Presentation slides for the following two papers:
- Leo Speidel, Konstantin Klemm, Víctor M. Eguíluz, Naoki Masuda.
New Journal of Physics, 18, 073013 (2016).
- Tomokatsu Onaga, James P. Gleeson, Naoki Masuda.
Physical Review Letters, 119, 108301 (2017).
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Kazushi Okamoto: Families of Triangular Norm Based Kernel Function and Its Application to Kernel k-means, Joint 8th International Conference on Soft Computing and Intelligent Systems and 17th International Symposium on Advanced Intelligent Systems (SCIS-ISIS2016), 2016.08.25
Stochastic methods for uncertainty quantification in numerical aerodynamicsAlexander Litvinenko
We developed a gPCE based surrogate. gPCE coefficients were computed with sparse Gauss-Hermite quadrature and compared with coefficients computed via MC and QMC methods
The work deals finite frequency H∞ control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H∞ lower can be by our method obtained developed where further comparison.
An Exponential Observer Design for a Class of Chaotic Systems with Exponentia...ijtsrd
In this paper, a class of generalized chaotic systems with exponential nonlinearity is studied and the state observation problem of such systems is explored. Using differential inequality with time domain analysis, a practical state observer for such generalized chaotic systems is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to demonstrate the validity, effectiveness, and correctness of the obtained result. Yeong-Jeu Sun "An Exponential Observer Design for a Class of Chaotic Systems with Exponential Nonlinearity" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38233.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38233/an-exponential-observer-design-for-a-class-of-chaotic-systems-with-exponential-nonlinearity/yeongjeu-sun
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Kazushi Okamoto: Families of Triangular Norm Based Kernel Function and Its Application to Kernel k-means, Joint 8th International Conference on Soft Computing and Intelligent Systems and 17th International Symposium on Advanced Intelligent Systems (SCIS-ISIS2016), 2016.08.25
Stochastic methods for uncertainty quantification in numerical aerodynamicsAlexander Litvinenko
We developed a gPCE based surrogate. gPCE coefficients were computed with sparse Gauss-Hermite quadrature and compared with coefficients computed via MC and QMC methods
The work deals finite frequency H∞ control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H∞ lower can be by our method obtained developed where further comparison.
An Exponential Observer Design for a Class of Chaotic Systems with Exponentia...ijtsrd
In this paper, a class of generalized chaotic systems with exponential nonlinearity is studied and the state observation problem of such systems is explored. Using differential inequality with time domain analysis, a practical state observer for such generalized chaotic systems is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to demonstrate the validity, effectiveness, and correctness of the obtained result. Yeong-Jeu Sun "An Exponential Observer Design for a Class of Chaotic Systems with Exponential Nonlinearity" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38233.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38233/an-exponential-observer-design-for-a-class-of-chaotic-systems-with-exponential-nonlinearity/yeongjeu-sun
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Characterization of Subsurface Heterogeneity: Integration of Soft and Hard In...Amro Elfeki
Park, E., Elfeki, A. M. M., Dekking, F.M. (2003). Characterization of subsurface heterogeneity: Integration of soft and hard information using multi-dimensional Coupled Markov chain approach. Underground Injection Science and Technology Symposium, Lawrence Berkeley National Lab., October 22-25, 2003. p.49. Eds. Tsang, Chin.-Fu and Apps, John A.
