Zeta functions of the 3-dimensional almost-Bieberbach groups

The subgroup zeta function and the normal zeta function of a finitely generated virtually nilpotent group can be expressed as finite sums of Dirichlet series admitting Euler product factorization. We compute these series except for a finite number of local factors when the group is virtually nilpotent of Hirsch length 3. We deduce that they can be meromorphically continued to the whole complex plane and that they satisfy local functional equations. The complete computation (with no exception of local factors) is presented for those groups that are also torsion-free, that is, for the 3-dimensional almost-Bieberbach groups.

The synaptic organization in the C. elegans neural network suggests significant local compartmentalized computations

Neurons are characterized by elaborate tree-like dendritic structures that support local computations by integrating multiple inputs from upstream presynaptic neurons. It is less clear if simple neurons, consisting of a few or even a single neurite, may perform local computations as well. To address this question, we focused on the compact neural network of C. elegans animals for which the full wiring diagram is available, including the coordinates of individual synapses. We find that the positions of the chemical synapses along the neurites are not randomly distributed, nor can they be explained by anatomical constraints. Instead, synapses tend to form clusters, an organization that supports local compartmentalized computations. In mutually-synapsing neurons, connections of opposite polarity cluster separately, suggesting that positive and negative feedback dynamics may be implemented in discrete compartmentalized regions along neurites. In triple-neuron circuits, the non-random synaptic organization may facilitate local functional roles, such as signal integration and coordinated activation of functionally-related downstream neurons. These clustered synaptic topologies emerge as a guiding principle in the network presumably to facilitate distinct parallel functions along a single neurite, effectively increasing the computational capacity of the neural network.

Development of Local Functional Food Made of Buffalo Milk Improved with Culture Probiotics (Lactobacillus casei)

The research was conducted to develop functional food products of milk-based livestock origin (Semi hard-type cheese), with the addition of pure culture Lactobacillus casei as a probiotic agent, and citric acid and Mucor meihei as milk coagulants. The research material was semi-hard type cheese made of approximately 35 liters of buffalo milk from West Sumbawa Regency as a basic ingredient with the probiotic pure culture. The results showed that the pure culture of probiotic (Lactobacillus casei) at levels of 10% and 15% can survive and develop quite well in semi-hard cheese during aging, from 1 day, 7 days, and 14 days, respectively (3.79 – 5.92) and (4.91 – 6.31) log cfu g-1. While the 0.025% rennet of the volume of milk from Mucor miehei gives a pretty good result, it can be seen from the product recovery which can reach (34.30 + 0.32) %. During aging for 14 days, an organoleptic quality which includes aroma, color, and texture was getting better, with the criteria of a semi-hard aroma, yellowish-white color, and semi-hard texture. It can be concluded, that semi-hard type cheese can be used as one of the functional foods of probiotic carriers. To get the therapeutic effect, this probiotic should be consumed at least 100 grams per serving.

Surface-Based Amplitude of Low-Frequency Fluctuation Alterations in Patients With Tinnitus Before and After Sound Therapy: A Resting-State Functional Magnetic Resonance Imaging Study

