scholarly journals Phase transitions and stability of dynamical processes on hypergraphs

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Guilherme Ferraz de Arruda ◽  
Michele Tizzani ◽  
Yamir Moreno
Keyword(s):  
Diffusion Processes ◽  
Weighted Graph ◽  
Social Contagion ◽  
General Interest ◽  
Dynamical Processes ◽  
Natural Systems ◽  
Pairwise Interactions ◽  
Diffusion Dynamics ◽  
Stability Of Dynamical Systems ◽  
The Stability

AbstractHypergraphs naturally represent higher-order interactions, which persistently appear in social interactions, neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet. In this paper, we derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph. The framework allows us to reveal that, near the fixed point, the relevant structure is a weighted graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process. We analytically solve two dynamics of general interest, namely, social contagion and diffusion processes, and show that the stability conditions can be decoupled in structural and dynamical components. Our results show that in social contagion process, only pairwise interactions play a role in the stability of the absorbing state, while for the diffusion dynamics, the order of the interactions plays a differential role. Our work provides a general framework for further exploration of dynamical processes on hypergraphs.

scholarly journals On minimum algebraic connectivity of graphs whose complements are bicyclic

2019 ◽  
Vol 17 (1) ◽  
pp. 1490-1502 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Javaid ◽  
Mohsin Raza ◽  
Naeem Saleem
Keyword(s):  
Connected Graph ◽  
Diffusion Processes ◽  
Laplacian Matrix ◽  
Group Differences ◽  
Algebraic Connectivity ◽  
Connected Graphs ◽  
Bicyclic Graph ◽  
Smallest Eigenvalue ◽  
Unique Graph ◽  
The Stability

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.

scholarly journals All adapted topologies are equal

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder
Keyword(s):  
Stochastic Processes ◽  
Weak Topology ◽  
Equilibrium Problems ◽  
Diffusion Processes ◽  
Temporal Structure ◽  
Wasserstein Distance ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Nested Distance ◽  
The Stability

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.

Continuous and Discontinuous Response to Smoothly Decreasing Effective Distance: An Analysis with Special Reference to ‘Overbanking’ in the 1920s

1977 ◽  
Vol 9 (4) ◽  
pp. 461-475 ◽  
Author(s):  
T R Smith
Keyword(s):  
Special Reference ◽  
Response Function ◽  
Banking System ◽  
General Interest ◽  
Relative Cost ◽  
Road Transportation ◽  
Effective Distance ◽  
The Usa ◽  
The Stability ◽  
The Individual

An important problem of general interest concerns the aggregate response of a system to increasing density (or decreasing effective distance between units). An analysis is made for a system in which the individual responses to changing density are smooth. The analysis is presented in terms of the ‘overbanked’ situation of the USA in the 1920s. Models are derived from micro-economic principles concerning the interaction of two banks in competition for deposits as road transportation decreases in relative cost. The conclusion drawn from analysis of the models is that aggregate deposits may increase in a smooth or in a discontinuous (jump) fashion, the jump depending on the nature of an individual banker's response function and occurring despite smooth individual responses. In the case where the system is always in equilibrium, the jump may be a catastrophe in the sense described by Thorn. The analysis indicates that improvements in road transportation may have significantly reduced the stability of the banking system to a point of catastrophic collapse (as well as, for example, overzealous chartering by the authorities). The analysis should have application to many other situations in which decreasing effective distance is an important fact.

scholarly journals Attitude and Actual Behaviour towards Water-Related Green Infrastructures and Sustainable Drainage Systems in Four North-Western Mediterranean Regions of Italy and France

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1474 ◽  
Author(s):  
Simone Maria Piacentini ◽  
Rudy Rossetto
Keyword(s):  
Financial Incentives ◽  
Coastal Region ◽  
Western Mediterranean ◽  
General Interest ◽  
Related Services ◽  
Drainage Systems ◽  
Natural Systems ◽  
Actual Behaviour ◽  
Italian Regions ◽  
Sustainable Drainage Systems

Water-related green infrastructures (WrGIs), also known as blue infrastructures, and sustainable drainage systems (SuDSs) offer services such as stormwater runoff management, water purification, water storage at the intersection of the built environment, and natural systems by mimicking natural hydrological processes. While several papers document the reliability of such infrastructures in providing a variety of water-related services, few studies investigated the actual behaviour and the attitude of different stakeholders to understand the limitations and barriers in WrGIs/SuDSs implementation. In this paper, we investigated these issues by posing a set of questions to 71 qualified stakeholders in three Italian regions (Toscana, Liguria, and Sardegna) and one French region (Provence-Alpes-Côte d’Azur) in the northwestern Mediterranean. The results of the investigation largely show a lack of knowledge on these innovative solutions, although there is a general interest in their implementation both in the Italian and French regions. Barriers are also constituted by the scarcity of the demonstrators implemented, little knowledge on construction and maintenance costs, the absence of a proper regulatory framework, and of fiscal and financial incentives to support private citizens and companies. We finally suggest tools and soft measures that, in our opinion, may contribute to supporting the implementation of WrGIs/SuDSs, especially in view of adapting Mediterranean territories to the challenges posed by climate change. The results of our analyses may be reasonably up-scaled to the whole Mediterranean coastal region.

