Lucas Nussbaum
email: lucas.nussbaum@ens-lyon.fr

Rebuilding Debian using Distributed Computing

Doing Quality Assurance work on Debian, a Linux distribution with more than 12000 packages, requires an impressive amount of computing power, which is usually not available for its developers. In this article, we report on the development of an infrastructure to run quality-assurance tasks on Debian using the Grid'5000 experimental platform. In particular, we focus on the problem of rebuilding all packages in Debian from source. We describe the details of this task, and the infrastructure we developed, with scalability and robustness in mind. The results we obtained are then presented, and we discuss possible improvements and lessons we learnt in the process, which might be useful in the context of other large-scale experiments.

I. INTRODUCTION

The Debian project builds an operating system -Debian GNU/Linux, usually simply called "Debian" -by gathering a very large amount of free software, and turning them into packages that can easily be installed by the user. It has been very successful since its creation in 1993, and serves as the basis for other Linux distributions, like Ubuntu. Debian is developed by more than 1000 volunteers, spread across the world and communicating over the Internet. As such, it is often regarded as one of the most important volunteer-based and distributed organizations.

Debian is well renowned for its robustness and its stability, and is known as a good choice for a server's operating system. This level of quality is mainly achieved by a great attention to details by the developers who maintain its 12000+ source packages. But some Quality Assurance (QA) tasks require computing power in addition to manpower, and, since 2006, we have used distributed computing on a Grid infrastructure to find defects in Debian.

We worked on two classes of problems. First, we focused on testing the installation and the removal of packages. Debian has more than 22000 binary packages (source packages are built to generate binary packages, which are installed by users). Each package's meta-data can express relationships with other packages (depends on another package, suggests the installation of another package, conflicts with another package). While the installability (whether a package can be installed) of a package can be determined statically [START_REF] Di Cosmo | Package upgrades in foss distributions: details and challenges[END_REF], other problems might arise during installation, which are harder to detect without actually installing the package: a package could contain the same file as another package without explicitly conflicting with that other package, a script executed after the installation of the package might fail because of a missing dependency, a programming error, or a change in the behaviour of another package since the developer did the initial packaging work. A tool, piuparts [START_REF]Piuparts: .deb package installation, upgrading and removal testing tool[END_REF], is available in Debian to perform tests on the installation, upgrade, and removal of packages. Running piuparts on all packages is an embarrassingly parallel problem: one could test each one of Debian's 22000 packages in parallel, and the packages that take the longest do not take more than half an hour. Since 2006, we ran several test campaigns using piuparts, and reported about 250 bugs, most of them considered critical. However, the result of those installation tests is relatively stable: while bugs might not be easy to find, new bugs are relatively rare, and running those tests does not need to be done on a frequent basis.

The second class of problems we looked at is more challenging. We examined the buildability of packages (whether packages can be built successfully). Since Debian contains only free software, the source code for each package is available, and for various reasons, it is important to ensure that it is possible, from a source package, to build the corresponding binary packages. Firstly, during the lifetime of a package, it might be necessary to change something in the source codeto correct a mistake, like a bug or a security problem. In that case, it will be necessary to rebuild the corresponding binary packages after the change has been made. Secondly, for legal reasons: the source code for programs covered by the GNU General Public License must be made available by Debian, and one could argue that shipping a source code that does not allow building the corresponding packages would be a license violation.

Debian packages can be built automatically: all source packages provide a simple interface, based on a Makefile named debian/rules, that hides the specifics of each program's build system (use of Automake or CMake, language-specific tools like Python's distutils or Perl's Makefile.pl ): each package can be built by calling one of the targets of debian/rules, or by using a wrapper like dpkg-buildpackage, which would use debian/rules itself. Unfortunately, packages often become impossible to build, for different reasons. A package needed to build another package (called a build-dependency) could be removed from Debian, or modified in a way that makes its reverse dependencies impossible to build: a compiler could become more strict by rejecting previously-accepted constructs, the API of a library could change in an incompatible way, the parameters of another program could be modified.

By rebuilding all packages in Debian, we not only ensure that Debian is self-contained (that all Debian packages can be rebuilt from Debian), we also stress-test the whole toolchainthe packages that are used to build other packages. This second role is at least as important as the first one: most packages in Debian lack a test suite, and using them to rebuild other packages often serves as some kind of automated test suite.

In the remainder of this paper, we report on the execution of rebuilds of the Debian archive using distributed computing, by providing feedback on improvements implemented since [START_REF] Nussbaum | Use of grid computing for debian quality assurance[END_REF]. In section II, we give some information on our workload. In section III, we present Grid'5000, which is the platform that we used to perform those rebuilds, and the specific infrastructure we developed to be able to run those tasks efficiently on Grid'5000. We then present the results we obtained in section IV and discuss possible optimizations in section V, before concluding in section VI.

