Customer Segment Prediction on Retail Transactional Data Using K-Means and Markov Model

Retailing is a dynamic business domain where commodities and goods are sold in small quantities directly to the customers.It deals with the end user customers of a supply-chain network and therefore has to accommodate the needs and desires of a large group of customers over varied utilities.The volume and volatility of the business makes it one of the prospectivefields for analytical study and data modeling.This is also why customer segmentation drives a key role in multiple retail business decisions such as marketing budgeting,customer targeting,customized offers,value proposition etc.The segmentation could be on various aspects such as demographics,historic behavior or preferences based on the use cases.In this paper,historic retail transactional data is used to segment the custo-mers using K-Means clustering and the results are utilized to arrive at a transition matrix which is used to predict the cluster movements over the time period using Markov Model algorithm.This helps in calculating the futuristic value a segment or a customer brings to the business.Strategic marketing designs and budgeting can be implemented using these results.The study is specifically useful for large scale marketing in domains such as e-commerce,insurance or retailers to segment,profile and measure the customer lifecycle value over a short period of time.

Management Tools for Random Demand Inventory and Supply

A mathematical management model’s added value is obtained only after the design and implementation of a user-friendly operating and usage tool. Fol-lowing work on developing an automated inventory management system and/or supplies, a dynamic model for the rational management of product stocks was established. Its implementation aims to limit or eliminate over-stocking and/or stock depletion. The orderable quantity prediction tool based on a settable and preset time period demonstrates the added value of incorporating probabilistic mathematical principles into supply management processes. In this context, this article discusses aspects of the design and implementation of random demand management algorithms based on Mar-kov chains. The goal is to forecast the state or behavior of goods marketing company’s product stocks and to develop a user supply management inter-face. The latter’s functional application will ultimately demonstrate the ac-curacy of the model. This paper also looks at how to use Markov chains to predict the reliability of any technical device, as well as how to implement an automated system with the desired technical specifications.

THE EXISTENCE AND MOMENTS OF CANONICAL BRANCHING CHAIN IN RANDOM ENVIRONMENT

The concepts of branching chain in random environmnet and canonical branching chain in random environment are introduced. Moreover the existence of these chains is proved. Finally the exact formulas of mathematical expectation and variance of branching chain in random environment are also given.

Multimodal process monitoring based on transition-constrained Gaussian mixture model

Reliable process monitoring is important for ensuring process safety and product quality.A production process is generally characterized bymultiple operation modes,and monitoring thesemultimodal processes is challenging.Most multimodal monitoring methods rely on the assumption that the modes are independent of each other,which may not be appropriate for practical application.This study proposes a transition-constrained Gaussian mixture model method for efficient multimodal process monitoring.This technique can reduce falsely and frequently occurring mode transitions by considering the time series information in the mode identification of historical and online data.This process enables the identified modes to reflect the stability of actual working conditions,improve mode identification accuracy,and enhance monitoring reliability in cases of mode overlap.Case studies on a numerical simulation example and simulation of the penicillin fermentation process are provided to verify the effectiveness of the proposed approach inmultimodal process monitoring with mode overlap.

Quantificational analysis on progress of river water quality in China

In order to understand the dynamic change of water quality in a specific period of time,a type of possibility transition matrix based on the theory of Markov process was established.The transition possibility with a weight to calculate the degree of absolute advancement was given based on the result of water quality evaluation.The concept of relative advancement was presented.It was used to evaluate the extent of water quality changed in a period of time.The method was used to calculate the degrees of relative advancement for 4 rivers in China,and the results were analyzed.

A note on overshoot estimation in pole placements

In this note we show that for a given controllable pair (A, B) and any λ > 0, a gain matrix K can be chosen so that the transition matrix e {(A+BK)t} of the system x = (A + BK) x decays at the exponential rate e ?λt and the overshoot of the transition matrix can be bounded by Mλ L for some constants M and L that are independent of λ. As a consequence, for any h > 0, a gain matrix K can be chosen so that the magnitude of the transition matrix e (A+BK)t can be reduced by 1/2 (or by any given portion) over [0, h]. An interesting application of the result is in the stabilization of switched linear systems with any given switching rate.

Stability of Nonlinear Feedback Shift Registers with Periodic Input

The stability of Non-Linear Feedback Shift Registers(NFSRs)plays an important role in the cryptographic security.Due to the complexity of nonlinear systems and the lack of efficient algebraic tools,the theorems related to the stability of NFSRs are still not well-developed.In this paper,we view the NFSR with periodic inputs as a Boolean control network.Based on the mathematical tool of semi-tensor product(STP),the Boolean network can be mapped into an algebraic form.Through these basic theories,we analyze the state space of non-autonomous NFSRs,and discuss the stability of an NFSR with periodic inputs of limited length or unlimited length.The simulation results are provided to prove the efficiency of the model.Based on these works,we can provide a method to analyze the stability of the NFSR with periodic input,including limited length and unlimited length.By this,we can efficiently reduce the computational complexity,and its efficiency is demonstrated by applying the theorem in simulations dealing with the stability of a non-autonomous NFSR.

A Modified Non-Homogeneous Model for Codon Preference and Primary Sequence Structure in Protein-Coding Regions

Based on non-homogeneous model, a modified model is proposed. The new model deals with codon preference in protein-coding regions, reflects more accurately the key biological features of the regions. In addition, it is demonstrated, via an example, the modified model offers better solutions than previous model does.

THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.

State and Mode Feedback Control for Discrete-time Markovian Jump Linear Systems With Controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems(MJLSs) with controllable mode transition probability matrix(MTPM) are investigated. In most achievements, controller design of MJLSs pays more attention to state/output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state/output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.

