Symmetry

Research

14 pages, 1247 KiB

Open AccessArticle

Integrated Inference of Asymmetric Protein Interaction Networks Using Dynamic Model and Individual Patient Proteomics Data

by Yan Yan, Feng Jiang, Xinan Zhang and Tianhai Tian

Symmetry 2021, 13(6), 1097; https://doi.org/10.3390/sym13061097 - 21 Jun 2021

Cited by 3 | Viewed by 2296

Abstract

Recent advances in experimental biology studies have produced large amount of molecular activity data. In particular, individual patient data provide non-time series information for the molecular activities in disease conditions. The challenge is how to design effective algorithms to infer regulatory networks using [...] Read more.

Recent advances in experimental biology studies have produced large amount of molecular activity data. In particular, individual patient data provide non-time series information for the molecular activities in disease conditions. The challenge is how to design effective algorithms to infer regulatory networks using the individual patient datasets and consequently address the issue of network symmetry. This work is aimed at developing an efficient pipeline to reverse-engineer regulatory networks based on the individual patient proteomic data. The first step uses the SCOUT algorithm to infer the pseudo-time trajectory of individual patients. Then the path-consistent method with part mutual information is used to construct a static network that contains the potential protein interactions. To address the issue of network symmetry in terms of undirected symmetric network, a dynamic model of ordinary differential equations is used to further remove false interactions to derive asymmetric networks. In this work a dataset from triple-negative breast cancer patients is used to develop a protein-protein interaction network with 15 proteins. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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7 pages, 253 KiB

Open AccessArticle

On a Semigroup Problem II

by Viorel Nitica and Andrew Torok

Symmetry 2020, 12(9), 1392; https://doi.org/10.3390/sym12091392 - 21 Aug 2020

Viewed by 2425

Abstract

We consider the following semigroup problem: is the closure of a semigroup S in a topological vector space X a group when S does not lie on “one side” of any closed hyperplane of X? Whereas for finite dimensional spaces, the answer [...] Read more.

We consider the following semigroup problem: is the closure of a semigroup S in a topological vector space X a group when S does not lie on “one side” of any closed hyperplane of X? Whereas for finite dimensional spaces, the answer is positive, we give a new example of infinite dimensional spaces where the answer is negative. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

19 pages, 823 KiB

Open AccessArticle

Observability and Symmetries of Linear Control Systems

by Víctor Ayala, Heriberto Román-Flores, María Torreblanca Todco and Erika Zapana

Symmetry 2020, 12(6), 953; https://doi.org/10.3390/sym12060953 - 4 Jun 2020

Cited by 3 | Viewed by 2092

Abstract

The goal of this article is to compare the observability properties of the class of linear control systems in two different manifolds: on the Euclidean space

R^{n}

and, in a more general setup, on a connected Lie group G. For that, [...] Read more.

The goal of this article is to compare the observability properties of the class of linear control systems in two different manifolds: on the Euclidean space

R^{n}

and, in a more general setup, on a connected Lie group G. For that, we establish well-known results. The symmetries involved in this theory allow characterizing the observability property on Euclidean spaces and the local observability property on Lie groups. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

29 pages, 29434 KiB

Open AccessArticle

Critically-Finite Dynamics on the Icosahedron

by Scott Crass

Symmetry 2020, 12(1), 177; https://doi.org/10.3390/sym12010177 - 19 Jan 2020

Cited by 3 | Viewed by 2743

Abstract

A recent effort used two rational maps on the Riemann sphere to produce polyhedral structures with properties exemplified by a soccer ball. A key feature of these maps is their respect for the rotational symmetries of the icosahedron. The present article shows how [...] Read more.

A recent effort used two rational maps on the Riemann sphere to produce polyhedral structures with properties exemplified by a soccer ball. A key feature of these maps is their respect for the rotational symmetries of the icosahedron. The present article shows how to build such “dynamical polyhedra” for other icosahedral maps. First, algebra associated with the icosahedron determines a special family of maps with 60 periodic critical points. The topological behavior of each map is then worked out and results in a geometric algorithm out of which emerges a system of edges—the dynamical polyhedron—in natural correspondence to a map’s topology. It does so in a procedure that is more robust than the earlier implementation. The descriptions of the maps’ geometric behavior fall into combinatorial classes the presentation of which concludes the paper. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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20 pages, 2010 KiB

Open AccessArticle

Nonlinear Dynamic Modelling of Two-Point and Symmetrically Supported Pipeline Brackets with Elastic-Porous Metal Rubber Damper

by Xin Xue, Shixin Ruan, Angxi Li, Hongbai Bai and Kun Xiao

Symmetry 2019, 11(12), 1479; https://doi.org/10.3390/sym11121479 - 4 Dec 2019

Cited by 7 | Viewed by 2282

Abstract

This paper aims to investigate the nonlinear dynamic properties of a two-point and symmetrically supported pipeline bracket system coated with the damping element using an elastic-porous metal rubber. The dynamic model of the studied two-point and symmetric pipeline system was established based on [...] Read more.