This study aimed to investigate abnormal tinnitus activity by evaluating brain surface-based amplitude of low-frequency fluctuation (ALFF) changes detected by resting-state functional magnetic resonance imaging (RS-fMRI) in patients with idiopathic tinnitus before and after 24 weeks of sound therapy. We hypothesized that sound therapy could gradually return cortical local brain function to a relatively normal range. In this prospective observational study, we recruited thirty-three tinnitus patients who had undergone 24 weeks of sound therapy and 26 matched healthy controls (HCs). For the two groups of subjects, we analyzed the spontaneous neural activity of tinnitus patients by cortical ALFF and detected its correlation with clinical indicators of tinnitus. Patients’ Tinnitus Handicap Inventory (THI) scores were assessed to determine the severity of their tinnitus before and after treatment. Two-way mixed model analysis of variance and Pearson’s correlation analysis were used in the statistical analysis. Student–Newman–Keuls tests were used in the post hoc analysis. Interaction effects between the two groups and between the two scans revealing local neural activity as assessed by ALFF were observed in the bilateral dorsal stream visual cortex (DSVC), bilateral posterior cingulate cortex (PCC), bilateral anterior cingulate and medial prefrontal cortex (ACC and MPC), left temporo-parieto-occipital junction (TPOJ), left orbital and polar frontal cortex (OPFC), left paracentral lobular and mid cingulate cortex (PCL and MCC), right insular and frontal opercular cortex (IFOC), and left early visual cortex (EVC). Importantly, local functional activity in the left TPOJ and right PCC in the patient group was significantly lower than that in the HCs at baseline and was increased to relatively normal levels after treatment. The 24-week sound therapy tinnitus group demonstrated significantly higher ALFF in the left TPOJ and right PCC than in the tinnitus baseline group. Also, compared with the HC baseline group and the 24-week HC group, the 24-week sound therapy tinnitus group demonstrated slightly lower or higher ALFF in the left TPOJ and right PCC, and there were no differences between the 24-week sound therapy tinnitus and HC groups. Decreased THI scores and ALFF changes in the abovementioned brain regions were not correlated. Taken together, surface-based RS-fMRI can provide more subtle local functional activity to explain the mechanism of tinnitus treatment, and long-term sound therapy had a normalizing effect on tinnitus patients.

Highly accurate local functional fingerprints and their stability

The neural underpinnings of individual identity reflected in cognition, behavior, and disease remain elusive. Functional connectivity profiles have been used as a "fingerprint" with which an individual can be identified in a dataset. These established functional connectivity fingerprints generally show high accuracy but are still sensitive to mental states. A truly unique, and especially state-independent, neural fingerprint will shed light on fundamental intra-individual brain organization. Moreover, a fingerprint that also captures inter-individual differences in brain-behavior associations will provide the necessary ingredients for the development of biomarkers for precision medicine. With resting-state and task fMRI-data of the Human Connectome Project and the enhanced Nathan Kline Institute sample, we show that the local functional fingerprint, and especially regional homogeneity (ReHo), is 1) a highly accurate neural fingerprint, 2) more stable within an individual regardless of their mental state (compared to the baseline functional connectome fingerprint), and 3) captures specific inter-individual differences. Our findings are replicable across parcellations as well as resilient to confounding effects. Further analyses showed that the attention networks and the Default Mode Network contributed most to individual "uniqueness". Moreover, with the OpenNeuro.ds000115 sample, we show that ReHo is also stable in individuals with schizophrenia and that its stability relates to intelligence subtest scores. Altogether, our findings show the potential of the application of local functional fingerprints in precision medicine.

Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration–a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration–determined from partial information decomposition–varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow.

Local Functional MR Change Pattern and Its Association With Cognitive Function in Objectively-Defined Subtle Cognitive Decline

