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Discrete groups are widely used in the expression of flavor symmetries of leptons. In this paper, we employ a novel mathematical object called group-algebra (GA) to describe symmetries of the leptonic mass matrices. A GA element is constructed by a discrete group with continuous parameters. For a GA element, there is an equivalent symmetry which can be continuous, discrete, and hybrid. According to the equivalence between a GA element and other symmetries, we perform a classification of 198 nontrivial elements of the GA generated by the group $S_{4}$. Based on the results of the classification, the phenomenological consequences of the $S_{4}$ GA are illustrated., Comment: 11 pages

Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account multiple rotational symmetries. By studying its statistics for two-dimensional disordered packings of hard particles along the jamming transition line, we observe the evolution from disordered-particle-rich states to ordered-particle-rich states with the increase of packing fraction, together with the unusual non-monotonic change of the degree of hyperuniformity. At the high packing fraction end of the jamming transition line, the packings are mostly composed of ordered particles and are nearly hyperuniform beyond a finite length. Our work links the local order fluctuations to the thermodynamic stability and density fluctuations of disordered solids. Taking advantage of the order parameter, we propose the structural characteristic of ultra-stable glasses: Although globally disordered evaluated by any single symmetry, they are rich of ordered particles and effectively `globally ordered' with crystal-like density fluctuations., Comment: 10 pages, 4 figures

Wireless federated learning (WFL) enables devices to collaboratively train a global model via local model training, uploading and aggregating. However, WFL faces the data scarcity/heterogeneity problem (i.e., data are limited and unevenly distributed among devices) that degrades the learning performance. In this regard, artificial intelligence generated content (AIGC) can synthesize various types of data to compensate for the insufficient local data. Nevertheless, downloading synthetic data or uploading local models iteratively takes a lot of time, especially for a large amount of devices. To address this issue, we propose to leverage non-orthogonal multiple access (NOMA) to achieve efficient synthetic data and local model transmission. This paper is the first to combine AIGC and NOMA with WFL to maximally enhance the learning performance. For the proposed NOMA+AIGC-enhanced WFL, the problem of jointly optimizing the synthetic data distribution, two-way communication and computation resource allocation to minimize the global learning error is investigated. The problem belongs to NP-hard mixed integer nonlinear programming, whose optimal solution is intractable to find. We first employ the block coordinate descent method to decouple the complicated-coupled variables, and then resort to our analytical method to derive an efficient low-complexity local optimal solution with partial closed-form results. Extensive simulations validate the superiority of the proposed scheme compared to the existing and benchmark schemes such as the frequency/time division multiple access based AIGC-enhanced schemes., Comment: 13 pages, submitted to IEEE TWC for possible publication

Rate splitting multiple access (RSMA) provides a flexible transmission framework that can be applied in mobile edge computing (MEC) systems. However, the research work on RSMA-assisted MEC systems is still at the infancy and many design issues remain unsolved, such as the MEC server and channel allocation problem in general multi-server and multi-channel scenarios as well as the user fairness issues. In this regard, we study an RSMA-assisted MEC system with multiple MEC servers, channels and devices, and consider the fairness among devices. A max-min fairness computation offloading problem to maximize the minimum computation offloading rate is investigated. Since the problem is difficult to solve optimally, we develop an efficient algorithm to obtain a suboptimal solution. Particularly, the time allocation and the computing frequency allocation are derived as closed-form functions of the transmit power allocation and the successive interference cancellation (SIC) decoding order, while the transmit power allocation and the SIC decoding order are jointly optimized via the alternating optimization method, the bisection search method and the successive convex approximation method. For the channel and MEC server allocation problem, we transform it into a hypergraph matching problem and solve it by matching theory. Simulation results demonstrate that the proposed RSMA-assisted MEC system outperforms current MEC systems under various system setups.

Order and disorder constitute two fundamental and opposite themes in condensed matter physics and materials science. Crystals are considered the epitome of order, characterised by long-range translational order. The discovery of quasicrystals, which exhibit rotational symmetries forbidden in crystals and lack periodicity, led to a paradigm shift in solid-state physics. Moving one step forward, it is intriguing to ask whether ordered matter can exist without apparent symmetry breaking. The same question arises considering how ordered amorphous (noncrystalline) solids can be structured. Here, we present the discovery of ideal noncrystals in two dimensions, which are disordered in the conventional sense, lacking Bragg peaks, but exhibit high orderliness based on the steric order, i.e., they are ideally packed. A path-integral-like scheme reveals the underlying long-range structural correlation. We find that these ideal noncrystals are characterised by phononic vibrational modes following the Debye law, fully affine elastic responses, and suppressed density fluctuations at longer wavelengths, reminiscent of hyperuniformity -- all characteristics typically associated with crystals. Therefore, ideal noncrystals represent a peculiar form of matter with a mixed nature -- noncrystalline yet possessing crystal-like properties. Notably, these states are found to be thermodynamically favourable, indicating them as a possible new class of ordered matter without apparent symmetry breaking. Our findings significantly broaden the conceptualization of ordered states of matter and may contribute to a deeper understanding of entropy-driven ordering, particularly in generic amorphous materials.

