Martyn Rittman

Introduction

Long-term sustainability must be a primary goal for any academic publisher. Without it, knowledge published in journals, books and other formats risks being damaged or lost. If one step in a series of research disappears, it casts doubt on subsequent work. Publishers, as disseminators of verified research, have a responsibility to ensure that published works remain available for future generations.

The aim of this paper is to present the point of view of a commercial open access publisher with regards to sustainability in the current publishing landscape. We briefly outline salient points from the history and current state of electronic publishing. The emphasis is on sustainability, and covers both the development of open access and the story of MDPI. We then move on to some current projects arising from our focus on sustainability. Putting sustainability at the heart of publishing activities is an imperative and in the age of electronic publishing new options are emerging that this goal make it easier to achieve. There are concrete steps that can be taken by any academic publisher to ensure the sustainability, preservation, and effective dissemination of knowledge.

MDPI sees two primary aspects to sustainability. The first pertains to the preservation of knowledge. Knowledge creation without sustainability makes little sense. New discoveries builds on older research, which must be archived and preserved, or what comes after it does not have a firm foundation. The second strand is MDPI's view that open propagation of knowledge will enhance mankind's future and preserve our environment. The founder of MDPI, Shu Kun Lin, built the company in the belief that advances in research are a key contributor to solving many of the most pressing needs of our age, including over-use of the world's resources and the threat of climate change. The implementation of both strands requires access, discoverability, security, and long-term preservation of knowledge. In other words, making all new research immediately available to as many as possible for as long as possible.

The progress of sustainability in electronic publishing

The early stages of electronic publishing took place in the late 1980s and into the 1990s. MDPI was founded in 1996 to preserve chemical samples synthesized in laboratories. Our first journal made the synthesis protocols public in a free, online format, allowing others access to both the chemical itself and the associated methods [START_REF] Lin | A Good Yield and a High Standard[END_REF]. This meant that both rare physical samples and the knowhow to make them was preserved. This was prior to wide use of the term open access. It was one of a number of electronic publishing initiatives, the development of which are charted in several places (Laasko 2012, Morrison, Suber).

It took some time for open access to find a way to work at scale. The formation of the public library of science (PloS), initially as an advocacy group and then also as a publisher, was a key step in challenging attitudes within publishing. Its most radical position as a publisher was that editors should not make subjective judgments on which content to publish; instead, they should decide whether work is scientifically sound and leave the question of value until after publication. The ability to do this is a direct result of online publication, since the page counts that limit print journals and force selectivity are not present. The policy supported sustainability by encouraging the publication of research that may otherwise have remained unpublished and undocumented, and therefore unpreserved.

At a similar time, in 1999, BioMed Central was launched. It generated revenue through article processing charges (APCs), establishing a business model that could bring financial sustainability and allow for open access journals to operate at larger scales. To date, this has been the primary model for large open access publishers. From a publisher's point of view, APCs are a straightforward solution to funding open access publication. Other options typically require lengthy negotiations with stakeholders and high levels of commitment from large institutions such as funding bodies, libraries, or national agencies. A large number of journals are run by philanthropic grants with no costs to authors, but the grants are often not large enough to permit journals to scale up to hundreds or thousands of papers per year. At the time of writing, the Directory of Open Access Journals (DOAJ) has 8,085 open access journals without APCs and 2,925 journals with an APC, and has historically seen a similar pattern (DOAJ 2016). However, these journals publish only a minority of the total papers: the top 7 largest publishers in DOAJ have published 34% of the total number of papers and all use APCs as their primary, if not exclusive, source of income.

Currently, MDPI offers almost all of its journals under an APC model. In the early years, funding came from grants, the chemical samples projects, some conferences, and donations from individual authors. To facilitate the expansion of MDPI, in 2006 APCs were introduced to all journals [START_REF] Lin | Open Access Publishing Policy and Efficient Editorial Procedure[END_REF]). This has only recently changed with the Knowledge Unlatched project (see below). In responses to a 2013 survey about where MDPI authors find funding to pay APCs, 68% claimed their money from their institution or directly from their funding body, 20% funded the APC personally, and the rest used personal discretionary funds.

The APC model has been adopted by most of the largest traditional publishers, at least under a hybrid model (where an APC can be paid for a paper in a subscription journal) and often in fully open access journals. As has been discussed elsewhere [START_REF] Kingsley | Paying for Publication: Issues and Challenges for Research Support Services[END_REF], hybrid open access suffers from a lack of trust that publishers are not charging twice for the same content, so-called double dipping. Prices are also typically higher than journals that only publish open access content.

The SCOAP3 project (https://scoap3.org) has sought to provide a way to fully convert the field of particle physics to open access, by raising revenue from libraries, funders, and other organizations. Participating journals are paid from the central fund depending on the number of papers they publish. A similar idea has been taken up by the Knowledge Unlatched project (http://www.knowledgeunlatched.org) which focuses on the humanities and social sciences, which also acts as a distributor of article processing fees using funding collected from participating university libraries. Nine MDPI journals are currently funded by Knowledge Unlatched (MDPI 2018).

The current state of open access

Open Access currently occupies around 15-20% and is "nuanced, growing well, but taking share slowly" [START_REF] Pollock | News & Views: 2018 Outlook[END_REF]. This suggests reluctance among at least some key stakeholders to make a fuller transition, and that early optimism around a complete switch to open access has not been fulfilled. It has led to reflection about what the future direction should be.

From MDPI's point of view, several of the key current themes in academic publishing are as follows:

Authors are not incentivized to choose open access when publishing their work. Although many authors express a preference for open access, other considerations-often related to career progression and status-are usually more important this when it comes to decisions on where to publish individual papers. We observe this frequently in author surveys, where open access is not one of the top reasons authors chose an MDPI journal.

Citations are frequently used as a proxy for quality. This applies both to quality of the editorial processes (is the journal reputable?) and the value of individual journals (is the standard of research in the journal high?). Editorial board members and potential authors frequently ask about the Impact Factor, and the ratings of scholars, journals and papers are primarily citation-based. In some contexts this may be acceptable in conjunction with other measures, but sole reliance on citation-based metrics reinforces a situation where perceived journal reputation and popularity are of higher value than integrity, transparency, and robust underlying editorial processes.

APCs may not adequately control the costs of publishing. Some hoped that gold open access would create market conditions and drive down prices. Instead, the opposite is often seen, and a higher APC can be interpreted as a mark of quality and reflect well on the prestige of a journal. Amounts over 2000 USD are common and much higher have been reported (see, for example, https://treemaps.intact-project.org/apcdata/openapc/ #publisher/). MDPI's average APC across all published papers was around 1000 USD in 2017. While publishing entails costs that publishers need to recover, it is not clear whether APCs are the best mechanism to control the flow of money to publishers. Despite APCs being a good option for publishers, as described above, they can prove to be a barrier for authors, especially for those in the developing world-even where discounts or fee waivers are available. MDPI's view is that APCs have played an important role in the development of open access to date. However, publishers should be open to alternatives where they provide opportunities to recover costs, can function at scale, and provide appropriate incentives to publish content that meets the standards expected by research communities.

Open science is a growing theme and can help to address issues of preservation. Open science covers open access, open data and open communication (see, for example, the European Commission's open science monitor https://ec.europa.eu/research/openscience/ index.cfm?pg=home&section=monitor). Thus far, we have not seen a significant move from authors towards more availability of data. However, this may change with the launch of the European Open Science Cloud and similar initiatives. The concept of preprints (research articles posted and archived before peer review has been completed) is a growing one and has expanded in recent years from mathematics, physics and economics (through arXiv and SSRN) to life sciences and other subjects. In 2016, MDPI launched Preprints.org as a multidisciplinary preprint server, which published its 3000th article in February 2018. While still a minority of MDPI authors choose preprints, we have seen increasing awareness and participation. We also operate Sciforum.net as a platform for recording alternative methods of research communication, including comments on published papers, and conferences.

To support efforts for global development, MDPI publishes the title Sustainability, a broadscope journal looking at aspects of sustainability in many different areas. It also runs the World Sustainability Forum and sponsor the World Sustainability Award (http:// sciforum.net/conference/ wsf-6/page/76), operated through the MDPI Sustainability Foundation (http:// wsforum.org/foundation). Sustainability is included in the scope of many MDPI journals, fulfilling the role we see to address issues of development and resource management through research and technology, and to support the United Nations Sustainable Development Goals.

Moving forward

The present does not feel like a time of consolidation for open access publishers. While the concept of open access is now well-known and generally accepted, there are challenges to improve business models, innovate technology, and increase the proportion of papers published in open access format. The expansion of open access alone is a step forward to achieving greater sustainability in publishing, however here we list some of the other initiatives MDPI is undertaking have a link with sustainability.

First, MDPI support umbrella initiatives that work towards sustainability. These include the UN Sustainable Development Goals, the Jussieau call (http://jussieucall.org), the Declaration on Research Assessment (DORA, https://sfdora.org), and the Initiative for Open Citations (https://i4oc.org). In particular, the Jussieau call commits MDPI to actively explore models other than APCs.

Second, MDPI invests in alternative business models and the preservation of nontraditional output. This includes Knowledge Unlatched, Preprints.org, online conferences (through sciforum.net), and running journals with non-traditional scopes or editorial processes. Our journals include Data-publishing descriptions of collected data sets;

Challenges-presenting hypotheses and introducing key research questions; Methods and Protocols-for the description of research techniques; and J and Sci-two broad-scoped journals aimed at providing rapid peer review based solely on scientific soundness, with Sci offering post-publication peer review. We have also recently launched Encyclopedia, a scholarly online encyclopedia to offer reference information on the latest research findings and hypotheses.

