Modulation coding, to limit the number of consecutive zeroes in a data stream, is essential in digital magnetic recording/playback systems. Additionally, such sys­ tems require error correction coding to ensure that the decoded output matches the recorder input, even if noise is present. Typically these two coding steps have been performed independently, although various methods of combining th...

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/ analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/ana...

In this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are sufficiently general to encompass many of the codes previously constructed from higherdimensional varieties, as well as those coming from curves. And still, the bounds obtained ar...

Background. The iterative sure independence screening (ISIS) is a popular method in selecting important variables while maintaining most of the informative variables relevant to the outcome in high throughput data. However, it not only is computationally intensive but also may cause high false discovery rate (FDR). We propose to use the FDR as a screening method to reduce the high dimension to ...

Topological stabilizer codes with different spatial dimensions have complementary properties. Here I show that the spatial dimension can be switched using gaugefixing. Combining 2D and 3Dgauge color codes in a 3Dqubit lattice, fault-tolerant quantum computation can be achievedwith constant time overhead on the number of logical gates, up to efficient global classical computation, using only loc...

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...

Background and purpose: Machine learning is a class of modern and strong tools that can solve many important problems that nowadays humans may be faced with. Support vector regression (SVR) is a way to build a regression model which is an incredible member of the machine learning family. SVR has been proven to be an effective tool in real-value function estimation. As a supervised-learning appr...