Mixed Pairs Research Articles

No calculation necessary: Accessing magnitude through decimals and fractions

Research on how humans understand the relative magnitude of symbolic fractions presents a unique case of the symbol-grounding problem with numbers. Specifically, how do people access a holistic sense of rational number magnitude from decimal fractions (e.g. 0.125) and common fractions (e.g. 1/8)? Researchers have previously suggested that people cannot directly access magnitude information from common fraction notation, but instead must use a form of calculation to access this meaning. Questions remain regarding the nature of calculation and whether a division-like conversion to decimals is a necessary process that permits access to fraction magnitudes. To test whether calculation is necessary to access fractions magnitudes, we carried out a series of six parallel experiments in which we examined how adults access the magnitude of rational numbers (decimals and common fractions) under varying task demands. We asked adult participants to indicate which of two fractions was larger in three different conditions: decimal-decimal, fraction-fraction, and mixed decimal-fraction pairs. Across experiments, we manipulated two aspects of the task demands. 1) Response windows were limited to 1, 2 or 5 s, and 2) participants either did or did not have to identify when the two stimuli were the same magnitude (catch trials). Participants were able to successfully complete the task even at a response window of 1 s and showed evidence of holistic magnitude processing. These results indicate that calculation strategies with fractions are not necessary for accessing a sense of a fractions meaning but are strategic routes to magnitude that participants may use when granted sufficient time. We suggest that rapid magnitude processing with fractions and decimals may occur by mapping symbolic components onto common amodal mental representations of rational numbers.

Females are more determinant than males in reproductive performance in the house sparrow Passer domesticus

Which sex has a more determinant role in reproductive performance? This is a long standing question in evolutionary ecology. Theory predicts and several pieces of evidence have indicated that females are more determinant than males. However, a direct test of this hypothesis has never been made. Here we perform such a direct test by using an alternative analytical approach, controlling for age and/or individual experience, and a captive population of the house sparrow Passer domesticus, a monogamous bi‐parental dimorphic species in which both sexes contribute with approximately equal amounts of parental care. In this species, it has been demonstrated that contribution by males to offspring parental care is crucial to maximize reproductive success. Captive conditions with absence of predators and availability of food ad libitum allow us to control several important factors that may affect reproductive performance, such as environmental fluctuations in resource availability and differences in territory quality, without affecting reproductive performance. We consider four types of pairs, and our main prediction derived from the hypothesis is that mixed pairs involving an experienced female (FBM × EF) should present better reproductive performance than mixed pairs involving a first‐time breeder female (EM × FBF). Our results confirm the general pattern reported in other bird species that older or more experienced individuals enjoy a higher reproductive success than first‐time breeders. In addition, in agreement with our main prediction, we found that FBM × EF produced significantly more fledglings and had higher fledging success than EM × FBF. Our results, for the first time demonstrate the broadly accepted statement that females have a more determinant role than males in reproductive performance.

Wild Dictyostelium discoideum social amoebae show plastic responses to the presence of nonrelatives during multicellular development.

When multiple strains of microbes form social groups, such as the multicellular fruiting bodies of Dictyostelium discoideum, conflict can arise regarding cell fate. Both fixed and plastic differences among strains can contribute to cell fate, and plastic responses may be particularly important if social environments frequently change. We used RNA‐sequencing and photographic time series analysis to detect possible conflict‐induced plastic differences between wild D. discoideum aggregates formed by single strains compared with mixed pairs of strains (chimeras). We found one hundred and two differentially expressed genes that were enriched for biological processes including cytoskeleton organization and cyclic AMP response (up‐regulated in chimeras), and DNA replication and cell cycle (down‐regulated in chimeras). In addition, our data indicate that in reference to a time series of multicellular development in the laboratory strain AX4, chimeras may be slightly behind clonal aggregates in their development. Finally, phenotypic analysis supported slower splitting of aggregates and a nonsignificant trend for larger group sizes in chimeras. The transcriptomic comparison and phenotypic analyses support discoordination among aggregate group members due to social conflict. These results are consistent with previously observed factors that affect cell fate decision in D. discoideum and provide evidence for plasticity in cAMP signaling and phenotypic coordination during development in response to social conflict in D. discoideum and similar microbial social groups.

Multiple Mittag-Leffler Stability of Delayed Fractional-Order Cohen-Grossberg Neural Networks via Mixed Monotone Operator Pair.