Third, we support aspects of open science, including preprints, open peer review, and open IDs (in particular ORCID). We have ensured that our journal requirements comply with at least level I of the TOP guidelines (https://cos.io/our-services/top-guidelines/). Scilit.net is an effort to index all academic articles, indicate which are open access, and allow scholars and others a free interface to find relevant articles.

Fourth, long-term preservation is achieved for our journals through CLOCKSS (https:// www.clockss.org/ clockss/ and the Swiss National Library's e-Helvetica archive (https://www.ehelvetica.nb.admin.ch/pages/main. jsf). This ensures that, even if MDPI does not achieve financial sustainability in the future, its published research will remain available. This is an action that any responsible publisher should take.

We firmly believe that open scholarship and infrastructures can support a healthy publishing industry that collaborates with the research communities that it serves and is not viewed as exploitative. Sustainability must remain a key value as we look for ways to better achieve this outcome. MDPI in neither unique nor comprehensive with the initiatives described above. We invite other publishers to join in working towards a sustainable research ecosystem, following the tradition of close cooperation with each other and the research communities we serve. Through these efforts and sharing of best practices, we can ensure the preservation and effective propagation of knowledge, and a better future for the world in which we live.

BIBLIOGRAPHY

Sustainability in Publishing: An Open Access Publisher's View ELPUB 2018

ABSTRACTS

Sustainability is an essential part of the work of publishers. Here, the view of an open access publisher, MDPI, is presented with regards to sustainability within publishing. MDPI's understanding of sustainability is given and some of the concrete actions it leads to. These


Mariya Maistrovskaya

Judy Hum-Delaney

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Despite increased outreach efforts and assistance provided by many Canadian academic libraries as well as Canadian not-for-profit publishers such as Canadian Science Publishing, compliance to the policy remains a challenge for researchers who are either unaware of the policy or unsure how to comply. Additional challenges for researchers stem from the fact that while the cost of open access publishing is an eligible grant expense, many grantees do not receive enough funding to cover author processing charges, particularly where multiple publications are produced in the course of a research project. The "green" repository route is usually free, but relies on understanding of publishers' self-archiving policies that often require the deposit of an accepted manuscript of a paper, a version that authors don't tend to keep. With the onus of compliance placed on grant recipients, and with no centralized infrastructure in place to facilitate the process, it is not surprising that researchers often feel trapped between a rock and a hard place, and compliance levels remain low.

To streamline compliance for their authors, Canadian Science Publishing, an independent, not-for-profit publisher of over 20 science journals approached the University of Toronto Libraries with an idea of automated transfer and deposit of author manuscripts into the U of T's research repository, TSpace 1 . This free service is available to authors publishing their papers in 21 CSP's NRC Research Press journals 2 and only takes authors one click to opt into. The partnership was launched in April 2015 and makes over 1,200 manuscripts openly available annually.

Workflow

The manuscript transfer and deposit workflow developed by the UTL's Information Technology Services team in close consultation with CSP is outlined in Figure 1 [START_REF] Maistrovskaya | Publisher-Repository Partnership for Funder Mandate Compliance[END_REF] and the script is shared on Github under the Apache License 2.0 (University of Toronto Libraries, 2018).

The process is initiated by the author in the CSP's peer-review submission system, ScholarOne, opting into their manuscript being archived in TSpace. A zip file containing the accepted manuscript, supplementary files, and metadata in PubMed XML is transferred to the library's SCP server. UTL's Python script scans the directory on an hourly basis and extracts each package. Beautiful Soup 3 is used to parse the received metadata into Dublin Core. The script then prepares DSpace Simple Archive for each manuscript and uses the DSpace import API to upload content into a respective journal's collection. An ingestion report is generated at this point and emailed to the CSP and TSpace staff. Transferred zip files as well as prepared DSpace Simple Archive directories are backed up for quick re-ingestion if needed.

Upon ingest, the manuscript is immediately released for public access in the repository and assigned a permanent URL (handle) in addition to the publisher supplied DOI that points to the final version on the journal website.

Challenges and opportunities 8

Automated repository workflows have been around for a while and can be implemented using a variety of tools and protocols. A common challenge they share is that even a welldeveloped and robust workflow cannot do entirely without human intervention which affects its overall sustainability. In the SCP-UTL case, while the script takes care of package processing, metadata crosswalk, and ingest, human assistance is still needed on both ends of the pipeline with CSP staff creating and depositing the packages and UTL staff maintaining repository collections and troubleshooting technical issues. Such issues are uncommon, but while the vast majority of deposits go smoothly and entirely automatically, the script depends on the consistent structure of the transferred packages and metadata, and occasionally fails when encountering unexpected elements. One promising development that may help address this through a standardized framework is the Manuscript Exchange Common Approach (MECA) recently accepted to be developed as a NISO standard (NISO, 2018).

Apart from technical challenges, establishing a publisher-repository partnership demands commitment, trust, and mutual investment of time and effort-something that can only be initiated when both parties share common values and goals in public sharing and preservation of research. While funder mandates, such as Tri-Agency Open Access Policy (Government of Canada, 2015) or NIH Public Access Policy (U.S. Department of Health & Human Services, 2016) have been a significant drive for these initiatives, our hope in sharing this workflow is to offer a fairly straightforward solution that can be implemented by small scale publishers and university presses looking to include green OA in their suite of services.

Conclusion

Making research openly accessible to the widest possible audience, and at the earliest possible opportunity has multiple benefits. Funded by Canadian federal grants, it makes the findings available to the public beyond journal subscriptions that are often limited to institutions and research organizations. Open availability of research benefits the authors and "science by accelerating dissemination and uptake of research findings" (Eysenbach, 2006, e157). It also facilitates societal advancement globally by "enabling researchers, scholars, clinicians, policymakers, private sector and not-for-profit organizations and the public to use and build on this knowledge." (Government of Canada, 2015).

Nonetheless compliance with funders' open access mandates remains challenging and complicated for many researchers, despite assistance available from their institutions in the form of consultations, institutional repository infrastructure, copyright support, and even mediated deposit services. As agreed by many Canadian institutional repository managers, one of the major stumbling blocks in streamlining compliance via the "green" route is getting hold of accepted manuscripts where publisher policy does not permit the deposit of a final article in a repository.

The automated manuscript deposit workflow removes the dependence on researchers keeping the ephemeral manuscript version. By transferring both the manuscript and accompanying metadata into a repository directly from the publisher's system, it makes compliance seamless and hassle free for grant recipients, and opens doors for further publisher-repository collaboration.

BIBLIOGRAPHY

  -Agency Open Access Policy on Publications (Government of Canada, 2015) in effect May 2015 presented federal grant recipients with a challenge of incorporating open access compliance into their research workflows. The policy requires that peer-reviewed articles arising from CIHR, SSHRC, or NSERC funding be made publicly available within 12 months of publication. Researchers have an option to comply by publishing in an open access or a hybrid journal or by depositing a copy of an article in an open access institutional or subject repository.

Figure 1 .

 1 Figure1. CSP-TSpace manuscript transfer and processing workflow[START_REF] Maistrovskaya | Publisher-Repository Partnership for Funder Mandate Compliance[END_REF]

JUDY HUM-DELANEY

Canadian Science Publishing, Canada judy.hum-delaney@cdnsciencepub.com (corresponding author)

ABSTRACTS

In April of 2015, Canadian Science Publishing (CSP) in partnership with the University of Toronto Libraries launched an automated manuscript deposit service. Upon author's opt-in, an automated workflow transfers their accepted manuscript from the publisher system into the University of Toronto research repository, TSpace, where it is made openly available with a reference to the final version on the journal website. This free service is available to authors publishing their work in CSP's NRC Research Press journals and is of particular interest to grant recipients looking to comply with the Tri-Agency Open Access Policy on Publications that came into effect in 2015. This paper provides an overview of the partnership and the workflow that makes over 1,200 manuscripts openly available annually. It also shares the script that can be adopted by other libraries and publishers looking to provide automated deposit service to authors for the purpose of funder mandate compliance, green OA, or preservation.


Gerd Vandersteen

Ludwig De Locht

Snezana Jenei

Yves Rolain

Rik Pintelon

Estimating scalable common-denominator Laplace-domain MIMO models in an errors-in-variables framework

Design of electrical systems demands simulations using models evaluated in different design parameters choices. To enable the simulation of linear systems, one often requires their modeling as ordinary differential equations given tabular data obtained from device simulations or measurements. Existing techniques need to do this for every choice of design parameters since the model representations dont scale smoothly with the external parameter.

The paper describes a frequency-domain identification algorithm to extract the poles and zeros of linear MIMO systems. Furthermore, it expresses the poles and zeros as trajectories that are functions of the design parameter(s). The paper describes the used framework, solves the startingvalue problem, presents a solution for high-order systems and provides a model-order selection strategy. The properties of the algorithm are illustrated on microwave measurements of inductors, a variable gain amplifier and a highorder SAW-filter. As shown by these examples, the proposed identification algorithm is very well suited to derive scalable, physically relevant models out of tabular frequencyresponse data.

Introduction

The design and simulation of high-performance electronic systems requires accurate and efficient models. The model requirements depend on the system type and on how the model is used in the design flow. The use of the model in an actual design requires that the model is parameterisable as function of external parameters. This makes it possible to predict the model of a system which was not simu-lated/measured yet. A practical example is the prediction of an inductor model out of measurements of related -though differently sized inductors. This will be highlighted in the examples given later.

