We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for uncovering spatio-temporal patterns and constructing low-dimensional models of dynamical systems, it suffers from significant performance degradation under noise due to its reliance on least-squares estimation for computing the linear time evolution operator. Existing robust variants typically modify the least-squares formulation, but they remain unstable and fail to ensure faithful low-dimensional representations. First, we introduce a convex optimization-based preprocessing method designed to effectively remove mixed noise, achieving accurate and stable mode extraction. Second, we propose a new convex formulation for dimensional reduction that explicitly links the robustly extracted modes to the original noisy observations, constructing a faithful representation of the original data via a sparse weighted sum of the modes. Both stages are efficiently solved by a preconditioned primal-dual splitting method. Experiments on fluid dynamics datasets demo
We investigate the impact of chemical equilibration and the resulting bulk viscosity on non-radial oscillation modes of warm neutron stars at temperatures up to $T\approx 5$ MeV, relevant for protoneutron stars and neutron-star post-merger remnants. In this regime, the relaxation rate of weak interactions becomes comparable to the characteristic frequencies of composition $g$-modes in the core, resulting in resonant damping. To capture this effect, we introduce the dynamical sound speed, a complex, frequency-dependent generalization of the adiabatic sound speed that encodes both the restoring force and the dissipative effects of bulk compression. Using realistic weak reaction rates and three representative equations of state, we compute the complex frequencies of composition $g$-modes with finite-temperature profiles. We find that bulk viscous damping becomes increasingly significant with temperature and can completely suppress composition $g$-modes. In contrast, the $f$-mode remains largely unaffected by bulk viscosity due to its nearly divergence-free character. Our results highlight the sensitivity of $g$-mode behavior to thermal structure, weak reaction rates, and the equation
The generation of mode-2 nonlinear internal waves (IWs) by the evolution of a mode-1 IW in a two-dimensional stratification is investigated. A generation model accounting for intermodal interaction is derived based on a multi-modal approach in a weakly nonlinear and non-hydrostatic configuration. The generation model is numerically solved to simulate the evolution of mode-1 and mode-2 IWs in an inhomogeneous pycnocline. The numerical experiments confirm that a mode-2 IW is generated due to linear and nonlinear intermodal interaction. The mode-2 IW continues growing and gradually separates with the mode-1 IW during the generation process. A non-dimensional quantity quantifying the energy of mode-2 IWs is used to investigate the favorable conditions for the formation of mode-2 IWs. The numerical results suggest that the pycnocline strength or depth prominently affects the formation of mode-2 IWs, followed by pycnocline thickness. A weakening or shoaling pycnocline favors the formation of mode-2 IWs by evidently enhancing linear and nonlinear intermodal interaction, whereas a thinning pycnocline favors the process mainly by enhancing nonlinear intermodal interaction. Shortening the fr
We present a systematic study of the low-energy collective modes for different insulating states at integer fillings in twisted bilayer graphene. In particular, we provide a simple counting rule for the total number of soft modes, and analyze their energies and symmetry quantum numbers in detail. To study the soft mode spectra, we employ time dependent Hartree-Fock whose results are reproduced analytically via an effective sigma model description. We find two different types of low-energy modes - (i) approximate Goldstone modes associated with breaking an enlarged U(4)$\times$U(4) symmetry and, surprisingly, a set of (ii) nematic modes with non-zero angular momentum under three-fold rotation. The modes of type (i) include true gapless Goldstone modes associated with exact symmetries in addition to gapped "pseudo-Goldstone" modes associated with approximate symmetries. While the modes of type (ii) are always gapped, we show that their gap decreases as the Berry curvature grows more concentrated. For realistic parameter values, the gapped soft modes of both types have comparable gaps of only a few meV, and lie completely inside the mean-field bandgap. The entire set of soft modes eme
