Stable marriage and roommates problems with restricted edges: complexity and approximability

In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs. Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs. Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs

The role of intradiscal steroids in the treatment of discogenic low back pain

LBP is one of the most common reasons for visiting a doctor and is the most common cause of disability under age 45.Amongst a variety of etiologies, internal disc disruption (IDD) has been postulated as an important cause of low back pain. Treating discogenic low back pain continues to be a challenge to physicians. Inflammation, either from direct chemical irritation or secondary to an autoimmune response to the nucleus pulposus has been implicated as the primary pain source. Both steroids and non-steroidal anti-inflammatory drugs have partial effectiveness in treating pain associated with inflammation. Therefore, the rationale for using intradiscal steroids is to suppress the inflammation within the disc, thereby alleviating the patient’s symptoms. The goal of this article is to review the literature regarding the efficacy of intradiscal steroids to treat low back pain of discogenic origin

Application of an electronic nose coupled with fuzzy-wavelet network for the detection of meat spoilage

Food product safety is one of the most promising areas for the application of electronic noses. During the last twenty years, these sensor-based systems have made odour analyses possible. Their application into the area of food is mainly focused on quality control, freshness evaluation, shelf-life analysis and authenticity assessment. In this paper, the performance of a portable electronic nose has been evaluated in monitoring the spoilage of beef fillets stored either aerobically or under modified atmosphere packaging, at different storage temperatures. A novel multi-output fuzzy wavelet neural network model has been developed, which incorporates a clustering pre-processing stage for the definition of fuzzy rules. The dual purpose of the proposed modelling approach is not only to classify beef samples in the relevant quality class (i.e. fresh, semi-fresh and spoiled), but also to predict their associated microbiological population. Comparison results against advanced machine learning schemes indicated that the proposed modelling scheme could be considered as a valuable detection methodology in food microbiology

Hydrothermal deposition of CdS on vertically aligned ZnO nanorods for photoelectrochemical solar cell application

CdS/ZnO nanorods composite nanofilms were successfully synthesized via hydrothermal method on indium doped tin oxide glass substrates. Sequentially deposited CdS formed cauliflower like nanostructures on vertically aligned ZnO nanorods. The morphological, compositional, structural and optical properties of the films were characterized by field emission scanning electron microscopy, energy dispersive X-ray analysis, X-ray diffraction and ultraviolet–visible spectroscopy. Photoelectrochemical conversion efficiencies were evaluated by photocurrent measurements in a mixture of Na2S and Na2SO3 akaline aqueous solution. The amount of deposit, as well as the diameter and crystallinity of the CdS cauliflower were found to increase with growth time. CdS/ZnO nanorods composite exhibited greater photocurrent response than ZnO nanorod arrays. Besides, the composite film with 90 min of growth duration displayed the highest photocurrent density which is nearly four times greater than plain ZnO nanorods under the illumination of halogen light. The result exhibited remarkable photoconversion efficiency (η) of 1.92 %