detected the modulated expression of autophagy markers such as NF-kB, p62/sqstm1, Atg5, LC3 and Beclin1, and inflammatory markers such as IL1B and IL18. Our findings suggest that PRGF promotes cell autophagy in response to exposure to blue light.

Impact of silver nanoparticles exposure on neuro-behavior, hematology, and oxidative stress biomarkers of African catfish (Clarias gariepinus)

Recently, silver nanoparticles (AgNPs) established a prospective value in aquaculture; however, extensive use afflicts fish and environment. Therefore, the current study represents a premier report to investigate the acute exposure of African catfish, Clarias gariepinus (B.) to AgNPs and the ethological alterations in a static renewal system. Additionally, AgNPs impact on blood profile, stress, brain activity, and branchial oxidative stress parameters were evaluated. Fish (50.71 ± 3.85 g) were exposed to different concentrations (0, 6.25, 12.5, 25, 50, and 100 mg L−1) of AgNPs for 96-h without water exchange. Finney's probit analysis was used to estimate the 96-h LC50 value of AgNPs which recorded 21.38 mg L−1. In comparison to the control, the AgNPs exposed fish exhibited different ethological responses such as surfacing for gasping air, restlessness, slow swimming movement, aggressiveness, and nervousness and the scores of these behaviors and mortalities reached the high values with increasing AgNPs concentrations. There were marked reductions in hematological indices (RBCs, Hb, Hct, and WBCs), acetylcholine esterase (AChE) activity, and oxidative stress indices (superoxide dismutase (SOD), catalase (CAT), and reduced glutathione content (GSH)) of exposed groups in an AgNPs dose-dependent manner relative to the control group. On the contrary, the levels of stress-mediated indices (glucose and cortisol) and 8 hydroxy 2 deoxyguanosine (8OH2dG) were markedly decreased in all AgNPs exposed groups as compared with the control group and the reduction increased with increasing the exposure concentration. We concluded that AgNPs exposure of C. gariepinus induced marked alterations in behavior, blood profile, neurological, and branchial antioxidant parameters, and the 96-h LC50 of AgNPs was 21.38 mg L−1 and this provides a basis for future applying AgNPs as a safe therapeutic agent after considering the acute toxicity.

Infinite DLR measures and volume-type phase transitions on countable Markov shifts

We consider the natural definition of DLR measure in the setting of σ-finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of conformal measures associated with Walters potentials. In the BIP case, or when the potential normalizes the Ruelle’s operator, we prove that the notions of DLR and conformal coincide. On the standard renewal shift, we study the problem of describing the cases when the set of the eigenmeasures jumps from finite to infinite measures when we consider high and low temperatures, respectively. For this particular shift, we prove that there always exist finite DLR measures, and we have an expression to the critical temperature for this volume-type phase transition, which occurs only for potentials with the infinite first variation.

The space of invariant measures for countable Markov shifts

It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov shifts, the space of invariant sub-probability measures is a Poulsen simplex and that its extreme points are the ergodic invariant probability measures together with the zero measure. In particular, we obtain that the space of invariant probability measures is a Poulsen simplex minus a vertex and the corresponding convex combinations. Our results apply to finite entropy non-locally compact transitive countable Markov shifts and to every locally compact transitive countable Markov shift. In order to prove these results we introduce a topology on the space of measures that generalizes the vague topology to a class of non-locally compact spaces, the topology of convergence on cylinders. We also prove analogous results for suspension flows defined over countable Markov shifts.

A hierarchy of topological systems with completely positive entropy

We define a hierarchy of systems with topological completely positive entropy in the context of countable amenable continuous group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the corresponding level of the aforementioned hierarchy and provide subshifts of finite type for the first three levels. We give necessary and sufficient conditions for entropy pairs by means of the asymptotic relation on systems with the pseudo-orbit tracing property, and thus create a bridge between a result by Pavlov and a result by Meyerovitch. As a corollary, we answer negatively an open question by Pavlov regarding necessary conditions for completely positive entropy.

On one-sided topological conjugacy of topological Markov shifts and gauge actions on Cuntz–Krieger algebras

AbstractWe characterize topological conjugacy classes of one-sided topological Markov shifts in terms of the associated Cuntz–Krieger algebras and their gauge actions with potentials.

Expanding the chemistry of borates with functional [BO2]\u2212 anions

More than 3900 crystalline borates, including borate minerals and synthetic inorganic borates, in addition to a wealth of industrially-important boron-containing glasses, have been discovered and characterized. Of these compounds, 99.9 % contain only the traditional triangular BO3 and tetrahedral BO4 units, which polymerize into superstructural motifs. Herein, a mixed metal K5Ba2(B10O17)2(BO2) with linear BO2 structural units was obtained, pushing the boundaries of structural diversity and providing a direct strategy toward the maximum thresholds of birefringence for optical materials design. 11B solid-state nuclear magnetic resonance (NMR) is a ubiquitous tool in the study of glasses and optical materials; here, density functional theory-based NMR crystallography guided the direct characterization of BO2 structural units. The full anisotropic shift and quadrupolar tensors of linear BO2 were extracted from K5Ba2(B10O17)2(BO2) containing BO2, BO3, and BO4 and serve as guides to the identification of this powerful moiety in future and, potentially, previously-characterized borate minerals, ceramics, and glasses.

