arXiv subjects

Mehdi Ghasemi

Publications and source records attributed to Mehdi Ghasemi.

At least 19 recordsLinked to original sources

arXiv2026

The Cone Generated by Positive Semidefinite Mean Polynomials

We study the cone $\mathcal{M}_{n,2d}$ of nonnegative mean polynomials---real $n$-variate forms of degree $2d$ that can be expressed as weighted power means $M_{q,p}(Y,w)$ with $q>p$. This cone simultaneously generalises the cone of sums of squares $\Sigma_{n,2d}$ and the cone of sums of nonnegative circuit polynomials $\mathcal{C}_{n,2d}$. We prove that every square of an arbitrary polynomial belongs to the mean polynomial preprime $T_{\mathrm{mean}}$, that $T_{\mathrm{mean}}$ is strongly generating, and consequently that every polynomial strictly positive on a compact semialgebraic set admits a representation with mean polynomial certificates. We exhibit the Robinson form $\hat{R}$ as a separating example that lies in $\mathcal{M}_{4,4}$ but outside $\mathrm{SOSONC}_{4,4}$. Finally, we outline a convergent hierarchy of lower bounds for polynomial optimization based on the mean polynomial cone and discuss tractable depth-truncated approximations via signomial programming.

math.OC↗

arXiv2025

Lower Bound for a Polynomial on a product of hyperellipsoids using geometric programming

Let $f$ be a polynomial in $n$ variables $x_1,\dots,x_n$ with real coefficients. In [Ghasemi-Marshal], Ghasemi and Marshall give an algorithm, based on geometric programming, which computes a lower bound for $f$ on $\mathbb{R}^n$. In [Ghasemi-Lasserre-Marshall] Ghasemi, Lasserre and Marshall show how the algorithm in [Ghasemi-Marshal] can be modified to compute a lower bound for $f$ on the hyperellipsoid $\sum_{i=1}^n x_i^d \le M.$ Here $d$ is a fixed even integer, $d \ge \max\{ 2, \deg(f)\}$ and $M$ is a fixed positive real number. Suppose now that $g_j := 1-\sum_{i\in I_j} (\frac{x_i}{N_i})^d$, $j=1,\dots,m$, where $d$ is a fixed even integer $d \ge \max\{ 2, \deg(f)\}$, $N_i$ is a fixed positive real number, $i=1,\dots,n$ and $I_1,\dots, I_m$ is a fixed partition of $\{ 1,\dots,n\}$. The present paper gives an algorithm based on geometric programming for computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_j\ge 0$, $j=1,\dots,m$. The algorithm is implemented in a SAGE program developed by the first author. The bound obtained is typically not as sharp as the bound obtained using semidefinite programming, but it has the advantage that it is computable rapidly, even in cases where the bound obtained by semidefinite programming is not computable. When $m=1$ and $N_i = \root d \of{M}$, $i=1,\dots,n$ the algorithm produces the lower bound obtained in [Ghasemi-Lasserre-Marshall]. When $m=n$ and $I_j = \{ j \}$, $j=1,\dots,n$ the algorithm produces a lower bound for $f$ on the hypercube $\prod_{i=1}^n [-N_i,N_i]$, which in certain cases can be computed by a simple formula.

math.OC↗

arXiv2025

Molecular Insights into Caprock Integrity of Subsurface Hydrogen Storage: Perspective on Hydrogen-induced Swelling and Mechanical Response

The geological storage of hydrogen (H_2) requires reliable long-term caprock sealing, yet the nanoscale interactions between H_2 and clay minerals remain critically underexplored despite their importance for storage security. This lack of understanding has limited the ability to predict mechanical stability and leakage risks in H_2 storage formations. Using molecular simulations, this study investigates the swelling behavior and mechanical properties of sodium montmorillonite (Mt), a common smectite clay, under varying hydration states and interlayer H_2 contents. Results show that H_2 accelerates hydration-state transitions, narrows the stability window of crystalline swelling, and promotes asymmetric plume formation in confined interlayers. H_2 alters cation and water coordination, thereby weakening Na^+--Mt electrostatic interactions and modulating H-bond networks at the interface and in the bulk. Mechanical analysis reveals pronounced anisotropy in Mt. In-plane stiffness is mainly governed by basal spacing expansion, whereas out-of-plane stiffness is highly sensitive to the initial presence of water or H_2, which weaken interlayer cohesion. Tensile and compressive strengths in the in-plane directions follow in-plane stiffness trends, while the out-of-plane tensile strength is governed by Mt--water H-bonds. The presence of H_2 further promotes Mt sheets separation by disrupting nanoscale liquid bridges. Collectively, these results provide the first atomistic-scale evidence that intercalated H_2 reshapes swelling energetics, elastic anisotropy, and failure pathways in Mt, highlighting critical nanoscale mechanisms that may compromise caprock integrity during underground H_2 storage.

