Modelling Three Dimensional Gene Regulatory Networks

We consider the three-dimensional gene regulatory network (GRN in short). This model consists of ordinary differential equations of a special kind, where the nonlinearity is represented by a sigmoidal function and the linear part is present also. The evolution of GRN is described by the solution vector X(t), depending on time. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way.

Baroreflex Curve Fitting Using a WYSIWYG Boltzmann Sigmoidal Equation

Arterial baroreflex assessment using vasoactive substances enables investigators to collect data pairs over a wide range of blood pressures and reflex reactions. These data pairs relate intervals between heartbeats or sympathetic neural activity to blood pressure values. In an X-Y plot the data points scatter around a sigmoidal curve. After fitting the parameters of a sigmoidal function to the data, the graph’s characteristics represent a rather comprehensive quantitative reflex description. Variants of the 4-parameter Boltzmann sigmoidal equation are widely used for curve fitting. Unfortunately, their ‘slope parameters’ do not correspond to the graph’s actual slope which complicates the analysis and bears the risk of misreporting. We propose a modified Boltzmann sigmoidal function with preserved goodness of fit whose parameters are one-to-one equivalent to the sigmoidal curve’s characteristics.

Design of Improved Version of Sigmoidal Function with Biases for Classification Task in ELM Domain

Extreme Learning Machine (ELM) is one of the latest trends in learning algorithm, which can provide a good recognition rate within less computation time. Therefore, the algorithm can sustain for a faster response application by utilizing a feed-forward neural network. In this research article, the ELM method has been designed with the presence of sigmoidal function of biases in the hidden nodes to perform the classification task. The classification task is very challenging with the existing learning algorithm and increased computation time due to the huge amount of dataset. While handling of the stochastic matrix for hidden layer, output provides the lower performance for learning rate and robustness in the determination. To address these issues, the modified version of ELM has been developed to obtain better accuracy and minimize the classification error. This research article includes the mathematical proof of sigmoidal activation function with biases of the hidden nodes present in the networks. The output matrix maintains the column rank in order to improve the speed of the training output weights (β). The proposed improved version of ELM leverages better accuracy and efficacy in classification and regression problems as well. Due to the inclusion of matrix column ranking in mathematical proof, the proposed improved version of ELM solves the slow training speed and over-fitting problems present in the existing learning approach.

Sigmoidal NMFD: Convolutional NMF with Saturating Activations for Drum Mixture Decomposition

In many types of music, percussion plays an essential role to establish the rhythm and the groove of the music. Algorithms that can decompose the percussive signal into its constituent components would therefore be very useful, as they would enable many analytical and creative applications. This paper describes a method for the unsupervised decomposition of percussive recordings, building on the non-negative matrix factor deconvolution (NMFD) algorithm. Given a percussive music recording, NMFD discovers a dictionary of time-varying spectral templates and corresponding activation functions, representing its constituent sounds and their positions in the mix. We observe, however, that the activation functions discovered using NMFD do not show the expected impulse-like behavior for percussive instruments. We therefore enforce this behavior by specifying that the activations should take on binary values: either an instrument is hit, or it is not. To this end, we rewrite the activations as the output of a sigmoidal function, multiplied with a per-component amplitude factor. We furthermore define a regularization term that biases the decomposition to solutions with saturated activations, leading to the desired binary behavior. We evaluate several optimization strategies and techniques that are designed to avoid poor local minima. We show that incentivizing the activations to be binary indeed leads to the desired impulse-like behavior, and that the resulting components are better separated, leading to more interpretable decompositions.

A Self-adaptive Hybrid Bio-inspired Optimization Algorithm by Using Sigmoidal Function

The article presents a new hybrid algorithm, which designs based on traditional bio-inspired optimization algorithms. The algorithm leverages the advantage of Particle Swarm Optimization (PSO), Differential Evolution (DE), and Artificial Bee Colony (ABC), replacing other algorithm weaknesses. A new algorithm we proposed is the Fast bio-inspired Optimization Algorithm (FOA). The DE uses multi-parent for trial vector calculation. It increases the diversity of the solution, while the sigmoidal function adds a self-adaptive characteristic to the proposed algorithm. The function replaces a weighting scheme of PSO. In sub-optimal avoidance, the FOA includes a scout bee behavior from ABC. It makes FOA providing the solution faster than traditional versions, while the solution quality is maintained at an acceptable level. According to a new design, an FOA can reduce the algorithm runtime up to 43.57%, 37.14%, 40.78%, and 31.30% compared to PSO, DE, ABC, and DEPSO, respectively. The DEPSO is the hybrid algorithm between DE and PSO. The best solution to FOA is better than the traditional version of the algorithms. The new algorithm design and the optimization speed improvement are the highlight contribution of this article.

Using Gaia DR2 to solve differential colour refraction and charge transfer efficiency issues

ABSTRACT The Gaia DR2 catalogue released in 2018 gives information about more than one billion stars, including their extremely precise positions that are not affected by the atmosphere, as well as the magnitudes in the G, RP, and BP passbands. This information provides great potential for the improvement of the ground-based astrometry. Based on Gaia DR2, we present a convenient method to calibrate the differential colour refraction (DCR). This method only requires observations with dozens of stars taken through a selected filter. Applying this method to the reduction of observations captured through different filters by the 1- and 2.4-m telescopes at Yunnan Observatory, the results show that the mean of the residuals between observed and computed positions (O − C) after DCR correction is significantly reduced. For our observations taken through an N (null) filter, the median of the mean (O − C) for well-exposed stars (about 15 G-mag) decreases from 19 to 3 mas, thus achieving better accuracy, i.e. mean (O − C). Another issue correlated is a systematic error caused by the poor charge transfer efficiency (CTE) when a CCD frame is read out. This systematic error is significant for some of the observations captured by the 1-m telescope at Yunnan Observatory. Using a sigmoidal function to fit and correct the mean (O − C), a systematic error up to 30 mas can be eliminated.

A Modified Rheological Model for the Dynamic Modulus of Asphalt Mixtures

In this paper, five rheological models, including a newly developed formulation based on the combination of the Christensen-Anderson-Marasteanu (CAM) model and the sigmoidal function, are used to evaluate the dynamic modulus of three different asphalt mixtures types. The effectiveness of the models in representing the experimental results is graphically and statistically compared. Clear differences in dynamic modulus computation are observed when using sigmoidal function-based models and CAM formulations. The newly introduced CAM model modified by the sigmodal function appears to provide reasonable fitting compared to the previously developed models and may represent an alternative formulation to be evaluated in the current pavement design software.

Characterization of the precision premium in astrometry

ABSTRACT The precision premium, a concept in astrometry that was first presented by Pascu in 1994, initially means that the relative positional measurement of the Galilean satellites of Jupiter will be more accurate when their separations are small. Correspondingly, many observations have been obtained of these Galilean satellites since it was introduced. However, the exact range of separations at which the precision premium takes effect is not clear yet, nor the variation of the precision with separation. In this article, observations of open cluster M35 are used to study the precision premium and the newest star catalogue Gaia DR2 is used in data reduction. Our results show that the precision premium applies at less than 100 arcsec for two specific objects and the relative positional precision can be well fitted by a sigmoidal function. Observations of Uranian satellites are also reduced as an example of the precision premium.