Benoit Combès

Anne Philippe
email: anne.philippe@univ-nantes.fr

Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating

Keywords: optically stimulated luminescence, chronometric dating, Bayesian analysis

Many dating techniques include significant error terms which are not independent between samples to date. This is typically the case in Optically Stimulated Luminescence (OSL) dating where the conversion from characteristic equivalent doses to the corresponding ages using the annual dosimetry data includes error terms that are common to all produced datings. Dealing with these errors is essential to estimate ages from a set of datings

whose chronological ordering is known. In this work, we propose and we study a Bayesian model to address this problem. For this purpose, we first consider a multivariate model with multiplicative Gaussian errors in a Bayesian framework. This model relates a set of characteristic equivalent doses to the corresponding ages while taking into account for the systematic and non-systematic errors associated to the dosimetry. It thus offers the opportunity to deal properly with stratigraphic constraints within OSL datings, but also with other datings possessing errors which are independent from systematic errors of OSL (e.g. radiocarbon). Then, we use this model to extend an existing Bayesian model for the assessment of characteristic equivalent doses from Single Aliquot and Regenerative (SAR) dose measurements. The overall Bayesian model leads to the joint estimation of all the variables (which include all the dose-response functions and characteristic equivalent doses) of a sequence of, possibly heterogeneous, datings. We also consider a more generic solution consisting in using directly the age model from a set of characteristic equivalent dose

Introduction

Ordering (or stratigraphic) constraints between samples to date constitute an essential element to build accurate and coherent chronologies. Such a prior information, typically modeled in a Bayesian setting [START_REF] Buck | Combining archaeological and radiocarbon information: a Bayesian approach to calibration[END_REF], consists of a basic element of several dedicated softwares e.g. OxCal [START_REF] Ramsey | Bayesian analysis of radiocarbon dates[END_REF], BCal [START_REF] Buck | Bcal : an on-line Bayesian radiocarbon calibration tool[END_REF] or Chronomodel [START_REF] Ph | Chronomodel : Chronological modelling of archaeological data using Bayesian statistics[END_REF][START_REF] Vibet | Chronomodel v1.5 user's manual[END_REF]. The associated models are typically designed to deal with datings associated to additive and independent errors, as it is the case for e.g. radiocarbon or archaeomagnetic datings. However, paleodosimetric datings do not fit such a frame and, to the best of our knowledge, there is still a lack of generic methods to incorporate them in analyses. Paleodosimetric dating methods [START_REF] Taylor | Chronometric Dating in Archaeology[END_REF] rely on the assessment of a characteristic equivalent dose D expressing the total absorbed radiation dose since last resetting event (e.g. last exposure to sunlight or heat) of the studied samples. Then, this characteristic equivalent dose can be converted into an age A using the annual dose-rate ḋ associated to the environment surrounding the studied sample. Given a characteristic equivalent dose estimate D and its standard error σ D , the common procedure to perform this conversion consists in [START_REF] Taylor | An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements[END_REF]:

1. summarizing the distribution of the annual dose-rate ḋ with a mean µ ḋ and standard error σ ḋ using combination rules, 2. approximating the point estimate and standard error for the associated age defined by the ratio A = D ḋ using the following quadrature formula:

 = D µ ḋ and σ A =  σ D D 2 + σ ḋ µ ḋ 2 . (1)
This solution has two main limitations:

A. it provides only a coarse characterization of the statistics of A, B. it does not permit to include additional information as ordering constraints between ages of a given stratigraphic sequence to improve the estimations. Moreover in practice, the dose-rate standard error σ ḋi for each dating i includes components that are common to all the datings (i.e. not independent), making existing models to deal with stratigraphic constraints inadequate.

To overcome these two limitations several solutions have been investigated. Rhodes et al. [START_REF] Rhodes | Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from old scatness broch excavations, shetland isles[END_REF] proposed to tackle limitation B by inferring the age according to Eq. 1 and then by simply ignoring the systematic part of the uncertainty in the analysis of the stratigraphic constraints (using the software Oxcal) [START_REF] Ramsey | Radiocarbon calibration and analysis of stratigraphy: the oxcal program[END_REF]. Finally, they used an external criterion to check the coherency of the inference. While pragmatic, this solution does not result in a consistent assessment of uncertainties on ages. Huntriss [START_REF] Huntriss | A Bayesian analysis of luminescence dating[END_REF] proposed to tackle limitation A by the following procedure. Two independent samples are generated according to the distributions of D and ḋ (assumed to be known). Then their ratio term by term is computed and the resulting sample, distributed according to the distribution of the age A = D/ ḋ, is used to estimate all needed statistics on A (e.g. mean, standard deviation, confidence interval). As we will see it, when the distribution for the annual dosimetry is Gaussian (which is nearly the case), our approach extends this one while dealing with limitation B.

Finally, Millard [START_REF] Millard | Bayesian analysis of ESR dates, with application to Border Cave[END_REF] designed a solution to tackle the two limitations. For that purpose, he proposed to model the dosimetry data through a likelihood structure: a latent variable is assigned to each quantity needed for the computation of the dose-rates, these latents (which are typically numerous) relate to observations through Gaussian distributions and to ages through characteristic equivalent doses. Priors are assigned to each latent and the posterior ages are estimated using a Markov Chain Monte Carlo method. The main drawback of this approach is that each dating laboratory may have its own complex protocol to estimate the dose-rate ḋi and for each of these protocols one needs to build a dedicated model that must be implemented, validated (particularly with respect to the choice of the associated priors) and made available to the community. In practice, these factors limit the practical impact of such an approach. Moreover, modeling the dosimetry data using observations can be problematic as some parts of the observations and of their associated uncertainties are not strictly speaking associated to observations but rather to expert information (e.g.

uncertainty on the water content). Similarly, the systematic component included in the error terms induces a dependence between observations and the associated Bayesian model is, in most cases, not identifiable. Thus the dosimetry data could be considered as a component of the prior structure of the dating model rather than observations. Notice however that for implementation facilities, Millard proposed then to recast the likelihood dependencies into priors (and similarly in a companion article [START_REF] Millard | Bayesian analysis of pleistocene chronometric methods[END_REF]).

In This simple model will be then considered in a multidimensional setting where a part of the dosimetry error is possibly common to several datings (Section 2.2) and where some datings can be constrained to be in a given order (Section 2.3). From that basis, we then consider two situations involving optically stimulated luminescence (OSL) datings [START_REF] Aitken | Introduction to Optical Dating : The Dating of Quaternary Sediments by the Use of Photon-stimulated Luminescence[END_REF][START_REF] Wintle | A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols[END_REF]. In a first setting, we consider that we have the raw OSL measurements at our disposal. We thus propose a model consisting in the addition of the age model derived in the previous sections to the Bayesian model, we developed in another paper [START_REF] Combès | A Bayesian central equivalent dose model for optically stimulated luminescence dating[END_REF], that infers a characteristic equivalent dose D from Single Aliquot and Regenerative (SAR) dose measurements (Section 3.1). In a second setting, we consider that we only have the output characteristic equivalent doses and their standard errors at our disposal. We thus directly consider their conversions to ages (Section 3.2). Then, we give an application of these two models to infer a chronology from a set of luminescence measurements of five OSL samples with stratigraphic constraints (Section 4). Finally, we summarize our contributions and recommendations (Section 5).

Age to equivalent dose relationship: multiplicative Gaussian error

Hereafter N (µ, σ 2 ) denotes the Gaussian distribution with mean µ and variance σ 2 .

Individual age model

Once the characteristic equivalent dose D is assessed, the age of the studied sediment since last resetting (corresponding to exposure to light) can be obtained by dividing D by the mean annual dose-rate ḋ. However in practice, ḋ is only known with an uncertainty aggregating many sources of errors due to measurements, calibrations and a low level of awareness of some characteristics of the deposit environment. As a result, even with a precise assessment of the characteristic equivalent dose D, the estimated age may be associated to a significant uncertainty. Formally, the relationship between the characteristic equivalent dose and the corresponding characteristic age A is handled by the following multiplicative gaussian error model:

D = A( ḋ + ), (2)
where is a Gaussian variable ∼ N (0, σ 2 ḋ ). It results in the following conditional distribution of D given A:

D ∼ N (A • ḋ, A 2 • σ 2 ḋ ). (3)
We are interested in estimating the age A > 0 from the observed characteristic equivalent dose D, and the dose-rate data ḋ and σ ḋ. One can show that the Jeffreys prior for A is

p(A) ∝ 1 A I [0,+∞[ (A). ( 4
)
where I is the indicator function i.e. for a set S, I S (x) = 1 if x ∈ S and 0 else. This is a particular case of the prior obtained in Appendix A.1. The prior is improper but the resulting posterior is proper for D = 0:

P (A|D) ∝ 1 A 2 exp(- (A ḋ -D) 2 2A 2 σ 2 ḋ )I [0,+∞[ (A), (5)
Note that even if A is not a scale parameter for the model defined in Eq. 3, the prior on A is the same as the Jeffreys prior for scale parameter. It is also important to note that if we choose the improper prior π(A) ∝ I [0,+∞[ (A), that is the Jeffreys' prior for a location parameter, then the posterior distribution is not defined. Moreover, A is not a location parameter and assigning it to an uniform prior has no objective justification.

Interestingly, the posterior distribution of A defined in Eq. 5 coincides with the distribution of the ratio D/d where D = 0 is fixed and where d is a truncated Gaussian random

variable d ∼ N ( ḋ, σ 2 ḋ ) • I ]0;∞[ (where I ]0;∞[ indicates that the density is truncated on ]0; ∞[).
To check this fact, we simply apply the change of variables formula. Let φ be the density

of the variable d, φ(d) ∝ exp(-(d -ḋ) 2 /(2σ 2 ḋ ))I ]0;∞[ (d)
, then the density of the variable

A = D/d on IR + is p(A) = | ∂ ∂A (D/A)|φ(D/A) = D/A 2 φ(D/A) ∝ D/(A 2 σ ḋ) exp(- ( ḋ -D/A) 2 2σ 2 ḋ ) ∝ 1 A 2 exp(- (A ḋ -D) 2 2A 2 σ 2 ḋ ),
which coincides with the distribution given by Eq. 5. So in this specific case, characterizing

A consists in simulating D/d with d ∼ N ( ḋ, σ 2 ḋ ) • I ]0;∞[
As mentioned in the introduction, this simulation based solution has been investigated in a previous work on OSL datings [START_REF] Huntriss | A Bayesian analysis of luminescence dating[END_REF].

