Miracle-dz/UniFAR-FTUs huggingface dataset:
Regular and semi-regular representations of groups by posets

By a result of Babai, with finitely many exceptions, every group $G$ admits a semi-regular poset representation with three orbits, that is, a poset $P$ with automorphism group $\textrm{Aut}(P) \simeq G$ such that the action of $\textrm{Aut}(P)$ on the underlying set is free and with three orbits. Among finite groups, only the trivial group and $\mathbb{Z}_2$ have a regular poset representation (i.e. semi-regular with one orbit), however many infinite groups admit such a representation. In this paper we study non-necessarily finite groups which have a regular representation or a semi-regular representation with two orbits. We prove that if $G$ admits a Cayley graph which is locally the Cayley graph of a free group, then it has a semi-regular representation of height 1 with two orbits. In this case we will see that any extension of the integers by $G$ admits a regular representation. Applications are given to finite simple groups, hyperbolic groups, random groups and indicable groups.
Benchmarking Test-Time Adaptation against Distribution Shifts in Image Classification

Test-time adaptation (TTA) is a technique aimed at enhancing the generalization performance of models by leveraging unlabeled samples solely during prediction. Given the need for robustness in neural network systems when faced with distribution shifts, numerous TTA methods have recently been proposed. However, evaluating these methods is often done under different settings, such as varying distribution shifts, backbones, and designing scenarios, leading to a lack of consistent and fair benchmarks to validate their effectiveness. To address this issue, we present a benchmark that systematically evaluates 13 prominent TTA methods and their variants on five widely used image classification datasets: CIFAR-10-C, CIFAR-100-C, ImageNet-C, DomainNet, and Office-Home. These methods encompass a wide range of adaptation scenarios (e.g. online adaptation v.s. offline adaptation, instance adaptation v.s. batch adaptation v.s. domain adaptation). Furthermore, we explore the compatibility of different TTA methods with diverse network backbones. To implement this benchmark, we have developed a unified framework in PyTorch, which allows for consistent evaluation and comparison of the TTA methods across the different datasets and network architectures. By establishing this benchmark, we aim to provide researchers and practitioners with a reliable means of assessing and comparing the effectiveness of TTA methods in improving model robustness and generalization performance. Our code is available at https://github.com/yuyongcan/Benchmark-TTA.
Finding Favourite Tuples on Data Streams with Provably Few Comparisons

One of the most fundamental tasks in data science is to assist a user with unknown preferences in finding high-utility tuples within a large database. To accurately elicit the unknown user preferences, a widely-adopted way is by asking the user to compare pairs of tuples. In this paper, we study the problem of identifying one or more high-utility tuples by adaptively receiving user input on a minimum number of pairwise comparisons. We devise a single-pass streaming algorithm, which processes each tuple in the stream at most once, while ensuring that the memory size and the number of requested comparisons are in the worst case logarithmic in n, where n is the number of all tuples. An important variant of the problem, which can help to reduce human error in comparisons, is to allow users to declare ties when confronted with pairs of tuples of nearly equal utility. We show that the theoretical guarantees of our method can be maintained for this important problem variant. In addition, we show how to enhance existing pruning techniques in the literature by leveraging powerful tools from mathematical programming. Finally, we systematically evaluate all proposed algorithms over both synthetic and real-life datasets, examine their scalability, and demonstrate their superior performance over existing methods.
On the permanence properties of interval homogeneous orthomodular lattices

An or thomodular lattice L is said to be interval homogeneous if it is a -complete and satisfies the following property: Whenever L is isomorphic to an interval [a, b] in L, then L is isomorphic to each interval [c, d] D [a, b]. This class was introduced in the effort to determine the orthomodular lattices which satisfy the Cantor-Bernstein theorem. In this paper we carry on the investigation of this important class. We investigate permanence properties of this class with respect to the formation of substructures and a -epimorphic images. We show tha t there are also fairly complex examples of interval homogeneous orthomodular lattices. In fact, we show as a main result tha t every a -complete or thomodu lar lattice (abbreviated a-OML) can be embedded into an interval homogeneous or thomodular lattice. In a somewhat dual sense, we find tha t each cr-OML is a a -epimorphic image of an interval homogeneous orthomodular lattice.
Superpositions of thermalisation states in relativistic quantum field theory

