By Te Research Articles

Assessments, assumptions and ableism: examining court-ordered parenting capacity assessments of parents with intellectual disability and cognitive difficulties

ABSTRACT Background Parental intellectual disability is considered a risk factor for child removal internationally. In New South Wales, Australia, authorised clinicians are court appointed experts who assess parenting and cognitive capacity in child protection matters. Method This study examined a sample of 20 assessment orders requesting parenting capacity and cognitive capacity assessments and corresponding authorised clinician reports. Results Authorised clinicians were requested to assess whether parental intellectual disability and cognitive impairment posed the risk of harm to children. Clinicians assessed parents as either “able with support” or “unable” to provide adequate care to their child. Conclusion Our findings highlight the law’s conceptualisation of risk, parenting capacity, and cognitive impairment in binary terms (i.e., risk or no risk, able or unable), which in turn limits casework planning and clinicians’ framing of parents’ abilities. We provide recommendations to improve fair and equitable assessment processes for parents with cognitive difficulties, as well as access to timely and appropriate services.

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks.

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI. The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints. The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels. The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

On Recursive Tiling of some Mathematical Objects.

This essay, in a novel way, uses various tiles, such as dominoes, square-, interlocking-, and flow-tiles, to visualize approximations to recursively defined, potentially infinite mathematical objects, such as binary code tables, and variants of the space-filling Hilbert curve. The power of L-systems is shown by defining these tiled objects as L-systems.

Maximum radial pattern matching for minimum star map identification

This paper proposes an all-sky star map identification algorithm that can simultaneously achieve high identification probability, low algorithm complexity, and small databases for well photometric and intrinsic parameters-calibrated star sensors. The proposed algorithm includes three main steps. First, a binary radial pattern table is constructed offline. Then, the maximum value matching of the radial pattern is performed between the star spots and the guide stars, and the star pairs (i.e., the minimum star map) after radial pattern matching undergo a coarse matching through angular distance cross-validation. Finally, a reference star map is designed based on the identified star pairs, and the matching of all the star spots in the field of view is realized. Simulation and analysis results show that the database required by the proposed algorithm for 5,000 guide stars is not larger than 200 KB. Also, when false and missing star spots account for 50% of all guide stars and the star spot extraction error is 0.5 pixel (the corresponding pointing error is 26″), the average star map identification time of the proposed algorithm is less than 2 ms, and its identification probability is higher than 98%. The results demonstrate that the proposed algorithm performs better than similar algorithms.

Multi-label feature selection based on minimizing feature redundancy of mutual information

Multi-label feature selection is an indispensable technology in the preprocessing of multi-label high-dimensional data. Approaches utilizing information theory and sparse models hold promise in this domain, demonstrating strong performance. Although there have been extensive literatures using l1 and l2,1-norms to identify label-specific features and common features in the feature space, they all ignore the redundant information interference problem when different features are learned simultaneously. Considering that features and labels in multi-label data are rarely linearly correlated, the MFS-MFR approach is presented to generate a representation of the nonlinear correlation between features and labels using the mutual information estimator. Following that, MFS-MFR detects specific and common features in the feature-label mutual information space using two coefficient matrices constrained by the l1 and l2,1-norms, respectively. In particular, we define a non-zero correlation constraint that effectively minimizes the redundant correlation between the two matrices. Moreover, a manifold regularization term is devised to preserve the local information of the mutual information space. To solve the optimization model with nonlinear binary regular term, we employ a novel solution approach called S-FISTA. Extensive experiments across 15 multi-label benchmark datasets, comparing against 11 top-performing multi-label feature selection methods, demonstrate the superior performance of MFS-MFR.