Note that in practice, the domain of validity of A is limited to a particular period of the history (often called the study period) [a min , a max ] with 0 < a min < a max . This information can modeled by modifying the prior as follows:

p(A) ∝ 1 A I [a min ,amax] (A). ( 6
)
Notice that bounding the support of the prior is motivated by the application, but is also needed to ensure the existence of the posterior moments. In the following synthetic experiments, we fix values for a min and a max such that they largely contain the ages of interest: the true ages are chosen in the interval [100; 200] while [a min ; a max ] is set to [1; 400].

Figure 1 shows how the posterior is modified as a function of σ ḋ. Particularly, when σ ḋ increases the distribution becomes more asymmetric so that its mode is shifted toward the left while its mean is shifted toward the right. This points out the problem of summary statistics for skewed distributions. The median is favored in this context, because it is invariant by reparametrization (e.g. logarithmic transformation). In a Bayesian context, this question is less crucial since the inference is based on credible regions, as the highest posterior density (HPD) regions, which take into account asymmetry. This also emphasizes the potential error committed using Eq. 1. In practice, the overlap between the 95% HPD intervals and the corresponding usual intervals [ Â -1.96σ A , Â + 1.96σ A ] (as get using Eq.

1) is in average of 97%, 95%, 91% and 88% for the different levels σ ḋ = 0.05, 0.1, 0.15, 0.2.

Multivariate model : sequence of ages

Let then consider the model for N ages indexed as A i , i = 1, . . . , N . For this purpose, we need to explicit the content of σ ḋ. In practice, the dose-rate is estimated as combinations of physical quantities that are known with an uncertainty. A part of this uncertainty is specific to the measured sample (e.g. counting errors due to the spectrometer) and another -the systematic error-is related to the measurement device and is common to all datings of the studied sequence (e.g. error on the calibration of the measurements device). Without loss of generality, we will consider in the following a simple case composed of these two sources of error (a more sophisticated instantiation leading to structurally the same model will be considered in Section 4):

D i = A i • ḋi + A i • ḋ,i + A i • α i • ḋ,c (7)
where

ḋ,i ∼ N (0, σ 2 ḋ,i ) is the individual error for sample i, ḋ,c ∼ N (0, σ 2 ḋ,c
) is the systematic error and α i > 0 is known and gives, for each dating i, the degree of contamination to the systematic error. Assuming that the noise terms ḋ,c and ḋ,i (for all i) are independent, the

conditional distribution of (D 1 , • • • , D N ) given (A 1 , • • • , A N ) can be written as a Gaussian vector with mean (A 1 ḋ1 , • • • , A N ḋN ) and covariance matrix Σ : (D 1 , • • • , D N ) ∼ N ((A 1 ḋ1 , • • • , A N ḋN ), Σ), (8)
where the covariance matrix Σ depends on A 1 , • • • , A N and writes:

for i = 1, . . . , N Σ i,i = A 2 i (σ 2 ḋ,i + α 2 i σ 2 ḋ,c ), (9)
and for i = j,

Σ i,j = A i A j α i α j σ 2 ḋ,c . (10)
This covariance matrix is positive definite as long as at least N of the variances

(σ 2 d,i ) i=1,N and σ 2 d,c
are not equal to zero (assuming that the α i are strictly positive). An example of derivation of a matrix Σ from a practical situation is discussed in Section 4.1 and described in Appendix B.

Again, the Jeffreys prior for (A 1 , • • • , A N ) writes:

P (A 1 , • • • , A N ) ∝ N i=1 1 A i I [a min ;amax] (A i ) ( 11
)
The proof is relegated in Appendix A.1. This choice of prior leads to the following posterior distribution:

P (A 1 , • • • , A N |D 1 , • • • , D N ) ∝ P (D 1 , • • • , D N |A 1 , • • • , A N )P (A 1 , • • • , A N ), (12)
that will be characterized using a Metropolis-within-Gibbs sampler [START_REF] Roberts | Examples of adaptive MCMC[END_REF].

Figure 2 shows how the inference on the same age A 1 is modified when N , the number of ages in the sequence, increases. Obviously, the studied model is different from the one in which the inferences on the ages are independent from each others. However, it is satisfactory to observe that the marginal posteriors for a given age are stable when N increases. We fix for all i σ ḋ,i = α i σ ḋ,c = 0.1 and the ḋi are randomly draw from a U (0.5, 1.5).

Sequence of ages with ordering constraints

In practice, the previous model is of few interest as none of the datings A i interacts directly with the others. Consequently the resulting inference is not so different from what we obtain from a set independent inferences. In this section, we consider the informative case where one knows that the ages are stratigraphically constrained i.e. they (or some of them) are in a known chronological order. This case can be implemented by adding a support constraint for the vector A 1 , • • • , A N into its prior [START_REF] Buck | Bayesian Approach to Intrepreting Archaeological Data[END_REF]. For that purpose, we consider B, the set of N -tuples satisfying the imposed stratigraphy (that can be incompletely stated i.e. some of the ages can be not fully ordered) and state:

p(A 1 , • • • , A N ) ∝ N i=1 1 A i I B (A 1 , • • • , A N ), (13)
where

I B (A 1 , • • • , A N ) = 1 if (A 1 , • • • , A N ) ∈ B and 0 else.
Moreover, it is possible to allow some of the datings of the sequence not to be affected by the systematic errors (or by different systematic terms). In practice, this situation typically happens when some of the datings are performed by different laboratories making the errors on the assessment of the dose-rates ḋi independent from each others or when some other unrelated dating methods (e.g. radiocarbon dating) are used. Here for a sake of simplicity, we will consider the first case. In practice, it implies to set to zero the covariance terms of Σ relating two ages/dosimetries being estimated by two different laboratories.

Let first consider the case where there is no systematic-error free dating. In the experiments displayed in Figures 3 and4, we used σ d,i = 0.1, α i σ d,c = 0.1 and (d i ) i randomly draw from a U (0.5, 1.5). Figure 3 shows how the error of estimation for a given age is modified when the number of stratigraphically constrained ages increases. Particularly, one observes that the mean and the variance errors decrease slowly with the number of observations. This observation is related to the systematic error term that cannot be inferred without additional information. Figure 4 shows typical posteriors on a given age with an increasing number of stratigraphically constrained ages.

Let then consider the effect of systematic-error free datings. In the experiments displayed in Figures 5 and6, we consider three settings: in the first one, we consider five datings without any stratigraphic constraints, all affected by the systematic error term. In the second one, we consider the same five datings with stratigraphic constraints (again, all affected by the systematic error term). In the third one, we consider that two of them are not affected by the systematic-error term (while keeping the same overall variance level).

Figure 5 shows how the error of estimation for a given age is modified for these different settings. Particularly, one observes that whereas the number of datings is the same in all cases and whereas the overall uncertainty level is similar, the estimation error is, as expected, highly reduced when adding independent datings. Figure 6 shows typical pos-

Two models for OSL dating

In this section, we consider the prior we developed in the previous section as a component of a full optically stimulated luminescence (OSL) dating model (Section 3.1). Then, we consider a two-steps approach consisting in assessing the posterior ages

(A 1 , • • • , A N )
from characteristic equivalent doses estimates and their standard errors ( Di , σ D,i ) that are computed separately (Section 3.2).

Full model

The model presented in this section is the combination of the age model developed below and of a model for the estimation of characteristic equivalent doses

(D 1 , • • • , D N )
from normalized luminescence observations (denoted as (N k,j i ) i,j,k , (σ N k,j i ) i,j,k ) presented elsewhere [START_REF] Combès | A Bayesian central equivalent dose model for optically stimulated luminescence dating[END_REF]. In practice, it simply consists in adding the prior structure

P (D 1 , • • • , D N |A 1 , • • • , A N )P (A 1 , • • • , A N )
as defined in Eq. 8 and 13 to the marginal model

P (D 1 , • • • , D N |(N k,j i ) i,j,k , (σ N k,j i ) i,j,k ).
The directed acyclic graph (DAG) representing the overall 4-stages hierarchical model is given in Figure 7. Notations are introduced in the caption (see the corresponding paper [START_REF] Combès | A Bayesian central equivalent dose model for optically stimulated luminescence dating[END_REF] for more details, the notations have been a bit recast for simplicity). For a sake of completeness, we also recall here the corresponding posterior distribution (removing the exogenous parameters ḋlab , t k,j i , ḋi , σ ḋ,i , σ ḋ,c , α i from the notations for a sake of simplicity):

P (A 1 , • • • , A N , D 1 , • • • , D N , (σ D i ) i , (D 1,j i ) i,j , (σ j f,i ) i,j , (θ j i ) i,j , (Q k,j i ) i,j,k |(N k,j i ) i,j,k , (σ N k,j i ) i,j,k ) ∝ i,k,j P (N k,j i |Q k,j i , σ N k,j i ) × i,k,j P (Q k,j i |σ j f,i , θ j i , D 1,j i ) i,j P (D 1,j i |D i , σ D,i )P (σ D,i |D i )P (σ j f,i )P (θ j i ) × P (D 1 , • • • , D N |A 1 , • • • , A N )P (A 1 , • • • , A N ),
with the age model

P (D 1 , • • • , D N |A 1 , • • • , A N )P (A 1 , • • • , A N )
as defined in Eq. 8 and 13.

