Integrated Calendar

Our everyday conscious memories are an intricate network of images and associations, constituting a record of our personal experiences that is continuously updated through an active organization of new information within the context of previous experience. Recollection is similarly recreative, and the course of remembering is determined by the nature of our memory organization. This type of memory is called episodic memory, and is therefore a multifaceted process involving a synthesis of episodic representations with our framework of general semantic knowledge that mediates our capacity for recollection. It is therefore typically considered to be too complex to be described by physics-style universal mathematical laws. In this thesis we characterize some of the processes governing episodic recall and point out the basic principles behind them. More specifically, we propose a search process governing recall of unconnected events, mathematically computed recall capacity and tested the resulting relationship in dedicated experiments. Next, we proposed how structured information may be encoded in the human brain and compared model predictions with available experimental data. In both cases experimental data were consistent with proposed mechanisms. Since time is an essential part of episodic memory we also studied the interaction between absolute and ordinal time representation in the brain. We found that ordinal information take precedence in the inference about absolute event times. Overall, the results presented in this thesis opens opportunity that complicated cognitive processes can be described by universal mathematical laws.

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The structural complexity of composite biomaterials and biomineralized particles arises from the hierarchical ordering of inorganic building blocks over multiple scales. While empirical observations of complex nanoassemblies are abundant, physicochemical mechanisms leading to their geometrical complexity are still puzzling, especially for non-uniformly sized components. These mechanisms are discussed in this talk taking an example of hierarchically organized particles with twisted spikes and other morphologies from polydisperse Au-Cys nanoplatelets [1]. The complexity of these supraparticles is higher than biological counterparts or other complex particles as enumerated by graph theory (GT). Complexity Index (CI) and other GT parameters are applied to a variety of different nanoscale materials to assess their structural organization. As the result of this analysis, we determined that intricate organization Au-Cys supraparticles emerges from competing chirality-dependent assembly restrictions that render assembly pathways primarily dependent on nanoparticle symmetry rather than size. These findings open a pathway to a large family of colloids with complex architectures and unusual chiroptical and chemical properties.
The GT-based design principles for complex chiral nanoassemblies are extended to engineer drug discovery platforms for Alzheimer syndrome [3], materials for chiral photonics, vaccines, and antivirals. Developed GT methods were applied to the design of complex biomimetic composites for energy and robotics applications [2,4] will be shown as a nucleus for discussions.
References
[1] W. Jiang, Z.-B. et al, Emergence of Complexity in Hierarchically Organized Chiral Particles, Science, 2020, 368, 6491, 642-648.
[2] Wang, M.; Vecchio, D.; et al Biomorphic Structural Batteries for Robotics. Sci. Robot. 2020, 5 (45), eaba1912. https://doi.org/10.1126/scirobotics.aba1912.
[3] Jun Lu, et al, Enhanced optical asymmetry in supramolecular chiroplasmonic assemblies with long-range order,
Science, 2021, 371, 6536, 1368
[4] D. Vecchio et al, Structural Analysis of Nanoscale Network Materials Using Graph Theory, ACS Nano 2021, 15, 8, 12847–12859.

Hippocampal place cells fire in a spatially selective manner and are thought to support the formation of a cognitive-map that allows the association of an event to its spatial context. It has long been thought that within familiar spatial contexts, such cognitive maps should be stable over time, and that individual place cells should retain their firing properties. However, recent findings have demonstrated that hippocampal spatial codes gradually change over timescales of minutes to weeks. These finding raised several fundamental questions: What are the contributions of the passage of the time and the amount of experience to the observed drift in hippocampal ensemble activity? To what extent are different aspect of place code stability affected by time and experience? To address these questions, I conducted a series of Ca2+ imaging experiments in which mice repeatedly explored familiar environments. Different environments were visited at different intervals, which allowed distinguishing between the contribution of time and experience to code stability. I found that time and experience differentially affected distinct aspects of hippocampal place codes: changes in activity rates were mostly affected by time, whereas changes in spatial tuning was mostly affected by experience. These findings suggest that different biological mechanisms underlie different aspects of representational drift in the hippocampus. These findings add to the growing body of research suggesting that representational drift is an inherent property of neural networks in vivo, and point to the different candidate mechanisms that could underlie this drift.

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Plants continuously monitor the presence of microorganisms through their immune system to establish an adaptive response. Unlike immune recognition of pathogenic bacteria, mechanisms by which beneficial bacteria interact with the plant immune system are not well understood. Analysis of colonization of Arabidopsis thaliana by auxin producing beneficial bacteria revealed that activating the plant immune system is necessary for efficient bacterial colonization and auxin secretion. A feedback loop is established in which bacterial colonization triggers an immune reaction and production of reactive oxygen species, which, in turn, stimulate auxin production by the bacteria. Auxin promotes bacterial survival and efficient root colonization, allowing the bacteria to compete with other members of the root microbial community and inhibit fungal infection, promoting plant health.

Let G be a complex reductive group with Lie algebra g and let V be a G-module. There is a natural
moment mapping : V  V  ! g and we denote 

Let G be a complex reductive group with Lie algebra g and let V be a G-module. There is a natural
moment mapping : V  V  ! g and we denote 

CRITERIA FOR THE ZERO FIBER OF A MOMENT MAP TO HAVE RATIONAL
SINGULARITIES, AND APPLICATIONS.
Let G be a complex reductive group with Lie algebra g and let V be a G-module. There is a natural
moment mapping : V  V  ! g and we denote