This article mainly investigates the multiple Mittag-Leffler stability of delayed fractional-order Cohen-Grossberg neural networks with time-varying delays. By using mixed monotone operator pair, the conditions of the coexistence of multiple equilibrium points are obtained for fractional-order Cohen-Grossberg neural networks, and these conditions are eventually transformed into algebraic inequalities based on the vertex of the divided region. In particular, when the symbols of these inequalities are determined by the dominant term, several verifiable corollaries are given. And then, the sufficient conditions of the Mittag-Leffler stability are derived for fractional-order Cohen-Grossberg neural networks with time-varying delays. In addition, two numerical examples are provided to illustrate the effectiveness of the theoretical results.

Effective Hamiltonian with tunable mixed pairing in driven optical lattices

Mixed pairing in ultracold Fermi gases can give rise to interesting many-body phases, such as topological nontrivial superfluids that support Majorana zero modes (MZMs) with various spatial configurations. Unfortunately, in ordinary lattice systems, the topological phase and the associated MZMs are suppressed by the dominant $s$-wave pairing. Here we present a proposal for engineering effective Hamiltonians with tunable mixed on- and off-site pairing based on driven optical lattices. The on- and off-site pairing can be changed independently by means of a periodical driving field rather than magnetic Feshbach resonances. It paves the way for suppressing the dominant on-site interaction that frustrates the emergence of topological superfluids and for synthesizing MZMs localized in edges or corners.

Inheritance of plumage morphs in Little Eagles Hieraaetus morphnoides in northern New South Wales

Polymorphism and inheritance of plumage colour in the Little Eagle Hieraaetus morphnoides were studied in northern New South Wales, by tallying records of parental morph combinations in breeding pairs and the morphs of their offspring in the 1980s, 2000s and 2017–2019 ( n = 41 pair combinations). The average ratio in breeding adults was 4.9 light:1 dark, with dark males outnumbering dark females (1.8:1). Light × light pairs always produced light young ( n = 32). Dark male × light female pairs variously produced light and dark offspring of both sexes ( n = 12). Light male × dark female pairs produced dark young of either sex ( n = 4) and one light young of unknown sex. One dark × dark pair produced a dark young. We conclude a Mendelian inheritance pattern with the dark morph recessive. From a small sample of mixed pairs with a dark male, the ratio of offspring morphs did not differ significantly from that expected by the Hardy–Weinberg equation, but mixed pairs with a light male produced 4 dark offspring to one light, versus the expected Hard –Weinberg ratio of 1.95 light: 1 dark. This outcome suggests a non-random transmission of the dark allele by heterozygous light males, and a similar pattern of inheritance to that in the related Booted Eagle H. pennatus .

The red admiral butterfly's living light sensors and signals.

We studied the wing colouration and the compound eyes of red admiral butterflies with optical methods. We measured reflectance spectra of the wing and scales of Vanessa atalanta and modelled the thin film reflectance of the wing membrane and blue scales. We utilized the eyeshine in the compound eye of Vanessa indica to determine the spectral and polarisation characteristics of its optical sensor units, the ommatidia. Pupil responses were measured with a large-aperture optophysiological setup as reduction in the eyeshine reflection caused by monochromatic stimuli. Processing of spectral and polarisation responses of individual ommatidia revealed a random array with three types of ommatidia: about 10% contain two blue-sensitive photoreceptors, 45% have two UV-sensitive photoreceptors, and 45% have a mixed UV-blue pair. All types contain six green receptors and a basal photoreceptor. Optical modelling of the rhabdom suggests that the basal photoreceptors have a red-shifted sensitivity, which might enhance the red admiral's ability to discriminate red colours on the wing. Under daylight conditions, the red shift of the basal photoreceptor is ∼30 nm, compared to the rhodopsin spectrum template peaking at 520 nm, while the shift of green photoreceptors is ∼15 nm.

