×
Download the Graph Image:

PNG (Image)  SVG (Hi-Res)

Download the Graph Data:

JSON  CSV  Gexf (Gephi)

Download the Text Data:

CSV with Tags   Plain Text
Top keywords (global influence):
Top topics (local contexts):
Explore the main topics and terms outlined above or see them in the excerpts from this text below.
See the relevant data in context: click here to show the excerpts from this text that contain these topics below.
Tip: use the form below to save the most relevant keywords for this search query. Or start writing your content and see how it relates to the existing search queries and results.
Tip: here are the keyword queries that people search for but don't actually find in the search results.

#detrended_fluctuation_analysis or #dfa is a method for determining the statistical #self_affinity of a #signal. It is useful for analysing #time_series that appear to be long-memory processes (diverging correlation time, e.g. #power_law decaying autocorrelation function) or #1f_noise.

   edit   unpin & show all

 

The obtained #exponent is similar to the #hurst_exponent, except that #dfa may also be applied to signals whose underlying statistics (such as #mean and #variance) or dynamics are #non_stationary (changing with time)

   edit   unpin & show all

 

In #dfa the scaling exponent #alpha is calculated as the #slope of a straight line fit to the log #log graph of F(n)}F(n) using leas #squares. an exponent of 0.5 would correspond to #uncorrelated #white_noise, an exponent of 1 is #pink_noise

   edit   unpin & show all

 

Another way to detect #pink_noise is to build a graph where the x axis are the #events while the y axis records a #time_series estimation relative to the #standard_deviation from the #average (#mean) time interval.

   edit   unpin & show all

 

At its essence #pink_noise is based on #self_affinity and #self_similarity, so that no matter what scale you look at, the pattern is #similar (#scale_free)

   edit   unpin & show all

 

#power_spectral_analysis describes distribution of #power across #frequency components composing the #signal - for #pink_noise we have a 1/f relationship — few powerful signals with low frequency, a long tail of less powerful ones (of which there are many) (hence #1f_noise)

   edit   unpin & show all

 

#envelope is a smooth #curve outlining the extremes of a #signal and it is also calculated in #hilbert_transform, which, in turn is used in calculating #dfa or #detrended_fluctuation_analysis

   edit   unpin & show all

 

#detrended_fluctuation_analysis (#dfa) has proven particularly useful, revealing that genetic #variation, normal development, or #disease can lead to differences in the #scale_free #amplitude #modulation of oscillations https://www.frontiersin.org/articles/10.3389/fphys.2012.00450/full

   edit   unpin & show all

 

The reason why #chaotic #variation (#pink_noise) is indicative of a #healthy state is because it reflects #winnerless_competition behind the process. If there's a deviation in this dynamics (eg some #patterns), it could mean that one process is #dominating the rest.

   edit   unpin & show all

 

#self_affinity is a property of #fractal #time_series where the small parts of the whole are #similar to the whole

   edit   unpin & show all

 

#self_affinity processes and #self_similar structures have in common that the statistical #distribution of the measured quantity follows a #power_law function, which is the only mathematical function without a characteristic scale. Self-affine and #self_similar phenomena are therefore called "#scale_free.”

   edit   unpin & show all

 

In #power_law #distribution the #mean would not necessarily be the same as the #median (which is are closer to each other in #normal #distribution)

   edit   unpin & show all

 

A #power_law #distribution means that there is big number of #small #variation and a small number of #big #variation (hence the line with a negative #slope when expressed as a #log)

   edit   unpin & show all

 

In a #1f #signal the lower #frequency objects have larger #amplitude than the higher #frequency objects (#1f_noise) https://www.frontiersin.org/files/Articles/23105/fphys-03-00450-HTML/image_m/fphys-03-00450-g001.jpg

   edit   unpin & show all

 

the #frequency of a certain #size of flower being inversely #proportional to its #size.

   edit   unpin & show all

 

#time_series in which all #frequency are represented with the same #amplitude will lack the rich variability of the #scale_free #time_series and is referred to as "#white_noise”

   edit   unpin & show all

 

To estimate the #scale_free property we calculate the #standard_deviation (#signal in relation to #mean) over the differently sized #time_windows. If as the #time_windows size increases the #standard_deviation also increases, we're dealing with a #scale_free process. If the #scaling_effect is not there, then it's not a scale free process.

   edit   unpin & show all

 

a stationary #random #fluctuating process has a #signal profile, which is #self_affine with a #scaling_exponent α = 0.5

   edit   unpin & show all

 

when we add #memory in the sense that the #probability of an action depends on the previous actions that the walker has made — we will get a process that will exhibit #self_affinity across scales (#scale_free)

   edit   unpin & show all

 

