Research Areas

ITS PSDM develops mathematical research and its application in the leading fields of ITS. The development of mathematical research in ITS PSDM is explained in the following fishbone research

Research in the field of analysis is emphasized on developing theories about functional analysis and wavelet analysis along with their application:

  1. Functional analysis research leads to research on the properties of sequence convergence, sequence limitations, continuity and functional limitations in norm-2 spaces, p-norm spaces, norm cone spaces, bi-metrics, partially metric. This research is expected to emerge new theorems related to the definition of metrics, norms, inner results and new operators.
  2. Wavelet analysis research is also carried out to develop theories in wavelet theory as well as research on fuzzy wavelets and Kalman filter wavelets and their applications.

Research on algebra is emphasized on the development of theories in the fields of algebra itself and several other related fields. Research topics on algebra are emphasized in several fields, namely:

  1. Cryptography of text and images using wavelet max plus transformation.
    The research that has been done is the use of wavelet max plus transformation for cryptography in the form of text. One question is how to determine the optimal keyspace. In addition, this study will be developed into cryptography with min max plus algebra and supertropical algebra.
  2. Supertropical matroid algebra.
    The research being carried out is developing a theory about max algebra plus matroid. One application of the theory obtained is for matrix decomposition of max plus algebra. Future research plans are to develop a theory for matroid in supertropical algebra.
  3. The general power algorithm on the bipartition system is min max plus
    Power algorithms have been developed for max plus systems, both irreducible and reducible. The research that will be carried out is to develop power algorithms for min max plus bipartition systems and supertropical algebra.
  4. Min max plus supertropical algebra
    The research that has been done is to develop a method for finding eigenvalues, determinants and eigenvectors in max plus supertropical algebra. The research that will be carried out is to develop these methods in min max plus supertropical algebra.
  5. Min max plus and supertropical bipartition system verification
    System verification method has been developed for system max plus. As a continuation of this research, the topic that will be developed is the system verification method for the bipartition system min max plus and also supertropical.

Data assimilation is actually an applied field of mathematics based on the fields of analysis and algebra. Data assimilation research emphasizes the development of data assimilation methods which are then applied to various fields to analyze the reliability of the development of the method.

Data assimilation research is supported by capabilities

  1. Modeling and systems
  2. Computing matrix
  3. Computer programming

Some research topics that can be taken include

  1. Data assimilation for linear systems: the development of data assimilation methods is done to reduce computation time
  2. Data assimilation for nonlinear systems: the development of data assimilation methods is done to improve result accuracy
  3. Data assimilation for large scale: the development of data assimilation methods is carried out to increase computation time while still considering the accuracy of estimation results

Biomathematics

Research in the field of control methods emphasizes the development of methods based on mathematical theories such as Linear Algebra and Matrix, Differential Equations and Systems theory. Linear algebra and matrix are supported by knowledge of matrix convolution transformations and eigen values. Differential equations cover ordinary differential equations, partial differential equations and also numerical differential equations. System theory includes linear and nonlinear systems, deterministic and stochastic systems and descriptor systems. While research that can be developed in the control method / design is