The modeling capabilities differ depending on the initial available model or data. Model reduction techniques determine a simplified model starting from known model equations [START_REF] Feldmann | Effi cient linear circuit analysis by Pade approximation via the Lanczos process[END_REF][START_REF] Odabasioglu | PRIMA: passive reduced-order interconnect macromodeling algorithm[END_REF]. Identification techniques start from the system response only, without the knowledge of the systems equations [START_REF] Coelho | Robust rational function approximation algorithm for model generation[END_REF][START_REF] Pintelon | System Identifi cation: A Frequency Domain Approach[END_REF]. An example of the latter is the identification of linear systems using observed inputs and outputs or using the transfer matrices obtained through simulations or measurements.

Scalable models need to describe physically relevant model properties. Poles and zeros of a linear system satisfy this constraint. This is why the pole/zero trajectories will be parameterized instead of the coefficients of a rational form. The use of an invariant guarantees that the dependency on the external parameter(s) is physically relevant.

Passivity will not be imposed in this work for two reasons. First, making a non-passive model passive implies that pole/zero locations are artificially modified which compromises the physical relevance of the scalable model. Second, it is possible to impose stability in a post-processing stage: A passive model can be obtained from a stable system using convex optimization [START_REF] Coelho | A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data[END_REF].

We propose a robust and efficient identification algorithm to extract a scalable model for Multiple-Input Multiple-Output (MIMO) linear systems starting from tabular frequency-dependent data. The parameterized MIMO linear model determines the pole/zero trajectories starting from a common-denominator transfer-matrix model. Such models can be used in SPICE-like transient simulators such as Spectre.

MIMO linear systems, described by ordinary differential equations, can be represented using a common-denominator transfer-matrix representation. This means that the exact inputs U 0 j (s) with j = 1 . . . n U and the exact outputs Y 0 i (s)

with i = 1 . . . n Y are related to each other using

Y 0 i (s) = nU j=1 N ij (s) d(s) U 0 j (s) (1)
where s represent the Laplace variable, d(s) the denominator polynomial and N ij (s) the numerator polynomials. All polynomials have real-valued coefficients. The poles of the system are presented by the zeros of the common denominator d(s). If some poles are not observable in certain transfer functions, then the influences of these poles are compensated by zeros. This does not lead to numerical conditioning problems if the appropriate orthogonal polynomials are used.

An errors-in-variables framework is used to derive the estimators. This implies that both the inputs and outputs are perturbed with zero-mean additive noise ∆U i (s) and ∆Y j (s)

U i = U 0 i + ∆U i ; Y j = Y 0 j + ∆Y j (2)
with the noise covariance equal to

σ 2 UiUj (s) = E ∆U i (s)∆U j (s) σ 2 UiYj (s) = E ∆U i (s)∆Y j (s) σ 2 YiYj (s) = E ∆Y i (s)∆Y j (s) . ( 3
)
Some of these (co-)variances can be equal to zero depending on the data source and the wanted approximation. Therefore, all identification steps are made robust to such degenerated cases. The two contributions of the paper are: setting up a robust MIMO-identification algorithm and demonstrating the modeling the pole/zero trajectories as function of external parameters.

The first contribution of this paper is to set up an efficient and robust MIMO identification algorithm in the errors-invariables framework. This requires the extension of several Single-Input Single-Output (SISO) solutions towards MIMO and demands a careful selection of the successive identification steps to obtain a robust identification algorithm. Section 2 describes the state-of-the-art, the required MIMO extension and the motivated selection of the identification steps to obtain a robust identification algorithm.

The second contribution of the paper is to demonstrate the modeling of the pole/zero trajectories as function of external parameters. Section 3 therefore gives an answer to the question: What is the most appropriate parameterization for modeling the pole/zero trajectories ?

The identification algorithm is illustrated in Section 4 using the following three examples: extracting a scalable inductor model starting from measurements, modeling a Variable Gain Amplifier (VGA) with respect to its gain setting and modeling a SAW-filter. All these results demonstrate the ability of estimating physically relevant pole/zero trajectories for (potentially high-order) linear systems, which is concluded in Section 5.

Frequency domain identification techniques

A high-performance identification technique for identifying high-order MIMO linear models must satisfy that 1. the class of models and the identification framework are according to the problem; 2. good starting values are provided for the final nonlinear minimization; 3. high-order systems can be handled without numerical conditioning problems; 4. a model selection strategy is available.

A robust, high-performance identification algorithm is presented after describing the state-of-the-art and the necessary extensions.

Identification framework

The framework chosen to identify the MIMO linear systems is a maximum-likelihood (ML) estimator under the assumption that • the linear system is represented using a commondenominator transfer matrix (1); • both the inputs and the outputs are perturbed with additive noise (2); • the uncertainties on inputs and outputs can be correlated and frequency dependent (3).

The maximum-likelihood estimate can be derived under the assumption that the noise is independent over the K frequencies and normally distributed with given covariance matrix [START_REF] Pintelon | System Identifi cation: A Frequency Domain Approach[END_REF]. The leads to the minimization of the ML cost,

L ML (p) = K k=1 e H k C -1 e k e k = K k=1 r H k r k , (4)
with respect to the real-valued parameter vector

p T = p T N11 • • • p T Nn Y n U p T d . (5)
Vector e k = e(p, ω k ) represent the error vector which equals to Matrix C e k = C e(p,ω k ) is the covariance matrix associated with e(p, ω k ).

nU j=1 N ij (p Nij , ω k )U j (ω k ) -d(p d , ω k )Y i (ω k ) (6
The ML cost can be minimized using standard Gauss-Newton-like minimization algorithms [START_REF] Fletcher | Practical Methods of Optimization[END_REF][START_REF] Guillaume | A Gauss-Newton-like optimization algorithm for "weighted" nonlinear least-squares problems[END_REF] with the residual vector r k given by

r k = C -1/2 e k e k . (7)
Gauss-Newton-like optimization methods demand the computation of the first derivative of the complex-valued r k with respect to the real-valued p. This Jacobian matrix J is formed by stacking the matrices

J k = ∂r k ∂p1 • • • ∂r k ∂pn p (8)
on top of each other. Generally, the analytic computation of the Jacobian is extremely difficult since it demands the derivative of

C -1/2 e k
. Analytical expressions are only convenient if C e k is reduced to a scalar or to a diagonal form. However, it is possible to use a pseudo-Jacobian which approximates the Jacobian such that their Gauss-Newton minimizers are identical [START_REF] Guillaume | A Gauss-Newton-like optimization algorithm for "weighted" nonlinear least-squares problems[END_REF]. This pseudo-Jacobian is compute as

J + k = j + k,1 • • • j + k,p , (9)
with

j + k,i = C -1/2 e k ∂e k ∂p i - 1 2 C -1/2 e k ∂C e k ∂p i C -1 e k e (10)

Solving the starting value problem

This section describes two algorithms -a weighted linear least-squares (WLLS) and a weighted generalized totalleast-squares (WGTLS) -that can be used to generate starting values for p. The starting values depend on the polynomial bases, P . (jω k ), and on the weighting, W , used. The polynomial bases used are described in Section 2.3.

A first starting value solution is to linearize (7) by taking C -1/2 e k constant which results in a WLLS estimator. Since C -1/2 e k depends on the (unknown) parameters p, it is necessary to determine the initial weighting empirically. This empirical weighting can only use the measured transfer matrices and the asymptotic behavior of the polynomials, given the orders of the polynomials. Such weighting has been proposed for the SISO case [START_REF] Rolain | Generating robust starting values for frequency domain transfer function estimation[END_REF]. In our MIMO case, we use the empirical weighting of [START_REF] Rolain | Generating robust starting values for frequency domain transfer function estimation[END_REF] for each transfer function separately and sum the contributions together for each output.

An alternative to the WLLS is to use a WGTLS estimator [START_REF] Pintelon | System Identifi cation: A Frequency Domain Approach[END_REF][START_REF] Van Huffel | Recent advances in total least squares techniques and errors-in-variables modeling, chapter Analyses, Development and Applications of TLS-Algorithms in Frequency Domain System Identifi cation[END_REF]. Observing that the error vector ( 6) is linear in the parameters makes it possible to write e = Ap with

A =      P N11 U 1 0 • • • 0 -P d Y 1 0 P N12 U 1 • • • 0 -P d Y 2 . . . . . . . . . . . . . . . 0 0 • • • P Nn U n Y U nU -P d Y nY     
The solution of the WGTLS is given by the singular value decomposition (SVD) of the matrix W AC -1 were W and C are weighting matrices mandatory to obtain consistent and nearly ML-efficient estimates [START_REF] Golub | Matrix Computations Third Edition[END_REF][START_REF] Pintelon | System Identifi cation: A Frequency Domain Approach[END_REF]. The matrix W weights the importance of each equation and therefore determines the efficiency of the estimator. Optimally,

W equals C -1/2 e
. The weighting matrix C makes the es-

timates consistent if C H C = E[(W A) H (W A)] [14].
Matrix C becomes singular when some of the inputs or outputs are known exactly. We therefore advise to compute the WGTLS solution using a generalized SVD (GSVD) [START_REF] Van Huffel | Recent advances in total least squares techniques and errors-in-variables modeling, chapter Analyses, Development and Applications of TLS-Algorithms in Frequency Domain System Identifi cation[END_REF]. This avoids the inversion of the -possibly singular -matrix C.