Surface superconductivity on Weyl semimetal induced by nonmagnetic and ferromagnetic tips

Topological superconductors showing Majorana fermions or bound states at the edge or surface are promising components for potential quantum computation and thus attract much attention in physical sciences. Recently, topological Weyl fermion states have been discovered in nonsuperconducting TaP crystals, which may offer a great platform to investigate topological nontrivial superconductivity if superconductivity can be induced wherein. Here we report the discovery of nonmagnetic and ferromagnetic tips induced unconventional interface superconductivity around the nanoscale point contact region on TaP crystals. The tip-induced superconductivity (TISC) at the contact is enhanced with the ferromagnetic Ni tip, comparing with nonmagnetic Au and PtIr tips. The point contact spectroscopy shows evidences of anisotropic superconductivity with the mixed spin-triplet pairing, indicating unconventional superconducting nature. Moreover, the Shubnikov--de Haas oscillations in magnetoresistance are detected from the tip-point-contact measurement, which demonstrate that the nonzero Berry phase or topological nontrivial property of TaP maintains under the tip point contact. The theoretical analysis shows that surface superconductivity plays a major role in this TISC and there exists a large spin-triplet mixing in the gap function. Therefore, our work suggests an intriguing Weyl surface superconducting state on TaP.

Familism, sibling relationship qualities, and sibling sex constellation as predictors of alcohol use among Mexican-origin adolescents.

Sibling relationship qualities and traditional family values (i.e., familism) are contextual factors relevant for early substance use risk among Mexican-origin adolescents. Yet limited research has examined whether familism moderates the effects of sibling relationship features on alcohol use. The present study examined whether familism enhanced or reduced the effects of sibling intimacy, negativity, and sibling deviance on later alcohol use, also testing whether sibling sex constellation (sisters, brothers, mixed) modified the patterns of influence. We analyzed two waves of data (N = 404) from the California Families Project, a longitudinal study of Mexican-origin youth. Using zero-inflated Poisson models, we examined unique and intersecting prospective influences of age 14 sibling contexts and familism on the likelihood of and degree of engagement in alcohol use at age 16. Results indicated a complex interplay of sibling features, familism values, and alcohol use patterns. Familism moderated the effects of sibling intimacy on later alcohol use patterns. For those with lower familism, increasing intimacy was associated with higher probability of any use, but decreasing degree of use (especially for brother pairs and sister pairs). Among those with higher familism, increasing intimacy predicted reduced probability of any use, but increases in the degree of use (for sister and mixed pairs). More sibling negativity was related to reduced alcohol use probability for brothers, and increased alcohol use in mixed sibling pairs. Sibling deviance was associated with greater age 16 alcohol use. This study highlights cultural considerations for including siblings in substance use prevention programs for Mexican-origin youth. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Volunteer Management in Charity Storehouses: Experience, Congestion and Operational Performance

We study volunteer management at a charity storehouse operated by a large faith‐based organization. The storehouse runs entirely on volunteer efforts. We investigate the role of volunteer experience and storehouse congestion in the preparation of orders using a multi‐method approach. First, we conduct a field study to explore these relationships and collect data at the level of volunteers’ teams. These teams can pair volunteers with either different levels of experience (mixed pairing) or equal levels of experience (no‐mixed pairing). Second, we estimate the effects of volunteer experience and storehouse congestion on the order processing times empirically. Third, we build a simulation model to study how operational decisions—volunteers’ pairing in teams and whether to allow or impede storehouse congestion—affect two performance metrics: on‐time order preparation rate and additional time to prepare the orders, in steady conditions. Then, we simulate disaster conditions at the storehouse, that is, simultaneous surges in supply of volunteers and demand of orders. Contrary to extant literature on team collaboration, we find that no‐mixed pairing outperforms mixed pairing under disaster conditions with storehouse congestion. In fact, no‐mixed pairing improves the on‐time order preparation by 4.32% and the additional time to prepare the orders by 14.42% compared to mixed pairing. Moreover, under disaster conditions, a “controlled congestion” policy at the storehouse delivers the best performance metrics.

Mixed emotion experiences for self or another person in adolescence

IntroductionThis study examined types of reported simultaneous mixed emotion experiences for the first time in adolescence for high and low intensity emotion pairs using an Analogue Emotion Scale which affords the graphing of two opposite valence emotions over time on the same graph. MethodsIn a cross sectional design, 163 participants based in schools across the UK formed two age groups representing early and mid-adolescence (12 years, 5 months-16 years, 9 months vs. 16 years, 10 months-18 years, 8 months) across two conditions considering either their own (n = 83) or another child's (n = 80) emotional experience divided equally for high (n = 80) or low (n = 83) intensity mixed emotion pairs presented in vignettes about themselves or another person. They were seen individually and completed an emotion presence interview and an Analogue Emotion Scale about the emotions experienced in the condition appropriate vignette. ResultsParticipants reported mixed emotions both sequentially and simultaneously. In particular we found that children showed that others experience emotions in a more sequential manner, while they themselves would experience more emotions in a highly simultaneous way. Emotion experience was different depending on the emotion pair and age group. ConclusionsAdolescents’ subjective mixed emotion experiences vary by intensity and patterns of simultaneity over time. Findings are discussed in relation to an evaluative space model of mixed emotion and applications of the AES with adolescent populations.

