Automorphic form twisted Shintani zeta functions over number fields
In this paper we study the twisted Shintani zeta function over number fields.
math.NT↗
arXiv subjects
Eun Hye Lee
Publications and source records attributed to Eun Hye Lee.
Uncertainty-Aware Genomic Classification of Alzheimer's Disease: A Transformer-Based Ensemble Approach with Monte Carlo Dropout
INTRODUCTION: Alzheimer's disease (AD) is genetically complex, complicating robust classification from genomic data. METHODS: We developed a transformer-based ensemble model (TrUE-Net) using Monte Carlo Dropout for uncertainty estimation in AD classification from whole-genome sequencing (WGS). We combined a transformer that preserves single-nucleotide polymorphism (SNP) sequence structure with a concurrent random forest using flattened genotypes. An uncertainty threshold separated samples into an uncertain (high-variance) group and a more certain (low-variance) group. RESULTS: We analyzed 1050 individuals, holding out half for testing. Overall accuracy and area under the receiver operating characteristic (ROC) curve (AUC) were 0.6514 and 0.6636, respectively. Excluding the uncertain group improved accuracy from 0.6263 to 0.7287 (10.24% increase) and F1 from 0.5843 to 0.8205 (23.62% increase). DISCUSSION: Monte Carlo Dropout-driven uncertainty helps identify ambiguous cases that may require further clinical evaluation, thus improving reliability in AD genomic classification.
q-bio.GN↗
DuAL-Net: A Hybrid Framework for Alzheimer's Disease Prediction from Whole-Genome Sequencing via Local SNP Windows and Global Annotations
Alzheimer's disease (AD) dementia is the most common form of dementia. With the emergence of disease-modifying therapies, predicting disease risk before symptom onset has become critical. We introduce DuAL-Net, a hybrid deep learning framework for AD dementia prediction using whole genome sequencing (WGS) data. DuAL-Net integrates two components: local probability modeling, which segments the genome into non-overlapping windows, and global annotation-based modeling, which annotates SNPs and reorganizes WGS input to capture long-range functional relationships. Both employ out-of-fold stacking with TabNet and Random Forest classifiers. Final predictions combine local and global probabilities using an optimized weighting parameter alpha. We analyzed WGS data from 1,050 individuals (443 cognitively normal, 607 AD dementia) using five-fold cross-validation. DuAL-Net achieved an AUC of 0.671 using top-ranked SNPs, representing 35.0% and 20.3% higher performance than bottom-ranked and randomly selected SNPs, respectively. ROC analysis demonstrated strong positive correlation between SNP prioritization rank and predictive power. The model identified known AD-associated SNPs as top contributors alongside potentially novel variants. DuAL-Net presents a promising framework improving both predictive accuracy and biological interpretability. The framework and web implementation offer an accessible platform for broader research applications.
q-bio.GN↗
Lower order terms in the shape of cubic fields
We demonstrate equidistribution of the lattice shape of cubic fields when ordered by discriminant, giving an estimate in the Eisenstein series spectrum with a lower order main term. The analysis gives a separate discussion of the contributions of reducible and irreducible binary cubic forms, following a method of Shintani. Our work answers a question posed at the American Institute of Math by giving a precise geometric and spectral description of an evident barrier to equidistribution in the lattice shape.
math.NT↗
A two variable zeta function associated to the space of binary forms of degree $d$
In this paper we prove the analytic continuation of a two variable zeta function defined using the vector space of binary forms of degree $d$ to the entire two dimensional complex space as a meromorphic function.
math.NT↗
On certain multiple Dirichlet series
In this paper we study the analytic properties of a multiple Dirichlet series associated to the prehomogeneous vector space of binary cubic forms.
math.NT↗
Subconvexity of Shintani's zeta function
Enumerating integral orbits in prehomogeneous vector spaces plays an important role in arithmetic statistics. We describe a method of proving subconvexity of the zeta function enumerating the integral orbits, illustrated by proving a subconvex estimate for the Shintani $ζ$ function enumerating class numbers of binary cubic forms.
math.NT↗
Subconvexity of twisted Shintani zeta functions
Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version.
math.NT↗
Eisenstein series twisted Shintani zeta function
We introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series. We prove the meromorphic continuation of this zeta function and identify its poles and their residues. We also identify the poles and residues of the zeta function when restricted to irreducible binary cubic forms. This zeta function can be used to prove the equidistribution of the lattice shape of cubic rings.
