id
stringlengths 64
64
| published
stringlengths 19
25
| title
stringlengths 7
262
| description
stringlengths 6
54.4k
| link
stringlengths 31
227
| category
stringclasses 6
values | image
stringlengths 3
247
|
|---|---|---|---|---|---|---|
26004cd14fc8d369135763d6087acdfdcb553c752aaa1144ba7c453b80322bb5
|
2026-01-16T00:00:00-05:00
|
Bridging Quantum Mechanics to Organic Liquid Properties via a Universal Force Field
|
arXiv:2508.08575v4 Announce Type: replace Abstract: Molecular dynamics (MD) simulations are essential tools for unraveling atomistic insights into the structure and dynamics of condensed-phase systems. However, the universal and accurate prediction of macroscopic properties from ab initio calculations remains a significant challenge, often hindered by the trade-off between computational cost and simulation accuracy. Here, we present ByteFF-Pol, a graph neural network (GNN)-parameterized polarizable force field, trained exclusively on high-level quantum mechanics (QM) data. Leveraging physically-motivated force field forms and training strategies, ByteFF-Pol exhibits exceptional performance in predicting thermodynamic and transport properties for a wide range of small-molecule liquids and electrolytes, outperforming state-of-the-art (SOTA) classical and machine learning force fields. The zero-shot prediction capability of ByteFF-Pol bridges the gap between microscopic QM calculations and macroscopic liquid properties, enabling the exploration of previously intractable chemical spaces. This advancement holds transformative potential for applications such as electrolyte design and custom-tailored solvent, representing a pivotal step toward data-driven materials discovery.
|
https://arxiv.org/abs/2508.08575
|
Academic Papers
|
svg
|
19404649def198dc08e7d57930e7ce04d023839f84e867710d153bd4b4f51f22
|
2026-01-16T00:00:00-05:00
|
Physics-Informed Neural Networks for Nonlocal Beam Eigenvalue Problems
|
arXiv:2509.04321v2 Announce Type: replace Abstract: The present study investigates the dynamics of nonlocal beams by establishing a consistent stress-driven integral elastic using the Physics-Informed Neural Network (PINN) approach. Specifically, a PINN is developed to compute the first eigenfunction and eigenvalue arising from the underlying sixth-order ordinary differential equation. The PINN is based on a feedforward neural network, with a loss function composed of terms from the differential equation, the normalization condition, and both boundary and constitutive boundary conditions. Relevant eigenvalues are treated as separate trainable variables. The results demonstrate that the proposed method is a powerful and robust tool for addressing the complexity of the problem. Once trained, the neural network is less computationally intensive than analytical methods. The obtained results are compared with benchmark analytical solutions and show strong agreement.
|
https://arxiv.org/abs/2509.04321
|
Academic Papers
|
svg
|
0ff5f6ea0f9d4cba5d5b7e3e0e6948b31f7f756e7691fd5875234c8fefd1dcde
|
2026-01-16T00:00:00-05:00
|
Detection of ultracold neutrons with powdered scintillator screens
|
arXiv:2509.04332v2 Announce Type: replace Abstract: Zinc sulfide (ZnS:Ag) scintillators coated with a thin 10B layer are widely used for ultracold neutron (UCN) detection, but their application is limited by long decay times and significant phosphorescence. We investigated two possible replacement scintillators: yttrium aluminum perovskite (YAP:Ce) and lutetium ttrium orthosilicate (LYSO:Ce). Both exhibit decay times on the order of 30-40 ns, which can help reduce dead time in high-count-rate experiments. YAP:Ce showed approximately 60% lower phosphorescence than ZnS:Ag after 2 days and detected about 20% more UCN. In contrast, LYSO:Ce exhibited higher phosphorescence and produced fewer UCN counts compared to both ZnS:Ag and YAP:Ce. While both tested scintillators are capable UCN detectors, YAP:Ce consistently outperformed LYSO:Ce across all measured performance metrics.
|
https://arxiv.org/abs/2509.04332
|
Academic Papers
|
svg
|
463770b7c02f63f22ab22075eb5377c3d24b312ff1489586e7fbec1db269866e
|
2026-01-16T00:00:00-05:00
|
All-Order Wichmann and Kroll Contribution in Heavy Electronic and Exotic Atoms
|
arXiv:2509.08763v2 Announce Type: replace Abstract: We present a theoretical study of the Wichmann and Kroll correction to the one-loop vacuum polarization (VP) to all-orders in $\alpha Z$. We consider electronic, muonic, and antiprotonic atoms for a wide range of nuclear charge numbers and explicitly investigate the influence of finite nuclear size effects and different nuclear models. Moreover, we place special emphasis on circular Rydberg states in the exotic atoms as they have recently attracted interest as a tool to perform isolated tests of strong-field QED. We find that the higher-order vacuum polarization is strongly enhanced in exotic atoms and remains large enough in highly excited Rydberg states that an accurate treatment is crucial for the analysis of upcoming spectroscopy experiments like PAX. Moreover, our calculations show that the VP contribution to the Lamb shift in these exotic Rydberg states has almost no dependence on the structure of the nucleus.
|
https://arxiv.org/abs/2509.08763
|
Academic Papers
|
svg
|
0d2087a8d2420e8020877d4c9a9d960e6bbb584ea219dcd28fdf827d4914f75a
|
2026-01-16T00:00:00-05:00
|
Systematic Study of Amorphous ABC Heterostructures at the Atomic Scale as a Second-Order Nonlinear Optical Metamaterial
|
arXiv:2509.21583v4 Announce Type: replace Abstract: Systematic exploration of amorphous ABC heterostructures revealed that nanoscale morphological modifications markedly improved their artificial bulk second-order susceptibility. These amorphous birefringent heterostructures were fabricated through plasma-enhanced atomic layer deposition of three oxides, effectively breaking the centrosymmetry on the nanoscale. We observe a dependence of the optical nonlinearity on the thickness variation of three constituent materials, SiO$_2$, TiO$_2$, and Al$_2$O$_3$, ranging from tens of nanometers to the atomic scale, and these thin films exhibit second-order susceptibility at their interfaces. Our findings reveal that the enhancement of nonlinear optical properties is strongly correlated with a high density of layers and superior interface quality, where the interface second-order nonlinearity transitions to bulk-like second-harmonic generation. An effective bulk second-order susceptibility of $\chi_{zzz} = 2.0 \pm 0.2$~pm/V at the wavelength of 1032~nm is achieved, comparable to typical values for conventional monocrystalline nonlinear materials.
|
https://arxiv.org/abs/2509.21583
|
Academic Papers
|
svg
|
386d9c82c3ea1d6bd552a6d62213ddfd9cf9833a3b51b99d4c7c661f19adc1b2
|
2026-01-16T00:00:00-05:00
|
Correlation function metrology for warm dense matter: Recent developments and practical guidelines
|
arXiv:2510.00493v2 Announce Type: replace Abstract: X-ray Thomson scattering (XRTS) has emerged as a valuable diagnostic for matter under extreme conditions, as it captures the intricate many-body physics of the probed sample. Recent advances, such as the model-free temperature diagnostic of Dornheim et al. [Nat.Commun. 13, 7911 (2022)], have demonstrated how much information can be extracted directly within the imaginary-time formalism. However, since the imaginary-time formalism is a concept often difficult to grasp, we provide here a systematic overview of its theoretical foundations and explicitly demonstrate its practical applications to temperature inference, including relevant subtleties. Furthermore, we present recent developments that enable the determination of the absolute normalization, Rayleigh weight, and density from XRTS measurements without reliance on uncontrolled model assumptions. Finally, we outline a unified workflow that guides the extraction of these key observables, offering a practical framework for applying the method to interpret experimental measurements.
|
https://arxiv.org/abs/2510.00493
|
Academic Papers
|
svg
|
a26adb9bc41ed6fe2a6278119a7d80c76933653c3f7c80b7ae45cad9b6995d3c
|
2026-01-16T00:00:00-05:00
|
Electronic phase-locking for three-color, two-pathway coherent control
|
arXiv:2510.08205v2 Announce Type: replace Abstract: We report a new method of two-pathway coherent control using three narrow-band cw laser sources, phase locked in an optical phase-lock loop, to maintain the high degree of optical coherence required for the coherent control process. In addition, we derive expressions for two-photon transition amplitudes and demonstrate their dependence on the polarization of the field components. This phase-locking technique expands the set of interactions to which coherent control techniques may be applied. It also allows for a constant low-frequency offset between the optical interactions, producing a continuous and constant phase ramp between the interactions, facilitating phase-sensitive detection of the modulating atomic signal. We illustrate this technique with two-photon vs.~one-photon excitation of a $\Delta F = 1$ component, and alternatively a $\Delta F = 0$ component, of the $6s \: ^2S_{1/2} \rightarrow 7s \: ^2S_{1/2}$ transition of atomic cesium.
|
https://arxiv.org/abs/2510.08205
|
Academic Papers
|
svg
|
e2a55db18f525ad3fbcb7d28369c1548aa2e79588ba35cebb1536c95c5ca1db6
|
2026-01-16T00:00:00-05:00
|
Detection of Earth's free oscillations utilizing TianQin
|
arXiv:2510.10107v2 Announce Type: replace Abstract: The measurement of Earth's free oscillations plays an important role in studying the Earth's large-scale structure. Space technology development presents a potential method to observe these normal modes by measuring inter-satellite distances. However, the disturbance from the Earth's low-degree gravity field makes it challenging for low Earth orbit gravity measurement satellites such as Gravity Recovery and Climate Experiment (GRACE) and TianQin-2 to extract signals from Earth's free oscillations directly. Here, we propose that by taking advantage of the high Earth orbit, the TianQin satellites can effectively avoid this disturbance, enabling direct measurement of Earth's free oscillations. We derive an analytical waveform to describe the response of Earth's free oscillations in TianQin. Based on this waveform, we use Bayesian analysis to extract the normal modes from numerical simulation data and perform parameter estimation. Our findings reveal that for a magnitude 7.9, Wenchuan-like earthquake, the resulting free oscillations will generate a signal that signal-to-noise ratio (SNR) is 73 in TianQin, and approximately 9 different modes can be distinguished. This result shows TianQin can open a new window to examine the Earth's free oscillations and study the Earth's interior and earthquakes independently from ground-based gravity measurement.
|
https://arxiv.org/abs/2510.10107
|
Academic Papers
|
svg
|
ca686ceadc0bfc020b41d1a41203ab3ba0ab24a9b676de6fbc727e02ab223a34
|
2026-01-16T00:00:00-05:00
|
Unravelling inter-channel quantum interference in below-threshold nonsequential double ionization with statistical measures
|
arXiv:2510.16135v2 Announce Type: replace Abstract: We present a systematic study of interchannel quantum interference in laser-induced nonsequential double ionization (NSDI) within the strong-field approximation. Focusing on the below-threshold intensity regime where the recollision-excitation with subsequent ionization (RESI) pathway dominates, we derive analytical phase conditions governing interference between distinct excitation channels for arbitrary driving fields. To quantify the interplay between channels resulting from a vast number of interfering processes, we introduce statistical metrics based on the Earth Mover's Distance, allowing us to assess the relative weight of each channel's contribution to the two-electron photoelectron momentum distributions (PMDs). We identify key factors that determine whether interchannel interference is appreciable such as comparable channel intensities, strong spatial overlap between the excited-state wavefunctions and the energy difference between contributing channels. We demonstrate that for linearly polarized few-cycle pulses, the typical intrachannel interference features associated with exchange, temporal shifts and combined exchange-temporal interference are retained with interchannel interference. Our findings establish a hierarchy of interference mechanisms in RESI and may provide practical guidelines for enhancing or suppressing interference in different regions of the momentum plane. The toolkit presented in this work is transferable to a wide range of interferometric schemes involving different excitation channels.
|
https://arxiv.org/abs/2510.16135
|
Academic Papers
|
svg
|
b66e3ecf783aa103cede16c17b0a2dd48fc7afad02464a97959f5910c88ce058
|
2026-01-16T00:00:00-05:00
|
Patch-MLP-Based Predictive Control: Simulation of Upstream Pointing Stabilization for PHELIX Laser System
|
arXiv:2510.26540v2 Announce Type: replace Abstract: High-energy laser facilities such as PHELIX at GSI require excellent beam pointing stability for reproducibility and relative independence for future experiments. Beam pointing stability has been traditionally achieved using simple proportional-integral-derivative (PID) control which removes the problem of slow drift, but is limited because of the time delay in knowing the diagnosis and the inertia in the mechanical system associated with mirrors. In this work, we introduce a predictive control strategy where the forecasting of beam pointing errors is performed by a patch-based multilayer perceptron (Patch-MLP) designed to capture local temporal patterns for more robust short-term jitter prediction. The subsequent conversion of these predicted errors into correction signals is handled by a PID controller. The neural network has been trained on diagnostic time-series data to predict beam pointing error. Using the feed-forward controller compensates for system delays. Simulations with a correction mirror placed upstream of the PHELIX pre-amplifier bridge confirm that the predictive control scheme reduces residual jitter compared to conventional PID control. Over a 10-hour dataset the controller maintained stable performance without drift, while standard pointing metrics showed consistent improvements of the order of 10 to 20 percent. The predictive controller operates without drift, and therefore may improve reproducibility and operational efficiency in high energy, low repetition rate laser experiment conditions.