Recent results in relativistic quantum information and quantum thermodynamics have independently shown that in the quantum regime, a system may fail to thermalise when subject to quantum-controlled application of the same, single thermalisation channel. For example, an accelerating system with fixed proper acceleration is known to thermalise to an acceleration-dependent temperature, known as the Unruh temperature. However, the same system in a superposition of spatially translated trajectories that share the same proper acceleration fails to thermalise. Here, we provide an explanation of these results using the framework of quantum field theory in relativistic noninertial reference frames. We show how a probe that accelerates in a superposition of spatial translations interacts with incommensurate sets of field modes. In special cases where the modes are orthogonal (for example, when the Rindler wedges are translated in a direction orthogonal to the plane of motion), thermalisation does indeed result, corroborating the here provided explanation. We then discuss how this description relates to an information-theoretic approach aimed at studying quantum aspects of temperature through quantum-controlled thermalisations. The present work draws a connection between research in quantum information, relativistic physics, and quantum thermodynamics, in particular showing that relativistic quantum effects can provide a natural realisation of quantum thermodynamical scenarios.
Dynamics of a discrete-time mixed oligopoly Cournot-type model with three time delays

The paper analyzes the interactions among one public firm and $n$ private firms on the market, in the framework of a discrete-time Cournot game with time delay. The production of the public firm is influenced by previous output levels of private firms. The productions of private companies are influenced by the past productions of the public company, as well as by the previous productions of the other private companies. The associated nonlinear system admits two equilibrium points: the positive one and the boundary equilibrium. After the stability analysis, we obtained that the boundary equilibrium point is a saddle point. If there is no delay, for the positive equilibrium point we have determined the stability region. Then, for different particular cases of delays, we found the conditions for which the positive equilibrium is asymptotically stable. The flip and Neimark-Sacker bifurcations are investigated. In addition, numerous numerical examples are performed to reveal the complex dynamic behavior of the system.
Intrinsic and tunable quantum anomalous Hall effect and magnetic topological phases in 
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By first-principles calculations, we study the magnetic and topological properties of XYBi2Te5-family (X, Y = Mn, Ni, V, Eu) compounds. The strongly coupled double magnetic atom-layers can significantly enhance the magnetic ordering temperature while keeping the topologically nontrivial properties. Particularly, NiVBi2Te5 is found to be a magnetic Weyl semimetal in bulk and a Chern insulator in thin film with both the Curie temperature (~150 K) and full gap well above 77 K. Ni2Bi2Te5, MnNiBi2Te5, NiVBi2Te5 and NiEuBi2Te5 exhibits intrinsic dynamic axion state. Among them, MnNiBi2Te5 has a Neel temperature over 200 K and Ni2Bi2Te5 even demonstrates antiferromagnetic order above room temperature. These results indicate an approach to realize high temperature quantum anomalous Hall effect and other topological quantum effects for practical applications.
Fast Estimation of Physical Error Contributions of Quantum Gates

Large-scale quantum computation requires a fast assessment of the main sources of error in the implemented quantum gates. To this aim, we provide a learning based framework that allows to extract the contribution of each physical noise source to the infidelity of a series of gates with a small number of experimental measurements. To illustrate this method, we consider the case of superconducting transmon architectures, where we focus on the diabatic implementation of the CZ gate with tunable couplers. In this context, we account for all relevant noise sources, including non-Markovian noise, electronics imperfections and the effect of tunable couplers to the error of the computation.
University of Birmingham Self-injurious behaviour in individuals with autism spectrum disorder and intellectual disability