THE THEOREM OF THE STABILITY OF LINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION AND ITS APPLICATION IN THE STABILITY ANALYSIS OF ROBOT

The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of[1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov ami the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stabilitv of robot has been presented by applying the theorem in this paper, which is closer to reality

THE THEOREM OF THE STABILITY OF NONLINEAR NONAUTONOMOUS SYSTEMS UNDER THE FREQUENTLY-ACTING PERTURBATION—LIAPUNOV’S INDIRECT METHOD

In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.

A further note on overshoot estimation in pole placements

Recently, it is proved in the literature that for a given controllable pair （A, B） with A ∈R^n×n, B ∈R^n×m, and any λ ≥ 1, a gain matrix K can be designed so that ‖e^（A＋BK）t‖ ≤Mλ^Le^-λt, where M and L are constants independent of λ. Here, we show that M and L can be chosen much smaller than that proposed above. As a consequence, the estimation on overshoot of a transition matrix can be bounded more precisely. This can be regarded as a complement to the existing result.

Analysis on Stochastic Passage Characteristics for Gun Barrel in Shooting Domain

Aiming at some weapon systems with shooting domain,the stochastic passage characteristics of the barrel were studied.On the basis of the exact definition of the stochastic passage characteristics,its opportunity-awaiting time,residence time and stochastic passage period were given by using the transition probability matrix,and they all obeyed the geometry distributions.Their means and variances were also derived,and the relations between the time indexes and the structure and parameters of weapon control system were established.Finally,the creditability of the conclusions was verified by the test data of weapon system in proving ground.

Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.

Electric dipole moment function and line intensities for the ground state of carbon monxide

An accurate electric dipole moment function(EDMF) is obtained for the carbon monoxide(CO) molecule(X1+Σ)by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is found using the highly accurate, multi-reference averaged coupled-pair functional(ACPF) approach with the basis set, aug-cc-p V6 Z, and a finite-field with ±0.005 a.u.(The unit a.u. is the abbreviation of atomic unit). This ab initio EDMF is very consistent with the fitted ones. The vibrational transition matrix moments and the Herman–Wallis factors, calculated with the Rydberg–Klein–Rees(RKR) potential and the fitted and ab initio EDMFs, are compared with experimental measurements. The consistency of these line intensities with the high-resolution transmission(HITRAN) molecular database demonstrates the improved accuracy of the fitted and ab initio EDMFs derived in this work.

Using Markov chains to predict the natural progression of diabetic retinopathy

AIM: To study the natural progression of diabetic retinopathy in patients with type 2 diabetes.METHODS: This was an observational study of 153 cases with type 2 diabetes from 2010 to 2013. The state of patient was noted at end of each year and transition matrices were developed to model movement between years. Patients who progressed to severe non-proliferative diabetic retinopathy(NPDR) were treated.Markov Chains and Chi-square test were used for statistical analysis.RESULTS: We modelled the transition of 153 patients from NPDR to blindness on an annual basis. At the end of year 3, we compared results from the Markov model versus actual data. The results from Chi-square test confirmed that there was statistically no significant difference(P =0.70) which provided assurance that the model was robust to estimate mean sojourn times. The key finding was that a patient entering the system in mild NPDR state is expected to stay in that state for 5y followed by 1.07 y in moderate NPDR, be in the severe NPDR state for 1.33 y before moving into PDR for roughly8 y. It is therefore expected that such a patient entering the model in a state of mild NPDR will enter blindness after 15.29 y.CONCLUSION: Patients stay for long time periods in mild NPDR before transitioning into moderate NPDR.However, they move rapidly from moderate NPDR to proliferative diabetic retinopathy(PDR) and stay in that state for long periods before transitioning into blindness.

Hierarchical Community Detection Based on Partial Matrix Convergence Using Random Walks

Random walks are a standard tool for modeling the spreading process in social and biological systems But in the face of large-scale networks, to achieve convergence, iterative calculation of the transition matrix in random walk methods consumes a lot of time. In this paper, we propose a three-stage hierarchical community detection algorithm based on Partial Matrix Approximation Convergence （PMAC） using random walks. First, this algorithm identifies the initial core nodes in a network by classical measurement and then utilizes the error function of the partial transition matrix convergence of the core nodes to determine the number of random walks steps. As such, the PMAC of the core nodes replaces the final convergence of all the nodes in the whole matrix. Finally based on the approximation convergence transition matrix, we cluster the communities around core nodes and use a closeness index to merge two communities. By recursively repeating the process, a dendrogram of the communities is eventually constructed. We validated the performance of the PMAC by comparing its results with those of two representative methods for three real-world networks with different scales

An Analysis of International Data Encryption Algorithm(IDEA) Security against Differential Cryptanalysis

The security of international date encryption algorithm （IDEA（16））, a mini IDEA cipher, against differential cryptanalysis is investigated. The results show that [DEA（16） is secure against differential cryptanalysis attack after 5 rounds while IDEA（8） needs 7 rounds for the same level of security. The transition matrix for IDEA（16） and its eigenvalue of second largest magnitude are computed. The storage method for the transition matrix has been optimized to speed up file I/O. The emphasis of the work lies in finding out an effective way of computing the eigenvalue of the matrix. To lower time complexity, three mature algorithms in finding eigenvalues are compared from one another and subspace iteration algorithm is employed to compute the eigenvalue of second largest module, with a precision of 0.001.

The Complexity of Recognition in the Single-Layered PLN Network with Feedback Connections

Regarding a single-layered PLN network with feedback connections as an associative memory network,the complexity of recognition is discussed.We have the main result:if the size of the network N is m,then the complexity of recognition is an exponential function of m.The necessary condition under which the complexity of recognition is polynomial is given.