arXiv subjects
Publications and source records attributed to Saikat Maity.
In recent years, several mathematicians have looked at a class of partitions called the overcubic partition $k$-tuples, for small values of $k$. They have proved several divisibility results satisfied by these partitions. We continue this study and prove a few infinite family of congruences. Our proofs use elementary techniques from $q$-series and number theory.
We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove infinite families of congruences modulo powers of $2$ and modulo $12$ satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary $q$-series techniques as well as the theory of modular forms to prove our results.
One of the main objectives of the current paper is to revisit the well known Laurent series expansions of the Riemann zeta function $ζ(s)$, Hurwitz zeta function $ζ(s,a)$ and Dirichlet $L$-function $L(s,χ)$ at $s=1$. Moreover, we also present a new Laurent series expansion of $L$-functions associated to cusp forms over the full modular group.
Attackers are now using sophisticated techniques, like polymorphism, to change the attack pattern for each new attack. Thus, the detection of novel attacks has become the biggest challenge for cyber experts and researchers. Recently, anomaly and hybrid approaches are used for the detection of network attacks. Detecting novel attacks, on the other hand, is a key enabler for a wide range of IoT applications. Novel attacks can easily evade existing signature-based detection methods and are extremely difficult to detect, even going undetected for years. Existing machine learning models have also failed to detect the attack and have a high rate of false positives. In this paper, a rule-based deep neural network technique has been proposed as a framework for addressing the problem of detecting novel attacks. The designed framework significantly improves respective benchmark results, including the CICIDS 2017 dataset. The experimental results show that the proposed model keeps a good balance between attack detection, untruthful positive rates, and untruthful negative rates. For novel attacks, the model has an accuracy of more than 99%. During the automatic interaction between network-devices (IoT), security and privacy are the primary obstacles. Our proposed method can handle these obstacles efficiently and finally identify, and classify the different levels of threats.