Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence

We construct the Hasse diagrams $G_2$ and $G_3$ for the closure ordering on the sets of congruence classes of $2\times 2$ and $3\times 3$ complex matrices. In other words, we construct two directed graphs whose vertices are $2\times 2$ or, respectively, $3\times 3$ canonical matrices under congruence and there is a directed path from $A$ to $B$ if and only if $A$ can be transformed by an arbitrarily small perturbation to a matrix that is congruent to $B$. A bundle of matrices under congruence is defined as a set of square matrices $A$ for which the pencils $A+\lambda A^T$ belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of $2\times 2$ or $3\times 3$ matrices have the same properties with respect to perturbations. We construct the Hasse diagrams $G_2^{\rm B}$ and $G_3^{\rm B}$ for the closure ordering on the sets of congruence bundles of $2\times 2$ and, respectively, $3\times 3$ matrices. We find the isometry groups of $2\times 2$ and $3\times 3$ congruence canonical matrices.Comment: 34 page

Data management, communication systems and the edge: Challenges for the future of transportation

Edge cloud systems have emerged as a new promising alternative to address the needs of many emerging latency-critical applicationssuch as autonomous vehicles. These applications are ill-suited for traditional clouds due to the end-to-end latency and the limited bandwidth between the cloud\u27s (few) data centers and these applications.In the edge cloud model, a myriad of small-scale computing clusters are brought next to the applications at the edge of the network. Many Applicationsin transportation engineering such as autonomous vehicle collision avoidance, and fleet management, requiring more global decision making for safety and correctness of operation, can thus make use of edge cloud systems, offloading their computations to these edge clusters.The edge can then analyze data from these vehicles to optimize the traffic flow, reduce accidents, and provide transportation systems with moreautonomy. The idea of edge computing today forms a cornerstone in the design of many future systems, including, 5G networks and autonomousvehicles, among many others

Трактування та класифікація витрат в сучасній економіці

In order to meet stringent performance requirements, system administrators must effectively detect undesirable performance behaviours, identify potential root causes and take adequate corrective measures. The problem of uncovering and understanding performance anomalies and their causes (bottlenecks) in different system and application domains is well studied. In order to assess progress, research trends and identify open challenges, we have reviewed major contributions in the area and present our findings in this survey. Our approach provides an overview of anomaly detection and bottleneck identification research as it relates to the performance of computing systems. By identifying fundamental elements of the problem, we are able to categorize existing solutions based on multiple factors such as the detection goals, nature of applications and systems, system observability, and detection methods

A Sensor-Actuator Model for Data Center Optimization

Cloud data centers commonly use virtualization technologies to provision compute capacity with a level of indirection between virtual machines and physical resources. In this paper we explore the use of that level of indirection as a means for autonomic data center configuration optimization and propose a sensor-actuator model to capture optimization-relevant relationships between data center events, monitored metrics (sensors data), and management actions (actuators). The model characterizes a wide spectrum of actions to help identify the suitability of different actions in specific situations, and outlines what (and how often) data needs to be monitored to capture, classify, and respond to events that affect the performance of data center operations

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given. The implementation of the method in MATLAB code is available.Comment: 19 pages, 3 figure

Adaptive and Application-agnostic Caching in Service Meshes for Resilient Cloud Applications

Service meshes factor out code dealing with inter-micro-service communication. The overall resilience of a cloud application is improved if constituent micro-services return stale data, instead of no data at all. This paper proposes and implements application agnostic caching for micro services. While caching is widely employed for serving web service traffic, its usage in inter-micro-service communication is lacking. Micro-services responses are highly dynamic, which requires carefully choosing adaptive time-to-life caching algorithms. Our approach is application agnostic, is cloud native, and supports gRPC. We evaluate our approach and implementation using the micro-service benchmark by Google Cloud called Hipster Shop. Our approach results in caching of about 80% of requests. Results show the feasibility and efficiency of our approach, which encourages implementing caching in service meshes. Additionally, we make the code, experiments, and data publicly available

Towards Soft Circuit Breaking in Service Meshes via Application-agnostic Caching

Service meshes factor out code dealing with inter-micro-service communication, such as circuit breaking. Circuit breaking actuation is currently limited to an "on/off" switch, i.e., a tripped circuit breaker will return an application-level error indicating service unavailability to the calling micro-service. This paper proposes a soft circuit breaker actuator, which returns cached data instead of an error. The overall resilience of a cloud application is improved if constituent micro-services return stale data, instead of no data at all. While caching is widely employed for serving web service traffic, its usage in inter-micro-service communication is lacking. Micro-services responses are highly dynamic, which requires carefully choosing adaptive time-to-life caching algorithms. We evaluate our approach through two experiments. First, we quantify the trade-off between traffic reduction and data staleness using a purpose-build service, thereby identifying algorithm configurations that keep data staleness at about 3% or less while reducing network load by up to 30%. Second, we quantify the network load reduction with the micro-service benchmark by Google Cloud called Hipster Shop. Our approach results in caching of about 80% of requests. Results show the feasibility and efficiency of our approach, which encourages implementing caching as a circuit breaking actuator in service meshes