http://www.lbl.gov/Conferences/UIST/index.html#topics
Foundation and Synchronization of the Dynamic Output Dual Systemsijtsrd
In this paper, the synchronization problem of the dynamic output dual systems is firstly introduced and investigated. Based on the time domain approach, the state variables synchronization of such dual systems can be verified. Meanwhile, the guaranteed exponential convergence rate can be accurately estimated. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result. Yeong-Jeu Sun "Foundation and Synchronization of the Dynamic Output Dual Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29256.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29256/foundation-and-synchronization-of-the-dynamic-output-dual-systems/yeong-jeu-sun
Exponential State Observer Design for a Class of Uncertain Chaotic and Non-Ch...ijtsrd
In this paper, a class of uncertain chaotic and non-chaotic systems is firstly introduced and the state observation problem of such systems is explored. Based on the time-domain approach with integral and differential equalities, an exponential state observer for a class of uncertain nonlinear systems is established to guarantee the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be calculated correctly. Finally, numerical simulations are presented to exhibit the feasibility and effectiveness of the obtained results. Yeong-Jeu Sun "Exponential State Observer Design for a Class of Uncertain Chaotic and Non-Chaotic Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: http://www.ijtsrd.com/papers/ijtsrd20219.pdf
http://www.ijtsrd.com/engineering/electrical-engineering/20219/exponential-state-observer-design-for-a-class-of-uncertain-chaotic-and-non-chaotic-systems/yeong-jeu-sun
This poster was created in LaTeX on a Dell Inspiron laptop with a Linux Fedora Core 4 operating system. The background image and the animation snapshots are dxf meshes of elastic waveform solutions, rendered on a Windows machine using 3D Studio Max.
Future cosmology with CMB lensing and galaxy clusteringMarcel Schmittfull
Next-generation Cosmic Microwave Background experiments such as the Simons Observatory, CMB-S4 and PICO aim to measure gravitational lensing of the Cosmic Microwave Background an order of magnitude better than current experiments. The lensing signal will be highly correlated with measurements of galaxy clustering from next-generation galaxy surveys such as LSST. This will help us understand whether cosmic inflation was driven by a single field or by multiple fields. It will also allow us to accurately measure the growth of structure as a function of time, which is a powerful probe of dark energy and the sum of neutrino masses. I will discuss the prospects for this, as well as recent progress on the theoretical modeling of galaxy clustering, which is key to realize the full potential of these anticipated datasets.
Response Surface in Tensor Train format for Uncertainty QuantificationAlexander Litvinenko
We apply low-rank Tensor Train format to solve PDEs with uncertain coefficients. First, we approximate uncertain permeability coefficient in TT format, then the operator and then apply iterations to solve stochastic Galerkin system.
extreme times in finance heston model.pptArounaGanou2
Stochastic Volatility Models. 3. I - CTRW formalism. First developed by Montroll and Weiss (1965); Aimed to study the microstructure of random processe
On Optimization of Manufacturing of a Two-level Current-mode Logic Gates in a...BRNSS Publication Hub
In this paper, we introduce an approach to increase the density of field-effect transistors framework a two-level current-mode logic gates in a multiplexer. Framework the approach we consider manufacturing the inverter in heterostructure with the specific configuration. Several required areas of the heterostructure should be doped by diffusion or ion implantation. After that, dopant and radiation defects should by annealed framework optimized scheme. We also consider an approach to decrease the value of mismatch-induced stress in the considered heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures during the manufacturing of integrated circuits with account mismatch-induced stress.
A class of coupled neural networks with different internal time-delays and coupling delays is
investigated, which consists of nodes of different dimensions. By constructing suitable Lyapunov
functions and using the linear matrix inequality, the criteria of exponential stabilization for the coupled
dynamical system are established, and formulated in terms of linear matrix inequality. Finally, numerical
examples are presented to verify the feasibility and effectiveness of the proposed theoretical results.
Global network structure of dominance hierarchy of ant workersAntnet slides-s...Naoki Masuda
Presentation slides for the following paper:
Hiroyuki Shimoji, Masato S. Abe, Kazuki Tsuji, Naoki Masuda.
Global network structure of dominance hierarchy of ant workers.
Journal of the Royal Society Interface, in press (2014).
Participation costs dismiss the advantage of heterogeneous networks in evolut...Naoki Masuda
Presentation slides for the following two papers (mainly (1)):
(1) Masuda. Proceedings of the Royal Society B: Biological Sciences, 274, 1815-1821 (2007).
