Alan Strickley
email: alan.strickley@sda-ltd.com

John Bertram

Dave Chapman

Michael Hart

Roy Hicks

Derek Kennedy

Mark Phillips

A National Single Indicator for Schools in England: Helping Parents Make Informed Decisions

Keywords: School performance tables, national single indicator, Ofsted, NSI, parents

With an ever-increasing measurement of pupil and school performance and presence of resultant statistical tables and indicators, parents are faced with a sometimes overwhelming plethora of data and information when monitoring the performance of their children's present or prospective school. The authors are part of a company that has developed a parent/careraccessible site to attempt to address issues and needs for parents/carers. Anecdotal evidence indicates that a single portal where parent/carers can find all the relevant data about schools in England would be an invaluable tool for monitoring and choosing a school. It was decided that such a site would be built around a National Single Indicator (NSI). The indicator is formed from an amalgam of expected progress measures: the main threshold level; pupils' average points score; and the value added measure. By changing the weight attributed to each of these measures, the website allows parents to modify their relative importance according to the value they place on them. This dynamically alters the overall result to give users their own "personal indicator", which means they can compare schools in a list tailored to their own specification.

Introduction

The data held in schools and shared with local and central governments in England has increased since the advent of computerised Management Information Systems (MISs) in the 1970s up until the current time [START_REF] Strickley | An evaluative study of the use of management information systems in Birmingham primary schools[END_REF]. In particular this has concerned:  Electronic replacement of the admissions' register [START_REF]DfE: Amendments to school attendance regulations[END_REF].  Electronic recording of attendance [START_REF]DfE: Amendments to school attendance regulations[END_REF].  The National Curriculum [START_REF]The national curriculum[END_REF].  Electronic examination entry and results [START_REF]AQA: Home page[END_REF].  End of Key Stage (age-related) entry and results [START_REF]Key Stage 2[END_REF].  Common transfer file (an interoperable file format used to transfer selected pupil data when that pupil moves from one school to another) [START_REF]CTF information[END_REF].

 Pupil level census (a central government electronic return by all schools which includes selected individual personal and performance data about pupils) [START_REF]School census information[END_REF].

With an increase in parental access to school admission procedures and the coordinated admission process which includes equal preferences [START_REF]School admissions code[END_REF], the choice of school is seen as a critical factor. With much of the data about schools being available in the public domain, school selection has become an important social and political concern within England at secondary and more recently at primary levels.

Data about schools is available in a plethora of formats and locations, from league tables (ranking of schools by government-agreed rating measures), attendance levels, Key Stage (age-related) results and value added from central government, the British Broadcasting Corporation (BBC) and newspapers are amongst those that publish this information [START_REF]Home page[END_REF][START_REF]School performance tables[END_REF][START_REF]Guardian: School league tables[END_REF][START_REF]Daily Mail: League tables[END_REF]. For many parents the information is disparate and often in a format that is confusing and complex to understand (as supported by [START_REF] Dearden | Schools, markets and league tables[END_REF]).

A decision was made by the authors to compile all of the available data from the various sources (but mainly the Department for Education in England -DfE) into a website which could be accessed by the public to help choose a new school or evaluate the performance of existing ones. The site would be underpinned by a fundamental value which was defined as the National Single Indicator (NSI) for each school. This would have a value (A-E) together with a less granular star rating, calculated on a set of key performance criteria (described in the next section) but could be fine-tuned by the user adjusting the weightings for each of these criteria. The result was the School Performance Tables [START_REF]SDA: School performance tables[END_REF] website which is described in detail later in this paper.

This paper looks at the basis of the NSI for schools, the fundamental design of the web interface, together with initial user reactions and considerations for further work.

Background

Performance tables have been published by the DfE [START_REF]School performance tables[END_REF], and its previous incarnations, since 1992 for Key Stage 4 (KS4) (aged 14 to 16 years) and 1996 for Key Stage 2 (KS2) (aged 7 to 11 years). The main aims of publication were to assist parents and carers in selecting schools for their children and to encourage school improvement by providing objective indicators against which schools' performance could be measured.

The current performance tables provide over 200 separate data items per school from which interested parties are expected to make judgements. This may be well within the capabilities of local government authority staff and others familiar with education performance data, but for parents and carers it can be a daunting task.

The aim of the National Single Indicator (NSI) is to provide a simple, but robust, method for parents and carers to be able to view schools' relative performance without needing to view multiple screens of data and without having to perform offline calculations.

It is important to note that the NSI does not aim to be a tool to aid school improvement -there are many available tools for this purpose and much expertise in schools, local authorities and support organisations focuses on this issue. As it stands, the NSI does not integrate with school MISs in any way; however, the option for schools to add context-sensitive information onto the site is a feature that will be added in the future.

The NSI is a single indicator describing school performance at KS2 and KS4. The indicators at both of these Key Stages are closely aligned, sharing expected progress, value added and average points scores as common components and differentiating only on the key indicators used to assess performance of Level 4+ (average expected attainment) at KS2 and 5A*-C (expected public examination attainment) at KS4.

The components at KS2 or KS4 (average points score, value added and expected progress) are given equal weighting with a default, notional, value of 2. This value can be varied between 0 and 4 in increments of 1 according to personal choice, or perceived importance, that users place on it. For example, it may be that a parent places more store by a school's ability to "add value" to their children's education than the school's performance measures.

What Data are used for the National Single Indicator?

The developers intended the NSI to be a well-rounded and justifiable indicator of a school's performance. This section explains how the indicator is calculated. The NSI is based on the following base components.