|
https://arxiv.org/abs/2510.26540
|
Academic Papers
|
svg
|
8bf51a678f8457d1c078998b0a18dcc3c759f539f603f492528c35fe93c8eefe
|
2026-01-16T00:00:00-05:00
|
Transmission Efficiency of the Recoil Mass Spectrometer EMMA at TRIUMF
|
arXiv:2511.05643v2 Announce Type: replace Abstract: The mean transmission efficiency of the EMMA recoil mass spectrometer at TRIUMF has been measured with 6 different angular apertures at 17 kinetic energy/charge deviations with respect to the central, reference trajectory. Measurements performed using a 148Gd alpha source installed at the target position of the spectrometer are compared to ion-optical calculations and Monte Carlo simulations. The transmission efficiency as a function of angle and kinetic energy/charge is described empirically using piecewise Gaussian functions whose parameters are fit to the data.
|
https://arxiv.org/abs/2511.05643
|
Academic Papers
|
svg
|
21e5f6e6e15390801d395097baf05dd0f1f500f125789511c6b698a5d9c8d29c
|
2026-01-16T00:00:00-05:00
|
Canonical Clocks and Hidden Geometric Freedom in Self-Imaging
|
arXiv:2601.08020v2 Announce Type: replace Abstract: Self-imaging represents a core hallmark of paraxial (quadratic)-wave evolution; yet, across its many realizations and generalizations over the past two centuries, the uniformity of recurrence planes along the propagation axis has been considered fundamental. However, by reframing the general phenomenon of self-imaging within its natural symplectic framework, we show that all self-imaging effects are necessarily tied to uniformly periodic recurrences in the canonical evolution coordinate -- metaplectic time -- and that the correspondence of that coordinate to the physical propagation axis represents an unexplored degree of freedom, which can be engineered arbitrarily by the initial transverse phase structure. Using a single programmable spatial light modulator, we demonstrate the construction of Talbot carpets characterized by recurrence spacings that accelerate and decelerate along the propagation axis, as well as those that follow polynomial, exponential, and sinusoidal axial trajectories, all of which preserve exact reconstruction in the canonical metaplectic time. These results establish metaplectic time as the fundamental invariant of self-imaging and reveal a regime of controllable axial dynamics previously thought to be fixed.
|
https://arxiv.org/abs/2601.08020
|
Academic Papers
|
svg
|
71cdb69cf719f0e618a16685e2e6af50c6d313257eb8a529f0e72e82265b4973
|
2026-01-16T00:00:00-05:00
|
Accelerating Density Fitting with Adaptive-precision and 8-bit Integer on AI Accelerators
|
arXiv:2601.08077v2 Announce Type: replace Abstract: The emergence of artificial intelligence (AI) accelerators like NVIDIA Tensor Cores offers new opportunities to speed up tensor-heavy scientific computations. However, applying them to quantum chemistry is challenging due to strict accuracy demands and irregular data patterns. We propose an adaptive precision algorithm to accelerate the density fitting (DF) method with Gaussian basis sets on AI accelerators using 8-bit integer (INT8) arithmetics. Implemented in the GPU-accelerated PySCF package, the algorithm is tested on more than twenty molecular systems with different NVIDIA GPUs. Compared to the standard FP64 code, our algorithm is up to 204\% faster on a RTX 4090 gaming GPU and up to 364\% faster on a RTX 6000 Ada workstation GPU without compromising the converged energy. This work demonstrates a practical approach to use AI hardware for reliable quantum chemistry simulations.
|
https://arxiv.org/abs/2601.08077
|
Academic Papers
|
svg
|
f63f7863007c5670f4ffc26cade683bad2a833ea7dad0983f964d342973b7c26
|
2026-01-16T00:00:00-05:00
|
The 1/3 Geometric Constant: Scale Invariance and the Origin of "Missing Energy" in 3D Quantum Fragmentation
|
arXiv:2601.08255v2 Announce Type: replace Abstract: We report a fundamental geometric constraint on the detection of kinetic energy release (KER) in three-dimensional quantum fragmentation. By investigating the sudden dissociation of Slater-type orbitals, physically motivated basis for localized states, we demonstrate that the ratio of the peak detected energy to the integrated mean, $R_E = E_{\text{peak}}/\langle E \rangle$, is strictly bounded below $0.5$ for all physical parameter spaces. We systematically map the behavior of $R_E$ across the orbital localization ($\zeta$) and effective repulsive charge ($Q$) landscape. Our results show that while $R_E$ exhibits sensitivity to the force-field geometry at atomic scales, it converges to a remarkably stable, scale-invariant constant of $\approx 0.33$ in the high-localization limit ($M \propto \zeta$) characteristic of subatomic ground states ($n=1$,$Q=1$). This $1/3$ geometric constant provides a provocative first-principles interpretation of the historical ``missing energy'' problem in nuclear physics. We suggest that the $1/3$ average energy ratio observed in Beta decay spectra may be a topological artifact of the $4\pi r^2$ volume weighting inherent to 3D wavefunctions, rather than exclusively a signature of undetected mass. This work establishes $R_E < 0.5$ as a universal geometric baseline for quantum simulations and offers a new framework for reconstructing the true energy budget in subatomic calorimetry by correcting for the intrinsic masking effects of 3D radial geometry.
|
https://arxiv.org/abs/2601.08255
|
Academic Papers
|
svg
|
5371db2de3bbe28159625829cbd9b0b46e4bbf8d8a7b3509cb913e072be500b6
|
2026-01-16T00:00:00-05:00
|
Terahertz Communications Using Effective-Medium-Slot Waveguides
|
arXiv:2601.08261v2 Announce Type: replace Abstract: All-dielectric effective-medium-clad waveguides have been widely exploited in terahertz communications owing to their extremely low loss, low dispersion, and broad bandwidth. In this work, we propose a substrateless effective-medium-slot waveguide. Additionally, we introduce a taper-free interface that allows terahertz waves to directly couple from a metallic hollow waveguide without requiring dielectric insertion. By engineering slot couplers with an effectivemedium channel for impedance and modal matching, the waveguide achieves a fractional 3-dB bandwidth of 40% with a maximum coupling efficiency of 90% in the WR-2.2 band (330-500 GHz). By employing a broadband uni-traveling-carrier photodiode transmitter and sub-harmonic mixer receivers, we achieve an aggregated data rate of 0.8 Tbit/s with quadrature amplitude modulation schemes across 14 channels from 330-600 GHz. The effective-medium-slot waveguide platform yields robust broadband coupling with enhanced mechanical protection, offering reliable interconnects for ultra-high-speed terahertz integrated systems.
|
https://arxiv.org/abs/2601.08261
|
Academic Papers
|
svg
|
5fdea6b99109b80eb8bd11e987874f46878c44fb0fafb26a8d10296e25f51a32
|
2026-01-16T00:00:00-05:00
|
Constraining axion-like dark matter with a radio-frequency atomic magnetometer
|
arXiv:2601.09638v2 Announce Type: replace Abstract: We report on a broadband search for axion-like-particle (ALP) interactions using a radio-frequency-operated $^{87}\mathrm{Rb}$ atomic magnetometer. The instrument provides wide spectral coverage and sensitivity to an oscillating pseudomagnetic field that may be generated by the gradient coupling of the ALP field to the constituent fermions of atoms. We search for an ALP-gradient signature in the mass range $2.40\times10^{-10}\,\mathrm{eV}/c^{2}$--$2.11\times10^{-9}\,\mathrm{eV}/c^{2}$. No statistically significant signatures of an oscillating magnetic field are observed, and we derive upper limits on the corresponding ALP-proton, -neutron and -electron couplings, $g_{\alpha pp}$, $g_{\alpha nn}$ and $g_{\alpha ee}$, respectively. The result on $g_{\alpha pp}$ improves over previous laboratory searches, while the limits on $g_{\alpha nn}$ and $g_{\alpha ee}$ complement earlier laboratory searches and astrophysical bounds. The work extends searches for ALP-fermion interactions into a mass region largely unexplored in a dark-matter context, demonstrating the potential of our method for broadband axion-like particle searches targeting the Galactic dark-matter halo.
|
https://arxiv.org/abs/2601.09638
|
Academic Papers
|
svg
|
2b3eb7d5c1f20aa22db98251613983168f20e0b99d50b6741b7978df3d44d2e6
|
2026-01-16T00:00:00-05:00
|
Rotational state changes in collisions of diatomic molecular ions with atomic ions
|
arXiv:1905.02130v3 Announce Type: replace-cross Abstract: We investigate rotational state changes in a single collision of diatomic molecular ions, polar or apolar, with an atomic ion. Rotational state changes may occur since the angular degree of freedom of the molecular ions interacts with the electric field due to the atomic ion. Thanks to the very different time and energy scales of translational and rotational motion, we may treat the collision classically and describe only the rotations quantum mechanically. We first investigate a number of example systems numerically and then derive closed-form approximations for the rotational excitation per collision, depending on the scattering energy and the molecular parameters. These findings provide the basis for estimating the accumulated rotational excitation in sympathetic cooling of molecular ions by laser-cooled atomic ions [arXiv:2410.22458 ] which involves many single collisions.
|
https://arxiv.org/abs/1905.02130
|
Academic Papers
|
svg
|
e24283cb640e95334e6d39f569d1a40d098eb020bad3a46974d2fa7b8de76497
|
2026-01-16T00:00:00-05:00
|
Theoretical Design of Effective Multilayer Optical Coatings Using Oxyhydride Thin Films
|
arXiv:2010.13502v2 Announce Type: replace-cross Abstract: Rare-earth metal oxyhydride compositions are currently attracting increasing attention to develop materials with unusual optical responses. Herein, using computer simulations of the electronic and optical properties, the optical responses of two stable yttrium oxyhydride compounds, Y4H10O and YHO, are studied for the visible light range. The emphasis is on modeling macroscopic optical characteristics, which are numerically derived within a conventional scheme using refractive indices, and absorption, transmittance, and reflection spectra. The main goal is twofold: first, to simulate spectral behavior of different single-phase and two-phase oxyhydride compositions and second, to conduct a comparative analysis that could explain the features of the transmission spectra measured for different samples. Based on the obtained results, models of new optical coatings are proposed in which yttrium oxyhydrides play the key role. In the context of nonlinear optics, the frequency profile of the second-order susceptibility for the noncentrosymmetric cubic structure of Y4H10O is evaluated and it is shown that this system could exhibit large optical nonlinearity.
|
https://arxiv.org/abs/2010.13502
|
Academic Papers
|
svg
|
847ae060f2e9dd7966a6fe7c21a00e9084dc8a9efe976119360cea80ada5fb2a
|
2026-01-16T00:00:00-05:00
|
Elastodynamical properties of Sturmian structured media
|
arXiv:2105.02548v2 Announce Type: replace-cross Abstract: In this paper, wave propagation in structured media with quasiperiodic patterns is investigated. We propose a methodology based on Sturmian sequences for the generation of structured mechanical systems from a given parameter. The approach is presented in a general form so that it can be applied to waveguides of different nature, as long as they can be modeled with the transfer matrix method. The bulk spectrum is obtained and its fractal nature analyzed. For validation of the theoretical results, three numerical examples are presented. The obtained bulk spectra show different shapes for the studied examples, but they share features which can be explained from the proposed theoretical setting.
|
https://arxiv.org/abs/2105.02548
|
Academic Papers
|
svg
|
d8cc353ca1b1e12289c63bb7856528be865d83766041f4b563f2ff8d0e67426d
|
2026-01-16T00:00:00-05:00
|
Rotational excitation in sympathetic cooling of diatomic molecular ions by laser-cooled atomic ions
|
arXiv:2410.22458v2 Announce Type: replace-cross Abstract: Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [arXiv:1905.02130] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion co-trapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.
|
https://arxiv.org/abs/2410.22458
|
Academic Papers
|
svg
|
585a15001fb53c177f00e3030bb32ed02d5587ab9a707ce0765248e24b2b8187
|
2026-01-16T00:00:00-05:00
|
Predicting the suitability of photocatalysts for water splitting using Koopmans spectral functionals: The case of TiO$_2$ polymorphs
|
arXiv:2412.17488v2 Announce Type: replace-cross Abstract: Photocatalytic water splitting has attracted considerable attention for renewable energy production. Since the first reported photocatalytic water splitting by titanium dioxide, this material remains one of the most promising photocatalysts, due to its suitable band gap and band-edge positions. However, predicting both of these properties is a challenging task for existing computational methods. Here we show how Koopmans spectral functionals can accurately predict the band structure and level alignment of rutile, anatase, and brookite TiO$_2$ using a computationally efficient workflow that only requires (a) a DFT calculation of the photocatalyst/vacuum interface and (b) a Koopmans spectral functional calculation of the bulk photocatalyst. The success of this approach for TiO$_2$ suggests that this strategy could be deployed for assessing the suitability of novel photocatalyst candidates.
