Functional analysis of high throughput experiments using pathway analysis is now ubiquitous. Though powerful, these methods often produce thousands of redundant results owing to knowledgebase redundancies upstream. This scale of results hinders extensive exploration by biologists and can lead to investigator biases due to previous knowledge and expectations. To address this issue, we present vissE, a flexible network-based analysis and visualisation tool that organises information into semantic categories and provides various visualisation modules to characterise them with respect to the underlying data, thus providing a comprehensive view of the biological system. We demonstrate vissE's versatility by applying it to three different technologies: bulk, single-cell and spatial transcriptomics. Applying vissE to a factor analysis of a breast cancer spatial transcriptomic data, we identified stromal phenotypes that support tumour dissemination. Its adaptability allows vissE to enhance all existing gene-set enrichment and pathway analysis workflows, empowering biologists during molecular discovery.

The classification of clinical samples based on gene expression data is an important part of precision medicine. In this manuscript, we show how transforming gene expression data into a set of personalized (sample-specific) networks can allow us to harness existing graph-based methods to improve classifier performance. Existing approaches to personalized gene networks have the limitation that they depend on other samples in the data and must get re-computed whenever a new sample is introduced. Here, we propose a novel method, called Personalized Annotation-based Networks (PAN), that avoids this limitation by using curated annotation databases to transform gene expression data into a graph. Unlike competing methods, PANs are calculated for each sample independent of the population, making it a more efficient way to obtain single-sample networks. Using three breast cancer datasets as a case study, we show that PAN classifiers not only predict cancer relapse better than gene features alone, but also outperform PPI (protein-protein interactions) and population-level graph-based classifiers. This work demonstrates the practical advantages of graph-based classification for high-dimensional genomic data, while offering a new approach to making sample-specific networks. Supplementary information: PAN and the baselines are implemented in Python. Source code and data are available at https://github.com/thinng/PAN.

This paper presents a modified model of a power grid which consists of renewable power systems and other types of traditional power systems. The rising demand of the electricity makes the ordinary fossil sources may not be adequate to accommodate this growth and the expansion of the power grid. On the other hand, these types of sources may not be interested due to their environmental impacts and economical issues. Instead, renewable sources are dramatically gained more focus due to their characteristics for providing clean and economic power. Regardless to these characteristics, since the renewable power systems depend on the weather, they suffer from irregular, intermittence, and unpredictable power that they produce. However, with adapting accurate weather forecast data to the control system, the performance, efficiency and reliability of the renewable power system are potentially improved. The implementation of the advanced forecast technology in the power systems makes the ability to predict the amount of the available power on the grid both instantaneously and for the future real. This reality can be taken as a basis for designing and developing a comprehensive future power smart grid.

Techniques for advanced logic design in spatial dimensions for the purposes of nano-devices and nanoICs are being formulated to incorporate certain topologies that satisfy certain requirements of nanotechnology. The hypercube is considered a relevant topology for the design of the N-hypercube in which switching functions are embedded. We propose using a similar topology for designing of sequential logic in spatial dimensions. The M-hypercube which is an extension of the hypercube topology is introduced as a building block for spatial sequential logic design. This cube can represent any finite state machine with any possible configuration. An MN-cell which is a combination of M- and N-hypercubes is introduced with several examples containing various embedding and assignment techniques of the M-hypercube and MN-cell. This paper presents logic design approaches to reduce the complexity of large M-hypercube representation via sequential machine decomposition. A study of the logic design of a basic computer in nanospace using M- and N-hypercube cells as building blocks is also presented with several examples included.

Two pattern recognition algorithms are proposed to detect two types of knots in lumber, lumped and surface knots, using an optical scanner. It is shown that lumped knots can be recognized by a log profile approach and surface knots can be detected by an image processing approach. A mathematical model for describing the geometry of the knots inside the log based on the surface parameters of the knots is presented. By a log breakdown strategy, the log can be cut into a maximum number of boards with prescribed dimensionalities. The mathematical knot model can be used to predict the locations, sizes, orientations, and shapes of the knots on these boards, whereby their lumber grades can be determined. Summing up the value yields of all the boards gives the value yield of the log. By computing all the possible value yields of the log from different log orientations, one can determine a maximum value yield of a log.>