(2) Masuda and Aihara. Physics Letters A, 313, 55-61 (2003).
Maximizing the spectral gap of networks produced by node removalNaoki Masuda
Presentation slides for the following two papers (currently available in the pdf format only).
(1) T. Watanabe, N. Masuda.
Enhancing the spectral gap of networks by node removal.
Physical Review E, 82, 046102 (2010).
(2) N. Masuda, T. Fujie, K. Murota.
Semidefinite programming for maximizing the spectral gap.
In: Complex Networks IV, Studies in Computational Intelligence, 476, 155-163 (2013).
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
1. Epidemic processes in time-
varying networks:
Commutator and concurrency
Naoki Masuda
State University of New York at Buffalo
naokimas@buffalo.edu
www.naokimasuda.net
4. Why does it matter?
time
A
A
B
B
C
C
D D
time
A
A
B
B
C
C
D D
“temporal network”
static (i.e. traditional)
network
✓ A → D (temporal path)
- D → A
5. • Key questions:
• How does time-dependence of networks change dynamical
processes on networks?
• How can we mine information from temporal network data?
Masuda & Lambiotte
(2016)
Masuda & Holme
Eds. (2017)
6. • Epidemic threshold βc
• Disease-free if β ≤ βc
• Outbreak/endemic if
β > βc
• βc value depends on
network structure
• On temporal networks,
the βc value depends …
Overview and aim
susceptible
(i.e. healthy)
infected
infection
β
8. Main results
1. When we can ignore stochastic fluctuations of the
dynamics, βc for temporal networks < βc for static
networks.(Speidel, Klemm, Eguíluz & Masuda, New J Phys, 2016).
2. Otherwise, a Markov chain approach reveals
“concurrency-induced transitions” (Onaga, Gleeson &
Masuda, Phys Rev Lett, 2017).
Temporal networks
facilitate contagion
(In the first scenario).
temporal
static
0 ˆc
⇤
c
% infected
infection rate
9. Main results
1. When we can ignore stochastic fluctuations of the
dynamics, βc for temporal networks < βc for static
networks.(Speidel, Klemm, Eguíluz & Masuda, New J Phys, 2016).
2. Otherwise, a Markov chain approach reveals
“concurrency-induced transitions” (Onaga, Gleeson &
Masuda, Phys Rev Lett, 2017).
Temporal networks
facilitate contagion
(In the first scenario).
temporal
static
0 ˆc
⇤
c
% infected
infection rate
10. Two representations of
static networks
v1 2
3
4 5
v
v v v
adjacency matrix
(good for theory)
edge list (good for data handling
and numerical simulations)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(2, 4)
(4, 5)
A =
0
B
B
B
B
@
0 1 1 1 1
1 0 0 1 0
1 0 0 0 0
1 1 0 0 1
1 0 0 1 0
1
C
C
C
C
A
11. Two representations of
temporal networks
contact sequence sequences of networks
(good for theory)
(1, 2, t1, 1)
(2, 3, t2, 2)
(2, 4, t3, 3)
(2, 3, t4, 4)
A1, A2, . . .
time
A
A
B
B
C
C
D D
fig for Masuda-Klemm-Eguiluz
(cf. Masuda & Lambiotte, A Guide to Temporal Networks, 2016)
We use this here.
