Fractal-like Structure Research Articles

Efficient Storage and Analysis of Genomic Data: A k-mer Frequency Mapping and Image Representation Method.

k-mer frequencies are crucial for understanding DNA sequence patterns and structure, with applications in motif discovery, genome classification, and short read assembly. However, the exponential increase in the dimension of frequency tables with increasing k-mer length poses storage challenges. In this study, we present a novel method for compressing k-mer data without information loss, aiming to optimize storage and analysis processes. We employed Chaos Game Representation (CGR) to map k-mers to coordinates and used these components to generate raster images of k-mers. The CGR maps were partitioned and labeled based on substrings, with each substring mapped to a subframe, creating a fractal-like structure. The entire k-mer frequency set of each genomic sequence was represented as a single image, with each pixel corresponding to a specific k-mer and its occurrence. This approach reduced file size by up to 16-fold compared to plain text and 3-fold compared to binary format. Furthermore, we demonstrated the feasibility of performing alignment-free similarity analyses on images derived from k-mer frequencies of whole genome sequences from 14 plant species. Our results highlight the potential of this method as a fast and efficient tool for accessing, processing, and analyzing large biological sequence datasets, enabling the retrieval of k-mer frequencies and image reconstruction.

Discrete element model of nanoparticle deposition during electrospraying

Electrospraying is a technique for the production and deposition of nanoparticles. However, deposited layer morphology is strongly dependent on the operating conditions and hard to predict. Here, we present a spatially 3D model based on the Discrete Element Method (DEM) with the analytical evaluation of interparticle forces and drag force and the numerical evaluation of electric force. The developed connection between mesh-free DEM and mesh-based Finite Volume Method (FVM) used for the evaluation of electric potential field enables to lower the computational time while maintaining accuracy of the predictions We focus on modelling the influence of interparticle forces on particle deposition and deposited layer morphology, which are phenomena usually neglected in the literature so far. Preferential landing of particles is indicated to be a consequence of both electric force and Van der Waals forces. Contact particle interactions allow particle stacking (creating thus fractal-like structure) or allow falling down of particles and their rearrangement (leading to compact layers).

The Efficiency of Surface Impedance Technique in the Transverse Wave Approach for the EM-Modeling of Fractal-Like Tree Structure used in 5G Applications

Fractal antenna technology is a promising approach for 5G applications because its complex nature offers optimization potential in terms of time and space trade-offs. However, the computational effort required to analyze such antennas is significant. This paper investigates the Advanced Transverse Wave Approach (ATWA), which utilizes the surface impedance technique to improve simulation efficiency. This study introduces and analyzes a fractal-like 5G tree structure, displaying improved computational accuracy and efficacy, as well as peak memory utilization compared to current works. The proposed approach demonstrates significant effectiveness in enhancing the performance of complex fractal antennas for 5G technology and shows promise for integration with cloud, fog, and edge computing environments. This integration could potentially optimize data processing and network efficiency in these advanced computing landscapes.

Spectral signatures of coexisting isolas and four-wave mixing under the effect of noise in photonic oscillators

The optical power spectrum is the prime observable to dissect, understand, and design the long- time behavior of small and large arrays of optically coupled semiconductor lasers. A long-standing issue has been identified within the literature of injection locking in photonic oscillators: first how the thickness of linewidth and the lineshape spectral envelope correlates with the deterministic evolution of the monochromatic injected laser oscillator and second how the presence of noise and the typically dense proximity in phase space of coexisting limit cycles of the coupled system are shaping and influencing the overall spectral behavior. In addition, we are critically interested in the regions where the basin of attraction has a fractal-like structure, still, the long-time orbits are P1 (period 1) and/or P3 (period 3) limit cycles. Numerically computed evidence shows that, when the coupled system lives in the regions of coexisting isolas and four-wave mixing (FWM) limit cycles, the overall optical power spectrum is deeply imprinted by a strong influence from the underlying noise sources. A particularly intriguing observation in this region of parameter space that we examine is that the isolas draw most of the trajectories on its phase space path.

