Conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay.

We provide conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay. We prove that our conditions actually imply asymptotically stable equilibrium and delay independence. Conditions include the same marginal cost and equal probability for evading taxes. We give examples of cost and inverse demand functions satisfying the proposed conditions. Some economic interpretations of our results are also included.

A Mobile App (iBeni) With a Neuropsychological Basis for Cognitive Stimulation for Elderly Adults: Pilot and Validation Study.

BACKGROUND: Cognitive impairment is considered one of the most feared chronic conditions among the older adult population since its incidence is approximately twice more frequent than that of dementia. In Mexico, no studies or reports of older adults using technology for cognitive interventions have been published, given that institutions usually frame cognitive stimulation tasks in paper and pencil (ie, in the traditional manner). OBJECTIVE: The objective of this study was to create and analyze the effect, viability, and impact of a mobile app for cognitive stimulation implemented among a group of elderly adults (over 60 years of age) from the state of Hidalgo in Mexico. METHODS: This study was a nonprobabilistic pilot trial using convenience sampling. An intervention was implemented among a group of 22 older adults between 60 and 80 years of age over 12 weeks. Half of the older adults were stimulated with the mobile app (experimental group) and the other half followed the traditional paper and pencil training (control group). Assessments with the Mini-Mental State Examination (MMSE) and the Neuropsi, a neuropsychological test validated in Mexico, were done before and after both cognitive stimulations. RESULTS: According to the analyzed data, 6/11 (55%) participants from the experimental group obtained better results in their cognitive skills, and 5 (45%) of the adults maintained their score, given that the participants were able to execute the exercises repetitively. Meanwhile, for the control group, only 3/11 (27%) participants obtained better results in the postevaluation. Significant values for results of the MMSE were obtained in the postevaluation for the experimental group compared to the control group, while results did not show significant differences in the Neuropsi. Regarding the validation of the app, all the participants evaluated its pertinence positively. CONCLUSIONS: The intervention data show that the experimental group obtained better results in the postevaluation given that the participants were able to execute the exercises repetitively. The control group could not accomplish this since they had to respond on the manual and no further attempts were provided. However, both groups increased their score in the neuropsychological evaluations. This suggests that a longer and more frequent intervention is required. REGISTERED REPORT IDENTIFIER: RR1-10.2196/9603.

The Color of Noise and Weak Stationarity at the NREM to REM Sleep Transition in Mild Cognitive Impaired Subjects.

In Older Adults (OAs), Electroencephalogram (EEG) slowing in frontal lobes and a diminished muscle atonia during Rapid Eye Movement sleep (REM) have each been effective tracers of Mild Cognitive Impairment (MCI), but this relationship remains to be explored by non-linear analysis. Likewise, data provided by EEG, EMG (Electromyogram) and EOG (Electrooculogram)-the three required sleep indicators-during the transition from REM to Non-REM (NREM) sleep have not been related jointly to MCI. Therefore, the main aim of the study was to explore, with results for Detrended Fluctuation Analysis (DFA) and multichannel DFA (mDFA), the Color of Noise (CN) at the NREM to REM transition in OAs with MCI vs. subjects with good performances. The comparisons for the transition from NREM to REM were made for each group at each cerebral area, taking bilateral derivations to evaluate interhemispheric coupling and anteroposterior and posterior networks. In addition, stationarity analysis was carried out to explore if the three markers distinguished between the groups. Neuropsi and the Mini-Mental State Examination (MMSE) were administered, as well as other geriatric tests. One night polysomnography was applied to 6 OAs with MCI (68.1 ± 3) and to 7 subjects without it (CTRL) (64.5 ± 9), and pre-REM and REM epochs were analyzed for each subject. Lower scores for attention, memory and executive funcions and a greater index of arousals during sleep were found for the MCI group. Results confirmed that EOGs constituted significant markers of MCI, increasing the CN for the MCI group in REM sleep. The CN of the EEG from the pre-REM to REM was higher for the MCI group vs. the opposite for the CTRL group at frontotemporal areas. Frontopolar interhemispheric scaling values also followed this trend as well as right anteroposterior networks. EMG Hurst values for both groups were lower than those for EEG and EOG. Stationarity analyses showed differences between stages in frontal areas and right and left EOGs for both groups. These results may demonstrate the breakdown of fractality of areas especially involved in executive functioning and the way weak stationarity analyses may help to distinguish between sleep stages in OAs.

Multichannel detrended fluctuation analysis reveals synchronized patterns of spontaneous spinal activity in anesthetized cats.

The analysis of the interaction and synchronization of relatively large ensembles of neurons is fundamental for the understanding of complex functions of the nervous system. It is known that the temporal synchronization of neural ensembles is involved in the generation of specific motor, sensory or cognitive processes. Also, the intersegmental coherence of spinal spontaneous activity may indicate the existence of synaptic neural pathways between different pairs of lumbar segments. In this study we present a multichannel version of the detrended fluctuation analysis method (mDFA) to analyze the correlation dynamics of spontaneous spinal activity (SSA) from time series analysis. This method together with the classical detrended fluctuation analysis (DFA) were used to find out whether the SSA recorded in one or several segments in the spinal cord of the anesthetized cat occurs either in a random or in an organized manner. Our results are consistent with a non-random organization of the sets of neurons involved in the generation of spontaneous cord dorsum potentials (CDPs) recorded either from one lumbar segment (DFA-α mean = 1.04[Formula: see text]0.09) or simultaneously from several lumbar segments (mDFA-α mean = 1.01[Formula: see text]0.06), where α = 0.5 indicates randomness while α = 0.5 indicates long-term correlations. To test the sensitivity of the mDFA method we also examined the effects of small spinal lesions aimed to partially interrupt connectivity between neighboring lumbosacral segments. We found that the synchronization and correlation between the CDPs recorded from the L5 and L6 segments in both sides of the spinal cord were reduced when a lesion comprising the left dorsal quadrant was performed between the segments L5 and L6 (mDFA-[Formula: see text] = 0.992 as compared to initial conditions mDFA-α = 1.186). The synchronization and correlation were reduced even further after a similar additional right spinal lesion (mDFA-α = 0.924). In contrast to the classical methods, such as correlation and coherence quantification that define a relation between two sets of data, the mDFA method properly reveals the synchronization of multiple groups of neurons in several segments of the spinal cord. This method is envisaged as a useful tool to characterize the structure of higher order ensembles of cord dorsum spontaneous potentials after spinal cord or peripheral nerve lesions.