12. Modeling temporal networks
by “switching networks”
1
3
2
4
1
3
2
time
4
1
3
2
4
1
3
2
A(0)
=
0
B
B
@
0 0 1 0
0 0 0 0
1 0 0 0
0 0 0 0
1
C
C
A A(1)
=
0
B
B
@
0 0 0 1
0 0 0 1
0 0 0 0
1 1 0 0
1
C
C
A A(2)
=
0
B
B
@
0 1 1 1
1 0 0 0
1 0 0 0
1 0 0 0
1
C
C
A A(3)
=
0
B
B
@
0 0 0 0
0 0 1 0
0 1 0 1
0 0 1 0
1
C
C
A
4
0 τ 2τ 3τ 4τ
A sequence of matrices (“snapshot” networks)
14. β
fractionofinfectednodes
0
0
0.5 1 1.5 2
0.02
0.04
0.06
0.08
0.1
(a)
τ = 0
τ = 0.05
τ = 0.5
0 1 2 3 4 5
βfractionofinfectednodes
0
0.02
0.04
0.06
0.08
0.1
(b)
On an online message
temporal network
(Opsahl & Panzarasa,
Soc Netw 2009)
On a sexual contact
temporal network
(Rocha et al., PNAS 2010)
(Speidel, Klemm, Eguíluz & Masuda, New Journal of Physics, 2016)
15. 1 2
3 4
1 2
3 4
1 2
3 4
1 2
3 4
M(1) M(2) M(3)
M * = (M(1) + M(2) + M(3)) / 3
0 τ 2τ 3τ
temporal network
static network
1
1 1 1
1
1
1
2/3
1/3
1
1/3
time
Edge (1,2) is used for
2τ “weight × time” in
total in both cases
16. • For temporal networks
• For static networks
Model
˙x(t) =M(0)
x(t), 0 t ⌧
˙x(t) =M(1)
x(t), ⌧ t 2⌧
...
˙x(t) =M(` 1)
x(t), (` 1)⌧ t `⌧
(Masuda, Klemm & Eguíluz, Physical Review Letters, 2013)
˙x(t) = M⇤
x(t) ⌘
P` 1
`0=0 M(`0
)
`
x(t), 0 t `⌧
17. “Individual-based approximation” (a.k.a.
“quenched mean-field theory”) for static
networks
Assuming all pi(t) ≈ 0
• A: adjacency matrix
• β: infection rate
• µ: recovery rate (= 1)
pi(t) = Pr(node i is infected)
˙pi(t) =
NX
j=1
Aji [1 pi(t)] pj(t) µpi(t)
⇡
NX
j=1
Ajipj(t) µpi(t)
With µ = 1, c = 1/ max(A)
˙p ⇡ ( A µI)p
18. In probability theory
xi(t) =
(
0 (node i is susceptible)
1 (node i is infected)
dxi =
NX
j=1
Aji(1 xi)xjd⇧
(vj ,vi)
xid⇧vi
µ
Stochastic differential equation with Poisson jumps:
Expectation:
dE[xi]
dt
=
NX
j=1
AjiE[(1 xi)xj] µE[xi]
NX
j=1
AjiE[xj] µE[xi]
Markov chain on 2N states
This slide is a mathematical side note.
20. p(t) e( A µI)t
p(0)
= sup{✏ : pi(t) Ce ✏t
for 9C > 0, 8i, 8p(0)}
Decay rate:
A quenched mean-field lower bound of the decay rate:
qMF ⌘ max( A µI)
qMF = 0 =)
✓
µ
◆
c
=
1
max(A)
This slide is a mathematical side note.
21. Individual-based approximation
for switching networks
where
β = βc ⬌ the leading eigenvalue of T(τ,ℓ) = 1
Assume pi(t) ≈ 0
• Infection rate = β
• Recovery rate = 1
pi(t) = Pr(vertex i is infected)
or
T(⌧, `) = exp
h
( A(` 1)
I)⌧
i
· · · exp
h
( A(1)
I)⌧
i
exp
h
( A(0)
I)⌧
i
˙p(t) = ( A(`0
)
I)p(t) where `0
⌧ t < (`0
+ 1)⌧
˙pi(t) =
NX
j=1
A
(`0
)
ji pj(t) pi(t)
p(`⌧) = T(⌧, `)p(0)
(Speidel, Klemm, Eguíluz & Masuda, New Journal of Physics, 2016)
22. Individual-based approximation
for switching networks
where
β = βc ⬌ the leading eigenvalue of T(τ,ℓ) = 1
This is to be compared with the leading eigenvalue of
where A⇤
=
1
`
` 1X
`0=0
A(`0
)
T(⌧, `) = exp
h
( A(` 1)
µI)⌧
i
· · · exp
h
( A(1)
µI)⌧
i
exp
h
( A(0)
µI)⌧
i
exp [( A⇤
µI)`⌧]
23. • If this holds,
• True for ℓ = 2 (Cohen et al., 1982)
• We want to know the case where φ is the largest eigenvalue.
