Are you wondering how the Hours For Art pledgers are doing, one month into their commitments?
I was wondering, so I asked them. (I started an email list so the pledgers can keep in touch with each other.) Here are a few of their updates.
Liz is primarily known as an artist/illustrator, but she also writes ~ and she set out to put some more time into writing fiction. She's written a detailed post at her own blog about her results so far, and I love her specificity around when and how she would meet her pledge. This woman knows how to build labyrinths!
The sixteen hours I put in did not net me a lot of readable pages but it took the project from a gleam in my eye, populated by a handful of interesting characters, to a still-somewhat-rickety framework on which the tapestry can actually be woven. It went from a wannabe novel to a novel in progress. I'll take that.
Liz declares this month a win, and I totally concur. Make sure you check out her thoughts on the benefits of writing early in the morning.
Rachel is a visual artist and photographer who wanted to spend more time drawing. She had another project show up and preempt the drawing for a few weeks, but is looking forward to getting back to it.
Alison, I'm so glad you set up the list – turns out I needed the nudge. Hmmm, that might be a negative voice telling me 'I'm doing it wrong.' The truth is that my pledge was to draw 4 nights a week for 1/2 hour each time. I did it fabulously the first week – even one night when I could barely see straight I was so tired I managed to encourage myself to take that time for my art. Then my husband, with whom I collaborate on art projects, came up with a cool project that involved spending a lot of late nights out of the house. I've also been putting in tons of hours organizing my photos for an upcoming show. Long and short – I've been putting in a lot of art hours in the last month, but I have not been putting in my drawing hours. HOWEVER, yesterday I was asked to possibly illustrate a children's book. That will give me lots of drawing time. Regardless, the project with my husband ends next week and I plan to find a very visible place for my drawing materials so I'll have a tangible reminder to keep working on my pledge.
Glad to see Rachel catching the voice of "you're doing it wrong" and questioning it. There's a lot right about spending many hours on art in the last month, even if it wasn't on the project she intended.
Rhonda, a poet and fiction writer, is using her pledge to figure out how much writing she can actually do in a week.
Well, I have to be honest and say that I thought I was making a pledge for ONE WEEK which is why I pledged so high, knowing I had some days off work that week. I don't think my life can sustain that amount of writing per week, but I may be surprised. I think at this point I need to revisit the pledge and see what's realistically possible. Revisiting how I've set up my labyrinth is probably also a good idea! I did get some work done in May but nothing like double digits per week. However, I feel okay about that…the pledge and all the set-up around that week gave me some good momentum.
I like Rhonda's commitment to renegotiating her pledge rather than dropping it altogether.
Laureen is a painter who has made some big changes to open time for her art practice, and is beginning to reap the benefits.
I knew when I made the pledge that it was an ongoing development sort of pledge rather than an immediate one, and that has definitely been the case. However, there has been no time since I made it when I haven't been aware of it. And that awareness has helped moved me toward keeping it.
For the first month, art time has probably been about 8 hours per week rather than 16. I still had some structural work to do and worked at that in support of my pledge, making the pledge more of a possibility than a dream. As well, I operate a seasonal commercial gallery on the edge of one of Canada's most beautiful and remote national parks (www.grasslandsgallery.com), and its season has now started. This means some time has gone into preparation and creation of the season. Some other time went into taking days off – my last chance until September, and I grabbed it!
As I fashioned the gallery to have a small studio corner, I am now working there instead of in my home studio. I've been concentrating really hard on developing the skills needed to combine the art gallery business and the art-making business on an comfortable and ongoing basis. I don't count time spent lugging art supplies and setting up lights and generally fiddling around, just time actually working on images. Incredibly, this coming week looks good to bring 12 to 15 hours of images. It requires both desire and discipline, but remembering what I pledged to do is making a lot of difference in getting me there. Wahoo!
One of the results of making the pledge for me has been a connection to a new community – of Alison's Hours for Art Pledge Makers. Because the area where I live is so remote and the population so small, it's a delight to have this link to an engaged and searching group of international art-makers. I look forward to all the unfolding chapters!
Laureen has been a long-time client and I love seeing her put these structures in place that will pay off for weeks and months to come.
Brenda is a mixed media visual artist who hit a bump in the road shortly after making her pledge.
How did it go? Well, I had surgery 4/27 that has kept be "down" and physically unable to spend the time in my studio as pledged. During my recovery time, though, I've been reading, watching creative programs and keeping notes on ideas for NEXT month. I've also created two new projects for clients who are excited, so this will keep the fire burning!
Surprised at results? Mostly disappointed in the timing and not being able to really get into it. I am very thankful for the accountability and look forward to continuing to hear and share!
And I'm really glad to be supporting Brenda and the other pledgers on their quest. These updates are a great illustration of how our good intentions fare when they hit the realities of life. Nice to see persistence and positivity when things don't go exactly as planned.
Until next month . . . I wish you all Hours For Art.
I've been swamped this week (so much that I didn't have time to compose a nice writeup of how things have been going after the pledge!), but I've definitely made the time for my art! I think that I'm still in that mode from the call where I don't feel like I'm having "typical" weeks, but they're still involving a lot of time in the studio. I'm currently pondering whether there really is such a thing as a "typical" week for me. Figuring out how to construct a labyrinth that can wind around the chaos. I think that manageable goals and projects are a better way to get things done than scheduling–if I know I *need* to finish something this week, I'll make time when I can find it, but if I'm busy, I'm tempted to drop that nebulous "go to the studio and do… something" block out of my schedule.
Hi Riv! Glad you showed up. I really dig your differentiation between schedules and projects as ways to get things done. I can't seem to keep general appointments with myself either, but I am unstoppable if I've got a deliverable and a deadline that I'm completely aligned with.


We make tank heads and circular blanks.
Our 14 ft. wide CNC burning table allows us to cut wide plates with ease.
We're conveniently located 1.5 miles from I-65 in downtown Birmingham, AL.
As I reflect over the past 20 years, what stands out the most in my mind is the loyalty and support I have received from all of you, my customers. The dream of owning my own business, putting my three daughters through college, creating good wages for our employees: none of this would have been possible without the business you have given us over these past two decades, and it is with deep humility that I say "thank you" for making all of these dreams come true. I will never forget that it was you that made possible the success we enjoy today.
On the eve of this milestone anniversary at Shamrock Steel, I renew this promise to all of you: that we will always strive to provide you with the best quality, price, and customer service that you can find in our industry. I look forward to working with you for the next twenty years and beyond.
Our plant provides storage for steel plate, circular blanks and finished heads.
Learn more about the steel products we produce and supply .
We are a member of the Steel Tank Institute and work closely with them to provide the products most needed in the industry.


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Changelog
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# 1.x release

## v1.1.0

- Enhance: Dependency update
- Enhance: WOFF font support
- Fix: Support newer version of opentype

## v1.0.1

- Fix: Documentation
- Fix: Define command in package.json

## v1.0.0

- Major: Initial public release

redpajama_set_name: RedPajamaGithub


Download Book Anatomic Pathology Board Review 2e in PDF format. You can Read Online Anatomic Pathology Board Review 2e here in PDF, EPUB, Mobi or Docx formats.
Clinical Pathology Board Review covers all of the major subject areas of clinical pathology, presenting you with an essential study guide for certification or recertification. Designed as a companion to Anatomic Pathology Board Review, 2nd Edition, this brand-new medical reference book will be a welcome resource for pathology residents and practicing pathologists alike. Understand all of the major subject areas of clinical pathology tested on the Clinical Pathology board exam, including chemistry, hematology, coagulation, microbiology, immunology (including HLA testing), transfusion medicine (including therapeutic apheresis), cytogenetics, and molecular diagnostics. Prepare for the boards with help from multiple-choice questions offered in a format that mimics that of the actual test. Effectively grasp key concepts with questions that integrate various areas of clinical pathology, as well as questions that bridge concepts in clinical pathology with those in anatomic pathology. Understand why an answer is correct or incorrect with help from brief explanations accompanying each. Review key concepts in laboratory medicine, correlate them to the associated clinical or laboratory information, and apply them to the diagnosis and management of human disease. Includes PIN-code access to the Clinical Pathology Board Review assessment and testing website, which features all of the questions in the print book, along with additional interactive questions presented in practice mode (with immediate feedback) or timed test mode (with feedback and score given after test is taken). The site will score and return metrics to highlight areas of strength and weakness. Designed as a companion to Anatomic Pathology Board Review, 2nd Edition (ISBN: 9781455711406).
Featuring hundreds of multiple-choice questions and full-color illustrations, Anatomic Pathology Board Review serves as a comprehensive resource for both certification and recertification exams. This fully updated medical reference book contains chapters covering general pathology, the major organ systems, and ancillary diagnostic techniques, as well as important topics including immunohistochemistry, cytopathology, and molecular diagnostics. It's the perfect tool to help you be as prepared as possible for the Anatomic Pathology boards! Consult this title on your favorite e-reader, conduct rapid searches, and adjust font sizes for optimal readability. Understand why an answer is correct or incorrect with help from brief explanations accompanying each. Access coverage of all of the major organ systems and ancillary diagnostic techniques. Prepare for the boards with updated coverage of all of the most important topics on the anatomic pathology board exam, as well as over 900 MCQs, 835 full-color illustrations, and a format that mimics that of the actual test. Easily find specific diagnostic entities through a new Index to Images and Topics. Get a clearer view of critical material thanks to an improved design and larger illustrations.
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In conjunction with drafting comprehensive legislation concerning compensation for health effects related to asbestos exposure (the Fairness in Asbestos Injury Act), the Senate Committee on the Judiciary directed the Institute of Medicine to assemble the Committee on Asbestos: Selected Health Effects. This committee was charged with addressing whether asbestos exposure is causally related to adverse health consequences in addition to asbestosis, mesothelioma, and lung cancer. Asbestos: Selected Cancers presents the committee's comprehensive distillation of the peer-reviewed scientific and medical literature regarding association between asbestos and colorectal, laryngeal, esophageal, pharyngeal, and stomach cancers.


Marcelo completed the 120-hour online TEFL certificate course with ITTT. In this TEFL review video he describes how the course is great for those who need to fit studying in around their schedule and how the materials he received are still useful to him in his teaching career.
It is more helpful lesson to understand why evaluating and testing the ability of the students are important. Evaluating and testing can give us idea to create things to the students to improve their ability and creativity.Thank you for the good examples. I need to review all the lessons and learn more from it and will apply it in my future teaching.This unit introduced the tricky topic of conditional and reported speech, which is important for students to master in order for their conversations to be natural. I think that some of the reported speech forms can be more flexible than the unit suggests, but it is still important for students to understand the forms and be able to access them easily.


