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Ali Mohammadi

Publications and source records attributed to Ali Mohammadi.

At least 19 recordsLinked to original sources
arXiv2026

PCB-Integrated CoPt Micromagnets for Magnetophoresis

Integration of magnetic material with scalable microfluidic platforms can significantly improve the throughput and precision in biotechnology processes. In this work we have developed a new magnetic platform based on printed circuit board (PCB) technology. Cobalt-Platinum (CoPt) micromagnets are electroplated on copper pads with an arbitrary footprint on a Kapton substrate to enable generation of different magnetic field gradients. The magnets are characterized by XRD and VSM, before and after thermal annealing. The ordered L10 phase appear in XRD results after annealing at 600 °C, and VSM results show around six times increase for in-plane magnetic remanence from 0.24T to 1.4T. The near equiatomic ratios of Co:Pt is confirmed by EDX observations. The performance of these magnets is experimentally validated by trapping magnetic nanoparticles in microfluidic channels. These results are in excellent agreement with FEA models presented in COMSOL Multiphysics.

cond-mat.other↗
arXiv2026

Bilinear Kloosterman sums over small boxes and uniformity of a random walk

Given an additive character $ψ$ of an arbitrary finite field $\mathbb{F}_{p^n}$ and elements $a,b\in \mathbb{F}_{p^n}$, $b\neq 0$, we prove a bound on bilinear Kloosterman sums $\sum_{x\in B_1}\sum_{y\in B_2}ψ(axy+bx^{-1}y^{-1})$, where $B_1, B_2$ denote boxes in $\mathbb{F}_{p^n}$. Here, a box is a coordinate parallelepiped obtained by restricting the coefficients of field elements, with respect to a fixed basis of $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$, to intervals in $\mathbb{F}_p$. Our estimates are nontrivial when $|B_1||B_2|>p^{n/2+ε}$ and hence in a range not accessible by the Weil bound. We also consider the random walk on $\mathbb{F}_{p^n}$ defined by $S_k=S_0+W_1+\cdots+W_k$, where $W_i=aX_iY_i+b(X_iY_i)^{-1}$ and $X_i,Y_i$ are independent uniformly distributed random variables on $B_1$ and $B_2$ respectively. We show that the nontrivial Fourier coefficients of $S_k$ decay exponentially. Consequently, every nonzero $\mathbb{F}_p$-linear projection of $S_k$, as well as the full distribution of $S_k$ converge to the uniform distribution on $\mathbb{F}_p$ and $\mathbb{F}_{p^n}$, respectively. We also obtain bounds on the rate at which the entropy of $S_k$ converges to its maximal value.

math.NT↗
arXiv2026

First server's effect on the expected number of games in tennis

We show that information on the first server influences the expected total number of games and margin in a tennis match under the standard assumption that each player's serve point win probability remains constant, and identify the exact regions, in terms of these probabilities, in which this effect is non-negligible. We confirm numerically that this effect is bounded by at most $0.4$ games at both the set and match level. This translates, for example, to roughly a $9$ percent shift in the probability that a match exceeds $19.5$ games when the players' serve point win probabilities differ by $10$ percent. We complement the analysis with an empirical comparison on professional match data, illustrating the adequacy of the constant-probability assumption for modelling the total number of games.

math.PR↗
arXiv2026

On the number of directions formed by Cartesian products in $\mathbb{F}_{p^2}^2$

We prove a lower bound on the number of directions determined by Cartesian products $A\times A$ in the affine plane over the finite field $\mathbb F_{p^2}$. Our lower bound holds for sets of size $p^{2/3}<|A|<p$, which are not contained in any affine copy of $\mathbb F_p$. The proof combines a structural result of Li and Roche-Newton on the set of directions formed by Cartesian products with a lower bound of Fancsali, Sziklai and Takáts. A key step shows that, unless the set of directions exhibits closure properties forcing subfield structure, one obtains a direction for which an algebraic multiplicity parameter in the latter theorem can be made explicit.