cond-mat.mtrl-sci↗

arXiv2024

HeteroSwitch: Characterizing and Taming System-Induced Data Heterogeneity in Federated Learning

Federated Learning (FL) is a practical approach to train deep learning models collaboratively across user-end devices, protecting user privacy by retaining raw data on-device. In FL, participating user-end devices are highly fragmented in terms of hardware and software configurations. Such fragmentation introduces a new type of data heterogeneity in FL, namely \textit{system-induced data heterogeneity}, as each device generates distinct data depending on its hardware and software configurations. In this paper, we first characterize the impact of system-induced data heterogeneity on FL model performance. We collect a dataset using heterogeneous devices with variations across vendors and performance tiers. By using this dataset, we demonstrate that \textit{system-induced data heterogeneity} negatively impacts accuracy, and deteriorates fairness and domain generalization problems in FL. To address these challenges, we propose HeteroSwitch, which adaptively adopts generalization techniques (i.e., ISP transformation and SWAD) depending on the level of bias caused by varying HW and SW configurations. In our evaluation with a realistic FL dataset (FLAIR), HeteroSwitch reduces the variance of averaged precision by 6.3\% across device types.

cs.LG↗

arXiv2024

The Truncated Moment Problem for Unital Commutative R-Algebras

We investigate when a linear functional $L$ defined on a linear subspace $B$ of a unital commutative real algebra $A$ admits an integral representation w.r.t. a positive Radon measure supported on a closed subset $K$ of the character space of $A$. We provide a criterion for the existence of such a representation for $L$ when $A$ is equipped with a submultiplicative seminorm. We then build on this result to prove our main theorem for $A$ not necessarily equipped with a topology. This allows us to extend well-known classical results on truncated moment problems.

math.FA↗

arXiv2021

A Molecular Dynamics Study on CO$_2$ Diffusion Coefficient in Saline Water Under a Wide Range of Temperatures, Pressures, and Salinity Concentrations: Implications to CO2 Geological Storage

Carbon dioxide (CO$_2$) sequestration in saline aquifers has been introduced as one of the most practical, long-term, and safe solutions to tackle a growing threat originating from the emission of CO$_2$. Successfully executing and planning the process necessitates a comprehensive understanding of CO$_2$ transport properties -- particularly the diffusion coefficient, influencing the behavior of CO$_2$ dissolution in water/brine regarding the shape of viscous fingers, the onset of instabilities, etc. In this research, Molecular Dynamics (MD) simulation was employed to compute the CO$_2$ diffusion coefficient in various NaCl saline water concentrations under the broad spectrum of temperatures and pressures to acquire a data-set. The NaCl concentration increase gives rise to a decrease in the CO$_2$ diffusion coefficient, by which the reduction is most notably at higher temperatures. In addition, the rise in the CO$_2$ diffusion at elevated temperatures can be explained by the cation's hydration shell size reduction with temperature increment due to intensifying repulsive forces among water molecules. A new precise correlation is proposed for estimating CO$_2$ diffusion coefficients. Regarding the pressure variation effects, no tangible changes are observed with pressure increase. Furthermore, the variability of the CO$_2$ diffusion coefficient in the presence of other salts, namely MgCl2, CaCl2, KCl, and Na2SO4, were computed separately. Comparing the influence of various salts, CaCl2 and KCl have the highest and lowest effect on the CO$_2$ diffusion coefficient, respectively. Finally, a set of direct numerical simulations was conducted to study the impact of the CO$_2$ diffusion coefficient on the CO$_2$ dissolution process. The results shed light on the importance of CO$_2$ diffusion coefficient changes under the saline water condition in predicting dissolution process behavior and further calculations.