Different classes of processes with #memory exist: #positive_correlation and those with #anti_correlation - anti-correlations can be seen as a #stabilizing mechanism - a future action is more likely to be opposite than the ones made before. In this case on longer windows (time scales) we will have lower #fluctuating so the coefficient will be lower (α 0 to 0.5) - has #memory, #anti_correlation. 0.5 - #random, 0.5 to 1 - has #memory and #positive_correlation (previous actions increase the likelyhood of that action taken again) https://www.frontiersin.org/files/Articles/23105/fphys-03-00450-HTML/image_m/fphys-03-00450-g003.jpg

   edit   unpin & show all

 

for #dfa the signal is transformed into the #cumulative_signal, then it is split into several #windows equal in size on the #log scale. then for each the data is #detrended and #standard_deviation is calculated for each #window. then #fluctuating function is calculated as the mean #standard_deviation for all the #windows. Then we plot that as a graph on #log scales. The #dfa exponent α is the #slope of the trend. If it follows a straight line 45° then it means that with every #window increase we do not have a #proportional increase in the mean of fluctuation (so it is #linear). If it is more, then it is #non_linear and shows that it is in fact #scale_free

   edit   unpin & show all

 

The lower end of the fitting range is at least four samples, because #linear #detrending will perform poorly with less points (Peng et al., 1994). For the high end of the fitting range, #dfa estimates for window sizes >10% of the #signal length are more noisy due to a low number of windows available for averaging (i.e., less than 10 windows). Finally, the 50% overlap between windows is commonly used to increase the number of windows, which can provide a more accurate estimate of the fluctuation function especially for the long-time-scale windows.

   edit   unpin & show all

 

A #brown_noise process can be obtained by successively summing data points in the #white_noise process. https://www.researchgate.net/publication/232236967_A_tutorial_introduction_to_adaptive_fractal_analysis/figures?lo=1

   edit   unpin & show all

 

Using the classical #dfa method, the #cumulative_sum of data are divided into segments, and the #variance of these sums is studied as a function of segment length after linearly detrending them in each segment. https://www.nature.com/articles/s41598-019-42732-7

   edit   unpin & show all

 

In #dfa, data are divided into segments of length L and are #linearly detrended. The #square_root of the #variance (called #fluctuation) of the detrended data is studied as a function of L. It can be shown that a #linear relationship between the #logarithm of the #fluctuation and the #logarithm of L is indicative of a #power_law behavior of the spectrum. https://www.nature.com/articles/s41598-019-42732-7

   edit   unpin & show all

 

If a #linear relationship between the length of a #segment or #time_windows and the strength of the #fluctuation (or the #square_root of the #variance of the #cumulative_signal) exists, the slope of the corresponding line is also referred to as #hurst_exponent.

   edit   unpin & show all

 

For #white_noise the #hurst_exponent or the relation between the #time_windows and the #fluctuation (square root of #variance) will be #linear: when we double the #time_windows the #fluctuation (or #variance of the #cumulative_sum) will also double.

   edit   unpin & show all

 

For #pink_noise #1f_noise the #hurst_exponent will equal #1 and will mean that for #time_windows twice longer the #fluctuation will increase about 4 times. In other words, the the longer is the #time_windows the more #fluctuation occurs (#positive_correlation).

   edit   unpin & show all

 

#hurst_exponent in this context is #alpha_exponent, because we use #alpha_exponent for #non_stationary processes

   edit   unpin & show all

 

if #alpha_exponent is more than 1, it means that for every increase of scale (#time_windows) the cumulative_sum of #fluctuation increases a lot. That means, the longer we look at the process, the more likely it is to have big #fluctuation — there is a tendency in the #short_term to be #small and in the #long_term there's a tendency to be #big.

   edit   unpin & show all

 

the #cumulative_sum of the difference from the #average of a #time_series will be #brown_noise (#random_walk) for the #white_noise

   edit   unpin & show all

 

In contrast, #0.5 < #hurst_exponent < #1 indicates a #correlated process for #f_gn or what is termed a #persistent process for #f_bm. In this case, #increases in the signal (for #f_gn) or increments of the signal (for #f_bm) are likely to followed by further #increase, and #decrease are likely to be followed by #decreases (i.e., a #positive #long_term #correlation). Anti-#persistent and #persistent processes contain #structure that distinguishes them from truly #random sequences of data. (2) (PDF) A tutorial introduction to adaptive fractal analysis. Available from: https://www.researchgate.net/publication/232236967_A_tutorial_introduction_to_adaptive_fractal_analysis [accessed Apr 21 2021].