Applications of fast convolution using Fermat and Mersenne number transforms to digital filtering are greatly limited by the short transform sequence-lengths of these transforms. The generalized modulo numbers M generated by the following equation: M=p/sup q/t/+or-(p-1), which include the Fermat and Mersenne numbers, are proposed: p, q, and r, are integers and p is always prime. By using the generalized modulus numbers in computing fast convolution, the transform sequence lengths can be much greater than those obtained by either Fermat numbers or Mersenne numbers. The removal of the sequence length constraint by using the generalized modulus numbers and m-valued logic arithmetic implementation makes the fast convolution more practically useful.>

This note points out several errors in the paper [1] by E. E. Swartzlander, Jr. et al. Corrected results are presented including detailed reasons and derivations.

FOCUS is a number system and supporting soft ware especially useful for microcomputer control and other signal processing applications. FOCUS has the wide ranging character of floating-point numbers with a uniformity of state distributions that give FOCUS approximately a fourfold accuracy advantage over an equal length floating-point system. FOCUS computations are typically five times faster than equal word length single precision fixed-point or integer arithmetic for a mixture of operations, comparable with hardware arithmetic in speed for many applications. Algorithms for 8-bit and two versions of 16-bit FOCUS are included. With FOCUS, an 8080A can perform the equivalent of over 20,000 18-bit floating-point additions, subtractions, multiplications, and divisions in one second, and store the results in 16-bit words. FOCUS is more than a theory, it is a completed system providing near hardware speed, 18-bit accuracy, floating-point range, and 8-bit cost.

This paper presents an analysis of roundoff error accumulation in the direct realization of a logarithmic-arithmetic digital filter and formulas for computing the ratio of the rms value of the roundoff error and that of the output signal of the digital filter. It is shown that for the case of the stochastic input, the theoretical error to signal ratio is less using logarithmic number systems as compared to using floating-point number systems. The theoretical results of the roundoff error analysis were verified in simulation experi ments. The experimental results also show that the logarithmic number system gives filtering performance superior to that of a floating-point system of equivalent word length and range and that the limitation in implementing digital filters with logarithmic number system is a function of the range of the numbers which may be represented.

In 1971 Kinsbury and Rayner, publishing under the title "Digital Filtering Using Logarithmic Arithmetic" [1] disclosed a sign-plus-logarithm number system, and a means of performing addition through single dimensional lookup using the formula c = b + F(a − b). The system was demonstrated on a computer. In 1975 Swartzlander and Alexopoulos disclosed Kinsbury's logarithmic arithmetic as "The Sign/Logarithm Number System" [2]. In 1977, without knowledge of prior art, we reinvented the wheel a third time, dubbing it "Focus," after the focus of resolution around the zero origin [3]. We wish now to acknowledge Kinsbury and Rayner as the pioneer authors, and also Swartzlander and Alexopoulos as prior to our publication.

This correspondence introduces a new number system, called the Focus number system which "focuses" on available resolution near zero much like an operational amplifier "focuses" on tiny deviations near virtual ground. This number system is supported by algorithms providing addition, multiplication, and higher order functions in a bare microcomputer at speeds rivaling those of existing integer arithmetic [1]-[3] performed with a costly arithmetic unit.

In this paper, binary-vector Boolean algebra, a generalization of ordinary Boolean algebra [6], is introduced. In this algebra, every element is represented by a binary vector and in addition to ordinary AND, OR, and NOT operations, a new operation called the rotation operation which rotates (rightward or leftward) the components of a binary vector is introduced. Moreover, the NOT or COMPLEMENTATION operation is extended to a more general operation called the generalized complement which includes the total complement (ordinary complement), the null complement (no complement), and newly introduced partial complements. Because of this generalization, all axioms and theorems of ordinary Boolean algebra are generalized. In particular, it is shown that DeMorgan's theorem, Shannon's theorem, and the expansion theorem are generalized into more general forms which include their corresponding ordinary version as a special case. It is also shown that any multivalued logic truth table can be represented by a vector Boolean function. Three compact canonical (sum-of-products and product-of-sums) forms of this function are presented.

This note describes an algorithm for identifying multivalued symmetric switching functions using parallel processing. Some general properties of multivalued symmetric functions have been investigated. The mixed multivalued symmetric switching function is defined and an algorithm for identifying it is also presented.