scholarly journals Using Zigzag Persistent Homology to Detect Hopf Bifurcations in Dynamical Systems

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 278
Author(s):  
Sarah Tymochko ◽  
Elizabeth Munch ◽  
Firas A. Khasawneh
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Persistent Homology ◽  
Computational Cost ◽  
Normal System ◽  
Step Method ◽  
Persistence Diagram ◽  
One Step ◽  
Entire Experiment ◽  
Zigzag Persistence

Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. In an experimental setting, this transition could lead to incorrect data or damage to the entire experiment. While standard persistent homology has been used in this setting, it usually requires analyzing a collection of persistence diagrams, which in turn drives up the computational cost considerably. Using zigzag persistence, we can capture topological changes in the state space of the dynamical system in only one persistence diagram. Here, we present Bifurcations using ZigZag (BuZZ), a one-step method to study and detect bifurcations using zigzag persistence. The BuZZ method is successfully able to detect this type of behavior in two synthetic examples as well as an example dynamical system.

An Alternate Algorithm for (3x3) Median Filtering of Digital Images

2012 ◽  
Vol 2 (1) ◽  
pp. 7-9 ◽  
Author(s):  
Satinderjit Singh
Keyword(s):  
Median Filter ◽  
Computational Cost ◽  
Spatial Coherence ◽  
General Purpose ◽  
Median Filtering ◽  
Basic Algorithm ◽  
Temporal Complexity ◽  
Filter Kernel ◽  
One Step ◽  
High Computational Cost

Median filtering is a commonly used technique in image processing. The main problem of the median filter is its high computational cost (for sorting N pixels, the temporal complexity is O(N·log N), even with the most efficient sorting algorithms). When the median filter must be carried out in real time, the software implementation in general-purpose processorsdoes not usually give good results. This Paper presents an efficient algorithm for median filtering with a 3x3 filter kernel with only about 9 comparisons per pixel using spatial coherence between neighboring filter computations. The basic algorithm calculates two medians in one step and reuses sorted slices of three vertical neighboring pixels. An extension of this algorithm for 2D spatial coherence is also examined, which calculates four medians per step.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Effect of Dynamic Crosslinking on Mechanical Properties of PP/EPDM Blends

1993 ◽  
Vol 58 (11) ◽  
pp. 2642-2650 ◽  
Author(s):  
Zdeněk Kruliš ◽  
Ivan Fortelný ◽  
Josef Kovář
Keyword(s):  
Mechanical Properties ◽  
Impact Strength ◽  
Shear Modulus ◽  
High Impact ◽  
Necessary Condition ◽  
Step Method ◽  
Melt Mixing ◽  
One Step ◽  
High Impact Strength ◽  
Dynamic Curing

The effect of dynamic curing of PP/EPDM blends with sulfur and thiuram disulfide systems on their mechanical properties was studied. The results were interpreted using the knowledge of the formation of phase structure in the blends during their melt mixing. It was shown, that a sufficiently slow curing reaction is necessary if a high impact strength is to be obtained. Only in such case, a fine and homogeneous dispersion of elastomer can be formed, which is the necessary condition for high impact strength of the blend. Using an inhibitor of curing in the system and a one-step method of dynamic curing leads to an increase in impact strength of blends. From the comparison of shear modulus and impact strength values, it follows that, at the stiffness, the dynamically cured blends have higher impact strength than the uncured ones.

Bismuth particles imbedded degradable nanohydrogel prepared by one-step method for tumor dual-mode imaging and chemo-photothermal combined therapy

2019 ◽  
Vol 375 ◽  
pp. 122000 ◽  
Author(s):  
Yang Xuan ◽  
Xian-Lin Song ◽  
Xiao-Quan Yang ◽  
Ruo-Yun Zhang ◽  
Zi-Yu Song ◽  
...  
Keyword(s):  
Combined Therapy ◽  
Dual Mode ◽  
Step Method ◽  
One Step

scholarly journals Potential Well in Poincaré Recurrence

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 379
Author(s):  
Miguel Abadi ◽  
Vitor Amorim ◽  
Sandro Gallo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Recurrence Time ◽  
Potential Well ◽  
Exponential Approximation ◽  
Mixing Processes ◽  
System Perspective ◽  
Return Times ◽  
Error Terms