We have the 2" Double Leather Collars, 2" Inch Single Collars, 1" inch collars and 3/4" collars, these collars are just stunning to look at and feel. Made from the same leather hides that we make our Premium Leashes from, (people will know the quality of these) you just wont find a better leather collar.
You can stop looking at the sites that have the sparkly, spiked inflexible leather collars, we have the collars that are actually STRONG.
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These collars are handmade, no two are alike, you may even say a light fingerprint of the old world craftsman who has been making leather gear for 50 years!


Expansion of agriculture, forestry and mining.
Liberia published its 5th EITI Report covering the fiscal year 2011/12 on 30 June. As with previous reports, Liberia EITI (LEITI) has gone beyond the EITI requirements by including forestry and agriculture, in addition to oil and mining.
Government revenues from the extractives sector remained relatively stable, with an increase from US $102 million (2010/11) to US $110million. The sum is equivalent to approximately 14% of Liberia's real GDP in the reporting period, and 34% of estimated total government revenue.
Compared to the previous year, there has been a significant shift in Liberia's revenue structure.
Comparison of revenue structure of 4th and 5th EITI Reports. Oil revenues decreased significantly by 59% while the other extractives sectors grew and compensate for the drop in oil income.
Payments from the oil industry dropped by 59%. Oil revenue had been unusually high in the previous report due to significant one-off payments. In late 2010, Chevron bought a majority stake in Liberian offshore oil blocks from Oranto Petroleum, which resulted in the government earning US $40million in taxes and signature bonuses from the companies.
Petroleum projects are still in the exploration phase and there is no production. Ten of Liberia's 30 oil blocks have been awarded to companies including Anardako, Chevron and Exxon. Oil has been discovered, although not yet in commercial quantities.
Mining is the most significant source of income and contributed over half of all government revenues from the extractive sector in 2011/12. Liberia is rich in iron ore, gold and diamonds.
One mining company alone, Western Cluster, contributed 25% to the total mining revenue. The company is developing several iron ore deposits in Liberia and paid signing fees worth US $25million. In August 2011, Western Cluster became a subsidiary of Sesa Goa Ltd, a Vedanta Group company.
Agriculture's share in extractive revenues climbed to reach 25%. Payments made by Firestone Liberia, a rubber producer, and Liberia Forest Production Inc, a palm oil company, increased from US $14 million to US $23million, pushing agriculture revenue up.
This sector employs approximately half of the population, compared with only 2% in mining.
Forestry remains less important in monetary terms, despite revenues from this sector doubling from US $5.5million to US $11million. Liberia's key exports include rubber, iron ore, palm oil and logs. In January 2013, President Sirleaf-Johnson introduced a moratorium on the export of timber to halt deforestation.
The extractive sector plays a substantial role in the economy, and especially mining has driven economic growth in past years, although limited infrastructure remains a challenge. The Report recommends further improving the database on extractive companies. There are ambitious plans to publish an on-line register soon.
For further information about the EITI Liberia, please visit the country page on the EITI website and the national LEITI website.


text:
U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex
A.J. Mason, R.R. Parrish, T.S. Brewer
The South Harris Complex of the Scottish Outer Hebrides forms a distinctive component of the Lewisian Complex and contains three supposedly co-magmatic meta-igneous bodies, a diorite, a 'norite' and an anorthosite, believed to be part of a Palaeoproterozoic arc. New U–Pb zircon ages obtained from these bodies of 1888 ± 2 Ma, 1890 +2/−1 Ma, and 2491 +31/−27 Ma, respectively, demonstrate that the anorthosite cannot be related to the younger calc-alkaline diorite and 'norite'. The diorite and 'norite', however, probably are related products of arc magmatism. The spatial association of the diorite and 'norite' with the substantially older anorthosite suggests that the younger intrusions were emplaced into continental crust. Any suture associated with the South Harris Complex remains cryptic, and is not marked by an obvious change in protolith ages in the adjacent tonalitic gneisses.
Journal of the Geological Society
https://doi.org/10.1144/0016-764902-140
10.1144/0016-764902-140
http://jgs.lyellcollection.org/cgi/doi/10.1144/0016-764902-140
Dive into the research topics of 'U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex'. Together they form a unique fingerprint.
Norite Earth and Planetary Sciences 100%
Diorite Earth and Planetary Sciences 100%
diorites INIS 100%
Anorthosite Earth and Planetary Sciences 75%
anorthosites INIS 75%
Lewisian Earth and Planetary Sciences 50%
Young Earth and Planetary Sciences 50%
Magmatism Earth and Planetary Sciences 25%
Mason, A. J., Parrish, R. R., & Brewer, T. S. (2004). U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex. Journal of the Geological Society, 161(1), 45-54. https://doi.org/10.1144/0016-764902-140
Mason, A.J. ; Parrish, R.R. ; Brewer, T.S. / U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex. In: Journal of the Geological Society. 2004 ; Vol. 161, No. 1. pp. 45-54.
@article{bbf1e7d887ad4e2eb31e015d20e256ee,
title = "U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex",
abstract = "The South Harris Complex of the Scottish Outer Hebrides forms a distinctive component of the Lewisian Complex and contains three supposedly co-magmatic meta-igneous bodies, a diorite, a {\textquoteleft}norite{\textquoteright} and an anorthosite, believed to be part of a Palaeoproterozoic arc. New U–Pb zircon ages obtained from these bodies of 1888 ± 2 Ma, 1890 +2/−1 Ma, and 2491 +31/−27 Ma, respectively, demonstrate that the anorthosite cannot be related to the younger calc-alkaline diorite and {\textquoteleft}norite{\textquoteright}. The diorite and {\textquoteleft}norite{\textquoteright}, however, probably are related products of arc magmatism. The spatial association of the diorite and {\textquoteleft}norite{\textquoteright} with the substantially older anorthosite suggests that the younger intrusions were emplaced into continental crust. Any suture associated with the South Harris Complex remains cryptic, and is not marked by an obvious change in protolith ages in the adjacent tonalitic gneisses.",
author = "A.J. Mason and R.R. Parrish and T.S. Brewer",
doi = "10.1144/0016-764902-140",
journal = "Journal of the Geological Society",
publisher = "Geological Society of London",
Mason, AJ, Parrish, RR & Brewer, TS 2004, 'U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex', Journal of the Geological Society, vol. 161, no. 1, pp. 45-54. https://doi.org/10.1144/0016-764902-140
U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex. / Mason, A.J.; Parrish, R.R.; Brewer, T.S.
In: Journal of the Geological Society, Vol. 161, No. 1, 01.01.2004, p. 45-54.
T1 - U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex
AU - Mason, A.J.
AU - Parrish, R.R.
AU - Brewer, T.S.
N2 - The South Harris Complex of the Scottish Outer Hebrides forms a distinctive component of the Lewisian Complex and contains three supposedly co-magmatic meta-igneous bodies, a diorite, a 'norite' and an anorthosite, believed to be part of a Palaeoproterozoic arc. New U–Pb zircon ages obtained from these bodies of 1888 ± 2 Ma, 1890 +2/−1 Ma, and 2491 +31/−27 Ma, respectively, demonstrate that the anorthosite cannot be related to the younger calc-alkaline diorite and 'norite'. The diorite and 'norite', however, probably are related products of arc magmatism. The spatial association of the diorite and 'norite' with the substantially older anorthosite suggests that the younger intrusions were emplaced into continental crust. Any suture associated with the South Harris Complex remains cryptic, and is not marked by an obvious change in protolith ages in the adjacent tonalitic gneisses.
AB - The South Harris Complex of the Scottish Outer Hebrides forms a distinctive component of the Lewisian Complex and contains three supposedly co-magmatic meta-igneous bodies, a diorite, a 'norite' and an anorthosite, believed to be part of a Palaeoproterozoic arc. New U–Pb zircon ages obtained from these bodies of 1888 ± 2 Ma, 1890 +2/−1 Ma, and 2491 +31/−27 Ma, respectively, demonstrate that the anorthosite cannot be related to the younger calc-alkaline diorite and 'norite'. The diorite and 'norite', however, probably are related products of arc magmatism. The spatial association of the diorite and 'norite' with the substantially older anorthosite suggests that the younger intrusions were emplaced into continental crust. Any suture associated with the South Harris Complex remains cryptic, and is not marked by an obvious change in protolith ages in the adjacent tonalitic gneisses.
U2 - 10.1144/0016-764902-140
DO - 10.1144/0016-764902-140
JO - Journal of the Geological Society
JF - Journal of the Geological Society
Mason AJ, Parrish RR, Brewer TS. U-Pb geochronology of Lewisian orthogneisses in the Outer Hebrides, Scotland: implications for the tectonic setting and correlation of the South Harris Complex. Journal of the Geological Society. 2004 Jan 1;161(1):45-54. doi: 10.1144/0016-764902-140

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
With the rapid rise of different social networking systems, such as online social networks, mobile networks~\cite{wu2009}, and collaboration networks~\cite{newman2001}, social network analysis has emerged as a critical research focus. One of the most intriguing tasks in social network analysis is community detection, which helps to identify meaningful group structures in the network. Despite community detection being well-covered in recent academic literature, it mainly focuses on detecting communities in static networks, i.e., networks without temporal properties. However, real-world networks, such as online social networks, are not static: they often possess temporal properties, as nodes and edges can appear and disappear. Conventional social network analysis methods aggregate all observed interactions over a period of time and build a static network to represent all the interactions over that period~\cite{wasserman1994}. Inevitably, such representation is unable to capture temporal changes in the communities. For example, in a Twitter retweet network~\cite{CINELLI2022113819, zola2020}, the evolution of the community structure could be caused by new users starting to retweet a specific account or by members of a community that suddenly stop doing so. Treating these types of networks as static can lead to invalid associations between the users, e.g., a user may show similarities with a community at a certain time and later move towards a different community. While this user would represent the only connection between the two communities, omitting the temporal properties poses the risks of obtaining the aggregation of these communities as a single large community. In addition, time can also affect content semantically: for example, the meaning of the hashtag \#MeToo changed dramatically with the emergence of the \#MeToo social movement. Thus, enabling community detection in such dynamic networks is crucial.