math.NT↗
Periodicity of Multidimensional Continued Fractions
It is known that the continued fraction expansion of a real number is periodic if and only if the number is a quadratic irrational. In an attempt to generalize this phenomenon to other settings, Jun-Ichi Tamura and Shin-Ichi Yasutomi have developed a new algorithm for multidimensional continued fractions (Algebraic Jacobi-Perron algorithm) that involves cubic irrationals, and proved periodicity in some cubic number fields, such as $\mathbb{Q}(\sqrt[3]{m^3+1})$ where $m\in\mathbb{Z}$, and $\mathbb{Q}(δ_m)$ where $δ_m$ is a root of $x^3-mx+1=0,\,\,m\in\mathbb{Z},\,\, m\geq3$ with the algorithm. In this paper, we study some other types of number fields that give rise to periodic continued fractions using the Algebraic Jacobi-Perron algorithm obtaining results for $\mathbb{Q}(\sqrt[l]{m^l+1})$ for any positive integer $l$. Furthermore, we find that some families of cubic equations, such as $x^3+3ax^2+bx+ab-2a^3+1=0,\,b\leq3a^2-3,\,a,b\in\mathbb{Z}$, have roots that have periodic multidimensional continued fractions.
math.NT↗
Deterministic photon-emitter coupling in chiral photonic circuits
The ability to engineer photon emission and photon scattering is at the heart of modern photonics applications ranging from light harvesting, through novel compact light sources, to quantum-information processing based on single photons. Nanophotonic waveguides are particularly well suited for such applications since they confine photon propagation to a 1D geometry thereby increasing the interaction between light and matter. Adding chiral functionalities to nanophotonic waveguides lead to new opportunities enabling integrated and robust quantum-photonic devices or the observation of novel topological photonic states. In a regular waveguide, a quantum emitter radiates photons in either of two directions, and photon emission and absorption are reverse processes. This symmetry is violated in nanophotonic structures where a non-transversal local electric field implies that both photon emission and scattering may become directional. Here we experimentally demonstrate that the internal state of a quantum emitter determines the chirality of single-photon emission in a specially engineered photonic-crystal waveguide. Single-photon emission into the waveguide with a directionality of more than 90\% is observed under conditions where practically all emitted photons are coupled to the waveguide. Such deterministic and highly directional photon emission enables on-chip optical diodes, circulators operating at the single-photon level, and deterministic quantum gates. Based on our experimental demonstration, we propose an experimentally achievable and fully scalable deterministic photon-photon CNOT gate, which so far has been missing in photonic quantum-information processing where most gates are probabilistic.
quant-ph↗
Decay dynamics and exciton localization in large GaAs quantum dots grown by droplet epitaxy
We investigate the optical emission and decay dynamics of excitons confined in large strain-free GaAs quantum dots grown by droplet epitaxy. From time-resolved measurements combined with a theoretical model we show that droplet-epitaxy quantum dots have a quantum efficiency of about 75% and an oscillator strength between 8 and 10. The quantum dots are found to be fully described by a model for strongly-confined excitons, in contrast to the theoretical prediction that excitons in large quantum dots exhibit the so-called giant oscillator strength. We attribute these findings to localized ground-state excitons in potential minima created by material intermixing during growth. We provide further evidence for the strong-confinement regime of excitons by extracting the size of electron and hole wavefunctions from the phonon-broadened photoluminescence spectra. Furthermore, we explore the temperature dependence of the decay dynamics and, for some quantum dots, observe a pronounced reduction in the effective transition strength with temperature. We quantify and explain these effects as being an intrinsic property of large quantum dots owing to thermal excitation of the ground-state exciton. Our results provide a detailed understanding of the optical properties of large quantum dots in general, and of quantum dots grown by droplet epitaxy in particular.
cond-mat.mes-hall↗
Fabrication and tuning of plasmonic optical nanoantennas around droplet epitaxy quantum dots by cathodoluminescence
We use cathodoluminescence to locate droplet epitaxy quantum dots with a precision $\lesssim$ nm before fabricating nanoantennas in their vicinity by electron-beam lithography. Cathodoluminescence is further used to evidence the effect of the antennas as a function of their length on the light emitted by the dot. Experimental results are in good agreement with numerical simulations of the structures.
physics.optics↗