arXiv subjects

Ali Zamani

Publications and source records attributed to Ali Zamani.

At least 19 recordsLinked to original sources

arXiv2026

DragonCrawl: A Generative, Intent-Based Framework for Scalable Mobile End-to-End Testing

As mobile applications grow in complexity, traditional End-to-End (E2E) testing frameworks struggle with UI volatility, maintenance overhead, and cross-platform scalability. This paper presents DragonCrawl, an AI-driven mobile testing system for continuous regression testing that has evolved from embedding-based similarity matching to generative intent-based reasoning using large language models. Unlike prior LLM-based testing research focused on exploratory testing and crash detection, DragonCrawl validates specific user flows on every code change, blocking commits that break critical functionality. By leveraging GPT-4o's multimodal capabilities, DragonCrawl achieves 91.6% pass rate on iOS and 92.2% on Android across 1,013 automated tests running continuously in CI/CD pipelines. The system reduces test onboarding time from 96-120 hours to under 4 hours and has saved an estimated 27 developer years in test maintenance effort. We present the architectural evolution from V1 (semantic embedding matching) to V2 (generative intent-based reasoning), discuss implementation challenges including token explosion and memory constraints, and report operational experience from production deployment. The integration of multimodal vision for end-state detection and tool calling for backend state transitions enables comprehensive regression testing that bridges UI interactions with system state. Our results demonstrate that AI-driven testing can maintain stability while eliminating the brittleness of traditional automated tests, enabling continuous quality assurance at scale.

cs.SE↗

arXiv2026

Scaling Mobile Chaos Testing with AI-Driven Test Execution

Mobile applications in large-scale distributed systems are susceptible to backend service failures, yet traditional chaos engineering approaches cannot scale mobile testing due to the combinatorial explosion of flows, locations, and failure scenarios that need validation. We present an automated mobile chaos testing system that integrates DragonCrawl, an LLM-based mobile testing platform, with uHavoc, a service-level fault injection system. The key insight is that adaptive AI-driven test execution can navigate mobile applications under degraded backend conditions, eliminating the need to manually write test cases for each combination of user flow, city, and failure type. Since Q1 2024, our system has executed over 180,000 automated chaos tests across 47 critical flows in Uber's Rider, Driver, and Eats applications, representing approximately 39,000 hours of manual testing effort that would be impractical at this scale. We identified 23 resilience risks, with 70% being architectural dependency violations where non-critical service failures degraded core user flows. Twelve issues were severe enough to prevent trip requests or food orders. Two caused application crashes detectable only through mobile chaos testing, not backend testing alone. Automated root cause analysis reduced debugging time from hours to minutes, achieving 88% precision@5 in attributing mobile failures to specific backend services. This paper presents the system design, evaluates its performance under fault injection (maintaining 99% test reliability), and reports operational experience demonstrating that continuous mobile resilience validation is achievable at production scale.

cs.SE↗

arXiv2024

On the weighted contraharmonic means

Let $\mathscr{A}$ be a unital $C^*$-algebra with unit $e$ and let $ν\in(0, 1)$. We introduce the concept of the $ν$-weighted contraharmonic of two positive definite elements $a$ and $b$ of $\mathscr{A}$ by \begin{align*} {C}_ν(a, b):= (1-ν)ν^{-1}b + ν(1-ν)^{-1}a - \left((1-ν)a^{-1}+νb^{-1}\right)^{-1}. \end{align*} We show that \begin{align*} {C}_ν(a, b)= \displaystyle{\max_{x+y=e}}\left\{(1-ν)^{-1}\left(νa - x^*ax\right) + ν^{-1}\left((1-ν)b - y^*by\right)\right\}, \end{align*} and then apply it to present some properties of this weighted mean.

math.FA↗

arXiv2024

New estimates for numerical radius in $C^*$-algebras

Several numerical radius inequalities in the framework of $C^*$-algebras are proved in this paper. These results, which are based on an extension of Buzano inequality for elements in a pre-Hilbert $C^*$-module, generalize earlier numerical radius inequalities.

math.OA↗

arXiv2024

An extension of the $ρ$-operator radii

We define a function on the $C^{\ast}$-algebra of all bounded linear Hilbert space operators, which generalizes the operator radii, and we present some basic properties of this function. Our results extend several results in the literature.