Key Stage 2

The following performance indicators are taken from the DfE's published Performance Tables data [START_REF]School performance tables[END_REF] (where the precise definitions of each may be found):



Key Stage 4

The following performance indicators are taken from the DfE's published Performance Tables data [START_REF]School performance tables[END_REF] where the precise definitions of each may be found: measure of the added value that the school has provided).  Total average (capped) points score per pupil (an average value based on the best GCSE results for each pupil in that school).



Calculation methodology

In generating a NSI, the following exception classes apply (i.e. no NSI score is calculated or provided) and are allocated as follows.

 New school: no results data are provided in the Performance Tables, so it is unclassifiedas a New School.  A school without data in one or more of the measures: will normally be either an independent school or a school with very small cohort numbers, so it is unclassified -with Insufficient Data.  Special school: schools where all (or the vast majority) of pupils have special educational needs and cannot fairly be compared to mainstream schools, so it is unclassified -as a Special School.

For schools not allocated an exception class, the following general methodology is used for both Key Stage 2 and Key Stage 4:

 Normalised scores are calculated: each of the performance measures described in sub-sections 3.1 and 3.2 above is normalised to provide a score between and 1. This is done by taking the actual values and calibrating them into a single scale from 0 to 1.  Weightings are allocated for the purposes of calculating the NSI: each of the main performance measures is given equal weighting. For the component measures of the main progress measure, equal weighting has been given to English and mathematics.  A single indicator score is calculated: an NSI score is calculated by multiplying each normalised score by its respective weighting and then divided by the sum of the weightings (4 for the NSI).  A single indicator band is calculated: the mean and standard deviation of NSI scores are determined. An NSI band is allocated depending on the number of standard deviations from the mean of each individual NSI score.

 Single indicator ranking within the band is calculated: for each ranking, the minimum and maximum normalised scores for each of the performance measures are determined and, consequently, the score range. Each NSI score is allocated an NSI ranking within each NSI band based on the difference between NSI score and the band's minimum score and that difference's proportion of the score range.

The final NSI is either: (a) an exception class; or (b) NSI band plus NSI ranking, represented as a value A to E, augmented by a finer graduation of 1 to 5 stars, each with quarterly intervals (i.e. quarter, half and three-quarter star shadings).

Whilst there continue to be arguments and discussions regarding the validity of the performance tables and the individual indicators used [START_REF] Goldstein | School league tables: what can they really tell us? Significance[END_REF][START_REF] Goldstein | League tables and their limitations: statistical issues in comparisons of institutional performance[END_REF], such arguments are for the DfE to address. The NSI is provided on the basis that the DfE and Ofsted (the school performance inspectorate) consider the performance tables and individual indicators to be valid and fit for purpose.

As part of the pre-launch evaluation of the site, a large sample of 1000 schools was selected, and their NSIs compared to the individual performance measures. The result of this testing showed a very accurate match in most cases indicating that the algorithm used in the calculation of the NSI was producing its intended outcome.

Design of the School Performance Website

The website -www.schoolperformancetables.com -is intended to be a simple, straightforward means of comparing schools, at both primary (KS2) and secondary (KS4) levels by means of a single indicator. It goes further in being the first such site to provide a search facility that can offer a user-defined set of given subjects beyond the core curriculum. In addition, it will offer schools the option of subscribing to the site, allowing them to both advertise and brand their school and also provide commentary and context to the performance data presented.

In common with the intention to provide a simple and straightforward experience, the site attempts to be intuitive to navigate, with the minimum amount of information necessary to convey a given point, and that information to be provided, for the most part, graphically. More complex information, where absolutely necessary, (such as the description of how our indicators are generated), is available through links. In addition, the site is mobile reactive, enabling a better experience for the increasing number of smartphone and tablet users. It, therefore, differs in look and approach from the traditional performance tables delivered by the DfE. Plenty of clean space and economical instructions prevail, as opposed to dense sets of data and exhaustive instructions and guidance.

Home page

Figure 1 shows the home page, which is the one that parents will be directed to from any external link. It is considered that parents and schools will be the main users of the site. Therefore, three main search criteria are invoked for the initial search, these being name, place and Key Stage. In addition, a subject search has been added for secondary schools. The school search box is versatile, allowing multiple postcodes, abbreviated school names, regions etc., to be included. The subject search box allows for any of the examination board subjects to be input. This is designed to be particularly useful where a user requires a particular subject or specialism to be available at a school. The types of searches are illustrated in the Tables 3 to 6 below.

Table 1, below, shows how the program interprets various postcodes and names from the home screen. For schools in a local authority (LA), it is possible to enter a postcode (for example, a home postcode); the schools will be listed in order of distance (see Table 3).

Law, Polish, Spanish and Statistics

Displays all schools where these subjects have been taken at GCSE Table shows how to combine the school search and subject search so that, for example, it is possible to find out the nearest school offering preferred subjects at GCSE, or find out all schools in a local authority that offer them. Displays all schools where these subjects have been taken at GCSE by distance from se1 1xw

The results of a search take the user through to the "Summary Page", comprising five tabs as shown in the next sub-section. This summary page shows schools selected, together with their NSI (and less granular star rating incorporating quarter stars as described in section 3.3), the postcode, distance in miles and yards (from the search post code; blank if no postcode given), age range, primary or secondary phase, intake gender, school type and religious orientation. From this screen a new search may be initiated, or by selecting the appropriate checkboxes next to the school name, a subset of the list may be generated for comparison purposes.

Summary page

Clicking on the school name takes the user to the NSI screen as shown in the "NSI" sub-section. Clicking on the various tabs gives more comparative information as described later.