Spin Drude weight for the integrable XXZ chain with arbitrary spin

Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight at zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices (T-functions) and derive functional relations (T- and Y-systems) satisfied by the T-functions and certain combinations of them (Y-functions). Through analytical arguments, the Y-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e. the Y-functions) can be explicitly written in terms of the T-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.

Low-Loading Mixed Matrix Materials: Fractal-Like Structure and Peculiarly Enhanced Gas Permeability.

Mixed matrix materials (MMMs) containing metal-organic framework (MOF) nanoparticles are attractive for membrane carbon capture. Particularly, adding <5 mass % MOFs in polymers dramatically increased gas permeability, far surpassing the Maxwell model's prediction. However, no sound mechanisms have been offered to explain this unusual low-loading phenomenon. Herein, we design an ideal series of MMMs containing polyethers (one of the leading polymers for CO2/N2 separation) and discrete metal-organic polyhedra (MOPs) with cage sizes of 2-5 nm. Adding 3 mass % MOP-3 in a polyether increases the CO2 permeability by 100% from 510 to 1000 Barrer at 35 °C because of the increased gas diffusivity. No discernible changes in typical physical properties governing gas transport properties are detected, such as glass transition temperature, fractional free volume, d-spacing, etc. We hypothesize that this behavior is attributed to fractal-like networks formed by highly porous MOPs, and for the first time, we validate this hypothesis using small-angle X-ray scattering analysis.

Stride-to-stride variability is altered when running to isochronous visual cueing but remains unaltered with fractal cueing

ABSTRACT Running synchronised to external cueing is often implemented in both clinical and training settings, and isochronous cueing has been shown to improve running economy. However, such cueing disregards the natural stride-to-stride fluctuations present in human locomotion which is thought to reflect higher levels of adaptability. The present study aimed to investigate how alterations in the temporal structure of cueing affect stride-to-stride variability during running. We hypothesised that running using cueing with a fractal-like structure would preserve the natural stride-to-stride variability of young adults. Thirteen runners performed four 8-min trials: one uncued (UNC) trial and three cued trials presenting an isochronous (ISO), a fractal (FRC) and a random (RND) structure. Repeated measures ANOVAs were used to identify changes in the dependent variables. We have found no main effect on the cardiorespiratory parameters, whereas a significant main effect was observed in the temporal structure of stride-to-stride variability. During FRC, the participants were able to retain the fractal patterns of their natural locomotor variability observed during the UNC condition, while during the ISO and RND they exhibited more random of fluctuations (i.e., lower values of fractal scaling). Our results demonstrate that cueing based on the natural stride-to-stride fluctuations opens new avenues for training and rehabilitation.

Distribution Generated by a Random Inhomogenous Fibonacci Sequence

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THE FRACTAL STRUCTURE OF ANALYTICAL SOLUTIONS TO FRACTIONAL RICCATI EQUATION

Analytical solutions to the fractional Riccati equation are considered in this paper. Solutions to fractional differential equations are expressed in the form of fractional power series in the Caputo algebra. It is demonstrated that solutions to higher-order Riccati fractional equations inherit some solutions from lower-order Riccati equations under special initial conditions. Such nested and fractal-like structure of solutions is investigated by means of analytical fractional differentiation operator techniques and computational experiments.

