In time series analysis, the ability to effectively handle data with varying sampling rates is crucial for accurate modeling and analysis. This paper presents the MR-BoF (Multi-Resolution Bag of Functions) framework, which leverages sampling-rate-independent techniques to decompose time series data while accommodating signals with differing resolutions. Unlike traditional methods that require uniform sampling frequencies, the BoF framework employs a flexible encoding approach, allowing for the integration of multi-resolution time series. Through a series of experiments, we demonstrate that the BoF framework ensures the precise reconstruction of the original data while enhancing resampling capabilities by utilizing decomposed components. The results show that this method offers significant advantages in scenarios involving irregular sampling rates and heterogeneous acquisition systems, making it a valuable tool for applications in fields such as finance, healthcare, industrial monitoring, IoT networks, and sensor networks.

Aquaculture's rapid expansion raises significant concerns regarding antibiotic resistance, particularly in freshwater systems where Escherichia coli (E. coli) serve as a key indicator of fecal contamination. This study investigates mutation frequencies of E. coli strains from aquatic environments under selective pressure from oxytetracycline and chloramphenicol. Given that E. coli's antibiotic resistance is a growing public health issue, understanding mutation dynamics is crucial. We evaluated mutation frequencies in five E. coli strains isolated from fish, water, and sediment samples. These strains were initially sensitive to chloramphenicol and oxytetracycline. The mutation rates for oxytetracycline ranged between 4.12 x10-8 and 5.52 x 10-8 , while chloramphenicol exposure led to mutation frequencies from 1.19 x 10-4 to 9.62 x 10-5 . Cluster analysis using hierarchical methods revealed distinct patterns: E. coli strains exposed to oxytetracycline exhibited more uniform mutation frequencies compared to those exposed to chloramphenicol. The proximity matrix and dendrogram analysis demonstrated that oxytetracycline-treated strains clustered closely together, indicating similar mutational responses. Conversely, chloramphenicol-treated strains displayed greater variability, suggesting that chloramphenicol causes more diverse genetic changes in E. coli. The findings highlight an alarming increase in mutation rates, especially under chloramphenicol exposure, which significantly exceeds typical environmental bacterial mutation rates. These findings indicate a significant risk of antibiotic resistance and underscore the need for strict regulations and regular monitoring in aquaculture to manage it. Future research should investigate the specific mutations, strain genomics, and environmental factors contributing to resistance to address public health concerns related to antibiotic-resistant bacteria.

For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the setting of σ-compact locally compact Abelian groups and show that the topological entropy of the associated Delone dynamical system is zero. For this we provide a suitable version of the variational principle. We furthermore construct counterexamples, which show that the patch counting entropy of such sets can be non-zero in this context. Other counterexamples will show that the patch counting entropy of such a set cannot be computed along a limit and even be infinite in this setting.

Abstract In this paper, we construct a uniformly recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent infinite word to admit uniform frequencies.

Given a positive integer N and x∈[0,1]∖Q, an N-continued fraction expansion of x is defined analogously to the classical continued fraction expansion, but with the numerators being all equal to N. Inspired by Sturmian sequences, we introduce the N-continued fraction sequencesω(x,N) and ωˆ(x,N), which are related to the N-continued fraction expansion of x. They are infinite words over a two letter alphabet obtained as the limit of a directive sequence of certain substitutions, hence they are S-adic sequences. When N=1, we are in the case of the classical continued fraction algorithm, and obtain the well-known Sturmian sequences. We show that ω(x,N) and ωˆ(x,N) are C-balanced for some explicit values of C and compute their factor complexity function. We also obtain uniform word frequencies and deduce unique ergodicity of the associated subshifts. Finally, we provide a Farey-like map for N-continued fraction expansions, which provides an additive version of N-continued fractions, for which we prove ergodicity and give the invariant measure explicitly.

We disclose a new class of patterns, called patched patterns, in arrays of non-locally coupled excitable units with attractive and repulsive interactions. The self-organization process involves the formation of two types of patches, majority and minority ones, characterized by uniform average spiking frequencies. Patched patterns may be temporally periodic, quasiperiodic, or chaotic, whereby chaotic patterns may further develop interfaces comprised of units with average frequencies in between those of majority and minority patches. Using chaos and bifurcation theory, we demonstrate that chaos typically emerges via a torus breakup and identify the secondary bifurcation that gives rise to chaotic interfaces. It is shown that the maximal Lyapunov exponent of chaotic patched patterns does not decay, but rather converges to a finite value with system size. Patched patterns with a smaller wavenumber may exhibit diffusive motion of chaotic interfaces, similar to that of the incoherent part of chimeras.