Performance tab

Figure 3 shows the performance components screen which gives the ability to "weight" the various indicator components described in the "NSI" section according to the importance individuals place on them. The "dials" are set at the median value of 2 by default. The "dials" above each of the performance indicators (as described in the NSI subsection) allow the user to weight each, resulting in a value in the "My Single Indicator" column. Fig. shows an example where the user has selected "% Level 4+ in reading, writing and mathematics" as the only and full weighted indicator. This makes a significant difference to the NSI for some of the schools shown.

Ofsted tab

Clicking on the Ofsted tab shows the selected schools' most recent inspection results in terms of overall, teaching, achievement, behaviour and leadership scores. Clicking on the inspection date takes the user to the appropriate full inspection report at the Ofsted website.

Contact details

The contact tab displays the various contact details of the school: address; telephone number; and website unique resource locator (URL) are included on this screen. Clicking on the website address takes the user to the school website.

Subject tab

Clicking on the subject tab gives the current subjects offered at GCSE. Note that if a primary school search is chosen, then this tab will not be available. By using the dropdown menu, various columns may be added, which will contain data shown from the tabs described in the previous sub-sections. For example, performance data, Ofsted information, contact details, subjects etc. may be appended to the right of the NSI column. This screen gives the breakdown of the NSI for the school with the individual percentages below the weighting "dial". The percentage making up expected progress is split into the component parts, reading, writing and mathematics. As with the performance tab (Fig. ) these "dials" may be moved to change the weightings which create the NSI. This tab displays a map, with the school selected marked with a "pin" ('A' in Figure 6). A speech box contains the options to view directions from a specific location, to search nearby and other "Google" options. In addition, the screen displays basic details about the school, contact details and other useful information about the school.

My summary

National single indicator

School page

Performance

This tab shows detailed performance about the school, including numbers on roll, number of free school meal (FSM) pupils, and Key Stage information pertaining to the school.

Ofsted

This tab shows the Ofsted information about the single school selected which gives details about the latest Ofsted inspection such as Overall Effectiveness and summary of the key findings for parents and pupils. This is a more detailed view than the information presented in section 0.

Links

The links tab shows useful links that are pertinent to the evaluation of the school, such as DfE performance tables, DfE statistics about the area, Office for National Statistics about the neighbourhood statistics, school details from the national database EduBase, Ofsted parent view and Ofsted inspection reports.

Menu

Research Methodology

The purpose of the work described in this paper was to ascertain the value, usage and feedback of a site which used the NSI as a basis for school selection and evaluation. As such this was considered to be action research.

Whilst the major target audience was parents, other appropriate groups were also informed of the launch, including all maintained schools, ministers for education, educationalists, academics and other interested parties.

As well as conducting beta tests with various parental groups, the site encouraged feedback via the contact email address and a continuing Twitter, Facebook and other social media promotional process is ongoing.

All responses were welcome in order to include every possible feedback and this, together with statistical data collected from the web site, will enable a more complete evaluation to be documented.

Results So Far

The site launched on schedule on 23 rd January 2014. The quotation below offers an example of the type of responses received as a result of all maintained school head teachers being informed of the launch.

"The idea of a single, graded indicator, applied to a school, is nonsensical. Schools are complex and multifaceted, and cannot be reduced to a single grade. What is the point of doing this?" Primary Headteacher This reply does not surprise. Schools do not like the idea of league tables or performance measures particularly when they do not score highly and for the reasons given in the quotation and accepted by the authors. However, these measures are currently the only available data that parents can use to judge a school by and the NSI attempts to make a simplified indicator that can then be used to look at more detailed information about the school. Indeed, if a parent were to look at the league tables available in much of the media, then finding more information would be a considerable task. A less critical view from a secondary school tends to support the view that a simplified approach has merits.

"It certainly is a very interesting idea and I have to applaud your desire to "to cut through the noise and get to the point." Deputy Headteacher, Secondary School

A quotation showing a different perspective follows. Parents are not necessarily expert in statistics and although the NSI is not a complete picture of a school's performance it does act as a benchmark for parents to begin their evaluation.

"This is a really useful tool for parents to help them selecting their children's school. It is easy to use and informative." Parent of a child applying for a place in September 2014

Another very encouraging comment, which confirmed the testing applied, regarding the reliability of the NSI and the general usability of the website, follows.

"I have checked the schools' website against the local schools here and I would say that it is very clear and helpful: it also ties in with what I know about these schools." Professor of Education

The Open Data Institute [18] is a key body encouraging and fostering the use of openness and transparency in data and information. Their endorsement of the underlying principles of the website follows.

"interesting and highly relevant example of good practice in the data meets education sphere." Open Data Institute (ODI)

Other comments have noted the speed that the results are generated in real time when adjustments are made to the various weightings of the components of the NSI. This was achieved even though the developers worked to very tight timescales and complex design specifications.

The site has received 5,157 visits since its launch, peaking at 1,713 on a single day, with an average 265 per day. These figures are expected to increase exponentially as word of mouth and publicity expands the user base.

Since the launch of the website, the government has indicated its intention to require schools to present "easier-to-understand" [START_REF]DfE: Parents to be given key information on schools' performance[END_REF][START_REF]DfE: Publishing performance measures on school and college web sites[END_REF] information on its performance and a group consisting of the Association of College and School Leaders (ACSL), National Association of Head Teachers (NAHT), United Learning and PiXL (an online resource company for schools) are intending to launch a new performance site in the autumn of 2014 [START_REF]United Learning: Education profession unites to publish performance tables[END_REF][START_REF]NAHT: Education profession unites to publish performance tables[END_REF][START_REF]PiXL: School performance tables[END_REF]. It would seem that others, including the government, feel that the current system is over complex and confusing for users.