Heritage as threshold: an autoethnographic exploration of the porticoes of Bologna (Italy)

The contents and aims of this paper derive from an autoethnographic exploration of the porticoes of Bologna, which in 2021 became part of the UNESCO World Heritage List. It was the difficulty of their candidacy process, which is not usual for Italian urban heritage, that shaped my concern with them. I conducted empirical research by walking under the porticoes in order to understand the reasons behind their otherness as official heritage and how these reasons can represent an interesting case for current geographical debates on heritage in its cultural dimension. Drawing first of all on the fact that my embodied experience of the porticoes was a liminal experience, I argue here that their otherness lies in being heritage as threshold by developing this idea in two ways. The first way consists of interpreting the spatiality of the porticoes in the light of the concept of threshold. To the extent that a threshold, as conceived here, is not a boundary but a zone of transition where binary terms are held together and interact with each other, the spatial nature of the porticoes as thresholds challenges the sedentary certainties and sharp boundaries of ‘authorized heritage discourse’. The second way in which I conceive and develop the idea of heritage as threshold consists of relating it, through the example of the porticoes, to the process of heritage-making. From this point of view, the idea of heritage as threshold is a spatial interpretation of the process of construction, deconstruction, reconstruction of heritage, whenever based on the interweaving of official discourses and everyday experiences, on their reciprocal influence and transformation. The construction of the narrative on the porticoes as heritage represents a perfect example of this process of transition and interchange between different perspectives – a process closely associated with the spatiality of thresholds.

3D Human Pose Estimation Based on Wearable IMUs and Multiple Camera Views

The problem of 3D human pose estimation (HPE) has been the focus of research in recent years, yet precise estimation remains an under-explored challenge. In this paper, the merits of both multiview images and wearable IMUs are combined to enhance the process of 3D HPE. We build upon a state-of-the-art baseline while introducing three novelties. Initially, we enhance the precision of keypoint localization by substituting Gaussian kernels with Laplacian kernels in the generation of target heatmaps. Secondly, we incorporate orientation regularized network (ORN), which enhances cross-modal heatmap fusion by taking a weighted average of the top-scored values instead of solely relying on the maximum value. This not only improves robustness to outliers but also leads to higher accuracy in pose estimation. Lastly, we modify the limb length constraint in the conventional orientation regularized pictorial structure model (ORPSM) to improve the estimation of joint positions. Specifically, we devise a soft-coded binary term for limb length constraint, hence imposing a flexible and smoothed penalization and reducing sensitivity to hyperparameters. The experimental results using the TotalCapture dataset reveal a significant improvement, with a 10.3% increase in PCKh accuracy at the one-twelfth threshold and a 3.9 mm reduction in MPJPE error compared to the baseline.

‘Keeping two cultures together’: the binary construction of belonging in narratives of professionals on children’s cultural identity

ABSTRACT This paper analyses interviews with Italian education professionals collected in the context of a European research project on the participation of children with a migration background, aiming to understand how interviewees’ construct children’s belonging and cultural identity. We also investigated whether these constructions change because of the gender of children involved in the narratives. We found that a narrative of incompleteness underpinned the professionals’ views. They described children’s trajectories as incomplete both because of their status as children and because of their perceived division in binary terms. Furthermore, through these narratives, the interviewees work out their own professional role identities and reconfirm established institutional discourses.

Dialectical Sentences and Social Contradictions in Nathaniel Hawthorne’s The House of the Seven Gables

This paper highlights formal and thematic expressions of discursive conflicts in Nathaniel Hawthorne’s The House of the Seven Gables. It focuses on Hawthorne’s use of the “dialectical sentence,” a type of sentence attributed to German dialectical thinkers, principally Theodor Adorno. Voicing two contradictory views in the same breath, the dialectical sentence provides formal expression of irresolvable discursive conflicts. Hawthorne’s dialectical sentence serves as a suitable medium for expressing the conflict of interests between the Pyncheon and Maule families. The discursive conflicts are expressed through a set of binary terms, including Pyncheon/Maule, novel/romance, present/past, reason/rumor and science/ superstition. The first term in each binary usually serves for the Pyncheons and the second, the Maules. Thus, expressed in dialectical sentences, the narrative voice oscillates between an irony which reflects the values of the former family and an enthusiasm which reflects those of the latter. Coming down firmly on neither side of the conflict, and through avoiding reconciliation, the novel takes on a dialectical structure which keeps the resolution of the discursive conflicts, as a utopian element, for a time outside the novel’s timeframe.

