Simple (γ, δ) algebras are associative

AbstractA (γ, δ) algebra over a field F is a nonassociative algebra satisfying an identity of the form, (a, b, c) + γ(b, a, c) + δ(c, a, b) = 0, for fixed γ, δ ϵ F, and γ2 − δ2 + δ = 1. We assume that F is of characteristic ≠ 2, ≠ 3; however, we do not assume that the algebra is finite-dimensional over F. We show that any simple (γ, δ) algebra is associative with the possible exception of the cases (± 1, 0) and (1, 1). The approach used in this paper is to represent the identities by matrices by way of the group algebra representation. This enables us to manipulate identities by the well-known techniques of matrix theory

Simple (γ, δ) algebras are associative

AbstractA (γ, δ) algebra over a field F is a nonassociative algebra satisfying an identity of the form, (a, b, c) + γ(b, a, c) + δ(c, a, b) = 0, for fixed γ, δ ϵ F, and γ2 − δ2 + δ = 1. We assume that F is of characteristic ≠ 2, ≠ 3; however, we do not assume that the algebra is finite-dimensional over F. We show that any simple (γ, δ) algebra is associative with the possible exception of the cases (± 1, 0) and (1, 1). The approach used in this paper is to represent the identities by matrices by way of the group algebra representation. This enables us to manipulate identities by the well-known techniques of matrix theory

Acellular Dermal Matrices and Radiotherapy in Breast Reconstruction: A Systematic Review and Meta-Analysis of the Literature

The increasing use of commercially available acellular dermis matrices for postmastectomy breast reconstruction seems to have simplified the surgical procedure and enhanced the outcome. These materials, generally considered to be highly safe or with only minor contraindications due to the necessary manipulation in preparatory phases, allow an easier one-phase surgical procedure, in comparison with autologous flaps, offering a high patient satisfaction. Unfortunately, the claim for a higher rate of complications associated with irradiation at the implant site, especially when the radiation therapy was given before the reconstructive surgery, suggested a careful behaviour when this technique is preferred. However, this hypothesis was never submitted to a crucial test, and data supporting it are often discordant or incomplete. To provide a comprehensive analysis of the field, we searched and systematically reviewed papers published after year 2005 and registered clinical trials. On the basis of a meta-analysis of data, we conclude that the negative effect of the radiotherapy on the breast reconstruction seems to be evident even in the case of acellular dermis matrices aided surgery. However, more trials are needed to make solid conclusions and clarify the poor comprehension of all the factors negatively influencing outcome

Cerebral Perfusion and Neuromonitoring during Complex Aortic Arch Surgery: A Narrative Review

: Complex ascending and aortic arch surgery requires the implementation of different cerebral protection strategies to avoid or limit the probability of intraoperative brain damage during circulatory arrest. The etiology of the damage is multifactorial, involving cerebral embolism, hypoperfusion, hypoxia and inflammatory response. These protective strategies include the use of deep or moderate hypothermia to reduce the cerebral oxygen consumption, allowing the toleration of a variable period of absence of cerebral blood flow, and the use of different cerebral perfusion techniques, both anterograde and retrograde, on top of hypothermia, to avoid any period of intraoperative brain ischemia. In this narrative review, the pathophysiology of cerebral damage during aortic surgery is described. The different options for brain protection, including hypothermia, anterograde or retrograde cerebral perfusion, are also analyzed, with a critical review of the advantages and limitations under a technical point of view. Finally, the current systems of intraoperative brain monitoring are also discussed

Natural history of non-lethal raine syndrome during childhood

Background: Raine syndrome (RS) is a rare autosomal recessive disorder caused by biallelic loss-of-function mutations of FAM20C. The most common clinical features are microcephaly, exophthalmos, hypoplastic nose and severe midface hypoplasia, leading to choanal atresia. The radiological findings include generalized osteosclerosis and brain calcifications. RS is usually lethal during the neonatal period due to severe respiratory distress. However, there exists a non-lethal RS form, the phenotype of which is extremely heterogeneous. There is paucity of data about clinical course and life expectancy of these patients.Results: This is the first description of follow-up features of non-lethal RS patients. Moreover, we present three unpublished cases. There are five Asian and two Arab patients. All were born to consanguineous parents. The most common neonatal comorbidity was respiratory distress secondary to choanal atresia. A variable degree of neurodevelopmental delay was seen in the majority of our cases and seizures and hearing or vision involvement were also frequent. Neurological and orthopedic issues were the most frequent complications seen at follow-up in our group. Persistent hypophosphatemic rickets was the most striking endocrinological manifestation, which was scarcely responsive to therapy with phosphate salts and alfacalcidol. Life expectancy of our patients goes beyond childhood, with the oldest of those described being 18 years old at present.Conclusions: Manifestations of RS in those surviving the neonatal period are being increasingly recognized. Our study supports previous findings and provides clinical and biochemical observations and data from longer follow up. Finally, we propose multidisciplinary follow up for patients with non-lethal RS

Predicting delirium in older non-intensive care unit inpatients: development and validation of the DELIrium risK Tool (DELIKT)