Waste frying oil derived carbon nano-onions as a cost-effective cathode material for high-voltage zinc-ion hybrid supercapacitors

Energy crisis and environmental pollution are two major worldwide issues that can be solved by developing sustainable, commercial, and long-durability energy storage systems from the reutilization of waste material. Waste frying oil, a known waste, is used as a carbon source for the synthesis of carbon nano-onions (CNOs) using economically viable and environmentally friendly wick pyrolysis techniques. The as-synthesized CNOs were used as a cost-effective cathode in zinc-ions hybrid supercapacitors (Zn–HSCs). CNOs with a fractal-like structure in an interconnected network and more accessible active available surface area provide great advantage as a cathode to fabricate Zn–HSCs. The CNOs-based active cathode material in aqueous Zn–HSCs presents a high specific capacitance of 342 F g−1 at a current density of 0.5 A g−1 under a high working potential window (0–1.9 V). Zn–HSCs achieve a maximum 8.2 kW kg−1 of power density and 164.33 W h kg−1 of energy density. More significantly, excellent long-term durability with 83 % of capacity retention and 100 % retention of coulombic efficiency was also achieved after 10,000 cycles at a high 10 A g−1 of current density. The overall work represents a way of utilizing waste frying oil as a cost-effective and efficient cathode material for aqueous Zn–HSCs, which could aid-in the commercialization of Zn–HSCs.

Oxidation dynamics of soot or carbon black accounting for its core-shell structure and pore network

Internal oxidation is most important for removal of soot in diesel particulate filters. Furthermore, it enhances the porosity of carbon blacks (CBs), increases their specific surface area, SSA, determining their performance in batteries, inks and tires, as well as their environmental and health impact. Current models for oxidation of soot or CB neglect its fractal-like pore network during internal oxidation and underestimate its SSA by 60 % on average! Here, a lattice Monte Carlo (LMC) model elucidates both external and internal oxidation dynamics of soot (or CB) accounting for its fractal-like pore structure, for the first time to the best of our knowledge. Random internal oxidation takes place at the bulk soot (or CB), expanding its pore network and increasing the pore fractal dimension, Dfp, up to 3, in good agreement with data. This increases the SSA up to a factor of ten at 75 % conversion. In the presence of a less reactive shell though, internal oxidation stops after the reactive core is consumed. Thus the SSA levels off at large conversions (>50 %). Hence, accounting for the realistic core-shell, fractal-like pore structure during simultaneous external and internal oxidation nicely explains several measurements of soot and CB Dfp, SSA and particle diameter. So the LMC-derived oxidation dynamics of soot or CB presented here can be used to assist the design of highly porous CB grades from first principles, as well as the mitigation of soot emissions by enhancing their oxidation.

THE TWO-SCALE FRACTAL DIMENSION: A UNIFYING PERSPECTIVE TO METABOLIC LAW

The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.

Fürjek és akácok

An important problem of Imre Oravecz’s trilogy is the relationship between man and nature. This brief analyses concentrates only on two motifs and provide a more detailed interpretation of a few short passages of the text, which show striking motivic and structural similarities and seem to be organized in a way that they interpret each other. The problem of the ’quail’, which is also the title of the volume, is one of the most important elements of a rather complex web of references. It signifies (often in a proleptic way) the changes occurring in the relationship between human and nature, domesticity and strangeness, community and individual, or even father and son. In order to gain a clearer picture of the novel’s fractal-like motivic structure, I concentrate on the episodes in which István encounters quails and point out that in each case, the birds are associated with similar feelings and emotions by the language of narration.

Research on Monitoring Method of Stock Market Systematic Crash Based on Market Transaction Data

Sharp rises and falls in stock prices have become increasingly frequent in recent years. Stock market crashes bring great risks to the stability of the securities markets. Using recurrence plot theory and a heuristic segmentation algorithm for detecting abrupt changes in nonlinear time series, this study investigates the problem of detecting abrupt endogenous structural changes before a stock market crash. Based on an analysis of crash events in 12 developed and 10 emerging countries and regions, the authors find the following: (1) The market laminar flow (LAM) value will fall greatly before a stock market crash; (2) the LAM sequence of the US stock market during the 2008 financial crisis presents a fractal-like self-similar structure, and blank bands appears in the recurrence plot, indicating a phase transition in the LAM sequence before the crash; and. (3) using a heuristic segmentation algorithm to detect abrupt changes in nonlinear time series, this study finds that before a crash, the endogenous structure of the market continuously experiences abnormal abrupt changes, and abnormal abrupt change time.

