arXiv subjects

Yunqing Tang

Publications and source records attributed to Yunqing Tang.

At least 19 recordsLinked to original sources

arXiv2026

A Zero-Shot Deep Image Prior Framework for Denoising and Deconvolution in Fluorescence Microscopy

Fluorescence microscopy images are degraded by noise and diffraction-induced blur, which compromise structural fidelity and limit quantitative analysis. Supervised deep learning methods achieve impressive restoration performance but require large-scale paired datasets that are difficult to obtain in practice. To address this issue, we propose SDIP, a zero-shot deep image prior (DIP) framework that sequentially performs denoising and deconvolution without external training data. An aSeqDIP-based module first suppresses noise while preserving fine structures through sequential autoencoding regularization. In the deconvolution stage, a wavelet-based background correction step is incorporated before the proposed RLG-DIP module performs artifact-reduced deconvolution. RLG-DIP uses the Richardson-Lucy deconvolution result as a physically consistent guidance prior, integrating the imaging model with the implicit prior of DIP to stabilize the ill-posed deconvolution process. Experiments on the BioSR dataset across multiple cellular structures demonstrate that SDIP improves both signal-to-noise ratio and resolution, achieving superior visual quality and improved quantitative performance on most evaluated structures. The proposed framework may also provide useful insights for designing physically guided DIP methods for other inverse problems.

eess.IV↗

arXiv2025

Computational TIRF enables optical sectioning beyond the evanescent field for widefield fluorescence microscopy

The resolving ability of widefield fluorescence microscopy is fundamentally limited by out-of-focus background owing to its low axial resolution, particularly for densely labeled biological samples. Although total internal reflection fluorescence (TIRF) microscopy provides strong near-surface sectioning, they are intrinsically restricted to shallow imaging depths. Here we present computational TIRF (cTIRF), a deep learning-based imaging modality that generates TIRF-like sectioned images directly from conventional widefield epifluorescence measurements without any optical modification. By integrating a physics-informed forward model into network training, cTIRF achieves effective background suppression and axial resolution enhancement while maintaining consistency with the measured widefield data. We demonstrate that cTIRF recovers near-surface structures with performance comparable to experimental TIRF, and further enables both single-frame and volumetric sectioned reconstruction in densely labeled samples where conventional TIRF fails. This work establishes cTIRF as a practical and deployable alternative to hardware-based optical sectioning in fluorescence microscopy, enabled by rapid adaptation to new imaging systems with minimal calibration data.

physics.optics↗

arXiv2025

Infinitely many primes of basic reduction for some abelian fourfolds

If $E$ is an elliptic curve, defined over $\mathbb{Q}$ or a number field having at least one real embedding, then Elkies proved that $E$ has supersingular reduction at infinitely many primes $p$. Baba and Granath extended this result to certain curves $C$ of genus $2$ with field of moduli $\mathbb{Q}$, under a condition on the endomorphism ring of the Jacobian. In this paper, we extend these results to certain curves of genus $4$ having an automorphism of order $5$, proving that the Jacobians of these curves have basic reduction (as defined by Kottwitz) for infinitely many primes $p$. To do this, we study the complex uniformization of the Deligne--Mostow Shimura variety $\mathrm{Sh}$ associated with the one dimensional family of these curves. By analyzing the real points on $\mathrm{Sh}$, we compute three geodesics in the upper half plane that are edges of a fundamental triangle for the action of the unitary similitude group. Using representations of quadratic forms, we determine the points on $\mathrm{Sh}$ which represent curves whose Jacobians have complex multiplication by certain quadratic extensions of the cyclotomic field $\mathbb{Q}(\zeta_5)$. We conclude by studying the equidistribution of these points and the reduction of these CM cycles on the Shimura variety.

math.NT↗

arXiv2025

Arithmetic holonomy bounds and effective Diophantine approximation

In this paper, we explore several threads arising from our recent joint work on arithmetic holonomy bounds, which were originally devised to prove new irrationality results based on the method of Ap\'ery limits. We propose a new method to address effective Diophantine approximation on the projective line and the multiplicative group. This method, and all our other results in the paper, emerged from quantifying our holonomy bounds in a way that directly yields effective measures of irrationality and linear independence. Applying these to a dihedral algebraic construction, we derive good effective irrationality measures for high order roots of an algebraic number, in an approach that might be considered a multivalent continuation of the classical hypergeometric method of Thue, Siegel, and Baker. A well-known Dirichlet approximation argument of Bombieri allows one to derive from this the classical effective Diophantine theorems, hitherto only approachable by Baker's linear forms in logarithms or by Bombieri's equivariant Thue--Siegel method. These include the algorithmic resolution of the two-variable $S$-unit equation, the Thue--Mahler equation, and the hyperelliptic and superelliptic equations, as well as the Baker--Feldman effective power sharpening of Liouville's theorem. We also give some other applications, including irrationality measures for the classical $L(2,\chi_{-3})$ and the $2$-adic $\zeta(5)$, and a new proof of the transcendence of $\pi$. Due to space limitations, a full development of these ideas will be deferred to future work.