The other densities (discussed in our previous paper) write:

P (N k,j i |Q k,j i , σ N k,j i ) ∝ exp - (N k,j i -Q k,j i ) 2 2σ 2 N k,j i P (Q k,j i |σ j f,i , θ j i , D 1,j i ) ∝ 1 √ 2πσ j f,i exp - (f θ j i (D k,j i ) -Q k,j i ) 2 2σ j f,i 2 , with D k,j i = t k,j i • ḋlab for k ≥ 2 P (σ j f,i ) ∝ e -20σ j f,i I IR + (σ f,i ), P (θ j i = [u j i , v j i , w j i , x j i ]) ∝ exp( (u j i -6.5) 2 170 )I IR + (u j ) exp( (v j i -50) 2 10 6 )I IR + (v j ) exp( (w j i -0.002) 2 0.0002 )I IR + (w j ) exp( (z j i -0.5) 2 12.5 )I [-u j ,∞[ (z j ), P (D 1,j i |D i , σ D,i ) ∝ σ D i (D 1,j i -D i ) 2 + σ 2 D i , P (σ D,i |D i ) = 0.16D i σ 2 D,i + (0.16D i ) 2 I IR + (σ D,i ).
The inference is then performed using a Metropolis-within-Gibbs sampler. In particular, we can provide estimates for the ages A 1 , • • • , A N from the normalized luminescence measurements (N k,j i ) i,j,k , their associated standard deviations (σ N k,j i ) i,j,k and the dosimetry data ḋi , σ ḋ,i , σ ḋ,c and α i . Some results will be discussed in Section 4.

Two-steps model

In this section, we consider that we want to infer a set of ages from a set of characteristic equivalent doses estimates Di , their associated standard errors σ D,i , the dose-rate estimates and standard errors and a set of stratigraphic constraints. This situation typically arises when the chronological scenario is built using several pool of datings published by other research groups. In such a case, the high-level results (such as the Di , σ D,i ) are commonly given in the corresponding publications but most of the times the raw luminescence data are not available. Moreover, such an approach allows users of other non-Bayesian approaches to estimate the Di , σ D,i (see [START_REF] Galbraith | Optical dating of single and multiple grains of quartz from jinmium rock shelter, northern australia: Part 1, experimental design and statistical models[END_REF][START_REF] Duller | Assessing the error on equivalent dose estimates derived from single aliquot regenerative dose measurements[END_REF]) to account properly for ordering constraints on their data.

A 1 , • • • , A N i = 1 to N ḋlab k = 2 to K j = 1 to J ḋi σ ḋ,i , α i , σ ḋ,c D i σ D,i D 1,j i Q 1,j i N 1,j i σ N 1,j i natural signal θ j i σ j f,i D k,j i t k,j i k = 1 Q k,j i N k,j i σ N k,j i

Individual age model

As for the previous model, the ages are related to the true characteristic equivalent doses D i through:

D i = A i ḋi + A i ḋ,i , (14)
which are themselves related to the inferred/measured characteristic equivalent dose Di by:

Di = D i + D,i , (15)
where ḋ,i ∼ N (0, σ 2 ḋ,i ) and D,i ∼ N (0, σ 2 D,i ) (σ D,i being the standard error associated to Di ) are independent. This results in:

Di |A i ∼ N (A i • ḋi , A 2 i • σ 2 ḋ,i + σ 2 D,i ). ( 16
)
For this specific model, we obtain the Jeffreys prior (proof in Appendix A.2):

p(A i ) ∝ A 2 i (2σ 4 ḋ,i + ḋ2 i σ 2 ḋ,i ) + σ 2 D,i ḋ2 i (A 2 i σ 2 ḋ,i + σ 2 D,i ) 2
for 0 < a min < A i < a max and 0 else. [START_REF] Taylor | An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements[END_REF] When σ D,i = 0, the graph of this function is equivalent (up to a multiplicative constant) to the one of

A i → 1/A i . When σ 2 D,i > 2σ 2
ḋ,i (which will be the case for our application), the graph is strictly decreasing.

Multidimensional model : sequence of ages

In this section, we consider a multidimensional extension of the model presented below analogously to what we performed in Section 2. For that purpose, we modified Eq. 14 as

D i = A i ḋi + A i ḋ,i + A i α i ḋ,c , (18)
where

ḋ,i ∼ N (0, σ 2 ḋ,i ), D,i ∼ N (0, σ 2 D,i ) and ḋ,c ∼ N (0, σ 2 ḋ,c
) are independent and where α i > 0 known gives, for each dating i, the degree of contamination to the systematic error. This results in:

D1 , • • • DN |A 1 , • • • , A N ∼ N ((A i • ḋi ) i , Σ + I σ 2 D,i ), ( 19
)
where I σ 2 D,i is the diagonal matrix such that I i,i = σ 2 D,i and Σ built as in Eq. 9 and 10. Then to be consistent with Eq. 17, we set the prior:

P (A 1 , • • • , A N ) ∝ N i=1 A 2 i (2(σ 2 ḋ,i + α 2 i σ 2 ḋ,c ) 2 + ḋ2 i (σ 2 ḋ,i + α 2 i σ 2 ḋ,c )) + σ 2 D,i ḋ2 i (A 2 i (σ 2 ḋ,i + α 2 i σ 2 ḋ,c ) + σ 2 D,i ) 2 I B (A 1 , • • • , A N ), (20)
we can then write the posterior:

P (A 1 , • • • , A N | D1 , • • • DN ) ∝ P ( D1 , • • • DN |A 1 , • • • , A N )P (A 1 , • • • , A N ), (21)
that can be characterized using a Metropolis-within-Gibbs sampler. In particular, we can provide estimates for the ages A 1 , • • • , A N from a set of inferred/measured characteristic equivalent doses Di , their associated standard errors σ D,i and the dosimetry data ḋi , σ ḋ,i , σ ḋ,c and α i . Some results will be discussed in Section 4.

Application

In this section, we first present a set of real measurements associated to five OSL samples stratigraphically constrained [START_REF] Tribolo | OSL and TL dating of the middle stone age sequence at diepkloof rock shelter (South Africa): a clarification[END_REF]. Then, we use the two methods presented in Section 3.1 and 3.2 to process these measurements.

Data and parameters

The five studied sediments respectively called OSL1, OSL4, OSL6, OSL7 and OSL8 (we kept the names given in the original publication) have been sampled from a sedimentary pile corresponding to the Middle Stone Age. This leads to the following upper and lower bound for the ages: a min = 25 ka and a max = 280 ka. The stratigraphy imposes the ages to be ordered such that

A 1 ≥ A 4 ≥ A 6 ≥ A 7 ≥ A 8 .
Details on the measurements protocol can be found in the original paper [START_REF] Tribolo | OSL and TL dating of the middle stone age sequence at diepkloof rock shelter (South Africa): a clarification[END_REF]. In the following, we focus on the way the dose-rate ḋi is characterized for this specific example. The dose-rate ḋi is considered as the sum of its β, γ and cosmic components (the α component is supposed to be negligible):

ḋi = ḋβ,i + ḋγ,i + ḋcos,i (22)
In practice, these three quantities are estimated through the combination of several physical quantities that are themselves not completely known. More specifically, for each sample i, one assesses values for the uranium, thorium and potassium contents U i , T h i and K i , the gamma radiation component γ i , the cosmic radiation component cos i , the saturation uptake content W i and the fraction of average water content F i . These six quantities are subject to systematic and independent errors (that are detailed in Appendix B). The corresponding error model relating these quantities to the total dose-rate ḋi is then linearized to get a sum of zero-mean gaussian error terms that fully define the covariance matrix Σ involved in our multivariate equivalent dose to age model (Eq. 8, 9 and 10). The resulting values for the studied sediments are given in Table 1. The derivation needed to get them are close to the ones used in practice to get µ ḋ and σ ḋ in the standard approach (Eq. 1) and are detailed in Appendix B. Another source of uncertainty that is commonly considered to estimate an age from an equivalent dose is the uncertainty on the laboratory source used for administering the regenerative and test doses. This source is only known with a calibration error of known standard error σ lab (which, considering that all the samples have been processed using the same experimental device, is a systematic term). The associated error is often called a percent error and impacts D i as a percentage of itself [START_REF] Aitken | Introduction to Optical Dating : The Dating of Quaternary Sediments by the Use of Photon-stimulated Luminescence[END_REF]. A convenient way to take into account for this supplemental source of uncertainty consists in simply modifying the covariance matrix as:

Σ i,i = A 2 i (σ 2 ḋ,i + α 2 i σ 2 ḋ,c + ḋ2 i σ 2 lab ),
for i = j, Σ i,j = A i A j (α i α j σ 2 ḋ,c + ḋi ḋj σ 2 lab ).

Here we set σ lab = 0.05.

Results

Preliminary

In this section, we study the full model of Section 3.1 without the stratigraphic constraints between the five samples. As for the simple model of Section 2.2, without constraint, we expect the age model not to affect the overall inference and particularly the posteriors on the characteristic equivalent doses D i . Figure 8

Comparison of the approaches

Figure 9 displays the posterior for each age of the sequence with and without imposing the stratigraphic constraints. Table 2 gives a summary of the inferences obtained using the full-model and the two-steps model (using the characteristic equivalent dose posteriors as inputs) when considering the five data-sets together or when studying them one by one (i.e. without the stratigraphic constraints). The ages obtained in the original publication [START_REF] Tribolo | OSL and TL dating of the middle stone age sequence at diepkloof rock shelter (South Africa): a clarification[END_REF] with a classical approach are also given. First, note that the estimated equivalent doses and ages (without the stratigraphic constraints) are notably higher than those obtained in the original publication. This point is not related to the age model and has been already noticed and analyzed on a set of controlled data [START_REF] Guérin | Testing the accuracy of a bayesian central-dose model for single-grain osl, using known-age samples[END_REF] where characteristic equivalent doses obtained using the Bayesian approach [START_REF] Combès | A Bayesian central equivalent dose model for optically stimulated luminescence dating[END_REF] have been observed to be more consistent with associated external datings than those obtained using a standard approach. Secondly, the results of the comparison can be summarized as:

• the ages have been made internally consistent with the stratigraphy,

• the posterior standard deviation is slightly reduced when using the stratigraphic constraints,

• the full and the two-steps models give similar inferences for the ages.

This last point is an interesting result suggesting that the two-steps method can be used with confidence when the OSL measurement data are not available.

Conclusion

In this work, we considered a multivariate model with multiplicative Gaussian error in a

Bayesian framework. This model was then used as a key component of OSL dating models from normalized luminescence data or from characteristic equivalent dose estimates. As mentioned in introduction, such a multiplicative model is not specific to OSL but related to any paleo-dosimetric dating method (e.g. Thermo-luminescence (TL), Electron Spin Resonance (ESR), Infrared stimulated luminescence (IRSL) datings) and we hope this work will be also useful to these approaches. Notice that interestingly, based on a more intuitive reasoning than the derivation we provide here, the use of the 1/A prior has already been evoked by Millard [START_REF] Millard | Bayesian analysis of pleistocene chronometric methods[END_REF] in a general discussion about prior distributions for ages and dates in chronometric modeling.