BACKGROUND Effective delirium prevention could benefit from automatic risk stratification of older inpatients using routinely collected clinical data. AIM Primary aim was to develop and validate a delirium prediction model (DELIKT) suitable for implementation in hospitals. Secondary aim was to select an anticholinergic burden scale as a predictor. METHOD We used one cohort for model development and another for validation with electronically available data collected within the first 24 h of admission. Included were patients aged ≥ 65, hospitalised ≥ 48 h with no stay > 24 h in an intensive care unit. Predictors, such as administrative and laboratory variables or an anticholinergic burden scale, were selected using a combination of feature selection filter method and forward/backward selection. The final model was based on logistic regression and the DELIKT was derived from the β-coefficients. We report the following performance measures: area under the curve, sensitivity, specificity and odds ratio. RESULTS Both cohorts were similar and included over 10,000 patients each (mean age 77.6 ± 7.6 years) with 11% experiencing delirium. The model included nine variables: age, medical department, dementia, hemi-/paraplegia, catheterisation, potassium, creatinine, polypharmacy and the anticholinergic burden measured with the Clinician-rated Anticholinergic Scale (CrAS). The external validation yielded an AUC of 0.795. With a cut-off at 20 points in the DELIKT, we received a sensitivity of 79.7%, specificity of 62.3% and an odds ratio of 5.9 (95% CI 5.2, 6.7). CONCLUSION The DELIKT is a potentially automatic tool with predictors from standard care including the CrAS to identify patients at high risk for delirium

Reversal of neurological deficits by painless nerve growth factor in a mouse model of Rett syndrome

: Rett syndrome is a rare genetic neurodevelopmental disease, affecting 1 in over 10,000 females born worldwide, caused by de novo mutations in the X-chromosome-located methyl-CpG-binding protein 2 (MeCP2) gene. Despite the great effort put forth by the scientific community, a therapy for this devastating disease is still needed. Here, we tested the therapeutic effects of a painless mutein of the Nerve Growth Factor, called human NGF painless (hNGFp), via a non-invasive intranasal delivery in female MeCP2+/- mice. Of note, previous work had demonstrated a broad biodistribution of hNGFp in the mouse brain by the nasal delivery route. We report that (1) the long-term lifelong treatment of MeCP2+/- mice with hNGFp, starting at 2 months of age, increased the chance of survival while also greatly improving behavioral parameters. Furthermore, when we assessed the phenotypic changes brought forth by (2) a short-term 1-month-long hNGFp-treatment, starting at 3 months of age (right after the initial presentation of symptoms), we observed the rescue of a well-known neuronal target population of NGF, cholinergic neurons in the medial septum. Moreover, we reveal a deficit in microglial morphology in MeCP2+/- mice, completely reversed in treated animals. This effect on microglia is in line with reports showing microglia to be a TrkA-dependent non-neuronal target cell population of NGF in the brain. To understand the immunomodulatory activity of hNGFp, we analyzed the cytokine profile after hNGFp treatment in MeCP2+/- mice, to discover that the treatment recovered the altered expression of key neuroimmune-communication molecules, such as fractalkine. The overall conclusion is that hNGFp delivered intranasally can ameliorate symptoms in the MeCP2+/- model of Rett syndrome, by exerting strong neuroprotection with a dual mechanism of action: directly on target neurons and indirectly via microglia

Longitudinal Study of Optic Disk Perfusion and Retinal Structure in Leber's Hereditary Optic Neuropathy

Purpose: The purpose of this study was to evaluate optic disk perfusion and neural retinal structure in patients with subacute Leber's hereditary optic neuropathy (LHON) and LHON carriers, as compared with healthy controls. Methods: This study included 8 patients with LHON in the subacute stage, 10 asymptomatic carriers of a LHON-associated mitochondrial DNA mutation, and 40 controls. All subjects underwent measurement of the retinal nerve fiber layer (RNFL) thickness, the ganglion cell-inner plexiform layer (GCIPL) thickness using optical coherence tomography and optic disk microvascular perfusion (Mean Tissue [MT]) using laser speckle flowgraphy (LSFG). Patients were re-examined after a median interval of 3 months from the baseline visit. Results: LHON carriers had higher values of RNFL thickness, GCIPL thickness, and disk area than controls (P < 0.05), whereas MT was not different between the two groups (P = 0.936). Median MT and RNFL thickness were 32% and 15% higher in the early subacute stage of the disease than in controls (P < 0.001 and P = 0.001). MT declined below the values of controls during the late subacute stage (P = 0.024), whereas RNFL thickness declined later during the dynamic stage (P < 0.001). GCIPL thickness was lower in patients with LHON than in controls independently of the stage of the disease (P < 0.001). Conclusions: The high blood flow at the optic disk during the early subacute stage may be the consequence of vasodilation due to nitric oxide release as compensation to mitochondrial impairment. Optic disk perfusion as measured by LSFG is a promising biomarker for LHON diagnosis and monitoring as well as an objective outcome measure for assessing response to therapies