|
https://arxiv.org/abs/2412.17488
|
Academic Papers
|
svg
|
6d565e8f3ee09624ca67815e3bae5a2a9c3999aa03f0b057df23991e7be367e8
|
2026-01-16T00:00:00-05:00
|
Cavity-QED Simulation of a Maser beyond the Mean-Field Approximation
|
arXiv:2412.21166v3 Announce Type: replace-cross Abstract: Based on the well-known Tavis-Cummings (TC) model of cavity quantum electrodynamics (QED), we introduce a method for quantum-mechanically simulating the dynamics of experimental masers beyond the mean-field approximation (MFA) that takes into account the spatial variation of the a.c. magnetic field of the maser's amplified microwave mode across its gain medium. The distribution in the coupling between the amplified mode and the medium's very large number (typically $10^{17}$) of spatially distributed quantum emitters can be determined straightforwardly for a given geometry and composition using an electromagnetic-field solver. Upon discretising this distribution as a histogram over a small finite number of bins, we assign -- as an approximation -- the same coupling to all emitters that fall within the same bin, where the value of this coupling equals the center value of the bin's range. With our approximate Hamiltonian arranged as a weighted sum over these bins, we generate expressions for expectation values of operators in the Heisenberg picture to second order in cumulant expansion, using the publicly available QuantumCumulants.jl package in Julia. For ten evenly spaced bins, our model, which can be run on a laptop computer, is used to simulate the recorded output from an experimental maser with a pentacene-doped para-terphenyl gain medium. We find that it replicates the quantum-mechanical features of the measured maser's dynamics, in particular its damped collective Rabi oscillations, more closely than the standard TC model under the MFA can, with an R$^2$ value of 0.774, as opposed to 0.265. Our model should thus aid the quantitative engineering of improved, optimised maser designs.
|
https://arxiv.org/abs/2412.21166
|
Academic Papers
|
svg
|
729192d7318d361de9cb7def44afc0d745557e0348771893faf983f6b924f554
|
2026-01-16T00:00:00-05:00
|
Time-domain extreme ultraviolet diffuse scattering spectroscopy of nanoscale surface phonons
|
arXiv:2502.18445v4 Announce Type: replace-cross Abstract: We report the observation of dynamic fringe patterns in the diffuse scattering of extreme ultraviolet light from surfaces, following femtosecond optical excitation. At each point on the detector, the diffuse scattering intensity exhibits oscillations at well-defined frequencies that correspond to surface phonons with wave vectors determined by the scattering geometry, indicating that the optical excitation generates coherent surface phonons propagating in all directions and spanning a wavelength range from 60 to 300 nm. This phenomenon is observed on a variety of samples, including single-layer and multilayer metal films, as well as bulk semiconductors. The measured surface phonon dispersions show good agreement with theoretical calculations. By comparing signal amplitudes from samples with different surface morphologies, we find that the excitation mechanism is linked to the natural surface roughness of the samples. However, the signal is still detectable on extremely smooth surfaces with sub-nanometer roughness. Our findings demonstrate a simple and effective method for optically exciting coherent surface phonons with nanoscale wavelengths on a wide range of solid samples and establish a foundation for surface phonon spectroscopy in a wave vector range well beyond the limit of conventional surface Brillouin scattering.
|
https://arxiv.org/abs/2502.18445
|
Academic Papers
|
svg
|
8be0fc15b92be25116c9ca782dfd64bf7b9325e6a037aed962406bcfa63dfb21
|
2026-01-16T00:00:00-05:00
|
Nonadiabatic H-Atom Scattering Channels on Ge(111) Elucidated by the Hierarchical Equations of Motion
|
arXiv:2509.16916v2 Announce Type: replace-cross Abstract: Atomic and molecular scattering at semiconductor interfaces plays a central role in surface chemistry and catalysis, yet predictive simulations remain challenging due to strong nonadiabatic effects causing the breakdown of the Born-Oppenheimer approximation. Here, we present fully quantum simulations of H-atom scattering from the Ge(111)c(2x8) rest site using the hierarchical equations of motion (HEOM) with matrix product states (MPS). The system is modeled by mapping a density functional theory (DFT) potential energy surface onto a Newns-Anderson Hamiltonian. Our simulations reproduce the experimentally observed bimodal kinetic energy distributions, capturing both elastic and energy-loss channels. By systematically examining atom-surface coupling, incident energy, and isotope substitution, we identify the strong-coupling regime required to recover the experimental energy-loss profile. This regime suppresses the elastic peak, implying additional site-specific scattering channels in the observed elastic peak. Deuterium substitution further produces a subtle shift in the energy-loss peak, consistent with experiment. These results establish HEOM as a rigorous framework for quantum surface scattering, capable of capturing nonadiabatic dynamics beyond electronic friction and perturbative approaches.
|
https://arxiv.org/abs/2509.16916
|
Academic Papers
|
svg
|
ae6bd401b2735f9e1499ffeb7f3967a6ef983bcd0518e3fa77bf712d90feff2f
|
2026-01-16T00:00:00-05:00
|
Graphical C(3)-T(6) implies CAT(0)
|
arXiv:2601.09751v1 Announce Type: new Abstract: Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with interesting features. In the classical setting, C(3)-T(6) small cancellation complexes are known to admit locally CAT(0) metrics. In this paper, we construct locally CAT(0) metrics for graphical C(3)-T(6) complexes.
|
https://arxiv.org/abs/2601.09751
|
Academic Papers
|
svg
|
0f910662c53b26656978a7ea254c5ff66190b8f5b5278ecf41929fc5e3f43021
|
2026-01-16T00:00:00-05:00
|
Structure and Decomposition of Deltoids in Abelian Groups
|
arXiv:2601.09774v1 Announce Type: new Abstract: Deltoids provide a natural framework for studying defective (partial) matchings in abelian groups, and we develop both structure and existence results in this setting. Given finite subsets $A$ and $B$ of an abelian group $G$, a matching is a bijection $f:A\to B$ such that $af(a)\notin A$ for all $a\in A$, a definition motivated by the study of canonical forms for symmetric tensors. We provide necessary and sufficient conditions for the existence of a partial matching with any prescribed defect, and then describe the minimal unavoidable defect for a pair $(A,B)$. We also define and examine a defective version of Chowla sets in the matching context. We prove a structure theorem identifying obstructions to the existence of partial matchings with small defect. Finally, within the deltoid setup, we establish max-min results on the partitioning of $A$ and $B$ into left- and right-admissible sets. Our tools mix results from transversal theory with ideas from additive number theory.
|
https://arxiv.org/abs/2601.09774
|
Academic Papers
|
svg
|
1221de64ffcff47df0b200c22762435cff778cf2667451d8e96f4230e1008c92
|
2026-01-16T00:00:00-05:00
|
Witt affine Springer theory
|
arXiv:2601.09798v1 Announce Type: new Abstract: This paper extends the affine Springer theory developed by Bouthier, Kazhdan, and the second author (see [BKV]) to the mixed characteristic case. In particular, we introduce a theory of perfectly placid perfect infinity stacks and establish their dimension theory. Furthermore, we prove that, in the Witt vector setting, the Chevalley morphism between arc spaces is flat.
|
https://arxiv.org/abs/2601.09798
|
Academic Papers
|
svg
|
3ea8ea9d619dfe4bdf64f3c36f76d5d90d9eee6a62e6ef910e078ed25e4df551
|
2026-01-16T00:00:00-05:00
|
Spectral projections of an anharmonic oscillator with complex polynomial potential
|
arXiv:2601.09800v1 Announce Type: new Abstract: For a broad class of polynomial potentials $V$, with an important and instructive representative being $V(x) = x^{2a} + i x^b$, $x \in \mathbb R$, $a, b \in \mathbb N$, we show that the system of spectral projections $\{P_n\}_n$ of an anharmonic operator $L = - (\mathrm{d}/ \mathrm{d}x)^2 + V(x)$ does not generate a (Riesz) basis in $L^2(\mathbb R)$ if $a - 1 0$ small enough, $\limsup_n \|P_n\|/ \exp(\gamma n^\sigma) = \infty$. Proofs are based on two groups of results which are of great interest on their own: (a) relationship between behavior (growth) of the norms of projections $\|P_n\|$ and of the resolvent $\|(z - L)^{-1}\|$ outside of the spectrum $\sigma(L)$; (b) partial fraction decompositions of special meromorphic functions $1/F$ where $F(w) = \prod_{k=1}^\infty \left( 1 + \frac{w}{a_k} \right)$, $a_{k+1} \geq a_k>0$, $k \in \mathbb N$, and the generalization of the first resolvent identity.
|
https://arxiv.org/abs/2601.09800
|
Academic Papers
|
svg
|
f50e46c4ecdf1750908d90add14b448c8925ea5a9b58fafe589b9018965bf582
|
2026-01-16T00:00:00-05:00
|
Kostant cuspidal permutations
|
arXiv:2601.09824v1 Announce Type: new Abstract: In relation to Kostant's problem for simple highest weight modules over the general linear Lie algebra, we prove a persistence result for Kostant negative consecutive patterns. Inspired by it, we introduce the notion of a Kostant cuspidal permutation as a minimal Kostant negative consecutive pattern. It is shown that Kostant cuspidality is an invariant of a Kazhdan-Lusztig left cell. We describe four infinite families of Kostant cuspidal involutions, including a complete classification of Kostant cuspidal fully commutative involutions. In particular, we show that the number of new Kostant cuspidal elements can be arbitrarily large, when the rank grows. This provides some potential explanation why Kostant's problem is hard.
|
https://arxiv.org/abs/2601.09824
|
Academic Papers
|
svg
|
5dabad174d91e5fdbeff77491c30725760353bdb9d257b5121cd6775c8cb6762
|
2026-01-16T00:00:00-05:00
|
When an Approximate Model Suffices for Optimal Control
|
arXiv:2601.09826v1 Announce Type: new Abstract: In this paper, we develop an optimal control framework for dynamical systems when only an approximate model of the underlying plant is available. We consider a setting in which the control strategy is synthesized using a model-based optimal control problem that includes a penalty term capturing deviation from the plant trajectory, while the same control input is applied to both the model and the actual system. For a general class of optimal control problems, we establish conditions under which the control minimizing the model-based Hamiltonian coincides with the plant-optimal control, despite mismatch between the model and the true dynamics. We further specialize these results to problems with quadratic control effort, where explicit and easily verifiable sufficient conditions guarantee equivalence and uniqueness of the resulting optimal control. These results show that accurate control synthesis does not require an exact model of the underlying system, but rather alignment of the optimality conditions that govern control selection. From a learning perspective, this suggests that data-driven efforts can focus on identifying regimes in which model-based and plant-based Hamiltonian minimizers coincide, thereby providing a theoretical basis for robust model-based decision making and the effective use of digital twins under modeling error. We provide examples to illustrate the theoretical findings and demonstrate equivalence of the resulting control trajectories even in the presence of significant model mismatch.
|
https://arxiv.org/abs/2601.09826
|
Academic Papers
|
svg
|
6783dbedd0d0c24a2ec9ae8d404758ef871c4876925d103fe9549e5597400cc9
|
2026-01-16T00:00:00-05:00
|
A note on absolutely minimal extensions in finite metric spaces
|
arXiv:2601.09840v1 Announce Type: new Abstract: Absolutely minimal Lipschitz extensions (AMLEs) are known to exist in many infinite metric settings, but the finite case is less settled. In metric spaces with at most four points, every function on a nonempty subset admits an AMLE in the sense that the Lipschitz constant cannot be further reduced on sets that are disjoint from the prescribed domain. We show that in five-point spaces such extensions may fail to exist.
|
https://arxiv.org/abs/2601.09840
|
Academic Papers
|
svg
|
c608546c62374e86904916e9896e03ddf08b731d8d494f3b5cc0c95082b458c2
|
2026-01-16T00:00:00-05:00
|
Non-commutative Factor theorem for tensor products of lattices in product groups
|
arXiv:2601.09875v1 Announce Type: new Abstract: We establish a non-commutative version of the Intermediate Factor Theorem for crossed products associated with product lattices. Given an irreducible lattice $\Gamma < G= G_1 \times \dots \times G_d$ in higher rank semisimple algebraic groups and a trace-preserving irreducible action $G \curvearrowright (\mathcal{N}, \tau)$, we show that every intermediate von Neumann algebra between $\mathcal{N}\rtimes\Gamma$ and $(L^\infty(G/P,\nu_P)\overline{\otimes}\mathcal{N})\rtimes\Gamma$ is again a crossed product of the form $(L^\infty(G/Q,\nu_Q)\overline{\otimes}\mathcal{N})\rtimes\Gamma$.
|
https://arxiv.org/abs/2601.09875
|
Academic Papers
|
svg
|
465066ca033e1ccb43b53baafbd5dc541e76e961b51c36672ae06d00ff9cba6f
|
2026-01-16T00:00:00-05:00
|
Asymptotic Stability and Equilibrium Selection in Quasi-Feller Systems with Minimal Moment Conditions
|
arXiv:2601.09880v1 Announce Type: new Abstract: We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in projection-based algorithms, learning in games, and systems with discontinuous decision rules, where classical Feller assumptions and small-noise or large-deviation techniques are not applicable. Under a global Lyapunov condition, we prove that any weak limit of invariant measures must be supported on the set of fixed points of the associated deterministic dynamics. Beyond localization, we establish a sharp exclusion principle for unstable equilibria: strict local maxima and saddle points of the Lyapunov function are shown to carry zero mass in limiting invariant measures under explicit and verifiable non-degeneracy conditions. Our analysis identifies a local mechanism driven by Lyapunov geometry and persistent variance, showing that equilibrium selection in constant-step dynamics is governed by typical fluctuations rather than rare events. These results provide a probabilistic foundation for stability and equilibrium selection in stochastic systems with persistent noise and weak regularity.
|
https://arxiv.org/abs/2601.09880
|
Academic Papers
|
svg
|
e58d28841d2f529601fea4d7257b56bab684d7b0595d29cafd2450398ccb6847
|
2026-01-16T00:00:00-05:00
|
Multiplicity one for equivariant min-max theory in prescribed homology classes
|
arXiv:2601.09884v1 Announce Type: new Abstract: For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show a generic multiplicity one theorem in equivariant min-max theory, and show in generic sense that there are infinitely many $G$-invariant minimal hypersurfaces in a fixed $G$-homology class. We also establish an equivariant min-max theory for $G$-invariant hypersurfaces of prescribed mean curvature with $G$-index upper bounds.