The WLLS and the WGTLS can also be used iteratively by plugging previous estimates of p into the weighting. Such WGTLS iterative estimators -known as the Bootstrapped Total Least-Squares (BTLS) estimator -generates strongly consistent estimates at each iteration [START_REF] Van Huffel | Recent advances in total least squares techniques and errors-in-variables modeling, chapter Analyses, Development and Applications of TLS-Algorithms in Frequency Domain System Identifi cation[END_REF].

Restarting the estimation with an improved weighting is required in three situations 1. If no nonlinear optimizer is available, then the parameters can be estimated by the iterative use of the WLLS or the BTLS. 2. If the ML nonlinear optimizer gets stuck into a local minima, then we advice to use the BTLS estimator to generate an alternative starting point. The BTLS estimator is more appropriate than the WLLS since the latter is a linearized version of the ML cost. Hence, the probability that the WLLS estimate gets stuck in the neighborhood of the nonlinear optimizer is significantly higher. 3. If the conditioning severely decreases during the optimization of the ML-cost, then a re-orthogonalization is required by restarting with the WLLS or the BTLS estimator using a weighting evaluated in the previous ML-estimates.

Forsythe orthogonal polynomial enable highorder models

Several strategies are proposed in the literature to improve the numerical conditioning of weighted [START_REF] Bultheel | Robust rational approximation for identifi cation[END_REF][START_REF] Forsythe | Generation and use of orthogonal polynomials for data fi tting with a digital computer[END_REF][START_REF] Rolain | Best conditioned parametric identifi cation of transfer function models in the frequency domain[END_REF] and unweighted least-squares problems [START_REF] Coelho | Robust rational function approximation algorithm for model generation[END_REF]. Optimal conditioning for polynomial models require Forsythe orthogonal polynomials which make J H J equals the identity for the WLLS and the WGTLS [START_REF] Forsythe | Generation and use of orthogonal polynomials for data fi tting with a digital computer[END_REF]. They are constructed using a 3-term recurrence algorithms for both real-valued polynomials evaluated over the real axis [START_REF] Forsythe | Generation and use of orthogonal polynomials for data fi tting with a digital computer[END_REF] and for complexvalued polynomials evaluated over the imaginary axis [START_REF] Rolain | Best conditioned parametric identifi cation of transfer function models in the frequency domain[END_REF].

Optimal conditioning for rational models can be obtained using vector orthogonal polynomials [START_REF] Bultheel | Robust rational approximation for identifi cation[END_REF]. These polynomials mix all basis functions of the denominator and all numerators. This makes the use of vector orthogonal polynomials significantly more complex and computationally slower.

A practical alternative for the complete orthogonalization uses the Forsythe orthogonal polynomials to represent the individual polynomials. Rational approximations using Forsythe orthogonal polynomials lead to the bestconditioned representation and are demonstrated up to order 120 [START_REF] Rolain | Best conditioned parametric identifi cation of transfer function models in the frequency domain[END_REF].

Model selection problem for MIMO

A model selection algorithm is required to determine the orders of the numerators N ij (s) and the denominator d(s). The model selection algorithm is based on the SISO model selection algorithm of [START_REF] Rolain | Order estimation for linear time-invariant systems using frequency domain identifi cation methods[END_REF]. This algorithm is a two-step order selection method with a coarse and a fine selection.

The coarse selection starts with an over-estimate of the order. It uses the singular values of a whitened Jacobian matrix to determine a (slight) over-estimate of the order [START_REF] Rolain | Order estimation for linear time-invariant systems using frequency domain identifi cation methods[END_REF]. Whitening the Jacobian is necessary to set the threshold for the selection procedure.

The fine selection is performed through elimination of poles/zeros without significant contribution to the model in the frequency band of interest. The fine selection for SISO models [START_REF] Rolain | Order estimation for linear time-invariant systems using frequency domain identifi cation methods[END_REF] is adapted when considering the distance between poles and zeros. A pole/zero pair cancels in the SISO case if their distance equals zero. This is generalized to MIMO by considering the distance between a pole and the zeros of each individual transfer function. A pole/zeros cancels if the distances of a pole to a zero in all numerators N ij (s) equal zero.

The proposed identification algorithm

An identification Algorithm 1 is based on the results of the previous sections. Its main properties are:

• each iteration uses a BTLS estimator as starting value generator. BTLS is preferred over WLLS since it is observed that the algorithm becomes less sensitive to local minima. • the initial weighting W for the BTLS estimator uses the empirical algorithm based on the measured transfer matrix and the orders of the polynomials. • each iteration restarts with a new weighting which converges to the optimal ML-weighting. • each iteration performs a re-orthogonalization to obtain a good conditioning of the final ML-estimate. Intermediate ML-estimates can suffer from bad conditioning. This occurs when the starting values differ significantly from the ML-estimates.

Algorithm 1: The proposed identification algorithm. weighting W = empirical weighting; L opt ML = ∞ ; repeat Compute the orthogonal bases; p = BTLS estimate using W ; p = nonlinear minimization of L ML ; if L ML (p) < L opt ML then p opt = p; L opt ML = L ML (p); end W = ML weighting (p); until no significant changes of L ML ;

Modeling the poles / zero trajectory

Pole/zero representations of a linear system are independent of the polynomial bases used. The pole/zero trajectories are therefore a good candidate to model the dependency on external parameter(s).

The modeling of the pole/zero trajectories requires the grouping of the poles and zeros such that they form a smooth trajectory as a function of the external parameter. The results obtained in Section 4 use a nearest neighbor algorithm to determine the pole/zero trajectories.

Another issue is the modeling of the pole/zero trajectories themselves: when two real poles move to each other and become a complex pole-pair, then the derivatives of the trajectory are discontinuous. This problem can be solved by either splitting the trajectory into pieces or by combining pole pairs into second-order sections. The latter strategyused in the below examples -writes the different polynomials as the product of first and second order polynomials.

Examples

The most important aspects of the proposed algorithm are illustrated on three examples.

A. The extraction of a scalable model from microwave measurements is required when introducing state-of-the-art inductor technology into a spice-like simulator.

The scalable inductor model was extracted for off-chip inductors made in MCM technology. The 1.5-turn inductors had identical inner diameters (100µm) and conductor spacing (20µm). The conductor width w was changed from 50µm, 77µm, 100µm till 150µm, resulting in nominal inductor values of 1.62, 1.74, 1.80, 2.04nH. All inductors were measured from 45MHz till 50GHz.

5 th order models were extracted out of the measurements from DC up to two times the frequency of the first minimum in S 21 . This minimum changes from 34GHz down to respectively 25, 20.8 and 14.8GHz for the 50µm, 77µm, 100µm and 150µm inductors. The wide frequency range used implies that the model is valid far beyond the region were it operates as an inductor.

The validation of the scalable model was done as follows:

1. 5 th order models were extracted for all inductors and the pole/zero trajectories were determined. The measurement allowed to obtain modeling errors of below -30dB for all extracted models. The trajectories of the poles are illustrated in Figure 1. The trajectories for the zeros are similar but are not shown due to the lack of space.

2. The poles and zeros for the 50µm, 77µm and 150µm inductors were used as reference to predict the poles and zeros from the 100µm inductor. Figure 1 shows the good correspondence of the predicted poles (using a cubic interpolation) and the estimated poles (obtained through the identification algorithm on the measured 100µm inductor).

3. The difference between the predicted and the measured S-parameters was determined, showing a prediction error of about -25 dB as illustrated in Figure 2.

The results in Figure 2 clearly demonstrate that it is possible to extract an accurate scalable model for microwave inductors using the proposed technique.

B. VGA modeling from network analyzer measurements for variable gain settings shows the ability of predicting the pole/zero trajectories of complex systems. The measured device is a three stage 5GHz BiCMOS VGA mounted on a PCB and connected through 3cm long transmission lines. The complete system is modeled from 500MHz to 14GHz with a 30 th order model, resulting in a relative accuracy of about -30 dB. The VGA is measured in 9 gain settings (from 5 to 25 dB). The pole trajectories are shown in Figure 3. Half of the poles were used as reference while the remaining poles are used to determine the interpolation error of a cubic interpolation.

C. SAW-filter modeling of 30 th order shows the ability of extracting high-order models. The model order selection scheme started at model order 60 without numerical problems. The measured and modeled transfer functions are given in Figure 4, together with the complex modeling errors.

Conclusions

This paper describes a frequency-domain identification technique to extract the pole/zero trajectories for systems which depend on an external parameter. The identification technique estimates a common-denominator MIMO rational model in an errors-in-variables framework. Solutions are presented to estimate high-order models, to deal with The proposed algorithm shows excellent results for extracting a scalable model for a microwave inductor and a variable gain amplifier. High-order models can also be handled as shown through the modeling of the SAW-filter. Stable models were extracted in all cases and the pole/zero trajectories were found to be smooth functions of the external parameter.

  ) with N ij (p Nij , ω k ) = P Nij (jω)p Nij and d(p d , ω k ) = P d (jω)p d where P . represents the polynomial basis used.

Figure 1 .Figure 2 .

 12 Figure 1. The pole trajectories of a 5 th order inductor model. A cubic interpolation is used to predict (•) starting from the estimates (+). Ideally, the interpolations (•) coincide with the estimates of the 100µm inductor (×).

Figure 3 .

 3 Figure 3. The pole trajectories of a 30 th order model for a three-stage VGA with transmission lines included. A cubic interpolation is used to predict (•) starting from the estimates (+). Ideally, the interpolations (•) coincide with the estimates (×).

  the starting value problem, to reduce the problem of local minima and to handle the model selection problem.