Device agnostic AI-based analysis of ambulatory ECG recordings

We study a special case of Hamming–Huffman trees, in which both data compression and data error detection are tackled on the same structure. Given a hypercubeQnof dimensionn, we are interested in some aspects of its vertex neighborhoods. For a subsetLof vertices ofQn, the neighborhood ofLis defined as the union of the neighborhoods of the vertices ofL. The minimum neighborhood problem is that of determining the minimum neighborhood cardinality over all those setsL. This is a well-known problem that has already been solved. Our interest lies in determining optimal Hamming–Huffman trees, a problem that remains open and which is related to minimum neighborhoods inQn. In this work, we consider a restricted version of Hamming–Huffman trees, called [k]-HHT s, which admit symbol leaves in at mostkdifferent levels. We present an algorithm to build optimal [2]-HHT s. For uniform frequencies, we prove that an optimal HHT is always a [5]-HHT and that there exists an optimal HHT which is a [4]-HHT . Also, considering experimental results, we conjecture that there exists an optimal tree which is a [3]-HHT .

Here we investigate the dynamic behavior of self-assembling achiral swimmers in viscous media. The response of magnetically actuated swimmers of two differing geometries is explored under various uniform rotational field frequencies and amplitudes. Kinematic characteristics obtained from tracked swimming motion, including speed, precession angle (wobbling angle), and re-orientation time (turning rate), are determined and reveal nonlinear relationships between the dynamic response of the achiral swimmers and fluid viscosity, which induces drag forces that reduce the speed of propulsion and turning rates. We also find distinct regimes of swimmer motion that are dependent on both fluid viscosity and swimmer geometry. Similar viscosity and geometric dependence is observed for turning rates of swimmers when undergoing rapid changes in field orientation. The characteristic results obtained for microswimmer motion in viscous fluids will contribute to the development of control strategies for propelling other simple swimmers with two or more planes of symmetry. Characterized propulsion kinematics will aid in the optimization of swimmer designs and actuation approaches, critical for future low Reynolds number applications.

A deep-subwavelength metal spiral structure (MSS) waveguide with arbitrary bending angles was proposed and demonstrated to propagate magnetic localized surface plasmons (MLSPs) in theoretical, simulated and experimental ways. The uniform coupling strengths and frequencies for adjacent MSSs with different azimuthal angles represent a significant advancement in the development of structures supporting MLSPs over arbitrary bending angles. The consistency among spectra, dispersion, and field distributions for five MSSs indicates that backward propagation of MLSPs over arbitrary bending angles is possible. In addition, a long S-chain consisting of adjacent MSSs at various angles holds promise for applications involving long-distance MLSPs waveguides.

Morphic words and equidistributed sequences

Refresh schemes have been the default approach in NAND flash memory to avoid data losses. The critical issue of the refresh schemes is that they introduce additional costs on lifetime and performance. Recent work proposed to minimize the refresh costs by using uniform refresh frequencies based on the number of program/erase (P/E) cycles. However, from our investigation, we find that the refresh costs still have a high burden on the lifetime performance. In this paper, a novel refresh minimization scheme is proposed by exploiting the process variation (PV) of flash memory. State-of-the-art flash memory always has significant PV, which introduces large variations on the retention time of flash blocks. In order to reduce the refresh costs, we first propose a new refresh frequency determination scheme by detecting the supported retention time of flash blocks. If the detected retention time is large, a low refresh frequency can be applied to minimize the refresh costs. Second, considering that the retention time requirements of data are varied with each others, we further propose a data hotness and refresh frequency matching scheme. The matching scheme is designed to allocate data to blocks with right higher supported retention time. Through simulation studies, the lifetime and performance are significantly improved compared with state-of-the-art refresh schemes.

Coverability and multi-scale coverability on infinite pictures

Abelian complexity in infinite words is a combinatorial tool which developed essentially during the last five years. In this paper, we undertake to establish connections between abelian complexity and uniform frequencies in infinite words. In particular, we focus on the binary case to link uniform equi-frequency with abelian complexity. We also provide various examples of infinite words to illustrate the absence of connection between usual complexity and abelian complexity. Some properties involving uniform recurrence are also given.

Quantitative constraint-based theories of optionality typically aim to model the frequency with which an individual speaker’s grammar maps one input onto various output forms. But existing studies in this area use population-level frequency data as a proxy for the frequencies produced by an individual speaker’s grammar. This practice is problematic for three reasons. First, population-level variation could result from aggregation over individuals with differing categorical behavior, not individual variation at all. Second, some theories predict that individuals with identical relative constraint rankings/weights can produce those outputs with different frequencies, while others predict uniform frequencies across speakers; these prediction cannot be tested without individual-level data. Third, if indeed individuals differ in their output frequencies, population-level averages may disguise true patterns of individual variation. This paper addresses these shortcomings through a corpus study of optional schwa deletion in French. We find that individual speakers do in fact show variable omission of schwa. We also find variation between speakers in the frequency of schwa’s appearance. Taken together, these results confirm that for French schwa, formal theories are correct to ascribe variation to a single speaker’s grammar, and they favor theories that decouple the means of producing variation from the account of output frequency.

