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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Czekaj, M. et al.: The Besancon Galaxy Model
Renewed I. Constraints on the Local Star Formation
History from Tycho Data. arXiv preprint
arXiv:</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Organization of Virtual Experiments in Data-Intensive Domains: Hypotheses and Workflow Specification</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>© Dmitry Kovalev</string-name>
          <email>dkovalev@ipiran.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>© Leonid Kalinichenko</string-name>
          <email>lkalinichenko@ipiran.ru</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Federal Research Center «Computer Science and Control» of Russian Academy of Sciences</institution>
          ,
          <addr-line>Moscow</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Proceedings of the XIX International Conference “Data Analytics and Management in Data Intensive Domains” (DAMDID/RCDL'2017)</institution>
          ,
          <addr-line>Moscow</addr-line>
          ,
          <country country="RU">Russia</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>1402</year>
      </pub-date>
      <volume>3257</volume>
      <fpage>293</fpage>
      <lpage>300</lpage>
      <abstract>
        <p>Organization and management of virtual experiments in data-intensive research has been widely studied in the several past years. Authors survey existing approaches to deal with virtual experiments and hypotheses, and analyze virtual experiment management in a real astronomy use-case. Requirements for a system to organize virtual experiments in data intensive domain have been gathered and overall structure and functionality for system running virtual experiments are presented. The relationships between hypotheses and models in virtual experiment are discussed. Authors also illustrate how to conceptually model virtual experiments and respective hypotheses and models in provided astronomy use-case. Potential benefits and drawbacks of such approach are discussed, including maintenance of experiment consistency and shrinkage of experiment space. Overall, infrastructure for managing virtual experiments is presented.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1 Introduction</title>
      <p>Data intensive research (DIR) is evolving according
to the 4th paradigm of scientific development and reflects
the fact that modern science is highly dependent on
knowledge extraction from massive datasets [5]. Data
intensive research is multidisciplinary in its nature,
bringing in many separate principles and techniques to
handle complex data analysis and management. Up to
80% of researcher’s time is spent on management of raw
and analytical data, including data collection, curation
and integration. The rest part requires knowledge
inference from collected data in order to test proposed
hypotheses, gather novel information and correctly
integrate it. Although, it is the core of scientific work, it
takes just 20% of researcher’s time. To overcome that, a
new approach for handling multidisciplinary DIR is
needed.</p>
      <p>Large-scale scientific experiments besides data
processing issues are highly sophisticated– they include
workflows, models and analytical methods. Every
implementation of DIR can be treated as virtual
experiment over massive collections of data. In [7] a
survey is presented discussing different approaches to
experiment modeling and how its core artifacts –
hypotheses, can be specified. The use of conceptual
representation of hypotheses and their corresponding
implementation is emphasized, thus leading to the need
of proper tools.</p>
      <p>The article aims at developing methods and tools to
support the execution and conceptual modeling of virtual
experiment and designing infrastructure to manage it.</p>
    </sec>
    <sec id="sec-2">
      <title>2 Related works</title>
      <p>Systems with explicit representation of hypotheses
are being rapidly developed during last several years [2–
4, 6, 10]. Authors analyzed 3 different systems for
executing virtual experiments and hypotheses:
Hephaestus, Upsilon-DB and SDI. Some requirements
for organizing and managing virtual experiments were
extracted during the analysis. Although these platforms
provide some important insights into defining and
handling hypotheses, they miss some important features.
First, they do not describe the perception of
automatically derived hypotheses by domain experts, do
not track their evolution, and do not discuss experiment
design principles.</p>
      <p>Hephaestus. It is a system for running virtual
experiments over existing collections of data. It provides
independence from resources and the system rewrites its
queries into data source queries. System hides underlying
implementation details from user, letting him work only
with Hephaestus language. The language itself is a
SQLlike language and is used to specify virtual experiment
and underlying hypotheses.</p>
      <p>Hephaestus separates two different classes of
hypotheses: top-down and bottom-up. Top-down
hypotheses are the one introduced by the researcher,
while bottom-up hypotheses are derived from data.
System supports the discovery of bottom-up hypotheses
by looking for the correlation in data. These hypotheses
are then ranked by some score (e. g. p-value of some
statistical test) and the one with highest are passed to the
researcher. Yet the system does not support automatical
finding of causality, which is an important requirement
for the future work. Hephaestus emphasizes the role of
the expert in understanding which relationships should
be further studied and which should not be chased.