A dynamic network can be represented by a time series of static networks called snapshots~\cite{wolf2006}. Each snapshot corresponds to the interactions aggregated over a defined period, such as a week or an hour. An intuitive method to detect communities from a dynamic network partitioned in this way consists in employing well-studied static community detection algorithms on each snapshot. Next, communities in dynamic social networks can be tracked by identifying the events that shape the evolution of a community over time~\cite{greene2010tracking, takaffoli2011, brodka2013ged}. This step involves matching the communities found in different snapshots through an algorithm, usually based on the similarity of community members. Therefore, an arbitrary threshold is required to determine if two or more communities found in different snapshots represent the same community at different times. The main drawback is that the final result may change drastically depending on the selected threshold value: a high similarity threshold means less tolerance for fluctuating members, whereas setting a too-low similarity threshold relates dissimilar communities to each other. The scarcity of threshold-free frameworks negatively affects their real-world implementation, which could instead prove useful in countering threats that plague online social platforms such as disinformation~\cite{MARTIN2022109265, QURESHI2022109649} and information manipulation~\cite{SUCHACKA2020105875, LI2022110038}.

In this paper, we propose a threshold-free framework to track communities evolution and structure over multiple snapshots of a dynamic network. Given the communities detected at each snapshot, we represent the entire network as a similarity network, where the nodes are the static communities found, and the weight of the edges corresponds to their similarity. By applying \textit{Local Modularity Optimization}~\cite{blondel2008}, we reveal the groups of nodes having high modularity and similarity. In this manner, we turn the community matching task into a modularity optimization problem where dynamic communities are found by optimizing modularity locally on all nodes. The node groups found embody the evolution of a community over time. Finally, each group is disentangled to reconstruct the temporal evolution of the represented dynamic community. Unlike most approaches, our framework does not require any threshold to be set.

To evaluate the proposed framework, we used four synthetic dynamic networks~\cite{greene2010tracking} containing embedded communities and events. Results show that, in most cases, our approach performs better than other state-of-the-art community tracking methods. In the second part of our evaluation, we show how the proposed approach can be applied to a real-world co-hashtag Twitter network~\cite{mazza2022} to extract relevant dynamic information about communities.

In the next section, we provide a brief overview of existing research in dynamic community tracking. In Section~\ref{sec:methods}, we provide a detailed description of the proposed framework. The evaluation and comparison of our framework with other approaches are given in Section~\ref{sec:evaluation}. Furthermore, Section~\ref{sec:evaluation} presents the results on a real-world Twitter co-hashtag network. Section~\ref{sec:conclusions} concludes the paper with a summary and suggestions for future work.

\section{Related work}
\label{sec:related}
Since most social networks evolve over time~\cite{newman2003social}, the evolution of social networks over time has attracted increasing interest from researchers over the last few years. In the following we report works that, like the one described in this paper, are based on existing static community detection algorithms that are adapted to deal with the temporal nature of social networks~\cite{KADKHODAMOHAMMADMOSAFERI2020113221}. This approach is appropriate for social networks with highly dynamic community structures~\cite{takaffoli2010framework}.
One of the first works in which static network snapshots have been used to track the evolution of the communities over time is~\cite{hopcroft2004tracking}. The authors proposed a method based on agglomerative hierarchical clustering to identify and track stable clusters over time.
Authors of~\cite{palla2007quantifying}, extended the clique percolation method to track events in the evolution of dynamic networks. After building joint graphs for pairs of consecutive snapshots, they subsequently matched the clique-based communities obtained using an autocorrelation function to find overlap between two states of a community. The authors of~\cite{asur2009event} described a community event identification strategy between communities detected in two consecutive snapshots that is implemented as bit operations. In~\cite{greene2010tracking} a community matching strategy is reported to efficiently identify and track dynamic communities in multiple snapshots through weighted bipartite matching, whereas \cite{takaffoli2010framework} provided an event-based framework to detect transitions between communities in consecutive snapshots. In a later work from the same authors~\cite{takaffoli2011}, the event definition formula has been improved to track community transitions throughout the observation time, no longer restricting it to consecutive snapshots.
The authors of~\cite{brodka2013ged} proposed the Group Evolution Discovery (GED) framework. This method, in addition to the similarity of community members, considers nodes position and importance within the community to match communities and identify the evolution of the community in successive snapshots. More recent research \cite{tajeuna2015tracking, tajeuna2016tracking} proposed a method to detect and model the evolution of a community based on a novel similarity measure, named mutual transition
In~\cite{KADKHODAMOHAMMADMOSAFERI2020113221}, a method for the Identification of Community Evolution by Mapping (ICEM) has been presented. In this approach, community evolution is tracked by the community members, which are implemented in a hash-map. More information on~\cite{greene2010tracking, takaffoli2011, takaffoli2010framework, brodka2013ged, tajeuna2015tracking, tajeuna2016tracking, KADKHODAMOHAMMADMOSAFERI2020113221} is provided in Section~\ref{sec:evaluation}, as these studies have been used for comparative purposes.

\section{Methods}
\label{sec:methods}
Before presenting the framework, let us describe a few general concepts related to dynamic social networks.

\subsection{Dynamic communities}
We represent a dynamic social network as a set of $n$ graphs $\{G_1, G_2, ..., G_n\}$ where $G_i$ includes only the set of nodes and edges in a particular snapshot $i$. Next, we define as $\mathbb{C}^i = \{C^i_1, C^i_2, ..., C^i_{k_i}\}$ the set of $k_i$ communities found at the $i^{th}$ snapshot. The problem we address is to find a set of $m$ dynamic communities $\mathbb{D} = \{D_1, D_2, ..., D_m\}$ that occur in one or more snapshots. Each dynamic community $D_j$ is represented by a timeline of its constituent communities ordered in time. Figure~\ref{fig:dynamic_schema} shows an example of timelines for five dynamic communities. When communities belonging to different dynamic communities are interconnected, such as $D_2$ and $D_3$ or $D_4$ and $D_5$, we can consider the dynamic communities independently or as a single entity composed of the union of all their communities; in this case, $D_{(2,3)}$ and $D_{(4,5)}$.

\begin{figure}
  \centering
  \includegraphics[width=0.5\linewidth]{figs/example.pdf}
  \caption{Example of five dynamic communities tracked over five snapshots, featuring growth, contraction, merging, splitting and death events.}
  \label{fig:dynamic_schema}
\end{figure}

\subsection{Critical events}
In order to track communities and their structural changes over time, we need to define structural events to describe the evolutionary behavior of dynamic social networks.
In~\cite{palla2007quantifying} and~\cite{asur2009event}, some types of events are proposed, but they do not cover all the possible ways in which a community can evolve. This paper uses the same models of critical events as proposed in~\cite{greene2010tracking}:
\textit{Growth} (a community gains new members),
\textit{Contraction} (a community loses some members),
\textit{Merging} (two or more communities merge into a new one),
\textit{Splitting} (a community is split into two or more new ones),
\textit{Birth} (a new community appears),
\textit{Death} (a community disappears).

Examples of such events are shown in Figure~\ref{fig:dynamic_schema}:
the community in $D_1$ \textit{grows} at the $2^{nd}$ snapshot;
the community in $D_4$ \textit{contracts} at the $3^{rd}$ snapshot;
the community in $D_3$ \textit{merges} with the community in $D_2$ at the $4^{th}$ snapshot;
the community in $D_4$ \textit{splits} into two communities, respectively, in $D_4$ and $D_5$ at the $5^{th}$ snapshot;
the communities in $D_1$, $D_2$ and $D_4$ were \textit{born} at the $1^{st}$ snapshot, the community in $D_3$ at the $2^{nd}$ snapshot, and the community in $D_5$ at the $5^{th}$ snapshot;
the community in $D_1$ \textit{dies} at the $4^{th}$ snapshot.

It is worth noting that a community may not necessarily be present in every snapshot. Considering the example in Figure\ref{fig:dynamic_schema}, the community in $D_2$ is observed at the $1$st snapshot and then again at the $3^{rd}$ snapshot. This ``intermittence'' can be caused by the behavior of community members or depend on the duration granularity of each snapshot.

\subsection{Similarity}
When tracking dynamic communities and the evolutionary events of their constituent communities, the key to finding relationships between communities from different snapshots is similarity. Most previous works require setting a similarity threshold: communities are considered related to each other only if their similarity value crosses this threshold. In dynamic social networks where the structure evolves, unstable communities may gradually lose members while gaining new ones.
Such communities can last long, even if all of their original members have left. An excessively high similarity threshold results in nonidentifying this type of community, whereas a low similarity threshold relates disparate communities to each other.

The framework proposed in this paper exploits similarity, but does not require any threshold to be set. Here, we compute the similarity as the \textit{overlap} of members between two communities. Let $\mathbb{C}^i$ and $\mathbb{C}^j$ denote the sets of communities found in the snapshots $i$ and $j$, where $i \neq j$. Further, let $\alpha  \in \mathbb{C}^i$ and $\beta \in \mathbb{C}^j$. We define the overlap between communities $\alpha$ and $\beta$ as:
\begin{equation}
overlap(\alpha, \beta) = \frac{|\alpha \cap \beta|}{min(|\alpha|,|\beta|)}
\end{equation}
where $|\alpha|$ and $|\beta|$ are the number of members, respectively, in $\alpha$ and $\beta$, while $|\alpha \cap \beta|$ is the number of members they share.
Although we opted for overlap as a similarity metric, the approach described here is not constrained to any particular metric. Therefore, it is possible to use a different measure as needed, for example, Jaccard as used in~\cite{greene2010tracking}.

\begin{figure*}[ht]
  \includegraphics[width=\textwidth]{figs/framework.pdf}
  \caption{Workflow of the proposed approach. Starting from a network, we proceed dividing it in snapshots. Then, we apply a static community detection algorithm on each snapshot. We build the community similarity network using the communities found in the previous step. Through local modularity optimization dynamic communities are found. For each dynamic network, communities are reordered by the origin snapshot, bringing out critical events.}
  \label{fig:t_window}
\end{figure*}

\section{Community tracking}
In order to identify the dynamic communities, communities extracted at each snapshot need to be matched with the communities belonging to other snapshots. In Figure~\ref{fig:t_window} are reported the steps that make up the framework. Starting with an initial network, we first break this down into snapshots. Second, we apply a static community detection method on each snapshot. Third, we construct the community similarity network, where each static community is represented by a node. This step does not consider the source snapshots of the various static communities, thus allowing matching between communities found in non-consecutive snapshots. Then we find the communities forming the dynamic communities by optimizing modularity locally on all nodes. Finally, we reconstruct the temporal evolution by reordering the communities at the temporal level and deriving the occurred events.