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

scholarly journals Bio-Based Polyurethane Networks Derived from Liquefied Sawdust

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3138
Author(s):  
Kamila Gosz ◽  
Agnieszka Tercjak ◽  
Adam Olszewski ◽  
Józef Haponiuk ◽  
Łukasz Piszczyk
Keyword(s):  
Biomass Conversion ◽  
Structural Features ◽  
Mechanical Analysis ◽  
Process Efficiency ◽  
Hydroxyl Number ◽  
Step Method ◽  
One Step ◽  
Liquefaction Process ◽  
The Fourier Transform ◽  
Liquefaction Temperature

The utilization of forestry waste resources in the production of polyurethane resins is a promising green alternative to the use of unsustainable resources. Liquefaction of wood-based biomass gives polyols with properties depending on the reagents used. In this article, the liquefaction of forestry wastes, including sawdust, in solvents such as glycerol and polyethylene glycol was investigated. The liquefaction process was carried out at temperatures of 120, 150, and 170 °C. The resulting bio-polyols were analyzed for process efficiency, hydroxyl number, water content, viscosity, and structural features using the Fourier transform infrared spectroscopy (FTIR). The optimum liquefaction temperature was 150 °C and the time of 6 h. Comprehensive analysis of polyol properties shows high biomass conversion and hydroxyl number in the range of 238–815 mg KOH/g. This may indicate that bio-polyols may be used as a potential substitute for petrochemical polyols. During polyurethane synthesis, materials with more than 80 wt% of bio-polyol were obtained. The materials were obtained by a one-step method by hot-pressing for 15 min at 100 °C and a pressure of 5 MPa with an NCO:OH ratio of 1:1 and 1.2:1. Dynamical-mechanical analysis (DMA) showed a high modulus of elasticity in the range of 62–839 MPa which depends on the reaction conditions.

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

Discussion on Repair Method of Concrete Highway Pavement

2013 ◽  
Vol 321-324 ◽  
pp. 209-212
Author(s):  
Chun Yan Xia
Keyword(s):  
Mechanical Properties ◽  
Preparation Program ◽  
Step Method ◽  
Concrete Technology ◽  
Concrete Material ◽  
Repair Method ◽  
Ordinary Concrete ◽  
One Step ◽  
Highway Pavement

nfluences on properties of the concrete highway pavement were analyzed in this paper, and the optimal formulation materials were gotten to use in the repair of used-broken cement blocks in the experiment. Polyurethane concrete material was prepared, combing the ordinary concrete technology with one-step method of the synthesis of polyurethane hard bubble, and then its mechanical properties of the relevant parameters were measured to determine the optimal preparation program. The results show that the polyurethane concrete also has sufficiently good mechanical properties while it has the characteristic of fast patching.

scholarly journals The Dynamics of Musical Participation

2021 ◽  
pp. 102986492098831
Author(s):  
Andrea Schiavio ◽  
Pieter-Jan Maes ◽  
Dylan van der Schyff
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Coordination Dynamics ◽  
Musical Experience ◽  
The Core ◽  
Interactive Dynamics ◽  
Interdisciplinary Scholarship ◽  
Core Features

In this paper we argue that our comprehension of musical participation—the complex network of interactive dynamics involved in collaborative musical experience—can benefit from an analysis inspired by the existing frameworks of dynamical systems theory and coordination dynamics. These approaches can offer novel theoretical tools to help music researchers describe a number of central aspects of joint musical experience in greater detail, such as prediction, adaptivity, social cohesion, reciprocity, and reward. While most musicians involved in collective forms of musicking already have some familiarity with these terms and their associated experiences, we currently lack an analytical vocabulary to approach them in a more targeted way. To fill this gap, we adopt insights from these frameworks to suggest that musical participation may be advantageously characterized as an open, non-equilibrium, dynamical system. In particular, we suggest that research informed by dynamical systems theory might stimulate new interdisciplinary scholarship at the crossroads of musicology, psychology, philosophy, and cognitive (neuro)science, pointing toward new understandings of the core features of musical participation.

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