Hephaestus also computes metrics about experiments to
estimate significance adequate to abandon further
computation. System is used in testing clinical trials. The
system does not catch the evolution of hypotheses or
experiments yet.</p>
      <p>Upsilon-DB. System enables researcher to code and
manage deterministic scientific hypotheses as uncertain
data. It uses internal database to form hypotheses as
relations and adds uncertainty parameter. Later, that
uncertainty parameter is used to rank hypotheses using
Bayes rule. Provided approach can be treated as
complementary to classical statistical approach. The
systems allows to work with two types of uncertainty
theoretical, which is brought by competing hypotheses,
and empirical uncertainty, which appears because of
alternative datasets used. The system introduces
algorithm to rank hypotheses using observed data. This
is done because several competing hypothesis can
explain the same observation well and some score to
distinguish them is needed. When new data becomes
available, this score can be adjusted accordingly.</p>
      <p>Hypotheses have mathematical representation and
authors provide method to translate its mathematical
representation into relations in database. The simulations
are also treated as data and respective relations are put
inside the same database as hypotheses. Authors
emphasize the need to support and develop the extraction
of hypotheses from data and methods to sample both
hypotheses and data. They illustrate that systems such as
Eureqa [8] can be used to learn formula representation
from data.</p>
      <p>Following example is presented in the paper: authors
present three different laws describing free fall and some
simulated data. They rank hypotheses accordingly.</p>
      <p>SDI. Platform is used to support scientific
experiments. The system has the ability to integrate open
data, reuse observed data and simulation data in the
further development of experiments. The system enables
multiple groups of researchers to access data and
experiments simultaneously. Components of the
framework are developed in such way that they could be
deployed, adapted and accessed in individual research
projects fast. SDI requires the support of lineage,
provenance, classification, indexing of experiments and
data, the whole cycle of obtaining data, curating and
cleaning it, building experiments to test hypotheses over
massive data, aggregating results is supported over long
periods of time. The use of semantics is required by the
system.</p>
    </sec>
    <sec id="sec-3">
      <title>3 Astronomical Use-case</title>
      <p>Surveyed systems do not cover several important
issues, including interaction between hypotheses in
single experiment, tracing experiment evolution,
perception of automatically derived hypotheses and
formulas by field experts.</p>
      <p>Authors’ further experience on how to deal with
virtual experiments and hypotheses is based on Besancon
Galaxy Model (BGM). BGM is based on “the population
synthesis approach … aims at assembling current
scenarios of galaxy formation and evolution, theories of
stellar formation and evolution, models of stellar
atmospheres and dynamical constraints, in order to make
a consistent picture explaining currently available
observations of different types (photometry, astrometry,
spectroscopy) at different wavelengths”.</p>
      <p>BGM which is being developed for more than 35
years represents a complex computational artifact,
described in a series of [1, 11, 12]and presented in several
major releases. Such a development represents a unique
experience for catching the evolution scenarios for the
model, changes to the model introduced both by using
new observations (e.g. Hypparcos and Tycho-2 surveys)
and the theoretical progress in the field. Both small
changes to parameters of the model and huge
improvements of the whole process were also made
during the lifetime of the model. Also, the BGM authors
enabled the community to change some parts of the
model.</p>
      <p>Due to the great experience collected by the BGM
authors in the respective articles and associated code,
now there is a possibility to collect the requirements for
the system to supports experiments and provide rationale
to choosing the appropriate methods and adequate
techniques for the infrastructure.</p>
      <p>BGM takes as input hypotheses and their parameters.
The examples of such hypotheses are star formation rate
(SFR), initial mass function (IMF), density laws,
evolutionary tracks and so on [1]. As the model is
evolving, new values for hypotheses parameters, even
new parameters have been introduced into the BGM, e.g.
for the IMF hypothesis in the last realization there has not
only been tests of several new values of the hypothesis,
but also separation of 2-slope and 3-slope instances of
IMF is done.</p>
      <p>It is very important to explicitly catch the relationship
between several hypotheses in VE. Hypotheses and their
parameters can be interrelated. For example, stellar
birthrate function is derived from both IMF and SFR
functions and local volume density function is based on
provided density law. The relationships between
hypotheses put constraints on the tuning of their
parameters – model can quickly become.</p>
      <p>Parameters of a single hypothesis can be linked to
each other directly through equations. There are also
indirect connections of parameters of several hypotheses,
e.g. SFR parameter correlates with the slopes of IMF.
This implies that one could not give the best solution for
a particular variable without correlating it with others.
