Our study essentially concerns the dynamic behavior of an SIRS epidemic model in discrete time. Two equilibrium points are obtained; one is disease-free while the other is endemic. We are interested in the endemic fixed point as well as its asymptotic stability. Depending on the parameters which are estimated using the data from US Department of health and SIRS modelling with optimization, two Flip and Transcritical bifurcations appear. We illustrate their diagrams, as well as their bifurcation curves using the method of Carcasses \cite{carcasses1993determination,carcasses1995singularities} for the Flip bifurcation and by an implicit function deduced from such an equation for the Transcritical bifurcation. We use the scanning of the parametric plane to have a global view of the behavior of the model and to highlight the zones of stability of the existing singularities. A superposition of the bifurcation curves with the parametric plane can show the overlap of the curves with the boundaries of the stability domains, which confirms the smooth running of the simulation and its correspondence with the theory, we finish this article with constrained optimal control applied to infection rate and recruitment rate for an SIRS discrete epidemic model. Pontryagin's maximum principle is used to determine these optimal controls. Finally using COVID-19 data in the USA, we obtain results that demonstrate the effectiveness of the proposed control strategy to mitigate the spread of the pandemic.

Abstract:Background: Foot ulcers, especially dorsal foot ulcers caused by straps in footwear, can lead to discomfort, pain, and severe complications, particularly in individuals with diabetes and leprosy. While plantar foot pressure measurements have been extensively studied, research on the impact of strap-induced pressure on the dorsal foot aspect remains limited.Research question: The main research question of this prospective study is: Does the implementation of a rolled inner seam strap design (RIS) in flip-flops result in reduced pressure at the toehold area compared to traditional strap designs (Control) in healthy volunteers?Methods: We studied healthy female volunteers, with 10 feet (5 left and 5 right) per arm of the study. Two types of flip-flops, RIS and Control, were compared in a standardized 5-step walk trial on a hardwood floor. Pressure at the toehold was measured using Pressure Sensitive Switches with portable, accurate, ultra-thin pressure sensors. Paired t-tests compared the maximum pressure at the toehold between RIS and Control flip-flops (p < 0.05).Results: The study revealed a statistically significant difference in pressure at the toehold between the RIS and Control flip-flops (p = 0.0014). The mean difference of -40.90 grams (95% CI: -61.22 to -20.58) indicated that the RIS exerted significantly lower pressure than the Control flip flops. The RIS group had a mean pressure of 29.30 grams. The Control group had a mean pressure of 70.20 grams at the toehold area.Significance: The findings of this study have significant clinical implications for individuals at risk of foot ulcers, particularly those with neuropathic conditions such as diabetes and leprosy. The implementation of the RIS design in flip-flops may offer a practical and cost-effective solution to reduce strap-induced pressure and mitigate the risk of strap-related foot ulcers, especially in resource-limited settings where comprehensive foot care is lacking.

Background and Objectives: The existing recommendations for female pelvic magnetic susceptibility weighted imaging MRI (FP-SWI) have not been optimized to capture the disease characteristics of the female pelvis. Therefore, it is imperative to explore acquisition parameters before conducting larger-scale studies. To establish optimized flip angle (FA) for acquiring FP-SWI to improve the image quality of female pelvic lesion sites. Materials and Methods: To evaluate signal quality and lesion conspicuity, regions of interest (ROIs) were manually drawn within the lesion on SWI sequences. Signal intensity was measured within the ROIs. Additionally, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were calculated for SWI sequences acquired at three FA: 10°, 15°, and 20°. Finally, a qualitative assessment of anatomical detail visualization, geometric distortion extent, artifacts, and lesion clarity was performed using a four-point scale. The Wilcoxon rank sum test was employed to compare the qualitative evaluation parameters. The intra-class correlation coefficient (ICC) was calculated to determine the consistency of subjective ratings between two observers. Results: FA=10° showed significantly higher SNR than FA=15° and 20° in most anatomical regions (P&lt;0.05), while the CNR was significantly higher than FA=15° and 20° (P&lt;0.05). Compared with FA=15° and 20°, the image quality of FA=10° was significantly higher, with less distortion and ghosting, and better image contrast (P&lt;0.05). Lesions with FA=10° exhibited higher clarity compared to FA=15° and 20° (P&lt;0.05). Conclusions: The image quality of FP-SWI images at FA=10° exceeds that at FA=15° and 20°. We recommend that when conducting SWI examination of the female pelvic cavity, the FA value should be set at 10° to stabilize the SWI sequence and improve image quality.

The catalytically inactive caspase-8-homologous protein, c-FLIP, is a potent antiapoptotic protein highly expressed in various types of cancers. c-FLIP competes with caspase-8 for binding to the adaptor protein FADD (Fas-Associated Death Domain) following Death Receptors (DRs) activation by the ligands of the TNF-R family. As a consequence, the extrinsic apoptotic signaling pathway involving DRs is inhibited. Inhibition of c-FLIP activity in tumor cells might enhance DR-mediated apoptosis and overcome immune and anticancer drug resistance. Based on an in silico approach, the aim of this work was to identify, new small inhibitory molecules able to bind selectively to c-FLIP and block its anti-apoptotic activity. Using a homology 3D model of c-FLIP, an in silico screening of 1880 compounds from the NCI database (National Cancer Institute) was performed. Nine molecules were selected for in vitro assays, based on their binding affinity to c-FLIP and their high selectivity compared to caspase-8. These compounds selectively bind to the Death Effector Domain 2 (DED2) of c-FLIP. We have tested in vitro the inhibitory effect of these 9 molecules using the human lung cancer cell line H1703 overexpressing c-FLIP. Our results showed that 6 of these newly identified compounds efficiently prevent FADD/c-FLIP interactions in a molecular pull-down assay, as well as in a DISC Immunoprecipitation assay. Overexpression of c-FLIP in H1703 prevents TRAIL-mediated apoptosis, however, combination of TRAIL with these selected molecules signifi-cantly restored TRAIL-induced cell death by rescuing caspase cleavage and activation. Altogether, our findings indicate that new inhibitory chemical compounds efficiently prevent c-FLIP recruit-ment into the DISC complex, thus restoring caspase-8 dependent apoptotic cascade. These results pave the way to design new c-FLIP inhibitory compounds that may serve as anticancer agents in tumors overexpressing c-FLIP.

The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The PQ penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper we investigate all possible finite games that can be played between the two players Q and Picard of the original PQ game. For this purpose we establish a rigorous connection between finite automata and the PQ game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the PQ game. What this means is that from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

The quadratic unconstrained binary optimization (QUBO) is a classic NP-hard problem with an enormous number of applications. Local search strategy (LSS) is one of the most fundamental algorithmic concepts that has been successfully applied to a wide range of hard combinatorial optimization problems. One LSS that has gained the attention of researchers is the r-flip (also known as r-Opt) strategy. Given a binary solution with n variables, the r-flip strategy ‘flips’ r binary variables to get a new solution if the changes improve the objective function. The main purpose of this paper is to develop several results for implementation of r-flip moves in QUBO, including a necessary and sufficient condition that when a 1-flip search reaches local optimality, the number of candidates for implementation of the r-flip moves can be reduced significantly. The results of the substantial computational experiments are reported to compare an r-flip strategy embedded algorithm and a multiple start tabu search algorithm on a set of benchmark instances and three very-large-scale QUBO instances. The r-flip strategy implemented within the algorithm makes the algorithm very efficient, very high-quality solutions within a short CPU time.

Objective: To compare the incidence of skin abrasions caused by traditional straight edge flip flop straps versus rolled inner seam (RIS) designs in a controlled laboratory setting using preserved fetal pig skin as a proxy for human skin.Methods: This study utilized a custom-built apparatus to apply friction from two flip flop strap designs to preserved fetal pig skin samples. Three trials were conducted for each strap design to determine the time to initial abrasion onset. A paired t-test was employed for statistical analysis.Results: The RIS design demonstrated a statistically significant delay in abrasion onset compared to the standard design across all trials (p < 0.05), indicating a gentler interaction with the skin.Conclusion: The RIS strap design may offer a beneficial alternative to traditional straps by reducing the friction that can lead to skin abrasions, suggesting a potential to decrease the risk of dorsal foot ulcers. Further studies involving human subjects are warranted to validate these findings in a real-world context.Keywords: Flip flop strap design, skin abrasions, dorsal foot ulcers, footwear design, developing countries, diabetic foot care.

Conjugated singlet ground state diradicals have received remarkable attention owing to their potential applications in optoelectronic devices. A distinctive character of these systems is the location of the double exciton state, a low lying excited state dominated by the doubly excited H,H→L,L configuration, which may influence optical and other photophysical properties. In this contribution we investigate this specific excited state, for a series of recently synthesized conjugated diradicals, employing time dependent density functional theory based on the unrestricted parallel spin reference configuration in the spin-flip formulation (SF-TDDFT) and standard TD calculations based on the unrestricted antiparallel spin reference configuration (TDUDFT). The quality of the computed results is assessed considering diradical and multiradical descriptors and the excited state wavefunction composition.