Magnetoelectric effects and spin switching phenomena at the interface of chiral domains in spin-triplet superconductors

Spin-triplet superconductors with time-reversal symmetry breaking can naturally lead to chiral domain walls in their interior. We study the magnetic properties emerging at the interface of chiral domains with opposite winding by focusing on the effects of a superconducting phase drop across the wall and an applied electric gating. The local inversion symmetry breaking at the domain wall drives mixed singlet-triplet pairing configurations that allow a phase- and electric-controllable magnetization with resulting parallel or antiparallel orientations on the two sides of the domain wall. The magnetic switching is also generally accompanied by both spin and charge currents flowing along the edges, whose amplitudes depend on the achieved parallel or antiparallel magnetic phase. The specific magnetoelectric properties of chiral domains with zero or nonvanishing net magnetization near the wall may have several implications. They can be employed to detect the presence of unconventional pairing as well as to design information storage units based on spin-polarized states attached to topological defects.

Is There Material Loss at the Conical Junctions of Modular Components for Total Knee Arthroplasty?

BackgroundClinical concern exists regarding fretting corrosion and material loss from taper junctions in orthopedic devices, with previous research focusing on the modular components from total hip arthroplasty. Comparatively little has been published regarding the fretting corrosion and material loss in modular knee devices. The purpose of this study is to evaluate fretting corrosion damage and quantify material loss for conical total knee arthroplasty taper interfaces. MethodsStem tapers of 166 retrieved modular knee devices were evaluated for fretting corrosion using a semiquantitative scoring method. High precision profilometry was then used to determine volumetric material loss and maximum wear depth for a subset of 37 components (implanted for 0.25-18.76 years). Scanning electron microscopy and energy-dispersive X-ray spectroscopy were used to characterize the observed damage. ResultsMild to severe fretting corrosion was observed on the majority of tapers, with 23% receiving a maximum visually determined damage score of 4. The median rate of volumetric material loss was 0.11 mm3/y (range 0.00-0.76) for femoral components (both cone and bore taper surfaces combined) and 0.01 mm3 (range 0.00-8.10) for tibial components. Greater rates of material loss were associated with mixed metal pairings. There was a strong correlation between visual fretting corrosion score and calculated material loss (ρ = 0.68, P < .001). Scanning electron microscopy revealed varying degrees of scratching, wear, fretting corrosion, and instances of cracking with morphology not consistent with fretting corrosion, wear, or fatigue. ConclusionAlthough visual evidence of fretting corrosion damage was prevalent and correlated with taper material loss, the measured volumetric material loss was low compared with prior reports from total hip arthroplasty.

A mixed pair of black and red kites in Ukraine, including DNA analysis of hybrid offspring

Red kite (Milvus milvus) is a European raptor. Kites of the nominal subspecies Milvus migrans migrans (hereafter called black kites) breed in the Western Palearctic and in Central Asia. Due to the extremely short period since their divergence, black and red kites can successfully hybridize. A mixed pair of black kite female and red kite male was observed during breeding seasons 2017 and 2018 in Poltva, Ukraine (i.e., in the easternmost part of red kites’ breeding territory). This pair produced three and three young in 2017 and 2018, respectively. DNA of the three young from 2018 was analyzed regarding their mitochondrial CytB haplotype and nuclear Myc gene alleles. All three young had a common black kite CytB haplotype. Myc alleles combinations suggest that the male parent could be not a pure red kite and could have a black kite among its ancestors. All three young from 2018 were presumed predated on or close to the nest by goshawk (Accipiter gentilis).