The two proposed dating models were then applied to a simple real dataset to illustrate the interest of including stratigraphic constraints when available. The inferences given by the full and the two-steps approaches are similar on this example. This is a positive result suggesting that the two-steps method can be used when the measurement data are not available. Notice that the dataset we used is unfortunately free of external dating allowing to correct the systematic components of the error. Datasets including such external datings (e.g. [START_REF] Rhodes | Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from old scatness broch excavations, shetland isles[END_REF]) would benefit greatly from these models. The two-steps model and the full model will be made available in a dedicated software to allow users to incorporate OSL datings in addition to other datings to build chronologies and to explore deeply their differences.

To our opinion, the main limitation of our approach consists on the assumption of gaussianity of the distributions associated to the dosimetry errors. While there is, strictly speaking, no reason to assume a gaussian shape for the dosimetry error, we think that this limitation is in practice a minor point. First, one can visualize the true error model on the dosimetry errors by simulation and then check that a gaussian shape is a good approximation (which has been observed to be the case [START_REF] Huntriss | A Bayesian analysis of luminescence dating[END_REF][START_REF] Zink | A coarse Bayesian approach to evaluate luminescence ages[END_REF] and which is, in most cases, performed in the standard approach). Second, one must remind here that some error terms involved in the dose rate estimation are not well characterized and that in practice, only coarse (and generally highly conservative [START_REF] Rhodes | Bayesian methods applied to the interpretation of multiple OSL dates: high precision sediment ages from old scatness broch excavations, shetland isles[END_REF]) estimations are available. After integration, we obtain

E[ ∂ 2 lf ∂ 2 w |w] i,j =      -1 w i w j [Σ -1 i,j (Σ i,j + α i α j )], if i = j -1 w 2 i [Σ -1 i,i (Σ i,i + α 2 i ) + 1], if i = j. (A.1)
Then,

I(w) = -det(E[ ∂ 2 lf ∂w 2 |w]) = det(d( 1 w i ) • C • d( 1 w i )) ∝ N i=1 1 w 2 i , (A.2)
where C is a N × N matrix with only positive entries and that does not depend from w.

Finally, one gets the density in θ by : • Measuring the U, Th, K and γ components of the dosimetry is subject to systematic percentage errors U,c , T h,c , K,c and γ,c of same variance σ 2 d,c related to the calibration of the measurement device (typically σ d,c = 0.1) .

• The assessment of the product W i F i is subject to an uncertainty modeled by a zeromean gaussian noise W F,i of given standard deviation σ W F,i which is independent across samples.

Other sources of errors are considered as negligible.

The equations relating all these quantities to the β, γ and cosmic dosimetries are the following [START_REF] Aitken | Introduction to Optical Dating : The Dating of Quaternary Sediments by the Use of Photon-stimulated Luminescence[END_REF]:

∀i ∈ [|1, N |], ḋβ,i = 1 1 + ψ β (W i F i + W F,i ) F β,U S β,U (U i + U,i )(1 + U,c ) + (B.2) F β,T h S β,T h (T h i + T h,i )(1 + T h,c ) + F β,K S β,K (K i + K,i )(1 + K,c )
where ψ β is the absorption of the β radiation by water, F β,U , F β,T h and F β,K are the β attenuation coefficients, S β,U , S β,T h and S β,K are the specific beta dose rates, ḋγ,i = (γ i + γ,i )(1 + γ,c )

1 + ψ γ W c i F c i 1 + ψ γ (W i F i + W F,i ) (B.3)
where ψ γ is the absorption of the γ radiation by water and W c i and F c i are respectively the saturation water uptake and the fractional average water at time of sampling, ḋcos,i = cos i + cos,i .

(B.4)

The noise terms U,c , T h,c , K,c and γ,c are common to the N equations. Similarly to the common practice to compute ḋ and its associated standard error, one then considers all error terms as independent and linearizes the previous error models to get the following age to characteristic equivalent-dose model:

∀i ∈ [1, N ], D i = A i ( ḋi + ḋ,i + α i ḋ,c ) with ḋi = 1 1 + ψ β W i F i (r U U i + r T h T h i + r K K i ) 1 + ψ γ W c i F c i 1 + ψ γ W i F i γ i + cos i (B.5)
calling r U = F β,U S β,U , r T h = F β,T h S β,T h and r K = F β,K S β,K and ḋ,i ∼ N (0, σ 2 ḋ,i ) with:

σ 2 ḋ,i = r 2 U σ 2 i,U + r 2 T h σ 2 i,T h + r 2 K σ 2 i,K (1 + ψ β W i F ) 2 + (1 + ψ γ W c i F c i ) 2 σ 2 i,γ (1 + ψ γ W i F i ) 2 + (B.6) σ 2 W i F i ψ β (1 + ψ β W i F i ) 2 (F β,U S β,U U i + F β,T h S β,T h T h i + F β,K S β,K K i ) + (B.7) γ i ψ γ (1 + ψ γ W i F i ) 2 (1 + W c i F c i ) 2 +σ 2 cos,i (B.8)
and

α 2 ḋ,i = F 2 β,U S 2 β,U U 2 i + F 2 β,T h S 2 β,T h T h 2 i + F 2 β,K S 2 β,K K 2 i (1 + ψ β W i F i ) 2 + ((1 + ψ γ W c i F c i )γ i ) 2 (1 + ψ γ W i F i ) 2 , (B.9)
which completely defines the covariance matrix Σ.

Figure 1 :

 1 Figure 1: Posterior distribution of A for σ ḋ = 0.05, 0.1, 0.15, 0.2 with ḋ = 1. The vertical line represents the true value of D/ ḋ.

Figure 2 :

 2 Figure 2: Posterior distribution for the age A 1 when the number of ages in the sequence increases (N = 1, 5, 10, 20). We fix for all i σ ḋ,i = α i σ ḋ,c = 0.1 and the ḋi are randomly draw from a

Figure 3 :Figure 4 :

 34 Figure 3: Box plots of the estimation error for a given age when the number of ages in the sequence increases (N = 1, 5, 10, 20) over a set of 100 realizations. From left to right, statistics on the 100 experiments for 1, 5, 10 and 20 stratigraphically constrained ages.

Figure 5 :Figure 6 :

 56 Figure 5: Box plots of the estimation error on the same age A 3 from a set of 100 realizations. From left to right, statistics on the 100 experiments for 5 ages no stratigraphically constrained, 5 stratigraphically constrained ages and 5 stratigraphically constrained ages whose two are free of systematic error.

Figure 7 :

 7 Figure 7: Directed acyclic graph (DAG) of the inference model. Sequence level: The vector of ages A 1 , • • • , A N is related to the vector of characteristic equivalent doses D 1 , • • • , D N by the age model taking into account for the different kinds of uncertainties on the dosimetry. Sample i level: For each sample i, the characteristic equivalent dose D i and dispersion σ D,i are common to all aliquots of the sample. Aliquot j level: Each aliquot j is associated with a natural dose D 1,j i , a set of regenerative dose D k,j i (k ≥ 2) and

Figure 8 :

 8 Figure 8: Marginalized posterior densities for the age A 1 (left) and for the characteristic equivalent dose D 1 (right) without stratigraphic constraint. The black curves are the posteriors estimated using a single age and the red ones are the posteriors estimated using the five ages (without stratigraphic constraint). The characteristic equivalent dose obtained when considering only the characteristic equivalent dose model is displayed in blue.

By denoting w

  the vector composed of [1/θ 1 , . . . , 1/θ N ], one can write the log-density as:d(y)Σ -1 d(y)w) + α T Σ -1 d(y)w,The Hessian matrix of the log-density lf equals:∂ 2 lf (y) ∂ 2 w = -d(y)Σ -1 d(y) -d([

p

  Θ (θ) ∝ p W ([1/θ 1 , . . . , 1/θ N ])

Table 1 :

 1 Summary of the quantities defining Σ for the five studied samples.

	18

  displays the posterior distribution for a given age when using one and five ages (left side) and for a given characteristic equivalent dose when using no age model, the age model with one age and the age model with the five ages (right side). One can observe that, as for the non-hierarchical model, the age and equivalent dose posteriors remain sensibly unchanged.

								0.06
		0.03				full sequence (5 samples) only sample 1	0.05						(5 samples) full sequence only sample 1 no age model
								0.04
	Density	0.02					Density	0.03
		0.01						0.02
								0.01
		0.00						0.00
		80	100	120	140	160	180	100	110	120	130	140	150	160	170

Table 2 :

 2 However this conclusion is related to the fact that the equivalent doses are estimated by the same Bayesian model in both situations. If the data ( Di , σ D,i ) i are estimated using an other equivalent dose model (e.g. the minimal age model or the finite mixture model), we cannot expect both our full model and two-step model to match well. The two-step model will be strongly affected by the quality of data ( Di σ D,i ) i , depending on the choice of the estimate. ± 7.78 102.79 ± 8.32 117.38 ± 10.14 110.68 ± 9.09 118.86 ± 11.01 two-steps 88.19 ± 7.82 102.03 ± 8.22 117.92 ± 10.07 110.86 ± 9.24 119.67 ± 11.05 Four first lines: Posterior means and standard deviations for the five ages for the full

	ages(ka)	100 120 140 160 180 200
		80
		60
	Figure 9: Violin plots from the marginalized posterior densities for the ages with stratigraphic
	constraints (blue) and without (red).

and the two-steps model with and without the stratigraphic constraints. Last line: Estimates as given in

[START_REF] Tribolo | OSL and TL dating of the middle stone age sequence at diepkloof rock shelter (South Africa): a clarification[END_REF]

.

Acknowledgments

The authors thank Guillaume Guérin, Chantal Tribolo and Norbert Mercier for introducing them the problem and providing and discussing the data of Section 4.

Using the fact that d(θ) is diagonal, a few algebra leads to rewrite the conditional density as:

where

and The likelihood function can be write of the form

so this model constitutes an exponential family of dimension 2. The log density is:

and

Finally,

and we obtain:

When setting σ = 0, one recovers p(θ) ∝ 1 |θ| .

Appendix B. Building the covariances

In this section, we show how to build the covariance matrix for a specific real example.