Future work

It is intended to enable schools, parents and other appropriate persons or bodies to add contextual information to the site that will help put the information into perspective. It is also hoped to add more information such as admissions policy, more detailed performance measures supplied by the school, behavioural data, homework policies, etc. The creation of an application for smart telephones is also a possible development with the added advantage of possible funding by users. Funding for the site is to be considered and such options as advertising and premium versions are to be considered.

Feedback from schools, parents and other relevant establishments is to be closely monitored as will the use of the site. These will feed back into the future developments and structure of the site.

Fig. 1 :

 1 Fig. 1: Home page

Fig 2

 2 Fig 2 shows the summary page based on search criteria.

Fig. 2 :

 2 Fig. 2: Summary page

Fig. 3 :

 3 Fig. 3: Performance tab

Fig. shows

  Fig. shows the "My Summary" tab which enables the user to put their data into a single screen.

Fig. 4 :

 4 Fig. 4: My summary tab

Fig. shows

  Fig. shows the NSI screen for the school selected from the summary screen.

Fig. 5 :

 5 Fig. 5: NSI tab

Fig. shows

  Fig. shows school information that is presented, including a map and various contact details.

Fig. 6 :

 6 Fig. 6: School page

Fig. shows

  Fig. shows the menu system that is available at the top right of all screens. These have the following functions:  My schools: brings up a list of schools that have been selected by the user from the comparative screens.  Search: returns the user to the main search page as shown in Fig. .  About: gives details and documentation about the single indicator.  Tutorials: help and advice on using the website.

Fig. 7 :

 7 Fig. 7: Menu

  Progress measure, comprising: o Percentage of pupils at the end of Key Stage 4 achieving the expected level of progress between Key Stage 2 and the national General Certificate of Secondary Education (GCSE) examination in English. o Percentage of pupils at the end of Key Stage 4 achieving the expected level of progress between Key Stage 2 and GCSE mathematics. o Percentage of pupils achieving 5 or more A*-C (or equivalents (the national expected standard) including A*-C in both English and mathematics GCSEs.  Value added measure based on the best 8 GCSE and equivalent results (a single

Table 1 :

 1 Search for schools using a postcode or name

	Postcode or	Results of search
	school name
	se1 1xw	Displays a list of all schools with distances from that postcode
	se11xw	Displays a list of all schools with distances from that postcode.
		Note that the postcode need not contain a space
	se1	Displays a list of schools within SE1
	albion school	Displays a list of schools that match this name. Note that it is
		not case sensitive
	Collège Français	Displays the school with this name
	Bilingue de
	Londres
	waltham forest	Displays a list of schools in Waltham Forest LA

Table 2 :

 2 Postcode and LA search

	Postcode or LA	Displays
	name
	se1 1xw	Displays all schools in Southwark and Lewisham, with distances
	southwark	from the postcode se1 1xw
	Lewisham

Table is a

 is useful feature that lets you search for schools by subjects taken at GCSE. This is only available as a search for secondary schools.

Table 3 :

 3 GCSE subject search

Table 4 :

 4 Postcode, LA and GCSE subject search

	se1 1xw (school search box) Law, Polish,
	Spanish and Statistics (subject search
	box)


D A Kilymis

J.-M Delaye

S Ispas

Density effects on the structure of irradiated sodium borosilicate glass: a Molecular Dynamics study

Keywords: borosilicate glass, molecular dynamics, irradiation effects, density

We have carried out Molecular Dynamics simulations on a sodium borosilicate glass in order to analyze how the structure of the glass during irradiation is affected by the choice of the density in the liquid state before cooling. In a pristine form generated through the usual melt-and-quench method, both short-and medium-range structures are affected by the compressive or tensile environment under which the glass model has been generated. Furthermore, Na-rich areas are much easier to compress, producing a more homogeneous glass, in terms of density, as we increase the confinement during the quench. When the glass is

subjected to displacement cascades, the structural modifications saturate at a deposited energy of approximately 8 eV/atom. Swelling appears for the glasses that were initially prepared under compression, while contraction is evident for the ones prepared under tension. We have equally prepared glass models using a fast quench method, and we have found that they present an analogous disorder as the glasses submitted to displacement cascades. Compared to the irradiated glass, we found that the magnitude of the modifications for the fast quenched glass is lower, most notably in terms of boron and sodium coordination, the percentage of non-bridging oxygens and in the ring distributions. This later result agrees with statements extracted from recent experimental works on nuclear glasses.

Introduction

Borosilicate glasses are of special interest to the nuclear industry, due to their use as confinement matrix for high-level waste. The R7T7 glass used in France is a complex borosilicate glass whose properties variation under irradiation has been shown to mostly depend on ballistic effects from recoil nuclei [1].

In parallel, it has been demonstrated that its behavior when subjected to irradiation can be adequately represented by more simplified glasses that contain only a few oxides [2].

The most important effect of α-irradiation, observed in both complex and simplified glasses, is the gradual appearance of swelling and its stabilization after a certain saturation level [3,4,2]. Swelling is expected to reflect the changes in the glassy matrix during irradiation, most notably the depolymerization of the glass and the general increase of disorder, which cause notable changes in the mechanical properties of the glasses, especially hardness [2,4,5].