Falconry Threatens Barbary Falcons in the Canary Islands Through Genetic Admixture and Illegal Harvest of Nestlings

Peregrine Falcons (Falco peregrinus) on the Canary Islands are considered to be of the Barbary Falcon subspecies (F. p. pelegrinoides). Here we report on lost falconry birds present among the wild population of resident falcons, and provide rough approximations of their abundance for Tenerife, the largest island of the Canaries. We observed lost falconry birds breeding with natural wild falcons, with at least one mixed pair producing fledglings. Only 54.1% of the breeding adults that we studied on the island showed typical Barbary Falcon plumage. Some nest sites were systematically poached, affecting the overall productivity of the population. Our findings suggest that the original Canarian Barbary Falcon population could be suffering from genetic mixing due to the presence of individuals originating from outside the population and from illegal harvest of nestlings. We recommend that local authorities continue to assess the degree of genetic admixture that occurs in this population, modify the current falconry regulations, implement management actions to prevent new escapes, eradicate exotic raptors, and put a stop to illegal nestling harvests.

Colour plumage polymorphism in the Booted Eagle: inheritance pattern and temporal stability of the morph frequencies

AbstractColour polymorphism occurs in several animal taxa and in around 3.5% of bird species. This phenomenon is disproportionately high in raptors, affecting approximately 30% of species. However, there are only four research studies in wildAccipitridaespecies and two inFalconidaespecies on colour plumage polymorphism. Here, we used the data collected over 23 years (1995‐2017) for non‐tagged individuals of three Spanish Booted Eagle (Hieraaetus pennatus) populations in order to evaluate the stability of morph frequencies during the study period, also for each sex and between sexes, and also the inheritance pattern of colour plumage polymorphism. Our results showed that morph ratios appeared stable over time and between sexes. In one of the studied populations, we found a biased proportion between dark males and dark females, with very few dark males. Our results suggest that this species follows the typical Mendelian inheritance pattern, the light allele being dominant, for which we propose a system involving two loci with epistasis and two alleles per loci. This system would explain all the cases of colour morphs observed in our studied populations and also that described in the main raptor identification guides. Although our results showed no sex‐linked morph inheritance, the offspring produced in mixed pairs with light males and dark females appear significantly linked to the colour morph of the female with a ratio 1:1.49 light/dark, contrarily to the ratio of 4.35:1 predicted by the Hardy‐Weinberg equilibrium equation. This fact suggests a transmission ratio distortion (TRD) phenomenon in heterozygous light morph males. Further investigation using molecular genetic markers will be necessary to check the genotypes of breeding adults and their offspring to confirm the inheritance mechanisms operating in this species.

Pairing Effects on Bubble Nuclei**Supported by the National Natural Science Foundation of China under Grant Nos U1832120 and 11675265, the State Scholarship Fund of China Scholarship Council under Grant No 201708130035, and the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China under Grant No A2018210146.

In the framework of the Skyrme–Hartree–Fock–Bogoliubov approach with the SkT interaction, the pairing effects on the proton bubble structures of 46Ar and 206Hg are discussed. In calculations, three kinds of pairing forces (volume, surface and mixed pairing interactions) are used. For 46Ar, it is shown that the bubble structure with the volume pairing is almost the same as that with the mixed pairing. The bubble with the surface pairing is less pronounced than those with the volume and mixed pairings. Analyzing the density distributions and occupation probabilities of the proton s states and the quasi-degeneracy between the proton 2s1/2 and 1d3/2 orbitals, we explain the difference between the bubble structure with the surface pairing and those with the volume and mixed pairings. For 206Hg, it is seen that the proton density distribution with the surface pairing is different from those with the volume and mixed pairings in the whole region of the radial distance. In addition, it is found that the bubbles with the three pairing forces are different from each other and the least pronounced bubble is obtained with the surface pairing. Thus the selection of the pairing force is important for the study of the nuclear bubble structure.

The roles of musical expertise and sensory feedback in beat keeping and joint action

Auditory feedback of actions provides additional information about the timing of one’s own actions and those of others. However, little is known about how musicians and nonmusicians integrate auditory feedback from multiple sources to regulate their own timing or to (intentionally or unintentionally) coordinate with a partner. We examined how musical expertise modulates the role of auditory feedback in a two-person synchronization–continuation tapping task. Pairs of individuals were instructed to tap at a rate indicated by an initial metronome cue in all four auditory feedback conditions: no feedback, self-feedback (cannot hear their partner), other feedback (cannot hear themselves), or full feedback (both self and other). Participants within a pair were either both musically trained (musicians), both untrained (nonmusicians), or one musically trained and one untrained (mixed). Results demonstrated that all three pair types spontaneously synchronized with their partner when receiving other or full feedback. Moreover, all pair types were better at maintaining the metronome rate with self-feedback than with no feedback. Musician pairs better maintained the metronome rate when receiving other feedback than when receiving no feedback; in contrast, nonmusician pairs were worse when receiving other or full feedback compared to no feedback. Both members of mixed pairs maintained the metronome rate better in the other and full feedback conditions than in the no feedback condition, similar to musician pairs. Overall, nonmusicians benefited from musicians’ expertise without negatively influencing musicians’ ability to maintain the tapping rate. One implication is that nonmusicians may improve their beat-keeping abilities by performing tasks with musically skilled individuals.

