Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution $P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,...$, independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the H$\acute{e}$non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.Comment: 23 pages, 12 figure

Entropy Production on Cooperative Opinion Dynamics

As one of the most widespread social dynamics, cooperative behavior is among the most fascinating collective phenomena. Several animal species, from social insects to human beings, feature social groups altruistically working for a common benefit. This collaborative conduct pervades the actions and opinions of individuals, yielding strategic decision-making between political, religious, ethnic, and economic social puzzles. Here, we explore how cooperative behavior phenomena impact collective opinion dynamics and entropy generation in social groups. We select a random fraction $f$ of community members as collaborative individuals and model the opinion dynamics using a social temperature parameter $q$ that functions as a social anxiety noise. With probability $q$, regular individuals oppose their companions about a social decision, assuming group dissent. Collaborative agents experience a reduced effective social noise $\mu q$, where $0 < \mu < 1$ is the social anxiety noise sensibility parameter that enhances social validation. We perform numerical simulations and mean-field analysis and find the system undergoes nonequilibrium order-disorder phase transitions with expressive social entropy production. Our results also highlight the effects of an individual social anxiety attenuation level in enhancing group consensus and inducing exuberant collective phenomena in complex systems

Longitudinal clinical, cognitive and biomarker profiles in dominantly inherited versus sporadic early-onset Alzheimer's disease

Approximately 5% of Alzheimer's disease cases have an early age at onset (<65 years), with 5-10% of these cases attributed to dominantly inherited mutations and the remainder considered as sporadic. The extent to which dominantly inherited and sporadic early-onset Alzheimer's disease overlap is unknown. In this study, we explored the clinical, cognitive and biomarker profiles of early-onset Alzheimer's disease, focusing on commonalities and distinctions between dominantly inherited and sporadic cases. Our analysis included 117 participants with dominantly inherited Alzheimer's disease enrolled in the Dominantly Inherited Alzheimer Network and 118 individuals with sporadic early-onset Alzheimer's disease enrolled at the University of California San Francisco Alzheimer's Disease Research Center. Baseline differences in clinical and biomarker profiles between both groups were compared using t-tests. Differences in the rates of decline were compared using linear mixed-effects models. Individuals with dominantly inherited Alzheimer's disease exhibited an earlier age-at-symptom onset compared with the sporadic group [43.4 (SD +/- 8.5) years versus 54.8 (SD +/- 5.0) years, respectively, P < 0.001]. Sporadic cases showed a higher frequency of atypical clinical presentations relative to dominantly inherited (56.8% versus 8.5%, respectively) and a higher frequency of APOE-epsilon 4 (50.0% versus 28.2%, P = 0.001). Compared with sporadic early onset, motor manifestations were higher in the dominantly inherited cohort [32.5% versus 16.9% at baseline (P = 0.006) and 46.1% versus 25.4% at last visit (P = 0.001)]. At baseline, the sporadic early-onset group performed worse on category fluency (P < 0.001), Trail Making Test Part B (P < 0.001) and digit span (P < 0.001). Longitudinally, both groups demonstrated similar rates of cognitive and functional decline in the early stages. After 10 years from symptom onset, dominantly inherited participants experienced a greater decline as measured by Clinical Dementia Rating Sum of Boxes [3.63 versus 1.82 points (P = 0.035)]. CSF amyloid beta-42 levels were comparable [244 (SD +/- 39.3) pg/ml dominantly inherited versus 296 (SD +/- 24.8) pg/ml sporadic early onset, P = 0.06]. CSF phosphorylated tau at threonine 181 levels were higher in the dominantly inherited Alzheimer's disease cohort (87.3 versus 59.7 pg/ml, P = 0.005), but no significant differences were found for t-tau levels (P = 0.35). In summary, sporadic and inherited Alzheimer's disease differed in baseline profiles;sporadic early onset is best distinguished from dominantly inherited by later age at onset, high frequency of atypical clinical presentations and worse executive performance at baseline. Despite these differences, shared pathways in longitudinal clinical decline and CSF biomarkers suggest potential common therapeutic targets for both populations, offering valuable insights for future research and clinical trial design