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multi-layered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multi-layered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

The recent reported Glashow resonance (GR) event shows a promising prospect in the test of the Lorentz violation (LV) by the high-energy astrophysical neutrinos (HANs) around the resonant energy. However, since the production source and the energy spectra of HANs are uncertain at present, moderate LV effects may be concealed at the TeV energy-scale. In this paper, we propose the LV Hamiltonian of a special texture which can lead to the decoupling of $\nu_{\mu}$ ($\bar{\nu}_{\mu}$). On the base of the decoupling, a noticeable damping of the GR event rate is shown for the HANs from the source dominated by $\bar{\nu}_{\mu}$, irrespective of the energy spectra of the HANs at Earth. Accordingly, the observation of GR events may bring stringent constraints on the LV and the production mechanism of HANs., Comment: 13pages, 3figures

Based on 2-minute cadence TESS data from sectors 1-50, we report the results of the systematic extraction of $\delta$ Scuti-type pulsations in the 6431 eclipsing binaries with orbital periods shorter than 13 days. A total number of 242 pulsators were found in those systems, including 143 new discoveries. We examined their pulsation properties based on the H-R diagram and the relationships between the dominant pulsation period $P_{\rm dom}$, orbital period $P_{\rm orb}$, and effective temperature $T_{\rm eff}$. As a consequence, 216 targets are likely $\delta$ Scuti stars (123 new), 11 likely $\gamma$ Doradus-$\delta$ Scuti hybrid stars (8 new), 5 likely $\beta$ Cephei stars (4 new), 4 likely $\delta$ Scuti-$\gamma$ Doradus hybrid stars (3 new), 3 likely Maia stars (3 new), 2 likely pulsating red giants (1 new), and a new unclassified star. As for the 6 new $\delta$ Scuti pulsators in eclipsing binaries with $P_{\rm orb}$ $<$ 0.65 days, we found that 3 of them significantly exceed the upper limits of the $P_{\rm dom}$/$P_{\rm orb}$ ratio. This may indicate that $P_{\rm dom}$ and $P_{\rm orb}$ are uncorrelated for them. Finally, we statistically analyzed the dominant pulsation periods of the 216 $\delta$ Scuti stars in eclipsing binaries. Those stars concentrate around 225 $\mu$Hz and the proportion of stars in the high-frequency region is significantly higher than that of single stars, which could be ascribed to the mass transfer process., Comment: 26 pages, 16 figures, 1 table, accepted for publication in ApJS

Leptonic mixing patterns are usually extracted on the basis of groups or algebraic structures. In this paper, we introduce an alternative geometric method to study the correlations between the leptonic mixing parameters. At the 3$\sigma$ level of the recent global fit data of neutrino oscillations, the distribution of the scattered points of the angles between the vectors, which are constructed by the element of the leptonic mixing matrix, is analysed. We find that the scattered points are concentrated on several special regions. Using the data in these regions, correlations of the leptonic mixing angles and the Dirac CP violating phase are obtained. The implications of the correlations are shown through the predicted flavor ratio of high-energy astrophysical neutrinos (HANs) at Earth., Comment: 21pages, 13figures

The progress of neutrino astronomy makes the precise measurement of the flavor ratio of high energy astronomical neutrinos (HANs) possible in the near future. Then matter effects and new physics effects on the flavor transition of HANs could be tested by the next-generation neutrino telescopes. In this paper we study matter effects in gas around the sources of HANs. The matter effects are dependent on both the decoherence schemes and the sources of neutrinos. We examine the predictions on the flavor ratio at Earth for typical sources with five decoherence schemes. For the adiabatic schemes, the matter effect is notable and may be identified in the special range of the electron density, irrespective of the production sources of HANs. Hence, the precise measurement of the flavor ratio would provide constrains on the propagation schemes and the matter parameter., Comment: 19pages, 10 figures

Semiconductor excitations can hybridize with cavity photons to form exciton-polaritons (EPs) with remarkable properties, including light-like energy flow combined with matter-like interactions. To fully harness these properties, EPs must retain ballistic, coherent transport despite matter-mediated interactions with lattice phonons. Here we develop a nonlinear momentum-resolved optical approach that directly images EPs in real space on femtosecond scales in a range of polaritonic architectures. We focus our analysis on EP propagation in layered halide perovskite microcavities. We reveal that EP-phonon interactions lead to a large renormalization of EP velocities at high excitonic fractions at room temperature. Despite these strong EP-phonon interactions, ballistic transport is maintained for up to half-exciton EPs, in agreement with quantum simulations of dynamic disorder shielding through light-matter hybridization. Above 50% excitonic character, rapid decoherence leads to diffusive transport. Our work provides a general framework to precisely balance EP coherence, velocity, and nonlinear interactions.

The optoelectronic and transport properties of two-dimensional transition metal dichalcogenide semiconductors (2D TMDs) are highly susceptible to external perturbation, enabling precise tailoring of material function through post-synthetic modifications. Here we show that nanoscale inhomogeneities known as nanobubbles can be used for both strain and, less invasively, dielectric tuning of exciton transport in bilayer tungsten disulfide (WSe2). We use ultrasensitive spatiotemporally resolved optical scattering microscopy to directly image exciton transport, revealing that dielectric nanobubbles are surprisingly efficient at funneling and trapping excitons at room temperature, even though the energies of the bright excitons are negligibly affected. Our observations suggest that exciton funneling in dielectric inhomogeneities is driven by momentum-indirect (dark) excitons whose energies are more sensitive to dielectric perturbations than bright excitons. These results reveal a new pathway to control exciton transport in 2D semiconductors with exceptional spatial and energetic precision using dielectric engineering of dark state energetic landscapes.

The leptonic mixing parameters of high precision and the next-generation neutrino telescopes make it possible to test new physics in the flavor transition of the high-energy astrophysical neutrinos(HAN). We introduce a nonsymmetric matrix to modify the predictions of the standard flavor transition matrix. It is constructed with the mixing matrix in vacuum and that at the source of the HAN. The mismatch of the mixing matrices results in the new expectation of the flavor ratio of the HAN at Earth. It also leads to a secondary effect called the apparent P violation (APV). The quantitative analyses of the new effects are performed with a moderate setup of the parameters at the source of the HAN. The correlations between the mixing parameters and the new predictions are shown. From the correlations, the dominant parameters determining the new-physics effects are identified., Comment: 19pages, 8 figures