Background: Autism spectrum disorder (ASD) has been identified as a risk marker for self-injurious behaviour. In this study we aimed to describe the prevalence, topography and correlates of self-injury in individuals with ASD in contrast to individuals with Fragile X and Down syndromes and examine person characteristics associated with self-injury across and within these groups. Method: Carers of individuals with ASD (N=149; mean age=9.98, SD=4.86), Fragile X syndrome (N=123; mean age=15.32, SD=8.74) and Down syndrome (N=49; mean age=15.84, SD=12.59) completed questionnaires relating to the presence and topography of self-injury Information was also gathered regarding demographic characteristics, affect, autistic behaviour, hyperactivity, impulsivity and repetitive behaviour. Results: Self-injurious behaviour was displayed by 50% of the ASD sample; a significantly higher prevalence than in the Down syndrome group (18.4%) but broadly similar to the prevalence in Fragile X syndrome (54.5%). Self-injury was associated with significantly higher levels of autistic behaviour within the Down and Fragile X syndrome groups. Within the ASD group, the presence of self-injury was associated with significantly higher levels of impulsivity and hyperactivity, negative affect and significantly lower levels of ability and speech. Conclusions: Self-injurious behaviour is prevalent in individuals with ASD and the presence of ASD phenomenology increases the risk of self-injury in individuals with known genetic disorders but without a diagnosis of idiopathic autism. Person characteristics associated with self-injury in ASD indicate a role for impaired behavioural inhibition, low levels of ability and negative affect in the development of self-injurious behaviour.
Single ion coupled to a high-finesse optical fibre cavity for cQED in the strong coupling regime

The research undertaken unites two distinct areas of quantum information processing: single ions stored in radio-frequency traps and single photons in optical fibres. Strings of ions are presently the most successful implementation of quantum computing, with elementary quantum algorithm and quantum simulations realised. The principal challenge in the field is to enhance the quantum processing power by scaling up current devices to larger systems. We pursue one of the most promising strategies: distributed quantum computation in which multiple small-scale ion processors are interlinked by exchanging photonic quantum bits via optical fibres. This requires a coherent quantum interface between ions and photons, mapping ionic to photonic quantum states and vice versa. To maximise fidelity and the success rate of the scheme, the interaction of ions and photons must take place in a microscopic optical cavity with high finesse. To this end, single 40Ca+ were trapped in a radio-frequency ion trap whose trapping electrodes are hollow cylinders. Optical fibres with mirrors machined on the facets are inserted into the electrodes to form a Fabry-Perot cavity. Because the fibres are shielded by the electrodes the detrimental distortion of the trapping field due to their presence is suppressed and ions can be trapped for several hours. 40Ca+ has a -type energy level scheme wherein the ion is cooled on the 42P1/2 ⇔ 42S1/2 transition and the cavity is tuned to the 42P1/2 ⇔ 32D3/2 transition. This thesis reports the successful coupling of single ions to a high finesse optical fibre based cavity, with coupling strength g = 2π · 4:6 MHz. The cavity has length 367 μm, finesse of 40,000 and linewidth 2k = 2π · 9:4 MHz. In this coupling regime, the enhancement of the ion's emission rate through the Purcell effect was observed. Further, anti-correlation was observed in the emission rates between the P1/2 ⇔ D3/2 and P1/2 ⇔ S1/2 transitions with an effective emission rate suppression of up to 60% in the latter transition. The built system offers greater promises. Once the position in the cavity mode has been optimised we expect to reach the long-sought after strong coupling regime with (g, k, y) = 2π · (12:2; 4:7; 11:2) MHz.
Arbuscular mycorrhizal fungi enhance phosphate uptake and alter bacterial communities in maize rhizosphere soil

