Searcharxiv⌕ Search

arXiv subjects

Amir Mohammadi

Publications and source records attributed to Amir Mohammadi.

At least 37 records · Page 2Linked to original sources
arXiv2022

Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

math.DS↗
arXiv2022

Property tau in positive characteristic

We prove a quantitative equidistribution statement for certain adelic homogeneous subsets in positive characteristic. As an application, we describe a proof of property tau for arithmetic groups in this context.

math.NT↗
arXiv2021

Benjamini-Schramm convergence of periodic orbits

We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.

math.DS↗
arXiv2021

Effective counting of simple closed geodesics on hyperbolic surfaces

We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a compact surface equipped with a Riemannian metric of negative curvature. The proof relies on the exponential mixing rate for the Teichmüller geodesic flow.

math.GT↗
arXiv2021

Geodesic planes in the convex core of an acylindrical 3-manifold

Let $M$ be a convex cocompact acylindrical hyperbolic 3-manifold of infinite volume, and let $M^*$ denote the interior of the convex core of $M$. In this paper we show that any geodesic plane in $M^*$ is either closed or dense. We also show that only countably many planes are closed. These are the first rigidity theorems for planes in convex cocompact 3-manifolds of infinite volume that depend only on the topology of M.

math.DS↗
arXiv2020

Iris Liveness Detection Competition (LivDet-Iris) -- The 2020 Edition

Launched in 2013, LivDet-Iris is an international competition series open to academia and industry with the aim to assess and report advances in iris Presentation Attack Detection (PAD). This paper presents results from the fourth competition of the series: LivDet-Iris 2020. This year's competition introduced several novel elements: (a) incorporated new types of attacks (samples displayed on a screen, cadaver eyes and prosthetic eyes), (b) initiated LivDet-Iris as an on-going effort, with a testing protocol available now to everyone via the Biometrics Evaluation and Testing (BEAT)(https://www.idiap.ch/software/beat/) open-source platform to facilitate reproducibility and benchmarking of new algorithms continuously, and (c) performance comparison of the submitted entries with three baseline methods (offered by the University of Notre Dame and Michigan State University), and three open-source iris PAD methods available in the public domain. The best performing entry to the competition reported a weighted average APCER of 59.10\% and a BPCER of 0.46\% over all five attack types. This paper serves as the latest evaluation of iris PAD on a large spectrum of presentation attack instruments.

cs.CV↗
arXiv2020

Locally Random Groups

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of small balls and provide several examples of such groups. In particular, this leads to new examples of groups satisfying such a mixing inequality. In the same context, we will develop a Littlewood-Paley decomposition and explore its connection to the existence of the spectral gap for random walks. Moreover, under the dimension condition alone, we will prove a multi-scale entropy gain result `a la Bourgain-Gamburd and Tao.

math.GR↗
arXiv2020

PCB Defect Detection Using Denoising Convolutional Autoencoders

Printed Circuit boards (PCBs) are one of the most important stages in making electronic products. A small defect in PCBs can cause significant flaws in the final product. Hence, detecting all defects in PCBs and locating them is essential. In this paper, we propose an approach based on denoising convolutional autoencoders for detecting defective PCBs and to locate the defects. Denoising autoencoders take a corrupted image and try to recover the intact image. We trained our model with defective PCBs and forced it to repair the defective parts. Our model not only detects all kinds of defects and locates them, but it can also repair them as well. By subtracting the repaired output from the input, the defective parts are located. The experimental results indicate that our model detects the defective PCBs with high accuracy (97.5%) compare to state of the art works.

eess.IV↗
arXiv2020

Life and death of a cold BaRb$^+$ molecule inside an ultracold cloud of Rb atoms

We study the evolution of a single BaRb$^+$ molecule while it continuously collides with ultracold Rb atoms. The initially weakly-bound molecule can undergo a sequence of elastic, inelastic, reactive, and radiative processes. We investigate these processes by developing methods for discriminating between different ion species, electronic states, and kinetic ion energy ranges. By comparing the measurements to model calculations we obtain a consistent description of the typical trajectory of the ion through the manifold of available atomic and molecular states. As a further result, we determine rates for collisional and radiative relaxation as well as photodissociation, spin-flip collisions, and chemical reactions.

physics.atom-ph↗
arXiv2019

Smartphone Multi-modal Biometric Authentication: Database and Evaluation

Biometric-based verification is widely employed on the smartphones for various applications, including financial transactions. In this work, we present a new multimodal biometric dataset (face, voice, and periocular) acquired using a smartphone. The new dataset is comprised of 150 subjects that are captured in six different sessions reflecting real-life scenarios of smartphone assisted authentication. One of the unique features of this dataset is that it is collected in four different geographic locations representing a diverse population and ethnicity. Additionally, we also present a multimodal Presentation Attack (PA) or spoofing dataset using a low-cost Presentation Attack Instrument (PAI) such as print and electronic display attacks. The novel acquisition protocols and the diversity of the data subjects collected from different geographic locations will allow developing a novel algorithm for either unimodal or multimodal biometrics. Further, we also report the performance evaluation of the baseline biometric verification and Presentation Attack Detection (PAD) on the newly collected dataset.

cs.CV↗
arXiv2019

Ergodicity of unipotent flows and Kleinian groups

Let M be a non-elementary convex cocompact hyperbolic 3 manifold and delta the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure provided that delta>1.

math.DS↗
arXiv2019

Effective equidistribution and property tau

We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters. We explain how this implies certain equidistribution theorems which, even in a qualitative form, are not accessible to measure-classification theorems. As another application, we describe another proof of property tau for arithmetic groups.

math.NT↗
arXiv2019

Minimizing rf-induced excess micromotion of a trapped ion with the help of ultracold atoms

We report on the compensation of excess micromotion due to parasitic rf-electric fields in a Paul trap. The parasitic rf-electric fields stem from the Paul trap drive but cause excess micromotion, e.g. due to imperfections in the setup of the Paul trap. We compensate these fields by applying rf-voltages of the same frequency but adequate phases and amplitudes to Paul trap electrodes. The magnitude of micromotion is probed by studying elastic collision rates of the trapped ion with a gas of ultracold neutral atoms. Furthermore, we demonstrate that also reactive collisions can be used to quantify micromotion. We achieve compensation efficiencies of about 1$\:\text{Vm}^{-1}$, which is comparable to other conventional methods.

cond-mat.quant-gas↗
arXiv2019

On effective equidistribution for quotients of SL(d)

We prove the first case of polynomially effective equidistribution of closed orbits of semisimple groups with nontrivial centralizer. The proof relies on uniform spectral gap, builds on, and extends work of Einsiedler, Margulis, and Venkatesh.

math.DS↗
arXiv2016

Logarithm laws for one parameter unipotent flows

We prove logarithm laws and shrinking target properties for unipotent flows on the homogenous space $Γ\bs G$ with $G=\SL_2(\bbR)^{r_1}\times\SL_2(\bbC)^{r_2}$ and $Γ\subseteq G$ an irreducible non-uniform lattice. Our method relies on certain estimates for the norms of (incomplete) theta series in this setting.

math.DS↗