**Double Orthogonal List in Hash Table (Dolha)**

A streaming graph is a graph formed by a sequence of incoming edges with time stamps. Unlike static graphs, the streaming graph is highly dynamic and time related. In the real world, the high volume and velocity streaming graphs such as internet traffic data, social network communication data and financial transfer data are bringing challenges to the classic graph data structures. We present a new data structure: double orthogonal list in hash table (Dolha) which is a high speed and high memory efficiency graph structure applicable to streaming graph. Dolha has constant time cost for single edge and near linear space cost that we can contain billions of edges information in memory size and process an incoming edge in nanoseconds. Dolha also has linear time cost for neighborhood queries, which allow it to support most algorithms in graphs without extra cost. We also present a persistent structure based on Dolha that has the ability to handle the sliding window update and time related queries. … **Loss Distributional Approach (LDA)**

While AMA does not specify the use of any particular modeling technique, one common approach taken in the banking industry is the Loss Distribution Approach (LDA). With LDA, a bank first segments operational losses into homogeneous segments, called unit of measure’s (UoMs). For each unit of measure, the bank then constructs a loss distribution that represents its expectation of total losses that can materialize in a one-year horizon. Given that data sufficiency is a major challenge for the industry, annual loss distribution cannot be built directly using annual loss figures. Instead, a bank will develop a frequency distribution that describes the number of loss events in a given year, and a severity distribution that describes the loss amount of a single loss event. The frequency and severity distributions are assumed to be independent. The convolution of these two distributions then give rise to the (annual) loss distribution. … **Bezier Simplex Model**

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M-1)-dimensional topological simplex (a curved line for M=2, a curved triangle for M=3, a curved tetrahedron for M=4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bezier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bezier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the post-optimization process and enable a better trade-off analysis. … **Consistency as Logical Monotonicity (CALM)**

A key concern in modern distributed systems is to avoid the cost of coordination while maintaining consistent semantics. Until recently, there was no answer to the question of when coordination is actually required. In this paper we present an informal introduction to the CALM Theorem, which answers this question precisely by moving up from traditional storage consistency to consider properties of programs. CALM is an acronym for ‘consistency as logical monotonicity’. The CALM Theorem shows that the programs that have consistent, coordination-free distributed implementations are exactly the programs that can be expressed in monotonic logic. This theoretical result has practical implications for developers of distributed applications. We show how CALM provides a constructive application-level counterpart to conventional ‘systems’ wisdom, such as the apparently negative results of the CAP Theorem. We also discuss ways that monotonic thinking can influence distributed systems design, and how new programming language designs and tools can help developers write consistent, coordination-free code. …

# If you did not already know

**03**
*Monday*
May 2021

Posted What is ...

in