|
https://arxiv.org/abs/2601.09884
|
Academic Papers
|
svg
|
3d9c196280875e0847776b5030a7e2ffd1591144471c13c018878178816fd214
|
2026-01-16T00:00:00-05:00
|
Graphs of Quasicircles and Quasiconformal Homeomorphisms
|
arXiv:2601.09892v1 Announce Type: new Abstract: We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface $S$ of genus at least $2$. In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles on $S$ that respect a canonical coarse ordering induced by quality constants. We also discuss the coarse geometry of this graph.
|
https://arxiv.org/abs/2601.09892
|
Academic Papers
|
svg
|
30cbc1439a331968647ff761983b524dffbe4eb602aa24df8e9aeee6881a49aa
|
2026-01-16T00:00:00-05:00
|
Complex Monge-Amp\`ere equation in Orlicz space and Diameter Bound
|
arXiv:2601.09893v1 Announce Type: new Abstract: In this paper, we establish diameter bounds for compact K\"ahler manifolds equipped with K\"ahler metrics $\omega$, assuming the associated measure lies in a specific Orlicz space and satisfies an integrability condition. Firstly, we prove a priori estimates for solutions of the complex Monge-Amp\`ere equation in Orlicz spaces, encompassing $L^{\infty}$ and stability estimates. This is achieved by employing Ko{\l}odziej's approach \cite{Ko98} and the argument of Guo-Phong-Tong-Wang \cite{GuPhToWa21}, respectively. Secondly, building on the work of Guo-Phong-Song-Sturm \cite{GuPhSoSt24-1}, we derive the uniform (local/global) estimates of the Green's function and its gradient for the associated K\"ahler metric $\omega$.
|
https://arxiv.org/abs/2601.09893
|
Academic Papers
|
svg
|
ad9222efe6fa7e57ba58b1bea6691cc036dd539401921d8739fd6ca9a9e20e2e
|
2026-01-16T00:00:00-05:00
|
Lossless Strichartz estimates on the square torus over short time intervals
|
arXiv:2601.09895v1 Announce Type: new Abstract: We prove lossless Strichartz estimates at the critical exponent $q_c = \frac{2(n+1)}{n-1}$ on the square torus for the Schr\"{o}dinger equation with frequency localized initial data on small time windows with length depending on the frequency parameter $\lambda \gg 1$.
|
https://arxiv.org/abs/2601.09895
|
Academic Papers
|
svg
|
a03671335c7aba373be107b7d5146c8d4660a6c82677fa0c04d00e6aa902b762
|
2026-01-16T00:00:00-05:00
|
Birman-Hilden theory for big mapping class groups
|
arXiv:2601.09897v1 Announce Type: new Abstract: Let $S$ and $X$ be two connected topological surfaces without boundary, and assume that $S$ is either of infinite type or has negative Euler characteristic. In this paper, we prove that if $p:S\rightarrow X$ is a fully ramified branched covering map, then $p$ satisfies the Birman-Hilden property. This generalizes a theorem of Winarski, and the known results in the literature, to the context of surfaces of infinite type and branched covering maps of infinite degree. As an application, we show that the mapping class group (respectively, the braid group on $k$-strands) of a non-orientable surface of infinite type can be realized as a subgroup of the mapping class group (respectively, the braid group on $2k$-strands) of its orientable double cover.
|
https://arxiv.org/abs/2601.09897
|
Academic Papers
|
svg
|
30b7161e6abb8b048fbc1352ac1c8b30c9059e5f427d5dd923cc58e5f16a07db
|
2026-01-16T00:00:00-05:00
|
The Morse Local-to-Global Property for Graph Products
|
arXiv:2601.09901v1 Announce Type: new Abstract: The Morse local-to-global property generalizes the local-to-global property for quasi-geodesics in a hyperbolic space. We show that graph products of infinite Morse local-to-global groups have the Morse local-to-global property. To achieve this, we generalize the maximization procedure of Abbott, Behrstock, and Durham for relatively hierarchically hyperbolic groups with clean containers. Under mild conditions satisfied by graph products, we show that stable embeddings into a relatively hierarchically hyperbolic space are exactly those which are quasi-isometrically embedded in the top level hyperbolic space by the orbit map. This shows that graph products of any infinite groups with no isolated vertices are Morse detectable.
|
https://arxiv.org/abs/2601.09901
|
Academic Papers
|
svg
|
2a5d5d965d418231244f0e3832a813fcc76c47873db2826df48b0a3e9aae321e
|
2026-01-16T00:00:00-05:00
|
A note on invariants of mixed-state topological order in 2D
|
arXiv:2601.09909v1 Announce Type: new Abstract: The classification of mixed-state topological order requires indices that behave monotonically under finite-depth quantum channels. In two dimensions, a braided $C^*$-tensor category, which corresponds to strong symmetry, arises from a state satisfying approximate Haag duality. In this note, we show that the $S$-matrix and topological twists of the braided $C^*$-tensor category are quantities that are monotone under finite-depth quantum channels.
|
https://arxiv.org/abs/2601.09909
|
Academic Papers
|
svg
|
72a3e6185ddf57c308bd6c48504a42226d208eac2daa74c5f39374f08c1e6321
|
2026-01-16T00:00:00-05:00
|
Cylinder type and $p$-divisible sets in $\mathbb{F}_p^3$
|
arXiv:2601.09910v1 Announce Type: new Abstract: A set of points $S \subseteq \mathbb{F}_p^n$ is called \emph{$p$-divisible} if every affine hyperplane in $\mathbb{F}_p^n$ intersects $S$ in $0 \pmod p$ points. The Strong Cylinder Conjecture of Ball asserts that if $S$ is a $p$-divisible set of $p^2$ points in $\mathbb{F}_p^3$, then $S$ is a cylinder. In this paper, we show that every $p$-divisible multiset $S$ is both a $\mathbb{F}_p$-linear and $\mathbb{Z}$-linear combination of characteristic functions of cylinders. In addition, the multisets of size $p^2$ are $\Z$-linear combinations of a plane and weighted differences of parallel lines.
|
https://arxiv.org/abs/2601.09910
|
Academic Papers
|
svg
|
0831e52bc0737f2d15ae9d8f497af4a1432afb4350e15b7a69c6cd5932dd11c8
|
2026-01-16T00:00:00-05:00
|
On the Dirichlet boundary value problem on Cartan-Hadamard manifolds
|
arXiv:2601.09930v1 Announce Type: new Abstract: In this paper, we investigate the Dirichlet boundary value problem on Cartan-Hadamard manifolds, focusing on the non-existence of bounded (viscosity) solutions to semi-linear elliptic equations of the form $\Delta u + f(u) = 0$ in domains with prescribed asymptotic boundary, extending previous results by Bonorino and Klaser originally established for hyperbolic spaces. Using a novel comparison technique based on convex hypersurfaces inspired by Choi, G\'alvez, and Lozano, we overcome the absence of totally geodesic foliations, which are instrumental in the hyperbolic space. Our results highlight the interplay between curvature, the spectrum of the Laplacian, and the geometry of the asymptotic boundary.
|
https://arxiv.org/abs/2601.09930
|
Academic Papers
|
svg
|
e2763cbded177c17db403fcb16fe26ce0db2a79a7ce10300cbb0c93c038ae043
|
2026-01-16T00:00:00-05:00
|
Algebras of distributions suitable for phase-space quantum mechanics. II. Topologies on the Moyal algebra
|
arXiv:2601.09934v1 Announce Type: new Abstract: The topology of the Moyal $*$-algebra may be defined in three ways: the algebra may be regarded as an operator algebra over the space of smooth declining functions either on the configuration space or on the phase space itself; or one may construct the $*$-algebra via a filtration of Hilbert spaces (or other Banach spaces) of distributions. We prove the equivalence of the three topologies thereby obtained. As a consequence, by filtrating the space of tempered distributions by Banach subspaces, we give new sufficient conditions for a phase-space function to correspond to a trace-class operator via the Weyl correspondence rule.
|
https://arxiv.org/abs/2601.09934
|
Academic Papers
|
svg
|
73ea55133abeb805c137f53d0b606f97f79ba9caf34e56dfc18019bc3f32e530
|
2026-01-16T00:00:00-05:00
|
Epstein surfaces for $G-$opers
|
arXiv:2601.09936v1 Announce Type: new Abstract: Given a complex semisimple Lie group $G$, we introduce the notion of an Epstein surface associated to a $G$-oper. These surfaces generalize Epstein's classical construction for $G=PGL_2 (\mathbb{C})$. As an application, we provide a criterion that ensures that the holonomy of the oper is $\Delta-$Anosov. Finally, we discuss how the developing map of the oper interacts with domains of discontinuity of the holonomy (whenever Anosov) and the transversality properties it satisfies. Along the way, we provide a quick review of opers that we hope serves as a self-contained introduction.
|
https://arxiv.org/abs/2601.09936
|
Academic Papers
|
svg
|
cf903a684e37e5612a56d910428d82d647c14dcbeadf2b5328fef3d38ec6a3d4
|
2026-01-16T00:00:00-05:00
|
On Schur Rings Over Semigroups
|
arXiv:2601.09940v1 Announce Type: new Abstract: We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two categories are provided. We prove some results for Schur rings over specific families of semigroups. We consider parallels between semigroup extensions and their Schur rings. We fully enumerate the Schur rings for all semigroups of orders 0-7, and some statistical analysis is performed.
|
https://arxiv.org/abs/2601.09940
|
Academic Papers
|
svg
|
64d33cef65b004c772c96b98226c2023c4decc889e42225fd75e84b7225bd11a
|
2026-01-16T00:00:00-05:00
|
Quantitative Supercritical Bounds for Disconnection in Bernoulli Site Percolation
|
arXiv:2601.09950v1 Announce Type: new Abstract: For any infinite, connected, locally finite graph $G=(V,E)$, any parameter $p>p^{\mathrm{site}}_{c}(G)$, and any (finite or infinite) set of vertices $S\subset V$, we derive explicit exponential-type upper bounds on the disconnection probability $\mathbb{P}_{p}(S\nleftrightarrow\infty)$. The estimates are expressed in terms of a packing profile of $S$, encoded by a $(p,\varepsilon,c)$--packing number, which counts how many well-separated vertices in $S$ exhibit controlled local-to-global connectivity. The proof combines a local functional characterization of $p^{\mathrm{site}}_{c}$ from \cite{ZL24,ZL26} with a packing construction and an amplification-by-independence argument, in the direction of Problem~1.6 in \cite{DC20}.
|
https://arxiv.org/abs/2601.09950
|
Academic Papers
|
svg
|
c028f07d1be1447b18948d34c57750af868f6870e4d531bf81d2b43d2b06b670
|
2026-01-16T00:00:00-05:00
|
Directed strongly regular graphs and divisible design graphs from Tatra association schemes
|
arXiv:2601.09955v1 Announce Type: new Abstract: In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. We also study the above association schemes, their fusions and isomorphisms.
|
https://arxiv.org/abs/2601.09955
|
Academic Papers
|
svg
|
00c1a13af40ea50a8f91a7fd8f58588590dc8fdb54d50f7c24e70897d7e8b5a5
|
2026-01-16T00:00:00-05:00
|
The Galois Structure of the Spaces of polydifferentials on the Drinfeld Curve
|
arXiv:2601.09956v1 Announce Type: new Abstract: Let $C$ be a smooth projective curve over an algebraically closed field ${\mathbb{F}}$ equipped with the action of a finite group $G$. When $p =\textrm{char}(\mathbb{F})$ divides the order of $G$, the long-standing problem of computing the induced representation of $G$ on the space $H^0(C,\Omega^{\otimes m}_C)$ of globally holomorphic polydifferentials remains unsolved in general. In this paper, we study the case of the group $G = \mathrm{SL}_2(\mathbb{F}_q)$ (where $q$ is a power of~$p$) acting on the Drinfeld curve $C$ which is the projective plane curve given by the equation $XY^q-X^qY-Z^{q+1} = 0$. When $q = p$, we fully decompose $H^0(C,\Omega^{\otimes m}_C)$ as a direct sum of indecomposable $\mathbb{F}[G]$-modules. For arbitrary $q$, we give a partial decomposition in terms of an explicit $\mathbb{F}$-basis of $H^0(C,\Omega^{\otimes m}_C)$.
