Jacobson’s lemma for the generalized Drazin inverse

Abstract0truemm0truemm We study properties of elements in a ring which admit the generalized Drazin inverse. It is shown that the element 1-ab is generalized Drazin invertible if and only if so is 1-ba and a formula for the generalized Drazin inverse of 1-ba in terms of the generalized Drazin inverse and the spectral idempotent of 1-ab is provided. Further, recent results relating to the Drazin index can be recovered from our theorems

Differential Consolidation and Pattern Reverberations within Episodic Cell Assemblies in the Mouse Hippocampus

One hallmark feature of consolidation of episodic memory is that only a fraction of original information, which is usually in a more abstract form, is selected for long-term memory storage. How does the brain perform these differential memory consolidations? To investigate the neural network mechanism that governs this selective consolidation process, we use a set of distinct fearful events to study if and how hippocampal CA1 cells engage in selective memory encoding and consolidation. We show that these distinct episodes activate a unique assembly of CA1 episodic cells, or neural cliques, whose response-selectivity ranges from general-to-specific features. A series of parametric analyses further reveal that post-learning CA1 episodic pattern replays or reverberations are mostly mediated by cells exhibiting event intensity-invariant responses, not by the intensity-sensitive cells. More importantly, reactivation cross-correlations displayed by intensity-invariant cells encoding general episodic features during immediate post-learning period tend to be stronger than those displayed by invariant cells encoding specific features. These differential reactivations within the CA1 episodic cell populations can thus provide the hippocampus with a selection mechanism to consolidate preferentially more generalized knowledge for long-term memory storage

Neural Population-Level Memory Traces in the Mouse Hippocampus

One of the fundamental goals in neurosciences is to elucidate the formation and retrieval of brain's associative memory traces in real-time. Here, we describe real-time neural ensemble transient dynamics in the mouse hippocampal CA1 region and demonstrate their relationships with behavioral performances during both learning and recall. We employed the classic trace fear conditioning paradigm involving a neutral tone followed by a mild foot-shock 20 seconds later. Our large-scale recording and decoding methods revealed that conditioned tone responses and tone-shock association patterns were not present in CA1 during the first pairing, but emerged quickly after multiple pairings. These encoding patterns showed increased immediate-replay, correlating tightly with increased immediate-freezing during learning. Moreover, during contextual recall, these patterns reappeared in tandem six-to-fourteen times per minute, again correlating tightly with behavioral recall. Upon traced tone recall, while various fear memories were retrieved, the shock traces exhibited a unique recall-peak around the 20-second trace interval, further signifying the memory of time for the expected shock. Therefore, our study has revealed various real-time associative memory traces during learning and recall in CA1, and demonstrates that real-time memory traces can be decoded on a moment-to-moment basis over any single trial

Perioperative nutritional risk and its influencing factors in patients with oral cancer: a longitudinal study

IntroductionWe aimed to investigate the nutritional risk status and dynamic changes in patients with perioperative oral cancer at different stages and analyze the factors influencing nutritional risk and the correlation among body mass index, nutrition-related symptoms, and nutritional risk.MethodsIn total, 198 patients with oral cancer who were hospitalized in the Head & Neck Surgery Departments of a tertiary cancer hospital in Hunan Province, China, from May 2020 to January 2021, were selected as participants. The Nutritional Risk Screening 2002 scale and Head and Neck Patient Symptom Checklist were used to assess patients on admission day, 7 days post-surgery, and 1 month post-discharge. Multivariate analysis of variance, paired t-test, and generalized estimating equation were used to analyze the trajectory and influencing factors of nutritional risk in patients with perioperative oral cancer. Spearman’s correlation analysis was used to explore the correlation among body mass index, symptoms, and nutritional risk.ResultsThe nutritional risk scores of patients with oral cancer at the three time points were 2.30 ± 0.84, 3.21 ± 0.94, and 2.11 ± 0.84, respectively, and the differences were significant (p < 0.05). The incidences of nutritional risk were 30.3, 52.5, and 37.9%, respectively. The factors influencing nutritional risk included education level, smoking status, clinical stage, flap repair, and tracheotomy (β = −0.326, 0.386, 0.387, 0.336, and 0.240, respectively, p < 0.05). Nutritional risk was negatively correlated with body mass index (rs = −0.455, p < 0.01) and positively correlated with pain, loss of appetite, sore mouth, bothersome smells, swallowing difficulty, taste changes, depression, chewing difficulty, thick saliva, and anxiety (rs = 0.252, 0.179, 0.269, 0.155, 0.252, 0.212, 0.244, 0.384, 0.260, and 0.157, respectively, p < 0.05).ConclusionThe incidence of nutritional risk in patients with perioperative oral cancer was high, and the trajectory of nutritional risk changed over time. Strengthening the nutritional monitoring and management of postoperative patients or those with low education level, advanced-stage cancer, flap repair, tracheotomy, and low body mass index; strengthening tobacco control management; and controlling nutrition-related discomfort symptoms in perioperative oral cancer patients are necessary

