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    Lewis Model Revisited: Option Pricing with Levy Processes
    (Malaysian Mathematical Sciences Soc, 2021) Beyazit, Mehmet Fuat; Eroglu, Kemal Ilgar
    This paper aims to discuss the mathematical details in Lewis' model by considering the analyticity and integrability conditions of characteristic functions and payoff functions of contingent claims. In his seminal paper, Lewis shows that it is much easier to compute the option value in the Fourier space than computing in terminal security price space. He computes the option value as an integral in the Fourier space, the integrand being some elementary functions and the characteristic functions of a wide range of Levy processes. The model also illustrates how the residue calculus leads to several variations of option formulas through the contour integrals. In this paper, we provide with, to a reasonable extent, some rigor into the mathematical background of Lewis' model and validate his results for particular Levy processes. We also simply give the analyticity conditions for the characteristic function of the Carr-Geman-Madan-Yor model and a simple derivation of the characteristic function of Kou's double exponential model.
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    Splitter: Faster Inference Through Channel Partitioning and Feature Fusion
    (IEEE Computer Society, 2025) Koyun, Onur Can; Eroglu, Kemal Ilgar; Töreyin, Behçet Ugur
    —This paper presents Splitter, a novel architecture designed to enhance feature extraction and optimize computational efficiency in deep learning models. Splitter employs a unique channel-splitting mechanism that divides input channels into three parallel path; Identity, Activation, and Spatial Mixing to perform distinct operations. By selectively applying spatial mixing via max-pooling or multi-head attention, Splitter balances computational frugality with representational richness. On the ImageNet-1k benchmark, Splitter-S achieves 74.4 % Top-1 accuracy at 9,347 images/s, while Splitter-M and Splitter-L deliver 76.2 % and 78.3 % Top-1 accuracy at 5,893 images/s and 4,719 images/s, respectively. When integrated into a RetinaNet detector on COCO, Splitter-S attains 32.1 % AP (52.4 % AP50, 33.7 % AP75). These results confirm that Splitter matches or surpasses state-of-the-art efficient models while significantly boosting throughput, making it exceptionally well-suited for deployment in resource-limited environments. ©2025 IEEE.