Tootfinder

Quantum mechanics, non-locality, and the space discreteness hypothesis
W. A. Z\'u\~niga-Galindo
https://arxiv.org/abs/2508.14836 https://arxiv.org/pdf/…

Quantum mechanics, non-locality, and the space discreteness hypothesis
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space $\mathcal{X}$ as a model for the space. However, we consider the time as a real variable. In this framework, the formalism of Dirac-von Neumann can be used. This discreteness hypothesis implies that given two different points in space, there is no continuous curve (a wor…

SDSO1 is a Ghost Planetary Nebula Bow Shock in Front of M31
Patrick Ogle, Mark Petersen, Tim Schaeffer, Lewis McCallum, Alberto Noriega-Crespo, R. Michael Rich, Biny Sebastian, Carl Bjork, Steeve Body, Sendhil Chinnasamy, Marcel Dreschsler, Tarun Kottary, Yann Sainty, Patrick Sparkman, Xavier Strottner
https://arxiv.org/abs/2507…

SDSO1 is a Ghost Planetary Nebula Bow Shock in Front of M31
We present new, deep narrow band imagery and discuss the nature of SDSO1, the large [O III]-emitting nebula centered 1.5 degrees SE of M31. We find strong evidence to support the hypothesis that SDSO1 is unrelated to M31 and is instead a bow shock driven by a faded, giant (D = 20 pc), 400 kyr-old, ghost planetary nebula (GPN) expelled by the symbiotic WD binary star EG Andromedae. Because EG And lags the rotation of the Milky Way, its hypersonic velocity of 107 km/s drives a shock into the loca…

Multiple Hypothesis Testing To Estimate The Number Of Communities in Stochastic Block Models
Chetkar Jha, Mingyao Li, Ian Barnett
https://arxiv.org/abs/2507.15471

Multiple Hypothesis Testing To Estimate The Number Of Communities in Stochastic Block Models
Clustering of single-cell RNA sequencing (scRNA-seq) datasets can give key insights into the biological functions of cells. Therefore, it is not surprising that network-based community detection methods (one of the better clustering methods) are increasingly being used for the clustering of scRNA-seq datasets. The main challenge in implementing network-based community detection methods for scRNA-seq datasets is that these methods \emph{apriori} require the true number of communities or blocks f…

Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph
Gautam Kamath, Alireza F. Pour, Matthew Regehr, David P. Woodruff
https://arxiv.org/abs/2509.16180 htt…

Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph
We propose an algorithm with improved query-complexity for the problem of hypothesis selection under local differential privacy constraints. Given a set of $k$ probability distributions $Q$, we describe an algorithm that satisfies local differential privacy, performs $\tilde{O}(k^{3/2})$ non-adaptive queries to individuals who each have samples from a probability distribution $p$, and outputs a probability distribution from the set $Q$ which is nearly the closest to $p$. Previous algorithms req…

On Vanishing of Gromov--Witten Invariants
Igor Pak, Colleen Robichaux, Weihong Xu
https://arxiv.org/abs/2508.15715 https://arxiv.org/pdf/2508.15715

On Vanishing of Gromov--Witten Invariants
We consider the decision problem of whether a particular Gromov--Witten invariant on a partial flag variety is zero. We prove that for the $3$-pointed, genus zero invariants, this problem is in the complexity class ${\sf AM}$ assuming the Generalized Riemann Hypothesis (GRH), and therefore lies in the second level of polynomial hierarchy ${\sf PH}$. For the proof, we construct an explicit system of polynomial equations through a translation of the defining equations. We also need to prove an …

Shanks bias in function fields
Seewoo Lee
https://arxiv.org/abs/2509.16142 https://arxiv.org/pdf/2509.16142

Shanks bias in function fields
We study the function field analogue of Shanks bias. For Liouville function $λ(f)$, we compare the number of monic polynomials $f$ with $λ(f) χ_m(f) = 1$ and $λ(f) χ_m(f) = -1$ for a nontrivial quadratic character $χ_m$ modulo a monic square-free polynomial $m$ over a finite field. Under Grand Simplicity Hypothesis (GSH) for $L$-functions, we prove that $λ\cdot χ_m$ is biased towards $+1$. We also give some examples where GSH is violated.

Squeezed Diffusion Models
Jyotirmai Singh, Samar Khanna, James Burgess
https://arxiv.org/abs/2508.14871 https://arxiv.org/pdf/2508.14871

Squeezed Diffusion Models
Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed Diffusion Models (SDM), which scale noise anisotropically along the principal component of the training distribution. As squeezing enhances the signal-to-noise ratio in physics, we hypothesize that scaling noise in a data-dependent manner can better assist dif…

An adaptive procedure for detecting replicated signals with $k$-family-wise error rate control
Ninh Tran
https://arxiv.org/abs/2508.15363 https://arxiv.org…

An adaptive procedure for detecting replicated signals with $k$-family-wise error rate control
Partial conjunction (PC) hypothesis testing is widely used to assess the replicability of scientific findings across multiple comparable studies. In high-throughput meta-analyses, testing a large number of PC hypotheses with k-family-wise error rate (k-FWER) control often suffers from low statistical power due to the multiplicity burden. The state-of-the-art AdaFilter-Bon procedure by Wang et al. (2022, Ann. Stat., 50(4), 1890-1909) alleviates this problem by filtering out hypotheses unlikely t…

Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies
Guanfu Liu, Pengfei Li, Yukun Liu, Xiaolong Pu
https://arxiv.org/abs/2507.14253

Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies
Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location-scale distribution family. We derive the limiting distribution of the LRT for the existence of the QTL effect in both location and s…

Testing Homogeneity in a heteroscedastic contaminated normal mixture
Xiaoqing Niu, Pengfei Li, Yuejiao Fu
https://arxiv.org/abs/2507.15630 https://

Testing Homogeneity in a heteroscedastic contaminated normal mixture
Large-scale simultaneous hypothesis testing appears in many areas such as microarray studies, genome-wide association studies, brain imaging, disease mapping and astronomical surveys. A well-known inference method is to control the false discovery rate. One popular approach is to model the $z$-scores derived from the individual $t$-tests and then use this model to control the false discovery rate. We propose a new class of contaminated normal mixtures for modelling $z$-scores. We further design…