math.NT↗

arXiv2025

Positive density of primes of ordinary reduction for abelian varieties of simple signature

By a result of Serre, if $A$ is an elliptic curve without CM defined over a number field $L$, then the set of primes of $L$ for which $A$ has ordinary reduction has density $1$. Katz and Ogus proved the same is true when $A$ is an abelian surface, after possibly passing to a finite extension of $L$. More recently, Sawin computed the density of the set of primes of $L$ for which an abelian surface $A$ has ordinary reduction, depending on the endomorphism algebra of $A$. In this paper, we prove some generalizations of these results when $A$ is an absolutely simple abelian variety of arbitrary dimension whose endomorphism algebra is a CM field $F$, under specific conditions on the signature of the multiplication action of $F$ on $A$. We include explicit examples from Jacobians of curves of genus three through seven admitting cyclic covers to the projective line.

math.NT↗

arXiv2024

The Unbounded Denominators Conjecture

We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). Our result includes also Mason's generalization of the original conjecture to the setting of vector-valued modular forms, thereby supplying a new path to the congruence property in rational conformal field theory. The proof involves a new arithmetic holonomicity bound of a potential-theoretic flavor, together with Nevanlinna's second main theorem, the congruence subgroup property of SL_2(Z[1/p]), and a close description of the Fuchsian uniformization D(0,1)/Γ_N of the Riemann surface C \setminus μ_N.

math.NT↗

arXiv2024

The linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$

We prove the irrationality of the classical Dirichlet L-value $L(2,χ_{-3})$. The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. In fact our work also establishes the $\mathbf{Q}$-linear independence of $1$, $ζ(2)$, and $L(2,χ_{-3})$. We also give a number of other applications of our method to other problems in irrationality.

math.NT↗

arXiv2024

Optoionic Impedance Spectroscopy (OIS): a model-less technique for in-situ electrochemical characterization of mixed ionic electronic conductors

Functional properties of mixed ionic electronic conductors (MIECs) can be radically modified by (de)insertion of mobile charged defects. A complete control of this dynamic behaviour has multiple applications in a myriad of fields including advanced computing, data processing, sensing or energy conversion. However, the effect of different MIECs state-of-charge is not fully understood yet and there is a lack of strategies for fully controlling the defect content in a material. In this work we present a model-less technique to characterize ionic defect concentration and ionic insertion kinetics in MIEC materials: Optoionic Impedance Spectroscopy (OIS). The proof of concept and advantages of OIS are demonstrated by studying the oxygen (de)insertion in thin films of hole-doped perovskite oxides. Ion migration into/out of the studied materials is achieved by the application of an electrochemical potential, achieving stable and reversible modification of its optical properties. By tracking the dynamic variation of optical properties depending on the gating conditions, OIS enables to extract electrochemical parameters involved in the electrochromic process. The results demonstrate the capability of the technique to effectively characterize the kinetics of single- and even multi- layer systems. The technique can be employed for studying underlying mechanisms of the response characteristics of MIEC-based devices.

physics.app-ph↗

arXiv2023

Ion Intercalation in Lanthanum Strontium Ferrite for Aqueous Electrochemical Energy Storage Devices

Ion intercalation of perovskite oxides in liquid electrolytes is a very promising method for controlling their functional properties while storing charge, which opens the potential application in different energy and information technologies. Although the role of defect chemistry in the oxygen intercalation in a gaseous environment is well established, the mechanism of ion intercalation in liquid electrolytes at room temperature is poorly understood. In this study, the defect chemistry during ion intercalation of La0.5Sr0.5FeO3-δ thin films in alkaline electrolytes is studied. Oxygen and proton intercalation into the LSF perovskite structure is observed at moderate electrochemical potentials (0.5 V to -0.4 V), giving rise to a change in the oxidation state of Fe (as a charge compensation mechanism). The variation of the concentration of holes as a function of the intercalation potential was characterized by in-situ ellipsometry and the concentration of electron holes was indirectly quantified for different electrochemical potentials. Finally, a dilute defect chemistry model that describes the variation of defect species during ionic intercalation was developed.

cond-mat.mtrl-sci↗

arXiv2022

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields

Given a K3 surface $X$ over a number field $K$ with potentially good reduction everywhere, we prove that the set of primes of $K$ where the geometric Picard rank jumps is infinite. As a corollary, we prove that either $X_{\overline{K}}$ has infinitely many rational curves or $X$ has infinitely many unirational specializations. Our result on Picard ranks is a special case of more general results on exceptional classes for K3 type motives associated to GSpin Shimura varieties. These general results have several other applications. For instance, we prove that an abelian surface over a number field $K$ with potentially good reduction everywhere is isogenous to a product of elliptic curves modulo infinitely many primes of $K$.