Introduction: To identify individuals with preclinical cognitive impairment, researchers proposed the concept of objectively-defined subtle cognitive decline (Obj-SCD). However, it is not clear whether Obj-SCD has characteristic brain function changes. In this study, we aimed at exploring the changing pattern of brain function activity in Obj-SCD individuals and the similarities and differences with mild cognitive impairments (MCI).Method: 37 healthy control individuals, 25 Obj-SCD individuals (with the impairment in memory and language domain), and 28 aMCI individuals were included. Resting-state fMRI and neuropsychological tests were performed. fALFF was used to reflect the local functional activity and compared between groups. Finally, we analyzed the correlation between the fALFF values of significantly changed regions and neuropsychological performance.Results: We found similar functional activity enhancements in some local brain regions in the Obj-SCD and aMCI groups, including the left orbital part of the inferior frontal gyrus and the left median cingulate and paracingulate gyri. However, some changes in local functional activities of the Obj-SCD group showed different patterns from the aMCI group. Compared with healthy control (HC), the Obj-SCD group showed increased local functional activity in the right middle occipital gyrus, decreased local functional activity in the left precuneus and the left inferior temporal gyrus. In the Obj-SCD group, in normal band, the fALFF value of the right middle occipital gyrus was significantly negatively correlated with Mini-Mental State Examination (MMSE) score (r = −0.450, p = 0.024) and Animal Verbal Fluency Test (AFT) score (r = −0.402, p = 0.046); the left inferior temporal gyrus was significantly positively correlated with MMSE score (r = 0.588, p = 0.002). In slow-4 band, the fALFF value of the left precuneus was significantly positively correlated with MMSE score (r = 0.468, p = 0.018) and AFT score (r = 0.600, p = 0.002). In the aMCI group, the fALFF value of the left orbital part of the inferior frontal gyrus was significantly positively correlated with Auditory Verbal Learning Test (AVLT) long delay cued recall score (r = 0.506, p = 0.006).Conclusion: The Obj-SCD group showed a unique changing pattern; the functional changes of different brain regions have a close but different correlation with cognitive impairment, indicating that there may be a complex pathological basis inside. This suggests that Obj-SCD may be a separate stage of cognitive decline before aMCI and is helpful to the study of preclinical cognitive decline.

An Effective Brain Imaging Biomarker for AD and aMCI: ALFF in Slow-5 Frequency Band

Background: As a potential brain imaging biomarker, amplitude of low frequency fluc-tuation (ALFF) has been used as a feature to distinguish patients with Alzheimer’s disease (AD) and amnestic mild cognitive impairment (aMCI) from normal controls (NC). However, it remains unclear whether the frequency-dependent pattern of ALFF alterations can effectively distinguish the different phases of the disease. Methods: In the present study, 52 AD and 50 aMCI patients were enrolled together with 43 NC in total. The ALFF values were calculated in the following three frequency bands: classical (0.01-0.08 Hz), slow-4 (0.027-0.073 Hz) and slow-5 (0.01-0.027 Hz) for the three different groups. Subsequently, the local functional abnormalities were employed as features to examine the effect of classification among AD, aMCI and NC using a support vector machine (SVM). Results: We found that the among-group differences of ALFF in the different frequency bands were mainly located in the left hippocampus (HP), right HP, bilateral posterior cingulate cortex (PCC) and bilateral precuneus (PCu), left angular gyrus (AG) and left medial prefrontal cortex (mPFC). When the local functional abnormalities were employed as features, we identified that the ALFF in the slow-5 frequency band showed the highest accuracy to distinguish among the three groups. Conclusion: These findings may deepen our understanding of the pathogenesis of AD and suggest that slow-5 frequency band may be helpful to explore the pathogenesis and distinguish the phases of this disease.

Acitretin reverses early functional network degradation in a mouse model of familial Alzheimer’s disease

Aberrant activity of local functional networks underlies memory and cognition deficits in Alzheimer’s disease (AD). Hyperactivity was observed in microcircuits of mice AD-models showing plaques, and also recently in early stage AD mutants prior to amyloid deposition. However, early functional effects of AD on cortical microcircuits remain unresolved. Using two-photon calcium imaging, we found altered temporal distributions (burstiness) in the spontaneous activity of layer II/III visual cortex neurons, in a mouse model of familial Alzheimer’s disease (5xFAD), before plaque formation. Graph theory (GT) measures revealed a distinct network topology of 5xFAD microcircuits, as compared to healthy controls, suggesting degradation of parameters related to network robustness. After treatment with acitretin, we observed a re-balancing of those network measures in 5xFAD mice; particularly in the mean degree distribution, related to network development and resilience, and post-treatment values resembled those of age-matched controls. Further, behavioral deficits, and the increase of excitatory synapse numbers in layer II/III were reversed after treatment. GT is widely applied for whole-brain network analysis in human neuroimaging, we here demonstrate the translational value of GT as a multi-level tool, to probe networks at different levels in order to assess treatments, explore mechanisms, and contribute to early diagnosis.