Rydberg-atom experiment for the integer factorization problem

The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms. Thus, it is crucial to develop quantum computing algorithms to address this problem. This study introduces a quantum approach that utilizes Rydberg atoms to tackle the factorization problem. Experimental demonstrations are conducted for the factorization of small composite numbers such as 6=2×3, 15=3×5, and 35=5×7. This approach involves employing Rydberg-atom graphs to algorithmically program binary multiplication tables, yielding many-body ground states that represent superpositions of factoring solutions. Subsequently, these states are probed using quantum adiabatic computing. Limitations of this method are discussed, specifically addressing the scalability of current Rydberg quantum computing for the intricate computational problem. Published by the American Physical Society 2024

(De)Gendering (English-Spanish) Translation of Legal Texts

Abstract Within Western culture, gender is frequently interpreted in terms of binarism (male versus female), derived from biological sex at birth. Nevertheless, there is an accelerating percentage of non-binary and transgender people, who are not related to binary nomenclature, and they also need to resort to legal documentation and their renderings into other languages. This fact becomes a troublesome issue that must be nowadays solved, especially when translating into Spanish, a grammatical gender language, from English, a non-grammatical gender language. In this paper we will first select a corpus of eight British legal documents representing highly demanded translation briefs. We will then search for 15 problematic lexical items, searching for their lexicographic definitions and translations, and we will later resort to their most feasible translations into the Spanish language, considering both gendered translations and genderless ones. Our research shows how the Spanish language has its own translation techniques, especially paraphrasing, to be able to provide the English-Spanish target readership with binary legal terms, and especially with non-binary ones.

Nativeness is a binary concept —Invasiveness and its management are not

In interdisciplinary fields such as biodiversity conservation or invasion science —where multiple perspectives from diverse disciplines often need to converge for effective environmental management, it is crucial to minimise terminological confusion in order to understand and transmit concepts accurately. The diversity of perspectives can exert a substantial influence on defining key terms in those interdisciplinary fields, potentially resulting in confusion. A lively topic within invasion science concerns the definitions of nativeness, non-nativeness, and invasiveness. While some academics dismiss the nativeness concept because it cannot be objectively defined, others advocate for its categorization, and a third perspective posits it as a binary term. Here we argue the inherent binary nature of nativeness, even when our capacity to observe is challenging. Nativeness (and consequently, non-nativeness) is an intrinsic and binary property of a species (i.e. the set of populations of a species) in a place, which should remain a central piece of information in biodiversity conservation and ecosystem restoration. In contrast, invasiveness, which relies on quantitative metrics (including abundance, spread, or impacts), should not be defined on binary terms. This underscores the importance of offering diverse, context-specific management strategies to deal with it. We illustrate the consistency of nativeness' binary nature and the need to rely on diverse management options to address different invasion scenarios with the example of the freshwater crayfish in the Iberian Peninsula.

New improved model for joint segmentation and registration of multi-modality images: application to medical images

Joint segmentation and registration of images is a focused area of research nowadays. Jointly segmenting and registering noisy images and images having weak boundaries/intensity inhomogeneity is a challenging task. In medical image processing, joint segmentation and registration are essential methods that aid in distinguishing structures and aligning images for precise diagnosis and therapy. However, these methods encounter challenges, such as computational complexity and sensitivity to variations in image quality, which may reduce their effectiveness in real-world applications. Another major issue is still attaining effective joint segmentation and registration in the presence of artifacts or anatomical deformations. In this paper, a new nonparametric joint model is proposed for the segmentation and registration of multi-modality images having weak boundaries/noise. For segmentation purposes, the model will be utilizing local binary fitting data term and for registration, it is utilizing conditional mutual information. For regularization of the model, we are using linear curvature. The new proposed model is more efficient to segmenting and registering multi-modality images having intensity inhomogeneity, noise and/or weak boundaries. The proposed model is also tested on the images obtained from the freely available CHOAS dataset and compare the results of the proposed model with the other existing models using statistical measures such as the Jaccard similarity index, relative reduction, Dice similarity coefficient and Hausdorff distance. It can be seen that the proposed model outperforms the other existing models in terms of quantitatively and qualitatively.