FrequencyFigure 4 .

 4 Figure 4. Comparison between the measured transfer function of the SAW-filter (×) and the 30 th order model (-). The complex difference (•) shows the excellent agreement between the data and the model.

Proceedings of the Design, Automation and Test in Europe Conference and Exhibition (DATE'05) 1530-1591/05 $ 20.00 IEEE

Proceedings of the Design, Automation and Test in Europe Conference and Exhibition (DATE'05)

We therefore recommend the proposed identification algorithm to extract the physically relevant pole/zero information for building scalable models out of tabular simulation or measurement results.

* This research was supported by the Fund for Scientific Research, Flanders, the Flemish government (GOA-ILINOS), and the Belgian program on Inter-university Poles of attraction (IUAP-5/22).


Sebastian Nordhoff

Felix Kopecky

Open Business Data and the Publisher's Cookbook

Introduction 1

For a long time, the discourse on Open Access has been dominated by the plights of the natural sciences. Skyrocketing journal subscription costs have laid a have burden on library budgets, and skyrocketing profits of the major publishers have raised ethical questions about the funnelling of public funds into shareholders' coffers. The solutions proposed have normally tried to resolve these issues, which are experienced in the natural sciences. For instance, the report by [START_REF] Schimmer | Disrupting the subscription journals' business model for the necessary large-scale transformation to open access[END_REF] explain in detail how the "system" can easily be changed to an author-pays system, since there is enough money in the "system", but at a closer look, the empirical evidence presented centers completely on article processing charges, leaving aside book-length works or non-APCbased models.

Gold, Green and Platinum Open Access

There have been criticisms of the Golden Road from the beginning, often advocating the Green Road. This again is modelled on practices in the sciences, where we find a culture of short works of article-length, a general propensity and openness for technical solutions and an acquaintance with parametrized work flows. This is not found in the humanities. Works are longer, techical solutions are less welcome and often met with suspicion, and parametrized work flows are all but absent. The discourse on Open Access up to now has by and large neglected the Other Side of Academia, i.e. the humanities. Generally meager funding means that the Golden Road is not a viable model; and lacking technical affinity among the practicioner population means that the Green Road is not a socially viable model either.

As an alternative to the Golden Road and the Green Road, so-called "Platinum Open Access" (or "Diamond Open Access") has been proposed [START_REF] Haspelmath | Science publication should be seen as a public service (just like science itself)[END_REF]. Diamond Open Access is dubbed "Publisher pays" by Haspelmath. This is misleading since any publisher has limited funds, which will eventually deplete and so some sources of revenue have to be found. "Community pays" seems to be a better term here. The precise kinds of revenue which can be tapped into by a Platinum Open Access publisher will be detailed further down.

Sustainability and Resilience

An important concept for running a publishing platform is sustainability. Sustainability means that the project can survive after the initial funding and can meet its running costs by its own revenues without requiring external funds. A more demanding concept is resilience. We define resilience as meaning a sustainable enterprise which is additionally guarded against risks of losing its community-based soul to the profit oriented sphere (compare Ottina 2013). An example of a sustainable and resilient project would be Arxiv.org, whereas an example of a sustainable project which proved non-resilient is Social Science Research Network (SSRN), which was sold to Elsevier in 2016.

The Need for Empirical Data

Community-based projects face the general challenge that the costs of scientific publications are completely opaque. Publishers give wildly varying quotes as to the costs of papers and books. Scielo publication costs are ~90 USD a paper, while Nature Communications charges 6,000 USD APCs. For books, we find Ubiquity Press with £3,450 and Brill with a quoted 18,500 EUR. [START_REF] Maron | The costs of publishing monographs: toward a transparent methodology[END_REF] find ranges between 15,140 and 129,909 USD as the cost price for books at university presses. All this means that new projects are completely in the dark about the costs they will be facing while setting up shop. A detail of the costs of an actual publisher as a yardstick to measure a new project against is direly needed. Adema & Stone (2017: 79) suggest a "Best practice toolkit", which would help Academic-Led Presses (ALP) in the setting up the publishing platform (also see Ferwerda, Pinter & Stern 2017: 10).

Furthermore, the provision of empirically tested-business models is a desideratum, as evidenced by Johnson et al. (2017: 65).

This is what is being provided by the project "Full disclosure" by Language Science Press.

Language Science Press

Language Science Press is a community-based platinum OA publishing initiative for monographs and edited volumes in linguistics. Since its inception in 2014, 60 books have been published, about 120 more are in the pipeline.

After initial funding provided by the Deutsche Forschungsgemeinschaft, Language Science Press is now relying on a supporter network of 100 institutions worldwide, which contribute to meeting its running costs.

Open publisher

Language Science Press has a strong commitment to openness and is always happy to share. Next to all books being CC-BY, the LaTeX source of all books is available on GitHub; all data and figures are being provide in as raw a format as possible; the LaTeX class is available on CTAN; all software is 100% Open Source. This means that the technical setup could easily be replicated. This being said, a software stack alone is not sufficient to run a publishing house. Next to the technical infrastructure, know-how in the domains of finance and community management is also required. In the context of the project "Full disclosure", Language Science Press releases all relevant business data. This includes downloads per book, sales per book, donations, fees, and institutional memberships as well as the costs for personnel, goods, services, and travel.

Lean publisher

Language science press is a lean publisher born digital. A number of legacy cost factors were cut out. These include: warehousing, acquisition editors, paywalling, authentication, billing, royalties, IPR management, marketing, book stands, involved author contracts. The author provides a pdf according to LangSci specifications and releases it under a CC-BY licence. The pdf is made available on the LangSci site and various aggregators, as well as via print-on-demand. PR is done via social media. Acquisition is done via the community network already in place.

Community-based publisher

The third principle of Language Science Press is that it is a community-based publisher. There are 20 autonomous series with autonomous editorial boards which see to the quality of publications in their respective subdiscipline (e.g. phonetics or translation studies). Reviewing is done by peers as usual, but also proofreading is done by volunteer researchers (currently 300 enrolled), who are keen on seeing early versions of a manuscript and making the book a better book. This is a kind of "donation of time" instead of a "donation of money", which nevertheless means that the cost of producing the book go down considerably.

A note on terminology

When talking about the pros and cons of nuclear power plants, one has to talk about Megawatts, Millisieverts, and risk percentages. There is an established vocabulary for talking about matters relating to nuclear power plants. One can agree or disagree about how many Megawatts the yield will be, how many Millisievert represent a critical dosis, or how high the risk percentage is, but the concept in and of themselves are useful to establish a discourse. That discourse can of course be critiqued, but the using the terms Megawatt, Millisievert or risk percentage does not make you an ardent proponent of nuclear power. To the contrary : in order to militate against nuclear power, you better know those terms. In the same vein, terms such as "revenue stream", "contribution margin", "depreciation" or more basic "product", "customer" or "value proposition" have clear definitions when talking about business models. A clear and established terminology makes the argumentation more transparent, and it helps shed light on what the critical components of a particular setup are, what aspects are in line with the chosen ethical standards, and what aspects are problematic. Using these terms when describing a setup does not logically entail a support or opposition to capitalism or any particular from thereof. In order to make clear that these terms are used in a technical sense without necessarily endorsing them on a society-wide level, we will put them in scare quotes.

Full disclosure

In the project "Full disclosure", Language Science Press shares its business model complemented by granular business data as Open Data. This will allow projects in other disciplines to evaluate in how far the model (or parts thereof) are suitable for their discipline. The business data provided can serve as a yard stick to gauge the attractivity of different "revenue streams" when planning for a post-grant future. These documents centered on financial and legal aspects are complemented by a "cookbook" with step-bystep recipes.

The provision of a schematic HowTo squared with actual business data will allow for the empirical evaluation of the proposed recipes and some benchmarking.

The availabilty of financial calculations will allow to offset one of the main advantages the traditional publishers have over new projects: experience in handling accountancy matters.

Business model

The business model comes in analyses of the business case, the market, the organisation, and funding. For all four aspects, a short general introduction is given. This is followed by a description of the solution adopted by LangSci and an explanation why this particular solution was chosen. This chosen solution is then evaluated in a third part, which highlights where the inital assumptions were correct and where they were completely off the mark, in the hope that other projects will find these lessons learned helpful. Each section closes with a discussion of other solutions which could have been chosen as well, and what changes in the outcome would be expected if they were chosen.

A "business model" starts with analyses of the "product", the "customers", and the "value propositions" made to the various groups. One important aspect is that the "customer" in academic publishing is actually no straightforward to pin down. A case can be made that authors, readers, universities, libraries, and the general public are indeed all potential "customers" of Open Access publication platforms in the sense that they derive a "benefit" from the existence of such platforms. This implies that these "customers" can be made to contribute a share of the "benefit" towards the enterprise.

The books being published by Language Science Press come from authors of countries all over the world, and are read internationally as well. This means that the "business model" must reflect this international character of the operations. A funding model restricted exclusively to, say, Germany, will be unfair, and it will be hard to convince the residents of only one country to fund operations which profit the whole world. This international setup has to be taken into account not only for financing, but also for distribution and marketing.

When we analyse the "benefits" OA publishing provides, we find that it is not only the readers who profit. Also the authors derive a "benefit" (more prestige, faster publication, greater reach). Furthermore, libraries also do "benefit" via a larger array of books they can provide to their patrons. The state at large also benefits (more cost-effective publishing; no dependency on monopolists), as does society at large (better and faster access to scientific findings).