  1. Robust control: research conducted in robust control uses H_infinity, and sliding control mode is applied in various cases such as aircraft systems, inverted care etc.
  2. intelligent control: research conducted in intelligent control includes the application of fuzzy logic control in some cases, predictive control model, intelligent control development by improvising with optimizations inspired by nature.
  3. optimal control: research on optimal control in addition to its application also carried out development by combining with developing optimization such as PSO, Firefly Algorithm etc.
  4. observer existence and optimization: research conducted on the existence and optimization of observers, among others, designs, analyzes the existence and optimization of expanded observers in system delay and system descriptors.
  5. Model reduction and variable state initialization: research on model reduction is carried out by developing a model reduction method on non-linear systems and descriptor systems and initiating variable states on the reduced system. This model reduction can also be combined to analyze observer design and low order controllers.
  1. Operation Research
    Research conducted in this field is the inventory system, both ,  deterministic and stochastic, which are applied to the evaluation of spare parts in an industrial company.  The research includes the evaluation of maintenance of the equipment, pricing, lifetime, and distance to the warehouse.  The evaluation is necessary to avoid the inavailability of the supply of  spare parts that will affect the production process.
  2. Optimization
    Collaborated with the theory of control mathematics and data assimilation method, the research has been growing in theory development and application. The applications are in the development of ship control and unattended air vehicle. Some theory of multipredictive control, adaptive and robust, are includes in this research.
  3. Probability and StatisticsTheory of probability and statistics lead to abroad range of research topic as they are one of the basic capability in mathematics.  Besides supporting the other field of research in Department of Mathematics, in this field some topics can be listed as follows:
    1. The application of Bayesian theory for rainfall model and text detection
    2. The application of statistics in quality control analysis for industry
    3. Some studies of probability distributions such as binomial and poisson distributions.
    4. The study and development of poisson model  for data count
  4. Time Series
    Being used for prediction and forecast tools, the methods in time series such as ARIMA, GARCH and GSTAR models are developed using Kalman Filter and applied.  The research topic related to these methods are :

    1. Prediction of stock price, oil price, and infation modified with Kalman Filter
    2. Prediction of blood demand modified with Kalman Filter
    3. Prediction of tourist attendance

Bioinformatika

Data mining is a branch of studies in computer science, mathematics, and statistics that have developed very rapidly in the last few decades. Data Mining is a term used to find new patterns (knowledge) in a large amount of data. Data mining uses mathematical methods, statistics, artificial intelligence and machine learning to extract and identify useful information and related knowledge from various sources of Big Data. It could also be said that data mining is a process to find meaningful relationships, patterns and tendencies by examining from a group of Big Data stored in storage media using methods that can be used for data pattern recognition.

Some methods in Mathematics developed into tools in data mining include fuzzy sets, rough sets, partial orders, graphs, hypergraf, size theory, probability and stochastic theories, artificial neural networks, and others.

Various applications that have been developed in research in the Department of Mathematics include:

  • discovery of associations between spatial objects and their attributes,
  • weather prediction,
  • classification of selection of types of insurance,
  • vehicle classification,
  • search for stock movement patterns with association rule and sequence mining approaches,
  • and applications in other fields

Research in the field of computational mathematics is emphasized in the analysis and development of algorithms and digital image processing methods and also the application of image processing on several real problems. In order to develop algorithms and image processing methods requires basic knowledge of mathematics, namely:

  1. Computational Mathematics:
    Image processing is basically processing on the matrix so that efficient matrix operations are needed in research. The computational mathematics required includes algebra and matrix, convolution operators and eigenvalue features.
  2. Statistics
    Filtering in the spatial domain and extracting features based on statistical features in digital images requires deep statistical science, including the mean, median, standard deviation. SVM and PCA are tools needed for image classification and clustering.
  3. Mathematical Morphology
    Mathematical Science Morphology has an important role in image processing and has been widely used for medical image processing. Mathematical morphology with some basic operations has a role for feature extraction and object decryption.
  4. Fourier transform
    Fourier transform is a mathematical tool that has been widely used in processing signals, images and video. Image filtering in the frequency domain that is by applying fourier transforms will provide better and faster results than done in the spatial domain. Fourier transformation algorithms that are often used are FFT and DFT
  5. Wavelet Transformation
    The concept of multiresolution owned by wavelet transforms is very useful in image and video processing, including for image / video compression and noise removal. The number of wavelet functions that can be selected greatly help image processing. The wavelet transformation algorithm used is a 2D discrete wavelet transformation
  6. Information Technology
    Image Processing Digial uses information technology to process it. Some tools, both libraries and applications that are often used include MATLAB, OpenCV and Java programming languages. As the internet grows quite high, with various multimedia content, both image, video and sound, it takes web-based video and image processing. Besides that the processing speed also needs to be considered in parallel processing (parallel computing)