|
https://arxiv.org/abs/2601.09956
|
Academic Papers
|
svg
|
ca8e2e96c92a5598e535d3236032df7da2039501a220c18f85d13e88c516834f
|
2026-01-16T00:00:00-05:00
|
Planar Site Percolation, End Structure, and the Benjamini-Schramm Conjecture
|
arXiv:2601.09958v1 Announce Type: new Abstract: Let $G$ be an infinite, connected, locally finite planar graph and consider i.i.d.\ Bernoulli$(p)$ site percolation. Write $p_c^{\mathrm{site}}(G)$ and $p_u^{\mathrm{site}}(G)$ for the critical and uniqueness thresholds. Using a well--separated Freudenthal embedding $G\hookrightarrow\mathbb S^2$, we introduce a cycle--separation equivalence on ends and associated ``directional'' thresholds $p^{\mathrm{site}}_{c,F}(G)$. When the set of end--equivalence classes is countable, we show that $p_c^{\mathrm{site}}(G)=\inf_F p^{\mathrm{site}}_{c,F}(G)$ and that for every $p\in\bigl(\tfrac12,\,1-p_c^{\mathrm{site}}(G)\bigr)$ there are almost surely infinitely many infinite open clusters. Combined with the $0/\infty$ theorem of Glazman--Harel--Zelesko for $p\le \tfrac12$, this yields non--uniqueness throughout the full coexistence interval $\bigl(p_c^{\mathrm{site}}(G),\,1-p_c^{\mathrm{site}}(G)\bigr)$, and hence $p_u^{\mathrm{site}}(G)\ge 1-p_c^{\mathrm{site}}(G)$ in this setting. This resolves the extension problem posed by Glazman--Harel--Zelesko for the upper half of the coexistence regime under a natural countability hypothesis. In contrast, for graphs with uncountably many end--equivalence classes we give criteria guaranteeing infinitely many infinite clusters above criticality, and we construct an explicit locally finite planar graph of minimum degree at least $7$ for which $p_u^{\mathrm{site}}(G)<1-p_c^{\mathrm{site}}(G)$. Consequently, the Benjamini--Schramm conjecture (Conjecture 7 in \cite{bs96}) that planarity together with minimal vertex degree at least 7 forces infinitely many infinite clusters for all $p\in(p_c,1-p_c)$ does not hold in full generality. Our proofs combine a cutset characterization of $p_c^{\mathrm{site}}$ with a planar alternating--arm exploration organized by an end--adapted boundary decomposition.
|
https://arxiv.org/abs/2601.09958
|
Academic Papers
|
svg
|
2be2cec5eb158b0088eb94e06f0d08f202e3951740de3a1219069772c9faa811
|
2026-01-16T00:00:00-05:00
|
Probabilistic heterogeneous Stirling numbers and Bell polynomials
|
arXiv:2601.09964v1 Announce Type: new Abstract: Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and Lah-Bell. By integrating the heterogeneous framework of Kim and Kim with probabilistic extensions, we derive explicit formulas, Dobi\'nski-like identities, and recurrence relations. We further establish connections to partial Bell polynomials and provide applications for Poisson and Bernoulli distributions.
|
https://arxiv.org/abs/2601.09964
|
Academic Papers
|
svg
|
73c981f1b4defd0ef3f29149c25aa1201cc4857299ffa65252be2adaed84cd96
|
2026-01-16T00:00:00-05:00
|
Stochastic Calculus for Rough Fractional Brownian Motion via Operator Factorization
|
arXiv:2601.09967v1 Announce Type: new Abstract: We develop an operator-theoretic framework for stochastic calculus with respect to rough fractional Brownian motion with Hurst parameter H < 1/2. Building on a covariant derivative defined via kernel factorization, we construct a closed unbounded operator on L2(Omega) adapted to the non-semimartingale setting. This approach yields explicit derivative representations for square-integrable functionals and provides a unified analytical framework compatible with rough path techniques. The results extend classical stochastic calculus beyond the semimartingale regime.
|
https://arxiv.org/abs/2601.09967
|
Academic Papers
|
svg
|
917dec14ec294e18bb262db9d39231e42f160964f5863a882d8a43ad6c3bd445
|
2026-01-16T00:00:00-05:00
|
Einstein and Yang-Mills implies conformal Yang-Mills
|
arXiv:2601.09975v1 Announce Type: new Abstract: There exist conformally invariant, higher-derivative, variational analogs of the Yang-Mills condition for connections on vector bundles over a conformal manifold of even dimension greater than or equal to six. We give a compact formula for these analogs and prove that they are a strict weakening of the Yang-Mills condition with respect to an Einstein metric. We also show that the conformal Yang-Mills condition for the tractor connection of an even dimensional conformal manifold is equivalent to vanishing of its Fefferman-Graham obstruction tensor. This result uses that the tractor connection on a Poincar\'e-Einstein manifold is itself Yang-Mills.
|
https://arxiv.org/abs/2601.09975
|
Academic Papers
|
svg
|
9a3b768a085474c54fc8783d472d3bad6ee780c42bdd5e4539ea84a714c4490d
|
2026-01-16T00:00:00-05:00
|
Stochastic Calculus as Operator Factorization
|
arXiv:2601.09976v1 Announce Type: new Abstract: We present a unified operator-theoretic formulation of stochastic calculus based on two principles: fluctuations factor through differentiation, predictable projection, and integration, and the appropriate stochastic derivative is the Hilbert adjoint of the stochastic integral on the energy space of the driving process. On an isonormal Gaussian space we recover the identity (Id - E)F = delta Pi D F, where D is the Malliavin derivative, Pi is predictable projection, and delta is the divergence operator. Motivated by this factorization, we define for a square-integrable process X admitting a closed stochastic integral an operator-covariant derivative on L2(Omega) via Riesz representation. This yields a canonical Clark-Ocone representation that unifies Malliavin, Volterra-Malliavin, and functional Ito derivatives and clarifies the operator geometry underlying stochastic calculus.
|
https://arxiv.org/abs/2601.09976
|
Academic Papers
|
svg
|
8c060b0cd64d86e81dc357f07f4c5c45ad09a2dc6e2f70ba8dfa7b3bc323e2be
|
2026-01-16T00:00:00-05:00
|
Polynomially effective equidistribution for unipotent orbits in products of $\mathrm{SL}_2$ factors
|
arXiv:2601.09983v1 Announce Type: new Abstract: We sketch the proof of an effective equidistribution theorem for one-parameter unipotent subgroups in $S$-arithmetic quotients arising from $\mathbf K$-forms of $\mathrm{SL}_2^{\mathsf n}$ where $\mathbf K$ is a number field. This gives an effective version of equidistribution results of Ratner and Shah with a polynomial rate. The key new phenomenon is the existence of many intermediate groups between the $\mathrm{SL}_2$ containing our unipotent and the ambient group, which introduces potential local and global obstruction to equidistribution. Our approach relies on a Bourgain-type projection theorem in the presence of obstructions, together with a careful analysis of these obstructions.
|
https://arxiv.org/abs/2601.09983
|
Academic Papers
|
svg
|
26380fec8d6a9248d8fa7b5126d74b3176b0e7fc15bbf23c4ff60650470d9958
|
2026-01-16T00:00:00-05:00
|
Remarks on the convex integration technique applied to singular stochastic partial differential equations
|
arXiv:2601.09990v1 Announce Type: new Abstract: Singular stochastic partial differential equations informally refer to the partial differential equations with rough random force that leads to the products in the nonlinear terms becoming ill-defined. Besides the theories of regularity structures and paracontrolled distributions, the technique of convex integration has emerged as a possible approach to construct a solution to such singular stochastic partial differential equations. We review recent developments in this area, and also demonstrate that an application of the convex integration technique to prove non-uniqueness seems unlikely for a particular singular stochastic partial differential equation, specifically the $\Phi^{4}$ model from quantum field theory.
|
https://arxiv.org/abs/2601.09990
|
Academic Papers
|
svg
|
388d9227b9ec8a5c480803dcf198baa31a549873830b7d595be45c135ccb1949
|
2026-01-16T00:00:00-05:00
|
On directional second-order tangent sets of analytic sets and applications in optimization
|
arXiv:2601.09991v1 Announce Type: new Abstract: In this paper we study directional second-order tangent sets of real and complex analytic sets. For an analytic set $X\subseteq\mathbb{K}^n$ and a nonzero tangent direction $u\in T_0X$, we compare the geometric second-order tangent set $T^2_{0,u}X$, defined via second-order expansions of analytic arcs, with the algebraic second-order tangent set $T^{2,a}_{0,u}X$, defined by initial forms of the defining equations. We prove the general inclusion $T^2_{0,u}X\subseteq T^{2,a}_{0,u}X$ and construct explicit real and complex analytic examples showing that the inclusion is strict. We introduce a second-jet formulation along fixed tangent directions and show that $T^2_{0,u}X=T^{2,a}_{0,u}X$ if and only if the natural second-jet map from analytic arcs in $X$ to jets on the tangent cone $C_0X$ is surjective. This surjectivity is established for smooth analytic germs, homogeneous analytic cones, hypersurfaces with nondegenerate tangent directions, and nondegenerate analytic complete intersections. As an application, we derive second-order necessary and sufficient optimality conditions for $C^2$ optimization problems on analytic sets.
|
https://arxiv.org/abs/2601.09991
|
Academic Papers
|
svg
|
763143b7ded071fd1fa4752e16b29a7d79ea9711f8904a1c946d03689d9206b3
|
2026-01-16T00:00:00-05:00
|
M\"obius-Type Structures in Non-Orientable Singular Semi-Riemannian Manifolds
|
arXiv:2601.10009v1 Announce Type: new Abstract: Our objective is to illuminate the global structure of non-orientable manifolds with signature-changing metrics. Using explicit constructions based on the topology of the M\"{o}bius strip, we produce examples of crosscap manifolds where the gluing junction serves as the locus of signature change. In another set of examples, we convert the M\"{o}bius strip into a singular signature-type changing manifold. For these resulting manifolds, we test whether the metric can be expressed as $\tilde{g}=g+fV^{\flat}\otimes V^{\flat}$, with $g$ a Lorentzian metric and $f$ a smooth interpolation function between the Lorentzian and Riemannian regions, separated by the signature change hypersurface $\mathcal{H}$. Our analysis reveals that the radical of the metric can transition from transverse to tangent at $\mathcal{H}$, pseudo-space orientability is obstructed by the Euler characteristic, and pseudo-time orientability may still hold. These examples illustrate subtle obstructions to applying standard transformation prescriptions for signature change and highlight novel phenomena in compact, non-orientable semi-Riemannian manifolds.
|
https://arxiv.org/abs/2601.10009
|
Academic Papers
|
svg
|
b92ab1d7c1412c3635cd0d34c7b8ef00204b4bc5a4f88fd06cd185500d4e4488
|
2026-01-16T00:00:00-05:00
|
On the Sasakian Structure of Manifolds with Nonnegative Transverse Bisectional Curvature
|
arXiv:2601.10017v1 Announce Type: new Abstract: In this paper, we concern with the Sasaki analogue of Yau uniformization conjecture in a complete noncompact Sasakian manifold with nonnegative transverse bisectional curvature. As a consequence, we confirm that any $5$-dimensional complete noncompact Sasakian manifold with positive transverse bisectional curvature and the maximal volume growth must be CR-biholomorphic to the standard Heisenberg group $\mathbb{H}_{2}$ which can be stated as the standard contact Euclidean $5$-space $\mathbb{R}^{5}$.
|
https://arxiv.org/abs/2601.10017
|
Academic Papers
|
svg
|
7541b21eb92529814e1a615b269024d2059c72e05ea29bb566ecd8cb9ebb39a2
|
2026-01-16T00:00:00-05:00
|
An introduction to weightings along submanifolds
|
arXiv:2601.10021v1 Announce Type: new Abstract: This article is based on a talk given at the Ghent Geometric Analysis Seminar in 2023. We review basic notions from the theory of weightings along submanifolds, with special emphasis on multiplicative weightings for Lie groupoids along subgroupoids.
|
https://arxiv.org/abs/2601.10021
|
Academic Papers
|
svg
|
76a90336c9309297ee11c32c8c2d349e5ed4f70d651999749db93dc42540e700
|
2026-01-16T00:00:00-05:00
|
A New Overture to Classical Simple Type Theory, Ketonen-type Gentzen and Tableau Systems
|
arXiv:2601.10026v1 Announce Type: new Abstract: In this paper, we introduce a Ketonen-type Gentzen-style classical simple type theory $\bf KCT$. Also the tableau system $\bf KCTT$ corresponding to $\bf KCT$ is introduced. Further inference-preserving Gentzen system $\bf KCT_h$ (equivalent to $\bf KCT$) and tableau system $\bf KCTT_h$ (equivalent to $\bf KCTT$) is introduced. We introduce the notion of Hintikka sequents for $\bf KCTT_h$.The completeness theorem and Takahashi-Prawitz's theorem are proved for $\bf KCTT_h$.
|
https://arxiv.org/abs/2601.10026
|
Academic Papers
|
svg
|
8a41442185d7fc7e5af02e6b27459e198f17c1f38132dc7c035084564fab77e0
|
2026-01-16T00:00:00-05:00
|
Stability and instability of small BGK waves
|
arXiv:2601.10030v1 Announce Type: new Abstract: The aim of this article is to prove that the linear stability or instability of small Bernstein-Green-Kruskal (BGK) waves is determined by the sign of the derivative of their energy distributions at $0$ energy.
|
https://arxiv.org/abs/2601.10030
|
Academic Papers
|
svg
|
66cae65ae58a580a97cd5fe6c9046509df874881192d019baf558017443378ae
|
2026-01-16T00:00:00-05:00
|
Convex combination of first and second eigenvalues of trees
|
arXiv:2601.10036v1 Announce Type: new Abstract: For a graph $G$, let $\lambda_1(G)$ and $\lambda_2(G)$ denote the largest and the second largest adjacency eigenvalue of $G$. The sum $\lambda_1(G) + \lambda_2(G)$ is called the \emph{spectral sum} of $G$. We investigate the spectral sum of trees of order $n$ and determine the extremal trees that achieve maximum/minimum. Moreover, for any $\alpha \in [0,1]$, we determine the extremal trees which maximize the convex combination $\alpha \lambda_1 + (1-\alpha)\lambda_2$ in the class of $n$-vertex trees.