• Counterexamples, but with negative entries (Thomson, 1965). cf.
Golden-Thompson inequality
• Supported by the analysis of two models (activity driven model,
Perra et al., Sci Rep, 2012, and its variant)
• Supported numerically
(eM(` 1)
eM(` 2)
· · · eM(0)
) (eM(` 1)
+M(` 2)
+···+M(0)
)
if all Ms have only nonnegative entries.
Conjecture:
Remarks:
ˆc ⇤
c
time-varying static
24. To quantify the difference
between time-varying
and static networks
29. C ⌘
1
(`↵⇤
max)2
` 1X
`0=1
`0
1X
`00=0
h
A(`0
)
, A(`00
)
i
2
↵⇤
max = largest eigenvalue of A⇤
time-varying
static
0 ˆc
⇤
c
% infected
c ⌘
⇤
c c
⇤
c
where
Reminder:
(Speidel, Klemm, Eguíluz & Masuda, New Journal of Physics, 2016)
A⇤
=
1
`
` 1X
`0=0
A(`0
)
30. Summary (1)
• Time-varying graphs always lessen the
epidemic threshold assuming the
conjecture.
• Individual-based approximation used
• Supported by analysis of commutators
• Quantifying the “size” of the commutator
However, the main result contradicts numerical results when
connected components of snapshot graphs are really small.
31. Main results
1. When we can ignore stochastic fluctuations of the
dynamics, βc for temporal networks < βc for static
networks.(Speidel, Klemm, Eguíluz & Masuda, New J Phys, 2016).
2. Otherwise, a Markov chain approach reveals
“concurrency-induced transitions” (Onaga, Gleeson &
Masuda, Phys Rev Lett, 2017).
Temporal networks
facilitate contagion
(In the first scenario).
temporal
static
0 ˆc
⇤
c
% infected
infection rate
33. What’s the issue?
• Individual-based approximation is valid only for large m (=
dhub), where stochastic effects are negligible.
• We found the opposite results in our numerical
simulations for small m (not published).
• Small m is relevant to applications (sexually transmitted
infections, conversations in small groups or dyads).
• Let’s look at small m with the activity-driven model.
• e.g., m=1 for monogamous sexual relationships
m=3
35. “Concurrency”
• Polygamy vs (a sequence of) monogamy?
• Concept coming from mathematical epidemiology and HIV/AIDs
studies in mid 1990s
• Measured in field
• There are mathematical models, but its implications remain unclear.
time
36. concurrent (polygamous), m = 4
non-concurrent (serial monogamous), m = 1
static
“activity-driven model” (Perra et al., Scientific Reports, 2012)
m = concurrency
Which case enhances infection more?
37. Modeling temporal networks
by “switching networks”
1
3
2
4
1
3
2
time
4
1
3
2
4
1
3
2
A(0)
=
0
B
B
@
0 0 1 0
0 0 0 0
1 0 0 0
0 0 0 0
1
C
C
A A(1)
=
0
B
B
@
0 0 0 1
0 0 0 1
0 0 0 0
1 1 0 0
1
C
C
A A(2)
=
0
B
B
@
0 1 1 1
1 0 0 0
1 0 0 0
1 0 0 0
1
C
C
A A(3)
=
0
B
B
@
0 0 0 0
0 0 1 0
0 1 0 1
0 0 1 0
1
C
C
A
4
0 τ 2τ 3τ 4τ
A sequence of matrices (“snapshot” networks)
38. • ρ1: prob that a hub with activity potential a is infected
after applying the star graph for time τ
• c1: prob that the hub is infected at time t+τ when the
hub is the only infected node at time t (complicated
expressions but doable)
• c2: prob that the hub is infected at time t+τ when only
a single leaf is infected at time t.