Notice that the assumptions of independence involved in this particular example are not restrictive: all the quantities involved in the dosimetric data (that can be more numerous than in this particular example) can be composed of any numbers of independent and not independent error terms (as long as they remain gaussian).

As performed in the original publication of the studied data-set [START_REF] Tribolo | OSL and TL dating of the middle stone age sequence at diepkloof rock shelter (South Africa): a clarification[END_REF], we consider here the dose-rate ḋi as the sum of its β, γ and cosmic components (the α component is supposed to be negligible):

In practice, these three quantities are estimated through the combination of several physical quantities that are themselves not completely known. More specifically, for each sample i, one assesses values for the uranium, thorium and potassium contents U i , T h i and K i , the gamma radiation component γ i , the cosmic radiation component cos i , the saturation uptake content W i and the fraction of average water content F i . These six quantities are subject to the following errors:

• Measuring each of the U i , T h i , K i , γ and cosmic components of the dosimetry is subject to a zero-mean gaussian noise. Noises are independent between measurements.

The corresponding standard deviations are known and called respectively, for each sample i, σ U,i , σ T h,i , σ K,i and σ cos,i .


Ammlan Ghosh
email: ammlan.ghosh@gmail.com

Anubhab Sahin
email: anubhab.s@hotmail.com

Anirban Silsarma
email: anirban.silsarma@gmail.com

Rituparna Chaki
email: rchaki@ieee.org

A New Contention Management Technique for Obstruction Free Transactional Memory

Keywords: Software Transactional Memory (STM), Obstruction-free Transactional Memory (OFTM), Contention Management, Concurrency

Transactional Memory, one of the most viable alternatives to lock based concurrent systems, was explored by the researchers for practically implementing parallel processing. The goal was that threads will run parallel and improve system performance, but the effect of their execution will be linear. In STM, the non-blocking synchronization can be implemented by Wait-Freedom, Lock-Freedom or Obstruction-Freedom philosophy. Though Obstruction Free Transactional Memory (OFTM) provides the weakest progress guarantee, this paper concentrates upon OFTM because of its design flexibility and algorithmic simplifications. In this paper, the major challenges faced by two state of the art OFTMs viz. Dynamic Software Transactional Memory (DSTM) and Adaptive Software Transactional Memory (ASTM), have been addressed and an alternative arbitration strategy has been proposed that reduces the abort percentage both in case of Read-Write as well as Write-Write conflicts.

Introduction

Developing systems with multiple threads that can execute concurrently is no more a notion, but a reality. And in the current era, it is more of a necessity to utilize the full capacity of multi-core processors. Improvement of performance within a single core becomes essential to utilize the computational power provided by chip level multiprocessing. Locking has been an in-vogue technique used by the programmers for writing parallel programs. Lock based synchronization, however, leads to a number of unwanted situations like occurrence of deadlocks, priority inversion of processes and complication of fine-grained locking.

Concept of transactional memory addresses these issues and provides a promising alternative to lock based synchronization. The idea is to allow concurrent execution of transactions maintaining atomicity, consistency and isolation (ACI property) of each, i.e. threads will run parallel and improve system performance, but the effect of their execution will appear linear. Unlike database transactions, transactional memory instructions are meant to be short span transactions that access a relatively smaller number of memory locations [START_REF] Harris | Transactional Memory 2 nd Ed[END_REF]. Transactional Memory systems can be purely hardware based (Hardware based Transactional Memory or HTM) [START_REF] Herlihy | Transactional memory: architectural support for lockfree data structures[END_REF], software-only (Software Transactional Memory or STM) [START_REF] Shavit | Software transactional memory[END_REF] or hybrid. Naturally, the level of flexibility in STM over modification and integration is maximum. In STM, the fundamental operations i.e. the processes of acquiring and releasing ownership of concurrent objects (shared memory locations) are done atomically by non-blocking synchronization techniques using design primitives LL/SC (Load Linked Store Conditional) [START_REF] Virendra | Using LL/SC to simplify word-based software transactional memory (poster)[END_REF] and CAS (Compare and Swap) [START_REF] Virendra | Using LL/SC to simplify word-based software transactional memory (poster)[END_REF][START_REF] Guerraoui | On Obstruction-Free Transactions[END_REF][START_REF] Herlihy | Wait-free synchronization[END_REF]. The key advantages are low space complexity and reduced performance overhead. These atomic operations are widely supported by multi-core processors.

The non-blocking implementations of STM systems have been mostly designed on the basis of either Lock-Freedom or Obstruction-Freedom philosophy. An STM system is lock free if some transactions are guaranteed to commit in a finite number of steps [START_REF] Virendra | A Qualitative Survey of Modern Software Transactional Memory Systems[END_REF]. Although Lock-Freedom often delivers exceptional results, there is a question mark over the correctness of semantics in these algorithms. An STM system is obstruction free if every transaction is guaranteed to commit in absence of contention. Obstruction freedom provides the weakest progress guarantee and also admits the possibility of livelocks. Still obstruction freedom has been the preferred choice of many as it substantially reduces the implementation complications i.e. codes are simple, flexible and depending upon the design, can considerably improve parallelism and scalability of a system with many cores.

In 2003, Herlihy et al. constructed one of the earliest obstruction-free STM systems called DSTM [START_REF] Herlihy | Software Transactional Memory for Dynamic-sized Data Structures[END_REF] to support dynamic sized data structures. Since then several OFTMs have been proposed including ASTM [START_REF] Marathe | Adaptive software transactional memory[END_REF], RSTM [START_REF] Marathe | The Rochester software transactional memory runtime[END_REF] and NZTM [START_REF] Tabba | NZTM: non-blocking zero-indirection transactional memory[END_REF], with considerable differences in their respective system designs. The researchers were mainly interested in improving the throughput and minimizing the computational overhead of transaction processing.

In this paper, some major challenges faced by two state of the art OFTMs viz. DSTM and ASTM, have been addressed and an alternative negotiation strategy has been proposed. Unlike the existing OFTM systems, the proposed method allows multiple Read-Only transactions to share data object concurrently along with Write transactions. When a Write transaction reaches its commit point it checks the maturity of the all active read-only transactions and decides which of them are allowed to be committed. The proposed algorithm also presents a new contention management policy to resolve conflicts between Write transactions. Section 2 describes some existing works, followed by section 3 which presents the proposed algorithm; section 4 evaluates the performance of the algorithm; finally we conclude and discuss future scope in section 5.

Background

The STM uses primitive atomic operations like and LL/SC (load-link and storeconditional) [START_REF] Virendra | Using LL/SC to simplify word-based software transactional memory (poster)[END_REF] and CAS (Compare and Swap) [START_REF] Guerraoui | On Obstruction-Free Transactions[END_REF] for implementing read, write, commit and abort statements. Load-link and store-conditional are a pair of instructions used together in multithreading to achieve synchronization. Load-link returns the current value of a memory location and a subsequent store-conditional will store a new value if no updates are made in that location meanwhile. CAS is used to read from a particular memory location and to write back the modified value in the same location after ensuring that the location has not been altered in between. Of late a slightly sophisticated version viz. DCAS (Double-word Compare and Swap) [START_REF] Attiya | The power of DCAS: highly-concurrent software transactional memory[END_REF] has been used in some STMs, which basically executes two CAS operations simultaneously. These primitive atomic operations are used to guarantee that consistency of the system is not hampered during an update. The common performance metrics for the various STM systems have been (i) Conflict Management, (ii) Transaction Granularity and (iii) Number of Basic Operations. In obstruction free environment, when a conflict occurs among two or more transactions (of which at least one is a Write transaction) over a particular resource, the management policy of the concerned system will determine which transaction(s) will progress and which will abort. This conflict management strategy of an OFTM is determined by the contention manager. The performance of an OFTM depends largely upon the efficiency of the contention manager [START_REF] Scherer | Advanced contention management for dynamic software transactional memory[END_REF]. Granularity is considered as the smallest data store memory unit that can be possessed by a transaction for its Read/Write operations. The authors have discussed two well known OFTM implementations viz. DSTM [START_REF] Herlihy | Software Transactional Memory for Dynamic-sized Data Structures[END_REF] and ASTM [START_REF] Marathe | Adaptive software transactional memory[END_REF] as the proposed methodology has been influenced by these implementations.

DSTM

Herlihy et al. proposed one of the earliest obstruction-free STM (OFTM) systems

called DSTM [START_REF] Herlihy | Software Transactional Memory for Dynamic-sized Data Structures[END_REF] to support dynamic sized data structures. The highlight of this system was assurance of progress in practice with the introduction of a modular contention manager, thus removing the single biggest drawback of OFTM. In DSTM, the TM-Object (Figure 1) points to a locator object with three pointers: pointer 1 points to the descriptor of the most recent transaction that held the object; pointers 2 and 3 point to the old and new versions of the data object. When a transaction successfully commits, the new version of the data object is made permanent. On the other hand, when a transaction is aborted by other transaction, the old version of the data object is read by the aborting transaction before its execution. Concepts of early release and visible/invisible reads were also coined by the DSTM developers, which have been applied in various forms in the latter STM designs. The idea of early release is that a transaction may release an opened object before committing. This sometimes proves really beneficial in case of data structures like trees. The read visibility helps to avoid unnecessary contention between Read only transactions. In this scheme, each transaction maintains a separate Read-list of the objects that have been opened by Read only transactions. Before commit, a Write transaction checks the Read-list to resolve the contention. The read visibility yields a large performance benefit, especially in read-dominated work load, due to its easy read-object validation.

Herlihy et al. [START_REF] Herlihy | Software Transactional Memory for Dynamic-sized Data Structures[END_REF] proposed two basic contention managers viz. Aggressive Manager and Polite Manager. An Aggressive Manager directly aborts the conflicting transaction(s) whereas Polite Manager uses exponential back-off to acquire ownership of the TM-Object.

ASTM

Adaptive Software Transactional Memory (ASTM) [START_REF] Marathe | Adaptive software transactional memory[END_REF] used the structures of DSTM along with a modified conflict management scheme to overcome the loopholes of DSTM. ASTM offered adaptive methodology to adjust the workload. A transaction acquires an object in two ways. In eager acquire methodology a transaction acquires the objects at the beginning, where as in lazy acquire scheme a transaction acquires objects at commit time. Eager acquire method allows a transaction to detect contention earlier and helps to ensure consistency. Naturally eager-ASTM works better in write dominated workload while lazy-ASTM works better in read dominated workload. The flip side is that it increases the overhead of the system because of the adaptive nature of acquire methodology.

