Combinatorial properties of the enhanced principal rank characteristic sequence over finite fields

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric matrix B ∈ 𝔽 n×n is defined as ℓ1ℓ2· · · ℓ n , where ℓ j ∈ {A, S, N} according to whether all, some but not all, or none of the principal minors of order j of B are nonzero. Building upon the second author’s recent classification of the epr-sequences of symmetric matrices over the field 𝔽 = 𝔽2, we initiate a study of the case 𝔽= 𝔽3. Moreover, epr-sequences over finite fields are shown to have connections to Ramsey theory and coding theory.

Striatal dopamine explains novelty-induced behavioral dynamics and individual variability in threat prediction

Animals exhibit diverse behavioral responses, such as exploration and avoidance, to novel cues in the environment. However, it remains unclear how dopamine neuron-related novelty responses influence behavior. Here, we characterized dynamics of novelty exploration using multi-point tracking (DeepLabCut) and behavioral segmentation (MoSeq). Novelty elicits a characteristic sequence of behavior, starting with investigatory approach and culminating in object engagement or avoidance. Dopamine in the tail of striatum (TS) suppresses engagement, and dopamine responses were predictive of individual variability in behavior. Behavioral dynamics and individual variability were explained by a novel reinforcement learning (RL) model of threat prediction, in which behavior arises from a novelty-induced initial threat prediction (akin to shaping bonus), and a threat prediction that is learned through dopamine-mediated threat prediction errors. These results uncover an algorithmic similarity between reward- and threat-related dopamine sub-systems.

Minimal Automaton for Multiplying and Translating the Thue-Morse Set

The Thue-Morse set $\mathcal{T}$ is the set of those non-negative integers whose binary expansions have an even number of $1$'s. The name of this set comes from the fact that its characteristic sequence is given by the famous Thue-Morse word $${\tt 0110100110010110\cdots},$$ which is the fixed point starting with ${\tt 0}$ of the word morphism ${\tt 0\mapsto 01}$, ${\tt 1\mapsto 10}$. The numbers in $\mathcal{T}$ are commonly called the evil numbers. We obtain an exact formula for the state complexity of the set $m\mathcal{T}+r$ (i.e. the number of states of its minimal automaton) with respect to any base $b$ which is a power of $2$. Our proof is constructive and we are able to explicitly provide the minimal automaton of the language of all $2^p$-expansions of the set of integers $m\mathcal{T}+r$ for any positive integers $p$ and $m$ and any remainder $r\in\{0,\ldots,m{-}1\}$. The proposed method is general for any $b$-recognizable set of integers.

Archerfish coordinate fin-maneuvers with their shots

Archerfish down a variety of aerial prey from a range of distances using water jets that they adjust to size and distance of their prey. We describe here that characteristic rapid fin maneuvers, most notably of the pectoral and pelvic fins, are precisely coordinated with the release of the jet. We discovered these maneuvers in two fish that had been trained to shoot from fixed positions at targets in different height, whose jets had been characterized in detail and who remained stable during their shots. Based on the findings in these individuals we examined shooting-associated fin-movement in 28 further archerfish of two species that could shoot from freely chosen positions at targets of different height. Slightly before onset of the water jet, at a time when the shooter remains stable, the pectoral fins of all shooters switched from asynchronous low-amplitude beating to a synchronized rapid forward flap. Onset and duration of the forward and subsequent backward flap were robust across all individuals and shooting angles but depended on target height. The pelvic fins are slowly adducted at the start of the jet and stop after its release. All other fins also showed a characteristic sequence of activation, some starting about 0.5 s before the shot. Our findings suggest that shooting-related fin-maneuvers are needed to stabilize the shooter and that they are an important component in the precise and powerful far-distance shooting in archerfish.

Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis

A combination of spectral kurtosis (SK), based on Choi–Williams distribution (CWD) and hidden Markov models (HMM), accurately identifies initial gearbox failures and diagnoses fault types of gearboxes. First, using the LMD algorithm, five types of gearbox vibration signals are collected and decomposed into several product function (PF) components and the multicomponent signals are decomposed into single-component signals. Then, the kurtosis value of each component is calculated, and the component with the largest kurtosis value is selected for the CWD-SK analysis. According to the calculated CWD-SK value, the characteristics of the initial failure of the gearbox are extracted. This method not only avoids the difficulty of selecting the window function, but also provides original eigenvalues for fault feature classification. In the end, from the CWD-SK characteristic parameters at each characteristic frequency, the characteristic sequence based on CWD-SK is obtained with HMM training and diagnosis. The experimental results show that this method can effectively identify the initial fault characteristics of the gearbox, and also accurately classify the fault characteristics of different degrees.

Pascal conductance series in ballistic one-dimensional LaAlO3/SrTiO3 channels

One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO3/SrTiO3) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e2/h, where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.

USING SEQUENCE PATTERNS TO IDENTIFY AND DESIGN NEW ANTIMICROBIAL PEPTIDES

Natural antimicrobial peptides (AMPs) are remarkably diverse, yet they all share some common structural and functional features. In an attempt to find what determines similar activities of non-homologous molecules, we performed a comprehensive analysis of sequence patterns in AMPs. We found that natural AMPs possess characteristic sequence patterns, and these patterns differ for peptides with α-helical and β-sheet structure. We showed that the patterns facilitate computational identification of AMPs in databases. We then used patterns to design new peptides, synthesized them and assayed for antibacterial activity. The most active among synthetic peptides exhibited activity against Gram(+) and Gram(-) pathogens comparable to best natural AMPs.

Type I Toxin-Antitoxin Systems in Clostridia

Type I toxin-antitoxin (TA) modules are abundant in both bacterial plasmids and chromosomes and usually encode a small hydrophobic toxic protein and an antisense RNA acting as an antitoxin. The RNA antitoxin neutralizes toxin mRNA by inhibiting its translation and/or promoting its degradation. This review summarizes our current knowledge of the type I TA modules identified in Clostridia species focusing on the recent findings in the human pathogen Clostridium difficile. More than ten functional type I TA modules have been identified in the genome of this emerging enteropathogen that could potentially contribute to its fitness and success inside the host. Despite the absence of sequence homology, the comparison of these newly identified type I TA modules with previously studied systems in other Gram-positive bacteria, i.e., Bacillus subtilis and Staphylococcus aureus, revealed some important common traits. These include the conservation of characteristic sequence features for small hydrophobic toxic proteins, the localization of several type I TA within prophage or prophage-like regions and strong connections with stress response. Potential functions in the stabilization of genome regions, adaptations to stress conditions and interactions with CRISPR-Cas defence system, as well as promising applications of TA for genome-editing and antimicrobial developments are discussed.