Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two

Let $K$ be any field with $\textup{char}K\neq 2,3$. We classify all cubic homogeneous polynomial maps $H$ over $K$ with $\textup{rk} JH\leq 2$. In particular, we show that, for such an $H$, if $F=x+H$ is a Keller map then $F$ is invertible, and furthermore $F$ is tame if the dimension $n\neq 4$.Comment: arXiv admin note: text overlap with arXiv:1609.0975

The linear dependence problem for power linear maps

AbstractLet Bl, l=1,…,k, be m×nl complex matrices and let x[l]∈Cnl,l=1,…,k, be complex vector variables. We show that the components of the map H=(B1x[1])(d1)∘⋯∘(Bkx[k])(dk) are linearly dependent over C if and only if det(B1B1∗)(d1)∘⋯∘(BkBk∗)(dk)=0, where ∘ means the Hadamard product, X∗ and X(d) denote the conjugate transpose and the dth Hadamard power of a matrix X respectively. Connections are established between the Homogenous Dependence Problem (HDP(n,d)), which arises in the study of the Jacobian Conjecture, and the dependence problem for power linear maps (PLDP(n,d)). An algorithm is given to compute counterexamples to PLDP(n,d) from those to HDP(n,d), and counterexamples to PLDP(n,3) are obtained for all n⩾67

A context-based study of serendipity in information research among Chinese scholars

Purpose: The current understanding of serendipity is based primarily on studies employing Westerners as participants, and it remains uncertain whether or not this understanding would be pervasive under different cultures, such as in China. In addition, there is not a sufficient systematic investigation of context during the occurrence of serendipity in current studies. This paper examines the above issues by conducting a follow-up empirical study with a group of Chinese scholars. Design/methodology/approach: The social media application “Wechat” was employed as a research tool. A diary-based study was conducted and 16 participants were required to send to the researchers any cases of serendipity they encountered during a period of two weeks, and this was followed by a post-interview. Findings: Chinese scholars experienced serendipity in line with the three main processes of encountering unexpectedness, connection-making and recognising the value. An updated context-based serendipity model was constructed, where the role of context during each episode of experiencing serendipity was identified, including the external context (e.g. time, location and status), the social context, and the internal context (e.g. precipitating conditions, sagacity/perceptiveness and emotion). Originality/value: The updated context model provides a further understanding of the role played by context during the different processes of serendipity. The framework for experiencing serendipity has been expanded, and this may be used to classify the categories of serendipity

Adaptive Biomimetic Neuronal Circuit System Based on Myelin Sheath Function

© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This is the accepted manuscript version of a conference paper which has been published in final form at https://doi.org/10.1109/TCE.2024.3356563Brain-inspired neuromorphic computing architectures are receiving significant attention in the consumer electronics field owing to their low power consumption, high computational capacity, and strong adaptability, where highly biomimetic circuit design is at the core of neuromorphic network research. Myelin sheaths are crucial cellular components in building stable circuits in biological neurons, capable of adaptively adjusting the conduction speed of neural signals. However, current research on neuronal circuits relies on simplified mathematical models and overlooks the adaptive functionality of myelin sheaths. This paper is based on the dynamic mechanism of myelination, utilizing physical devices such as memristors and voltage-controlled variable capacitors to simulate the physiological functions of myelin sheaths, and other organelles. Furthermore, adaptive biomimetic neuronal circuit system (ABNCS) is constructed by connecting various devices according to the physiological structure of neurons. PSpice simulations show that the ABNCS can adjust its parameters autonomously as the number of action potentials (APs) increase, which modifies the neuron’s activation criteria and firing rate. Through circuit experiments, PSpice simulations were further validated. Implementing myelin sheath functions in the neuronal circuit improves adaptability and reduces power consumption, and when combined with artificial synapses to construct neural networks, can form more stable neural circuits.Peer reviewe

A Review of Research Methodologies Employed in Serendipity Studies in the Context of Information Research

Background: The concept of serendipity has become increasingly interesting for those undertaking serendipity research in recent years. However, serendipitous encounters are subjective and rare in a real-world context, making this an extremely challenging subject to study. Methods: Various methods have been proposed to enable researchers to understand and measure serendipity, but there is no broad consensus on which methods to use in different experimental settings. A comprehensive literature review was first conducted, which summarizes the research methods being employed to study serendipity. It was followed by a series of interviews with experts that specified the relative strengths and weaknesses of each method identified in the literature review, in addition to the challenges usually confronted in serendipity research. Results: The findings suggest using mixed research methods to produce a more complete picture of serendipity and contribute to the verification of any research findings. Several challenges and implications relating to empirical studies in the investigation of serendipity have been derived from this study. Conclusions: This paper investigated research methods employed to study serendipity by synthesizing finding from a literature review and the interviews with experts. It provides a methodological contribution to serendipity studies by systematically summarizing the methods employed in the studies of serendipity and identifying the strengths and weakness of each method. It also suggests the novel approach of using mixed research methods to study serendipity. This study has potential limitations related to a small number of experts involved in the expert interview. However, it should be noted that the nature of the topic is a relatively focused area, and it was observed after interviewing the experts that new data seems to not contribute to the findings owing to its repetition of comment

Design of Artificial Neurons of Memristive Neuromorphic Networks Based on Biological Neural Dynamics and Structures

© 2024, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This is the accepted manuscript version of a conference paper which has been published in final form at https://doi.org/10.1109/TCSI.2023.3332496Memristive neuromorphic networks have great potentialand advantage in both technology and computationalprotocols for artificial intelligence. Efficient hardware design ofbiological neuron models forms the core of research problems inneuromorphic networks. However, most of the existing researchhas been based on logic or integrated circuit principles, limitedto replicating simple integrate-and-fire behaviors, while morecomplex firing characteristics have relied on the inherent propertiesof the devices themselves, without support from biologicalprinciples. This paper proposes a memristor-based neuron circuitsystem (MNCS) according to the microdynamics of neuronsand complex neural cell structures. It leverages the nonlinearityand non-volatile characteristics of memristors to simulate thebiological functions of various ion channels. It is designed basedon the Hodgkin-Huxley (HH) model circuit, and the parametersare adjusted according to each neuronal firing mechanism. BothPSpice simulations and practical experiments have demonstratedthat MNCS can replicate 24 types of repeating biological neuronalbehaviors. Furthermore, the results from the Joint Inter-spikeInterval(JISI) experiment indicate that as the background noiseincreases, MNCS exhibits pulse emission characteristics similarto those of biological neurons.Peer reviewe