math.FA↗

arXiv2024

Characterizations of $w_ρ$-Birkhoff--James orthogonality and $w_ρ$-parallelism

We study the concepts of Birkhoff--James orthogonality and parallelism in Hilbert space operators, induced by the operator radius norm $w_ρ(\cdot)$. In particular, we completely characterize Birkhoff--James orthogonality and parallelism with respect to $w_ρ(\cdot)$. As an application of the results presented, we obtain a well-known characterization due to R.~Bhatia and P.~Šemrl for the classical Birkhoff--James orthogonality of Hilbert space operators. Some other related results are also discussed.

math.FA↗

arXiv2023

$A$-spectral permanence property for $C^*$-algebras

For a positive element $A$ of a $C^*$-algebra $\mathfrak{A}$, let ${\|X\|}_{A}$ denote the $A$-operator semi-norm of $X\in\mathfrak{A}$. In this paper, we aim to introduce and study the notion of $A$-spectrum for $X$ such that ${\|X\|}_{A}<\infty$. In particular when $A$ is well-supported, we establish an $A$-spectral permanence property for $C^*$-algebras.

math.OA↗

arXiv2022

An extension of the $a$-numerical radius on $C^*$-algebras

Let $a$ be a positive element in a unital $C^*$-algebra $\mathfrak{A}$. We define a semi-norm on $\mathfrak{A}$, which generalizes the $a$-operator semi-norm and the $a$-numerical radius. We investigate basic properties of this semi-norm and prove inequalities involving it. Further, we derive new upper and lower bounds for the $a$-numerical radii of elements in $\mathfrak{A}$. Some other related results are also discussed.

math.OA↗

arXiv2022

A geometric approach to inequalities for the Hilbert--Schmidt norm

We define angle $Θ_{X,Y}$ between non-zero Hilbert--Schmidt operators $X$ and $Y$ by $\cosΘ_{_{X,Y}} = \frac{{\rm Re}{\rm Tr}(Y^*X)}{{\|X\|}_{_2}{\|Y\|}_{_2}}$, and give some of its essentially properties. It is shown, among other things, that \begin{align*} \big|\cosΘ_{_{X,Y}}\big|\leq \min\left\{\sqrt{\cosΘ_{_{|X^*|,|Y^*|}}}, \sqrt{\cosΘ_{_{|X|,|Y|}}}\right\}. \end{align*} It enables us to provide alternative proof of some well-known inequalities for the Hilbert--Schmidt norm. In particular, we apply this inequality to prove Lee's conjecture [Linear Algebra Appl. 433 (2010), no.~3, 580--584] as follows \begin{align*} {\big\|X + Y\big\|}_{_2} \leq \sqrt{\frac{\sqrt{2} + 1}{2}}\,{\big\|\,|X| + |Y|\,\big\|}_{_2}. \end{align*} A numerical example is presented to show the constant $\sqrt{\frac{\sqrt{2} + 1}{2}}$ is smallest possible. Other related inequalities for the Hilbert--Schmidt norm are also considered.

math.FA↗

arXiv2022

C*-module operators which satisfy in the generalized Cauchy--Schwarz type inequality

Let $\mathcal{L}(\mathscr{H})$ denote the $C^*$-algebra of adjointable operators on a Hilbert $C^*$-module $\mathscr{H}$. We introduce the generalized Cauchy-Schwarz inequality for operators in $\mathcal{L}(\mathscr{H})$ and investigate various properties of operators which satisfy the generalized Cauchy--Schwarz inequality. In particular, we prove that if an operator $A\in\mathcal{L}(\mathscr{H})$ satisfies the generalized Cauchy-Schwarz inequality such that $A$ has the polar decomposition, then $A$ is paranormal. In addition, we show that if for $A$ the equality holds in the generalized Cauchy-Schwarz inequality, then $A$ is cohyponormal. Among other things, when $A$ has the polar decomposition, we prove that $A$ is semi-hyponormal if and only if $\big\|\langle Ax, y\rangle\big\| \leq \big\|{|A|}^{1/2}x\big\|\big\|{|A|}^{1/2}y\big\|$ for all $x, y \in\mathscr{H}$.