math.NT↗

arXiv2021

Pushing the Study of Point Defects in Thin Film Ferrites to Low Temperatures Using In Situ Ellipsometry

Unveiling point defects concentration in transition metal oxide thin films is essential to understand and eventually control their functional properties, employed in an increasing number of applications and devices. Despite this unquestionable interest, there is a lack of available experimental techniques able to estimate the defect chemistry and equilibrium constants in such oxides at intermediate-to-low temperatures. In this study, the defect chemistry of a relevant material such as La1-xSrxFeO3-d (LSF) with (x = 0.2, 0.4 and 0.5 (LSF20, LSF40 and LSF50 respectively) is obtained by using a novel in situ spectroscopic ellipsometry approach applied to thin films. Through this technique, the concentration of holes in LSF is correlated to measured optical properties and its evolution with temperature and oxygen partial pressure is determined. In this way, a systematic description of defect chemistry in LSF thin films in the temperature range from 350dC to 500dC is obtained for the first time, which represents a step forward in the understanding of LSF20, LSF40 and LSF50 for emerging low temperature applications.

cond-mat.mtrl-sci↗

arXiv2020

Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture

Let $\mathscr{X} \rightarrow C$ be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve $C$ in characteristic $p \geq 5$. We prove that the geometric Picard rank jumps at infinitely many closed points of $C$. More generally, suppose that we are given the canonical model of a Shimura variety $\mathcal{S}$ of orthogonal type, associated to a lattice of signature $(b,2)$ that is self-dual at $p$. We prove that any generically ordinary proper curve $C$ in $\mathcal{S}_{\overline{\mathbb{F}}_p}$ intersects special divisors of $\mathcal{S}_{\overline{\mathbb{F}}_p}$ at infinitely many points. As an application, we prove the ordinary Hecke orbit conjecture of Chai--Oort in this setting; that is, we show that ordinary points in $\mathcal{S}_{\overline{\mathbb{F}}_p}$ have Zariski-dense Hecke orbits. We also deduce the ordinary Hecke orbit conjecture for certain families of unitary Shimura varieties.

math.NT↗

arXiv2020

Reductions of abelian surfaces over global function fields

Let $A$ be a non-isotrivial ordinary abelian surface over a global function field with good reduction everywhere. Suppose that $A$ does not have real multiplication by any real quadratic field with discriminant a multiple of $p$. We prove that there are infinitely many places modulo which $A$ is isogenous to the product of two elliptic curves.

math.NT↗

arXiv2019

Newton polygon stratification of the Torelli locus in PEL-type Shimura varieties

We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo $p$ reduction of certain PEL-type Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic $p$ whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems which demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the twenty special PEL-type Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if $p>>0$ in the supersingular cases).

math.NT↗

arXiv2018

Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line

By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. For each of these, we compute the Newton polygons, and the $μ$-ordinary Ekedahl--Oort type, occurring in the characteristic $p$ reduction of the Shimura variety. We prove that all but a few of the Newton polygons appear on the open Torelli locus. As an application, we produce multiple new examples of Newton polygons and Ekedahl--Oort types of Jacobians of smooth curves in characteristic $p$. Under certain congruence conditions on $p$, these include: the supersingular Newton polygon for genus $5,6,7$; fourteen new non-supersingular Newton polygons for genus $5-7$; eleven new Ekedahl--Oort types for genus $4-7$ and, for all $g \geq 6$, the Newton polygon with $p$-rank $g-6$ with slopes $1/6$ and $5/6$.

math.NT↗

arXiv2018

Newton polygons of cyclic covers of the projective line branched at three points

We review the Shimura-Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic $p$. Under certain congruence conditions on $p$, these include: the supersingular Newton polygon for each genus $g$ with $4 \leq g \leq 11$; nine non-supersingular Newton polygons with $p$-rank $0$ with $4 \leq g \leq 11$; and, for all $g \geq 5$, the Newton polygon with $p$-rank $g-5$ having slopes $1/5$ and $4/5$.

math.NT↗

arXiv2017

Exceptional splitting of reductions of abelian surfaces

Heuristics based on the Sato--Tate conjecture suggest that an abelian surface defined over a number field has infinitely many places of split reduction. We prove this result for abelian surfaces having real multiplication. Similar to Charles' theorem on exceptional isogeny of reductions of a given pair of elliptic curves and Elkies' theorem on supersingular reductions of a given elliptic curve, our theorem shows that a density-zero set of primes pertaining to the reduction of abelian varieties is infinite. The proof relies on the Arakelov intersection theory on Hilbert modular surfaces.

math.NT↗

arXiv2017

Cycles in the de Rham cohomology of abelian varieties over number fields

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of $\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus' prediction for some families of abelian varieties. These families include abelian varieties that have both prime dimension and nontrivial endomorphism ring. The proof is based on a crystalline analogue of Faltings' isogeny theorem due to Bost and the known cases of the Mumford--Tate conjecture.

math.AG↗