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- mean = 1.040.09) or simultaneously from several lumbar segments (mDFA- mean = 1.010.06), where  = 0.5 indicates randomness while 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- = 0.992 as compared to initial conditions mDFA- = 1.186). The synchronization and correlation were reduced even further after a similar additional right spinal lesion (mDFA- = 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.

In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. For a special case, this result can be improved so that it is the convex hull of the union of the numerical ranges of only two matrices. A conjecture is stated for the general case.

Abstract. Let (Y, T) be a minimal suspension flow built over a dynamical system (X, S) and with (strictly positive, continuous) ceiling function f : X → R. We show that the eigenvalues of (Y, T) are contained in the range of a trace on the K 0 -group of (X, S). Moreover, a trace gives an order isomorphism of a subgroup of K 0 (C(X) ⋊ S Z) with the group of eigenvalues of (Y, T). Using this result, we relate the values of t for which the time-t map on the minimal suspension flow is minimal with the K-theory of the base of this suspension.

: We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N. Chandler-Wilde et al. and R. Hagger, which rely on limit operator techniques, we are able to provide more general results although the closure of the numerical range needs to be taken.

A classification of D-branes in Type IIB Op − orientifolds and orbifolds in terms of Real and equivariant KK-groups is given. We classify D-branes intersecting orientifold planes from which are recovered some special limits such as the spectrum for D-branes on top of Type I Op − orientifold and the bivariant classification of Type I D-branes. The gauge group and transformation properties of the low energy effective field theory living in the corresponding unstable D-brane system are computed by extensive use of Clifford algebras. Some speculations about the existence of other versions of KK-groups, based on physical insights, are proposed. In the orbifold case, some known results concerning D-branes intersecting orbifolds are reproduced and generalized. Finally, the gauge theory of unstable systems in these orbifolds is recovered.

BackgroundCognitive 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).ObjectiveThe 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.MethodsThis 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.ResultsAccording 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.ConclusionsThe 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 IdentifierRR1-10.2196/9603

The pandemic caused by the SARS-CoV-2 virus spreads more rapidly in densely populated areas. The number of confirmed cases is counted by the millions in some countries, such as USA, Brazil, and Mexico. These three countries also report the world’s highest cumulative death tolls caused by the disease as of February 2021. In this study, a comparative analysis of urban development, economic level, and the number of COVID-19 cases in Mexico City, is conducted. Mexico City, the capital city of Mexico, is among the most densely populated metropolitan areas and one of the largest financial centers in the continent. Among the sixteen municipalities, in which Mexico City is divided, there exist enormous economic and urban development gaps. Based in a comparability index (CI), this study found a correlation between the number of confirmed cases of the COVID-19 disease with the population density, the per capita income, and the dwelling occupancy index in each municipality.

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