cond-mat.mes-hall↗

arXiv2020

Enabling Incremental Knowledge Transfer for Object Detection at the Edge

Object detection using deep neural networks (DNNs) involves a huge amount of computation which impedes its implementation on resource/energy-limited user-end devices. The reason for the success of DNNs is due to having knowledge over all different domains of observed environments. However, we need a limited knowledge of the observed environment at inference time which can be learned using a shallow neural network (SHNN). In this paper, a system-level design is proposed to improve the energy consumption of object detection on the user-end device. An SHNN is deployed on the user-end device to detect objects in the observing environment. Also, a knowledge transfer mechanism is implemented to update the SHNN model using the DNN knowledge when there is a change in the object domain. DNN knowledge can be obtained from a powerful edge device connected to the user-end device through LAN or Wi-Fi. Experiments demonstrate that the energy consumption of the user-end device and the inference time can be improved by 78% and 71% compared with running the deep model on the user-end device.

cs.CV↗

arXiv2019

A Novel Design of Adaptive and Hierarchical Convolutional Neural Networks using Partial Reconfiguration on FPGA

Nowadays most research in visual recognition using Convolutional Neural Networks (CNNs) follows the "deeper model with deeper confidence" belief to gain a higher recognition accuracy. At the same time, deeper model brings heavier computation. On the other hand, for a large chunk of recognition challenges, a system can classify images correctly using simple models or so-called shallow networks. Moreover, the implementation of CNNs faces with the size, weight, and energy constraints on the embedded devices. In this paper, we implement the adaptive switching between shallow and deep networks to reach the highest throughput on a resource-constrained MPSoC with CPU and FPGA. To this end, we develop and present a novel architecture for the CNNs where a gate makes the decision whether using the deeper model is beneficial or not. Due to resource limitation on FPGA, the idea of partial reconfiguration has been used to accommodate deep CNNs on the FPGA resources. We report experimental results on CIFAR-10, CIFAR-100, and SVHN datasets to validate our approach. Using confidence metric as the decision making factor, only 69.8%, 71.8%, and 43.8% of the computation in the deepest network is done for CIFAR-10, CIFAR-100, and SVHN while it can maintain the desired accuracy with the throughput of around 400 images per second for SVHN dataset.

cs.CV↗

arXiv2019

Exploring Diseases and Syndromes in Neurology Case Reports from 1955 to 2017 with Text Mining

Background: A large number of neurology case reports have been published, but it is a challenging task for human medical experts to explore all of these publications. Text mining offers a computational approach to investigate neurology literature and capture meaningful patterns. The overarching goal of this study is to provide a new perspective on case reports of neurological disease and syndrome analysis over the last six decades using text mining. Methods: We extracted diseases and syndromes (DsSs) from more than 65,000 neurology case reports from 66 journals in PubMed over the last six decades from 1955 to 2017. Text mining was applied to reports on the detected DsSs to investigate high-frequency DsSs, categorize them, and explore the linear trends over the 63-year time frame. Results: The text mining methods explored high-frequency neurologic DsSs and their trends and the relationships between them from 1955 to 2017. We detected more than 18,000 unique DsSs and found 10 categories of neurologic DsSs. While the trend analysis showed the increasing trends in the case reports for top-10 high-frequency DsSs, the categories had mixed trends. Conclusion: Our study provided new insights into the application of text mining methods to investigate DsSs in a large number of medical case reports that occur over several decades. The proposed approach can be used to provide a macro level analysis of medical literature by discovering interesting patterns and tracking them over several years to help physicians explore these case reports more efficiently.