Stride-to-Stride Fluctuations of Human Gait Are Affected By Chronobiology: An Exploratory Study.

Physiological processes present daily oscillations of ≈24 h, called circadian rhythms. Motor performance, for example, reaches its peak in the afternoon, although this can be affected by chronotype. Certain motor activities, for example, walking, can also be affected by circadian rhythms. Healthy walking exhibits stride-to-stride fluctuations with a fractal-like structure that enables adaptability. While pathology and aging are shown to lead to random-like fluctuations; and, therefore, decreased adaptability; the influence of circadian rhythms remains unknown. This study investigates how these fluctuations present in healthy gait are affected by the time of day and chronotype. Eighteen young adults walk for 10 min every 2 h, from 8 a.m. to 6 p.m. Footswitches are used to determine heel-strike and calculate stride time. Then, detrended fluctuation analysis is used to calculate fractal scaling. A mixed-model Analysis of Varianceis used and followed by a backward stepwise elimination process. Tukey's tests are used for pairwise comparisons. The statistical model shows the effect of time during the day (12 p.m. exhibits a higher fractal scaling compared to 8 a.m.); and chronotype (evening-types exhibit higher fractal scaling compared to morning-types). This study reveals the influence of chronobiology on stride-to-stride fluctuations. These findings open new perspectives to integrate circadian medicine in biomechanics.

Design Methodology for Development of Experimental Setup for Fabrication of Controlled Micro and Meso Fractals

Recently various control methodology has been demonstrated by researchers to fabricate the spontaneously multiscale fractal-like structure. These multiscale fractal structures mimic different living structures available in nature, such as a leaf, vascular systems in the animal kingdom etc. This paper presents the design methodology for the development of the system to fabricate these multiscale fractal structures spontaneously with the flexibility to vary the control parameters on a wide range. Various components require in the system are a system of two plates arresting fluid in between them. One plate out of two is fixed while the other is allowed to move. The primary attributes for the generation of fractal structures are the separation distance between plates, the volume of fluid trapped in the plates, the separation velocity, and the provision for lift orientation. The paper discusses a cost-effective way to develop a setup embodying different processing parameters and finally yielding precise fabrication of micro-fractals. The designed experimental setup can be used to successfully fabricate micro-fractals with different process parameters.

IDENTIFICATION OF PATTERNS IN GRADUATES’ PROFESSIONAL INTENTIONS WHEN PROCESSING THE RESULTS OF THE UNIFIED STATE EXAM IN THE UDMURT REPUBLIC

The article summarizes the experience of research devoted to statistical analysis and data processing of the results of the unified state exam (USE) of school graduates of the Udmurt Republic for different periods. It is shown, that the rank-power law of Zipf-Mandelbrot makes it possible to identify the professional intentions of USE respondents who have the property of self-similarity. Thus, the distribution of USE respondents of the Udmurt Republic is similar to the distribution in a separate school or district, which means that the object of study has a fractal-like structure. The metric characteristic of the structure under study is the fractal dimension determined from the Zipf-Mandelbrot regularity. The fractal nature of such an instrument of pedagogical measurement and diagnostics of the control of the education system, which in essence should be the Unified State Exam, has a psychological conditioning: any pedagogical object has its own measure and dimension and is didactically unique, as each individual is unique. This technique allows us to identify a kind of vector of professional intentions, general social trends of professional orientation of school graduates. Therefore, it seems appropriate to include such an analysis in the relevant reporting documents of the upcoming Unified State Exam and to take these trends into account when planning the career guidance work of universities.