So, there is a need to support for a correlation search
between hypotheses parameters and to store relationships
between parameters of a single hypothesis.</p>
      <p>Not all model ingredients are allowed to be changed
by the user. This is done because if some hypothesis is
changed in the model and no further adjustments for the
dependant hypotheses are made a model consistency is
broken. Furthermore, the model has a property of being
self-consistent meaning that when input values change,
if it is possible hypotheses derived by the one changed
are properly adjusted in order not to break fundamental
equations of astronomy. Therefore, derived by
relationship needs to be modeled. Also, system
component should enable the adjustment and calibration
of any hypothesis available in the model.</p>
      <p>AgeBins
DensityLaw</p>
      <p>SFR
IMF</p>
      <p>LocalVolume</p>
      <p>Density</p>
      <p>AgeVelocity</p>
      <p>Dispersion
StellarBirth Evolutionary</p>
      <p>Rate Tracks</p>
      <p>LocalLuminosity</p>
      <p>DynamicalSelf</p>
      <p>Consistency</p>
      <p>Apart from explicit hypotheses, there are also implicit
hypotheses in the model. They are not described in the
articles and are tacit. The example of such hypothesis is
that no stars come from outside of the Galaxy. It is
important to explicitly store such hypotheses and
understand how to extract such hypotheses from
publications and data sources.</p>
      <p>Workflow is used to implement BGM experiment
specifying when each model which conforms to related
hypotheses should be invoked. The workflow has also
evolved since the first version, e.g. for thin disk treatment
new activities dependent on IMF and SFR hypotheses are
introduced. This development can only be tracked using
publications. Some activities in model structure require
the usage of statistical methods, tests and tools, which are
used on both local hypotheses and on the general
simulations from the whole experiment.</p>
      <p>As the number of experiments is huge due to the
increasing size of competing hypotheses family, now not
all of the possible are run against the whole sky. Studying
the ways to reduce the number of experiments which give
the best fit and to choose when and if to abandon further
computations of experiment is a major part of
requirements to the new system. Using the information
from experiment run done both locally and by other
research groups can be helpful in achieving that goal.</p>
      <p>Some researches of data-intensive analysis
emphasize the role of error bars. As the data in astronomy
is provided usually with errors, the BGM uses special
methods to work with such type of uncertainty. A
component supporting statistical tools which works with
error bars is a major requirement for the infrastructure.
4 Hypotheses and Models in Virtual
Experiment</p>
      <sec id="sec-3-1">
        <title>4.1 Main Notions</title>
        <p>Extracted information needs to be formally
specified. For that, authors define additional artifact
– virtual experiment. It is a tuple &lt;O, H, M, R, W,
C&gt;, where O is a domain ontology. Domain
ontology is a set of concepts and relationships in
applied domain formally specified with some
language.</p>
        <p>H is a set of hypotheses specifications
and relationships between them. H is a part of ontology
and uses concepts from it. Together they form the
ontology of virtual experiment. Hypothesis is a
proposed explanation of a phenomenon that still
has to be rigorously tested.</p>
        <p>M is a set of models. Each model is a set of
functions. Every model implements a hypothesis
specification. If model generates expected
behavior of some phenomenon, it is said that
model and respective hypothesis are supported by
observations.</p>
        <p>R: H -&gt; M, is a mapping from the set of
hypotheses and into the models.</p>
        <p>W is a workflow. Workflow is a set of
tasks, orchestrated by specific constructs (workflow
patterns - split, join, etc.). Each task represents a
function with predefined signature, which invokes
models from M. Workflow implements experiment
specifying when each model that conforms to related
hypotheses should be invoked.</p>
        <p>C is a configuration for each experiment run.
It consists of a total mapping from workflow tasks into
sets of function parameter values.</p>
        <p>There exist a lot of possible
hypotheses representations – mathematical
models, Boolean networks, ontologies, predicates in
first-order logic, etc. Authors use ontologies to specify
hypotheses.</p>
        <p>Possible relationships between hypotheses
are competes_with, which is used to relate
competing hypotheses and derived_by to relate two
hypotheses, one of which was used to derive another.
Derived_bycan be used to form hypotheses lattice [9] –
algebraic structure with partial order relation.
Hypotheses derived from a single hypothesis are
atomic, otherwise – complex (see Fig. 1).</p>
        <p>Model, which implements hypothesis,
should conform to the hypothesis specification. If
model generates expected behavior of some
phenomenon, it is said that model and respective
hypothesis are supported by observations.</p>
      </sec>
      <sec id="sec-3-2">
        <title>4.2 Remarks on methodology</title>
        <p>Since hypotheses become the core artifact of
virtual experiment, there is a shift in treating data to
successfully manage it. Fig. 2 depicts the process of
specifying virtual experiment.</p>
        <p>First, hypotheses are extracted from articles. Usually,
it is text or formulas. Sometimes, there is a need to
provide external hypotheses and substitute existing ones.