America Needs a Realistic Ukraine Debate

A healthy democracy ought to be able to develop and debate its national-security options honestly, openly and vigorously. This has not been the case when it comes to the United States’ policy on Ukraine. The American debate is instead polarised between supporting Ukraine for ‘as long as it takes’ and withdrawing support altogether. To view the war in such binary terms is not good for the United States. Nor is it good for Ukraine. There is obviously a strategic logic to punishing the Kremlin for its aggression, and we can continue to hope that Ukraine emerges from this war as a democracy with a bright European future. On the current course, however, Americans are in for a very long and very costly war over a relatively small amount of territory of limited strategic relevance to the United States. Unless US policymakers can arrive at a constructively pragmatic realism, disaffected voters could revolt in a manner that exacerbates America’s existing domestic political fractures.

Effect of COVID-19 Pandemic on Labour Market Outcomes in Kenya

Purpose: This paper investigated the effect of COVID-19 pandemic on the labour market outcomes in Kenya, using quarterly labour force survey data (2019 to 2021), 2019 census data and COVID-19 wave II of a novel high-frequency phone survey collected from May 30th to June 6th, 2020. The study also estimated the impact of COVID-19 pandemic on unemployment rate by using the quarterly Labour Force Survey data from 2019 to 2022.
 Methodology: The study applied probit models because of the non-linearity of the variables. More specifically, the dependent variables are binary terms, hence maximum likelihood estimation techniques are the most appropriate.
 Findings: The findings of the study reveal that COVID-19 was associated with a 25-percentage point’s increase in the unemployment rate in the country with certain counties witnessing the highest spikes in unemployment. Although there has been some recovery, the unemployment rate remains elevated compared to pre-pandemic levels, signifying ongoing labour market challenges. COVID-19 impact on the labour market varied significantly by sector. The education sector experienced a higher incidence of employment loss, while income losses were more pronounced in sectors such as mining, manufacturing, retail, transport, and construction. Particularly, women workers in the retail and transport sectors faced twice the likelihood of income loss compared to their male counterparts. The pandemic disproportionately affected low-income workers and casual labourers, accentuating income inequalities in the labour market. Casual workers, who often lack labour protections and benefits, were significantly impacted.
 Unique Contribution to Theory, Practice and Policy: Considering these findings, the study provides several policy recommendations: Implementing targeted interventions and support programs in counties with the highest unemployment spikes. These interventions can include skill development programs to enhance workers' employability and tailored employment and income support strategies adapted to each county's unique economic circumstances. Prioritize the adoption of Information and Communication Technology (ICT) to enhance resilience and adaptability across sectors. Governments, both at the national and county levels, should prioritize policies aimed at enhancing the incomes of disadvantaged households. Through expanding access to social protection programs, enforcing minimum wage regulations, and improving working conditions, especially for casual workers and low-income households. The study's insights provide valuable guidance for shaping future economic recovery strategies, particularly in the event of economic shocks in the labour market.

Nonparametric estimation of the random effects distribution for the risk or rate ratio in rare events meta-analysis with the arm-based and contrast-based approaches.

Rare events are events which occur with low frequencies. These often arise in clinical trials or cohort studies where the data are arranged in binary contingency tables. In this article, we investigate the estimation of effect heterogeneity for the risk-ratio parameter in meta-analysis of rare events studies through two likelihood-based nonparametric mixture approaches: an arm-based and a contrast-based model. Maximum likelihood estimation is achieved using the EM algorithm. Special attention is given to the choice of initial values. Inspired by the classification likelihood, a strategy is implemented which repeatably uses random allocation of the studies to the mixture components as choice of initial values. The likelihoods under the contrast-based and arm-based approaches are compared and differences are highlighted. We use simulations to assess the performance of these two methods. Under the design of sampling studies with nested treatment groups, the results show that the nonparametric mixture model based on the contrast-based approach is more appropriate in terms of model selection criteria such as AIC and BIC. Under the arm-based design the results from the arm-based model performs well although in some cases it is also outperformed by the contrast-based model. Comparisons of the estimators are provided in terms of bias and mean squared error. Also included in the comparison is the mixed Poisson regression model as well as the classical DerSimonian-Laird model (using the Mantel-Haenszel estimator for the common effect). Using simulation, estimating effect heterogeneity in the case of the contrast-based method appears to behave better than the compared methods although differences become negligible for large within-study sample sizes. We illustrate the methodologies using several meta-analytic data sets in medicine.

