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Linear independence of periods for the symmetric square $L$-functions
Tianyu Ni, Hui Xue
https://arxiv.org/abs/2507.17608 https://arx…

Linear independence of periods for the symmetric square $L$-functions
For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$, then any $n$ such periods are linearly independent. With some extra assumption, we also prove that for $k\geq e^{12}$, we can always pick up to $\frac{\log k}{4}$ arbitrary linearly independent periods.

Canard cycles of non-linearly regularized piecewise smooth vector fields
Peter De Maesschalck, Renato Huzak, Otavio Henrique Perez
https://arxiv.org/abs/2506.18099

Canard cycles of non-linearly regularized piecewise smooth vector fields
The main purpose of this paper is to study limit cycles in non-linear regularizations of planar piecewise smooth systems with fold points (or more degenerate tangency points) and crossing regions. We deal with a slow fast Hopf point after non-linear regularization and blow-up. We give a simple criterion for upper bounds and the existence of limit cycles of canard type, expressed in terms of zeros of the slow divergence integral. Using the criterion we can construct a quadratic regularization of…

Phase-optimised linearly-constrained minimum-variance beamformers
Hugh L Kennedy
https://arxiv.org/abs/2507.14937 https://arxiv.org/p…

Phase-optimised linearly-constrained minimum-variance beamformers
A novel procedure for the determination of the optimal group-delay for a Linearly-Constrained Minimum-Variance (LCMV) beamformer is proposed. Two ways of selecting the optimal delay are recommended: the first is the solution that minimizes the noise power; the second is the solution that minimizes the processing delay. The potential of this hitherto unexplored degree of design freedom is explored using simulated Very-High-Frequency (VHF) communication, and Ultra-High-Frequency (UHF) bistatic ra…

AlphaGo Moment for Model Architecture Discovery
Yixiu Liu, Yang Nan, Weixian Xu, Xiangkun Hu, Lyumanshan Ye, Zhen Qin, Pengfei Liu
https://arxiv.org/abs/2507.18074 https://

AlphaGo Moment for Model Architecture Discovery
While AI systems demonstrate exponentially improving capabilities, the pace of AI research itself remains linearly bounded by human cognitive capacity, creating an increasingly severe development bottleneck. We present ASI-Arch, the first demonstration of Artificial Superintelligence for AI research (ASI4AI) in the critical domain of neural architecture discovery--a fully autonomous system that shatters this fundamental constraint by enabling AI to conduct its own architectural innovation. Movi…

Linearly-polarized few-cycle pulses drive carrier envelope phase-sensitive coherent magnetization injection
Ofer Neufeld
https://arxiv.org/abs/2507.15490 h…

Linearly-polarized few-cycle pulses drive carrier envelope phase-sensitive coherent magnetization injection
Circularly-polarized light is well-known to induce, or flip the direction of, magnetization in solids. At its heart, this arises from time-reversal symmetry breaking by the vector potential, causing inverse-Faraday or analogous physical effects. We show here that very short few-cycle pulses can cause similar phenomena even when they are linearly-polarized and off-resonant. We analyze the new effect with ab-initio calculations and demonstrate that it similarly arises due to broken time-reversal …

Severi varieties on Enriques surfaces of base change type and on rational elliptic surfaces
Simone Pesatori
https://arxiv.org/abs/2506.18453 https://

Severi varieties on Enriques surfaces of base change type and on rational elliptic surfaces
If an irreducible curve on the very general Enriques surface splits in the K3 cover, its preimage consists of two linearly equivalent irreducible curves. We prove the nonemptiness of countable families of Severi varieties of curves of any genus on Enriques surfaces of base change type, whose members split in nonlinearly equivalent curves in the K3 cover. Our machinery leads us to provide examples of special superabundant logarithmic Severi varieties of curves of any genus on rational elliptic s…

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
Linwan Feng, David Shirokoff, Wooyoung Choi
https://arxiv.org/abs/2506.16045

Preconditioning and Linearly Implicit Time Integration for the Serre-Green-Naghdi Equations
The treatment of the differential PDE constraint poses a key challenge in computing the numerical solution of the Serre-Green-Naghdi (SGN) equations. In this work, we introduce a constant coefficient preconditioner for the SGN constraint operator and prove rigorous bounds on the preconditioned conditioning number. The conditioning bounds incorporate the effects of bathymetry in two dimensions, are quasi-optimal within a class of constant coefficient operators, highlight fundamental scalings for…

Effects of quantum geometry on the decoherence induced by black holes
Max Joseph Fahn, Alessandro Pesci
https://arxiv.org/abs/2507.16911 https://arxiv.org/…

Effects of quantum geometry on the decoherence induced by black holes
Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been kept open. In this, the effects of the horizon have been derived using a classical spacetime picture for the latter. In the present note we point out that quantum aspects of the geometry itself of the quantum black hole could significantly affect the results. In…

Twisted periods of modular forms
Tianyu Ni, Hui Xue
https://arxiv.org/abs/2507.17041 https://arxiv.org/pdf/2507.17041

Twisted periods of modular forms
Let $S_k$ denote the space of cusp forms of weight $k$ and level one. For $0\leq t\leq k-2$ and primitive Dirichlet character $χ$ mod $D$, we introduce twisted periods $r_{t,χ}$ on $S_k$. We show that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$ and $D$, then any $n$ periods with the same twist but different indices are linearly independent. We also prove that if $k$ is sufficiently large relative to $D$ then any $n$ periods with the same index but different tw…

1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
Yuanling Niu, Shuai Wang, Ying Zhang
https://arxiv.org/abs/2507.14562

1/2 order convergence rate of Euler-type methods for time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients
This paper investigates the convergence rates of two Euler-type methods for a class of time-changed stochastic differential equations with super-linearly growing drift and diffusion coefficients. Building upon existing research, we adapt the backward Euler method to time-changed stochastic differential equations where both coefficients exhibit super-linear growth and introduce an explicit counterpart, the projected Euler method. It is shown that both methods achieve the optimal strong convergen…