q-bio.QM↗

arXiv2017

CryptoDL: Deep Neural Networks over Encrypted Data

Machine learning algorithms based on deep neural networks have achieved remarkable results and are being extensively used in different domains. However, the machine learning algorithms requires access to raw data which is often privacy sensitive. To address this issue, we develop new techniques to provide solutions for running deep neural networks over encrypted data. In this paper, we develop new techniques to adopt deep neural networks within the practical limitation of current homomorphic encryption schemes. More specifically, we focus on classification of the well-known convolutional neural networks (CNN). First, we design methods for approximation of the activation functions commonly used in CNNs (i.e. ReLU, Sigmoid, and Tanh) with low degree polynomials which is essential for efficient homomorphic encryption schemes. Then, we train convolutional neural networks with the approximation polynomials instead of original activation functions and analyze the performance of the models. Finally, we implement convolutional neural networks over encrypted data and measure performance of the models. Our experimental results validate the soundness of our approach with several convolutional neural networks with varying number of layers and structures. When applied to the MNIST optical character recognition tasks, our approach achieves 99.52\% accuracy which significantly outperforms the state-of-the-art solutions and is very close to the accuracy of the best non-private version, 99.77\%. Also, it can make close to 164000 predictions per hour. We also applied our approach to CIFAR-10, which is much more complex compared to MNIST, and were able to achieve 91.5\% accuracy with approximation polynomials used as activation functions. These results show that CryptoDL provides efficient, accurate and scalable privacy-preserving predictions.

cs.CR↗

arXiv2015

Seminormed $\ast$-subalgebras of $\ell^{\infty}(X)$

Arbitrary representations of a commutative unital ($\ast$-) $\mathbb{F}$-algebra $A$ as a subalgeba of $\mathbb{F}^X$ are considered, where $\mathbb{F}=\mathbb{C}$ or $\mathbb{R}$ and $X\neq\emptyset$. The Gelfand spectrum of $A$ is explained as a topological extension of $X$ where a seminorm on the image of $A$ in $\mathbb{F}^X$ is present. It is shown that among all seminormes, the $\sup$-norm is of special importance which reduces $\mathbb{F}^X$ to $\ell^{\infty}(X)$. The Banach subalgebra of $\ell^{\infty}(X)$ of all $Σ$-measurable bounded functions on $X$, is studied for which $Σ$ is a $σ$-algebra of subsets of $X$. In particular, we study lifting of positive measures from $(X, Σ)$ to the Gelfand spectrum of this algebra and observe an unexpected shift in the support of measures. In the case that $Σ$ is the Borel algebra of a topology, we study the relation of the underlying topology of $X$ and the one of the Gelfand spectrum.

math.FA↗

arXiv2015

Lower Bounds for a Polynomial on a basic closed semialgebraic set using geometric programming

$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$. The paper shows that there is an algorithm for computing such a lower bound, based on geometric programming, which applies in a large number of cases. The algorithm extends and generalizes earlier algorithms of Ghasemi and Marshall, dealing with the case $m=0$, and of Ghasemi, Lasserre and Marshall, dealing with the case $m=1$ and $g_1= M-(x_1^d+\cdots+x_n^d)$. Here, $d$ is required to be an even integer $d \ge \max\{2,°(f)\}$. The algorithm is implemented in a SAGE program developed by the first author. The bound obtained is typically not as good as the bound obtained using semidefinite programming, but it has the advantage that it is computable rapidly, even in cases where the bound obtained by semidefinite programming is not computable.

math.OC↗

arXiv2014

Moment problem in infinitely many variables

The multivariate moment problem is investigated in the general context of the polynomial algebra $\mathbb{R}[x_i \mid i \in Ω]$ in an arbitrary number of variables $x_i$, $i\in Ω$. The results obtained are sharpest when the index set $Ω$ is countable. Extensions of Haviland's theorem [Amer. J. Math., 58 (1936) 164-168] and Nussbaum's theorem [Ark. Math., 6 (1965) 179-191] are proved. Lasserre's description of the support of the measure in terms of the non-negativity of the linear functional on a quadratic module of $\mathbb{R}[x_i \mid i \in Ω]$ in [Trans. Amer. Math. Soc., 365 (2013) 2489-2504] is shown to remain valid in this more general situation. The main tool used in the paper is an extension of the localization method developed by the third author.

math.FA↗

arXiv2014

On the topologies induced by a cone

Let $A$ be a commutative and unital $\mathbb{R}$-algebra, and $M$ be an Archimedean quadratic module of $A$. We define a submultiplicative seminorm $\|\cdot\|_M$ on $A$, associated with $M$. We show that the closure of $M$ with respect to $\|\cdot\|_M$-topology is equal to the closure of $M$ with respect to the finest locally convex topology on $A$. We also compute the closure of any cone in $\|\cdot\|_M$-topology. Then we omit the Archimedean condition and show that there still exists a lmc topology associated to $M$, pursuing the same properties.