|
https://arxiv.org/abs/2601.10036
|
Academic Papers
|
svg
|
069088ec77187ba12ca31ddcac6f54e74579e8e5caccf3b07d7e9e0d54fb8bef
|
2026-01-16T00:00:00-05:00
|
Recurrence relations for the coefficients of the confluent and Gauss hypergeometric functions in the complex plane
|
arXiv:2601.10040v1 Announce Type: new Abstract: For $a,b,c,z,p, \theta \in \mathbb{C}$, where $\mathbb{C}$ is the complex plane, $-c\notin \mathbb{N\cup }\left\{ 0\right\} $, let \begin{equation*} \mathcal{M}\left( z\right) =\left( 1-\theta z\right) ^{p}M\left(a;c;z\right) =\sum_{n=0}^{\infty }u_{n}z^{n}, \end{equation*} where $|z| <\frac{1}{\theta}$, $|\arg (1-\theta z)| < \pi$, and let \begin{equation*} \mathcal{G}\left( z\right) =(1-\theta z) ^{p}F(a,b;c;z) =\sum_{n=0}^{\infty }v_{n} z^{n}, \end{equation*} where $|z| < 1$, $|\arg (1-\theta z)| < \pi$. In this paper, we prove that the coefficients $u_{n}$ and $v_{n}$ for $n\geq 0$ satisfy a 3-order recurrence relation. These offer a new way to study confluent hypergeometric function $M(a;c;z)$ and Gauss hypergeometric function $F(a,b;c;z)$. And we provide other special functions' recurrence relations of their coefficients, such as error function, Bessel function, incomplete gamma function, complete elliptic integral and Chebyshev polynomials.
|
https://arxiv.org/abs/2601.10040
|
Academic Papers
|
svg
|
627158d1069fec4cbe7cef122e7fdc939e1e3589fc33dfcd947e273d4b205f25
|
2026-01-16T00:00:00-05:00
|
A note on exact approximations
|
arXiv:2601.10051v1 Announce Type: new Abstract: Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.
|
https://arxiv.org/abs/2601.10051
|
Academic Papers
|
svg
|
33f304c1047e9e2705fac2890995a44cf7e082a5af8f5a8d5356b631f37590a5
|
2026-01-16T00:00:00-05:00
|
Kov\'acs' conjecture on characterisation of projective space and hyperquadrics
|
arXiv:2601.10055v1 Announce Type: new Abstract: We prove Kov\'acs' conjecture that claims that if the $p^{th}$ exterior power of the tangent bundle of a smooth complex projective variety contains the $p^{th}$ exterior power of an ample vector bundle then the variety is either projective space or the $p$-dimensional quadric hypersurface. This provides a common generalization of Mori, Wahl, Cho-Sato, Andreatta-Wi\'sniewski, Kobayashi-Ochiai, and Araujo-Druel-Kov\'acs type characterizations of such varieties.
|
https://arxiv.org/abs/2601.10055
|
Academic Papers
|
svg
|
d272c7f1e8431626f06325e212de117427e453473b2bb9b10f576ddcbd9c7c8e
|
2026-01-16T00:00:00-05:00
|
Global convergence of the subgradient method for robust signal recovery
|
arXiv:2601.10062v1 Announce Type: new Abstract: We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. These objectives are nonsmooth and nonconvex, and may have unbounded sublevel sets, so standard arguments for analyzing first-order optimization algorithms based on descent and coercivity do not apply. For locally Lipschitz semialgebraic objectives, we develop a convergence framework under the assumption that continuous-time subgradient trajectories are bounded: for sufficiently small step sizes of order \(1/k\), any subgradient sequence remains bounded and converges to a critical point. We verify this trajectory boundedness assumption for the robust objectives by adapting and extending existing trajectory analyses, requiring only a mild nondegeneracy condition in the matrix sensing case. Finally, for rank-one symmetric robust PCA, we show that the subgradient method avoids spurious critical points for almost every initialization, and therefore converges to a global minimum under the same step-size regime.
|
https://arxiv.org/abs/2601.10062
|
Academic Papers
|
svg
|
e94664ccf8712813740b25ba47934d5ddb014252ca2fb73875d0bbefedfc9816
|
2026-01-16T00:00:00-05:00
|
Transport equation theory in the Triebel-Lizorkin spaces and its applications to the ideal fluid flows
|
arXiv:2601.10071v1 Announce Type: new Abstract: In this paper, we develop a general theory for the transport equation within the framework of Triebel-Lizorkin spaces. We first derive commutator estimates in these spaces, dispensing with the conventional divergence-free condition, via the Bony paraproduct decomposition and vector-valued maximal function inequalities. Building on these estimates and combining the method of characteristics with a compactness argument, we then obtain the new a priori estimates and prove local well-posedness for the transport equation in Triebel-Lizorkin spaces. The resulting theory is applicable to a wide range of evolution equations, including models for incompressible and compressible ideal fluid flows, shallow water waves, among others. As an illustration, we consider the incompressible ideal magnetohydrodynamics (MHD) system. Employing the general transport theory developed here yields a complete local well-posedness result in the sense of Hadamard, covering both sub-critical and critical regularity regimes, and provides corresponding blow-up criteria for the ideal MHD equations in Triebel-Lizorkin spaces. Our results refine and substantially extend earlier work in this direction.
|
https://arxiv.org/abs/2601.10071
|
Academic Papers
|
svg
|
e25291a7f6e0b0e5982519f50841d02c30070037d985b2e204eb3b8bcefedb90
|
2026-01-16T00:00:00-05:00
|
Simplicial spheres with $g_k=1$
|
arXiv:2601.10072v1 Announce Type: new Abstract: For $d\geq 4$, Kalai (1987) characterized all simplicial $(d-1)$-spheres with $g_2=0$, and for $k\geq 2$ and $d\geq 2k$, Murai and Nevo (2013) characterized all simplicial $(d-1)$-spheres with $g_k=0$. In addition, for $d\geq 4$, Nevo and Novinsky (2011) characterized all simplicial $(d-1)$-spheres with $g_2=1$. Motivated by these results, we characterize, for any $k\geq 2$ and $d\geq 2k+1$, all simplicial $(d-1)$-spheres with no missing faces of dimension larger than $d-k$ that satisfy $g_k=1$. When $d=2k$, we obtain a characterization of simplicial $(d-1)$-spheres with $g_k=1$ and no missing faces of dimension greater than $k$, under the additional assumption that there exists at least one missing face of dimension $k$. Finally, for $k=3$, we are able to remove this assumption and characterize all simplicial $5$-spheres with no missing faces of dimension larger than $3$ that satisfy $g_3=1$.
|
https://arxiv.org/abs/2601.10072
|
Academic Papers
|
svg
|
0ce34a210d1be2c67e404f48d5ba293e13539b434ef9376b2c1a1e2fc6902cd7
|
2026-01-16T00:00:00-05:00
|
Sharp propagation of chaos in R\'enyi divergence
|
arXiv:2601.10076v1 Announce Type: new Abstract: We establish sharp rates for propagation of chaos in R\'enyi divergences for interacting diffusion systems at stationarity. Building upon the entropic hierarchy established in Lacker (2023), we show that under strong isoperimetry and weak interaction conditions, one can achieve $\mathsf R_q(\mu^1 \,\lVert\, \pi) = \widetilde O(\frac{d q^2}{N^2})$ bounds on the $q$-R\'enyi divergence.
|
https://arxiv.org/abs/2601.10076
|
Academic Papers
|
svg
|
6941a034e453e9617bd9382706ca66852d4959d68e2d7a919413d0ba9d2e4084
|
2026-01-16T00:00:00-05:00
|
A $p$-adic interpolation of the Cogdell lift
|
arXiv:2601.10077v1 Announce Type: new Abstract: In this paper we obtain several results related to the $p$-adic interpolation of the classical Cogdell lift, mapping special cycles on Picard modular surfaces to elliptic modular forms. The results have a three-fold nature: in the first part of the paper, we $p$-adically interpolate the adjoint Kudla lift, exploiting the previously constructed $\Lambda$-adic Kudla lift. In the second part, we construct higher weight cycles in Kuga-Sato varieties attached to Picard modular surfaces, and show modularity of the generating series of these cycles, thus obtaining a higher weight analogue of the Cogdell lift. Finally, we apply the formalism introduced by Loeffler to construct $p$-adic analytic cohomology classes of special cycles, whose generating series is proved to be a Hida family interpolating the Cogdell lifts in the weight and level variables.
|
https://arxiv.org/abs/2601.10077
|
Academic Papers
|
svg
|
ce32896b4b5582f30e7b110f1d46af6277e09959c6fe40a571fa274d538aa238
|
2026-01-16T00:00:00-05:00
|
Line-search and Adaptive Step Sizes for Nonconvex-strongly-concave Minimax Optimization
|
arXiv:2601.10086v1 Announce Type: new Abstract: In this paper, we propose a novel reformulation of the smooth nonconvex-strongly-concave (NC-SC) minimax problems that casts the problem as a joint minimization. We show that our reformulation preserves not only first-order stationarity, but also global and local optimality, second-order stationarity, and the Kurdyka-{\L}ojasiewicz (KL) property, of the original NC-SC problem, which is substantially stronger than its nonsmooth counterpart in the literature. With these enhanced structures, we design a versatile parameter-free and nonmonotone line-search framework that does not require evaluating the inner maximization. Under mild conditions, global convergence rates can be obtained, and, with KL property, full sequence convergence with asymptotic rates is also established. In particular, we show our framework is compatible with the gradient descent-ascent (GDA) algorithm. By equipping GDA with Barzilai-Borwein (BB) step sizes and nonmonotone line-search, our method exhibits superior numerical performance against the compared benchmarks.
|
https://arxiv.org/abs/2601.10086
|
Academic Papers
|
svg
|
2f33281941527882ce4c502299da35237e9763f80b7afc25c42f89aa657a16cf
|
2026-01-16T00:00:00-05:00
|
Admissibility Breakdown in High-Dimensional Sparse Regression with L1 Regularization
|
arXiv:2601.10100v1 Announce Type: new Abstract: The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. Classical consistency theory identifies the rate of the Lasso tuning parameter, and numerous studies have established non-asymptotic guarantees. Nevertheless, the question of optimal tuning within a non-asymptotic framework has not yet been fully resolved. We establish tuning criteria above which the Lasso becomes inadmissible under mean squared prediction error. More specifically, we establish thresholds showing that certain classical tuning choices yield Lasso estimators strictly dominated by a simple Lasso-Ridge refinement. We also address how the structure of the design matrix and the noise vector influences the inadmissibility phenomenon.
|
https://arxiv.org/abs/2601.10100
|
Academic Papers
|
svg
|
2d7fa40841c60fb70690d707e8a8855ec9ebe99ee29627b33cbd7677d5afac4c
|
2026-01-16T00:00:00-05:00
|
Fano threefolds of genus 12 with large automorphism group in positive and mixed characteristic
|
arXiv:2601.10106v1 Announce Type: new Abstract: We study prime Fano threefolds of genus 12 ($V_{22}$-varieties) with positive-dimensional automorphism groups in positive and mixed characteristic. We classify such varieties over any perfect field. In particular, we prove that $V_{22}$-varieties of Mukai-Umemura type over $k$ exist if and only if $\mathrm{char}\ k \neq 2$, $5$. We also prove the same result for $\mathbb{G}_a$-type. As arithmetic applications, we show that the Shafarevich conjecture holds for $V_{22}$-varieties of Mukai-Umemura type and of $\mathbb{G}_m$-type, while it fails for $V_{22}$-varieties of $\mathbb{G}_a$-type. Moreover, we prove that there exists $V_{22}$-varieties over $\mathbb{Z}$, whereas there do not exist $V_{22}$-varieties over $\mathbb{Z}$ whose generic fiber has a positive-dimensional automorphism group.
|
https://arxiv.org/abs/2601.10106
|
Academic Papers
|
svg
|
997178762bc50f3d1b3a880771543074f49ed512ffc1473e57d1bd04c996f379
|
2026-01-16T00:00:00-05:00
|
Shifted bilinear sums of Sali\'e sums and the distribution of modular square roots of shifted primes
|
arXiv:2601.10113v1 Announce Type: new Abstract: We establish various upper bounds on Type-I and Type-II shifted bilinear sums with Sali\'e sums modulo a large prime $q$. We use these bounds to study, for fixed integers $a,b\not \equiv 0 \bmod q$, the distribution ofsolutions to the congruence $x^2 \equiv ap+b \bmod q$, over primes $p\le P$. This is similar to the recently studied case of $b = 0$, however the case $b\not \equiv 0 \bmod q$ exhibits some new difficulties.
|
https://arxiv.org/abs/2601.10113
|
Academic Papers
|
svg
|
07534bf20c363e340458e29b16f49697643fe9bdcba33535fd54d38776515070
|
2026-01-16T00:00:00-05:00
|
Calabi affine maximal surfaces and centroaffine Bernstein problems
|
arXiv:2601.10125v1 Announce Type: new Abstract: Motivated by Calabi's calculation of the second variation sign for locally strongly convex affine maximal surfaces in equiaffine geometry, we first prove that every Calabi extremal surface is also maximal in the Calabi affine geometry. By employing suitably chosen orthonormal frame fields and analyzing the corresponding Codazzi equations, we then obtain local classifications for certain special classes of Calabi affine maximal surfaces and hyperbolic centroaffine extremal surfaces. These examples inspire the construction of new, complete Calabi affine maximal surfaces and centroaffine extremal hypersurfaces. Notably, the complete centroaffine extremal hypersurfaces we establish answer all five centroaffine Bernstein problems posed by Li- Li-Simon in 2004.