math.CO↗
arXiv2025

Enhanced molecular diffusion near a soft fluctuating membrane

Particles diffusing near interfaces face anisotropic resistance to motion due to hydrodynamic interactions. While this has been extensively studied near \textit{hard} interfaces since the works of Lorentz and Brenner, our understanding of diffusion near \textit{soft, thermally fluctuating} interfaces remains limited. Previous studies have predominantly focused on particles much larger than the molecular scale at which thermal fluctuations become important. In this work, we numerically investigate the dynamics of individual solvent molecules near a thermally fluctuating lipid membrane, a canonical soft interface in biology. We observe that diffusive motion of solvent molecules near the fluctuating membrane is slightly enhanced compared to a flat rigid interface and significantly more so than near an undulated rigid interface. This enhancement in diffusive motion of solvent molecules arises from spontaneous momentum exchanges between the moving membrane and adjacent molecules, promoting mixing. Notably, this dispersion effect overcomes geometric trapping that slows diffusion near the rigid undulated interface. Our analysis reveals that the momentum transfer near the fluctuating membrane is so efficient that it resembles an effective slip boundary condition over a length scale equal to the fluctuation height. These molecular-scale mechanisms differ from those of larger particles, where hydrodynamic memory and elasticity effects can be at play as they relax over timescales comparable to significant diffusive motion. Our findings advance understanding of enhanced diffusive motion and promoted mixing near soft fluctuating membranes involved in diverse biological processes and soft-matter technologies containing natural and model cell membranes.

cond-mat.soft↗
arXiv2023

Empowering Distributed Solutions in Renewable Energy Systems and Grid Optimization

This study delves into the shift from centralized to decentralized approaches in the electricity industry, with a particular focus on how machine learning (ML) advancements play a crucial role in empowering renewable energy sources and improving grid management. ML models have become increasingly important in predicting renewable energy generation and consumption, utilizing various techniques like artificial neural networks, support vector machines, and decision trees. Furthermore, data preprocessing methods, such as data splitting, normalization, decomposition, and discretization, are employed to enhance prediction accuracy. The incorporation of big data and ML into smart grids offers several advantages, including heightened energy efficiency, more effective responses to demand, and better integration of renewable energy sources. Nevertheless, challenges like handling large data volumes, ensuring cybersecurity, and obtaining specialized expertise must be addressed. The research investigates various ML applications within the realms of solar energy, wind energy, and electric distribution and storage, illustrating their potential to optimize energy systems. To sum up, this research demonstrates the evolving landscape of the electricity sector as it shifts from centralized to decentralized solutions through the application of ML innovations and distributed decision-making, ultimately shaping a more efficient and sustainable energy future.

cs.LG↗
arXiv2023

On some matrix counting problems

We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound of V. Blomer and J. Li (2022).

math.NT↗
arXiv2023

Anti-$\mathcal{PT}$ Transformations And Complex Non-Hermitian $\mathcal{PT}$-Symmetric Superpartners

We propose a new algebraic formalism for constructing complex non-Hermitian $\mathcal{PT}$-symmetric superpartners by extending a conventional shape-invariant superpotential into the complex domain. The resulting potential is an unbroken super- and parity-time ($\mathcal{PT}$)-symmetric shape-invariant potential with real energy eigenvalues, maintaining this property for all parameter values. In order to restore the probabilistic interpretation within a true quantum theory, a new inner product called the $\mathcal{CPT}$-inner product is defined in $\mathcal{PT}$-symmetric quantum mechanics, replacing the Dirac Hermitian inner product. In this work, we propose a new version of the inner product called the anti-$\mathcal{PT}$ ($\mathcal{APT}$)-inner product, $\langle A|B\rangle\equiv |A\rangle^{\mathcal{APT}}.|B\rangle$, which replaces the previous versions without any additional considerations. This $\mathcal{PT}$-supersymmetric quantum mechanics framework also allows for the unification of various areas of physics, including classical optics and quantum mechanics. To validate the theory, we present exact solutions for optical waveguides and the quantum tunneling probability, demonstrating excellent agreement with experimental data for the probability of crossing the potential barrier in the $\rm ^{3}H(d,n)^{4}He$ reaction.

