Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Joel Cohen offers a historical and prospective analysis of the relationship between mathematics and biolog

Zipf's Law and Avoidance of Excessive Synonymy

Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped satisfactory theoretical explanation. We suggest that Zipf's law may arise from the evolution of word semantics dominated by expansion of meanings and competition of synonyms.Comment: 47 pages; fixed reference list missing in v.

A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing

The partially observable generalized linear model (POGLM) is a powerful tool for understanding neural connectivity under the assumption of existing hidden neurons. With spike trains only recorded from visible neurons, existing works use variational inference to learn POGLM meanwhile presenting the difficulty of learning this latent variable model. There are two main issues: (1) the sampled Poisson hidden spike count hinders the use of the pathwise gradient estimator in VI; and (2) the existing design of the variational model is neither expressive nor time-efficient, which further affects the performance. For (1), we propose a new differentiable POGLM, which enables the pathwise gradient estimator, better than the score function gradient estimator used in existing works. For (2), we propose the forward-backward message-passing sampling scheme for the variational model. Comprehensive experiments show that our differentiable POGLMs with our forward-backward message passing produce a better performance on one synthetic and two real-world datasets. Furthermore, our new method yields more interpretable parameters, underscoring its significance in neuroscience

Markovian Gaussian Process: A Universal State-Space Representation for Stationary Temporal Gaussian Process

Gaussian Processes (GPs) and Linear Dynamical Systems (LDSs) are essential time series and dynamic system modeling tools. GPs can handle complex, nonlinear dynamics but are computationally demanding, while LDSs offer efficient computation but lack the expressive power of GPs. To combine their benefits, we introduce a universal method that allows an LDS to mirror stationary temporal GPs. This state-space representation, known as the Markovian Gaussian Process (Markovian GP), leverages the flexibility of kernel functions while maintaining efficient linear computation. Unlike existing GP-LDS conversion methods, which require separability for most multi-output kernels, our approach works universally for single- and multi-output stationary temporal kernels. We evaluate our method by computing covariance, performing regression tasks, and applying it to a neuroscience application, demonstrating that our method provides an accurate state-space representation for stationary temporal GPs

The Progress, Problems and Forsight of Scholarship of Teaching Research in China Since 2000

Since 2000, Chinese researchers have introduced American ideology of scholarship of teaching (SoT), and conduct localizationas analysis on its definition, connotation and assessing standards, and initially form SoT theoretical framework based on Chinese reality. Researchers have carried out empirical investigations for Chinese SoT levels in universities, and discussed on overall design of Chinese university SoT system from such aspects as SoT cultivating system, value acceptance system, teaching administrative and quality guarantee system based on SoT, teachers’ specialty development system in the view of SoT, and SoT communicating and sharing system. Although SoT research has greatly developed in China, there still exist the following problems: just advocating foreign theories without taking consideration of Chinese context; taking old route in research path; more theoretical imagination but less investigation, many difficulties to implementation recommendation. It will be a tendency for future research to further clarify SoT theoretical foundation, explore the practice from the bottom up and probe into new epistemology and research paradigm applied to SoT

Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process (GP) and Linear Dynamical System (LDS), each with unique strengths. The GP-based approach effectively discovers latent variables with frequency bands and communication directions. Conversely, the LDS-based approach is computationally efficient but lacks powerful expressiveness in latent representation. In this study, we merge both methodologies by creating an LDS mirroring a multi-output GP, termed Multi-Region Markovian Gaussian Process (MRM-GP). Our work establishes a connection between an LDS and a multi-output GP that explicitly models frequencies and phase delays within the latent space of neural recordings. Consequently, the model achieves a linear inference cost over time points and provides an interpretable low-dimensional representation, revealing communication directions across brain regions and separating oscillatory communications into different frequency bands

Extraction and Recovery of Spatio-Temporal Structure in Latent Dynamics Alignment with Diffusion Models

In the field of behavior-related brain computation, it is necessary to align raw neural signals against the drastic domain shift among them. A foundational framework within neuroscience research posits that trial-based neural population activities rely on low-dimensional latent dynamics, thus focusing on the latter greatly facilitates the alignment procedure. Despite this field's progress, existing methods ignore the intrinsic spatio-temporal structure during the alignment phase. Hence, their solutions usually lead to poor quality in latent dynamics structures and overall performance. To tackle this problem, we propose an alignment method ERDiff, which leverages the expressivity of the diffusion model to preserve the spatio-temporal structure of latent dynamics. Specifically, the latent dynamics structures of the source domain are first extracted by a diffusion model. Then, under the guidance of this diffusion model, such structures are well-recovered through a maximum likelihood alignment procedure in the target domain. We first demonstrate the effectiveness of our proposed method on a synthetic dataset. Then, when applied to neural recordings from the non-human primate motor cortex, under both cross-day and inter-subject settings, our method consistently manifests its capability of preserving the spatiotemporal structure of latent dynamics and outperforms existing approaches in alignment goodness-of-fit and neural decoding performance

Global distribution of a key trophic guild contrasts with common latitudinal diversity patterns

Most hypotheses explaining the general gradient of higher diversity toward the equator are implicit or explicit about greater species packing in the tropics. However, global patterns of diversity within guilds, including trophic guilds (i.e., groups of organisms that use similar food resources), are poorly known. We explored global diversity patterns of a key trophic guild in stream ecosystems, the detritivore shredders. This was motivated by the fundamental ecological role of shredders as decomposers of leaf litter and by some records pointing to low shredder diversity and abundance in the tropics, which contrasts with diversity patterns of most major taxa for which broad-scale latitudinal patterns haven been examined. Given this evidence, we hypothesized that shredders are more abundant and diverse in temperate than in tropical streams, and that this pattern is related to the higher temperatures and lower availability of high-quality leaf litter in the tropics. Our comprehensive global survey (129 stream sites from 14 regions on six continents) corroborated the expectedlatitudinal pattern and showed that shredder distribution (abundance, diversity and assemblage composition) was explained by a combination of factors, including water temperature (some taxa were restricted to cool waters) and biogeography (some taxa were more diverse in particular biogeographic realms). In contrast to our hypothesis, shredder diversity was unrelated to leaf toughness, but it was inversely related to litter diversity. Our findings markedly contrast with global trends of diversity for most taxa, and with the general rule of higher consumer diversity at higher levels of resource diversity. Moreover, they highlight the emerging role of temperature in understanding global patterns of diversity, which is of great relevance in the face of projected global warming. © 2011 by the Ecological Society of America.Peer Reviewe