Reactions leading to the first excited states ofLi7andBe7and isospin-mixed states inBe8

Background: Ratios of cross sections for mirror reactions sometimes deviate from the values expected on the basis of charge symmetry. These deviations are attributed to smoothly varying charge-dependent effects (proton charge, different $Q$ values) and to the effects of isospin mixed states in the compound nucleus. The effects are large and well known for certain positive-parity states in $^{8}\mathrm{Be}$, but information is lacking for negative-parity states.Purpose: We measure the excitation functions of angle integrated cross sections for two pairs of reactions that involve $^{8}\mathrm{Be}$ as an intermediate state: (1) $^{6}\mathrm{Li}$ ($d,{p}^{\ensuremath{'}})^{7}\mathrm{Li}$ (0.478 MeV) and $^{6}\mathrm{Li}$ ($d,{n}^{\ensuremath{'}}$) $^{7}\mathrm{Be}$ (0.429 MeV) and (2) $^{7}\mathrm{Li}$ ($p,{p}^{\ensuremath{'}})^{7}\mathrm{Li}$ (0.478 MeV) and $^{7}\mathrm{Li}$ ($p,{n}^{\ensuremath{'}}$) $^{7}\mathrm{Be}$ (0.429 MeV), measure the ratios of the neutron-emitting and proton-emitting reactions, and examine the implications for the structure of $^{8}\mathrm{Be}$.Method: The ratios were determined by observing the isotropically emitted $\ensuremath{\gamma}$ rays from the decay of $^{7}\mathrm{Li}$ (0.478 MeV) and $^{7}\mathrm{Be}$ (0.429 MeV). Shell model calculations were performed for both positive- and negative-parity states. Results were compared to existing information.Results: Ratios, usually with an accuracy of $\ifmmode\pm\else\textpm\fi{}2%$, were obtained for deuteron energies from 0.15 to 7.2 MeV and proton energies from 3.0 to 10.0 MeV. There were relatively strong deviations from expectations based on charge symmetry at the lowest deuteron energies and smaller deviations between ${E}_{d}=$ 2 and 4 MeV. There were very strong deviations for proton energies near 3 and 5.5 MeV, with strong neutron strength near 3 MeV and strong proton strength near 5 MeV. The shell model calculations were generally in good agreement for the positive-parity states and, with some exceptions, for negative-parity states. There is reasonable evidence for the lowest lying ${2}^{\ensuremath{-}}\phantom{\rule{0.16em}{0ex}}T=1$ state at ${E}_{x}=20.2$ MeV and for two new isospin mixed pairs, one for ${2}^{+}$ states near 22 MeV and another for ${2}^{\ensuremath{-}}$ states near 24 MeV.Conclusions: The results will constrain future calculations for isospin mixed states in $^{8}\mathrm{Be}$.

All Possible Topologies of the Fractional-Order Wien Oscillator Family Using Different Approximation Techniques

This paper introduces all the possible topologies of the Wien bridge oscillator family. This family has 72 topologies, 24 of them contain only RC or RL pairs, and the rest contain mixed pairs. The complete mathematical analysis of all twelve possible capacitive-based topologies is proposed in the fractional-order domain. The investigated circuits can be categorized into two groups, each with a similar characteristic equation. Three integer-order approximation techniques for the Laplacian operator $$s^\alpha $$ are employed to solve and simulate the Wien bridge system. The studied approximations are those of Matsuda, Oustaloup, and Valsa’s network. Fractional-order capacitor (FOC) emulators are built using these approximations and applied in the circuit simulation. Comparisons are made on different levels, starting with the mathematical solution of the characteristic equation, followed by PSpice simulation, which compares topologies of the Wien bridge oscillator family. Hardware implementation of the FOC emulators is presented applying passive discrete components using the Foster-I technique. Additionally, sensitivity tests of the discrete components of the FOC emulators are performed using Monte Carlo analysis. Experimental results are introduced to validate the theoretical findings.