|
https://arxiv.org/abs/2601.10125
|
Academic Papers
|
svg
|
cee318c19dcc2ecf45aaa2804e079f83835ff8968ca328733cea317b30f5b5f9
|
2026-01-16T00:00:00-05:00
|
Curvature-driven manifold fitting under unbounded isotropic noise
|
arXiv:2601.10133v1 Announce Type: new Abstract: Manifold fitting aims to reconstruct a low-dimensional manifold from high-dimensional data, whose framework is established by Fefferman et al. \cite{fefferman2020reconstruction,fefferman2021reconstruction}. This paper studies the recovery of a compact $C^3$ submanifold $\mathcal{M} \subset \mathbb{R}^D$ with dimension $d0$ and achieves a state-of-the-art Hausdorff distance of $O(\sigma^2)$ to $\mathcal{M}$. Numerical experiments confirm the quadratic decay of the reconstruction error and demonstrate the computational efficiency of the estimator $F$. Our work provides a curvature-driven framework for denoising and reconstructing manifolds with second-order accuracy.
|
https://arxiv.org/abs/2601.10133
|
Academic Papers
|
svg
|
e4e5f4df06f89203bef50349bb928b013792c29e934323301191f1b3f83739f7
|
2026-01-16T00:00:00-05:00
|
A new contraction principle on the perimeters of triangles and related results
|
arXiv:2601.10138v1 Announce Type: new Abstract: In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed point of our newly introduced mapping. In support of our result, we present several examples.
|
https://arxiv.org/abs/2601.10138
|
Academic Papers
|
svg
|
562df49b929106cade72ac02c90b8ed617f8444e3623666c09e7087c219a4a5a
|
2026-01-16T00:00:00-05:00
|
On Quaternionic Fock Spaces: Kernel-induced Integral Operators, Berezin Transforms and Toeplitz Operators
|
arXiv:2601.10162v1 Announce Type: new Abstract: In this paper, we study quaternionic Fock spaces and develop an operator-theoretic framework centered around kernel-induced integral operators, Berezin transforms and Toeplitz operators. More precisely, the following results are obtained: (i) Global quaternionic Fock structure. We introduce a global Gaussian $L^p$--norm for slice functions on $\mathbb H$ and prove that the resulting global quaternionic Fock space $F_\alpha^p$ coincides with the slice-defined Fock space $\mathfrak F_\alpha^p$, with equivalent norms. In particular, $F_\alpha^2$ becomes a right quaternionic reproducing kernel Hilbert space with an explicit reproducing kernel, yielding a slice-independent Fock projection onto $F_\alpha^2$. (ii) Kernel-induced integral operators and Fock--Carleson measures. We investigate kernel-induced integral operators and characterize quaternionic Fock--Carleson measures. These embedding theorems provide the measure-theoretic basis that underlies boundedness and compactness criteria for operators on quaternionic Fock spaces. (iii)Berezin transforms and Toeplitz operators. We define the Berezin transform for slice functions and prove its fundamental properties, including semigroup behavior and fixed-point features. Building on the slice-independent projection and the slice product, we introduce Toeplitz operators with slice-function symbols and with measure symbols, and develop their basic algebraic properties. We then obtain complete boundedness and compactness characterizations for Toeplitz operators with two natural symbol classes: positive measures and slice $\mathrm{BMO}^1$ symbols, expressed in terms of Berezin-type transforms and slice/symmetric averaging quantities.
|
https://arxiv.org/abs/2601.10162
|
Academic Papers
|
svg
|
d3a2c8f70bd6237170e83a1f1ffc54c5b1428277eb1c18583bc9bd6f96eaf64b
|
2026-01-16T00:00:00-05:00
|
Advances on two spectral conjectures regarding booksize of graphs
|
arXiv:2601.10163v1 Announce Type: new Abstract: The \emph{booksize} $ \mathrm{bk}(G) \) of a graph $ G $, introduced by Erd\H{o}s, refers to the maximum integer $ r $ for which $G$ contains the book $ B_r $ as a subgraph. This paper investigates two open problems in spectral graph theory related to the booksize of graphs. First, we prove that for any positive integer $r$ and any $ B_{r+1} $-free graph $ G $ with $ m \geq (9r)^2 $ edges, the spectral radius satisfies $ \rho(G) \leq \sqrt{m} $. Equality holds if and only if $ G $ is a complete bipartite graph. This result improves the lower bound on the booksize of Nosal graphs (i.e., graphs with $ \rho(G) > \sqrt{m} $) from the previously established $ \mathrm{bk}(G) > \frac{1}{144}\sqrt{m} $ to $ \mathrm{bk}(G) > \frac{1}{9}\sqrt{m} $, presenting a significant advancement in the booksize conjecture proposed Li, Liu, and Zhang. Second, we show that for any positive integer $r$ and any non-bipartite $ B_{r+1} $-free graph $ G $ with $ m \geq (240r)^2 $ edges, the spectral radius $\rho$ satisfies $\rho^2<m-1+\frac{2}{\rho-1}$, unless $G$ is isomorphic to $S^+_{m,s}$ for some $s\in\{1,\ldots,r\}$. This resolves Liu and Miao's conjecture and further reveals an interesting phenomenon: even with a weaker spectral condition, $\rho^2\geq m-1+\frac2{\rho-1}$, we can still derive the supersaturation of the booksize for non-bipartite graphs.
|
https://arxiv.org/abs/2601.10163
|
Academic Papers
|
svg
|
a60afbe37d3766707ef2bfc276cef9ffddbdb94fd7cbb8ca98ac765938641e25
|
2026-01-16T00:00:00-05:00
|
Characteristics of drift effects in the quasi-geostrophic equation arising from nonlinear symmetry
|
arXiv:2601.10185v1 Announce Type: new Abstract: This paper compares two similar diffusion equations that appear in meteorology. One is the quasi-geostrophic equation, and the other is the convection-diffusion equation. Both are two-dimensional bilinear equations, and the order of differentiation is the same. Naturally, their scales also coincide. However, the direction in which the nonlinear effects act differs: one acts along the isothermal surface, while the other acts along the temperature gradient in a specified direction. The main assertion quantifies this difference through the large-time behavior of their solutions. In particular, the nonlinear distortions in the asymptotic profiles of both equations are compared. In this context, the spatial symmetry of the first approximation plays a crucial role, but the solutions require no symmetry.
|
https://arxiv.org/abs/2601.10185
|
Academic Papers
|
svg
|
752c200a8d5dea36b8b3db65862169128189dd5d2386945dc860fb15f6a1d792
|
2026-01-16T00:00:00-05:00
|
Outlier eigenvalues and eigenvectors of generalized Wigner matrices with finite-rank perturbations
|
arXiv:2601.10204v1 Announce Type: new Abstract: A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under certain assumptions on the perturbation and the matrix structure, we derive the first-order behavior of these eigenvalues and show that they are well separated from the bulk. The fluctuations of these eigenvalues are shown to follow a multivariate Gaussian distribution, and the asymptotic behavior of the associated eigenvectors is also studied. We prove central limit theorems that describe the asymptotic alignment of these eigenvectors with the perturbation's eigenvectors, as well as their Gaussian fluctuations around the origin for non-aligned components. Furthermore, we discuss the convergence of the eigenvector process in a Sobolev space framework.
|
https://arxiv.org/abs/2601.10204
|
Academic Papers
|
svg
|
0ada95684754788e7d53f1453a9e4556682720c0f548162776ad99535defc9b3
|
2026-01-16T00:00:00-05:00
|
Biharmonic and Interpolating Sesqui-Harmonic Vector Fields with Respect to the varphi-Sasakian Metric
|
arXiv:2601.10216v1 Announce Type: new Abstract: This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-K\"ahler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit characterizations are established for vector fields satisfying the corresponding variational conditions-namely, biharmonicity and interpolating sesqui-harmonicity. Furthermore, several examples are presented to illustrate the general theory and to elucidate the distinctions between harmonic, biharmonic, and interpolating sesqui-harmonic behaviors. These results extend and complement existing research on higher-order harmonicity in pseudo-Riemannian geometry.
|
https://arxiv.org/abs/2601.10216
|
Academic Papers
|
svg
|
a2ba9a949c5ffaeb2247e6a0c4c8ee934c47b9143d0110e6f1000ad2d96507c5
|
2026-01-16T00:00:00-05:00
|
Nuclear Toeplitz operators between Fock spaces
|
arXiv:2601.10217v1 Announce Type: new Abstract: We study Toeplitz operators with measure-valued symbols acting between Fock spaces. Given $1\le p,q\le\infty$ and a Borel measure $\mu$ on $\mathbb C$, we investigate when the associated Toeplitz operator \[ T_\mu : F^p_\alpha \to F^q_\alpha \] belongs to the nuclear class. For positive measures $\mu$ and in the range $1\le q\le p\le\infty$, we obtain necessary and sufficient conditions for the nuclearity of $T_\mu$ in terms of the Berezin transform of $\mu$. As a consequence, nuclearity in this setting exhibits a rigidity property: if $T_\mu$ is nuclear from $F^p_\alpha$ to $F^q_\alpha$ for some $q\le p$, then it is nuclear for all such $q$. In the case $p<q$, we show that the situation is more delicate. We provide separate necessary and sufficient conditions for nuclearity, indicating that the Berezin transform alone does not yield a complete characterization. The proofs rely on tools from Banach space operator theory combined with kernel estimates on Fock spaces. Our results extend naturally to Fock spaces on $\mathbb C^n$.
|
https://arxiv.org/abs/2601.10217
|
Academic Papers
|
svg
|
3b99dc62f09cf59210ea7bda7417ea6d29c7730450432fe418258f419d302eb0
|
2026-01-16T00:00:00-05:00
|
Unrefinable Partitions into Distinct Parts and Numerical Semigroups
|
arXiv:2601.10227v1 Announce Type: new Abstract: This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising unrefinable partitions are established. A correspondence between missing parts and the gaps of numerical semigroups is developed, extending previous classifications and enabling the characterisation of partitions with maximal numbers of missing parts. In particular, the results show that certain families of unrefinable partitions correspond precisely to symmetric numerical semigroups when the maximal part is prime. Further structural consequences, examples, and a decomposition of unrefinable partitions by minimal excludant are discussed, together with implications for the study of maximal unrefinable partitions.
|
https://arxiv.org/abs/2601.10227
|
Academic Papers
|
svg
|
9802ca5b30ec1ab181b72c5986c9e01a5822ac986d2061dd3ec7af0abde657e8
|
2026-01-16T00:00:00-05:00
|
Inconsistency of Reinhardt cardinals with $\mathsf{ZF}$
|
arXiv:2601.10231v1 Announce Type: new Abstract: A proof will be presented that the existence of a non-trivial $\Sigma_1$-elementary embedding $j: V_{\lambda+3} \prec V_{\lambda+3}$ is inconsistent with $\textsf{ZF}$. Sections 1 and 2 shall review various important contributions from the literature, notably including \cite{Goldberg2020}, \cite{Schlutzenberg2020}, and \cite{Woodin2010}, the latter reference being where the crucial forcing construction is presented. Section 3 shall introduce some new large cardinal properties, of consistency strength intermediate between $\mathsf{I_3}$ and $\mathsf{I_2}$, and greater than $\mathsf{I_1}$, respectively. The proof of the inconsistency with $\mathsf{ZF}$ of the existence of a non-trivial $\Sigma_1$-elementary embedding $j:V_{\lambda+3} \prec V_{\lambda+3}$ shall be given in Section 4. The claims of Sections 2 and 4 are provable in $\textsf{ZF}$; those of Section 3, with the exception of the last two theorems, in $\textsf{ZFC}$.
|
https://arxiv.org/abs/2601.10231
|
Academic Papers
|
svg
|
6d578b47d0cb91336cf2d7fa5ffa8f679bdd522fde5d3bf30fe8fa9be87d5f2c
|
2026-01-16T00:00:00-05:00
|
Synchronization and Hopf Bifurcation in Stuart--Landau Networks
|
arXiv:2601.10234v1 Announce Type: new Abstract: The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type synchronization through networks of Stuart--Landau oscillators, which arise as the universal normal form near a Hopf bifurcation. For identical natural frequencies, we analyze synchronization in two complementary regimes. Away from criticality, we establish topology-robust complete synchronization for general connected networks under explicit sufficient conditions that preclude amplitude death. At criticality, we exploit network symmetries to analyze the onset of collective oscillations via Hopf bifurcation theory, demonstrating the emergence of synchronized periodic states in ring-symmetric networks. Our results clarify how amplitude dynamics enrich the structure of synchronized states and provide a bridge between classical Kuramoto synchronization and amplitude-inclusive models in complex networks.
|
https://arxiv.org/abs/2601.10234
|
Academic Papers
|
svg
|
ce87ff094460a6126c854b295ee4e58300fb565d397884228d6ff99f5cb4663d
|
2026-01-16T00:00:00-05:00
|
A flower theorem in $\mathbb{C}^n$
|
arXiv:2601.10235v1 Announce Type: new Abstract: We prove an analog of the flower theorem for non-degenerate reduced tangent to the identity germs that fix the coordinate hyperspaces in any dimension.
