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Register a new userPositional information, positional error, and read-out precision in morphogenesis: a mathematical framework
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The concept of positional information is central to our understanding of how cells in a multicellular structure determine their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine which features of expression patterns increase or decrease positional information. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with single cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.
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Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multi-cellular organisms.
For present e-commerce platforms, session-based recommender systems are developed to predict users preference for next-item recommendation. Although a session can usually reflect a users current preference, a local shift of the users intention within the session may still exist. Specifically, the interactions that take place in the early positions within a session generally indicate the users initial intention, while later interactions are more likely to represent the latest intention. Such positional information has been rarely considered in existing methods, which restricts their ability to capture the significance of interactions at different positions. To thoroughly exploit the positional information within a session, a theoretical framework is developed in this paper to provide an in-depth analysis of the positional information. We formally define the properties of forward-awareness and backward-awareness to evaluate the ability of positional encoding schemes in capturing the initial and the latest intention. According to our analysis, existing positional encoding schemes are generally forward-aware only, which can hardly represent the dynamics of the intention in a session. To enhance the positional encoding scheme for the session-based recommendation, a dual positional encoding (DPE) is proposed to account for both forward-awareness and backward-awareness. Based on DPE, we propose a novel Positional Recommender (PosRec) model with a well-designed Position-aware Gated Graph Neural Network module to fully exploit the positional information for session-based recommendation tasks. Extensive experiments are conducted on two e-commerce benchmark datasets, Yoochoose and Diginetica and the experimental results show the superiority of the PosRec by comparing it with the state-of-the-art session-based recommender models.
Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of temperature sensing are poorly understood. Unlike in chemical concentration sensing, the precision of temperature sensing is not limited by extrinsic fluctuations in the temperature field itself. Instead, we find that precision is limited by the intrinsic copy number, turnover, and binding kinetics of temperature-sensitive proteins. Developing a model based on the canonical TlpA protein, we find that a cell can estimate temperature to within 2%. We compare this prediction with in vivo data on temperature sensing in bacteria.
Biological cells are often found to sense their chemical environment near the single-molecule detection limit. Surprisingly, this precision is higher than simple estimates of the fundamental physical limit, hinting towards active sensing strategies. In this work, we analyse the effect of cell memory, e.g. from slow biochemical processes, on the precision of sensing by cell-surface receptors. We derive analytical formulas, which show that memory significantly improves sensing in weakly fluctuating environments. However, surprisingly when memory is adjusted dynamically, the precision is always improved, even in strongly fluctuating environments. In support of this prediction we quantify the directional biases in chemotactic Dictyostelium discoideum cells in a flow chamber with alternating chemical gradients. The strong similarities between cell sensing and control engineering suggest universal problem-solving strategies of living matter.
Multilingual neural machine translation has shown the capability of directly translating between language pairs unseen in training, i.e. zero-shot translation. Despite being conceptually attractive, it often suffers from low output quality. The difficulty of generalizing to new translation directions suggests the model representations are highly specific to those language pairs seen in training. We demonstrate that a main factor causing the language-specific representations is the positional correspondence to input tokens. We show that this can be easily alleviated by removing residual connections in an encoder layer. With this modification, we gain up to 18.5 BLEU points on zero-shot translation while retaining quality on supervised directions. The improvements are particularly prominent between related languages, where our proposed model outperforms pivot-based translation. Moreover, our approach allows easy integration of new languages, which substantially expands translation coverage. By thorough inspections of the hidden layer outputs, we show that our approach indeed leads to more language-independent representations.
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