Next step is to define mapping between hypotheses and
models, which implement these hypotheses, and build
some workflow specifying the sequence of tasks.
Forming a research lattice is a next step. Virtual
experiment needs configuration and execution plan.
After that, one can launch virtual experiment.</p>
        <sec id="sec-3-2-1">
          <title>Extract hypotheses from articles</title>
        </sec>
        <sec id="sec-3-2-2">
          <title>Define external hypotheses</title>
        </sec>
        <sec id="sec-3-2-3">
          <title>Define mapping between hypotheses and models</title>
        </sec>
        <sec id="sec-3-2-4">
          <title>Define workflow</title>
        </sec>
        <sec id="sec-3-2-5">
          <title>Build research lattice</title>
        </sec>
        <sec id="sec-3-2-6">
          <title>Define experiment configuration</title>
        </sec>
        <sec id="sec-3-2-7">
          <title>Build execution plan</title>
        </sec>
        <sec id="sec-3-2-8">
          <title>Configure statistical tests</title>
        </sec>
        <sec id="sec-3-2-9">
          <title>Run virtual experiment</title>
        </sec>
        <sec id="sec-3-2-10">
          <title>Use hypotheses cache</title>
        </sec>
      </sec>
      <sec id="sec-3-3">
        <title>4.3 Virtual Experiment Specification</title>
        <p>Conceptual schema to define virtual experimentis
provided. It is written with the simplified OWL
functional syntax (Declaration keyword is omitted;
property, domain, and range declarations are
combined).Virtual experiment (VirtualExperiment class)
has associated set of hypotheses, single workflow,
observed_data against which experiment will run and
probability, which describes how well underlying model
suits observed data. Closer probability is to 1, better the
underlying model simulates phenomenon.</p>
        <p>Ontology(&lt;http://synthesis.ipi.ac.ru/virtual_ex
periment/ontology&gt;
Class(VirtualExperiment)
ObjectProperty(Hypothesis
domain(VirtualExperiment) range(Hypothesis))
ObjectMinCardinality(1 Hypothesis</p>
        <p>VirtualExperiment)
DataProperty(workflow domain(VirtualExperiment)
range(xsd:anyURI))
DataMinCardinality(1 workflow</p>
        <p>VirtualExperiment)
DataProperty(mediatordomain(VirtualExperiment)
range(xsd:anyURI))
DataMinCardinality(1 mediator</p>
        <p>VirtualExperiment)
DataProperty(probability</p>
        <p>domain(VirtualExperiment)
range(xsd:float))</p>
        <p>DataExactCardinality(1 probability
VirtualExperiment))</p>
        <p>Hypothesis is specified in the same ontology as
virtual experiment. Every hypothesis has name,
description, author(s) and associated articles. It also has
a model associated with it. Following [4] associated
probability of hypothesis is introduced.</p>
        <p>Several hypotheses explaining one and the same
phenomena are called competing. Also hypothesis can be
derived by some other hypothesis. Hypotheses lattice is
formed with derived_by relationship on hypotheses
space.</p>
        <p>Class(Hypothesis)
DataProperty(probability domain(Hypothesis)
range(xsd:float))
DataExactCardinality(1probabilityHypothesis)
DataProperty(name domain(Hypothesis)</p>
        <p>range(xsd:string))
DataExactCardinality(1name
Hypothesis)
DataProperty(description domain(Hypothesis)
range(xsd:string))
DataMinCardinality(1descriptionHypothesis)
DataProperty(author
domain(Hypothesis)range(xsd:string))
DataMinCardinality(1authorHypothesis)
DataProperty(article domain(Hypothesis)
range(xsd:anyURI))
DataMinCardinality(1article
Hypothesis)
DataProperty(model domain(Hypothesis)
Hypothesis)
DataExactCardinality(1 model range(xsd:anyURI))
Class(HypothesisMetaClass)
ClassAssertion(HypothesisMetaClassHypothesis)
ObjectProperty(competes
domain(HypothesisMetaClass)
range(HypothesisMetaClass))
ObjectProperty(derivedBydomain(HypothesisMetaCl
ass)
range(HypothesisMetaClass))</p>
      </sec>
      <sec id="sec-3-4">
        <title>4.4 Hypotheses Specification</title>
        <p>Examples of hypotheses and their relationships come