math.FA↗

arXiv2014

Integral representation of linear functionals on function spaces

Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $σ$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be representable as an integral with respect to a measure $μ$ on $X$ such that elements of $\mathcal{A}$ are $μ$-measurable. This general result then is applied to the case where $X$ carries a topological structure and $A$ is a family of continuous functions and naturally $\mathcal{A}$ is the Borel structure of $X$. As an application, short solutions for the full and truncated $K$-moment problem are presented. An analogue of Riesz-Markov-Kakutani representation theorem is given where $C_{c}(X)$ is replaced with whole $C(X)$. Then we consider the case where $A$ only consists of bounded functions and hence is equipped with $\sup$-norm.

math.FA↗

arXiv2012

Using Orthogonal Channels for Supporting Multicast Service in Multi-channel Wireless Mesh Networks

Unlike wired networks, the capacity of a wireless network is interference limited due to the broadcast nature of wireless medium. Some multicast wireless network protocols do not consider channel assignment issue, that they cause interference at transmission nodes, hence do not use full capacity of the network. Interference can be reduced and throughput improved with the use of multichannel features. Therefore, this paper used orthogonal channels for sending and receiving nodes in the network. We propose EWM (Efficient Wireless Multicast) method that is distributed scheme for constructing multicast tree in multi-channel multi-interface wireless mesh networks (MIMC-WMN) which selects relay nodes and in distributed form assign orthogonal radio channels to them. To more decrease of interference in adding a branch to the tree, the route with minimum end-to-end delay from the source to the multicast receiver will be chosen. Thus, the tree is suitable for multimedia applicants. We also employ the broadcast nature of the wireless media to reduce the number of relay nodes. The proposed algorithm is compared with MCM algorithm in NS2.

cs.NI↗

arXiv2012

Lower bounds on the global minimum of a polynomial

We extend the method of Ghasemi and Marshall [SIAM. J. Opt. 22(2) (2012), pp 460-473], to obtain a lower bound $f_{{\rm gp},M}$ for a multivariate polynomial $f(x) \in \mathbb{R}[x]$ of degree $ \le 2d$ in $n$ variables $x = (x_1,...,x_n)$ on the closed ball ${x \in \mathbb{R}^n : \sum x_i^{2d} \le M}$, computable by geometric programming, for any real $M$. We compare this bound with the (global) lower bound $f_{\rm gp}$ obtained by Ghasemi and Marshall, and also with the hierarchy of lower bounds, computable by semidefinite programming, obtained by Lasserre [SIAM J. Opt. 11(3) (2001) pp 796-816]. Our computations show that the bound $f_{{\rm gp},M}$ improves on the bound $f_{\rm gp}$ and that the computation of $f_{{\rm gp},M}$, like that of $f_{\rm gp}$, can be carried out quickly and easily for polynomials having of large number of variables and/or large degree, assuming a reasonable sparsity of coefficients, cases where the corresponding computation using semidefinite programming breaks down.

math.OC↗

arXiv2012

Application of Jacobi's Representation Theorem to locally multiplicatively convex topological real Algebras

Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $ρ$ be a seminorm on $A$ which satisfies $ρ(ab)\leqρ(a)ρ(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$ in the topology induced by $ρ$, for any integer $d\ge1$. We show that this closure is exactly the set of all elements $a\in A$ such that $α(a)\ge0$ for every $ρ$-continuous $\mathbb{R}$-algebra homomorphism $α: A \rightarrow \mathbb{R}$ with $α(S)\subseteq[0,\infty)$, and that this result continues to hold when $ρ$ is replaced by any locally multiplicatively convex topology $τ$ on $A$. We obtain a representation of any linear functional $L : A \rightarrow \reals$ which is continuous with respect to any such $ρ$ or $τ$ and non-negative on $S$ as integration with respect to a unique Radon measure on the space of all real valued $\reals$-algebra homomorphisms on $A$, and we characterize the support of the measure obtained in this way.

math.FA↗