   edit   unpin & show all

 

The difference between the #exponent or #exponential_decay and the #power_law #decay is that #power_law #decay is slower: there are more values with a low #amplitude in the case of the #power_law https://math.stackexchange.com/questions/164436/difference-between-power-law-distribution-and-exponential-decay

   edit   unpin & show all

 
tags:
     
    total nodes:  extend
    merged nodes:
    unmerge all
    copy to global

        
    Show Nodes with degree > 0:

    0 0

    Filter Graphs:


    Filter Time Range
    from: 0
    to: 0


    Recalculate Metrics   Reset Filters
          
    Hide Labels for Nodes < 0:

    0 0


    Edges Type:



    Layout Type:


     

    Reset to Default
    mindviral immunity:
    ×
             
    Main Topical Groups:

    N/A
    +     ?

    The topics are the nodes (words) that tend to co-occur together in the same context (next to each other).

    We use a combination of clustering and graph community detection algorithm (Blondel et al based on Louvain) to identify the groups of nodes are more densely connected together than with the rest of the network. They are aligned closer to each other on the graph and are given a distinct color.
    Most Influential Elements:
    N/A
    +     Reveal Non-obvious   ?

    We use the Jenks elbow cutoff algorithm to select the top prominent nodes that have significantly higher influence than the rest.

    Click the Reveal Non-obvious button to remove the most influential words (or the ones you select) from the graph, to see what terms are hiding behind them.

    The most influential nodes are either the ones with the highest betweenness centrality — appearing most often on the shortest path between any two randomly chosen nodes (i.e. linking the different distinct communities) — or the ones with the highest degree.

    Network Structure:
    N/A
     ?

    Modularity
    0
    Influence Distribution
    0
    %
    Topics Nodes in Top Topic Components Nodes in Top Comp
    0
    0
    %
    0
    0
    %
    Nodes Av Degree Density Weighed Betweenness
    0
    0
    0
    0
     


    Reset Graph   Export: Show Options
    Action Advice:
    N/A
    Structural Gap
    (ask a research question that would link these two topics):
    N/A
    Reveal the Gap   ?
     
    A structural gap shows the two distinct communities (clusters of words) in this graph that are important, but not yet connected. That's where the new potential and innovative ideas may reside.

    This measure is based on a combination of the graph's connectivity and community structure, selecting the groups of nodes that would either make the graph more connected if it's too dispersed or that would help maintain diversity if it's too connected.

    Latent Topical Brokers
    :
    N/A
    ?

    These are the latent brokers between the topics: the nodes that have an unusually high rate of influence (betweenness centrality) to their freqency — meaning they may appear not as often as the most influential nodes but they are important narrative shifting points.

    These are usually brokers between different clusters / communities of nodes, playing not easily noticed and yet important role in this network, like the "grey cardinals" of sorts.

    Emerging Topics
    N/A

    Top Relations
    (both directions):

    ⤓ Download   ⤓ Directed Bigrams CSV   ?

    The most prominent relations between the nodes that exist in this graph are shown above. We treat the graph as undirected by default as it allows us to better detect general patterns.

    As an option, you can also downloaded directed bigrams above, in case the direction of the relations is important (for any application other than language).

     
    Main Topics
    (according to Latent Dirichlet Allocation):
    loading...

    Most Influential Words
    (main topics and words according to LDA):
    loading...

    LDA works only for English-language texts at the moment. More support is coming soon, subscribe @noduslabs to be informed.

    Show Overlapping Nodes Only
     
    download data: CSV  Excel
    Please, enter a search query to visualize the difference between what people search for (related queries) and what they actually find (search results):

     
    We will build two graphs:
    1) Google search results for your query;
    2) Related searches for your query (Google's SERP);
    Click the Missing Content tab to see the graph that shows the difference between what people search for and what they actually find, indicating the content you could create to fulfil this gap.
    Find a market niche for a certain product, category, idea or service: what people are looking for but cannot yet find*

     
    We will build two graphs:
    1) the content that already exists when you make this search query (informational supply);
    2) what else people are searching for when they make this query (informational demand);
    You can then click the Niche tab to see the difference between the supply and the demand — what people need but do not yet find — the opportunity gap to fulfil.
    Please, enter your query to visualize the search results as a graph, so you can learn more about this topic:

     
       advanced settings    add data manually
    Enter a search query to analyze the Twitter discourse around this topic (last 7 days):

         advanced settings    add data manually

    Sign Up