Viscosity is the resistance of a liquid to flow, governed by atomic-scale friction between its constituent atoms. While viscosity can be directly computed using the Green-Kubo formalism, its microscopic origin remains poorly understood. In this work, we calculate the viscosity of a $\mathrm{Cu_{50}Zr_{50}}$ metallic liquid and a Kob-Andersen model in a large range of temperatures and compare the results with a theoretical formula based on nonaffine linear response and instantaneous normal mode theory. This analysis reveals that, above approximately the mode-coupling temperature ($T_{\text{MC}}$), unstable localized instantaneous normal modes (ULINMs) control the viscosity, suggesting a microscopic definition of it as diffusive momentum transport facilitated by local structural excitations mediated by ULINMs as precursors. On the other hand, at $ \approx T_{\text{MC}}$, we observe a dynamical crossover below which the viscosity is governed by stable modes. This behavior is compatible with the topological transition that emerges in the potential energy landscape between minima dominated dynamics ($T<T_{\text{MC}}$), corresponding to stable modes, and saddles dominated dynamics ($T
To elucidate low-frequency vibrational modes, we investigate a benzoxazolium--coumarin (BCO+) donor-pi-acceptor derivative using transmission terahertz time-domain spectroscopy (THz-TDS). The retrieved complex refractive index reveals distinct modes at 0.62, 0.85, 1.30, 1.81, and 2.07 THz. Gas-phase density functional theory (DFT) agrees well with these features and enables assignment of specific intramolecular motions. Together, THz-TDS and DFT identify the characteristic low-frequency modes of BCO+ and suggest their connection to intramolecular charge transfer-relevant nuclear motions, highlighting that THz-TDS can serve as a sensitive probe of vibrational signatures in donor-pi-acceptor systems.
The mode of a collection of values (i.e., the most frequent value in the collection) is a key summary statistic. Finding the mode in a given range of an array of values is thus of great importance, and constructing a data structure to solve this problem is in fact the well-known Range Mode problem. In this work, we introduce the Subtree Mode (SM) problem, the analogous problem in a leaf-colored tree, where the task is to compute the most frequent color in the leaves of the subtree of a given node. SM is motivated by several applications in domains such as text analytics and biology, where the data are hierarchical and can thus be represented as a (leaf-colored) tree. Our central contribution is a time-optimal algorithm for SM that computes the answer for every node of an input $N$-node tree in $O(N)$ time. We further show how our solution can be adapted for node-colored trees, or for computing the $k$ most frequent colors, for any given $k=O(1)$, in the optimal $O(N)$ time. Moreover, we prove that a similarly fast solution for when the input is a sink-colored directed acyclic graph instead of a leaf-colored tree is highly unlikely. Our experiments on real datasets with trees of up
In this study, we investigate the dynamics of system composed of a single cavity consisting of an optical parametric amplifier (OPA) and a YIG sphere influenced by a bias magnetic field. This bias field leads to magnetostrictive effects on magnon modes that induces phonons. We investigate the position fluctuation spectrum and the output field spectrum, finding that at G =0, the system displays a single peak, indicative of weak coupling between the optical and phononic modes. As G increases (e.g., G =0.1 kappa_a, 0.2 kappa_a, 0.4 kappa_a, we observe a transition to double peak, which reflects stronger coupling in the vicinity of cavity along with phonon modes that leads to normal mode splitting (NMS) in cavity magnomechanic system. Furthermore, we examine that the OPA amplifies the Y quadrature while squeezing the X quadrature of the output field spectrum. This sensitive behavior results in a more pronounced splitting in the Y quadrature spectra compared to the X quadrature. Our findings emphasize the essential role of the OPA in adjusting the interaction strength between the optical and phononic modes as well as underscore the importance of quadrature analysis in characterizing the
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional topological insulators the boundary modes are chiral, one-dimensional propagating modes along the edges of the system. Thus, topological photonic insulators with large Chern numbers naturally display a topologically protected multimode waveguide at their edges. Here, we show how to take advantage of these topologically protected propagating modes by interfacing them with quantum emitters. In particular, using a Harper-Hofstadter lattice, we find situations in which the emitters feature quasiquantized decay rates due to the increasing number of edge modes, and where their spontaneous emission spatially separates in different modes. We also show how using a single $π$-pulse the combination of such spatial separation and the interacting character of the emitters leads to the formation of a single-photon time-bin entangled state with no classical analog, which we characterize computing its entanglement entropy. Finally, we also show how the emitters can se