It can be interpreted as a result of a local melting event along the path of each displacement cascade, followed by a quench at an elevated fictive temperature [6,7,8,9,4,10,11]. Such similarities between the irradiated glass and the effects of the quenching temperature have been also studied experimentally by means of nuclear magnetic resonance (NMR) and Raman spectroscopies, indicating the existence of analogies between the two processes [12]. Based on these experimental results, a numerical method using a rapid quenching proposed recently has been proven to emulate the results of the displacement cascades and to be effective in terms of computational time, especially when applied to large systems where a long series of cascades would be computationally prohibitive [13,14].

In this work we present the results of Molecular Dynamics (MD) simulations on the structural properties of a borosilicate glass (called hereafter SBN14 and equally known as CJ1) when it is cooled from different volumes in the liquid state. This glass composition is the best analogy to the R7T7, in terms of simplified borosilicate glasses, due to its similar [Na 2 O]/[B 2 O 3 ] molar ratio. After the cooling to room temprature, we have launched a series of displacement cascades for each glass in order to analyze the role of density during the irradiation process. Alongside, we have prepared a glass by means of rapid quenching method and we have compared the structures generated using the two methods.

The paper is organized as follows. In Section 2 we describe the computational methodology used, while Section 3 contains the results of the simulations. We first describe the dependence of the pristine glass structure on the choice of the initial liquid volume, prior to quenching. Then, we present the effects of displacement cascades on the glass prepared with different initial liquid volumes, followed by the description of the glass structure obtained using fast quenching.

Section 4 contains the discussion and Section 5 the conclusions.

Computational details

The SBN14 glass has a composition of 67.73% SiO 2 , 18.04% B 2 O 3 and 14.23% Na 2 O and an experimental density of 2.45 g/cm 3 [15]. In order to fabricate the glass, we started with a random distribution of 10.000 atoms heated at 5000 K and reproducing the stoichiometry, namely 2015 silicon, 6064 oxygen, 1074 boron and 847 sodium atoms. The liquid was equilibrated at 5000 K for 100 ps using the constant volume-constant temperature ensemble (NVT), and was then cooled to room temperature using the same ensemble and a quench rate of 5×10 12 K/s. At room temperature, we switched to the constant pressureconstant temperature ensemble (NPT) with the pressure set to zero and the box size was allowed to relax for 20 ps. It should be stressed that the glasses are expected to contract during this stage and thus the density after cooling will be higher than the one of the liquid. The NPT run was followed by a production run of 5 ps in the constant volume-constant energy ensemble (NVE). We prepared six glasses with different initial volumes in the liquid state in order to investigate how the density of the liquid affects the structure after cooling. We chose values of the initial liquid volume varying between -30% to 20%, when compared to the experimental volume of the glass, and with 10% increments.

Further on they will be referred to by the value V l , defined as the liquid volume over the experimental volume of the glass. These six glass structures correspond to the form called pristine glass.

The six glass structures were then submitted to a series of displacement cascades. For each cascade, one Si atom was given a high mass and launched along the main diagonal of the computational cell, with a 0.8 keV initial kinetic energy. Throughout the phase of the cascades, the NVE ensemble was used, while a 1.5 Å layer along the border of the cell was thermostatted at 293 K.

In total, 190 cascades were launched in order to reach a deposited energy of approximately 15 eV/atom. After the cascades, the simulation cell was equilibrated for 50 ps using the NPT ensemble in order to relax any accumulated pressure, and it was followed by a 10 ps production run using NVE.

To prepare the fast quenched glass form, we firstly selected the pristine glass exhibiting the lowest potential energy. We then launched a series of calculations where this structure was heated to temperatures varying between 2000 K and 3000 K, and then relaxed for 50 ps using the NPT ensemble with a zero target pressure. The glasses were then cooled down to 300 K with a quench rate of 10 14 K/s and the NPT ensemble at zero pressure. At room temperature, further runs were carried out for 20 ps and 5 ps using the NPT and NVE ensemble, respectively. Concerning the employed quench rates for both the pristine and fast quenched glass, it should be noted that, although they are much faster than the ones encountered in experiments, they have been successfully used in the past to model the structure of sodium borosilicates [15,13,14,16].

All calculations have been performed using a modified version of the DL POLY 3.0 Molecular Dynamics code [17] with the interatomic pair potential for sodium borosilicates proposed by Kieu et al. [15]. The potential has a Buckingham-Coulomb form:

Φ(r αβ ) = A αβ exp - r αβ ρ αβ - C αβ r 6 αβ + q α q β e 2 r αβ (1)
where α, β ∈ {Si, B, O, Na}, r αβ is the distance between atoms of type α and β.

The effective charges of type α and β atoms are given by q α and q β , while A αβ , ρ αβ and C αβ are the rest of the potential parameters. In this potential, the effective charges, as well as the A B-O parameter, are adjustable. The values used in this work are given in Table 1.

Parameter Value q' Si 1.868456 q' B 1.596549 q' O -0.966544 q' N a 0.450956 A B-O (eV) 229700.881498
Table 1: Interatomic potential parameters used in this work.

For short-range interactions between the projectile and the glass atoms the Ziegler-Biersack-Littmark (ZBL) potential [18] was employed alongside appropriate high-order polynomials linking it to the corresponding long-range potentials, ensuring continuity of the energy, forces and force derivatives. The integration step used was equal to 1 fs, except in the phase of the displacement cascades where it was variable, down to 0.02 fs for the initial phase of each cas- [3] O of the glass structures generated using varying V l initial liquid volume.