from Besancon Galaxy Model (BGM). For the sake of
clarity not all hypotheses in BGM are specified. All of
the BGM hypotheses are treated as subclasses of
Hypothesis class.</p>
        <p>Initial Mass Function is the mass distribution of a
given population of stars and is represented by standard
power law. Due to construction of the hypothesis in the
BGMIMF has a mathematical representation as a
piecewise function with 2 or 3 pieces (slopes) where it is
defined for mass regions. As there are just 2 possible
sizes of the piecewise function, we put this into two
disjoint subclasses. There are restrictions on available
mass to Sol mass ratio. For IMF, authors test 10 different
versions of a hypothesis, 4 of them are 2-slope functions
and 6 of them are 3-slope function. All of tested
hypotheses are competing. Example instance from each
subclass is given.</p>
        <p>Class(Slope)
DataProperty(alpha domain(Slope)
range(xsd:float))
DataProperty(minMass domain(Slope)
range(xsd:float))
DataProperty(maxMass domain(Slope)
range(xsd:float))
DataExactCardinality(1 alpha Slope)
DataExactCardinality(1 minMassSlope)
DataExactCardinality(1 maxMassSlope)
SubClassOf(IMF Hypothesis)
ObjectProperty(Slopes domain(IMF) range(Slope))
DataProperty(availableMass domain(IMF)
range(xsd:float))
DataExactCardinality(1 availableMass IMF )
DataProperty(outputStarMass domain(IMF)
range(xsd:float))
DataExactCardinality(1 outputStarMass IMF )
SubClassOf(ThreeSlopeIMF IMF)
ObjectExactCardinality(3 Slopes ThreeSlopeIMF)
SubClassOf (TwoSlopeIMF IMF)
ObjectExactCardinality(2 Slopes TwoSlopeIMF )
DisjointClasses(TwoSlopeIMFThreeSlopeIMF)
ObjectPropertyAssertion(competes TwoSlopeIMF
IMF)
ObjectPropertyAssertion(competes ThreeSlopeIMF
IMF)
ClassAssertion(Slope HaywoodSlope1)
DataPropertyAssertion(alpha HaywoodSlope1
"1.7"^^xsd:float)
DataPropertyAssertion(minMass HaywoodSlope1
"0.09"^^xsd:float)
DataPropertyAssertion(maxMass HaywoodSlope1
"1.0"^^xsd:float)
ClassAssertion(Slope HaywoodSlope2)
DataPropertyAssertion(alpha HaywoodSlope2
"2.5"^^xsd:float)
DataPropertyAssertion(minMass HaywoodSlope2
"1.0"^^xsd:float)
DataPropertyAssertion(maxMass HaywoodSlope2
"3.0"^^xsd:float)
ClassAssertion(Slope HaywoodSlope3)
DataPropertyAssertion(alpha HaywoodSlope3
"3.0"^^xsd:float)
DataPropertyAssertion(minMass HaywoodSlope3
"3.0"^^xsd:float)
DataPropertyAssertion(maxMass HaywoodSlope3
"120.0"^^xsd:float)
ClassAssertion(ThreeSlopeIMFHaywoodIMF)</p>
        <p>ObjectPropertyAssertion(Slopes
HaywoodIMFHaywoodSlope1)
ObjectPropertyAssertion(Slopes HaywoodIMF
HaywoodSlope2)
ObjectPropertyAssertion(Slopes HaywoodIMF
HaywoodSlope3)</p>
        <p>Star Formation Rate, Ψ(t) represents the total mass of
stars born per unit time per unit mass of Galaxy. Star
formation rate has subclasses for representing constant
Ψ(t) = C and exponential function Ψ(t) = exp{-γt} where
γ is a parameter. Authors tested several competing
hypotheses - two possible values for gamma (0.12 and
0.25) and one constant value. They can be stated as
instances of respective classes.</p>
        <p>SubClassOf(SFR Hypothesis)
DataProperty(time domain(SFR) range(xsd:float))
DataExactCardinality(7 time SFR )
DataProperty(bornStarMass domain(SFR)</p>
        <p>range(xsd:float))
DataExactCardinality(7 bornStarMass SFR )
SubClassOf(ConstantSFR SFR)
DataProperty(constant domain(ConstantSFR)
range(xsd:float))
DataExactCardinality(1 constant )
SubClassOf(ExponentSFR SFR)
DataProperty(gamma domain(ExponentSFR)
range(xsd:float))
DataExactCardinality(1 gamma)
DisjointClasses(ExponentSFRConstantSFR)
ObjectPropertyAssertion(competes ConstantSFR
SFR)
ObjectPropertyAssertion(competes ExponentSFR
SFR)
ClassAssertion(ExponentSFRRobinSFR)
DataPropertyAssertion(gamma RobinSFR</p>
        <p>"0.12"^^xsd:float)</p>
        <p>BGM apart from model ingredients has also implicit
hypotheses, which are not marked as ingredients. For
example, 1) thin disk is divided into seven age bins; 2)
no stellar population comes from the outside of the
galaxy. For the first example we can specify additional
class AgeBins which has exactly seven age bins.