\subsection{Community similarity network}
In our framework, the matching step relies on a weighted undirected community similarity network $G_c=(V_c, E_c, W_c)$ where the vertex set (nodes) $V_c$ is made up of all the communities found at each snapshot, $E_c$ is the set of edges (links) linking the communities, and $W_c$ the set of weights assigned to each edge, corresponding to the similarity value between the linked communities. An edge exists between two communities only if they originate from different snapshots and their similarity value is greater than zero.

\subsection{Local modularity optimization}
After building the similarity network, we identify groups of similar nodes by optimizing modularity locally on all nodes. Modularity is a scale value between $[-0.5,1]$ and measures the density of links within communities compared to links between communities. Modularity is the most widely used metric to evaluate community structures~\cite{chen2013measuring}. By optimizing modularity, we seek a community assignment for each node in the network such that modularity $M$ is maximized using the function defined by:
\begin{equation}
    M={\frac {1}{2m}}\sum \limits _{ij}{\bigg [}A_{ij}-{\frac {k_{i}k_{j}}{2m}}{\bigg ]}\delta (c_{i},c_{j})
\end{equation}
where $A$ is the adjacency matrix with $A_{ij}$ representing the weight of the edge between the vertices $i$ and $j$, $k_i = \Sigma_j A_{ij} $ is the sum of the weights of the edges attached to the vertex $i$, $c_i$ is the community to which vertex $i$ belongs, $\delta$ is the Kronecker delta function $\delta(c_i,c_j)$ returns 1 if $c_i=c_j$ and 0 otherwise and $m = \Sigma_{ij}A_{ij}$ is the sum of the weights of all edges in the graph. In modularity optimization, weights are interpreted as the strength of connection, influencing the optimization process. To optimize modularity, each vertex in the network is assigned to its community. Then, each vertex $i$ is removed from its community and moved to the community of each neighbor $j$. When a vertex is assigned to a new community, the modularity increase is calculated:
\begin{equation}
\begin{gathered}
\Delta M={\bigg [}{\frac {\Sigma _{in}+2k_{i,in}}{2m}}-{\bigg (}{\frac {\Sigma _{tot}+k_{i}}{2m}}{\bigg )}^{2}{\bigg ]}-\\{\bigg [}{\frac {\Sigma _{in}}{2m}}-{\bigg (}{\frac {\Sigma _{tot}}{2m}}{\bigg )}^{2}-{\bigg (}{\frac {k_{i}}{2m}}{\bigg )}^{2}{\bigg ]}
\end{gathered}
\end{equation}
where $\Sigma _{in}$ is the sum of all the weights of the links within the community $i$ is moving, $k_i$ is the weighted degree of $i$, $k_{i,in}$ is the sum of the weights of the edges between $i$ and other nodes in the community that $i$ is moving, and $m$ is the sum of the weights of all edges in the network. Then, once $\Delta M$ is calculated for all communities connected to $i$, the community that resulted in the most significant increase in modularity encompasses $i$. If no increment is encountered, $i$ remains in its original community. The process described above is applied to all vertices until no modularity increase occurs. This is the same approach as the Louvain algorithm in its first phase~\cite{blondel2008}. However, differently from our approach, it proceeds with a second phase, building a new network where the vertices represent the communities found in the previous phase. Then it applies the first phase to it, further optimizing the modularity. A complete run of both phases is called a pass. Such passes are carried out repeatedly until a maximum of modularity is achieved. As our goal is to aggregate vertices with high similarity and not to reach maximum modularity, we leverage only the first step. Moreover, due to the underlying characteristics of the community similarity network, applying the entire procedure provided by Louvain may result in obtaining a low granular set of communities, thus resulting in communities where some members can be poorly related to others. Therefore, by applying local modularity optimization to the vertices of the community similarity network, we obtain groups with high modularity composed of similar communities that correspond to the dynamic communities featured in the dynamic network.

\subsection{Events reconstruction}
Once the dynamic communities have been extracted from the community similarity network, we proceed with the identification of the events that describe their evolutionary behavior. Given a group of communities $D$, let us define more formally each critical event as follows:

\begin{itemize}
    \item Growth -- a community grows at the $i^{th}$ snapshot $C^i \in D$, if there exists a community at the $j^{th}$ snapshot $C^j \in D$, where $i > j$, that shares members and is smaller than $C_i$
    \begin{equation*}
    \begin{gathered}
        growth(C^i) = 1 \qquad if \\
        \exists \ C^j \in D: \quad i>j, \quad \lvert C^i \cap C^j \rvert > 0, \quad \lvert C^i \rvert > \lvert C^j \rvert
    \end{gathered}
    \end{equation*}

    \item Contraction -- a community contracts at the $i^{th}$ snapshot $C^i \in D$, if there exists a community at the $j^{th}$ snapshot $C^j \in D$, where $i > j$, that shares members and is bigger than $C_i$
    \begin{equation*}
    \begin{gathered}
        contract(C^i) = 1 \qquad if \\
        \exists \ C^j \in D: \quad i>j, \quad \lvert C^i \cap C^j \rvert > 0, \quad \lvert C^i \rvert < \lvert C^j \rvert
    \end{gathered}
    \end{equation*}

    \item Merging -- a community $C^i$ is the result of a merge at the $i^{th}$ snapshot, if there exists a set of communities $C^j_{set}=\{C^j_1, C^j_2, ..., C^j_n\}$, where $C^j_{set} \in D$ and $i > j$, where each community in $C^j_{set}$ shares members with $C^i$
    \begin{equation*}
    \begin{gathered}
        merge(C^i) = 1 \qquad if \\
        \exists \ C^j_{set} = \{C^j_1, C^j_2, ..., C^j_n\}: \quad i>j, \\
        \forall \ C^j \in C^j_{set}: \quad \lvert C^i \cap C^j \rvert > 0
    \end{gathered}
    \end{equation*}

    \item Split -- a community $C^i$ is the result of a split at the $i^{th}$ snapshot, if it belongs to a set of communities $C^i_{set}=\{C^i_1, C^i_2, ..., C^i_n\}$, where $C^i_{set} \in D$ and if there exist a community $C^j \in D$, where $i > j$, where each community in $C^i_{set}$ shares members with $C^j$
    \begin{equation*}
    \begin{gathered}
        split(C^i) = 1 \qquad if \\
        \exists \ C^i_{set} = \{C^i_1, C^i_2, ..., C^i_n\}: \quad i>j, \\
        \forall \ C^i \in C^i_{set}: \quad \lvert C^i \cap C^j \rvert > 0
    \end{gathered}
    \end{equation*}

    \item Birth -- a community $C^i$ is born at the $i^{th}$ snapshot, if there does not exist a community at the $j^{th}$ snapshot $C^j \in D$, where $i > j$, that shares members with $C_i$
    \begin{equation*}
    \begin{gathered}
        birth(C^i) = 1 \qquad if \\
        \nexists \ C^j \in D: \quad i>j, \quad \lvert C^i \cap C^j \rvert > 0
    \end{gathered}
    \end{equation*}

    \item Death -- a community $C^i$ is dead at the $i^{th}$ snapshot, if there does not exist a community at the $j^{th}$ snapshot $C^j \in D$, where $j > i$, which shares members with $C_i$
    \begin{equation*}
    \begin{gathered}
        death(C^i) = 1 \qquad if \\
        \nexists \ C^j \in D: \quad j>i, \quad \lvert C^i \cap C^j \rvert > 0.
    \end{gathered}
    \end{equation*}
\end{itemize}

\section{Experiments and Results}
\label{sec:evaluation}

In this section we describe the experiments to compare our framework with the state of the art. Also, we provide an example based on real-world data to show the potential of our framework in extracting valuable information from social interactions.

\subsection{Datasets}
To validate our method, we use synthetic and real-world datasets. For benchmarking purposes, we use the synthetic networks contained in the four \textit{benchmark datasets} proposed in \cite{greene2010tracking}. These synthetic networks have been constructed through a dynamic extension of the static LFR benchmark~\cite{lancichinetti2009benchmarks} to model different types of evolutionary behavior of communities over time. Each graph comprises 15,000 vertices and contains five static networks, which means there are five snapshots to simulate evolving communities. For each snapshot, the ground-truth information about communities is available.
The nodes in each of the four synthetic networks have a mean degree of $20$, a maximum degree of $40$, and a mixing parameter value of $\mu=0.2$, which controls the overlap between communities. Furthermore, at each snapshot, $20\%$ of the nodes changed their memberships to reflect the natural movement of members between communities over time. Synthetic networks were designed to contain all types of community evolution events:
\begin{itemize}
    \item \textit{BirthDeath}: 40 new communities are constructed to replace 40 existing communities.
    \item \textit{ExpandContract}: 40 randomly selected communities expand or contract their $25\%$ size at each snapshot.
    \item \textit{MergeSplit}: 40 communities are randomly selected to be split, while 40 mergings of two random communities happen.
    \item \textit{Intermittent}: $10\%$ of existing communities are unobserved for their concealment at each snapshot.
\end{itemize}

\subsection{Evaluation metric and experimental setup}
As noted previously, our framework is independent of the choice of the static community detection algorithm applied at each snapshot. To produce a fair evaluation, we used the same approach for static community detection for all the considered competitors, namely the Louvain algorithm~\cite{blondel2008} choosing the hierarchical level at which the number of communities most closely matches the number of communities in the ground-truth at the $1^{st}$ snapshot.
To evaluate the performance in dynamic network tracking, we adopted the same approach as in~\cite{greene2010tracking, HE2017438, folino2014}. For each evaluated competitor, dynamic network tracking was performed considering two scenarios: i) using the ground-truth of memberships to static networks at each snapshot; ii) using the static networks derived by Louvain as mentioned above. Then, we used Normalized Mutual Information (NMI) to compare the memberships to dynamic networks found in these two scenarios.