On the Interplay of Direct Topological Factorizations and Cellular Automata Dynamics on Beta-Shifts

We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. We show that any reversible CA [Formula: see text] has an almost equicontinuous direction whenever [Formula: see text] is not sofic. This has the corollary that non-sofic beta-shifts are topologically direct prime, i.e. they are not conjugate to direct topological factorizations [Formula: see text] of two nontrivial subshifts [Formula: see text] and [Formula: see text]. We also give a simple criterion to determine whether [Formula: see text] is conjugate to [Formula: see text] for a given integer [Formula: see text] and a given real [Formula: see text] when [Formula: see text] is a subshift of finite type. When [Formula: see text] is strictly sofic, we show that such a conjugacy is not possible at least when [Formula: see text] is a quadratic Pisot number of degree [Formula: see text]. We conclude by using direct factorizations to give a new proof for the classification of reversible multiplication automata on beta-shifts with integral base and ask whether nontrivial multiplication automata exist when the base is not an integer.

Shadowing, finite order shifts and ultrametric spaces

Inspired by a recent novel work of Good and Meddaugh, we establish fundamental connections between shadowing, finite order shifts, and ultrametric complete spaces. We develop a theory of shifts of finite type for infinite alphabets. We call them shifts of finite order. We develop the basic theory of the shadowing property in general metric spaces, exhibiting similarities and differences with the theory in compact spaces. We connect these two theories in the setting of zero-dimensional complete spaces, showing that a uniformly continuous map of an ultrametric complete space has the finite shadowing property if, and only if, it is an inverse limit of a system of shifts of finite order satisfying the Mittag-Leffler Condition. Furthermore, in this context, we show that the shadowing property is equivalent to the finite shadowing property and the fulfillment of the Mittag-Leffler Condition in the inverse limit description of the system. As corollaries, we obtain that a variety of maps in ultrametric spaces have the shadowing property, such as similarities and, more generally, maps which themselves, or their inverses, have Lipschitz constant 1. Finally, we apply our results to the dynamics of p-adic integers and p-adic rationals.

285 Pilot field study of Ambulatory Sleep-Staging in Shift-Working Air Traffic Controllers

Abstract Introduction The simplicity of wrist actigraphy for sleep-wake monitoring in the field contributes to its ubiquity in shift-work research. However, devices based solely on recording activity levels are generally not suitable to quantify sleep architecture. This is a limitation as quantifying changes in sleep stages caused by circadian misalignment is important to better assess the consequences of sleep-wake disruption in shift-working populations. This pilot study was conducted to evaluate whether sleep stages vary with respect to different shift types. Methods Six male air traffic controllers aged 48.5±8.4 years (mean±SD) completed the protocol which entailed two ~9-day periods, each with up to 6 workdays. Schedules comprised 1 or 2 early night shifts (19:30–03:30h), followed by an evening shift (15:00–23:00h), day shift (09:00–17:00h), morning shift (06:30–14:30h), and 1 or 2 full night shifts (23:00–7:00h). A portable sleep-staging device (Somno-Art, Paris, France) that monitored activity levels and heart rate was worn on the non-dominant forearm during bedtime and produced estimates of REM and NREM sleep stages with a proprietary algorithm. Total sleep time (TST) and sleep stages were assessed per shift type with mixed-effects models. Results Final analyses were based on 70 sleep periods preceding workdays, standardized to 24 h to account for the different intervals between consecutive shifts. Analyses revealed significant effects of shift type for TST (p=.016), stages N1 (p=.010) and N2 (p=.043), but none for N3 (p=.055) or REM (p=.117) sleep. TST and stage N1 sleep prior to night shifts was shorter than for day, evening, or early night shifts (all p<.05). Participants obtained less stage N2 sleep prior to night shifts than days shifts (p=.049). Conclusion This pilot study suggests variations in TST across shifts were predominantly due to differences in light sleep stages, whereas no significant differences in N3 and REM sleep were observed. Thus, while TST was reduced for night shifts, participants obtained similar durations of the most recuperative stages. These findings highlight the importance of refined monitoring of sleep in field research involving shift-work. Support (if any) Project funded by NAV Canada. Devices lent by the Somno-Art company. A.K. received a postdoctoral fellowship from the Fonds de Recherche en Santé du Québec (FRQS).

Asymptotic Counting in Conformal Dynamical Systems

In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former.We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights.These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results.Our new approach is founded on spectral properties of complexified Ruelle–Perron–Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.

Ahlfors regularity and fractal dimension of Smale spaces

AbstractWe prove that, up to topological conjugacy, every Smale space admits an Ahlfors regular Bowen measure. Bowen’s construction of Markov partitions implies that Smale spaces are factors of topological Markov chains. The latter are equipped with Parry’s measure, which is Ahlfors regular. By extending Bowen’s construction, we create a tool for transferring the Ahlfors regularity of the Parry measure down to the Bowen measure of the Smale space. An essential part of our method uses a refined notion of approximation graphs over compact metric spaces. Moreover, we obtain new estimates for the Hausdorff, box-counting and Assouad dimensions of a large class of Smale spaces.