SubClassOf(AgeBins Hypothesis)
DataProperty(ageBin domain(AgeBins)
range(xsd:integer))
DataExactCardinality(7 ageBin AgeBins)</p>
        <p>It is more difficult to deal with the second one. As a
possible solution, additional hypothesis could later be
specified.</p>
        <p>Hypotheses lattice is modeled with derived Byobject
property. Some classes can be specified using Equivalent
Classes construction. Hypotheses lattice for BGM was
created manually, but later it should be constructed
automatically by system for executing experiments. (Part
of) hypotheses lattice for BGM is shown in Fig. 1.
ObjectPropertyAssertion(derivedBy SFR AgeBins)
ObjectPropertyAssertion(derivedByAgeVelocityDis
persionAgeBins)
ObjectPropertyAssertion(derivedBy SFR
LocalVolumeDensity)
ObjectPropertyAssertion(derivedByDensityLawLoca
lVolumeDensity)</p>
        <p>For IMF class and there are relations between slopes,
output Mass and available Mass. Based on available
Mass parameter alpha is chosen and then output Mass is
computed. If available Mass is inside the respective
interval, alpha is taken and output Mass is computed.
Next, post-condition for ExponentSFR is written. It says
that born stars should have mass respective to the
exponential equation. Other pre- and post-conditions are
specified in the same manner.</p>
        <p>Document(
Group(Forall ?IMF ?am ?s ?om ?a ?min ?max (
AND (?IMF[AvailableMass -&gt; ?am Slopes -&gt; ?s
outputStarMass -&gt;</p>
        <p>?om] ?s[alpha -&gt; ?a minMass -&gt; ?min
maxMass -&gt; ?max])
:</p>
        <p>AND (External(pred:numeric-greater-than(?am
External(func:numericmultiply(?mincon:solMass)))
External(pred:numeric-less-than(?am
External(func:numericmultiply(?max con:solMass))))
))))
Forall ?ExponentSFR ?g ?t ?m (
?ExponentSFR[Gamma -&gt; ?g Time-&gt;?t
BornStarMass&gt; ?m]:- AND(
External(pred:numeric-equal(?m
External(func:numeric-exponent(func:numericmultiply(
"-1.0"^^xsd:float?t)?g)))))))</p>
      </sec>
      <sec id="sec-3-5">
        <title>4.5 Workflow Specification</title>
        <p>The model of mass determination consists of a local
mass normalization, the simulation of the local
neighborhood and calculating vertical density
distribution. These tasks can be further divided into
several subtasks:
1. getRSVDensity. Relative density is calculated using
Einasto density law. After that for each population this
density ρ(r, l, b, i) is integrated in the vertical direction
ratio of surface to volume density (RSV) is computed.
2. getSurfaceDenisty. For each thin disk subcomponent
surface density is calculated and then summed.
Surface density of each age subcomponent has to be
proportional to the intensity of SFR in its respective
age bin.
3. getVolumeDensity. Volume stellar mass densities are
calculated and summed Total volume is checked to fit
the observations.
4. adjustSurfaceDensity. If the difference occurs surface</p>
        <p>and volume density are adjusted and recomputed.
5. getLNSimulations. Provided with specific hypotheses
(IMF, SFR, evolutionary tracks and so on) stars and
their parameters are simulated in the local
neighborhood.
6. getAliveStarsRemnants. Stars are splitted into alive
stars and remnants. Remnants -are possible stars for
which the age and mass combination was not on the
evolutionary tracks.
7. solvePotentialEquation. Poisson equation is solved
with the input of stellar content of thin disk.
8. constrainPotential. Calculated potential should be
constrained by observed Galactic rotation curve. The
central mass and corona parameters are computed in
such a way that the potential reproduces the observed
rotation curve.
9. calculatePotentialParameters. Based on the
calculated potential central mass parameters and
corona parameters are computed.
10. solveBoltzmannEquation. Boltzmann collisionless
equation for an isothermal and relaxed stellar
population is solved in order not to break
fundamentals of the model.
