Many works have shown strong connections between learning and regularization techniques for ill-posed inverse problems. A careful analysis shows that a rigorous connection between learning and regularization for inverse problem is not straightforward. In this study, pattern recognition will be viewed as an ill-posed inverse problem and applications of methods from the theory of inverse problems to pattern recognition are studied. A new learning algorithm derived from a well-known regularization model is generated and applied to the task of reconstruction of an inhomogeneous object as pattern recognition. Particularly, it is demonstrated that pattern recognition can be reformulated in terms of inverse problems defined by a Riesz-type kernel. This reformulation can be employed to design a learning algorithm based on a numerical solution of a system of linear equations. Finally, numerical experiments have been carried out with synthetic experimental data considering a reasonable level of noise. Good recoveries have been achieved with this methodology, and the results of these simulations are compatible with the existing methods. The comparison results show that the Regularization-based learning algorithm (RBA) obtains a promising performance on the majority of the test problems. In prospects, this method can be used for the creation of automated systems for diagnostics, testing, and control in various fields of scientific and applied research, as well as in industry.

Extensive research has been devoted to the multi-mode resource constrained project scheduling problem (MRCPSP). However, little attention has been paid to problems where preemption is allowed. This paper involves the preemptive multi-mode resource constrained project scheduling problem (P-MRCPSP) to minimize the project makespan subject to mode changeability after preemption. This problem is a more realistic model and extended case of multi-mode resource constrained project scheduling problem. A binary integer programing formulation is proposed for the problem. The problem formed in this way is an NP-hard one forcing us to use the Simulated Annealing (SA) algorithm to obtain a global optimum solution or at least a satisfying one. The performance of the proposed algorithm is evaluated on 480 test problems by statistically comparing in term of the objective function and computational times. The obtained computational results indicate that the proposed algorithm is efficient and effective. Also, it is concluded from the results that mode change is very effective to improve the optimal makespan of the project.

Depression is considered to be a chronic mood disorder. This paper attempts to mathematically model how psychiatrists clinically perceive the symptoms and then diagnose depression states. According to Diagnostic and Statistical Manual (DSM)-IV-TR, fourteen symptoms of adult depression have been considered. The load of each symptom and the corresponding severity of depression are measured by the psychiatrists (i.e. the domain experts). Using the Principal Component Analysis (PCA) out of fourteen symptoms (as features) seven has been extracted as latent factors. Using these features as inputs, a hybrid system consisting of Mamdani’s Fuzzy logic controller (FLC) on a Feed Forward Multilayer Neural Net (FFMNN) has been developed. The output of the hybrid system was tuned by a back propagation (BPNN) algorithm. Finally, the model is validated using 302 real-world adult depression cases and 50 controls (i.e. normal population). The study concludes that the hybrid controller can diagnose and grade depression with an average accuracy of 95.50%. Finally, it is compared with the accuracies obtained by other techniques.