quant-ph↗
arXiv2023

On the constant roll complex scalar field inflationary models

In this paper we wish to point out the possibility of using a complex scalar field in a constant roll inflationary model, as needed for observational viability. We extend the idea of real field inflaton with constant rate of roll to a complex field, showing the feasibility of solving Einstein Klein-Gordon equations constrained by an \emph{appropriate} form of constant roll definition. As compared to the well known (two-parametric class of) real field models, there is one more degree of flexibility in constant roll inflationary solutions which is represented by an arbitrary function of time, $γ(t)$. We work with an arbitrary but constant function $γ$ (where $γ=0$ refers to the corresponding real field model) and find new inflationary class of potentials. In this class of models, the behavior of real and complex field models are similar in some aspects, for example the solutions with large constant roll parameter are not stable and should be considered as early time transients. These field solutions relax at late time on a dual attractor trajectory. However, complex fields phase space trajectories reach this stable regime after real fields. We performed the stability analysis on $γ$ function space solutions and found that dynamically stable trajectories in phase space are stable under $γ$ variations. We extended this study by considering multifield models of constant roll inflation with non-canonical kinetic terms. By enlarging the size of field space, we showed that a multifield constant roll model is dynamically a single field effective theory. If field space is parametrized by $N$ non-canonical fields, there will be $N$ free parameters in the potential that can be attributed to the interaction between the fields.

gr-qc↗
arXiv2023

Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading

Additive manufacturing has been recognized as an industrial technological revolution for manufacturing, which allows fabrication of materials with complex three-dimensional (3D) structures directly from computer-aided design models. The mechanical properties of interpenetrating phase composites (IPCs), especially response to dynamic loading, highly depend on their 3D structures. In general, for each specified structural design, it could take hours or days to perform either finite element analysis (FEA) or experiments to test the mechanical response of IPCs to a given dynamic load. To accelerate the physics-based prediction of mechanical properties of IPCs for various structural designs, we employ a deep neural operator (DNO) to learn the transient response of IPCs under dynamic loading as surrogate of physics-based FEA models. We consider a 3D IPC beam formed by two metals with a ratio of Young's modulus of 2.7, wherein random blocks of constituent materials are used to demonstrate the generality and robustness of the DNO model. To obtain FEA results of IPC properties, 5,000 random time-dependent strain loads generated by a Gaussian process kennel are applied to the 3D IPC beam, and the reaction forces and stress fields inside the IPC beam under various loading are collected. Subsequently, the DNO model is trained using an incremental learning method with sequence-to-sequence training implemented in JAX, leading to a 100X speedup compared to widely used vanilla deep operator network models. After an offline training, the DNO model can act as surrogate of physics-based FEA to predict the transient mechanical response in terms of reaction force and stress distribution of the IPCs to various strain loads in one second at an accuracy of 98%. Also, the learned operator is able to provide extended prediction of the IPC beam subject to longer random strain loads at a reasonably well accuracy.

cs.LG↗
arXiv2023

TM-vector: A Novel Forecasting Approach for Market stock movement with a Rich Representation of Twitter and Market data

Stock market forecasting has been a challenging part for many analysts and researchers. Trend analysis, statistical techniques, and movement indicators have traditionally been used to predict stock price movements, but text extraction has emerged as a promising method in recent years. The use of neural networks, especially recurrent neural networks, is abundant in the literature. In most studies, the impact of different users was considered equal or ignored, whereas users can have other effects. In the current study, we will introduce TM-vector and then use this vector to train an IndRNN and ultimately model the market users' behaviour. In the proposed model, TM-vector is simultaneously trained with both the extracted Twitter features and market information. Various factors have been used for the effectiveness of the proposed forecasting approach, including the characteristics of each individual user, their impact on each other, and their impact on the market, to predict market direction more accurately. Dow Jones 30 index has been used in current work. The accuracy obtained for predicting daily stock changes of Apple is based on various models, closed to over 95\% and for the other stocks is significant. Our results indicate the effectiveness of TM-vector in predicting stock market direction.

q-fin.ST↗
arXiv2022

Product of sets on varieties in finite fields

Let $V$ be a variety in $\mathbb{F}_q^d$ and $E\subset V$. It is known that if any line passing through the origin contains a bounded number of points from $E$, then $|\prod(E)|=|\{x\cdot y\colon x, y\in E\}|\gg q$ whenever $|E|\gg q^{\frac{d}{2}}$. In this paper, we show that the barrier $\frac{d}{2}$ can be broken when $V$ is a paraboloid in some specific dimensions. The main novelty in our approach is to link this question to the distance problem in one lower dimensional vector space, allowing us to use recent developments in this area to obtain improvements.