Just as it would be unfair to have one country shoulder the operating costs alone, burdening only one group with the costs (e.g. via "author pays" ' models) is questionable as well. So the question is: how can the "operational costs" be shared among the "stakeholders" in such a way that everybody contributes, and that no one is charged beyond their capacities? And how can that be done without undermining the basic tenets of Open Access?

Language Science Press has opted for a broad basis for financing its operations. The diversification of "revenue streams" means not only that each of the various "stakeholders" participates, but it also reduces the risk of "funding gaps" as compared to one large funder. If one "revenue stream" breaks down or does not contribute the expected amount, this can then potentially be compensated by the other streams. The analysis of "clients" above shows that the "product" provided by Language Science Press is complex and can access a variety of "markets" with different "target groups."

The basic assumption is that each group of "stakeholders" will have have both egoistic motivations (purchase a book for reading it yourself) as well as altruistic motivations (create societal benefit, ensure free access to the knowledge of humanity, ...). We acknowledge both kinds of motivation as valid.

The "business model" is based on five pillars, which are supported by the different audiences:

1. print margins (readers) 2. individual memberships (authors, readers) 3. optional author fees (authors) 4. donations (authors, readers)

institutional memberships (institutions)

Each channel comes with an "overhead" in administration. For instance, institutional memberships require effort to liaise with libraries, and to get the fiscal setup right. This means that less than 100% of the sum on the invoice will be available for book production. But ideally each channel will provide some "net contribution" towards financing the core task of producing books. An evaluation of the LangSci estimates can be found below in the section "Evaluation".

The descriptive part of the business model is complemented by a freely available spread sheet with a 5-year projection, where publishing projects can enter their estimates about projected number of books; time needed for various tasks; flat costs like rent; and estimated sales/author fees/downloads/institutional memberships. With all estimates filled in, the spreadsheet will show whether the project will be sustainable 5 years down the road.

Open Business Data

The model is complemented by all business data from Language Science Press in 2017 in *.csv format at https://github.com/langsci/opendata. This shared data resource (possibly called "Accountancy Commons") includes all download figures, all sales figures, all expenses (design, travel, salaries, as far as privacy laws permit). This data can be squared with the original business model and allows its empirical evaluation. It will allow other interested disciplines to estimate the costs in their field, adjusting for particular usages of theirs. For instance, a field with mainly prose text might reduce the typesetting estimates compared to linguistics, while a field with heavy use of photographs will have to add additional budget for this.

Cookbook

The final element is the "cookbook" of how to set up a community-based publisher with recipes, timelines, and pitfalls to avoid. This is based on the setup of Language Science Press since 2012. Aspects discussed are the generation and the signalling of:

• prestige;

• governance;

• the creation of a community spirit;

• gamification;

• community proofreading;

• marketing; and

• generating revenue.

Evaluation

When the business model was devised in 2015, the revenue listed in Table 1 was assumed for each of the streams. The actual revenue for 2017 is given in that table as well. People buy a lot less printed books than expected, they donate less than expected, and they pay less optional author fees than expected. Even if we adjust for the fact that only half the expected books were produced, the numbers are still below the expectations in all domains, with the exception of institutional memberships. We share our misconceptions here so that other projects can learn from our errors.

In 2016, a cooperation with Knowledge Unlatched was started. The idea was to have Knowledge Unlatched do the acquisition of institutional members since they have the relevant expertise and contacts. It became soon clear that this was a more viable revenue stream than any of the others, with considerably less overhead.

While the total sum of 120,000€ stated in the business model could not be raised, the number of books was also lower, and the position of an accountant was not filled, leading to 1.0 FTE instead of 1.5 FTE and hence lower personnel costs.

Community Efforts

An important aspect which outweighs the financial bean counting is the community participation. Language Science Press has been successful in creating a community of linguists interested in Open Access Publication. This community cares for Language Science Press and wants it to survive and to thrive. There are currently over 900 registered public supporters, 300 community proofreaders and over 100 different authors. Even if the scale of operations has to be adjusted following the revenue situation, there is no doubt that Language Science Press as a project will be resilient enough to continue.

Replication

It is hoped that the Cookbook, which will be available for the conference, will inspire other disciplines to set up community-based publishing projects as well, and that the business model and the empirical data will help them see where Language Science Press succeeded, where it failed and how these failures can be avoided in future projects. Ideally, these other projects would also make their assumptions available and offer a critical evaluation of what happened to their plans when they hit reality.

Critical perspectives

I would like to close by some critical perspectives on open data. Opening up this data means that we are going one step further towards commodification of science. If a book in linguistics can cost as little as 3,000 €, how could one argue that for a particular publishing project in, say, archeology, you have to budget 25,000€? Obviously, there are huge differences between the two disciplines, but will this be clear to funding bodies? If the person-hours dedicated to a book are disclosed, will this not lead to books being selected as to their requiring less-than-average person-hours in order to have a nice balance sheet? Who would continue doing works like "Tone in Yongning Na" about a small language in China with very complex typesetting when a prose text of 300 pages will also give you a book to add to your list of deliverables? Weighing these issues, we feel that disclosing the experiences Language Science Press has made at this point in time is more important for the general enterprise of free access to knowledge, but we want to caution against overemphasising the value of metrics in scientific publication.

BIBLIOGRAPHY

Table 1 :

 1 Revenue as projected and realised in 2017

	Revenue stream	Projected Realised
	Print margin	24,000 €	5977.31€

Table 1

 1 makes it abundantly clear that the initial estimates were completely off the mark.


G Chen
email: guilchen@cse.psu.edu

M Kandemir
email: kandemir@cse.psu.edu

M Karakoy
email: m.karakoy@ic.ac.uk

A Constraint Network Based Approach to Memory Layout Optimization*

While loop restructuring based code optimization for array intensive applications has been successful in the past, it has several problems such as the requirement of checking dependences (legality issues) and transformation of all of the array references within the loop body indiscriminately (while some of the references can benefit from the transformation, others may not). As a result, data transformations, i.e., transformations that modify memory layout of array data instead of loop structure have been proposed. One of the problems associated with data transformations is the difficulty of selecting a memory layout for an array that is acceptable to the entire program (not just to a single loop). In this paper, we formulate the problem of determining the memory layouts of arrays as a constraint network, and explore several methods of solution in a systematic way. Our experiments provide strong support in favor of employing constraint processing, and point out future research directions.

Introduction

Data locality of array-based computations has been an exciting research area for the last decade or so. Most of the prior proposals to the problem are based on loop transformations [START_REF] Lam | The cache performance and optimizations of blocked algorithms[END_REF] [START_REF] Li | A singular loop transformation framework based on nonsingular matrices[END_REF][10] [START_REF] Wolfe | High Performance Compilers for Parallel Computing[END_REF], i.e., modifying the order of loop iterations to make data access pattern more cache friendly. Loop transformations have several key advantages that make them appealing to compiler writers and users alike. First, there is a comprehensive theory behind them developed over the years [START_REF] Wolfe | High Performance Compilers for Parallel Computing[END_REF] and supported through several commercial implementations. Second, they are proven to be effective in enhancing both temporal and spatial locality. Third, and maybe most importantly, transformation of a loop nest is independent of transformations of other nests in the same application *This work is supported in part by NSF Career Award #0093082.

code. In other words, its impact is localized to the nest in question. Consequently, for each loop nest, one can use the best loop transformation from the data locality perspective without worrying about the interactions between neighboring loop nests. However, recent research has revealed several drawbacks of loop transformations such as the requirement of checking dependences (legality issues) and transformation all of the references within the loop body indiscriminately (while some of the references can benefit from the transformation, others may not). As a result, data transformations [START_REF] Catthoor | Data Access and Storage Management for Embedded Programmable Processors[END_REF][6] [START_REF] O'boyle | Nonsingular data transformations: definition, validity, and application[END_REF], i.e., transformations that modify memory layout of array data instead of loop structure have been proposed. While data transformations do not have the problems associated with loop transformations, it has proven to be difficult to implement robust data transformation frameworks, mainly because of the fact that a memory layout modification affects all references to the array in question in all the loop nests of the application (i.e., localized optimization is not possible). In other words, its impact is global and difficult to capture. Therefore, prior efforts mainly concentrated on heuristic approaches whose results could not have been validated in formal terms.

In this work, we focus on data transformations from a different perspective, and treat them within the paradigm of constraint processing. In more specific terms, we formulate the problem of determining the memory layouts of arrays for a given application as a constraint network [START_REF] Dechter | Constraint Processing[END_REF], and explore several methods of solution in a systematic way. In doing so, our ultimate goal is two-fold. First, we want to show that constraint processing provides an attractive approach to implement a data transformation framework. Second, using the solutions returned by this framework, we want to take a fresh look at previously proposed heuristic solutions to the problem, and check how they compare to our constraint network based approach. This paper reports on our experience with this constraint processing based solution, and presents an empirical evaluation. Specifically, we designed and implemented a constraint network specialized for solving memory layout problems. Our experiments provide strong support in favor of employing constraint processing, and point out future research directions.

The rest of this paper is organized as follows. The next section discusses our memory layout representation based on linear algebra. Section 3 describes our constraint network and gives a formal definition of the problem. Section 4 discusses backtracking and backjumping based solutions to the problem. An experimental evaluation of our approach is presented in Section 5, and we conclude the paper in Section 6.