This paper aims to investigate the nonlinear dynamic properties of a two-point and symmetrically supported pipeline bracket system coated with the damping element using an elastic-porous metal rubber. The dynamic model of the studied two-point and symmetric pipeline system was established based on impulse response matrix for accurate and reliable description on its nonlinear behaviours, e.g., energy dissipation and loss factor. The experimental verification of the developed model was performed by means of dynamic test as well as the analyses of nonlinear damping characteristics. The experimental results show a good agreement with the prediction results obtained from the proposed dynamic model. This work provides an alternative method to investigate the dynamics of pipeline vibration system equipped with a damping structure. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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13 pages, 355 KiB

Open AccessArticle

An E-Sequence Approach to the 3x + 1 Problem

by Sanmin Wang

Symmetry 2019, 11(11), 1415; https://doi.org/10.3390/sym11111415 - 15 Nov 2019

Viewed by 2071

Abstract

For any odd positive integer x, define

{(x_{n})}_{n ⩾ 0}

and

{(a_{n})}_{n ⩾ 1}

by setting [...] Read more.

For any odd positive integer x, define

{(x_{n})}_{n ⩾ 0}

and

{(a_{n})}_{n ⩾ 1}

by setting

x_{0} = x, x_{n} = \frac{3 x_{n - 1} + 1}{2^{a_{n}}}

such that all

x_{n}

are odd. The

3 x + 1

problem asserts that there is an

x_{n} = 1

for all x. Usually,

{(x_{n})}_{n ⩾ 0}

is called the trajectory of x. In this paper, we concentrate on

{(a_{n})}_{n ⩾ 1}

and call it the E-sequence of x. The idea is that we generalize E-sequences to all infinite sequences

{(a_{n})}_{n ⩾ 1}

of positive integers and consider all these generalized E-sequences. We then define

{(a_{n})}_{n ⩾ 1}

to be

Ω

-convergent to x if it is the E-sequence of x and to be

Ω

-divergent if it is not the E-sequence of any odd positive integer. We prove a remarkable fact that the

Ω

-divergence of all non-periodic E-sequences implies the periodicity of

{(x_{n})}_{n ⩾ 0}

for all

x_{0}

. The principal results of this paper are to prove the

Ω

-divergence of several classes of non-periodic E-sequences. Especially, we prove that all non-periodic E-sequences

{(a_{n})}_{n ⩾ 1}

with

\underset{n \to \infty}{lim^{¯}} \frac{b_{n}}{n} > {log}_{2} 3

are

Ω

-divergent by using Wendel’s inequality and the Matthews and Watts’ formula

x_{n} = \frac{3^{n} x_{0}}{2^{b_{n}}} \prod_{k = 0}^{n - 1} (1 + \frac{1}{3 x_{k}})

, where

b_{n} = \sum_{k = 1}^{n} a_{k}

. These results present a possible way to prove the periodicity of trajectories of all positive integers in the

3 x + 1

problem, and we call it the E-sequence approach. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

13 pages, 292 KiB

Open AccessArticle

About the Orbit Structure of Sequences of Maps of Integers

by Viorel Niţică and Jeroz Makhania

Symmetry 2019, 11(11), 1374; https://doi.org/10.3390/sym11111374 - 6 Nov 2019

Viewed by 2422

Abstract

Motivated by connections to the study of sequences of integers, we study, from a dynamical systems point of view, the orbit structure for certain sequences of maps of integers. We find sequences of maps for which all individual orbits are bounded and periodic [...] Read more.

Motivated by connections to the study of sequences of integers, we study, from a dynamical systems point of view, the orbit structure for certain sequences of maps of integers. We find sequences of maps for which all individual orbits are bounded and periodic and for which the number of periodic orbits of fixed period is finite. This allows the introduction of a formal

ζ

-function for the maps in these sequences, which are actually polynomials. We also find sequences of maps for which the orbit structure is more complicated, as they have both bounded and unbounded orbits, both individual and global. Most of our results are valid in a general numeration base. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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10 pages, 256 KiB

Open AccessArticle

Some Chaos Notions on Dendrites

by Asmaa Fadel and Syahida Che Dzul-Kifli

Symmetry 2019, 11(10), 1309; https://doi.org/10.3390/sym11101309 - 17 Oct 2019

Cited by 3 | Viewed by 2564

Abstract

Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is [...] Read more.

Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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8 pages, 676 KiB

Open AccessArticle

Filtering Method Based on Symmetrical Second Order Systems

by Cristian Toma

Symmetry 2019, 11(6), 813; https://doi.org/10.3390/sym11060813 - 20 Jun 2019

Viewed by 2127

Abstract

This study presents a filtering and sampling structure based on symmetrical second order systems working on half-period. It is shown that undamped second order oscillating systems working on half-period could provide: (i) a large attenuation coefficient for an alternating signal (due to the [...] Read more.

