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Fatemeh Jafari

Publications and source records attributed to Fatemeh Jafari.

5 recordsLinked to original sources

How Much Temporal Modeling is Enough? A Systematic Study of Hybrid CNN-RNN Architectures for Multi-Label ECG Classification

Accurate multi-label classification of electrocardiogram (ECG) signals remains challenging due to the coexistence of multiple cardiac conditions, pronounced class imbalance, and long-range temporal dependencies in multi-lead recordings. Although recent studies increasingly rely on deep and stacked recurrent architectures, the necessity and clinical justification of such architectural complexity have not been rigorously examined. In this work, we perform a systematic comparative evaluation of convolutional neural networks (CNNs) combined with multiple recurrent configurations, including LSTM, GRU, Bidirectional LSTM (BiLSTM), and their stacked variants, for multi-label ECG classification on the PTB-XL dataset comprising 23 diagnostic categories. The CNN component serves as a morphology-driven baseline, while recurrent layers are progressively integrated to assess their contribution to temporal modeling and generalization performance. Experimental results indicate that a CNN integrated with a single BiLSTM layer achieves the most favorable trade-off between predictive performance and model complexity. This configuration attains superior Hamming loss (0.0338), macro-AUPRC (0.4715), micro-F1 score (0.6979), and subset accuracy (0.5723) compared with deeper recurrent combinations. Although stacked recurrent models occasionally improve recall for specific rare classes, our results provide empirical evidence that increasing recurrent depth yields diminishing returns and may degrade generalization due to reduced precision and overfitting. These findings suggest that architectural alignment with the intrinsic temporal structure of ECG signals, rather than increased recurrent depth, is a key determinant of robust performance and clinically relevant deployment.

cs.LG↗

Improved bounds on the size of permutation codes under Kendall $τ$-metric

In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation is proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size $P(n, d)$ of permutation codes of length $n$, i.e., subsets of the set $S_n$ of all permutations on $\{1,\ldots, n\}$ with the minimum distance at least $d\in\{1,\ldots ,\binom{n}{2}\}$ under the Kendall $τ$-metric. By presenting an algorithm and some theorems, we managed to improve the known lower and upper bounds for $P(n,d)$. In particular, we show that $P(n,d)=4$ for all $n\geq 6$ and $\frac{3}{5}\binom{n}{2}< d \leq \frac{2}{3} \binom{n}{2}$. Additionally, we prove that for any prime number $n$ and integer $r\leq \frac{n}{6}$, $ P(n,3)\leq (n-1)!-\dfrac{n-6r}{\sqrt{n^2-8rn+20r^2}}\sqrt{\dfrac{(n-1)!}{n(n-r)!}}. $ This result greatly improves the upper bound of $P(n,3)$ for all primes $n\geq 37$.

cs.IT↗

New Upper Bounds on the Size of Permutation Codes under Kendall $τ$-Metric

We first give two methods based on the representation theory of symmetric groups to study the largest size $P(n,d)$ of permutation codes of length $n$ i.e. subsets of the set $S_n$ all permutations on $\{1,\dots,n\}$ with the minimum distance (at least) $d$ under the Kendall $τ$-metric. The first method is an integer programming problem obtained from the transitive actions of $S_n$. The second method can be applied to refute the existence of perfect codes in $S_n$.\\ Here we reduce the known upper bound $(n-1)!-1$ for $P(n,3)$ to $(n-1)!-\lceil\frac{n}{3}\rceil+2\leq (n-1)!-2$, whenever $n\geq 11$ is any prime number. If $n=6$, $7$, $11$, $13$, $14$, $15$, $17$, the known upper bound for $P(n,3)$ is decreased by $3,3,9,11,1,1,4$, respectively.

math.CO↗

Cardinality of product sets in torsion-free groups and applications in group algebras

Let $G$ be a unique product group, i.e., for any two finite subsets $A$ and $B$ of $G$ there exists $x\in G$ which can be uniquely expressed as a product of an element of $A$ and an element of $B$. We prove that, if $C$ is a finite subset of $G$ containing the identity element such that $\langle C\rangle$ is not abelian, then for all subsets $B$ of $G$ with $|B|\geq 7$, $|BC|\geq |B| + |C| + 2$. Also, we prove that if $C$ is a finite subset containing the identity element of a torsion-free group $G$ such that $|C| = 3$ and $\langle C\rangle$ is not abelian, then for all subsets $B$ of $G$ with $|B|\geq 7$, $|BC|\geq |B| + 5$. Moreover, if $\langle C\rangle$ is not isomorphic to the Klein bottle group, i.e., the group with the presentation $\langle x, y \;|\; xyx = y\rangle$, then for all subsets $B$ of G with $|B|\geq 5$, $|BC|\geq |B| + 5$. The support of an element $α=\sum_{x\in G} α_x x$ a group algebra $F[G]$ ($F$ is any field), denoted by $supp(α)$, is the set $\{x\in G \;|\; α_x \neq 0\}$. By the latter result, we prove that if $αβ= 0$ for some non-zero $α,β\in F[G]$ such that $|supp(α)| = 3$, then $|supp(β)|\geq 12$. Also, we prove that if $αβ= 1$ for some $αβ\in F[G]$ such that $|supp(α)| = 3$, then |supp(α)|\geq 10$. These results improve a part of results in Schweitzer [J. Group Theory, 16 (2013), no. 5, 667-693] and Dykema et al. [Exp. Math., 24 (2015), 326-338] to arbitrary fields, respectively.

math.GR↗

Zero divisor and unit elements with support of size 4 in group algebras of torsion free groups

Kaplansky Zero Divisor Conjecture states that if $G $ is a torsion free group and $ \mathbb{F} $ is a field, then the group ring $\mathbb{F}[G]$ contains no zero divisor and Kaplansky Unit Conjecture states that if $G $ is a torsion free group and $ \mathbb{F} $ is a field, then $\mathbb{F}[G]$ contains no non-trivial units. The support of an element $ α= \sum_{x\in G}α_xx$ in $\mathbb{F}[G] $, denoted by $supp(α)$, is the set $ \{x \in G|α_x\neq 0\} $. In this paper we study possible zero divisors and units with supports of size $ 4 $ in $\mathbb{F}[G]$. We prove that if $ α, β$ are non-zero elements in $ \mathbb{F}[G] $ for a possible torsion free group $ G $ and an arbitrary field $ \mathbb{F} $ such that $ |supp(α)|=4 $ and $ αβ=0 $, then $|supp(β)|\geq 7 $. In [J. Group Theory, $16$ $ (2013),$ no. $5$, $667$-$693$], it is proved that if $ \mathbb{F}=\mathbb{F}_2 $ is the field with two elements, $ G $ is a torsion free group and $ α,β\in \mathbb{F}_2[G]\setminus \{0\}$ such that $|supp(α)|=4 $ and $ αβ=0 $, then $|supp(β)|\geq 8$. We improve the latter result to $|supp(β)|\geq 9$. Also, concerning the Unit Conjecture, we prove that if $\mathsf{a}\mathsf{b}=1$ for some $\mathsf{a},\mathsf{b}\in \mathbb{F}[G]$ and $|supp(\mathsf{a})|=4$, then $|supp(\mathsf{b})|\geq 6$.

math.GR↗