Field measurements of second-mode internal solitary waves (mode-2 ISWs) during the winter on the upper continental slope of the northern South China Sea were reported in Yang et al. (2009), but their generation mechanism remains elusive. We investigated this issue with a multi-modal evolution model and theoretical analysis, which suggest that the observed mode-2 ISWs were generated by a shoaling mode-2 semidiurnal internal tide (IT) that emanated from the Luzon Strait. The results show that two groups of mode-2 ISWs usually appear within one semidiurnal tidal period, successively riding on expanded and subsequently compressed pycnoclines. The number of wave groups largely depends on the amplitudes of the ITs; that is, a larger IT produces larger mode-2 ISWs. Furthermore, intermodal coupling dominates the evolution of a mode-1 IT, highlighting the importance of considering mode scattering in the propagation of low-mode ITs.
Advances in computing power enable more widespread use of the mode, which is a natural measure of central tendency since, as the most probable value, it is not influenced by the tails in the distribution. The properties of the half-sample mode, which is a simple and fast estimator of the mode of a continuous distribution, are studied. The half-sample mode is less sensitive to outliers than most other estimators of location, including many other low-bias estimators of the mode. Its breakdown point is one half, equal to that of the median. However, because of its finite rejection point, the half-sample mode is much less sensitive to outliers that are all either greater or less than the other values of the sample. This is confirmed by applying the mode estimator and the median to samples drawn from normal, lognormal, and Pareto distributions contaminated by outliers. It is also shown that the half-sample mode, in combination with a robust scale estimator, is a highly robust starting point for iterative robust location estimators such as Huber's M-estimator. The half-sample mode can easily be generalized to modal intervals containing more or less than half of the sample. An application
This paper presents the development of a sliding mode controller using the backstepping approach. The controller is employed to synthesize tracking errors and Lyapunov functions. A novel state-space representation is formulated by incorporating the dynamics of the quadrotor and accounting for non-holonomic constraints. The proposed sliding mode controller effectively addresses system nonlinearities and improves tracking of predefined trajectories. Simulation results are presented graphically to demonstrate the controller's performance.
Recently, the LHCb collaboration reported the observation of the decay mode $B_{c}^{-}\rightarrow\overline{B}_{s}^{0}π^{-}$ with the largest exclusive branching fraction amongst the known decay modes of all the $B$ mesons. Here we propose a search for a few lepton-number violating decay modes of $B_c$ which can only be induced by Majorana neutrinos. Distinguishing between Dirac and Majorana nature of neutrinos is an outstanding problem and hence, all possible searches for Majorana neutrinos need to be carried out. Since the lepton number violating modes are expected to be rare, when using meson decay modes for these searches one expects CKM favoured modes to be the preferred ones; $B_{c}\rightarrow B_{s}$ is one such transition. With a resonance enhancement of the Majorana neutrino mediating the $B_{c}^{-}\rightarrow\overline{B}_{s}^{0}\ell_{1}{-}\ell_{2}^{-}π^{+}$ modes one can hope to observe these rare modes, or, even their non-observation can be used to obtain constraints on the mixing angles of the heavy Majorana singlet with the light flavour neutrinos from upper limits of the branching fractions which are tighter or compatible with results from earlier studies. Also, we find
Eigen mode selection ought to be a practical issue in some real game systems, as it is a practical issue in the dynamics behaviour of a building, bridge, or molecular, because of the mathematical similarity in theory. However, its reality and accuracy have not been known in real games. We design a 5-strategy game which, in the replicator dynamics theory, is predicted to exist two eigen modes. Further, in behaviour game theory, the game is predicted that the mode selection should depends on the game parameter. We conduct human subject game experiments by controlling the parameter. The data confirm that, the predictions on the mode existence as well as the mode selection are significantly supported. This finding suggests that, like the equilibrium selection concept in classical game theory, eigen mode selection is an issue in game dynamics theory.