This study presents a filtering and sampling structure based on symmetrical second order systems working on half-period. It is shown that undamped second order oscillating systems working on half-period could provide: (i) a large attenuation coefficient for an alternating signal (due to the filtering second order system), and (ii) a robust sampling procedure (the slope of the generated output being zero at the sampling time moment). Unlike previous studies on the same topics, these results are achieved without the use of an additional integrator. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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37 pages, 8940 KiB

Open AccessArticle

Symmetric Networks with Geometric Constraints as Models of Visual Illusions

by Ian Stewart and Martin Golubitsky

Symmetry 2019, 11(6), 799; https://doi.org/10.3390/sym11060799 - 16 Jun 2019

Cited by 7 | Viewed by 4559

Abstract

Multistable illusions occur when the visual system interprets the same image in two different ways. We model illusions using dynamic systems based on Wilson networks, which detect combinations of levels of attributes of the image. In most examples presented here, the network has [...] Read more.

Multistable illusions occur when the visual system interprets the same image in two different ways. We model illusions using dynamic systems based on Wilson networks, which detect combinations of levels of attributes of the image. In most examples presented here, the network has symmetry, which is vital to the analysis of the dynamics. We assume that the visual system has previously learned that certain combinations are geometrically consistent or inconsistent, and model this knowledge by adding suitable excitatory and inhibitory connections between attribute levels. We first discuss 4-node networks for the Necker cube and the rabbit/duck illusion. The main results analyze a more elaborate model for the Necker cube, a 16-node Wilson network whose nodes represent alternative orientations of specific segments of the image. Symmetric Hopf bifurcation is used to show that a small list of natural local geometric consistency conditions leads to alternation between two global percepts: cubes in two different orientations. The model also predicts brief transitional states in which the percept involves impossible rectangles analogous to the Penrose triangle. A tristable illusion generalizing the Necker cube is modelled in a similar manner. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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17 pages, 390 KiB

Open AccessArticle

Multi-Criteria Decision Making Approach for Hybrid Operation of Wind Farms

by Harsh S. Dhiman, Dipankar Deb, Vlad Muresan and Mihaela-Ligia Unguresan

Symmetry 2019, 11(5), 675; https://doi.org/10.3390/sym11050675 - 16 May 2019

Cited by 26 | Viewed by 3828

Abstract

Hybrid operation of wind farms has been in the limelight in recent years wherein the stochastic nature of wind causes market operators to choose an optimal strategy to maximize profit. The current work deals with a multi-criteria decision making approach to choose the [...] Read more.

Hybrid operation of wind farms has been in the limelight in recent years wherein the stochastic nature of wind causes market operators to choose an optimal strategy to maximize profit. The current work deals with a multi-criteria decision making approach to choose the best possible alternatives for a hybrid wind farm operation. A set of three, non-beneficial criteria, namely wind wakes, wind curtailment, and forced outages, were chosen to evaluate the best alternative. Three methods, (i) Simple Additive Weighting (SAW), (ii) the Technique for Order or Preference by Similarity to Ideal Solution (TOPSIS) and (iii) Complex Proportional Assessment (COPRAS), were applied to identify the best alternative, and the results revealed that for all three methods, borrowing deficit power from a neighboring wind farm is the best alternative. Comparative analyses in terms of the data requirement, the effect of dynamic decision matrices, and rank reversal in wind farm application have also been pioneered. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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17 pages, 43385 KiB

Open AccessArticle

Dynamic Modeling and Experiment Research on Twin Ball Screw Feed System Considering the Joint Stiffness

by Meng Duan, Hong Lu, Xinbao Zhang, Yongquan Zhang, Zhangjie Li and Qi Liu

Symmetry 2018, 10(12), 686; https://doi.org/10.3390/sym10120686 - 1 Dec 2018

Cited by 23 | Viewed by 6213

Abstract

It is of great significance to study the dynamic characteristics of twin ball screw (TBS) feed system to improve the precision of gantry-type dual-driven computer numerical control (CNC) machine tools. In this paper, an equivalent dynamic model of the TBS feed system is [...] Read more.

It is of great significance to study the dynamic characteristics of twin ball screw (TBS) feed system to improve the precision of gantry-type dual-driven computer numerical control (CNC) machine tools. In this paper, an equivalent dynamic model of the TBS feed system is established utilizing lumped mass method considering the stiffness of joints. Equivalent axial stiffness of screw-nut joints and bearing joints are both calculated by Hertz contact theory. Furthermore, a friction model is proposed because the friction force of the screw nut affects the stiffness of the joints. Then, the friction parameters are obtained by using the nonlinear system identification method. Meanwhile, a finite element model (FEM) is developed to assess the dynamic characteristics of TBS feed system under the stiffness of joints. Finally, validation experiments are conducted, and the results show that the positions of the nut and the velocities of worktable greatly affect the dynamic characteristics of the TBS feed system. Compared with the theoretical calculation, FEM and experiments indicate that the dynamic modeling proposed in this article can reach a higher accuracy. Full article

(This article belongs to the Special Issue Symmetry and Dynamical Systems)

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