math.FA↗

arXiv2021

Numerical radius in Hilbert $C^*$-modules

Utilizing the linking algebra of a Hilbert $C^*$-module $\big(\mathscr{V}, {\|\!\cdot\!\|}\big)$, we introduce $Ω(x)$ as a definition of numerical radius for an element $x\in\mathscr{V}$ and then show that $Ω(\cdot)$ is a norm on $\mathscr{V}$ such that $\frac{1}{2}{\|x\|} \leq Ω(x) \leq {\|x\|}$. In addition, we obtain an equivalent condition for $Ω(x) = \frac{1}{2}{\|x\|}$. Moreover, we present a refinement of the triangle inequality for the norm $Ω(\cdot)$. Some other related results are also discussed.

math.FA↗

arXiv2021

From norm derivatives to orthogonalities in Hilbert $C^*$-modules

Let $\big(\mathscr{X}, \langle\cdot, \cdot\rangle\big)$ be a Hilbert $C^*$-module over a $C^*$-algebra $\mathscr{A}$ and let $\mathcal{S}(\mathscr{A})$ be the set of states on $\mathscr{A}$. In this paper, we first compute the norm derivative for elements $x$ and $y$ of $\mathscr{X}$ as follows \begin{align*} ρ_{_{+}}(x, y) = \max\Big\{\mbox{Re}\,φ(\langle x, y\rangle): \, φ\in \mathcal{S}(\mathscr{A}), φ(\langle x, x\rangle) = \|x\|^2\Big\}. \end{align*} We then apply it to characterize different concepts of orthogonality in $\mathscr{X}$. In particular, we present a simpler proof of the classical characterization of Birkhoff--James orthogonality in Hilbert $C^*$-modules. Moreover, some generalized Daugavet equation in the $C^*$-algebra $\mathbb{B}(\mathcal{H})$ of all bounded linear operators acting on a Hilbert space $\mathcal{H}$ is solved.

math.OA↗

arXiv2021

Orthogonality Hilbert A-modules and operators preserving multi-A-linearity

In this paper we present results concerning orthogonality in Hilbert $C^*$-modules. Moreover, for a $C^*$-algebra $\mathscr{A}$, we prove theorems concerning the multi-$\mathscr{A}$-linearity and its preservation by $\mathscr{A}$-linear operators. New version of solution of the orthogonality equation on Hilbert $C^*$-modules and mappings preserving orthogonality are also investigated.

math.OA↗

arXiv2021

The weighted Hilbert--Schmidt numerical radius

Let $\mathbb{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a Hilbert space $\mathcal{H}$ and let $N(\cdot)$ be a norm on $\mathbb{B}(\mathcal{H})$. For every $0\leq ν\leq 1$, we introduce the $w_{_{(N,ν)}}(A)$ as an extension of the classical numerical radius by \begin{align*} w_{_{(N,ν)}}(A):= \displaystyle{\sup_{θ\in \mathbb{R}}} N\left(νe^{iθ}A + (1-ν)e^{-iθ}A^*\right) \end{align*} and investigate basic properties of this notion and prove inequalities involving it. In particular, when $N(\cdot)$ is the Hilbert--Schmidt norm ${\|\!\cdot\!\|}_{2}$, we present several the weighted Hilbert--Schmidt numerical radius inequalities for operator matrices. Furthermore, we give a refinement of the triangle inequality for the Hilbert--Schmidt norm as follows: \begin{align*} {\|A+B\|}_{2} \leq \sqrt{2w_{_{({\|\!\cdot\!\|}_{2},ν)}}^2\left(\begin{bmatrix} 0 & A \\ B^* & 0 \end{bmatrix}\right) - (1-2ν)^2{\|A-B\|}_{2}^2} \leq {\|A\|}_{2} + {\|B\|}_{2}. \end{align*} Our results extend some theorems due to F.~Kittaneh et al. (2019).

math.FA↗

arXiv2021

Orthogonality preserving property for pairs of operators on Hilbert $C^*$-modules