In this paper we investigate the low energy shear modes in fluid systems with spontaneously broken translations by a specific holographic model. In absence of momentum relaxation, we find that there exist two decoupled gapless modes in the transverse channel, one of which is purely diffusive and the other corresponds to vortex like excitations. The diffusive mode is associated with the conservation of momentum and the vortex mode can be viewed as the Goldstone mode of the spontaneous symmetry breaking. Switching on an external source which breaks the translations explicitly but weakly, the would-be gapless modes both get relaxed and acquire a tiny mass gap. Finally, in the strong momentum relaxation regime, we find a (pseudo-)diffusive-to-sound crossover that is set by a momentum gap.
The success of contrastive language-image pretraining (CLIP) relies on the supervision from the pairing between images and captions, which tends to be noisy in web-crawled data. We present Mixture of Data Experts (MoDE) and learn a system of CLIP data experts via clustering. Each data expert is trained on one data cluster, being less sensitive to false negative noises in other clusters. At inference time, we ensemble their outputs by applying weights determined through the correlation between task metadata and cluster conditions. To estimate the correlation precisely, the samples in one cluster should be semantically similar, but the number of data experts should still be reasonable for training and inference. As such, we consider the ontology in human language and propose to use fine-grained cluster centers to represent each data expert at a coarse-grained level. Experimental studies show that four CLIP data experts on ViT-B/16 outperform the ViT-L/14 by OpenAI CLIP and OpenCLIP on zero-shot image classification but with less ($<$35\%) training cost. Meanwhile, MoDE can train all data expert asynchronously and can flexibly include new data experts. The code is available at http
Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including both the effects of gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that of Owen et al. (1998) in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that, while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B >= 10^14 ( us/300 Hz)^2 G, where us is the spin frequency, the spindown rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfven wave emission in the neutron star magnetosphere. The Alfven wave driving of the r-mode becomes more import
Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can define sheaves of coinvariants on pointed coordinatized curves from $V$-modules. We show that if the mode transition algebras admit multiplicative identities with certain properties, these sheaves deform as wanted on families of curves with nodes (so $V$ satisfies smoothing). Consequently, coherent sheaves of coinvariants defined by vertex operator algebras that satisfy smoothing form vector bundles. We also show that mode transition algebras give information about higher level Zhu algebras and generalized Verma modules. As an application, we completely describe higher level Zhu algebras of the Heisenberg vertex algebra for all levels, proving a conjecture of Addabbo--Barron.
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on multifractality and universal fluctuations, which is conceptually different from periodic-orbit scarring.
Calcium fluoride (CaF$_2$) crystalline whispering gallery mode resonators (WGMRs) exhibit ultrahigh intrinsic quality factors and a low power anomalous dispersion in the communication and mid-infrared bands, making them attractive platforms for microresonator-based comb generation. However, their unique negative thermo-optic effects pose challenges when achieving thermal equilibrium. To our knowledge, our experiments serve as the first demonstration of soliton microcombs in Q > 109 CaF$_2$ WGMRs. We observed soliton mode-locking and bidirectional switching of soliton numbers caused by the negative thermo-optic effects. Additionally, various soliton formation dynamics are shown, including breathing and vibrational solitons, which can be attributed to thermo-photomechanical oscillations. Thus, our results enrich the soliton generation platform and provide a reference for generating solitons from WGMRs that comprise other materials with negative thermo-optic effects. In the future, the ultrahigh quality factor of CaF$_2$ crystal cavities may enable the generation of sub-milliwatt-level broad-spectrum soliton combs.