Jenseits der pädagogischen Illusion? Historischvergleichende Überlegungen zur Wirkungsgeschichte der moralischen Bildung von Kindern und Jugendlichen

This article can be broken down into two parts, perhaps somewhat unequally as far as its orientation is concerned. In the first part, the author takes the reader on a kind of exploration of the history of moral education, a subject which, at first glance and from the perspective of the years he spent studying educational historiography, appears to be rather undeveloped terrain. Since the piece is related to the awarding of the Comenius Medal, Comenius himself already provides a good starting point for this round of studies. As in the case of Herbart, another classic within the canon of educational history, Comenius held the opinion that morality plays a key role in upbringing of young people, which became increasingly scintillating in appearance from the Enlightenment onwards. For in a well-regulated society, it was by means of upbringing and education that individual freedom could be created. However, in the course of the 20th century and to the shame of humanity, people were forced to witness how the idea that people and society could be shaped by social engineering could equally give rise to a lack of freedom, as the aberrations of Nazism, fascism and ultimately Marxism-Leninism unequivocally demonstrated. So can such “reversals” of modern-day thought ultimately teach us any overall lessons about the content, manner and results with which moral curricula are imposed? Or must we first set out to identify the “abnormal” cases that society first branded as such and only subsequently extract those lessons? In other words, can extraordinary situations and events teach us something about the everyday reality of moral education as manifested in the so-called “civilising offensive” that took place from the end of the 18th century onwards? As far as the Low Countries are concerned, the author is, for that matter, setting foot on familiar ground. By utilising previous research on Belgium, Flanders and the (Belgian) Congo, the second part of the article wastes no time in examining what moral education meant in more specific terms in the 20th century. In that regard, the focus not only lies on contextualising the insights and questions raised by the first part, as a “tour d’horizon”, but equally on analysing them in greater depth. After all, the author’s years of research already provide three interesting points of reference: 1) the strong continuity of the patronising perspective; 2) the problematic nature of thinking about educational innovations and didactic innovations in binary terms, such as “old” and “new”, and 3) the lack of a straightforward link between parenting and educational goals on the one hand and their results and effects (including and especially in the long term) on the other. Which leads inevitably to the conclusion that education, important as it is, must not be overestimated. Nor should history for that matter. Perhaps both are nothing more than an opportunity to partake of a meaningful encounter that may be effective, but whose outcome one can never be sure of. Which in turn does not take away from the fact that we must still place our hopes on it. For hope is probably the most positive thing that human beings carry within them, just as Comenius himself proved in his lifetime, by the way.

Rethinking organized crime in Africa

Much of the existing research on organized crime in Africa has emphasised its development and proliferation from state and security perspectives. Such research often relies upon inflated facts for captivating public attention, is fuelled by sensationalist media reports and draws from conceptualisations that give an incomplete picture of the significance of illicit activities, both for the state and their role in enabling and sustaining people’s livelihoods. In contrast, this special issue proposes that more empirical research and analysis is needed to reveal the disjunctures between state and on-the-ground perceptions. Greater attention to a bottom-up vision of illicit activities can demonstrate how defining and understanding these practices through such binary terms as legal/illegal does not necessarily indicate how those engaged in them perceive them. Through bringing together a range of contributions from different disciplinary, theoretical and empirical perspectives, this special issue explores the space between official, policy-driven narratives of crime and the realities of the everyday nature of these practices, in a bid to rethink and challenge the ‘organized crime’ lens through which these activities are increasingly framed.

