Alternated Superior Chaotic Biogeography Based Algorithm for Optimization Problems

In this study, we consider a switching strategy that yields a stable desirable dynamic behaviour when it is applied alternatively between two undesirable dynamical systems. From the last few years, dynamical systems employed “chaos1 + chaos2 = order” and “order1 + order2 = chaos” (vice-versa) to control and anti control of chaotic situations. To find parameter values for these kind of alternating situations, comparison is being made between bifurcation diagrams of a map and its alternate version, which, on their own, means independent of one another, yield chaotic orbits. However, the parameter values yield a stable periodic orbit, when alternating strategy is employed upon them. It is interesting to note that we look for stabilization of chaotic trajectories in nonlinear dynamics, with the assumption that such chaotic behaviour is not desirable for a particular situation. The method described in this paper is based on the Parrondo’s paradox, where two losing games can be alternated, yielding a winning game, in a superior orbit.

The skull

The human skull is the skeleton of the head and is considered along with the mandible. It consists of paired bones and unpaired midline bones that contribute to the muscular attachments for mastication and facial expression, a bony foundation for the upper aerodigestive tract and support and housing for the special sensory organs, brain and other structures susceptible to trauma. The skull without the mandible is termed the cranium and consists of the neurocranium and viscerocranium (facial skeleton). The upper third of the skull is principally formed by the frontal bones and exaggerated at the superciliary ridges of the superior orbit and smooth glabella region centrally. The paired maxillary bones form the middle third, creating the circumference of the piriform aperture between, and are separated from the frontal and temporal bones by the zygoma laterally. They house the maxillary sinuses and meet in the midline inferiorly to form the upper jaw and most of the hard palate at the intermaxillary suture.

Orbital Rhabdomyosarcoma – A Case Series of 12 Patients from North – West Pakistan

Purpose: The purpose of this study is to find out demographic characteristics, clinical behavior and outcome of this neoplasm in North West Pakistan. Study Design: Retrospective Case series. Place and Duration of Study: Department of Ophthalmology, Khyber Teaching Hospital Peshawar Pakistan, from 2015 to 2019. Methods: All patients with Orbital Rhabdomyosarcoma consulting our department were registered and a self-designed proformawas used to document demography, clinical features, management, and follow-up of all cases. At the end of study, the data was analyzed using SPSS version 25 and result compiled. Results: Twelve patients with “Orbital Rhabdomyosarcoma” were included in the study with mean age of7.2 ± 1.6 years. Majority of patients presented with mass in upper lid with proptosis. On CT-Scan and/or MRI orbit proved that in seven (58.3%) cases the mass was occupying the superior orbit, in 3 (25%) cases inferior orbit and in 2 (16.6%) cases the tumor was advance enough to occupy the whole orbit.Biopsy showed embryonic type (66.7%), alveolar type (25%) and undifferentiated (8.3%). All patients received chemotherapy and radiotherapy with excision of tumor in 16.7% and exenteration in 41.7% patients. The course of follow-up extended from 7 to 24 months. Five (41.7%) patients felt well at the end of last follow-up and four (33.3%) developed recurrence. At the end of follow-up, 3 (25%) patients died of tumor. Conclusion: In North West Pakistan patients with Orbital Rhabdomyosarcoma present late and the prognosis is poor due to not following the proper protocol for follow-up. Key Words: Rhabdomyosarcoma, Orbital rhabdomyosarcoma, IRS Staging.

Assessment of the Learning Curve for Virtual Surgical Planning in Orbital Fractures

Virtual surgical planning (VSP) is becoming more widely used in maxillofacial reconstruction and can be surgeon-based or industry-based. Surgeon-based models require software training but allow surgeon autonomy. We evaluate the learning curve for VSP through a prospective cohort study in which planning times and accuracy of 7 otolaryngology residents with no prior VSP experience were compared to that of a proficient user after a single training protocol and 6 planning sessions for orbital fractures. The average planning time for the first session was 21 minutes 41 seconds ± 6 minutes 11 seconds with an average maximum deviation of 2.5 ± 0.8 mm in the lateral orbit and 2.3 ± 0.6 mm in the superior orbit. The average planning time for the last session was 13 minutes 5 seconds ± 10 minutes and 7 seconds with an average maximum deviation of 1.4 ± 0.5 mm in the lateral orbit and 1.3 ± 0.4 mm in the superior orbit. Novice users reduced planning time by 40% and decreased maximum deviation of plans by 44% and 43% in the lateral and superior orbits, respectively, approaching that of the proficient user. Virtual surgical planning has a quick learning curve and may be incorporated into surgical training.

Bifurcation Analysis of Logistic Map using Four Step Feedback Procedure

The logistic map occupies a renowned place in the dynamics of chaos theory and in diverse areas of science. Picard orbit and Superior orbit (Mann orbit) have been used to control this discrete chaotic dynamical system. In this article, we further extend the analytical study of logistic map using a four step feedback procedure (SP orbit). The dynamical properties such as fixed point, range of convergence and stability, periodicity and chaos of the logistic map have been investigated. These properties are illustrated experimentally by adopting dynamical techniques like fixed point analysis and bifurcation plot. Using this approach, one can easily control the chaotic system and make the system stable for higher values of population growth parameter r by selecting the control parameters carefully.

Traumatic Orbital Apex Syndrome: An Uncommon Sequela of Facial Trauma

Orbital apex syndrome (OAS) is a rare ocular complication following craniomaxillofacial trauma. This traumatic syndrome is a combination of features seen in both superior orbital fissure syndrome and traumatic orbital neuropathy due to nerve impingement. Due in part to the rarity of this disorder, the optimal treatment of traumatic OAS has yet to be determined. We present a case in which traumatic OAS was caused by direct compression due to a displaced fracture segment from the superior orbit. The patient was successfully treated with a combination of emergent decompression and urgent reconstruction suggesting that this may be an effective strategy in OAS resulting from direct nerve compression as a result of craniomaxillofacial fracture.