The NMI is a well-known entropy measure in information theory, which measures the similarity of two clusters. It is defined as:
The NMI is defined as:
\begin{equation*}
\begin{gathered}
N\!M\!I(X,Y) = \frac{H(X)+H(Y)-H(\!X,Y\!)}{(H(X)+H(Y))/2}
\end{gathered}
\end{equation*}
where $H(X)$ is the entropy of the random variable $X$ associated with an identified community, $H(Y)$ is the entropy of the random variable $Y$ associated with a ground-truth, and $H(X,Y)$ is the joint entropy.
A NMI closer to 1 indicates higher similarity, and thus a more robust dynamic community detection with respect to the presence of noise in the information related to the static communities available at each snapshot. Such resilience is paramount to be able to perform reliable dynamic communities tracking in real-world data.

Since the datasets consist of five snapshots, we obtained five values of NMI per dataset.
For each dataset, we calculated the NMI in five sequential experiments. While for the first evaluation, the timeline is composed solely of the $1^{st}$ snapshot, for each succeeding experiment, we added the subsequent snapshot, ending with the evaluation where the entire timeline composed of five snapshots is analyzed. As mentioned above, we compared our framework with other state-of-the-art approaches using the same community sets derived by Louvain for an objective and consistent comparison. Since some of these approaches require a threshold to be set, we tested them with different threshold values: (0.1; 0.3; 0.5).
To select a threshold value to use for comparison, we calculated the average of the five NMI values for each dataset. Then, for each approach, we selected the threshold value that gave the highest average NMI.

\subsection{Algorithms}
\label{sec:algo}

In this section, we briefly describe the state-of-the-art algorithms used to compare our proposed method. The approaches we will describe are those proposed by: \textit{Greene}~\cite{greene2010tracking}, \textit{Takaffoli}~\cite{takaffoli2011, takaffoli2010framework}, \textit{Brodka}~\cite{brodka2013ged}, \textit{Tajeuna}~\cite{tajeuna2015tracking, tajeuna2016tracking}, and \textit{Mohammadmosaferi}~\cite{KADKHODAMOHAMMADMOSAFERI2020113221}. Virtually, these frameworks and ours begin by considering the dynamic network as a series of snapshots. Then, they independently identify community structures at each of these snapshots using a community detection algorithm,. However, the approaches differ in the strategy and measure of similarity used to track and detect the changes that communities may undergo over time.

\textit{Greene et al.}~\cite{greene2010tracking}: in this work, the authors proposed a heuristic threshold-based method, which allows for many-to-many mappings between communities across different time
steps. The strategy proceeds as follows. First, a static community finding algorithm is applied at each snapshot. Communities belonging to the $1$st snapshot are assigned to a dynamic community. Then, the consecutive snapshot communities are compared with each dynamic network's front community. The front community of a dynamic network is the community found in the most recent snapshot belonging to that dynamic community. To perform the matching, the authors used the Jaccard coefficient for binary sets~\cite{10.2307/2427226}:
\begin{equation}
sim(\alpha, \beta) = \frac{|\alpha \cap \beta|}{|\alpha \cup \beta|}
\end{equation}
The pair is matched if similarity exceeds a matching threshold $k$. Furthermore, the authors assumed that a community emerged at a certain snapshot $t$ is considered dissolved if there was no matching after $d$ consecutive snapshots. This condition allows the discovery of evolving communities at non-consecutive snapshots. For our comparisons, we assumed $d=inf$ to enable matching with all non-consecutive snapshots. The approach gave the best results with $k=0.1$.

\begin{table}[!h]
\centering
\begin{tabular}{lrrr}
        \toprule
        \textbf{}        & \multicolumn{3}{c}{\textbf{Threshold}}                                      \\ \midrule
        \textbf{Dataset} & \multicolumn{1}{c}{\textbf{0.1}} & \multicolumn{1}{c}{\textbf{0.3}} & \multicolumn{1}{c}{\textbf{0.5}} \\ \midrule
        BirthDeath       & 0.984                  & 0.948                  & 0.926                  \\
        ExpandContract   & 0.986                  & 0.940                  & 0.921                  \\
        MergeSplit       & 0.969                  & 0.949                  & 0.936                  \\
        Intermittent     & 0.981                  & 0.936                  & 0.913                  \\
        \end{tabular}
        \caption{NMI values obtained for each dataset with the Greene framework.}\label{tab:greene}
\end{table}

\textit{Takaffoli et al.}~\cite{takaffoli2011, takaffoli2010framework}: in their method, after producing sets of static communities for each snapshot, the authors looked for critical events occurring at consecutive and non-consecutive snapshots. The tracking process compares communities at distinct snapshots, through the following similarity measure:
\begin{equation}
sim(\alpha, \beta) = \left \{ \begin{array}{ll}
\frac{|\alpha \, \cap \, \beta|}{max(|\alpha|, \, |\beta|)} \quad if \quad \frac{|\alpha \, \cap \, \beta|}{max(|\alpha|, \, |\beta|)} \geq k \\\\
0 \qquad \qquad \qquad \quad otherwise
\end{array}
\right.
\end{equation}
In their work, the authors automatically determined threshold similarity $k$ using a text-mining approach, since they assessed their approach on networks incorporating content information. Since we evaluate synthetic networks, it is not possible to determine the threshold automatically. From our experiments, we obtained the best results for $k=0.3$.

\begin{table}[!h]
\centering
\begin{tabular}{lrrr}
    \toprule
    \textbf{}        & \multicolumn{3}{c}{\textbf{Threshold}}                                      \\ \midrule
    \textbf{Dataset} & \multicolumn{1}{c}{\textbf{0.1}} & \multicolumn{1}{c}{\textbf{0.3}} & \multicolumn{1}{c}{\textbf{0.5}} \\ \midrule
    BirthDeath       & 0.941                  & 0.950                  & 0.921                  \\
    ExpandContract   & 0.943                  & 0.946                  & 0.913                  \\
    MergeSplit       & 0.921                  & 0.928                  & 0.909                  \\
    Intermittent     & 0.940                  & 0.941                  & 0.903                  \\
    \end{tabular}
    \caption{NMI values obtained for each dataset with the Takaffoli framework.}\label{tab:takaffoli}
\end{table}

\textit{Brodka et al.}~\cite{brodka2013ged}: the authors of this work developed a framework called group evolution discovery (GED), which can identify overlapping communities. The authors of previous approaches relied on a similarity metric to identify the changes and evolution that communities can undergo. In this work, this measure has been extended by including a topological metric in their comparison:
\begin{equation}
I(\alpha, \beta) = \frac{|\alpha \, \cap \, \beta|}{|\alpha|} \cdot \frac{\sum_{x \in (\alpha \cap \beta)} NI_{\alpha(x)}}{\sum_{x \in (\alpha)} NI_{\alpha(x)}}
\end{equation}
where $NI_{\alpha}(x)$ is the value of the importance of node $x$ within the community $\alpha$. This measure can be any centrality metric, e.g., centrality degree, social position, betweenness degree, page rank, etc. Although the comparison is made at consecutive timestamps, the inclusion effect helps to track overlapping and non-overlapping communities. The method requires two threshold values, $k$ and $j$. We used the same value for $k$ and $j$ and obtained the best results for $k,j=0.1$.

\begin{table}[!h]
\centering
\begin{tabular}{lrrr}
        \toprule
        \textbf{}        & \multicolumn{3}{c}{\textbf{Threshold}}                                      \\ \midrule
        \textbf{Dataset} & \multicolumn{1}{c}{\textbf{0.1}} & \multicolumn{1}{c}{\textbf{0.3}} & \multicolumn{1}{c}{\textbf{0.5}} \\ \midrule
        BirthDeath       & 0.933                  & 0.931                  & 0.923                  \\
        ExpandContract   & 0.936                  & 0.932                  & 0.925                  \\
        MergeSplit       & 0.925                  & 0.923                  & 0.917                  \\
        Intermittent     & 0.926                  & 0.923                  & 0.918                  \\
        \end{tabular}
        \caption{NMI values obtained for each dataset with the Brodka framework.}\label{tab:brodka}
\end{table}

\textit{Tajeuna et al.~\cite{tajeuna2015tracking, tajeuna2016tracking}}: in this approach, each community has been represented as a vector (\textit{transition probability vector}) containing information on the number of members in common between communities over time. Then, the authors compared the vectors corresponding to different communities: given two communities $\alpha$ and $\beta$ and their transition probability vectors $v_{\alpha}$ and $v_{\beta}$ the similarity between the communities is found as:
\begin{equation}
sim(\alpha, \beta) = \left \{ \begin{array}{ll}
\sum^{N_{c}}_{x=1} 2 \,
\frac{p_{\alpha, x} \, \cdot \, p_{\beta, x} }{p_{\alpha, x} \, + \, p_{\beta, x}} \\\\ \quad if \,\, \sum^{N_{c}}_{x=1} 2 \,
\frac{p_{\alpha, x} \, \cdot \, p_{\beta, x} }{p_{\alpha, x} \, + \, p_{\beta, x}} > k
\\\\
0 \qquad \qquad \qquad \quad otherwise
\end{array}
\right.
\end{equation}
where probabilities $p_{\alpha, x}$ and $p_{\beta, x}$ are components of the vectors $v_{\alpha}$ and $v_{\beta}$ respectively. The threshold value $k$ is set automatically as the predicted point of intersection of two Gamma curves based on the non-zero values obtained by rating the similarity of two transition probability vectors.

\begin{table}[!h]
\centering
\begin{tabular}{lrll}
        \toprule
        \textbf{}        & \multicolumn{3}{c}{\textbf{Threshold}} \\ \midrule
        \textbf{Dataset} & \multicolumn{3}{c}{Automatically set}                \\ \midrule
        BirthDeath       & \multicolumn{3}{r}{0.965}             \\
        ExpandContract   & \multicolumn{3}{r}{0.968}             \\
        MergeSplit       & \multicolumn{3}{r}{0.929}             \\
        Intermittent     & \multicolumn{3}{r}{0.965}             \\
        \end{tabular}
        \caption{NMI values obtained for each dataset with the Tajeuna framework.}\label{tab:tajeuna}
\end{table}

\begin{figure}[t]

  \centering

  \subfloat[Birthdeath]{
  \includegraphics[width=0.5\columnwidth]{figs/birthdeath.pdf}
  \label{fig:trainingRedALL}}
  \subfloat[ExpandContract]{
  \includegraphics[width=0.5\columnwidth]{figs/expandcontract.pdf}
  \label{fig:trainingRedSeq}}
  \hfill
  \subfloat[MergeSplit]{
  \includegraphics[width=0.5\columnwidth]{figs/mergesplit.pdf}
  \label{fig:trainingRedSeq}}
  \subfloat[Intermittent]{
  \includegraphics[width=0.5\columnwidth]{figs/intermittent.pdf}
  \label{fig:trainingRedSeq}}