Regular Double p-Algebras: A Converse to a Katriňák Theorem and Applications

ABSTRACT In 1973, Katriňák proved that regular double p-algebras can be regarded as (regular) double Heyting algebras by ingeniously constructing binary terms for the Heyting implication and its dual in terms of pseudocomplement and its dual. In this paper, we prove a converse to Katriňák’s theorem, in the sense that in the variety ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] of regular dually pseudocomplemented Heyting algebras, the implication operation → satisfies Katriňák’s formula. As applications of this result together with the above-mentioned Katriňák’s theorem, we show that the varieties ℝ D B L ℙ \[\mathbb{R}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{P}\] , ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] , ℝ ℙ ℂ ℍ d \[\mathbb{R}\mathbb{P}\mathbb{C}{{\mathbb{H}}^{d}}\] and ℝ D B L ℍ \[\mathbb{R}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{H}\] of regular double p-algebras, regular dually pseudocomplemented Heyting algebras, regular pseudocomplemented dual Heyting algebras, and regular double Heyting algebras, respectively, are term-equivalent to each other and also that the varieties ℝ D M ℙ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{P}\] , ℝ D M ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{H}\] , ℝ D M D B L ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{H}\] , ℝ D M D B L ℙ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{D}\mathbb{B}\mathbb{L}\mathbb{P}\] of regular De Morgan p-algebras, regular De Morgan Heyting algebras, regular De Morgan double Heyting algebras, and regular De Morgan double p-algebras, respectively, are also term-equivalent to each other. From these results and recent results of Adams, Sankappanavar and Vaz de Carvalho on varieties of regular double p-algebras and regular pseudocomplemented De Morgan algebras, we deduce that the lattices of subvarieties of all these varieties have cardinality 2 ℵ 0 \[{{2}^{{{\aleph }_{0}}}}\] . We then define new logics, ℛ D P C ℋ \[\mathcal{R}\mathcal{D}\mathcal{P}\mathcal{C}\mathcal{H}\] , ℛ P C ℋ d \[\mathcal{R}\mathcal{P}\mathcal{C}{{\mathcal{H}}^{d}}\] and ℛ D ℳ ℋ \[\mathcal{R}\mathcal{D}\mathcal{M}\mathcal{H}\] , and show that they are algebraizable with ℝ D ℙ ℂ ℍ \[\mathbb{R}\mathbb{D}\mathbb{P}\mathbb{C}\mathbb{H}\] , ℝ ℙ ℂ ℍ d \[\mathbb{R}\mathbb{P}\mathbb{C}{{\mathbb{H}}^{d}}\] and ℝ D M ℍ \[\mathbb{R}\mathbb{D}\mathbb{M}\mathbb{H}\] , respectively, as their equivalent algebraic semantics. It is also deduced that the lattices of extensions of all of the above mentioned logics have cardinality 2 ℵ 0 \[{{2}^{{{\aleph }_{0}}}}\] .

Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction

The recent results from the Pulsar Timing Array (PTA) collaborations show the first evidence for the detection of a stochastic background of gravitational waves at the nHz frequencies. This discovery has profound implications for the physics of both the late and the early Universe. In fact, together with the interpretation in terms of supermassive black hole binaries, many sources in the early Universe can provide viable explanations as well. In this paper, we study the gravitational wave background sourced by a network of axion-like-particle (ALP) domain walls at temperatures around the QCD crossover, where the QCD-induced potential provides the necessary bias to annihilate the network. Remarkably, this implies a peak amplitude at frequencies around the sensitivity range of PTAs. We extend previous analysis by taking into account the unavoidable friction on the network stemming from the topological coupling of the ALP to QCD in terms of gluon and pion reflection off the domain walls at high and low temperatures, respectively. We identify the regions of parameter space where the network annihilates in the scaling regime ensuring compatibility with the PTA results, as well as those where friction can be important and a more detailed study around the QCD crossover is required.