We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product structure of a Hilbert $C^*$-module is determined essentially by the module structure and by the orthogonality structure, pairs of linear and local orthogonality-preserving mappings are investigated, not a priori bounded. The intuition is that most often $C^*$-linearity and boundedness can be derived from the settings under consideration. In particular, we obtain that if $\mathscr{A}$ is a $C^{*}$-algebra and $T, S:\mathscr{E}\longrightarrow \mathscr{F}$ are two bounded ${\mathscr A}$-linear mappings between full Hilbert $\mathscr{A}$-modules, then $\langle x, y\rangle = 0$ implies $\langle T(x), S(y)\rangle = 0$ for all $x, y\in \mathscr{E}$ if and only if there exists an element $γ$ of the center $Z(M({\mathscr A}))$ of the multiplier algebra $M({\mathscr A})$ of ${\mathscr A}$ such that $\langle T(x), S(y)\rangle = γ\langle x, y\rangle$ for all $x, y\in \mathscr{E}$. In particular, for adjointable operators $S$ we have $T=(S^*)^{-1}$, and any bounded invertible module operator $T$ may appear. Varying the conditions on the mappings $T$ and $S$ we obtain further affirmative results for local operators and for pairs of a bounded and of an unbounded module operator with bounded inverse, among others. Also, unbounded operators with disjoint ranges are considered. The proving techniques give new insights.

math.OA↗

arXiv2020

Some upper bounds for the $\mathbb{A}$-numerical radius of $2\times 2$ block matrices

Let $\mathbb{A}=\left( \begin{array}{cc} A & 0 \\ 0 & A \\ \end{array} \right)$ be the $2\times2$ diagonal operator matrix determined by a positive bounded operator $A$. For semi-Hilbertian operators $X$ and $Y$, we first show that \begin{align*} w^2_{\mathbb{A}}\left(\begin{bmatrix} 0 & X \\ Y & 0 \end{bmatrix}\right) &\leq \frac{1}{4}\max\Big\{{\big\|XX^{\sharp_A} + Y^{\sharp_A}Y\big\|}_{A}, {\big\|X^{\sharp_A}X + YY^{\sharp_A}\big\|}_{A}\Big\} + \frac{1}{2}\max\big\{w_{A}(XY), w_{A}(YX)\big\}, \end{align*} where $w_{\mathbb{A}}(\cdot)$, ${\|\cdot\|}_{A}$ and $w_{A}(\cdot)$ are the $\mathbb{A}$-numerical radius, $A$-operator seminorm and $A$-numerical radius, respectively. We then apply the above inequality to find some upper bounds for the $\mathbb{A}$-numerical radius of certain $2\times 2$ operator matrices. In particular, we obtain some refinements of earlier $A$-numerical radius inequalities for semi-Hilbertian operators. An upper bound for the $\mathbb{A}$-numerical radius of $2\times 2$ block matrices of semi-Hilbertian space operators is also given.

math.FA↗

arXiv2020

On an extension of operator transforms

We introduce the $λ$-mean transform $M_λ(T)$ of a Hilbert space operator $T$ as an extension of some operator transforms based on the Duggal transform $T^D$ by $M_λ(T) := λT + (1-λ)T^D$, and present some of its essentially properties. Among other things, we obtain estimates for the operator norm and numerical radius of the $λ$-mean transform $M_λ(T)$ in terms of the original operator $T$.

math.FA↗

arXiv2020

Numerical radius orthogonality in $C^*$-algebras

In this paper we characterize the Birkhoff--James orthogonality with respect to the numerical radius norm $v(\cdot)$ in $C^*$-algebras. More precisely, for two elements $a, b$ in a $C^*$-algebra $\mathfrak{A}$, we show that $a\perp_{B}^{v} b$ if and only if for each $θ\in [0, 2π)$, there exists a state $φ_{_θ}$ on $\mathfrak{A}$ such that $|φ_{_θ}(a)| = v(a)$ and $\mbox{Re}\big(e^{iθ}\overline{φ_{_θ}(a)}φ_{_θ}(b)\big)\geq 0$. Moreover, we compute the numerical radius derivatives in $\mathfrak{A}$. In addition, we characterize when the numerical radius norm of the sum of two (or three) elements in $\mathfrak{A}$ equals the sum of their numerical radius norms.

math.FA↗