Hyperplane-Based Memory Layout Representation

Our memory layout representation is based on linear algebra and makes use of spatial locality in memory space. In a k-dimensional space, a hyperplane is defined as a set of tuples (x1 x2 … xk) that satisfy the equation x1y1+x2y2+…+xkyk = c, where (y1 y2 … yk) represents hyperplane coefficients (also called hyperplane vector) and c is the hyperplane constant. Note that (y1 y2 …yk) represents a hyperplane family, each member of which has a different constant (c value) [START_REF] Kolman | Linear Algebra with Applications[END_REF]. Two points represented by column vectors, d1 and d2, are said to belong to the same hyperplane if:

(y 1 y 2 …y k )•d 1 = (y 1 y 2 …y k ) •d 2 , where • denotes point multiplication. 1 As an example, in a two-dimensional data space, the hyperplane vector (1 0) indicates that two array elements belong to the same hyperplane as long as they have the same value for the row index.

Let us now focus explicitly on a two-dimensional space (an extension to higher dimensional spaces will be discussed later). Note that, a hyperplane family can be used to partially describe the memory layout of an array. For example, if we do not care about the relative order of hyperplanes, we can use hyperplane vector ).

An important point to note here is that, in order to have good data locality, data access pattern should be along the same direction with the hyperplane vector. Let us focus on a row-major memory layout for illustrative purposes (see Figure 1(a)). In order to have good spatial locality, two successive loop iterations, denoted by I and I n (not that in a nest with multiple loops I and I n are vectors), should access the array elements d 1 and d 2 such that (1 0)

• d 1 = (1 0) • d 2 .
In this paper, however, we are interested in determining the best memory layout for a given data access pattern. Therefore, our problem is to choose a hyperplane vector (y1 y2) such that:

(y 1 y 2 ) • d 1 = (y 1 y 2 ) • d 2 , assuming that d 1 and d 2 are the array elements accessed by I and I n . As an example, consider the nested loop shown in Figure 2. In this nest, we have two references to two different arrays (Q 1 and Q 2 ). Assuming that I = (i 1 i 2 ) T and I n = (i 1 i 2 +1) T are two successive loop iterations that do not cross loop bounds, for array Q 1 , we should find a

(1 0) (a) (0 1) (1 -1) (1 1) (b) (c) (d)
Figure 1 Different memory layouts for a twodimensional array (data space) and the corresponding hyperplane vectors.

for (i 1 =0;i 1 <N;i 1 ++) for(i 2 =0;i 2 <N;i 2 ++) …Q 1 [i 1 +i 2 ][i 2 ]…Q 2 [i 1 +i 2 ][i 1 ]… Figure 2.
An example loop nest.

hyperplane vector (y 1 y 2 ) representing its memory layout such that the following equality should be satisfied:

(y 1 y 2 )•(i 1 +i 2 i 2 ) T = (y 1 y 2 )•(i 1 +i 2 +1 i 2 +1) T ,
which means (y 1 y 2 ) = (1 -1), i.e., the diagonal layout. 2Similarly, for array Q 2 , we need to satisfy: (y 1 y 2 )•(i 1 +i 2 i 1 ) T = (y 1 y 2 )•(i 1 +i 2 +1 i 1 ) T , which gives us (y 1 y 2 ) = (0 1), i.e., the column-major layout.

When the same array is accessed in multiple nests, however, the problem of determining memory layouts program-wide becomes a complex problem (e.g., different loop nests may require different memory layouts). In Section 3, we discuss our constraint processing based solution to the problem of memory layout determination.

It is to be noted that, if a loop restructuring is applied to the nest being optimized, one can have a different data access pattern from the original one, and this can affect the memory layout selection as well. For example, if the two loops shown in Figure 2 are interchanged, the best memory layouts for arrays Q1 and Q2 would be (0 1) and (1 -1), respectively.

We now briefly discuss how we handle arrays with more than two dimensions. In such cases, to define a memory layout, instead of a hyperplane vector/family, we use an ordered set of hyperplane vectors/families. For example, two data elements in a three dimensional array stored as column-major have spatial locality with respect to (0 0 1) and (0 1 0); that is, if they have the same indices except for the first dimension. Therefore, to represent such a layout, we use a matrix with two rows: Y1 = (0 0 1) and Y2 = (0 1 0). Then, the two data elements, d1 and d2, map on the same column if and only if both of the following equalities are satisfied:

Y 1 • d 1 = Y 1 • d 2 and Y 2 • d 1 = Y 2 • d 2 .
The idea is easily generalized to higher dimensionalities as well.

Constraint Network Formulation

A constraint network (CN) can be described as a triple CN = <P,M,S>, where P is a finite set of variables, M is a list of possible values for each variable, and S is a set of constraints on P [START_REF] Dechter | Constraint Processing[END_REF]. In our context, P = {Q1, Q2, …, Qz} is the set of arrays manipulated by the application code to be optimized. M, which represents the domain for variables, contains the set of memory layouts for each array (variable). Specifically, for every array Qi where 1 ≤ i ≤ z, we have a set Mi = {hi1, hi2, …, hif(i)}, which contains the hyperplane vectors that can be assumed by Qi. Here, f(i) is the number of potential layouts for array Qi. The set S, on the other hand, contains s constraints. Each Sij ∈ S contains a set of (hyperplane) pairs that capture the allowable layouts for arrays Qi and Qj from the locality viewpoint. Each pair represents the best layout choice under a given loop restructuring. In the rest of our discussion, when there is no confusion, we use the terms "array" and "variable" interchangeably. As an example, consider the following constraint network that captures layout information for a program that manipulates four different arrays (Q1,Q2,Q3,Q4): In this constraint network, M1 indicates that array Q1 can assume three different memory layouts, represented by hyperplane vectors (1 0), (0 1), and (1 1), which correspond to row-major, column-major, and antidiagonal layouts, respectively. Other domain sets can be interpreted in a similar fashion. S12 indicates that, as far as arrays Q1 and Q2 are concerned, there are two preferable memory layout combinations. The first combination is that Q1 has layout (1 0) and Q2 has layout (1 1), whereas the second combination is that Q1 and Q2 have layouts (0 1) and (1 -1), respectively. Note that this is similar to the situation given in Figure 2. Other constraints can be interpreted similarly. Note that, based on the way that it is encoded above, this constraint network is a binary constraint network [START_REF] Dechter | Constraint Processing[END_REF] as each constraint is defined on a pair of variables. While a nonbinary formulation is also possible, there are also techniques that can be used to convert non-binary formulations to binary ones. However, since it is not the main focus of this paper, we do not elaborate on this issue any further.

CN = <P,M,S>, where P={Q 1 ,Q 2 ,Q 3 ,Q 4 } M={M 1 ,M 2 ,M 3 ,M 4 }, where M 1 ={(1 0), (0 1), ( 1
1)}; M 2 ={(1 -1), ( 1
A solution to a constraint network problem is to select a pair from each Sij such that all the selected pairs are consistent with each other, i.e., there is no contradiction when all the members of S are considered, meaning that each array has a single memory layout. For our example above, we obtain a solution by selecting hyperplanes (1 0), (1 1), (0 1), and (1 0) for arrays Q1, Q2, Q3 and Q4, respectively. The next section discusses our strategy for finding solutions for a given constraint network (when a solution exists).

Proposed Solutions

In this section, we first discuss a backtracking based solution to the problem of memory layout determination. After that, we discuss how we can shorten the solution time by enhancing the backtracking based solution with several heuristics. Before moving into the discussion of backtracking however, let us make an important definition: consistent partial instantiation.

In a constraint network, a partial instantiation of a subset of variables is an assignment to each variable from its domain. A consistent partial instantiation, on the other hand, is a partial instantiation that satisfies all the constraints that involve only the instantiated variables [START_REF] Dechter | Constraint Processing[END_REF]. A backtracking algorithm traverses the state space of partial instantiations in a depth-first manner. It starts with an assignment of a variable (e.g., randomly selected) and then increases the number of partial instantiations. When it is found that no solution can exist based on the current partial instantiation, it backtracks to the previous variable instantiated, and re-instantiates it with a different value from its domain. Therefore, a backtracking algorithm has both forward (where we select the next variable and instantiate it with a value) and backward phases (where we return to the previously instantiated variable and assign a new value to it). In the rest of the paper, this backtracking based scheme is referred to as the base scheme.

The base scheme makes random decisions at several points. The first random decision is to select the next variable (array) to instantiate during the forward phase. The second random decision occurs when selecting the value (layout) with which the selected variable is instantiated (again in the forward phase). In addition, in the base scheme, when we find out that the current instantiation cannot generate a solution, we always backtrack to the previously assigned variable, which may not necessarily be the best option. One can improve these three aspects of the base scheme as follows. As for the first random decision, we replace it with an improved approach that instantiates, at each step, the variable that maximally constrains the rest of the search space. The rationale behind this is to be able to detect a dead-end as early as possible during the search. Similarly, when selecting the values to be assigned to the instantiated variable, instead of selecting a value randomly, we can select the value that maximizes the number of options available for future assignments. The rationale behind this is to increase the chances for finding a solution quickly (if one exists). Finally, we can expedite our search by backjumping, i.e., instead of backtracking to the previously instantiated value, we can backtrack further when it is beneficial to do so. This can be best explained using the following scenario. Suppose that, in the previous step, we selected the layout hid for array Qi, and in the current step we selected the layout hje for array Qj. If, at this point, we see that there cannot be any solution based on these assignments, the base approach returns to array Qi and assigns a new layout (say hil) to it (assuming that we tried all alternatives for Qj). However, it must be noted that, if there is no constraint in the network in which both Qi and Qj (i.e., their layouts) appear together, assigning a new value (layout) to Qi would not generate a solution, as Qi is not the culprit for reaching the dead-end. Instead, backjumping skips Qi and determines an array (say Qk) among the arrays that have already been instantiated that co-appears with Qj in a constraint, and assigns a new value (layout) to it (i.e., different from its current value). In this way, backjumping can prevent useless assignments and, as a result, expedite our search. Figure 3 gives an illustration that compares backtracking and backjumping. In the remainder of the paper, the solution scheme supported by these three improvements is referred to as the enhanced scheme. The next section presents experimental data for both the base and enhanced schemes. Before going into our experimental analysis though, we need to make one point clear. If a solution exists to the problem under consideration, both the base and enhanced schemes will find it. However, if multiple solutions exist, they can find different solutions.