  \caption{NMI of the proposed dynamic community tracking framework and state-of-the-art methods on the four synthetic datasets.}

  \label{fig:results}
\end{figure}

\textit{Mohammadmosaferi et al.~\cite{KADKHODAMOHAMMADMOSAFERI2020113221}}: the authors of this work introduced a novel method for Identification of Community Evolution by Mapping (ICEM). In this approach, a hash map is used to map the members of each community into a pair, which includes the snapshot and a community index. From the second snapshot, ICEM builds a similarity list for each community and determines the evolution of a community based on that list. In addition to common critical events, the authors identified \textit{partial} events resulting from partial similarity between two communities:
\begin{equation}
sim(\alpha, \beta) = \frac{|\alpha \cap \beta|}{|\alpha|}
\end{equation}
\begin{equation}
sim(\beta, \alpha) = \frac{|\alpha \cap \beta|}{|\beta|}
\end{equation}
where $\alpha$ is a community from the $i^{th}$ snapshot and $\beta$ a community from the $j^{th}$ snapshot, where $i < j$.
The communities $\alpha$ and $\beta$ are partially similar if $sim(\alpha, \beta) > k$ and $sim(\beta, \alpha) > k$, while they are very similar if $sim(\alpha, \beta) > j$. Therefore, $k$ and $j$ are the  thresholds to identify partially similar and very similar communities, respectively. Since our concern is not to distinguish different types of critical events in this evaluation, we set $j=0.5$ and obtained the best results for $k=0.1$.

\begin{table}[!h]
\centering

\begin{tabular}{lrrr}
\toprule
\textbf{}        & \multicolumn{3}{c}{\textbf{Threshold}}                                      \\ \midrule
\textbf{Dataset} & \multicolumn{1}{c}{\textbf{0.1}} & \multicolumn{1}{c}{\textbf{0.3}} & \multicolumn{1}{c}{\textbf{0.5}} \\ \midrule
BirthDeath       & 0.973                  & 0.972                  & 0.936                  \\
ExpandContract   & 0.975                  & 0.970                  & 0.930                  \\
MergeSplit       & 0.935                  & 0.956                  & 0.923                  \\
Intermittent     & 0.974                  & 0.967                  & 0.922                  \\
\end{tabular}
\caption{NMI values obtained for each dataset with the Mohammadmosaferi framework.}\label{tab:mohammadmosaferi}
\end{table}

\subsection{Results of the evaluation and comparison}

Table~\ref{tab:results} shows the NMI values per dataset achieved by the proposed framework at each snapshot. We observe that the worst results are obtained with the \textit{MergeSplit} dataset. Merge and split events are the ones that most distort the dynamic communities structure and, therefore, the most difficult to track.

\begin{table}[!h]
\centering

\small
\begin{tabular}{lrrrrr}
\toprule
                 & \multicolumn{5}{c}{\textbf{Snapshot}} \\
\midrule
\textbf{Dataset} & \multicolumn{1}{c}{1} & \multicolumn{1}{c}{2} & \multicolumn{1}{c}{3} & \multicolumn{1}{c}{4} & \multicolumn{1}{c}{5} \\ \midrule
  BirthDeath      & 0.971 & 0.968 & 0.985 & 0.985 & 0.979 \\
  ExpandContract  & 0.971 & 0.993 & 0.995 & 0.993 & 0.987 \\
  MergeSplit      & 0.971 & 0.988 & 0.977 & 0.979 & 0.966 \\
  Intermittent    & 0.971 & 0.973 & 0.991 & 0.991 & 0.979 \\
\end{tabular}
\caption{NMI values obtained for each dataset with our framework.}
\label{tab:results}
\end{table}

Figure~\ref{fig:results} shows the results of the community tracking framworks applied to the synthetic datasets. Our method is among the most effective overall, surpassed only in some cases. Greene, Tajeuna, and ICEM perform well, while GED and Takaffoli obtain the worst results. The poor results obtained by GED may depend on its inability to relate non-consecutive communities to each other, thus leaving the newly identified dynamic communities without a proper follow-up. Interestingly, the evaluated approaches achieve their worst results with the \textit{MergeSplit} dataset. However, even for this dataset, our method does not fall below 0.96 in terms of NMI. The design of our framework seems effective in handling this type of event since, instead of performing sequential matching, it aims to optimize modularity in a network where the temporal component is omitted. This makes it more robust to structural changes in communities across snapshots. Moreover, using a threshold parameter also affects the number of dynamic communities found by a given method. Figure~\ref{fig:n_comm} shows the number of communities found by each method on the \textit{MergeSplit} dataset. Our proposed method, along with Tajeuna and Takaffoli, produces a number of communities quite close to that present in the ground-truth. The reason why Greene and ICEM have fewer communities is related to the low threshold value set. Low-value results in more matches between communities, merging them together. On the other hand, GED, as noted earlier, suffers from comparing only communities present in consecutive snapshots.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.5\linewidth]{figs/n_comm.pdf}
  \caption{Number of communities found on the \textit{MergeSplit} synthetic dynamic network, by the proposed dynamic community tracking method and state-of-the-art methods, relative to the number of communities in the ground-truth.}
  \label{fig:n_comm}
\end{figure}

\begin{figure}[ht]
    \centering
  \includegraphics[width=0.5\linewidth]{figs/comm_stats.pdf}
  \caption{Points are plotted against the days of activity on the $y$ axis and the overall number of members on the $x$ axis. Each point represents a dynamic community and the color encodes the average hashtags overlap value.}
  \label{fig:mut_top}
\end{figure}

\subsection{Application to Real-World Data}

\begin{figure*}[ht]
  \includegraphics[width=\textwidth]{figs/alluvial.pdf}
  \caption{Alluvial diagram representing the structure of the analyzed dynamic community.}
  \label{fig:alluvial}
\end{figure*}

In our second evaluation, we used the dataset provided by~\cite{mazza2022} to test the behavior of the proposed framework on a real dataset. This is a dataset containing the activity of 63,358 fake Twitter accounts, which produced 5,457,758 tweets during 2020. By the term fake account, we refer to those social media accounts that contain false information or pretend to be a real person or organization~\cite{mazza2_2022}. This kind of dataset is ideal for experimenting with the proposed method, as the tweets from the accounts were not collected using predefined languages or keywords that tied the activity to specific topics. We preprocessed the data to produce a weighted undirected graph for each snapshot, which in this instance equals one day of activity. Daily graphs were obtained by constructing a co-hashtag network: in this graph, two users are connected if they used the same hashtag on the same day. The weight of each edge is given by the number of hashtags used in common between two users. To find the static communities at each snapshot, we used the Order Statistics Local Optimization Method (OSLOM)~\cite{lancichinetti2011}, which is based on measuring the  significance of communities compared to a null model without community structure~\cite{molloy1995}.
After identifying statistically significant communities by agglomerating neighborhood nodes, OSLOM performs several iterations of adjustments, like node deletion or addition, in order to increase the significance of the communities.
We chose OSLOM for its good performance in community detection in online social networks~\cite{darmon2015, wendel2017}. Its main drawback is that it tends to find low-dimensional static communities~\cite{KUMAR2017103} that may not represent the meaningful community structure of the network~\cite{SHI2013394}. The latter is not relevant to the experiment, since through the proposed framework, the identified static communities will be joined into bigger dynamic communities.

Having the static communities identified by OSLOM, we applied our framework, obtaining 103 dynamic communities.

To investigate the behavior of the found dynamic communities over time, we extracted the hashtags used in each static community, namely the hashtags used daily by each dynamic community.
Then, we introduced a new metric related to a dynamic community: the \textit{average hashtags overlap}. Given two sets of hashtags $h_1$ and $h_2$, the hastags overlap is found as:
\begin{equation}
Hashtags \, Overlap = \frac{|h_1 \, \cap \, h_2|}{min(|h_1|, |h_2|)}
\end{equation}
The average hastags overlap of a dynamic community $D$ is found by averaging all the hastags overlaps between the static communities belonging to $D$.
An acceptable alternative metric might have been the one used in~\cite{takaffoli2011}, where instead of keywords or hashtags, the authors relied on topics. Moreover, since this is a dataset composed of the activity of sold fake accounts during a one-year period, it is not unlikely that communities of accounts used quite different sets of hashtags on different days. Despite this, a set of hashtags effectively represents a community on a specific day.

By averaging the hashtag overlap values among all static communities belonging to a dynamic community we obtain insights on the characteristics of the identified dynamic communities. In Figure~\ref{fig:mut_top} we plotted the found dynamic communities against the overall number of members on the $x$ axis and and the days of activity on the $y$ axis. Moreover, through color, we reported the average hashtags overlap of each dynamic community. A correlation between the number of members and the days of activity emerges from Figure~\ref{fig:mut_top}, i.e., the more users there are, the more days a community tends to be active, and vice versa. In addition, dynamic communities with high values in terms of members and days of activity also exhibit a low value of average hashtags overlap, meaning that during the one-year period, these dynamic communities discussed disparate topics.  A low value of average hashtag overlap does not imply that a dynamic community is not relevant, as this metric may be affected by other factors, such as the strategy eventually employed.

As an example, in Figure~\ref{fig:alluvial}, we reported a time glimpse of a dynamic community ranging from February 9 to February 13, 2020. To better understand temporal behavior, each community is represented by its ten most used hashtags. We observe that initially, there is only one community using mostly generic hashtags such as \#relax, \#beach, and \#nature and some more specific ones such as \#apple and \#iphone. The next day, this community split into two communities, one of which turns out to be larger than the initial one due to the arrival of new users. This community resumes the hashtags used in the previous day regarding apple products, introducing others such as \#iphone11 and \#iphone12. Instead, the other community focuses on cryptocurrency and blockchain technology through the hashtags \#btc, \#bitcoin and \#blockchain. On the following day, a portion of users from one and the other merge into a new community centered on hemp-related topics: \#cannabis, \#cbd, \#cannabisnews. However, this community expands on the subsequent day, reverting to more generic hashtags. This behavior continues the next day, where we find \#funny yet also \#valentines\_day since it is Valentine's Eve.

The given example shows how the topics addressed by users of an online social network can vary drastically from day to day. Observing this kind of phenomenon and, more generally, studying the behavior of a community over time is possible exclusively by taking into account its temporal properties, that is, by analyzing it as a dynamic community.