Arbuscular mycorrhizal fungi (AMF) can symbiose with many plants and improve nutrient uptake for their host plant. Rhizosphere microorganisms have been pointed to play important roles in helping AMF to mobilize soil insoluble nutrients, especially phosphorus. Whether the change in phosphate transport under AMF colonization will affect rhizosphere microorganisms is still unknown. Here, we evaluated the links of interactions among AMF and the rhizosphere bacterial community of maize (Zea mays L.) by using a maize mycorrhizal defective mutant. Loss of mycorrhizal symbiosis function reduced the phosphorus concentration, biomass, and shoot length of maize colonized by AMF. Using 16S rRNA gene amplicon high-throughput sequencing, we found that the mutant material shifted the bacterial community in the rhizosphere under AMF colonization. Further functional prediction based on amplicon sequencing indicated that rhizosphere bacteria involved in sulfur reduction were recruited by the AMF colonized mutant but reduced in the AMF- colonized wild type. These bacteria harbored much abundance of sulfur metabolism-related genes and negatively correlated with biomass and phosphorus concentrations of maize. Collectively, this study shows that AMF symbiosis recruited rhizosphere bacterial communities to improve soil phosphate mobilization, which may also play a potential role in regulating sulfur uptake. This study provides a theoretical basis for improving crop adaptation to nutrient deficiency through soil microbial management practices.
Immuno-PET Imaging of CD69 Visualizes T-Cell Activation and Predicts Survival Following Immunotherapy in Murine Glioblastoma

Glioblastoma (GBM) is the most common and malignant primary brain tumor in adults. Immunotherapy may be promising for the treatment of some patients with GBM; however, there is a need for noninvasive neuroimaging techniques to predict immunotherapeutic responses. The effectiveness of most immunotherapeutic strategies requires T-cell activation. Therefore, we aimed to evaluate an early marker of T-cell activation, CD69, for its use as an imaging biomarker of response to immunotherapy for GBM. Herein, we performed CD69 immunostaining on human and mouse T cells following in vitro activation and post immune checkpoint inhibitors (ICI) in an orthotopic syngeneic mouse glioma model. CD69 expression on tumor-infiltrating leukocytes was assessed using single-cell RNA sequencing (scRNA-seq) data from patients with recurrent GBM receiving ICI. Radiolabeled CD69 Ab PET/CT imaging (CD69 immuno-PET) was performed on GBM-bearing mice longitudinally to quantify CD69 and its association with survival following immunotherapy. We show CD69 expression is upregulated upon T-cell activation and on tumor-infiltrating lymphocytes (TIL) in response to immunotherapy. Similarly, scRNA-seq data demonstrated elevated CD69 on TILs from patients with ICI-treated recurrent GBM as compared with TILs from control cohorts. CD69 immuno-PET studies showed a significantly higher tracer uptake in the tumors of ICI-treated mice compared with controls. Importantly, we observed a positive correlation between survival and CD69 immuno-PET signals in immunotherapy-treated animals and established a trajectory of T-cell activation by virtue of CD69-immuno-PET measurements. Our study supports the potential use of CD69 immuno-PET as an immunotherapy response assessment imaging tool for patients with GBM. Significance: Immunotherapy may hold promise for the treatment of some patients with GBM. There is a need to assess therapy responsiveness to allow the continuation of effective treatment in responders and to avoid ineffective treatment with potential adverse effects in the nonresponders. We demonstrate that noninvasive PET/CT imaging of CD69 may allow early detection of immunotherapy responsiveness in patients with GBM.
$J$ -stability of expanding maps in non-Archimedean dynamics

The aim of this paper is to show $J$ -stability of expanding rational maps over an algebraically closed, complete and non-Archimedean field of characteristic zero. More precisely, we will show that for any expanding rational map, there exists a neighborhood of it such that the dynamics on the Julia set of any rational map in the neighborhood is the same as the dynamics of the expanding rational map as a non-Archimedean analogue of a corollary of Mañé, Sad and Sullivan’s result [On the dynamics of rational maps. Ann. Sci. Éc. Norm. Supér. (4) 16 (1983), 193–217] in complex dynamics.
Effective omalizumab treatment influenced eosinophil function in severe allergic asthmatics