Initially ASTM did not introduce any new manager, but shortly ASTM-2 [START_REF] Frank | Adaptive Software Transactional Memory: A Dynamic Approach to Contention Management[END_REF] was released with Adaptive Contention Management Policies. The Adaptive Contention Manager uses the idea of machine learning motivated by behaviorist psychology, i.e. from previous experience a manager decides how to take action in a particular environment so as to maximize transaction throughput. ASTM2 includes a number of contention managers viz. Karma Manager, Eruption Manager and Greedy Manager. Karma Manager gives absolute priority to the transaction that has done more work. Eruption Manager is based on the principle that the more number of transactions a particular transaction is blocking, the higher priority the blocker transaction should have. Finally Greedy Manager does not abort the conflicting transaction unless it has a lower priority or is currently waiting for another transaction; otherwise it aborts the running transaction.

For Write transactions (acquired state), the TM-Object points to a locator with similar structure as that of DSTM. But by default the TM-Object points to the data objects (unacquired state). So when a Read transaction follows a Write transaction, the former suffers indirection overhead, not only for acquiring the ownership of the TM-Object but also for the extra CAS for changing the direction of the pointer from locator to data. Analysis of this STM system over simulated test cases also verifies this finding; as expected, in workloads dominated by either read or write operations, ASTM gives excellent performance. But in case of a uniformly mixed set of Reads and Writes, the throughput degrades drastically.

The above STM systems use object granularity where there is no need to change the original object structure for converting a normal program to a transactional one. Object granularity also perfectly suits object oriented programming style.

Both in case of ASTM and DSTM, a transaction that opens n objects in write mode requires n CASes to acquire the objects and an additional CAS to commit which makes a total of n+1 CASes. But the cost might increase manifold in ASTM as the subsequent readers might perform up to n CASes to return the objects to unacquired state [START_REF] Virendra | A Qualitative Survey of Modern Software Transactional Memory Systems[END_REF].

Proposed scheme of arbitration over a resource between two or more competing transactions

From the above inductive analysis we observe two major challenges common to both DSTM and ASTM: (i) Considerably high number of aborts, and (ii) The complexity involved in implementing modular contention management policy leads to a higher computational overhead

The frequent roll-backs of write transactions hamper the transactional processing greatly as normally write transactions execute longer than read-only transactions. The loss proves much costlier when a lengthy write transaction gets aborted by a much smaller write because of the rigidity of the concerned contention management policy. Also modular contention management schemes discussed above requires imparting intelligence in the software system such that based on the workload pattern the system can decide for itself which contention manager to use in a particular situation. Keeping these two major challenges in mind, this paper proposes a generic conflict management strategy aiming at reducing the abort percentage. The technique is based on the use of a single contention manager for all types of workload patterns. The proposed method uses lazy conflict detection scheme for both read-only as well as write transactions. In a bid to avoid spurious aborts for read-only transactions, a list of 'matured' read transactions (on the basis of their execution time) is maintained. When a write transaction tries to commit, it checks this list and backs-off to give a chance to these read-only transactions to commit. When a transaction detects conflicts, it either backs-off for certain time to give chance to the conflicting transactions or aborts conflicting transactions or aborts itself. The decision is taken after consulting the contention manager, in order to achieve synchronization in a non-blocking manner.

TM-Object structure in proposed OFTM

The proposed OFTM maintains the TM Object structure (Figure 2) similar to that of DSTM. Additionally, this TMObject has a pointer to the write transaction's Q_RdrLst, a list of qualified read-only transaction, on the basis of which a write transaction decides its back-off policy. Also for log file storage a descriptor is maintained by every transaction that stores the transaction metadata. The descriptor remains in the thread local storage (TLS) and is created right at the beginning, i.e. during thread initialization. The underlying assumption is that work done by a transaction is roughly an increasing linear function of its total execution time. The following is an exhaustive list of term definitions used to describe the functioning of the system.

t µ

W : mean time taken by the CPU to finish a write transaction. t µ R : mean commit time of a read-only transaction. #T s w : number of committed write transactions whose execution time is less than or equal to t µ w . ∑ n i=1 T i R/W : set of all transactions that initiate and commit within time span 't'. #T w : total number of committed write transactions. t i : total time for which a transaction T i R/W has executed, as calculated at that particular time instant. T i R/W may be in active/aborted/committed state. RdrLst: all active read-only transactions are stored in this list.

T i

w .Q_RdrLst ⊂ RdrLst: Qualified Reader List is a 2-tuple {j, Init j R } list corresponding to write transaction T i w , which is the set of all active read-only transactions that started before T i w 's try_commit point.  j: Identity of the read-only transaction  Init j R : timestamp at the initiation of T j

R

We have categorized the active Write transactions in terms of their total time of execution as maturity_level = LO and maturity_level = HI. Reverse ratio has been assumed while defining t w max because experimental results reveal that the number of committed write transactions which execute for less than 't µ w ' time is considerably greater than #Tw/2.

Random generation of threads

We can visualize the system threads that use a particular object (say O) in the form of the following function, i = {(Rand(x) Mod #T n ) + 1} This function gives a very good virtualization of random order acquisition of an object by different transactions (For e.g. T i can be T 5 , T 33 , T 17 , etc.).

But if all the threads are independent, i.e. they do not share any common object, each will commit on reaching its try_commit point without bothering the others. This, however is a trivial case and is very unlikely to happen in practical systems.

Checking before Write commit

Before a write transaction commits, the system basically performs the following: it checks if any read-only transaction(s) is holding an old version of the same object; next it verifies if the maturity_level of the try_commit write transaction is LO; if the outcome of this second check is affirmative, it performs the final check, i.e. if the transaction under consideration is forcing another write transaction with maturity_level = HI to roll back. From the outcome of this threefold checking, it effectively makes way for most read-only transactions (if not all) to commit and also saves any lengthy write transaction which would have been sacrificed otherwise. The value of back-off time t b is environment dependent and might vary from one workload set to another. This is shown in the Figure 3a and3b. Table 1 compares two wellknown OFTMs i.e. DSTM and ASTM with the proposed one, by characterizing some important designing parameters.

Metric of evaluation

There are various parameters of evaluating the performance of an STM system. One fundamental approach is by measuring the percentage of committed transactions.

Performance Summary:

The simulation results on the three different workload sets reveal that performance of the proposed algorithm is always better than performance of both these managers in case of read-write conflicts. This is because of the sensible back-off performed by the contention manager whenever there is a contention between a read transaction and a write transaction. Also it is found that performance of the proposed manager with respect to the others improves significantly with decrease in the domination of reads in the workload. From the graphs, it can be concluded that though the proposed manager performs slightly better than Karma manager, but it surpasses the commit percentage of Aggressive Manager by miles over all workloads. By a non-weighted average across all the four test cases, our manager achieves a flat betterment of 36.85% over the performance of Aggressive Manager and 4.34% over that of Karma Manager.

Conclusion and Future Scope

The proposed OFTM aims at reducing the number of aborts. It gives a fair amount of time period to the active read-only transactions so that they can complete execution and commit. In many cases it will not abort any of the read-only transactions. The novelty of this system lies in the fact that in case of write-write conflicts, it saves the matured writes, instead of aborting it. The system also performs clean-ups for all unsuccessful transactions and frees the corresponding memory locations. On the flip side, this STM system is not strictly non-blocking as putting T i w off to sleep is

Fig. 1 .

 1 Fig. 1. Transactional Object (TM Object) structure in DSTM

Fig. 2 .

 2 Fig. 2. TM Object structure in proposed OFTM

Fig. 3 .

 3 Fig. 3. a. Case 1. T 2 waits for T 7 to commit

Fig. 4 .FigFig. 4 .

 44 Fig. 4.a. 10% Write Set

Table 1 .

 1 Analysis of DSTM, ASTM and the proposed OFTM based on some designing parameters.

	Designing Parameters	DSTM	ASTM	PROPOSED OFTM
	Synchronization	Obstruction Freedom	Obstruction Freedom	Obstruction Freedom
	Granularity	Object Based	Object Based	Object Based

  To compare the performance of the various Contention Managers, we have created a pool of fifty threads. With variation in the percentage of writes, we have executed two very well-known Contention Managers, viz. Aggressive Manager proposed by Herlihy et. al. in DSTM and Karma Manager of ASTM-2 in the thread pool. On the same test beds we have tested our proposed manager. Here contention over a single resource has been considered. The start time and execution time of the transactions were generated randomly and the following results were achieved.The following figures show the results of evaluation.

Mtr_lvl i

W : maturity_level of the i th write transaction; if any write transaction executes lesser than t µ w , then maturity_level of that transaction is considered as LO; if any write transaction executes longer than t w max , then maturity_level of that transaction is considered as HI,

The values of t µ W and t µ R get modified every time a new write transaction or a new read-only transaction commits. Maturity_level is considered only for active write transactions.

Proposed Algorithm

For all transactions T i w that modified object O and has reached its try_commit point

Q_RdrLst that reach their respective try_commit points within this time period; remove them from RdrLst and T

Case Study

Normally it is observed that within a workload, even the longest read-only transaction executes for a shorter period than the smallest write transaction. But exceptions may happen especially in case of reads involving indirect addressing. In the proposed negotiation strategy, neither absolute free hand has been given to read-only transactions, nor occurrence of a conflict results in indiscriminate aborting of all reads under consideration. An intermediate approach has been adopted where only those read-only transactions that can finish execution within a stipulated time (t b ) are allowed to commit.

Performance Evaluation

The efficiency and performance improvement of the proposed method over the existing OFTMs [START_REF] Herlihy | Software Transactional Memory for Dynamic-sized Data Structures[END_REF], [START_REF] Marathe | Adaptive software transactional memory[END_REF] depends a lot upon the level of domination of reads in the set. This has been analyzed here in three different categories. However, towards the end of this section, it would be established that the proposed approach would guarantee at least equivalent throughput as compared to the existing approaches.