Q i Q j Q k Instantiated Variables Uninstantiated Variables Backtracking Q i Q j Q k Instantiated Variables Uninstantiated Variables

Empirical Analysis

In this section, we present an experimental analysis of our constraint processing based approach to the memory layout determination problem. To conduct such an analysis, we used five array-based embedded benchmarks, whose important properties are given in Table 1. The third column gives the total search space size (i.e., the sum of the domain sizes of the arrays in the corresponding application). The last column of this table gives the total data size manipulated by each application. We implemented our constraint network using C++. Excluding the libraries linked and comment lines, the network code itself is about 1700 C++ lines.

In our experimental evaluation, our focus is on two metrics: solution time and quality of solution. The first of these gives the time it takes for determining the memory layouts of arrays, and the second one gives the execution time of the resulting optimized code (or percentage improvement brought by the optimized code over the original one). To be fair in our evaluation, we also compare our approach to a previously proposed heuristic solution to memory layout optimization approach. This previous approach [START_REF] Leung | Optimizing data locality by array restructuring[END_REF] is linear algebra based and can be summarized as follows. First, the loop nests in the program are ordered according to an importance criterion (e.g., time taken by each nest). After that, the heuristic approach processes each nest in turn, starting with the most important one (as determined by the previous step). For each loop nest being processed, it determines a good combination of loop transformation and memory layouts (for the arrays accessed by that nest). It then propagates these layouts to the second most important nest, and proceeds the same way as in the first nest except that it only determines the layouts of the arrays which are not accessed in the first nest (but accessed in the current one). In this way, it keeps propagating the memory layouts across the nests until all the layouts have been determined. Notice that, since the loop nests are ordered beforehand, this approach tends to give priority to satisfying the layout requirements of costly nests.

Our experiments have been performed using the SimpleScalar infrastructure [START_REF]SimpleScalar Simulator[END_REF].

Specifically, we modeled an embedded processor that can issue and execute two instructions in parallel. The machine configuration we use includes separate L1 instruction and data caches; each is an 8KB, 2-way set-associative with a line size of 32 bytes, and a unified 64KB L2 cache (4-way associative with a 64 bytes line size). The L1 and L2 latencies are 1 and 6 cycles respectively; and, the main memory latency is 70 cycles.

Table 2 gives the solution times for different optimized versions (in seconds) obtained on a 500MHz Sun Sparc architecture. The second, third and fourth columns give the solution times taken by the heuristic, base and enhanced schemes, respectively. We see that our base scheme takes much more time compared to the heuristic method. However, the enhanced scheme reduces these solution times dramatically, making them even comparable to those of the heuristic solution in two cases. Overall, we see that the solution times taken by our approaches are not excessive for an embedded system.

To explain how the enhanced scheme improves the solution times over the base scheme, we give in Figure 4 the percentage of reductions (in solution times) brought by each of the three enhancements discussed earlier in Section 4 (i.e., their individual contributions to the overall savings achieved by the enhanced scheme). The first enhancement is to do with the selection of the variable to instantiate next; the second one is related to the selection of the value to be assigned to the selected variable; and the last one is to employ backjumping instead of backtracking. We see the results from Figure 4 that, while most of the benefits come from backjumping, all three enhancements are very useful in general and contribute a lot to the overall reduction in solution times.

Table 3 gives the execution times for our benchmarks achieved by the original codes, heuristic approach and our constraint based approach. We see from these results that, while the heuristic solution improves over the original codes significantly (42.49% on average), the savings brought by the base and enhanced schemes are much larger: 57.17% and 57.95% on average respectively. The additional improvements are due to more comprehensive search space traversal implemented by the constraint network based approach. We also observe a small difference between the base and enhanced schemes. This difference is due to the fact that these two schemes can find "different solutions" if there are multiple solutions to the underlying network (as in the case of Med-Im04, Radar, and Track).

Conclusions and Future Directions

Recent years have witnessed, from both embedded system community and scientific computing community, a large number of studies targeting at improving data cache behavior of array based codes. Data transformations in particular have been found attractive as they do not have the drawbacks of commonly used loop transformations. This paper presents a novel constraint processing based approach to data transformations, where the problem of memory layout determination is captured as finding solutions in a constraint network. Our empirical analysis shows that the proposed approach is very effective in practice, and further enhancements are possible to expedite the search in the constraint graph.

We plan to extend this work in two directions. First, we would like to give weights to constraints. This will help us distinguish between different solutions to a given network. Second, we would like to expand our constraint network formulation to accommodate dynamic memory layouts, i.e., the layouts that can change during execution based on the requirements of the different segments of the program.

  (1 0) to denote row-major memory layout in a two-dimensional space. This is because two array elements d 1 = (d 11 d 12 ) T and d 2 = (d 21 d 22 ) T belong to the same row if and only if: (1 0) • (d 11 d 12 ) T = (1 0) • (d 21 d 22 ) T ; that is, if and only if d 11 = d 21 . In other words, as long as the two array elements have the same row index, they belong to the same hyperplane, which corresponds to a row in a two-dimensional array. Note that, while all the rows of the array have the same hyperplane vector, their hyperplane coefficients (c values) are different from each other (in fact, a hyperplane coefficient in this example corresponds to the row number). Figure 1(a) depicts such a row-major layout and shows hyperplanes explicitly. Figures 1(b) through 1(d), on the other hand, illustrate different memory layouts and give their hyperplane vectors. Let us briefly concentrate on the diagonal layout shown in Figure 1(c). In this layout, the two data elements d 1 = (d 11 d 12 ) T and d 2 = (d 21 d 22 ) T are stored in the same diagonal if and only if (1 -1) • (d 11 d 12 ) T = (1 -1) • (d 21 d 22 ) T , which means d 11 -d 12 = d 21 -d 22 . For example, (5 3) T and (7 5) T are stored in the same diagonal, whereas (5 3) T and (5 4) T are on two different diagonals. Note that, there are other possible diagonal layouts as well. For example, hyperplane vectors (1 -2) and (2 -1) also indicate diagonal layouts (which are different from (1 -1)

  1)}; M 3 ={(0 1), (1 1), (1 2)}; M 4 ={(1 0), (0 1), (1 1)}; S={S 12 ,S 13 ,S 14 ,S 23 ,S 24 ,S 34 }, where S 12 ={[(1 0), (1 1)], [(0 1), (1 -1)]} S 13 ={[(1 0), (0 1)], [(0 1), (1 1)], [(1 1), (1 2)]} S 14 ={[(1 0), (1 0)], [(0 1), (0 1)]} S 23 ={[(1 1), (0 1)], [(1 -1), (1 1)]} S 24 ={[(1 0), (0 1)], [(1 1), (1 0)]} S 34 ={[(0 1), (1 0)]}.

Figure 3 .

 3 Figure 3. (a) Backtracking. (b) Backjumping.

Figure 4 .

 4 Figure 4. Breakdown of benefits coming from the enhanced scheme.

Table 1 .

 1 Benchmark codes.

	Benchmark	Brief		Domain	Data Size
		Description	Size
	Med-Im04 medical image	258	825.55KB
		reconstruction
	MxM triple	matrix	34	1,173.56KB
		multiplication
	Radar radar imaging	422	905.28KB
	Shape pattern		656	1,284.06KB
		recognition and
		shape analysis
	Track visual tracking	388	744.80KB
		control

Table 2 . Solution times taken by different versions.

 2

	Benchmark Heuristic	Base	Enhanced
	Med-Im04 7.14sec	97.34sec	12.22sec
	MxM 5.18sec	36.62sec	9.24sec
	Radar 11.33sec	129.51sec	53.81sec
	Shape 16.52sec	197.17sec	82.06sec
	Track 10.09sec	155.02sec	68.50sec

Table 3 . Execution times achieved by different versions.

 3

	Benchmark Original	Heuristic	Base	Enhanced
	Med-Im04 204.27sec 128.14sec 82.55sec	81.07sec
	MxM 69.31sec	28.33sec	28.33sec	28.33sec
	Radar 192.44sec 110.78sec 83.92sec	85.15sec
	Shape 233.58sec 140.30sec 106.45sec 106.45sec
	Track 231.00sec 127.61sec 97.28sec	95.30sec

Proceedings of the Design, Automation and Test in Europe Conference and Exhibition (DATE'05) 1530-1591/05 $ 20.00 IEEE

The point multiplication of two vectors (x 1 x

x

… x k ) and (y 1 y 2 y 3 … y k ) T is x 1 y 1 +x 2 y 2 +x 3 y 3 +… +x k y k .

While one can claim that we could have used (2 -2) or other similar vectors as well instead of (1 -1), this would increase the resulting data space size as some elements of the transformed data space would not be used.