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The new Coronavirus or simply Covid-19 causes an acute deadly disease. It has spread rapidly across the world, which has caused serious consequences for health professionals and researchers. This is due to many reasons including the lack of vaccine, shortage of testing kits and resources. Therefore, the main purpose of this study is to present an inexpensive alternative diagnostic tool for the detection of Covid-19 infection by using chest radiographs and Deep Convolutional Neural Network (DCNN) technique. In this paper, we have proposed a reliable and economical solution to detect COVID-19. This will be achieved by using X-rays of patients and an Incremental-DCNN (I-DCNN) based on ResNet-101 architecture. The datasets used in this study were collected from publicly available chest radiographs on medical repositories. The proposed I-DCNN method will help in diagnosing the positive Covid-19 patient by utilising three chest X-ray imagery groups, these will be: Covid-19, viral pneumonia, and healthy cases. Furthermore, the main contribution of this paper resides on the use of incremental learning in order to accommodate the detection system. This has high computational energy requirements, time consuming challenges, while working with large-scale and regularly evolving images. The incremental learning process will allow the recognition system to learn new datasets, while keeping the convolutional layers learned previously. The overall Covid-19 detection rate obtained using the proposed I-DCNN was of 98.70\% which undeniably can contribute effectively to the detection of COVID-19 infection.

In our research, we are interested in the three-dimensional multiple-bin-size bin packing problem (MBSBPP). We deal with the real word application of cutting mousse blocks proposed by a Tunisian industrial company. First, we present the general context related to our optimization problem. Second we formulate it as a mathematical problem without considering the guillotine constraint, and then we tested it on small instances taken from the industry. Thereafter, we propose and test a lower bound for large instances from the same industrial company. Finally, some computational results are presented.

The cutting and packing problem belongs to the combinatorial optimization problems; it covers a wide range of practical cases in industries. The present paper investigates a new real world problem needs to be solved through a daily operations of cutting foam blocks in an industrial company. The problem is considered as one of non-classical problems in the cutting and packing area. It represents a variant of the three dimensional Cutting Stock Problem. The originality of the studied problem is indicated by a specific set of constraints related to the production process and the cutting ways. A constructive heuristic was developed to provide cutting patterns in advance. All possible combinations established from the ways of cutting right rectangular prisms from foam blocks define the cutting patterns. This heuristic performs well and shows promising results in reasonable computational times to provide efficient cutting plans in order to reduce the total material loss.

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