arXiv subjects

Chengpu Wang

Publications and source records attributed to Chengpu Wang.

7 recordsLinked to original sources

arXiv2024

Statistical Taylor Expansion: A New and Path-Independent Method for Uncertainty Analysis

Statistical Taylor expansion is a rigorous extension of conventional Taylor expansion that replaces each precise input variable with a random variable of known distribution and sample count, then computes the mean, deviation, and a bounding reliability of every result. By tracking the propagation of input uncertainties through all intermediate steps, it renders the final result path-independent, with precise quantification of the tracking quality. This path-independence sets it fundamentally apart from conventional numerical approaches, which are path-dependent. This study presents an implementation called variance arithmetic and demonstrates its performance across diverse mathematical applications. This study also reveals the potentially substantial impact of numerical errors in library functions, the defect of applying input uncertainties as weights in conventional regression, and the modeling error of the discrete Fourier transformation. The concept of statistical algebra is also introduced.

stat.CO↗

arXiv2023

Is Parallel Postulate Necessary?

As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot.

math.LO↗

arXiv2014

Type Expressiveness and Its Application in Separation of Behavior Programming and Data Management Programming

A new behavior descriptive entity type called spec is proposed, which combines the traditional interface with test rules and test cases, to completely specify the desired behavior of each method, and to enforce the behavior-wise correctness of all compiled units. Using spec, a new programming paradigm is proposed, which allows the separation programming space into 1) a behavior domain to aggregate all behavior programming in the format of specs, 2) a object domain to bind each concrete spec to its data representation in a particular address space, and 3) a realization domain to connect the behavior domain and the object domain. Such separation guarantees the strictness of behavior satisfaction at compile time, while allows flexibility of dynamical binding of actual implementation at runtime. A new convention call type expressiveness to allow data exchange between different programming languages and between different software environments is also proposed.

cs.PL↗

arXiv2011

Common Signal Analysis

A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal among three signals.

cs.IT↗

arXiv2011

Toward Functionality Oriented Programming

The concept of functionality oriented programming is proposed, and some of its aspects are discussed, such as: (1) implementation independent basic types and generic collection types; (2) syntax requirements and recommendations for implementation independence; (3) unified documentation and code; (4) cross-module interface; and (5) cross-language program making scheme. A prototype example is given to demonstrate functionality oriented programming.

cs.PL↗

arXiv2006

Concurrent Processing Memory

A theoretical memory that embeds limited, application-specific processing power and nearest-neighbor connectivity at every storage element is proposed. Such a memory performs parallel computation within itself to solve generic array problems, while remaining pin- and function-compatible with conventional random-access memory. The applicability of this in-memory, finest-grain, massive-SIMD approach is examined in detail through a family of increasingly capable devices---content movable, searchable, value-comparable, and computable memory. For an array of $N$ items, the approach reduces the instruction-cycle count of universal operations (insertion, deletion, and match finding) to $\sim 1$, of local operations (filtering and template matching) to $\sim$ the operation footprint, and of global operations (summation and finding minimum/maximum) to $\sim \sqrt{N}$. It eliminates most data-processing traffic on the system bus, yet remains general-purpose, easy to program, backward-compatible with existing bus-sharing architectures and operating systems, and practical to implement along a clear road map.

cs.DC↗

arXiv2006

Precision Arithmetic: A New Floating-Point Arithmetic

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding range. Its stable rounding error distribution is approximated by a truncated normal distribution. Generic standards and systematic methods for validating uncertainty-bearing arithmetics are discussed. The precision arithmetic is found to be better than interval arithmetic in both uncertainty-tracking and uncertainty-bounding for normal usages. The precision arithmetic is available publicly at http://precisionarithm.sourceforge.net.

cs.DM↗