Large-scale neural ensemble recording in the brains of freely behaving mice

Abstract With the availability of sophisticated genetic techniques, the mouse is a valuable mammalian model to study the molecular and cellular basis of cognitive behaviors. However, the small size of mice makes it difficult for a systematic investigation of activity patterns of neural networks in vivo. Here we report the development and construction of a high-density ensemble recording array with up to 128-recording channels that can be formatted as single electrodes, stereotrodes, or tetrodes. This high-density recording array is capable of recording from hundreds of individual neurons simultaneously in the hippocampus of the freely behaving mice. This large-scale in vivo ensemble recording techniques, once coupled with mouse genetics, should be valuable to the study of complex relationship between the genes, neural network, and cognitive behaviors

Mesoscale eddy modulation of subsurface chlorophyll maximum layers in the South China Sea

Subsurface chlorophyll maximum (SCM) layers contribute considerably to the integrated biomass of the water column and can be strongly modulated by mesoscale eddies that are ubiquitous in the global ocean. The mechanisms of eddy-induced surface chlorophyll concentration have been extensively examined in the South China Sea (SCS). However, the potential impact of mesoscale eddies on SCM layers remains unclear. We examined the influence of mesoscale eddies on the depth, thickness and magnitude of SCM layers in the SCS using output from an eddy-permitting biological–physical coupled model over a 22-year period. Our study shows that nutrient distribution is largely driven by eddy dynamics, with cyclonic eddies enhancing the supply of inorganic nutrients in the upper layers by uplifting the thermocline, and downward displacement of the thermocline in anticyclonic eddies, reducing the nutrient supply into the euphotic zone from the depth. We found that anticyclonic (cyclonic) eddies are responsible for increased (decreased) SCM depth and decreased (increased) SCM magnitude; SCM thickness decreased in cyclonic eddies but slightly increased in anticyclonic eddies. The effects of mesoscale eddies depend on eddy amplitude. Maximal anomalies in depth, thickness and magnitude always occur near the center of eddies. Phytoplankton community structure at SCM layers is also affected by eddies, with more diatoms in cyclonic eddies and more coccolithophores in anticyclonic eddies. Our study will advance our understanding of mesoscale physical–biogeochemical interactions

Dynamic genome evolution in a model fern

The large size and complexity of most fern genomes have hampered efforts to elucidate fundamental aspects of fern biology and land plant evolution through genome-enabled research. Here we present a chromosomal genome assembly and associated methylome, transcriptome and metabolome analyses for the model fern species Ceratopteris richardii. The assembly reveals a history of remarkably dynamic genome evolution including rapid changes in genome content and structure following the most recent whole-genome duplication approximately 60 million years ago. These changes include massive gene loss, rampant tandem duplications and multiple horizontal gene transfers from bacteria, contributing to the diversification of defence-related gene families. The insertion of transposable elements into introns has led to the large size of the Ceratopteris genome and to exceptionally long genes relative to other plants. Gene family analyses indicate that genes directing seed development were co-opted from those controlling the development of fern sporangia, providing insights into seed plant evolution. Our findings and annotated genome assembly extend the utility of Ceratopteris as a model for investigating and teaching plant biology