Background Omalizumab is an effective anti-immunoglobulin E (IgE) treatment for allergic asthma. Eosinophil plays a critical role in the pathogenesis of allergic airway inflammation. This study aimed to explore the influence of effective omalizumab treatment on circulating eosinophils. Methods Allergic asthmatics enrolled in the study were treated with omalizumab for at least 16 weeks and exhibited a good or excellent response according to the global evaluation of treatment effectiveness (GETE) assessed by each patient and specialist physician. For eosinophil functional evaluation, peripheral blood eosinophils were separated; and examined the expression of human leukocyte antigen (HLA)-DR and co-stimulatory molecules cluster of differentiation (CD) 80, CD86 and CD40 by Flow Cytometry and serum were to measure the concentration of eotaxin-1 before and after 16 weeks of omalizumab treatment. Results Totally 32 allergic asthma patients who responded positively to omalizumab treatment were included. Omalizumab responders showed a significant decline in the expression of co-stimulatory molecules CD40, CD80, and CD86 on peripheral eosinophils and in serum eotaxin-1 concentration after treatment. Negative correlations (r=−0.61, P=0.048) were observed between the change in CD80+ eosinophils and the change in forced expiratory volume in the first second (FEV1)/forced vital capacity (FVC)% predicted and maximal expiratory flow (MEF) 25% after omalizumab treatment. Omalizumab improved FEV1/FVC% predicted (3.88, P=0.033), fractional exhaled nitric oxide (FeNO, −22.24, P=0.028), asthma control test (ACT, 4.22, P<0.001), mini asthma quality of life questionnaire (mini-AQLQ, −14.44, P=0.019), Leicester cough questionnaire (LCQ, 3.03, P=0.009) and visual analogue scale (VAS) for allergic symptoms (−13.00, P=0.001) in patients with severe allergic asthma statistically; reduced mini rhino-conjunctivitis quality of life questionnaire (mini-RQLQ, −8.50, P=0.047), and self-rating anxiety scale (SAS, −5.08, P=0.040) in allergic asthmatics with concomitant allergic rhinitis (AR) or anxiety, respectively. Conclusions Our findings show a unique role of omalizumab in reducing co-stimulatory molecules expression on eosinophil and serum eotaxin-1 levels in severe allergic asthmatics accompanied by improvement of multiple clinical parameters of allergic diseases.
Integrated lipidomic and transcriptomic analyses reveal the mechanism of lipid biosynthesis and accumulation during seed development in sesame

Sesame is one of the most important oilseed crops and attracts significant attention because of its huge nutritional capacity. However, the molecular mechanisms underlying oil accumulation in sesame remains poorly understood. In this study, lipidomic and transcriptomic analyses in different stages of sesame seed (Luzhi No.1, seed oil content 56%) development were performed to gain insight into the regulatory mechanisms that govern differences in lipid composition, content, biosynthesis, and transport. In total, 481 lipids, including fatty acids (FAs, 38 species), triacylglycerol (TAG, 127 species), ceramide (33 species), phosphatidic acid (20 species), and diacylglycerol (17 species), were detected in developing sesame seed using gas and liquid chromatography-mass spectrometry. Most FAs and other lipids accumulated 21–33 days after flowering. RNA-sequence profiling in developing seed highlighted the enhanced expression of genes involved in the biosynthesis and transport of FAs, TAGs, and membrane lipids, which was similar to that seen during lipid accumulation. Through the differential expression analysis of genes involved in lipid biosynthesis and metabolism during seed development, several candidate genes were found to affect the oil content and FA composition of sesame seed, including ACCase, FAD2, DGAT, G3PDH, PEPCase, WRI1 and WRI1-like genes. Our study reveals the patterns of lipid accumulation and biosynthesis-related gene expression and lays an important foundation for the further exploration of sesame seed lipid biosynthesis and accumulation.
Cosmological Viability of Theories with Massive Spin-2 Fields

Theories of spin-2 fields take on a particular role in modern physics. They do not only describe the mediation of gravity, the only theory of fundamental interactions of which no quantum field theoretical description exists, it furthermore was thought that they necessarily predict massless gauge bosons. Just recently, a consistent theory of a massive graviton was constructed and, subsequently, generalized to a bimetric theory of two interacting spin-2 fields. This thesis studies both the viability and consequences at cosmological scales in massive gravity as well as bimetric theories. We show that all consistent models that are free of gradient and ghost instabilities behave like the cosmological standard model, LCDM. In addition, we construct a new theory of massive gravity which is stable at both classical background and quantum level, even though it suffers from the Boulware-Deser ghost.