Results

Dependence of the glass structure on the initial liquid volume

Some structural characteristics of the six glasses prepared with different V l initial liquid volume are given in Table 2. As expected, effects of confinement for the glasses prepared with a low initial volume are evidenced in the B and Na average coordination numbers and the percentage of [3] O, which increase as we decrease the initial volume. On the contrary, Si remains perfectly tetracoordinated in all cases, a fact that can be attributed to the high rigidity of the SiO 4 units in the glass. Also, the percentage of non-bridging oxygen (NBO) does not follow a linear trend but exhibits a minimum value present in the glass with V l = 0.9.

Concerning the final density, we can see that it best reproduces the experimental value for V l = 1.1, due to the swelling for small V l and contraction for large V l at the time of the quench. Furthermore if we inspect the evolution of the potential energy for the different glasses, we observe that the minimum energy structure lies towards lower values, at V l = 0.9 (see Figure 1). A similar result has been recently reported by Jolley et al. for a borosilicate glass with a similar composition (called SBN12 glass in some works), where it has been pointed out that the current potential does not predict the glass with the experimental density to lie at the minimum of the potential energy curve [20].

In Figure 2 we present the radial distribution functions (RDF) for the glasses

Table 2 :

 2 Density, B and Na average coordinations as well as the percentages of NBO and


Iván Cores

Patricia Gonzalez

Emmanuel Jeannot

Maria J Martin

Gabriel Rodriguez

Patricia González

María J Martín

Gabriel Rodríguez

An application-level solution for the dynamic reconfiguration of MPI applications

Keywords: HPC, MPI, Checkpointing, Migration, Scheduling

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Introduction

High performance computing (HPC) is nowadays dominated by the MPI paradigm. Most MPI applications follow the SPMD (single program, multiple data) programming model and they are executed in HPC systems by specifying a fixed number of processes running over a fixed number of processors. The resource allocation is statically specified during job submission, and maintained constant during the entire execution. Thus, MPI applications are unable to dynamically adapt to changes in resource availability.

The aim of this work is to propose a solution to transform existing MPI applications into malleable jobs, that is, jobs that are capable of adapting their executions, to changes in the environment. There are several proposals in the literature that use a stop-and-restart approach to implement malleable MPI applications [START_REF] Vadhiyar | SRS -a framework for developing malleable and migratable parallel applications for distributed systems[END_REF][START_REF] Raveendran | A framework for elastic execution of existing MPI programs[END_REF][START_REF] Agbaria | Starfish: Fault-tolerant dynamic MPI programs on clusters of workstations[END_REF]. However, stop and restart solutions imply a job requeueing, with the consequent loss of time. Dynamic reconfiguration [START_REF] Martín | Enhancing the performance of malleable MPI applications by using performance-aware dynamic reconfiguration[END_REF][START_REF] Weatherly | Dyn-MPI: Supporting MPI on non dedicated clusters[END_REF][START_REF] Ribeiro | Autonomic malleability in iterative mpi applications[END_REF][START_REF] Huang | Adaptive MPI[END_REF], on the other hand, allows to change the number of processors while the program is running without having to stop and relaunch the application. Most of these solutions [START_REF] Martín | Enhancing the performance of malleable MPI applications by using performance-aware dynamic reconfiguration[END_REF][START_REF] Weatherly | Dyn-MPI: Supporting MPI on non dedicated clusters[END_REF][START_REF] Ribeiro | Autonomic malleability in iterative mpi applications[END_REF] change the number or processes to adapt to the number of available processors, which implies a redistribution of the data and, thus, they are very restrictive with the kind of application they support. On the other hand, in AMPI [START_REF] Huang | Adaptive MPI[END_REF] the number of processes is preserved and the application adapts to changes in the number of resources through migration based on virtualization.

Besides AMPI, there exist in the literature different research works that provide process migration through the use of virtualization technologies. However, virtualization solutions present important performance penalties due to larger memory footprints [START_REF] Wang | Proactive process-level live migration and back migration in HPC environments[END_REF]. Moreover, the performance of MPI applications relies heavily on the performance of communications. Currently virtualization of CPU and memory resources presents a low overhead. However, the efficient virtualization of network I/O is still work in progress. For instance, recent results in migration over Infiniband networks [START_REF] Guay | Early experiences with live migration of sr-iov enabled infiniband[END_REF] show very high overhead, strong scalability limitations and tedious configuration issues.

In this paper we propose a dynamic reconfiguration solution based on process migration of non-virtualized MPI processes. In [START_REF] Rodríguez | Improving an MPI application-level migration approach through checkpoint file splitting[END_REF] an application-level checkpointing tool, CPPC (ComPiler for Portable Checkpointing), was extended to achieve efficient dynamic migration of MPI processes. In this work, we present a mapping algorithm that decides which processes should be migrated and where they should be allocated based on their affinity (gathered through dynamic monitoring) and the underlying hardware topology. The proposed approach is applicable to general SPMD MPI applications. It does not need user or system interaction and it allows both to shrink or to expand the number of processors.

The structure of this paper is as follows. Section 2 describes the solution proposed to automatically and transparently transform existing MPI application into malleable jobs. Section 3 evaluates the performance of the proposal. Finally, Section 4 concludes the paper.

Reconfiguration of MPI applications

The proposed solution is based on dynamic live process migration. If a node becomes unavailable, the processes on that node will be migrated to other available ones (without stopping the application), overloading nodes when necessary. Our proposal relies on a monitoring system that provides dynamical information about the available resources. There are in the literature many proposals for different environments and objectives. For this work we assume that an availability file is set up for each malleable MPI job. This file contains the names of all the nodes that are assigned to execute the MPI job together with their number of available cores. Previous to the start of the migration operation, the processes to be migrated and their mapping to the available resources need to be selected.