\section{Conclusions}
\label{sec:conclusions}
In this paper, we have described a framework to track dynamic communities and their evolution over time. Unlike most frameworks proposed in the literature, the community matching phase does not require a threshold value since it is based on modularity optimization, which is applied on a weighted undirected community similarity network. We used synthetic graphs with embedded events to evaluate the framework and compared the results with those obtained using other state-of-the-art frameworks. Notably, for most competitor frameworks we first performed a series of experiments to determine the best threshold value. Notwithstanding, our framework achieved scores comparable with the others, even outperforming them in several instances. Notwithstanding, our framework mostly got better scores without the need to compute a threshold value. In addition, we have presented a preliminary evaluation on a real-world Twitter network. Our framework revealed 103 dynamic communities with different characteristics. Experiments on this network suggest that, especially with regard to networks built from online social media, dynamic communities found can be very dynamic in terms of covered topics. Since our method is free from any threshold value, it provides consistent outcomes independent from the frequency of fluctuations of the community members. Moreover, the proposed framework is independent of the choice of the underlying community detection algorithm, therefore the latter may be chosen based on the properties of the network, e.g., weighted or unweighted, directed or undirected. When used on online social media, the proposed framework turns out to be useful as it facilitates the identification of user groups with similar interests or behaviors. In addition, tracking dynamic communities can assist in studying the behavior of influencers and key opinion leaders within a community from a temporal perspective, thus providing a valuable addition to research applications.

\section*{Acknowledgements}

This work is supported by the European Union – Horizon 2020 Program under the scheme "INFRAIA-01-2018-2019 – Integrating Activities for Advanced Communities", Grant Agreement n.871042,  "SoBigData++: European Integrated Infrastructure for Social Mining and Big Data Analytics" (http://www.sobigdata.eu).

\linespread{1.1}\selectfont
\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


Framed flowers are gorgeous decorative embellishments for all sorts of art and craft. They look pretty where ever you hang them. Whether in your dining room, lounge or beside your bed, they look perfect everywhere. They also give you a sense of peacefulness to be calm and relaxed. It could also be a new hobby you pick up to get your mind off things after a break-up.
Crafting your very own pressed flower frames is quite simple. The pressed flowers can be used craft wedding cards, phone cases and much more. But the best of all the things is the frames of the pressed flower.
The list of things which are required to make pressed flower frames are scissors, tweezers, ruler, pencil, pressed flowers (you can get them from a shop and also craft them yourself), paper, glue and a wooden frame. These are the things used to make pressed flower frames for your rooms.
After you've collected the material, start making the frames. Making the frames is quite simple. All you need to do is cut the wooden frames like you want and glue it together. After you are done with making the frame. Place a white paper or any colored paper to give it a neat finish. Now the next thing you need to do is place the dried and pressed flower in between the frame and put a glass in front of it. And you are done with making the beautiful pressed flower frames.
You can decorate the exterior of the frame if you like. It will give a nice and neat finish to the frame. But it's totally up to you. If you don't want fancy, keep it simple.
This is how you DIY a frame of the pressed flower. Isn't it simple and amazing? Well if you think that too, you should definitely try it.


Following the huge popularity of our Wood RetroPod we knew it was time to add another Photo Booth to our collection. When we discovered this beauty we were smitten!
Just arrived, we've named it the LuxePod, which fits perfectly alongside our other Pod photo booths!
We had searched all over the world for our next Photo Booth; so when we discovered this one just up the road it seemed like it was meant to be!
Seeing the craftsmanship that has gone into producing this booth meant we could see how this is the perfect addition as our luxury photo booth experience. Everything about the LuxePod just oozes style and sophistication.
The LuxePod looks amazing and will really add the wow factor to any venue. It's actually more like a piece of furniture than a photo booth. Until we first saw it up close rather than in photos we never realised just how impressive it would be. Due to her solid wood design she stands a little larger than the BoothPod and RetroPod; yet still remains compact with the photos and printing all happening inside.
Like our other open style photo booths, the LuxePod can be paired with one of our stylish backdrops. We have a huge range to choose from! We are very often asked to use fabulous feature walls within the venues that have been so carefully chosen by our clients. So if your venue has a gorgeous brick wall or cool wallpaper ask us if this will work for your images.
The LuxePod comes with a new feature not found on our other booths. It has a rear touchscreen for easy viewing and sharing of photos right there at the event. Guests can email their images to themselves or just simply browse everyone else's photos! As the sharing screen is on the back of the LuxePod, this keeps the front free for more photo taking!
If you're looking for a high end photo booth experience for your wedding that will really wow your crowd then the LuxePod is for you! In fact, we chose the LuxePod because we know how fabulous it will look in many of the venues we already go to regularly, including Swancar Farm Country House, Hazel Gap Barn, the West Mill and Haarlem Mill to name just a few! So whether your venue is rustic in style or a chic urban spot we know this design led Booth will be an attention grabber!
If you're looking for a luxury photo booth experience for your wedding or special event please get in touch. With our extensive knowledge of the wedding and events industry we can help advise on the best way to style your photo booth experience, including backdrop choices and print design options. We can also collaborate with your existing suppliers such as florists to customise your backdrop. If you need any recommendations we can help with that too.
If you'd like to have the LuxePod be a part of your celebration, get in touch with us and tell us about your plans!


for those who know me, know I love colour - it inspires me and really makes me tick - I found these pictures in my "to post" file on my computer - references are not my strong point - so sorry, but look at the detail in each image and imagine yourself there and then try something new at your place - don't be afraid of colour, embrace it, its FUN and MEMORABLE!!!!
one of my all time favorite vintage posters!
happy Tuesday peeps, I'm off to school tonight to learn about computer aided drawings (CAD).........not sure if I am liking it yet, they say every designer/stylist needs it!!!!!!!!
rejigging the whole house using what I already have......I almost wish I never started!!!
Have a lovely evening, LEARNING!!!


text:
Why Weight Watchers International Stock Tumbled Today
Shares of Weight Watchers International (NASDAQ: WTW) , now rebranded as WW, were plummeting today after the wellness company offered underwhelming guidance and indicated problems retaining its subscriber base. The news was just the latest sign that WW's once strong momentum was grinding to a halt, and the stock was down 33.1% as of 2:25 p.m. EST.
WW said its subscriber base contracted for the third quarter in a row, falling to 3.9 million from 4.2 million in the third quarter, though that figure was still up 22% from a year ago. Fourth-quarter revenue also missed the mark as the top line increased 5.7% to $330.4 million, well below estimates of $347 million. However, adjusted earnings per share ( EPS) increased from $0.37 to $0.63, topping estimates of $0.60, but that offered little consolation to investors.
On the earnings call , management acknowledged that the rebranding may have cost it some momentum, but nonetheless defended the move, saying it would pay off to shift from a weight-loss focus to wellness. The company also said that subscriber growth was weak to start the year during the key New Year's resolutions period when Americans tend to sign up for weight-loss and wellness programs.
Commenting on the year ahead, CFO Nick Hotchkin said, "Due to the soft start to the key Winter Season, we expect member recruitment for 2019 to be below 2018 levels, resulting in lower revenue and earnings for the year. We are focused on driving member recruitment and exercising strict cost discipline, while continuing to invest in the areas that will drive future growth."
Now what
For 2019, WW sees revenue coming in at $1.4 billion, down from $1.5 billion last year, and projected earnings per share of $1.25 to $1.50, much worse than the adjusted total of $2.71 i t report ed for 2018. Both figures were well below the analyst consensus for 2019 at revenue of $1.66 billion and EPS of $3.43.
WW shares are now down more than 80% from their peak last July; the stock has now given up nearly all of the monster gains it got after Oprah Winfrey joined the company in 2015. WW has a new ad campaign with Winfrey at the center coming this spring. That could turn around the company's momentum, but it's clear that management needs to figure out some way to stem the bleeding at this point.
10 stocks we like better than Weight Watchers International
David and Tom just revealed what they believe are the ten best stocks for investors to buy right now... and Weight Watchers International wasn't one of them! That's right -- they think these 10 stocks are even better buys.
Jeremy Bowman has no position in any of the stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. The Motley Fool has a disclosure policy .


Social media giant Snapchat and streaming service Netflix have joined in on the Indian Premier League furore this season, partnering up with several big league teams in the Twenty20 tournament.
Snapchat has joined hands with the Mumbai Indians, Royal Challengers Bangalore, Delhi Daredevils and the Rajasthan Royals for the upcoming season.
All four teams are each set to have their own official account on Snapchat and will appear on Snapchat's 'Discover' page, allowing the 300 million plus users of the photo and video sharing platform exclusive glimpses into life behind the scenes of an IPL tournament via its 'Stories' feature.
This is Snapchat's first ever engagement with a sporting event in India, making it a milestone moment for Indian sports coverage.
Meanwhile, Netflix has launched a new sports documentary centred on three-time IPL champions, the Mumbai Indians.
The series is being produced by Condé Nast Entertainment, showcasing the team in action both on the field and behind the scenes, in an original unscripted eight-part documentary series.
The documentary will be a Netflix exclusive, available to stream in 190 countries.


Here's the most significant benefit of tankLess water heater. They've the capability of providing on-demand hot water whenever needed without any delay. You can enjoy hot water anytime in the 24 hours.
So there are families with more members and all of them love to clean themselves up. Unlike the tank water heaters the tankless gas or electricity water heaters provide a constant supply of hot water so that one after the other, all family members could enjoy warm water in winter, wash dishes, do the laundry or whatever. It is available constantly dudes.
Who has that space to accommodate an appliance that takes lots of space? We certainly want home comfort appliances to be as small I'm size as possible so that they do affect the home decor. While the tank water heaters take large accommodation, the Tankless Water Heaters are not just elegant in appearance but are also relatively much smaller in size than the conventional water heaters. This type can, therefore, be ideal for people living in small houses and have less space to install large appliances.
While you might not be in a habit to use the tap water for drinking, there's still something to consider; how clean is your tap water? In the case of tank water heaters, a lot of sedimentary, rust and other particles keep adding in the everyday use water because the water remains stored in a tank. This does not happen in the case of Tankless Water Heaters where water is directly supplied without any storage.
It takes a headache to install tank water heaters. The Tankless Water Heaters, on the other hand, are easy to install and can even be installed doing a self-service.
They save you in long run. High-efficiency water heaters are 80% more efficient than others. In addition to that, they help save energy by only working on demand, consequently saving energy bills too.
Tankless Water Heaters have a relatively longer warranty. You've the choice of replacement or return of appliance if it doesn't suit you and is a great deal. Also, in case the appliance shows less efficiency than the proclaimed, or gets damaged within the warranty period, it can be replaced.
Everything needs maintenance but keeping maintenance of some home comfort appliances is not so easy. It takes time, effort and professionalism. While tank water heaters are hard to tackle when it comes to maintenance, Tankless Water Heaters are much easier to maintain. DIY hacks can be used to clean and to do other necessary maintenance of tankless water heaters.
To have a 24/7 availability of hot water or what they call, hot water for life, these water heaters are the best choice to make.
I wasn't aware about the most desirable features of tankless water heating system unless I visited Gotankless.info that provides complete details about it, so now it would be easier for me to make the right selection easily.