|
https://arxiv.org/abs/2601.10235
|
Academic Papers
|
svg
|
709ef9b98b295455ca5ba435d1092155d8e12ef69e34639a9216ae753dcdff90
|
2026-01-16T00:00:00-05:00
|
Ramsey number of a cycle versus a graph of a given size
|
arXiv:2601.10238v1 Announce Type: new Abstract: In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $2m+\lfloor \frac{k-1}{2} \rfloor$, provided $m$ is sufficiently large with respect to $k$. This settles a problem of Erd\H{o}s, Faudree, Rousseau and Schelp.
|
https://arxiv.org/abs/2601.10238
|
Academic Papers
|
svg
|
66b233ae850fe9af446f37d532231aa9c3a63a66ffe1a21cd857af5885c05bde
|
2026-01-16T00:00:00-05:00
|
Model order reduction of piecewise linear mechanical systems using invariant cones
|
arXiv:2601.10241v1 Announce Type: new Abstract: We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant contact laws. The key idea is to make the absence of a local linearization around the equilibrium tractable by leveraging the positive homogeneity property. This property simplifies the invariance equations defining the geometry of the invariant cones, from a set of partial differential equations to a system of ordinary differential equations, enabling their effective solution. We introduce two techniques to compute these invariant cones. First, an intuitive graph-style parametrization is proposed that utilizes Fourier expansions and Chebyshev polynomials to derive explicit reduced-order models in closed form. Second, an arc-length parametrization is introduced to robustly compute invariant cones with complex folding geometries, which are intractable with a standard graph-style technique. The approach is demonstrated on mechanical oscillators with unilateral visco-elastic supports, showcasing its applicability for systems with both continuous (unilateral elastic) and discontinuous (unilateral visco-elastic) unilateral force laws.
|
https://arxiv.org/abs/2601.10241
|
Academic Papers
|
svg
|
7758e0f006d77cad05150d117aa512829293fb549e7ebe61f627e78e13134ae5
|
2026-01-16T00:00:00-05:00
|
Critical time of the almost 2-regular random degree constrained process
|
arXiv:2601.10249v1 Announce Type: new Abstract: We study the phase transition of the random degree constrained process (RDCP), a time-evolving random graph model introduced by Ruci\'nski and Wormald that generalizes the random $d$-process to the non-regular setting: each vertex of the complete graph $K_n$ has its pre-assigned degree constraint (i.e., a number from the set $\{2,\dots,\Delta \}$), we attempt to add the edges one-by-one in a uniform random order, but a new edge is added only if it does not violate the degree constraints at its end-vertices. Warnke and Wormald identified the critical time of the RDCP when the giant component emerges as $n \to \infty$. R\'ath, Sz\H{o}ke and Warnke identified the local weak limit of the RDCP and gave an alternative characterization of the critical time in terms of the principal eigenvalue of the branching operator of the multi-type branching process that arises as the local limit object. In the current paper we use this spectral characterization to study the critical time of the RDCP in the almost 2-regular case, i.e., when the degree constraint of most of the vertices is equal to 2. In this case the giant component emerges quite late, and our main result provides the precise asymptotics of the critical time as the model approaches 2-regularity. Interestingly, our formula asymptotically matches the well-known Molloy-Reed formula, despite the fact that Molloy, Surya and Warnke proved that the final graph of the RDCP is not contiguous to the configuration model with the same degree sequence.
|
https://arxiv.org/abs/2601.10249
|
Academic Papers
|
svg
|
3473fd57a10f254dcb7fa2f46082a50f9a0c9173c848577302bf39fc88b3405e
|
2026-01-16T00:00:00-05:00
|
Controllability score for linear time-invariant systems on an infinite time horizon
|
arXiv:2601.10260v1 Announce Type: new Abstract: We introduce a scaled controllability Gramian that can be computed reliably even for unstable systems. Using this scaled Gramian, we reformulate the controllability scoring problems into equivalent but numerically stable optimization problems. Their optimal solutions define dynamics-aware network centrality measures, referred to as the volumetric controllability score (VCS) and the average energy controllability score (AECS). We then formulate controllability scoring problems on an infinite time horizon. Under suitable assumptions, we prove that the resulting VCS and AECS are unique and that the finite-horizon scores converge to them. We further show that VCS and AECS can differ markedly in this limit, because VCS enforces controllability of the full system, whereas AECS accounts only for the stable modes. Finally, using Laplacian dynamics as a representative example, we present numerical experiments that illustrate this convergence.
|
https://arxiv.org/abs/2601.10260
|
Academic Papers
|
svg
|
46ea618684f9d459e0c3a2f998011586030f1108a659c7a38eea18932012772b
|
2026-01-16T00:00:00-05:00
|
Three-dimensional compact Heterotic solitons with parallel torsion
|
arXiv:2601.10270v1 Announce Type: new Abstract: We obtain a rigidity result for compact three-dimensional Heterotic solitons with parallel non-trivial torsion. We show that they are either hyperbolic three-manifolds or compact quotients of the Heisenberg group equipped with a left-invariant metric. In particular, the latter arise both as solitons with completely skew-symmetric torsion as well as with non-vanishing twistorial component. As a corollary, we obtain the universal bound $-24$ for the scalar curvature of Heterotic solitons with parallel skew-symmetric torsion, which prevents it from being arbitrarily large.
|
https://arxiv.org/abs/2601.10270
|
Academic Papers
|
svg
|
80cd76a1a7925f360c2241915cba46a6223be1ff53247ba1c9e3b68e33aa5c9b
|
2026-01-16T00:00:00-05:00
|
On a general identity and a resulting class of umbral operators
|
arXiv:2601.10275v1 Announce Type: new Abstract: We prove a new universal identity for umbral operators. This motivates the definition of a subclass obeying a simplified identity, which we then fully characterize. The results are illustrated with common examples of the theory of umbral calculus.
|
https://arxiv.org/abs/2601.10275
|
Academic Papers
|
svg
|
ff9bca114897880e4de3f0081dfd2a25d1ddb2e731d7486d2e9b8609926c6d00
|
2026-01-16T00:00:00-05:00
|
New Upper Bounds on the Ribbonlength of Alternating Links with Bipartite Dual Graphs
|
arXiv:2601.10278v1 Announce Type: new Abstract: The ribbonlength of a link is a geometric invariant defined as the infimum of the ratio of the length to the width of a folded ribbon realization of the link. In this paper, we prove that if an alternating link admits an alternating diagram with a bipartite dual graph, then its ribbonlength satisfies $$ \mathrm{Rib}(L) \le \sqrt{3} \, c(L). $$ Using this result, we present improved upper bounds on the ribbonlength for several knots and links with small crossing numbers, and determines the exact ribbonlength of the Hopf link to be $2\sqrt{3}$.
|
https://arxiv.org/abs/2601.10278
|
Academic Papers
|
svg
|
a3dc207bccd5c86bea51b078d12a931e26d06bf2328fb4c273a85992a3136c30
|
2026-01-16T00:00:00-05:00
|
Optimisation of the lowest Robin eigenvalue in exterior domains of the hyperbolic plane
|
arXiv:2601.10280v1 Announce Type: new Abstract: We consider the Robin Laplacian in the exterior of a bounded simply-connected Lipschitz domain in the hyperbolic plane. We show that the essential spectrum of this operator is $[\frac14,\infty)$ and that, under convexity assumption on the domain, there exist discrete eigenvalues below $\frac14$ if, and only if, the Robin parameter is below a non-positive critical constant, which depends on the shape of the domain. As the main result, we prove that the lowest Robin eigenvalue for the exterior of a bounded geodesically convex domain $\Omega$ in the hyperbolic plane does not exceed such an eigenvalue for the exterior of the geodesic disk, whose geodesic curvature of the boundary is not smaller than the averaged geodesic curvature of the boundary of $\Omega$. This result implies as a consequence that under fixed area or fixed perimeter constraints the exterior of the geodesic disk maximises the lowest Robin eigenvalue among exteriors of bounded geodesically convex domains. Moreover, we obtain under the same geometric constraints a reverse inequality between the critical constants.
|
https://arxiv.org/abs/2601.10280
|
Academic Papers
|
svg
|
f23c000a1662fcb934879fb8840202aa582034e9501917f41c97d74a943278b6
|
2026-01-16T00:00:00-05:00
|
On holonomy groups of K-contact sub-pseudo-Riemannian manifolds
|
arXiv:2601.10286v1 Announce Type: new Abstract: This article investigates the holonomy groups of K-contact sub-pseudo-Riemannian manifolds. The primary result is a proof that the horizontal holonomy group either coincides with the adapted holonomy group or acts as its normal subgroup of codimension one. The theory is adapted for metrics of indefinite signature, bypassing the problem of subspace degeneracy that previously prevented the use of established orthogonal decomposition methods. It is established that, in the sub-Lorentzian case, the adapted holonomy group corresponds to the holonomy group of a certain Lorentzian manifold. This work also provides a complete classification of codimension-one ideals for Lorentzian holonomy algebras and presents specific examples of structures based on Cahen-Wallach spaces and K\"ahler manifolds.
|
https://arxiv.org/abs/2601.10286
|
Academic Papers
|
svg
|
54605890afd607bc58c1678e7f04d615f3af04ffb911e4d3283fe91f7be2999d
|
2026-01-16T00:00:00-05:00
|
High-Contrast Transmission Resonances for the Lam\'e System
|
arXiv:2601.10290v1 Announce Type: new Abstract: We consider the Lam\'e transmission problem in $\mathbb{R}^3$ with a bounded isotropic elastic inclusion in a high-contrast setting, where the interior-to-exterior Lam\'e moduli and densities scale like $1/\tau$ as $\tau\to0$. We study the scattering resonances of the associated self-adjoint Hamiltonian, defined as the poles of the meromorphic continuation of its resolvent. We obtain a sharp asymptotic description of resonances near the real axis as $\tau\to0$. Near each nonzero Neumann eigenvalue of the interior Lam\'e operator there is a cluster of resonances lying just below it in the complex plane; in this wavelength-scale regime the imaginary parts are of order $\tau$ with non-vanishing leading coefficients. In addition, near zero (a subwavelength regime), we identify resonances with real parts of order $\sqrt{\tau}$ and prove a lifetime dichotomy: their imaginary parts are of order $\tau$ generically, but of order $\tau^2$ for an explicit admissible set $\mathcal E$. This yields a classification of long-lived elastic resonances in the high-contrast limit. We also establish resolvent asymptotics for both fixed-size resonators and microresonators. We derive explicit expansions with a finite-rank leading term and quantitative remainder bounds, valid near both wavelength-scale and subwavelength resonances. For microresonators, at the wavelength scale the dominant contribution is an anisotropic elastic point scatterer. Near the zero eigenvalue, the leading-order behaviour is of monopole or dipole type, and we give a rigorous criterion distinguishing the two cases.
|
https://arxiv.org/abs/2601.10290
|
Academic Papers
|
svg
|
1307b675e92cc1821058be0b3e43fbc1fbc47d192f6f84c7250c4809b762d7ab
|
2026-01-16T00:00:00-05:00
|
Two dimensional covering systems and possible prime producing $a^m-b^n$
|
arXiv:2601.10296v1 Announce Type: new Abstract: We exhibit a new application of two dimensional covering systems, examples of integer pairs $a,b$ for which $a^m-b^n$ has a prime divisor from some given finite set of primes, for every pair of integers $m,n\geq 0$. This leads us to conjecture what are the only possible obstructions to $|a^m-b^n|$ taking on infinitely many distinct prime values.
|
https://arxiv.org/abs/2601.10296
|
Academic Papers
|
svg
|
0a621c0c0cb94ffc35ebdf08d792792fc8886ff614e273bad9cdc42f9c43fca6
|
2026-01-16T00:00:00-05:00
|
Global minimizers for a two-sided biharmonic Alt-Caffarelli problem
|
arXiv:2601.10297v1 Announce Type: new Abstract: We study global minimizers of biharmonic analogues of the Alt-Caffarelli functional. It turns out that half-space solutions are global minimizers for the two-sided Alt-Caffarelli functional, but not in the one-sided case. In addition, we identify a further class of global minimizers, all of which have constant Laplacian. Recent work by J. Lamboley and M. Nahon reduces potential global minimizers in dimension two to four possible categories. Our work shows that three of these categories persist in any dimension and are in fact global minimizers. Moreover, we show that minimizers of the two-sided biharmonic Alt-Caffarelli problem do in general not satisfy a partial differential equation, not even with a signed measure as right-hand-side. This is in sharp contrast to the corresponding one-sided problem.
|
https://arxiv.org/abs/2601.10297
|
Academic Papers
|
svg
|
fbf0bba617f2be1f7d19bfc20d3636504f534086745c395197eef67e65a80391
|
2026-01-16T00:00:00-05:00
|
Kummer-faithful fields with finitely generated absolute Galois group
|
arXiv:2601.10298v1 Announce Type: new Abstract: This paper studies the structure of the Mordell--Weil groups of semiabelian varieties over algebraic extensions of number fields whose absolute Galois group is finitely generated, with particular emphasis on that generated by a single element. A probabilistic argument using the Haar measure on the absolute Galois group of a number field shows that almost all such fields are Kummer-faithful, i.e., the Mordell--Weil group of any semiabelian variety over any finite extension of such a field has trivial divisible part. This result implies that there exists a Kummer-faithful field algebraic over a number field whose absolute Galois group is abelian.
|
https://arxiv.org/abs/2601.10298
|
Academic Papers
|
svg
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.