scholarly journals Journal of Food Quality Thermal Degradation of Plum Anthocyanins: Comparison of Kinetics from Simple to Natural Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mihaela Turturică ◽  
Nicoleta Stănciuc ◽  
Claudia Mureșan ◽  
Gabriela Râpeanu ◽  
Constantin Croitoru
Keyword(s):  
Antioxidant Activity ◽  
Citric Acid ◽  
Thermal Degradation ◽  
Fluorescence Spectra ◽  
Degradation Rate ◽  
Natural Systems ◽  
Degradation Rate Constant ◽  
Higher Temperature ◽  
Lower Temperature ◽  
The Stability

The stability of anthocyanin was assessed over a temperature range of 50–120°C in different simulated plum juices in order to compare the thermal behavior in the presence of certain compounds. The results were correlated with the antioxidant activity and intrinsic fluorescence spectra. The results suggested significant changes, especially at higher temperature; hence, increase in the fluorescence intensity and some bathochromic and hypsochromic shifts were observed. Anthocyanins in natural matrices presented the highest rate for degradation, followed by the anthocyanins in juices with sugars. Values of the activation energies were 42.40 ± 6.87 kJ/mol for the degradation in water, 40.70 ± 4.25 kJ/mol for the juices with citric acid, 23.03 ± 3.53 kJ/mol for the juices containing sugars, 35.99 ± 3.60 kJ/mol for simulated juices with mixture, and 14.19 ± 2.39 kJ/mol for natural juices. A protective effect of sugars was evidenced, whereas in natural matrices, the degradation rate constant showed lower temperature dependence.

scholarly journals Quantitative and Qualitative Methods in the Study of some Dynamic Systems

2015 ◽  
Vol 13 ◽  
pp. 168-171 ◽  
Author(s):  
Dumitru Bălă
Keyword(s):  
Dynamical Systems ◽  
Qualitative Methods ◽  
Dynamic Systems ◽  
Viscous Damping ◽  
Stability Of Dynamical Systems ◽  
The Stability ◽  
Quantitative And Qualitative Methods

In this paper we present several methods for the study of stability of dynamical systems. We analyze the stability of a hammer modeled by the free vibrator that collides with a sprung elastic mass taking into consideration the viscous damping too.

scholarly journals Improving the stability, lithium diffusion dynamics, and specific capacity of SrLi2Ti6O14 via ZrO2 coating

2020 ◽  
Author(s):  
Hong-Li Ding ◽  
Hai-Tao Yu ◽  
Xiao-dong Wang ◽  
Chen-Feng Guo ◽  
Bing Zheng ◽  
...  
Keyword(s):  
Specific Capacity ◽  
Zro2 Coating ◽  
Diffusion Dynamics ◽  
Lithium Diffusion ◽  
The Stability

scholarly journals ANALYTICAL APPROACH TO BIT-STRING MODELS OF LANGUAGE EVOLUTION

2008 ◽  
Vol 19 (04) ◽  
pp. 569-581 ◽  
Author(s):  
DAMIÁN H. ZANETTE
Keyword(s):  
Analytical Approach ◽  
Diffusion Processes ◽  
Language Evolution ◽  
Replicator Dynamics ◽  
Mean Field ◽  
Homogeneous State ◽  
Numerical Resolution ◽  
The Stability ◽  
String Models ◽  
And Diffusion

A formulation of bit-string models of language evolution, based on differential equations for the population speaking each language, is introduced and preliminarily studied. Connections with replicator dynamics and diffusion processes are pointed out. The stability of the dominance state, where most of the population speaks a single language, is analyzed within a mean-field-like approximation, while the homogeneous state, where the population is evenly distributed among languages, can be studied. This analysis discloses the existence of a bistability region, where dominance coexists with homogeneity as possible asymptotic states. Numerical resolution of the differential system validates these findings.

scholarly journals On the Stability of Kalman--Bucy Diffusion Processes

2017 ◽  
Vol 55 (6) ◽  
pp. 4015-4047 ◽  
Author(s):  
Adrian N. Bishop ◽  
Pierre Del Moral
Keyword(s):  
Diffusion Processes ◽  
The Stability

scholarly journals Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data

2014 ◽  
Vol 750 ◽  
Author(s):  
F. Viola ◽  
G. V. Iungo ◽  
S. Camarri ◽  
F. Porté-Agel ◽  
F. Gallaire
Keyword(s):  
Stability Analysis ◽  
Wind Tunnel ◽  
Wind Turbine ◽  
Eddy Viscosity ◽  
General Interest ◽  
Mean Velocity ◽  
Vortex Instability ◽  
Viscosity Models ◽  
Wind Tunnel Data ◽  
The Stability

AbstractThe instability of the hub vortex observed in wind turbine wakes has recently been studied by Iungo et al. (J. Fluid Mech., vol. 737, 2013, pp. 499–526) via local stability analysis of the mean velocity field measured through wind tunnel experiments. This analysis was carried out by neglecting the effect of turbulent fluctuations on the development of the coherent perturbations. In the present paper, we perform a stability analysis taking into account the Reynolds stresses modelled by eddy-viscosity models, which are calibrated on the wind tunnel data. This new formulation for the stability analysis leads to the identification of one clear dominant mode associated with the hub vortex instability, which is the one with the largest overall downstream amplification. Moreover, this analysis also predicts accurately the frequency of the hub vortex instability observed experimentally. The proposed formulation is of general interest for the stability analysis of swirling turbulent flows.

Sign in / Sign up

Export Citation Format

Share Document