11. checkDynamicalConsistency. As equations in 6,7,8
are solved separately, the potential does not satisfy
both constraints. These tasks should be run until the
changes in the potential and other parameters are less
than 0.01.</p>
        <p>Workflow is specified as a RIF-PRD document. The
ontology for virtual experiment and BGM ontology are
imported. Rules in the document are separated into two
groups. The first group with priority 2 is used to define
workflow input and output parameters and variables. Part
of specification describes several hypotheses passed as
input parameters and calculated local surface density for
each age bin as output. GetLocalSurfaceDensity task is
specified in a group with priority 1. Task gets as input
SFR hypothesis and total surface density vector (initially
a guess) and multiplies provided values. Task checks if
Xor of dependent tasks is done.</p>
        <p>Document( Dialect(RIF-PRD)
Base(&lt;http://synthesis.ipi.ac.ru/virtualexperim
ent/workflow#&gt;)
Import(&lt;http://synthesis.ipi.ac.ru/virtualexper
iment/ontology#&gt;)
Import(&lt;http://synthesis.ipi.ac.ru/bgm/ontology
#&gt;)Prefix(bgm&lt;http://sy
nthesis.ipi.ac.ru/bgm/ontology#&gt;)
Prefix(ve&lt;http://synthesis.ipi.ac.ru/virtualexp
eriment/ontology#&gt;)
Group 2 (
Do(
Assert(External(wkfl:parameterdefinition(sfrbgm:SFRIN)))
Assert(External(wkfl:parameterdefinition(imfbgm:IMF IN)))
Assert(External(wkfl:parameter-definition(avd
Assert(External(wkfl:parameter-definition(dl
bgm:DensityLaw IN)))
Assert(External(wkfl:parameter-definition(et
bgm:EvolutionaryTracks IN)))
Assert(External(wkfl:variabledefinition(lsdsList(xsd:float)
IN)))
Assert(External(wkfl:variable-definition(clsds
List(xsd:float)</p>
        <p>OUT)))
Group 1 (
Do(
Assert(External(wkfl:variable-value(clsd
List())))
Forall ?sfr?bsm?lsd ?lsds ?clsd ?clsds such
that (
External(wkfl:variable-value(lsds ?lsds))
External(wkfl:variable-value(clsds ?clsds))
External(wkfl:variable-value(sfr ?sfr))
?lsd#?lsds
?clsd#?clsds
?sfr[bornStarMass -&gt; ?bsm]
(
IfOr(Not(External(wkfl:end-oftask(getRSVDensity)))
External(wkfl:end-oftask(adjustSurfaceDensity)) )
Then Do( Modify(?clsd
-&gt;External(func:numericmultiply(?bsm</p>
        <p>?lsd)) )
Assert(External(wkfl:end-oftask(getSurfaceDensity))) ))</p>
      </sec>
      <sec id="sec-3-6">
        <title>4.6 Choosing parameters of hypotheses for virtual experiment execution</title>
        <p>Since some hypotheses can take quite a few values,
the number of possible models can reach thousands. This
poses a question about the order of model execution and
how to make these executions effective (and not to
recompute previous unchanged results). For that we use
special structures to cache and store results. The system
can put model execution in some order and use the results
of previous executions. This could drastically increase
the speed of model computation, especially on big
amount of data. To implement this we use properties of
hypotheses lattices.</p>
        <p>The researcher can run several experiments finding
the probability of each, which can be later queried by
other researchers. For example, following query takes
two experiments, which have underlying models best
explaining observed data, and fixed values for hypothesis
SFR and workflow specified by URI. Since there could
be thousands of possible experiments, there is a need to
order them by their probability. As in [3] we don't want
the researched to bury in thousands of possible models
and just take several best ones.</p>
        <p>SELECT ?experiment
WHERE {
?experiment probability ?probability .
?experiment workflow ?workflow .
?experiment Hypothesis ?hypothesis .