Tapalina Bhattasali
email: tapolinab@gmail.com

Khalid Saeed
email: 2saeed@agh.edu.pl

Nabendu Chaki
email: nabendu@ieee.org

Rituparna Chaki
email: rchaki@ieee.org

A Survey of Security and Privacy Issues for Biometrics based Remote Authentication in Cloud 1

Keywords: Cloud Storage, Remote Authentication, Security, Privacy, Biometrics

Rapid development of smart technologies enables use of cloud service for large-scale data storage. Remote access of original data as well as biometric data from cloud storage enhances several challenges. It is inevitable to prevent unauthorized access of data stored in cloud. Biometrics authentication is more efficient than the known traditional authentication mechanisms. Authentication is a major security feature used to protect data privacy, whereas additional security features used to protect data may adversely affect it. There must be a balance between security and privacy during secure authentication design. Here a survey of security and privacy issues for biometrics based remote authentication in cloud is briefly presented and the research gaps are identified to attract more research on this domain in near future.

Introduction

Amount of digital content has been growing day by day with the exponential increase in number of devices connected to Internet. High volume data not only demand for huge storage space, but also looking for intelligent processing in a cost-effective manner. The popular choice in such cases is the cloud environment, which provides unlimited storage space, on demand service, parallel processing and rapid distribution of data. Cloud service provider provides a flexible way for users to access their data from anywhere and at any time. The flexibility of data usage however takes away control from the data owner. Thus the manner in which data are accessed, and by whom, is essentially under the control of cloud service provider. In such a scenario, the authentication of user is very important, so as to guarantee security of data and privacy of data source. Remote user authentication mechanism is useful in distributed domain to identify validity of remote users. There exist several techniques for remote authentication. Some of the essential requirements for enhancing quality of remote authentication in cloud are given below.

 Third party cloud service provider is not able to retrieve original data, or associated metadata stored in cloud.  Ensure that an impostor cannot be impersonated as a legitimate user.  System should be capable to respond to any incoming valid request.  No intruder is allowed to modify original message.  If timestamps are used, then it must be synchronized.  System must optimize bandwidth usage in a cost effective manner.

Password-based authentication with smart card can be used to identify the validity of a remote user. Traditional identity-based authentication mechanisms are mainly based on password, which are very easy to break because of its simplicity. Cryptographic secret keys can also be used in remote authentication framework. Major drawback is that they are difficult to memorize, lost or even be stolen. As a result, it is very difficult to identify valid users accurately. As opposed to traditional password based remote user authentication, biometrics based authentication is increasingly popular because of its reliability [START_REF] Tang | A Formal Study of the Privacy Concerns in Biometric-based Remote Authentication Schemes[END_REF] and efficiency to authenticate remote users. Cloud based remote authentication provides enhanced security by using biometrics traits [START_REF] Jain | Biometrics: A Tool for Information Security[END_REF] such as fingerprint verification, keystroke analysis, ECG analysis, iris analysis, facial analysis, handwritten signature verification etc. Each biometrics trait used in authentication has its own strengths and weaknesses. Biometrics based authentication may be unimodal having single biometrics trait or multimodal, combining multiple biometrics features. Cloud based biometrics technology has high potential market value and attracts interest of many researchers from all around the world.

Cloud framework and remote authentication technique have several challenges of their own. Preserving a balance between security and privacy is a major concern in remote framework of cloud. Privacy is the ability to decide what information should go where. Security acts as significant safeguard for privacy by protecting data. Security and privacy are often considered from two complementary angles. Despite a couple of surveys of biometrics authentication or remote authentication, a comprehensive survey of biometrics based remote authentication in cloud does not exist. The main objective of this paper is to study the balance between security and privacy in biometrics based remote authentication and point out the research gap in this domain. The contributions of this paper are as follows.

─ To extensively survey some of the existing schemes that may be used for biometrics based remote authentication in cloud and determine general trends. ─ To discuss open issues for future research area.

The rest of the paper contains the following. Section 2 gives a brief introduction of security challenges faced by biometrics techniques. Section 3 presents an extensive survey of some of the existing schemes in this area. Section 4 gives a comparative analysis of this study. Section 5 presents the open research issues in this area, and section 6 concludes the paper.

Security Challenges faced by Biometrics Techniques

The biometrics features, although unique, face several threats in reality [START_REF] Ignatenko | Biometric Systems: Privacy and Secrecy Aspects[END_REF]. One of the most common threats involves spoofing, whereby users' biometrics templates can be misused. Impostor can produce fake biometrics during enrollment. Genuine templates can be replaced by impostor's template to gain unauthorized access. Spoofing attack involves replay of either raw data or biometrics features extracted from raw data to fool the system into believing an impostor as a real user. User's biometrics features may have extra noise and thus match with incorrect user template, causing false detection. Enhancement of interclass similarity or intra-class variability in the feature sets may cause high false detection rate. Impostors can easily enter into system because of increase in false acceptance rate (zero-effort attack). Data acquisition unit may fail to acquire biometrics trait of user due to limits of capturing technology or adverse environmental conditions. This may lead to failure-to-acquire (FTA) or failure-to-enroll (FTE) errors.

Literature Survey

This section provides a literature survey of some of the existing works. There are several works on cloud security and remote authentication. Here, we present a literature survey of existing works depending on the number of biometrics traits used and the additional security features for safeguarding the biometrics template.

Authentication based on Singular Biometrics Features

Fingerprint based authentication [START_REF] Arora | A Quantitative Survey of Various Fingerprint Enhancement Techniques[END_REF] is the most popularly used technique in cloud environment because of its acceptability, uniqueness and immutability. Keystroke pattern analysis is another popular choice to authenticate users. Most important requirement of biometrics based remote authentication is liveliness detection, which is feasible by ECG based authentication. For this reason, a brief idea about some of the existing works on fingerprint, keystroke and ECG is presented here, where template data protection may not be major concern. During fingerprint verification, several image enhancement techniques [START_REF] Arora | A Quantitative Survey of Various Fingerprint Enhancement Techniques[END_REF] could be used such as histogram based, frequency transformation based, Gabor filter based enhancement. Gabor filter in wavelet domain improves accuracy level of fingerprint verification. Concept of Toeplitz matrix [START_REF] Surmacz | Robust Algorithm for Fingerprint Identification with a Simple Image Descriptor[END_REF] is considered for fingerprint verification without information loss about fingerprint image. In [START_REF] Liu | Efficient Fingerprint Search based on Database Clustering[END_REF], fingerprint search algorithm was proposed based on database clustering. It speeds up the search process and improves the retrieval accuracy. Fingerprint can be verified by using spectral minutiae representation [START_REF] Xu | Fingerprint Verification using Spectral Minutiae Representations[END_REF] which can be either location based (SML) or orientation based (SMO). Both techniques have pros and cons in different scenarios. However, fusion of two techniques shows better result. Fingerprint verifier enables template protection scheme along with fixed length feature vectors. Work on keystroke analysis is vast in the literature [START_REF] Karnan | Biometric personal authentication using keystroke dynamics: A review[END_REF]. Most of the user authentication techniques are based on measuring the distance between the user keystroke pattern and enrolled keystroke for fixed text or free text. Assessment of keystroke dynamics is based on the traditional statistical analysis or relatively newer pattern recognition techniques such as z-test, Bayesian classifiers, and neural network. Pattern matching may suffer from long search times. This issue can be solved by clustering user profiles. In [START_REF] Rudrapal | Improvisation of Biometrics Authentication and Identification through Keystrokes Pattern Analysis[END_REF], a combined standard deviation of keystroke duration and degree of disorder for keystroke latency along with disorder for keystroke duration is used for identification and authentication. In pressure-based user authentication system, the discrete time signal is transformed into the frequency domain. It is costly as it requires additional hardware to measure keystroke pressure. In a few cases, instability of typing patterns is reduced by introducing artificial rhythm concept. Keystroke recognition has been investigated for the virtual keyboard that used to interact with the hand held electronic devices, such as PDAs, and mobile phones. In ECG based authentication, correlation coefficient [START_REF] Hegde | Human Authentication Based on ECG Waves using Radon Trans-form[END_REF] between input image and feature vector stored in database is computed to check authentic person. Confusion matrix is generated to determine False Acceptance Rate (FAR) and False Rejection Rate (FRR). Gurkanet al. [START_REF] Gurkan | Modeling of Electrocardiogram Signals using Predefined Signature and Envelope Vector Sets[END_REF] proposed ECG authentication technique based on combining AC/DCT features, Mel-Frequency Cepstrum Coefficients (MFCC) features and QRS beat information of the Lead-I ECG signals. According to [START_REF] Da Silva | Check Your Biosignals Here: A New Dataset for Off-The-Person ECG Biometrics[END_REF], authentication is possible by collecting ECG signal from fingertips. However, it may contain more noise compared to data collected directly from heart. In [START_REF] Singha | Fusion of Electrocardiogram with Unobtrusive Biometrics: An Efficient Individual Authentication System[END_REF], feasibility of ECG is tested in a multi-biometric framework where it combines with fingerprint biometrics for individual authentication. Performance is evaluated using Equal Error Rate (EER), Receiver Operating Characteristics (ROC).