• Assumptions
• segregated stars in each time window
• Near the epidemic threshold
39. ⇢2(a, a0
, t + ⌧) = c3⇢(a, t) + c4⇢(a0
, t) + c5(m 1)h⇢(t)i
⇢(a, t + ⌧) =a⇢1(a, t + ⌧) +
Z
da0
F(a0
)ma0
⇢2(a, a0
, t + ⌧)
+(1 a mhai)e ⌧
⇢(a, t)
⇥(z, t + ⌧) =c0
1⇥(1)
(z, t) + c0
2⇥(1, t)g(1)
(z) + c0
3⇥(z, t)
+
h
c0
4⇥(1)
(1, t) + c0
5⇥(1, t)
i
g(z)
where c0
1 ⌘ c1 e ⌧
, c0
2 ⌘ mc2, . . .
g(z) ⌘
Z
daF(a)za
, ⇥(z, t) ⌘
Z
daF(a)⇢(a, t)za
A leaf is infected
An arbitrary vertex is infected
⇢1(a, t + ⌧) = c1⇢(a, t) + c2mh⇢(t)i
A hub is infected
0 τ τ2 τ3 t
40. Maclaurin series: ⇢(a, t) =
1X
n=1
wn(t)an 1
w(t + ⌧) = T (⌧)w(t)
T =
0
B
B
B
B
B
B
B
@
c0
3 + haic0
4 + c0
5 ha2
ic0
4 + haic0
5 ha3
ic0
4 + ha2
ic0
5 ha4
ic0
4 + ha3
ic0
5 ha5
ic0
4 + ha4
ic0
5 · · ·
c0
1 + c0
2 haic0
2 + c0
3 ha2
ic0
2 ha3
ic0
2 ha4
ic0
2 · · ·
0 c0
1 c0
3 0 0 · · ·
0 0 c0
1 c0
3 0 · · ·
0 0 0 c0
1 c0
3 · · ·
...
...
...
...
...
...
1
C
C
C
C
C
C
C
A
→ An eigenvalue problem → Epidemic threshold
• Carefully model cases of different concurrency
• Formulate a Markov chain
• Generating functions
• Maclaurin series
• Matrix algebra
Linear map:
41. Phase diagrams
✔ Also for scale-free networks
In the “regular graph” case,
mc =
3
1 4a
⌧⇤ = ln
1 (1 + m)a
1 (1 + m)2a
(Onaga, Gleeson & Masuda, Physical Review Letters, 2017)
(concu
rrency)
time-varying
graph
static
graph
m = 4, polygamy
m = 1, serial monogamy
5
100
βc
10
50
τ
1
5
mc
10
0 0.2 0.80.60.4 1
m die out
enhanced
suppressed
0 τ τ2 τ3 t
42. Summary (2)
• Practical message: Temporal monogamy
(low concurrency) is safer than temporal
polygamy (high concurrency).
43. Conclusions
• Individual-based approximation and stochastic dynamics
• At high concurrency, temporal networks boost infection.
• At low concurrency, temporal networks suppress infection.
• A “commutator norm” tells how much the epidemic threshold
is moved by the temporality of the network. Analysis of
stochastic dynamics
• Further questions:
• Mobility
• Applications? Interventions? Design of “smart” interaction
orders?
• More on coevolutionary networks
• Similar theory for SIR (cf. Rocha & Masuda, Sci Rep 2016)
and other processes?