A piezoelectric actuator using the third and fourth bending vibration modes was proposed, designed, fabricated and tested with the aim of accomplishing rotary driving by boltclamped transducer. By superimposing the third and fourth bending vibrations, elliptical movements are formed on the two leading ends of the actuator. When a ring type rotor is in contact with the two diving tips and the vertical preload is applied, the horizontal movements of the driving tips generated by the third bending vibration will push the rotor into motion by frictional forces while the vertical movements produced by the fourth bending vibration will overcome the preload. A method of tuning the resonance frequency of the third bending mode to the fourth bending one was discussed. The horn shape was adjusted to make the two bending modes have nearly uniform frequencies. The vibration characteristic and mechanical ability of a prototype were tested, and the tested resonance frequencies agreed well with the calculated ones. The prototype achieved maximum speed and torque of 86 r/min and 2.5 Nm, respectively.

Chagas disease is a trypanosomiasis whose causative agent is the protozoan parasite Trypanosoma cruzi, which is transmitted to humans by hematophagous insects known as triatomines and affects a large proportion of South America. The digestive tract of the insect vectors in which T. cruzi develops constitutes a dynamic environment that affects the development of the parasite. Thus, we set out to investigate the chemical composition of the triatomine intestinal tract through a metabolomics approach. We performed Direct Infusion Fourier Transform Ion Cyclotron Resonance Mass Spectrometry on fecal samples of three triatomine species (Rhodnius prolixus, Triatoma infestans, Panstrongylus megistus) fed with rabbit blood. We then identified groups of metabolites whose frequencies were either uniform in all species or enriched in each of them. By querying the Human Metabolome Database, we obtained putative identities of the metabolites of interest. We found that a core group of metabolites with uniform frequencies in all species represented approximately 80% of the molecules detected, whereas the other 20% varied among triatomine species. The uniform core was composed of metabolites of various categories, including fatty acids, steroids, glycerolipids, nucleotides, sugars, and others. Nevertheless, the metabolic fingerprint of triatomine feces differs depending on the species considered. The variable core was mainly composed of prenol lipids, amino acids, glycerolipids, steroids, phenols, fatty acids and derivatives, benzoic acid and derivatives, flavonoids, glycerophospholipids, benzopyrans, and quinolines. Triatomine feces constitute a rich and varied chemical medium whose constituents are likely to affect T. cruzi development and infectivity. The complexity of the fecal metabolome of triatomines suggests that it may affect triatomine vector competence for specific T. cruzi strains. Knowledge of the chemical environment of T. cruzi in its invertebrate host is likely to generate new ways to understand the factors influencing parasite proliferation as well as methods to control Chagas disease.

A cline in the frequency of melanic morphs of the two-spot ladybird, Adalia bipunctata, was first surveyed in 1980 along a transect extending inland from the coast in the Netherlands. At that time, the frequency of melanics increased over some 40 km from 10% near the coast to nearly 60% inland. Additional surveys made in 1991 and 1995 demonstrated some progressive change in cline shape. New samples from 1998 and 2004 confirm these dynamics, and show that over a period of about 50 generations for the beetle, the cline had decayed rapidly to yield rather uniform frequencies of melanic morphs at around 20% along the whole transect by 2004. Climate data and evidence for thermal melanism in this species support our contention that these dynamics reflect a dramatic example of a rapid genetic response within populations to climate change and local selection.

Shaking table test was carried out to obtain dynamic characteristics of TLCDs with uniform and non-uniform sections for both horizontal and vertical tubes. The input to the table is harmonic acceleration with constant magnitude. The output is horizontal dynamic force which is measured by load cell installed below the TLCD. Transfer functions are experimentally obtained using the ratio of input and output. Natural frequency, the most important design factor, is compared to that by theoretical equation for TLCDs with five different water levels. System identification process is performed for experimentally obtained transfer functions to find the dynamic characteristics of head loss coefficient and effective mass of TLCDs. It is found that their magnitudes are larger for a TLCD with non-uniform section than with uniform section and natural frequencies are close to theoretical ones.

The genic variability at twenty loci in marginal, submarginal and central populations of Drosophila subobscura has been studied by starch gel electrophoresis. The samples from marginal populations orginate from Finland, the submarginal ones from Sweden and Denmark, whereas flies collected from France and northeastern Italy are taken to represent central populations. The average degrees of genic polymorphism are undifferentiated over the distribution area of D. subobscura. Most loci have fairly uniform allele frequencies in all populations. Local differences have been found at six loci. These fluctuations represent adaptations to local environmental differences.