?hypothesis name ?name .</p>
        <p>FILTER(?name = 'RobinSFR' &amp;&amp; ?workflow =
URI)
}
LIMIT 2
ORDER BY desc(?probability)
5 Requirements for Infrastructure for
Managing Virtual Experiments</p>
        <p>In a series of experiment run it is important to keep
track on evolution of models, hypotheses and
experiments, as well as identifying new data sources.</p>
        <p>Operations to manipulate virtual experiments and its
components need to be defined. Next, the system needs
to capture dependencies (competes, derived by) between
hypotheses, invariants in single hypothesis. Correlations
between parameters of several hypotheses should also be
considered.</p>
        <p>Second, infrastructure should contain components
responsible for automatic extraction of dependencies
between hypotheses, parameters in single and multiple
hypotheses. Obtained data is used in deciding which
experiments should be abandoned and also used in
keeping hypotheses in a single experiment consistent.</p>
        <p>Third, one needs components for maintaining
experiment consistency and constraining the number of
possible experiments as well as defining the metric which
is used to define if experiment poorly explains
phenomena and abandon further computations. Methods
for removing poor experiments based on previous
experiments runs are also required. Experiments and
hypotheses should stay consistent when parameters of a
hypotheses change.</p>
        <p>As soon as several hypotheses in some experiments
could explain some phenomena well and due to errors in
data, researcher needs to deal with uncertainty and needs
methods to rank experiments and competing hypotheses
on massive datasets.</p>
        <p>While experiment could change slightly from a
previous experiment run (e. g. one hypothesis parameter
changes), system should store some data about previous
executions. Methods for understanding which parts of
experiments should be recomputed and which are not
should be developed as well. Defining structures to
store results of previous experiments and query these
results is important. Since there could be thousands of
possible experiments system should use a method to form
a plan to execute experiments in such way that stored
results are mostly used and no additional recomputations
are made.</p>
        <p>Some stages will investigate and adopt or reject [2] Demchenko, Y. et al.: Addressing Big Data Issues in
certain values such as a velocity hypothesis, then Scientific Data Infrastructure. Collaboration
continue. The design of the paths to be followed is called Technologies and Systems (CTS), 2013 International
experimental design that as in the scientific method is the Conference on, pp. 48-55 (2013)
hardest part of the analysis. In principle, as in many [3] Duggan, J., Brodie, M.L.: Hephaestus: Data Reuse
systems, Hephaestus could pursue multiple paths in for Accelerating Scientific Discovery. (2015).
parallel using some metric to determine when to abandon [4] Gonçalves, B. et al.: Υ-DB: A system for Data-driven
a path. Some have criticized DeepDive and others for Hypothesis Management and Analytics. (Nov. 2014)
following a single path. [5] Hey, A.J. et al. eds.: The fourth paradigm:
data</p>
        <p>Reducing computational experiments (what we call intensive scientific discovery. Microsoft Research
virtual experiments), as mentioned above using metrics Redmond, WA (2009)
to estimate significance adequate to abandon further [6] Kalinichenko, L. et al.: Rule-based Multi-dialect
computation. Infrastructure for Conceptual Problem Solving over
Heterogeneous Distributed Information Resources.
6 Conclusion New Trends in Databases and Information Systems.
sscmpyoaserntecTeaimhfagiercisntaiaagftairnotvcdinticsrulteousoefafalcitmtehahxsesaeptdearraeteitpqmedpureerrmvnoeemitan.lcoeaHhpnt.iyitonspBngoaytrohaeafenenstxeaehstlwreyaazcrmiaentpeagdbpser.seocFxaomoicmsrhotmiidnnteaggoll [[87]] ISLRHKnpyeayfr,plopiirrnnoemgtishceeaDherntesi.ItcLinanssk.t-t,ieDaoLorn,nrindpisaLvstAeoo.iAonfnpn.,pHalReylictebPasrHuateiildb.ao.:l:rniDcs,Mhhy9inLen(aStge1hmua,)op,rpidncpppsaiop.nlr.a6gtS2n:1y8d-s6-At58eTS4moy(S2(oms2u0l.s0rb1Jv1o3.ef5l)ooiy)crf.
from BGM is presented in the OWL syntax. Machine Learning Research.,13, pp. 3585-3618, Dec</p>
        <p>Further work should be concentrated on developing (2012)
metasystem for handling hypotheses, models and other [9] Porto, F. et al.: A Scientific Hypothesis Conceptual
metadata in virtual experiment. Model. Advances in Conceptual Modeling, pp.
101Acknowledgments 110. Springer (2012)
[10] Porto, F., Schulze, B.: Data Management for</p>
        <p>This research was partially supported by the eScience in Brazil. Concurrency and Computation:
Russian Foundation for Basic Research (projects 15-29- Practice and Experience, 25 (16), pp. 2307-2309
06045, 16-07-01028). (2013)
[11] Robin, A., Crézé, M.: Stellar Populations in the Milky
References Way-A Synthetic Model. Astronomy and
Astrophysics, 157, pp. 71-90 (1986)
[12] Robin, A.C. et al.: A Synthetic View on Structure and</p>
        <p>Evolution of the Milky Way. Astronomy &amp;
Astrophysics, 409 (2), pp. 523-540. (2003)</p>
      </sec>
    </sec>
  </body>
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