Authentication Systems with Encrypted Biometrics Features

Instead of storing original biometrics, transformed biometrics and transformation are stored in cloud database. Biometrics template protection [START_REF] Isobe | Security Performance Evaluation for Biometric Template Protection Techniques[END_REF] scheme can be categorized into two ways, (i) Biometric Cryptosystem, (ii) Feature Transformation. Biometric cryptosystem includes key binding (Fuzzy Vault), and key generation (Fuzzy Extractor). Features can be generally transformed either by biometric salting or biohashing and non-invertible transformation or cancellable biometrics template. For data protection, biometrics templates can be encrypted by chaotic encryption method [START_REF] Gao | A New Chaotic Algorithm for Image Encryption[END_REF], which makes the system more robust against attacks. It becomes dynamic by using the concept of one time biometrics. Blind protocol [START_REF] Nandakumar | Fingerprint-based Fuzzy Vault: Implementation and Performance[END_REF] could be used on any biometrics feature to reveal only identity without any additional information about the user. Real identity of the user is hidden to the server to provide better privacy by making the protocol completely blind. It is also secure under variety of attacks. In blind authentication, focus is on user's privacy, template protection, and trust issue. Cryptobiometric authentication protocol carries out authentication in fully automatic fuzzy vault [START_REF] Upmanyu | Blind Authentication: A Secure Crypto-Biometric Verification Protocol[END_REF], which aligns transformed template and query minutiae set of fingerprint without leaking data. Bio-capsule [START_REF] Sui | Design and Analysis of a Highly User-Friendly, Secure, Privacy-Preserving, and Revocable Authentication Method[END_REF] is user-friendly technique adaptive to any environment. It provides security even if authentication server is compromised. It can be applied to several biometrics. This irreversible cryptographic hash function [START_REF] Jin | Biohashing: Two Factor Authentication Featuring Fingerprint Data and Tokenised Random Number[END_REF] is completely independent from any operating threshold. Non-invertible Gabor transform [START_REF] Ratha | Generating Cancelable Fingerprint Templates[END_REF] is resistant to minor translation error and rotation distortion. In [START_REF] Ratha | Generating Cancelable Fingerprint Templates[END_REF], user can be given number of cancellable biometric identifiers created from fingerprint image according to the requirement by issuing a new transformation key. The identifiers can be cancelled and replaced when compromised. User's biometrics can be verified using bio-hashing [START_REF] Jin | Biohashing: Two Factor Authentication Featuring Fingerprint Data and Tokenised Random Number[END_REF]. This scheme is efficient due to usage of one-way hash function and XOR operations. Remote user authentication use nonce or long pseudorandom numbers and timestamps for better security and strong mutual authentication between user and server. Sometimes accuracy level of biometrics can be enhanced by fusing it with multiple factors. Smartcard based authentication uses biometrics along with password and smart card. According to Li et al.'s two factor authentication scheme [START_REF] Li | An Efficient Biometrics based Remote User Authentication Scheme using Smart Cards[END_REF] , user tries to login to remote server by inserting smart card into card reader and input personal biometrics for verification. It fails to provide strong authentication. Fan et al. [START_REF] Fan | Provably Secure Remote Truly Three-Factor Authentication Scheme with Privacy Protection on Biometrics[END_REF] proposed a three-factor authentication scheme by fusing password, smart card and biometrics. Yeh et al. [START_REF] Yeh | Robust Elliptic Curve Cryptography-based Three Factor User Authentication Providing Privacy of Biometric Data[END_REF] proposed an elliptic curve cryptography-based authentication scheme that is improved according to security requirements. However, it is seen from the comparative study of different multi-factor biometrics authentication schemes, that Huang et al.'s proposal [START_REF] Huang | A Generic Framework for Three-Factor Authentication: Preserving Security and Privacy in Distributed Systems[END_REF] on generic framework based on three factor remote user authentication provides better results from the aspects of security and privacy. This type of authentication is flexible in nature. User's biometrics traits are kept secret from the server to enhance privacy and to avoid single point of failure.

Analysis

From the above study, it is observed that the following parameters are generally used as performance metrics for biometric systems. After analyzing major biometrics traits like fingerprint, keystroke and ECG, it can be said that accuracy level of fingerprint is better than keystroke and ECG. Keystroke is better than other two because of its simplicity and cost-effectiveness. ECG is better than other two because of its capacity to prove liveliness which is a major issue in biometric authentication. However, ECG suffers from several limitations. Time variation nature of ECG enhances interclass similarity of sample. Few random traces of abnormality can exist in a normal user, resulting into misclassification. Data acquisition is costly and it takes longer time. As ECG data acquisition needs to go through ethical approval, accuracy level is affected due to lack of data sample. Only fingerprint is capable to authenticate users accurately provided fingerprint scanner has very high resolution. However, this type of scanner is very costly and may not be affordable for all type of applications. So fingerprint verification can be fused with other factors to enhance accuracy level using low resolution fingerprint scanner. Keystroke dynamics gains its popularity among the behavioral biometric solutions for providing feasible authentication in distributed environment, because of its simple and natural way to enhance security. Keystroke biometrics is cheaper to implement in distributed framework than other biometrics. It has been studied that performance of keystroke based bio-password is better than vein pattern recognition [START_REF]Bio Password White Paper: Authentication Solutions through Keystroke Dynamics[END_REF] and is similar to fingerprint and voice recognition. Keystroke does not depend upon the location of the user as data can be collected from anywhere using Internet. It is a globally accepted mechanism which is easy to deploy and use. Keystroke analysis cannot be used alone because of its low permanence in data collectivity. Therefore, physiological trait fingerprint and behavioral trait keystroke analysis can be considered for remote authentication in cloud.

Open Issues

From the above analysis, several research gaps are identified and presented as open issues which need to be solved in near future for better performance.

5.1

Design of Effective Framework for Achieving Balance between Security and Privacy

At present, most of the remote authentication techniques are based on either biometrics traits such as iris, fingerprints, voice or the traditional authentication proof such as passwords. It is found through the analysis that remote user authentication schemes become useless if user-id is compromised. In the present social structure, it is very important to focus on balancing security and privacy while designing remote authentication schemes using individual biometrics features. Acceptable limit of security and privacy trade-off need to be determined. There is no privacy implementation without sufficient security. Privacy issues have different meanings in different cases and protection levels are provided according to state laws.

Design of Energy Efficient Multi-Modal Biometrics based Authentication Scheme for Different State-of-the-Art Applications

At present, pervasive computing has given way to Internet of Things domain, where the application may demand recording of the user's each and every move, in order to assist in remote applications such as healthcare. However, these type of data are confidential to the user, and need to be protected from unauthorized access. Sensors used for sensing and data collectors used for sending information are rather low on energy and hence the authentication schemes involving them have to be highly energy efficient. The use of single biometrics features also fail to sufficiently safeguard the data, hence a fusion of different biometrics traits need to be used for effective protection [START_REF] Nagar | Multibiometric Cryptosystems Based on Feature-Level Fusion[END_REF].

Consideration of Psychological or Other Environmental Effects on Biometrics Features of an Individual for better Authentication

As has been noticed earlier, keystrokes based authentication is an easy to implement technique. However, not much have been researched about the effect an individual might have on the typing pattern when he or she is either sick or depressed. There comes the effect of humidity, temperature, etc. to be considered with fingerprints.

Design of Cost-Effective Means to Record Biometrics Features

The devices available for recording the features need to be engineered so as to achieve energy efficiency and accuracy. As such, usage of any specialized device itself is often considered as an addditional overhead. This overhead can be justified only by improved efficiency in terms of biometrics feature extraction.

Conclusion

In today's world, use of third party cloud environment has become mandatory for the organizations handling huge amount of data cost-effectively. Securing data stored in cloud is a big challenge. Therefore, one of the most important challenges is to how to control access of data stored in cloud from remote location. Authentication is necessary step in security implementation for remote data access. It is studied that biometrics authentication is feasible solution in cloud. With growing popularity of biome-trics features, database containing biometrics template and user details are also stored in cloud and vulnerable to various threats. Authentication mechanism has no significance without security. Similarly, complex security mechanism affects usability and accuracy of authentication. In this paper, we present a survey of security and privacy issues of biometrics based remote authentication in cloud after analyzing existing works from different angles. An insight into the open research issue is also presented. The objective of this survey is to determine the challenges in biometrics based remote authentication in cloud; so that more effective user authentication could be proposed to resist attacks in remote environment besides identifying users accurately.

True Rejection Rate (TRR) -

  Probability to correctly detect non-matching input pattern to any template stored in the database. It measures the percent of invalid inputs which are correctly rejected.  False Acceptance Rate (FAR) -Probability to incorrectly match input pattern to a non-matching template stored in the database. It measures the percent of invalid inputs which are incorrectly accepted. It is more dangerous than FRR.

	 Equal Error Rate or Crossover Error Rate (EER or CER) -Rate at which both
	acceptance and rejection errors are equal. Value of EER can be easily obtained
	from ROC curve. Lowest EER represents high accuracy.
	 Accuracy -Percentage of ratio of true detection (TAR+TRR) and overall detection
	(TAR+TRR+FAR+FRR).
	 Peak Signal to Noise Ratio (PSNR)-It is a measure of peak error in decibels be-
	tween two images. It is used as a quality measurement between original and recon-
	structed image.
	 Computation Time (CT) -It estimates processing time involved in computation
	(e.g. enhancing the image).
	 False Rejection Rate (FRR) -Probability to fail to detect a match between the
	input pattern and a matching template in the database. It measures the percent of
	valid inputs which are incorrectly rejected.
	 Receiver Operating Characteristic (ROC) -ROC plot is a visual characterization
	of the trade-off between FAR and FRR.

 True Acceptance Rate (TAR) -Probability to correctly match input pattern to a matching template. It measures the percent of valid inputs which are correctly accepted. 

Table 1

 1 gives a quantitative analysis of few biometrics traits based on previously discussed performance metrics. It compares the estimated values of several existing works based on evaluation metrics and checks whether additional security features affect the performance of those works or not. It gives an idea about the security and privacy trade-off in biometric authentication level.

Table 1 .

 1 Quantitative Analysis of Few Biometric Features

	Topic	Additional Security	Evaluation Metrics	Estimated Values
		Features
	Fingerprint verification	No	Equal Error Rate (EER),	9.345% EER
	with image enhance-		Peak Signal to Noise	41.56db PSNR
	ment [4]		Ratio (PSNR), Compu-	0.894 sec CT
			tation Time (CT)
	Fingerprint verification	Yes	Equal Error Rate (EER),	6.4% EER for SML;
	using spectral minutiae	Template	Fused EER	6.1 % EER for SMO;
	representation [7]	Protection		4.8% EER for Fusion
				of SML and SMO
	Continuous Dynamic	No	False Acceptance Ratio	20.25% FAR
	Authentication for		(FAR), False Rejection	4.18% FRR
	Identification [25]		Ratio (FRR)
	Bio Password (keys-	No	EER	3% EER
	troke fused with pass-
	word) [26]
	ECG based authentica-		True Acceptance Rate	84.97% TAR
	tion by high frame rate	No	(TAR), True Rejection	99.48% TRR
	system for imaging [27]		Rate (TRR)
	ECG based authentica-	No	TAR, TRR	97.25% TAR
	tion using predefined			99.91% TRR
	signature and envelope
	vector sets [11]
	Fingertips based ECG	No	EER	9.1 % EER
	[12]
	ECG plus Fingerprint	No	TAR	95% TAR