math.NT↗
arXiv2022

A Point-Conic Incidence Bound and Applications over $\mathbb F_p$

In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on certain variations of distinct distances problems. These include new lower bounds on the number of pinned algebraic distances as well as improvements of results of Koh and Sun (2014) and Shparlinski (2006) on the size of the distance set formed by two large subsets of finite dimensional vector spaces over finite fields. We also prove a variant of Beck's theorem for conics.

math.CO↗
arXiv2022

Almost orthogonal subsets of vector spaces over finite fields

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of Rosenfeld and an almost version of a theorem of Berlekamp.

math.CO↗
arXiv2021

Low-energy decomposition results over finite fields

We prove various low-energy decomposition results, showing that we can decompose a finite set $A\subset \mathbb{F}_p$ satisfying $|A|<p^{5/8}$, into $A = S\sqcup T$ so that, for a non-degenerate quadratic $f\in \mathbb{F}_p[x,y]$, we have \[ |\{(s_1,s_2,s_3,s_4)\in S^4 : s_1 + s_2 = s_3 + s_4\}| \ll |A|^{3 - \frac15 + \varepsilon} \] and \[ |\{(t_1,t_2,t_3,t_4)\in T^4 : f(t_1, t_2) = f(t_3, t_4)\}|\ll |A|^{3 - \frac15 + \varepsilon}\,. \] Variations include extending this result to large $A$ and a low-energy decomposition involving additive energy of images of rational functions. This gives a quantitative improvement to a result of Roche-Newton, Shparlinski and Winterhof as well as a generalisation of a result of Rudnev, Shkredov and Stevens. We consider applications to conditional expanders, exponential sum estimates and the finite field Littlewood problem. In particular, we improve results of Mirzaei, Swaenepoel and Winterhof and Garcia.

math.CO↗
arXiv2021

An energy decomposition theorem for matrices and related questions

Given $A\subseteq GL_2(\mathbb{F}_q)$, we prove that there exist disjoint subsets $B, C\subseteq A$ such that $A = B \sqcup C$ and their additive and multiplicative energies satisfying \[ \max\{\,E_{+}(B),\, E_{\times}(C)\,\}\ll \frac{|A|^3}{M(|A|)}, \] where \begin{equation*} \label{eqn:MAminBVPolyLSSS} M(|A|) = \min\Bigg\{\,\frac{q^{4/3}}{|A|^{1/3}(\log|A|)^{2/3}},\, \frac{|A|^{4/5}}{q^{13/5}(\log|A|)^{27/10}}\,\Bigg\}. \end{equation*} We also study some related questions on moderate expanders over matrix rings, namely, for $A, B, C\subseteq GL_2(\mathbb{F}_q)$, we have \[|AB+C|, ~|(A+B)C|\gg q^4,\] whenever $|A||B||C|\gg q^{10 + 1/2}$. These improve earlier results due to Karabulut, Koh, Pham, Shen, and Vinh (2019).

math.CO↗
arXiv2021

Electromagnetic actuation for a vibrotactile display: Assessing stimuli complexity and usability

Sensory substitution has influenced the design of many tactile visual substitution systems with the aim of offering visual aids for the blind. This paper focuses on whether a novel electromagnetic vibrotactile display, a four by four vibrotactile matrix of taxels, can serve as an aid for dynamic communication for visually impaired people. A mixed methods approach was used to firstly assess whether pattern complexity affected undergraduate participants' perceptive success, and secondly, if participants total score positively correlated with their perceived success ratings. A thematic analysis was also conducted on participants' experiences with the vibrotactile display and what methods of interaction they used. The results indicated that complex patterns were less accurately perceived than simple and linear patterns respectively, and no significant correlation was found between participants' score and perceived success ratings. Additionally, most participants interacted with the vibrotactile display in similar ways using one finger to feel one taxel at a time; arguably, the most effective strategy from previous research. This technology could have applications to navigational and communication aids for the visually impaired and road users.

cs.HC↗
arXiv2021

Attaining the exponent $5/4$ for the sum-product problem in finite fields

We improve the exponent in the finite field sum-product problem from $11/9$ to $5/4$, improving the results of Rudnev, Shakan and Shkredov. That is, we show that if $A\subset \mathbb{F}_p$ has cardinality $|A|\ll p^{1/2}$ then \[ \max\{|A\pm A|,|AA|\} \gtrsim |A|^\frac54 \] and \[ \max\{|A\pm A|,|A/A|\}\gtrsim |A|^\frac54\,. \]

math.CO↗