In MPI applications the communication overhead plays an important role in the global performance of the parallel application. To be able to migrate the processes efficiently we need to know the affinity between the processes so as to map those with a high communication rate as close to each other as possible. For this aim TreeMatch [START_REF] Jeannot | Near-Optimal Placement of MPI processes on Hierarchical NUMA Architectures[END_REF] and Hwloc [START_REF] Broquedis | hwloc: A generic framework for managing hardware affinities in HPC applications[END_REF] are used. TreeMatch is an algorithm that obtains the optimized process placement based on the communication pattern among the processes and the hardware topology of the underlying computing system. It tries to minimize the communications at all levels, including network, memory and cache hierarchy. It takes as input both a matrix modeling the communications among the processes, and a representation of the topology of the system. The topological information is provided by Hwloc (represented as a tree) and it is obtained dynamically during application execution. TreeMatch returns as output an array with the core ID that should be assigned to each process.

Dynamic communication monitoring

The communication matrix needed by TreeMatch is obtained dynamically, just before the scheduling algorithm is triggered, using a monitoring component developed for Open MPI that monitors all the communications at the lower level of Open MPI (i.e., once collective communications have been decomposed into send/recv communications). Therefore, contrary to the MPI standard profiling interface (PMPI) approach where the MPI calls are intercepted, here the actual point-to-point communications that are issued by Open MPI are monitored, which is much more precise. This monitoring component was previously developed by one of the authors and it will be released in Open MPI 2.0.

The overhead of this monitoring is very low, less than 0.7% on the LU3 NAS benchmark [START_REF]The NAS Parallel Benchmarks[END_REF].

Mapping processes to cores using TreeMatch

TreeMatch focuses on minimizing the communication cost in a parallel execution. Thus, if TreeMatch is directly applied to find the processes mapping during a reconfiguration phase, it could lead to a complete replacement of all the application processes. This would involve unnecessary process migrations and, thus, unnecessary overheads. To avoid this behavior, a two-step mapping algorithm was designed. The first step decides the number and the specific processes to be migrated. The second step finds the best target nodes and cores to place these processes. An interesting feature of TreeMatch is that the topology given as an input can be a real machine topology or a virtual topology designed to separate group of processes in clusters such that communication within clusters are maximized while communication outside the clusters are minimized.

-Step1: identify processes to migrate. A process should be migrated either because it is running in nodes that are going to become unavailable, or because it is running in oversubscribed nodes and new resources have become available. To know the number of processes that need to be migrated, all processes exchange, via MPI communications, the numbers of the node and core in which they are currently running. Then, using this information, each application process calculates the current computational load of each node listed in the availability file associated to the application. A load array is computed, where load(i) is the number of processes that are being executed in node n i . Besides, each process also calculates the maximum number of processes that could be allocated to each node n i in the new configuration:

maxP rocs(i) = nCores(i) × N nT otalCores
where nCores(i) is the number of available cores of node n i , N is the number of processes of the MPI application, and nT otalCores is the number of total available cores. If load(i) > maxP rocs(i) then load(i) -maxP rocs(i) processes have to be migrated. If the node is no longer available, maxP rocs(i) will be equal to zero and all the processes running in that node will be identified as migrating processes. Otherwise, TreeMatch is used to identify the migrating processes. The aim is to maintain in each node the most related processes according to the application communication pattern. Figure 1 illustrates an example with two 16-core nodes executing a 56-process application in an oversubscribed scenario. When two new nodes become available, 12 processes per node should be migrated to the new resources. To find the migrating processes, TreeMatch is queried once for each oversubscribed node. The input is a virtual topology breaking down the node into two virtual ones: one with maxProcs(i) cores and the other with load(i)-maxProcs(i) cores. TreeMatch uses in runtime this virtual topology, and a sub-matrix with the communication pattern between the processes currently running on the node, to identify the processes to be migrated, that is, those mapped to the second virtual node.

-Step 2: identify target nodes. Once the processes to be migrated are identified, the target nodes (and the target cores inside the target nodes) to place these processes have to be found. TreeMatch is again used to find the best placement for each migrating process. It uses a sub-matrix with the communication pattern of the migrating processes, and a virtual topology built from the real topology of the system but restricted to use only the potential target nodes in the cluster. The potential targets are those nodes that satisfy load(i) < maxP rocs(i). They can be empty nodes, nodes already in use but with free cores, or nodes that need to be oversubscribed. Since TreeMatch only allows the mapping of one process per core, if there are no sufficient real target cores to allocate the migrating processes, a virtual topology will simulate maxP rocs(i) -load(i) extra cores in the nodes that need to be oversubscribed. Figure 2 illustrates the second step of the algorithm for the same example of Figure 1. In this example, the virtual topology used consists of the new available nodes in the system, two 16-core nodes to map the 24 processes. After executing TreeMatch, the target cores and, therefore, the target nodes for the migrating processes obtained in the step 1 are identified and CPPC can be used to perform the migration.

The performance of this mapping algorithm is assessed in next section.

Experimental Results

This section aims to show the feasibility of the proposal and to evaluate the cost of the reconfiguration whenever a change in the resource availability occurs.

... Fig. 2.

Step 2: identifying target nodes. Topology built to map the migrating processes selected in step 1 to the empty cores in the system.