Fractal structures of PA6/POE blend nanocomposites and their dynamic properties

We investigate the effect of minor phase rheological properties and compatibilizer on the phase morphology and graphene 3D structure in polyamide-6 (PA6)/polyolefin elastomer (POE) blends. It is revealed that in blends containing low viscosity (LV) POE, graphene is better dispersed facilitating its localization at the interface. In the blend containing high viscosity (HV) POE with poor graphene dispersion, large graphene aggregates are observed inside the POE phase with less interfacial coverage. Interestingly, graphene induces a co-continuous morphology and electrical and rheological percolation in both systems, although at a lower graphene content for the LV system. The LV system exhibits a more interconnected morphology, while in the HV system we observe a compact fractal-like POE structure with a lower degree of interconnectivity. Our morphological observation suggests that co-continuous morphology in the LV system is dominated by sheet formation, while in the HV system it is dominated by coalescence between moderately elongated domains. Fractal analysis of the graphene 3D network (based on the rheological characterization) is correlated with the higher degree of connectivity of the graphene 3D structure in the LV system. The 2D fractal dimension of the POE phase (host phase for graphene) is in line with the fractal dimension of the graphene flocs, indicating that the graphene flocs influence the blend morphology. The addition of compatibilizer to the HV system did not result in improved electrical properties.

Influence of polymer molar mass and mixture stoichiometry on polyelectrolyte complexes of poly(l-arginine) and Poly(l-glutamic acid)

Poly(l-arginine) (PARG) and poly(l-glutamic acid) (PLGA) homopolypeptides were custom synthesized by precision N-carboxyanhydride ring-opening polymerization methods with two molar masses, matched for pairs of cationic and anionic polypeptides (degrees of polymerization n = 100 and n = 500). The conformations of the homopolypeptides were probed using circular dichroism (CD) and FTIR spectroscopy which revealed the presence of mainly polyproline II (PPII) conformation. Small-angle X-ray scattering (SAXS) showed concentration-dependent polyelectrolyte peaks and form factor with high q scaling due to the excluded volume behaviour of the wormlike chains. We then examined polyelectrolyte complexation in mixtures of pairs of PARG and PLGA polypeptides with matched molar masses. Precipitation was generally observed and the structures of precipitates, supernatant and resuspended precipitates were investigated using CD, SAXS and cryo-TEM. These revealed that, contrary to prior suggestions in the literature, the precipitates contain mostly polypeptides in a PPII-like conformation, and there is only a minimal β-sheet content (which is enhanced upon drying the sample during preparation for certain measurements). The precipitates have a fractal-like structure as revealed by cryo-TEM and SAXS. Our findings on the structure of polypeptide complex precipitates contribute to the understanding of phase separation of polyelectrolyte complexes and coacervation and may shed light on the formation of inter-cellular bodies of proteins and peptides such as Lewy and other inclusion bodies.

3D Printed Fractal-like Structures with High Percentage of Drug for Zero-Order Colonic Release.

Colonic drug delivery of drugs is an area of great interest due to the need to treat high prevalence colonic local diseases as well as systemic conditions that may benefit from the advantages associated to this route of drug administration. In the last decade, the use of 3D printing technologies has expanded, offering the possibility of preparing personalized medicines in small batches directly at the point of care. The aim of this work is to design a high drug loaded 3D printed system prepared by a combination of Fused Deposition Modelling (FDM) and Injection Volume Filling (IVF) techniques intended for zero-order colonic drug release. For this purpose, different batches of binary and ternary filaments based on the thermoplastic polyurethane Tecoflex EG-72D (TPU), theophylline anhydrous (AT) as model drug, and magnesium stearate as lubricant have been developed and characterized. Filaments with the highest drug load and the best rheological properties were selected for the manufacture of a printed fractal-like structure based on multiple toroids. This design was proposed to provide high surface area, leading to increased drug release and water uptake in the colonic region. This structure was 3D printed by FDM and then coated in a unique step by IVF technology using the enteric polymer DrugCoat S 12.5. This way, an additional coating process is avoided, reducing costs and production time. Studies of drug release confirmed the ability of the structures to provide a five-hour period of constant drug delivery in the colonic region.