Some of the most memorable weddings are those that take place outside. Unfortunately, many of them are memorable for bad reasons, as well as, good ones! We are going to talk about the different types of outdoor weddings as well as give some tips for planning one.
Community Park Weddings- Almost every community has a variety of beautiful parks that can serve as a venue for weddings. Often these venues have a low cost to utilize, which can be helpful on a tight budget. Contact your town or cities Parks and Recreation Department for rates and regulations. Often these locations have shelters or buildings that can be utilized if the weather turns bad.
Backyard Weddings- If you or a friend or relative have a large backyard, this can often be a very low cost venue. A nearby garage or home can be an emergency back up shelter if the weather turns.
Beach Weddings- If you live near a beach, or are doing a destination wedding, beach weddings can be some of the most exotic and beautiful venues around.
Sports Stadium Weddings- If your dream wedding involves a local sports team, the stadium parking lot can be a low cost venue. Flexibility is key for a venue like this.
Ranch or Farm Weddings- For a country themed wedding, a farm or a ranch can be a great location....often with barns or other buildings in the backdrop, pictures can also be wonderful.
Make sure whatever venue you use, that you have permission to use it. While public parks are open to the public, that doesn't mean you can throw a large party there without permission. You may need a permit or pay a small fee to the parks department. When dealing with a sports stadium make sure you contact the stadium manager for details ahead of time.
Make sure you clean up before the ceremony as well as after...can anyone say "pooper scooper" if there is a dog around!
Have a back up plan. Weather can be an outdoor weddings worse friend. In case of bad weather you need to have a building you can move to, or at the very least a tent set up and ready to go.
Check local ordinances. If you are having alcohol, many parks and local beaches will have restrictions...make sure you know what they are.
Beware the bugs. Pretty self-explanatory but 'skeeter spray may be a good idea.
Dress for the temperature. A heavy wedding dress, while beautiful, is not good if you pass out from heat stroke. Also, saying your vows while stuttering with cold isn't a good memory. In summer, dress appropriately, have parasols or umbrellas for sun protection. Slippers instead of high heels if you are walking on the beach or the grass so you don't trip.
Keep track of the kiddies. Kids will be kids, even more so when they are out in the open. The desire to run and play will often win out over the parents wishes to sit still.
Beware the wind. Not only do you need to make sure all decorations are securely fastened, let's not forget what the wind can do to a veil or hairdo.
K.I.S.S.- Keep it Simple Sweetie is a good rule to follow. With the opportunity from wind and weather for more things to go wrong, the simpler the wedding is the less likely for problems. Tone down the decorations and other things you bring in and highlight the natural beauty of the venue.
happens if the weather turns, if the wind kicks up or the mosquitoes swarm? Plan for the worse and hope for the best and you will not be disappointed.


Degree in Nursing from Edinboro University; both schools are located in Pennsylvania.
and became a Nurse Practitioner in 2004. She worked in Family Practice with special interest in Geriatrics until joining Gastroenterology, Ltd. in 2010.
Her husband, Scott, works in banking. They have a daughter and a son. Her hobbies include knitting & crocheting, reading, and playing with her children.


Miton Global Opportunities plc ("MIGO") is a London-listed investment trust. MIGO invests in closed-end investment funds traded on the London Stock Exchange's Main Market, but has the flexibility to invest in investment funds listed or dealt on other recognised stock exchanges, in unlisted closed-end funds (including, but not limited to, funds traded on AIM) and in open-ended investment funds. It has tended to be instinctively contrarian in approach, aiming to profit from the cycle of investor sentiment and the driving forces and catalysts for change in the market.
Frostrow Capital was appointed by MIGO in January 2016 to provide distribution, accounting, company secretarial and administrative services alongside the appointed Portfolio Manager, Miton Asset Management.


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Theater openings
May 6, 2004 |Updated Mar 15, 2011 4:00 p.m.
BIRDS IN WINTER: Playwright and composer Herbert Bergel presents a blend of silent film, theater, dance and live music featuring the performance trio The Typing Explosion and staff members of the Northwest Film Forum. Opens May 13. Through May 22. Thursday-Saturday, 8 p.m. The Little Theatre, 610 19th Ave. E. Tickets: $7, $5 youth/senior, Pay-what-you-can: May 16; 206-219-3167.
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HIDING HANNAH: May 10, 7 p.m. Mirror Stage Company presents a staged reading of Seattle playwright Joy McCullough-Carranza's drama about a family trying to put itself back together again after a missing woman reappears and her brother leaves prison. Hugo House, 1634 11th Ave. Donation: $5. Reservations: 206-686-3729.
HOW THE OTHER HALF LOVES: Bellevue Civic Theatre presents Alan Ayckbourn's comedy about what happens when spouses in three couples are tangled in an affair. Opens May 7. Through May 15. Friday-Saturday, 8 p.m.; Thursday, 7:30 p.m.; Sunday, 2 p.m. The Theatre at Meydenbauer Center, 11100 N.E. Sixth St., Bellevue. Tickets: $25, student/senior discount. 425-235-5087.
HOW TO SUCCEED IN BUSINESS WITHOUT REALLY TRYING: Village Theatre closes its season with the musical about a young window washer who works his way up the corporate ladder. Preview: May 12. Opens May 13. Through June 27. Tuesday-Saturday, 8 p.m.; weekend matinees, 2 p.m.; Sunday, 7 p.m. American Sign Language interpreted: May 29, 2 p.m. Post-show discussion: June 15. Francis J. Gaudette Theatre, 303 Front St. N., Issaquah. Tickets: $30-$44; 425-392-2202.
IN-SITE: INDUSTRIAL PERFORMANCE PROJECT: Defibrillator Productions presents a theater festival with six ensembles utilizing the 6,000 square feet available to them to stage new works in the unconventional space. Preview: May 12, 8 p.m. Opens May 13. Through May 22. Thursday-Saturday, 8 p.m. After-show parties: May 15 and 22. Sand Point Magnuson Park, Building 67, 7400 Sand Point Way. Tickets: $15, pay-what-you-can preview. 800-838-3006 or www.brownpaperticket.com
LATE NIGHT CLUB: May 7, 10:15 p.m. New City Theater presents another edition of its late-night blend of comedy, hip-hop, poetry and more. Warehouse, 2110 Airport Way S. Tickets: $5. 206-271-4430.
MARK RUSSELL: May 7, 7:30 p.m. The piano-playing political satirist performs at Pantages Theater, 901 Broadway. Tickets: $10-$45; 253-591-5894.
MELANCHOLY PLAY: Macha Monkey Productions presents Sarah Ruhl's farce about a group of contented townfolk who get their lives overturned by a melancholy stranger. Opens May 7. Through May 22. Friday-Saturday, 8 p.m. Hugo House, 1634 11th Ave. Tickets: $12; 206-860-2970.
MY FAIR LADY: Off The Wall Theater joins with Take a Bough Productions for a staging of the classic musical about a poor flower girl who is transformed into an aristocrat. Opens May 7. Through May 23. Friday-Saturday, 8 p.m.; Sunday, 2 p.m. Frank Wagner Auditorium, 639 W. Main St., Monroe. Tickets: $12, $10 senior/student; 360-805-5699.
ONCE UPON A MATTRESS: The Plateau Community Players presents the musical based on the fairy tale "The Princess and the Pea." Opens May 13. Through May 22. Thursday-Saturday, 7:30 p.m. White River High School Performing Arts Center, 240 N. C St, Buckley. Tickets: $10, $8 child/senior, $5 matinee. 360-825-0774.
RED, PORK AND BLUE: THE POLITICS OF THE OTHER WHITE MEAT: The Seattle Asian American comedy troupe Pork Filled Players presents a new set of sketches skewering current events, at home and abroad. Opens May 7. Through May 22. Friday-Saturday, 8 p.m. Odd Duck Studio, 1214 10th Ave. Tickets: $12, $9student/senior/group; 206-850-7882.
SPIN THE BOTTLE: May 7, 11 p.m. Annex Theatre presents another installment in its monthly late night cabaret. Freehold's East Hall Theatre, 915 E. Pine St. Tickets: $7; 206-728-0933.
SQUATTERS: Troupe du Jour makes its debut as well as the Seattle premiere of Bryan LaPorte's surreal and darkly comic exploration of strangers taking over someone's home. Opens May 7. Through May 30. Friday-Saturday, 8 p.m.; Sunday, 2 p.m. Northwest Actors Studio, 1110 E. Pike St. Tickets: $10. 206-595-5565 or www.troupedujour.org Note: Not suitable for children.
THE STAY UP LATE SHOW: May 8, 11 p.m. The live talk show returns for another edition, with guests Seattle P-I columnist/NPR "Rewind" show Bill Radke, comedian Lisa Todhunter, chef Kenyetta Carter, music by The Mercury Four and host Rebecca Davis. Empty Space Theater, 3509 Fremont Ave. N. Tickets: $10. 206-547-7500. 21+.
TRAIN OF THOUGHT: The Seattle sketch comedy troupe presents a new show, this time using New York as its inspiration for scenes about dating, interviewing celebrities and bringing children to the workplace. Opens May 7. Through June 12. Friday-Saturday, 10 p.m. Northwest Actor's Studio, 1100 E. Pike St. Tickets: $10, $8 student.
ZELDA, SCOTT AND ERNEST: May 9, 7:30 p.m. Writers Calvin Trillin, Robert Stone and Mary Karr bring to life literary icons F. Scott and Zelda Fitzgerald and Ernest Hemingway using letters sent among themselves as well as their works. Town Hall, 1119 Eighth Ave. Tickets: $12-$50. 206-621-2230 and www.lectures.org
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