Hypothalamic Neuroendocrine Functions in Rats with Dihydrotestosterone-Induced Polycystic Ovary Syndrome: Effects of Low-Frequency Electro-Acupuncture

Adult female rats continuously exposed to androgens from prepuberty have reproductive and metabolic features of polycystic ovary syndrome (PCOS). We investigated whether such exposure adversely affects estrous cyclicity and the expression and distribution of gonadotropin-releasing hormone (GnRH), GnRH receptors, and corticotrophin-releasing hormone (CRH) in the hypothalamus and whether the effects are mediated by the androgen receptor (AR). We also assessed the effect of low-frequency electro-acupuncture (EA) on those variables. At 21 days of age, rats were randomly divided into three groups (control, PCOS, and PCOS EA; n = 12/group) and implanted subcutaneously with 90-day continuous-release pellets containing vehicle or 5α-dihydrostestosterone (DHT). From age 70 days, PCOS EA rats received 2-Hz EA (evoking muscle twitches) five times/week for 4–5 weeks. Hypothalamic protein expression was measured by immunohistochemistry and western blot. DHT-treated rats were acyclic, but controls had regular estrous cycles. In PCOS rats, hypothalamic medial preoptic AR protein expression and the number of AR- and GnRH-immunoreactive cells were increased, but CRH was not affected; however, GnRH receptor expression was decreased in both the pituitary and hypothalamus. Low-frequency EA restored estrous cyclicity within 1 week and reduced the elevated hypothalamic GnRH and AR expression levels. EA did not affect GnRH receptor or CRH expression. Interestingly, nuclear AR co-localized with GnRH in the hypothalamus. Thus, rats with DHT-induced PCOS have disrupted estrous cyclicity and an increased number of hypothalamic cells expressing GnRH, most likely mediated by AR activation. Repeated low-frequency EA normalized estrous cyclicity and restored GnRH and AR protein expression. These results may help explain the beneficial neuroendocrine effects of low-frequency EA in women with PCOS

Reduced Bone Mass and Muscle Strength in Male 5α-Reductase Type 1 Inactivated Mice

Androgens are important regulators of bone mass but the relative importance of testosterone (T) versus dihydrotestosterone (DHT) for the activation of the androgen receptor (AR) in bone is unknown. 5α-reductase is responsible for the irreversible conversion of T to the more potent AR activator DHT. There are two well established isoenzymes of 5α-reductase (type 1 and type 2), encoded by separate genes (Srd5a1 and Srd5a2). 5α-reductase type 2 is predominantly expressed in male reproductive tissues whereas 5α-reductase type 1 is highly expressed in liver and moderately expressed in several other tissues including bone. The aim of the present study was to investigate the role of 5α-reductase type 1 for bone mass using Srd5a1−/− mice. Four-month-old male Srd5a1−/− mice had reduced trabecular bone mineral density (−36%, p<0.05) and cortical bone mineral content (−15%, p<0.05) but unchanged serum androgen levels compared with wild type (WT) mice. The cortical bone dimensions were reduced in the male Srd5a1−/− mice as a result of a reduced cortical periosteal circumference compared with WT mice. T treatment increased the cortical periosteal circumference (p<0.05) in orchidectomized WT mice but not in orchidectomized Srd5a1−/− mice. Male Srd5a1−/− mice demonstrated a reduced forelimb muscle grip strength compared with WT mice (p<0.05). Female Srd5a1−/− mice had slightly increased cortical bone mass associated with elevated circulating levels of androgens. In conclusion, 5α-reductase type 1 inactivated male mice have reduced bone mass and forelimb muscle grip strength and we propose that these effects are due to lack of 5α-reductase type 1 expression in bone and muscle. In contrast, the increased cortical bone mass in female Srd5a1−/− mice, is an indirect effect mediated by elevated circulating androgen levels