A Distributed Denial of Service Attack (DDoS) is an attack in which multiple systems compromised by a Trojan are maliciously used to target a single system. The attack leads to the denial of a certain service on the target system. In a DDoS attack, both the target system and the systems used to perform the attack are all victims of the attack. The compromised systems are also called Botnets. These attacks occur on networked systems, among them the cloud computing facet. Scholars have tried coming up with separate mechanisms for detecting and preventing such attacks long before they occur. However, as technology progresses in advancement so do the attack mechanisms. In cloud computing, security issues affect various stakeholders who plan on cloud adoption. DDoS attacks are such serious concerns that require mitigation in the cloud. This paper presents a survey of the various mechanisms, both traditional and modern, that are applied in detecting cloud-based DDoS attacks.

Abstract:
Distributed Denial of Service (DDoS) attacks are performed from multiple agents towards a single victim. Essentially, all attacking agents generate multiple packets towards the victim to overwhelm it with requests, thereby overloading the resources of the victim. Since it is very complex and expensive to conduct a real DDoS attack, most organizations and researchers result in using simulations to mimic an actual attack. The researchers come up with diverse algorithms and mechanisms for attack detection and prevention. Further, simulation is good practice for determining the efficacy of an intrusive detective measure against DDoS attacks. However, some mechanisms are ineffective and thus not applied in real life attacks. Nowadays, DDoS attack has become more complex and modern for most IDS to detect. Adjustable and configurable traffic generator is becoming more and more important. This paper first details the available datasets that scholars use for DDoS attack detection. The paper further depicts the a few tools that exist freely and commercially for use in the simulation programs of DDoS attacks. In addition, a traffic generator for normal and different types of DDoS attack has been developed. The aim of the paper is to simulate a cloud environment by OMNET++ simulation tool, with different DDoS attack types. Generation normal and attack traffic can be useful to evaluate developing IDS for DDoS attacks detection. Moreover, the result traffic can be useful to test an effective algorithm, techniques and procedures of DDoS attacks.

Abstract:
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by statisticians and our presentation gives an alternative view than most standard probability textbooks. In particular, this functional approach clarifies the underlying topological structure of weak convergence. We hope this short note is helpful for those who are interested in weak convergence as well as instructors of measure theoretic probability.

Abstract:
For a quasimartingale majorized by another quasimartingale, it is natural to ask whether a third quasimartingale can be inserted between them. In this paper, we give an affirmative answer to this problem. We also establish a dominated decomposition property of quasimartingales. In addition, we show that a weak interpolation property holds for supermartingales and local supermartingales. Our approach also yields the interpolation property and dominated decomposition property for Markov chains.

Abstract:
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Robert-Namioka-type characterization and Fremlin-type characterization of locally solid topological lattice-ordered groups. In particular, we show that a group topology on a lattice-ordered group is locally solid if and only if it is generated by a family of translation-invariant lattice pseudometrics. We also investigate (1) the basic properties of lattice group homomorphism on locally solid topological lattice-ordered groups; (2) the relationship between order-bounded subsets and topologically bounded subsets in locally solid topological lattice-ordered groups; (3) the Hausdorff completion of locally solid topological lattice-ordered groups.

Abstract:
It is known that random variables have the Riesz decomposition property and the interpolation property. These properties are not only interesting in their own rights; they have been applied to quantitative finance and actuarial mathematics. One would naturally ask whether the same holds for stopping times. We give an affirmative answer in this paper. We also point out that optional times possess these two properties too.

Abstract:
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probability and Bayes' theorem in Riesz spaces; we also prove an inclusion-exclusion formula in Riesz spaces. Several examples are provided to show that the law of total probability, Bayes' theorem and inclusion-exclusion formula in probability theory are special cases of our results.

Abstract:
In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subset is topologically bounded and (2) whether a topologically bounded subset is order bounded. A classical result gives a partial answer to (1) by saying that an order bounded subset of a locally solid Riesz space is topologically bounded. This paper attempts to further investigate these two questions. In particular, we show that (i) there exists a non-locally solid topological Riesz space in which every order bounded subset is topologically bounded; (ii) if a topological Riesz space is not locally solid, an order bounded subset need not be topologically bounded; (iii) a topologically bounded subset need not be order bounded even in a locally convex-solid Riesz space. Next, we show that (iv) if a locally solid Riesz space has an order bounded topological neighborhood of zero, then every topologically bounded subset is order bounded; (v) however, a locally convex-solid Riesz space may not possess an order bounded topological neighborhood of zero even if every topologically bounded subset is order bounded; (vi) a pseudometrizable locally solid Riesz space need not have an order bounded topological neighborhood of zero. In addition, we give some results about the relationship between order bounded subsets and positive homogeneous operators.

Abstract:
Generalized conditional expectations, optional projections and predictable projections of stochastic processes play important roles in the general theory of stochastic processes, semimartingale theory and stochastic calculus. They share some important properties with ordinary conditional expectations. While the characterization of ordinary conditional expectations has been studied by several authors, no similar work seems to have been done for these three concepts. This paper aims at undertaking this task by giving And$\hat{o}$-Douglas type characterization theorem for each of them.

Abstract:
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties.