We reelaborate on the basic properties of PT symmetry from a geometrical Perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

Atherosclerosis (AS) is a chronic progressive disease caused by various factors, and causes various cerebrovascular and cardiovascular diseases (CVDs). Reducing the plasma levels of low-density lipoprotein-cholesterol (LDL-C) is the primary goal in preventing and treating AS. Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9) plays a crucial role in regulating LDL-C metabolism. Panax notoginseng has potent lipid-reducing effects and protects against CVDs, and its saponins induce vascular dilatation, inhibit thrombus formation, and are used in treating CVDs. However, the anti-AS effect of the secondary metabolite, 20(S) -protopanaxatriol (20(S)-PPT), remains unclear. In this study, the anti-AS effect and molecular mechanism of 20(S)-PPT were investigated in vivo and in vitro by western blotting, real time-polymerase chain reaction (RT-PCR), Enzyme-linked Immunosorbent Assay (ELISA), immunofluorescence staining, and other assays. The in vitro experiments revealed that 20(S)-PPT reduced the levels of PCSK9 in the supernatant of HepG2 cells, upregulated low density lipoprotein receptor (LDLR) protein levels, promoted LDL uptake by HepG2 cells, and reduced PCSK9 mRNA transcription by upregulating the levels of FoxO3 protein and mRNA and decreasing the levels of HNF1α protein and mRNA. The in vivo experiments revealed that 20(S)-PPT upregulated aortic αSMA expression, increased the stability of atherosclerotic plaques, and reduced aortic plaque formation induced by a high-cholesterol fed in ApoE-/- mice (HCF group). Additionally, 20(S)-PPT reduced the aortic expression of CD68, reduced inflammation in the aortic root, and alleviated the hepatic lesions in the HCF group. The study revealed that 20(S)-PPT inhibited LDLR degradation via PCSK9 to alleviate AS.

Magnetic nanoparticles based on iron oxides (MNPs-Fe) with magnetite or maghemite phases have been widely employed in bio-applications. Thus, they have been used as contrast agents in magnetic resonance imaging (MRI) and oncological treatments through different therapies. Besides, due to the vast health problem of multidrug-resistant bacterial infections, several studies have proposed MNPs-Fe as photothermal agents (PTAs) within antibacterial photothermal therapy (PTT). This work presents a quick and easy green synthesis (GS) to obtain MNPs-Fe using orange peel extract from orange waste from local commerce, which presents an environmentally friendly approach compared to traditional methods such as coprecipitation. The GS can be irradiated with microwaves to reduce the synthesis time drastically. We evaluated the weight yield of the GS and the physical-chemical and magnetic features of the synthesized MNPs-Fe. Besides their cytotoxicity in animal cell line ATCC RAW 264.7, their antibacterial activity against Staphylococcus Aureus (S. Aureus) and Escherichia Coli (E. Coli) was assessed. We found that the MNPs-Fe synthesized using the GS, with 50% v/v of NH4OH and 50% v/v of orange peel extract (50GS-MNPs-Fe) had an excellent weight yield, negligible cytotoxicity for concentrations of MNPs-Fe below 250 µg·mL-1 in 24 hours, and 8 days. In the MNPs-Fe surface, we identified a coating of organic molecules (~ 25 nm) such as terpenes, aldehydes, etc. MNPs-Fe inhibited S. Aureus and 2.54 log10 (CFU) of E. Coli under red LED light irradiation (630 nm, 65.5 mW·cm-2, 30 min). Likewise, they exhibited a superparamagnetic (SPM) behavior for temperatures above 60 K, with a size of 49.3±9.6 nm and saturation magnetization (Ms) of 72.83 and 44.16 emu·g-1 at 60 and 300 K, respectively. Therefore, 50GS-MNPs-Fe are excellent candidates as broad-spectrum PTAs in antibacterial PTT, magnetic hyperthermia (MH), or MRI.

Current pharmacological treatments of Fibromyalgia (FM) are merely symptom palliative, as clinical trials have so far failed to provide overall benefits without associated harms. Polypharmacy often leads to patient´s health deterioration and chronic drug use to an eventual lack of patient´s response. Emerging evidence support that physiotherapy treatments based on mechanical triggers improve FM symptoms and therefore could be used for therapeutic purposes by themselves, or in combination with current pharmacological treatments, as part of integrative medicine programs. However, a paucity of studies rigorously and systematically evaluating this possibility exists. This study uses scores from validated standardized questionnaires, algometer pressure point threshold (PPT) readings and responses from a custom self-developed questionnaire to determine the impact of a pressure-controlled manual protocol on FM hyperalgesia/allodynia, fatigue and patient´s quality of life. The results show that patient´s baseline sensitivity to pain inversely correlates with treatment response in FM. Moreover, patients presenting comorbid ME/CFS do not seem to respond to the applied therapy as those presenting FM only. Thus, pre-treatment PPTs and ME/CFS comorbidity may serve as indicators to predict patient´s response to physiotherapy programs based on mechanical triggers, as the one evaluated here. These unexpected findings grant further explorations including the study of gene expression profiles associating to patient´s treatment response in the blood collection of samples generated by this study.