A multicore cluster was used to carry out these experiments. It consists of 16 nodes, each powered by two octa-core Intel Xeon E5-2660 CPUs with 64 GB of RAM. The cluster nodes are connected through an InfiniBand FDR network. The working directory is mounted via network file system (NFS) and it is connected to the cluster by a Gigabit Ethernet network. The application testbed was composed of the eight applications in the MPI version of the NAS Parallel Benchmarks v3.1 [START_REF]The NAS Parallel Benchmarks[END_REF] using class C. Only results for the FT benchmark are reported here due to space limitations. The FT benchmark presents the larger checkpoint files and the highest migration times of the NAS testbed. Additionally, the Himeno benchmark [START_REF]HIMENO Benchmark[END_REF] was also tested. Himeno uses the Jacobi iteration method to solve the Poissons's equation, evaluating the performance of incompressible fluid analysis code, being a benchmark closer to real applications.

The MPI implementation used was Open MPI v1.8.1 modified to enable dynamic monitoring. The mpirun environment has been tuned using MCA parameters to allow the reconfiguration of the MPI jobs. Specifically, the parameter orte allowed exit without sync has been set to allow some processes to continue their execution when other processes have finished their execution safely. The parameter mpi yield when idle was also set to force degraded execution mode and, thus, to allow progress in an oversubscribed scenario.

To evaluate the feasibility of the proposed solution and its performance, different scenarios have been forced during the execution of the applications. Figure 3 illustrates these scenarios. The applications were initially launched in a 64-process configuration running on 4 available nodes of the cluster (16 cores per node). Then, after a time, one of the nodes becomes unavailable. In this scenario, the 16 processes running on the first node should be moved to the empty node, and the application execution continues in a 4 node configuration. After a while, the 4 nodes where the application is running start to become unavailable sequentially, first one, then another, without spare available nodes to replace them, until only one node is available and the 64 processes are running on it. Finally, in a single step, the last node fails but 4 nodes become available again, and the processes are migrated to return again to using 4 nodes. To demonstrate the feasibility of the solution, the iteration time was measured across the execution in those scenarios. Measuring iteration time allows to have a global vision on the instantaneous performance impact.

Figure 4 shows the benchmarks results in the scenarios illustrated in Figure 3. These results demonstrate that, using the proposed solution, the applications are capable of adjusting the execution to changes in the environment. The high peaks in these figures correspond to reconfiguration points. The iteration time is broken down into: scheduling, migration, and compute times. The scheduling time is the execution time needed for the scheduling algorithm to identify processes to be moved and the target nodes. The migration time is the time needed to perform the migration itself. Finally, the compute time is the computational time of each iteration (excluding the scheduling and migration times when needed). As it can be seen, the scheduling time is negligible in comparison with the migration time, being always smaller than 0.1 s. The computational time of the iteration involved in the reconfiguration (compute), is higher than the computational time of the rest of the iterations. This is in part due to the cache misses caused by the data movement, and in part due to an overhead observed in the first MPI communication after the communicators are reconfigured. For comparison purposes, the compute times that would be attained if the application could adjust its granularity to the available resources4 , instead of oversubscribing them without modifying the original number of processes are also shown (black line).

The overhead that would introduce the data distribution needed to adjust the application granularity is not shown in the figure.

Concluding Remarks

In this paper a proposal to automatically and transparently adapt MPI applications to available resources is proposed. The solution relies on a previous application-level migration approach, incorporating a new scheduling algorithm based on TreeMatch, Hwloc and dynamic communication monitoring, to obtain well balanced nodes while preserving performance as much as possible.

The experimental evaluation of the proposal shows successful and efficient operation, with an overhead of less than 1 second for the proposed scheduling algorithm, and of only a few seconds for the complete reconfiguration, which will be negligible in large applications with a realistic reconfiguration frequency.

Proposals like the one in this paper will be of particular interest in future large scale computing systems, since applications that are able to dynamically reconfigure themselves to adapt to different resource scenarios will be key to achieve a tradeoff between energy consumption and performance.

Fig. 4 .

 4 Fig.[START_REF] Huang | Adaptive MPI[END_REF]. Iteration execution times in the scenarios illustrated in Figure3

  Step 1: identifying processes to be migrated. Virtual topology built to migrate 12 processes from a 16-core node where 28 processes are running (16 processes remain and 12 processes migrate).

		28 p n0	maxProcs(0) = 16 load(0) = 28	Virtual Topology	System level
	N = 56 nTotalCores = 64	28 p n1		Node "remain"		Node "migrate"	Node level
		Empty
		Empty n2 n3		16 processes (maxProcs)		... 12 processes (load -maxProcs)	Core level
						Processes IDs to
						migrate from Node 0
	Node 2 (maxProcs) 16 processes (16 cores) Fig. 1. ... n3 28 p 28 p Empty N = 56 nTotalCores = 64 Empty n0 n1 n2 12 processes IDs to migrate from Node 0 12 processes IDs to migrate from Node 1 { Step 1	Topology	Node 3 8 processes ... (16 cores)	System level Node level Core level . . .
						Processes IDs to migrate to Node 3
						Processes IDs to migrate to Node 2

The LU kernel is the one that sends the largest number of messages from among all the 8 MPI NAS benchmarks.

This time is measured executing the application with different number of processes depending on the hardware available (16 processes version when only 1 node is available, 32 processes version when 2 nodes are available, etc.)

Acknowledgments.

This research was partially supported by the Ministry of Economy and Competitiveness of Spain and FEDER funds of the EU (Project TIN2013-42148-P), by the Galician Government and FEDER funds of the EU (consolidation program of competitive reference groups GRC2013/055) and by the EU under the COST programme Action IC1305, Network for Sustainable Ultrascale Computing.