II. WORKLOAD ANALYSIS

The implementation decisions that we will have to make depend greatly on the workload we would like to process with our application. In this section, we describe the characteristics of the Debian source packages set. We use Debian 5.0 'Lenny', released in February 2009, on the i386 architecture, as the basis for our study. Previous releases of Debian do not differ significantly from those results, and it can be expected that future releases will not fundamentally differ either, except by increasing the number of packages.

Debian lenny is composed of 12123 source packages, of which about 12000 can be built on the i386 architecture (Debian supports 12 different architectures, and some packages provide functionality that is specific to some architectures, due to specific hardware, for example). The total size of the source packages is 16.3 GB (compressed using gzip).

Figure 1 shows the distribution of the size of packages. A lot of the packages are relatively small (44% smaller than 128 kB, 82% smaller than 1 MB, 99% smaller than 20 MB). However, a few packages are much larger (openoffice.org -346 MB, nexuiz-data -377 MB). As one can see on Building source packages into binary packages requires several steps. First, a clean build environment is needed. It consists of a minimal chroot in which are installed the Debian packages that are always expected to be present when building. This includes the GCC compiler, binutils, and Debianspecific tools. In our setup, this chroot is stored as a tar archive, taking 73 MB compressed (200 MB uncompressed).

Each source package can also specify other packages that must be installed before building. For example, a Fortran program will require the Fortran compiler to be installed, as this package is not expected to be installed by default in the build environment. The installation of those build-dependencies can take a significant amount of time, as some packages require the installation of a lot of them: openoffice.org requires 485 additional build-dependencies, and linphone requires 392 of them. Of the 22311 binary packages in Debian lenny, 5723 are build-dependencies of other packages. Also, those packages have to be fetched from a local mirror before they are installed.

III. SOFTWARE INFRASTRUCTURE

A. Grid'5000

Grid'5000 [START_REF] Cappello | Grid'5000: a large scale, reconfigurable, controlable and monitorable Grid platform[END_REF], [START_REF]Grid'5000 website[END_REF] is an experimental platform for research on large-scale parallel and distributed systems. Grid'5000 is being developed under the INRIA ALADDIN development action, with support from CNRS, RENATER, and several universities as well as other funding bodies.

Grid'5000 consists of about 2000 compute nodes, split in a dozen of clusters, located in 9 locations in France. Those 9 sites are connected with a dedicated 10 Gbps backbone (see figure 3).

Grid'5000 aims at providing a reconfigurable, controllable, and monitorable experimental platform. As such, once compute nodes have been reserved, it is possible to deploy one's Fig. 3. Grid'5000 sites on top of the Renater 5 network infrastructure. 10 Gbps links connect the various Grid'5000 sites together. own work environment using Kadeploy [START_REF] Georgiou | A tool for environment deployment in clusters and light grids[END_REF]. This allows installing specific software (including kernel) and to get administrator (root) access on the nodes.

B. Infrastructure for Debian rebuilds

To rebuild all Debian packages efficiently on Grid'5000, we developed our own software infrastructure (figure 4). We had the following goals in mind:

• most of the infrastructure should be deployed dynamically during the rebuilds, using Kadeploy;

• it should be robust. The rebuilds are supposed to be run unattended, and should not fail;

• it should be scalable. As we will see in section IV, we will be able to run the rebuild on 50 to 100 compute nodes at the same time. Our infrastructure is composed of two parts: a static part, located in the Grenoble Grid'5000 site, and a dynamic part that can be deployed on any Grid'5000 site, depending on where resources are available.

The static part of the infrastructure consists of an NFS server hosting all the necessary data:

• A full Debian mirror internal to Grid'5000;

• The scripts and configuration files, as well as some data files needed by the compute nodes;

• The logs generated by the builds. An Apache web server is also configured next to the NFS server, and serves the Debian mirror over HTTP. This proved to be more efficient than distributing the packages directly using NFS, and also provides an opportunity for caching, thus reducing the load on the NFS server. The deployment of the dynamic part of the infrastructure is done in several steps.

1) Nodes are reserved using the OAR Batch Scheduler;

2) The reserved nodes are deployed using Kadeploy. A standard environment, available on all Grid'5000 clusters, is used. The deployment is managed by Katapult, to allow the failed nodes to be re-deployed if necessary. This takes 3 to 5 minutes; 3) From the frontend, a script is executed (over SSH) on one of the deployed nodes (the master node). Basic configuration is done on the node (like the mounting of a shared NFS directory); 4) From the frontend, a script located on the shared NFS directory is executed on the master node to continue the configuration of the nodes; 5) From the frontend, a last script located on the shared NFS directory is executed. This script will control the rest of the operations; 6) The script running on the master node executes the same process on the other nodes: it first copies a script to the nodes, executes it to mount the shared NFS directory, then run another script to finish the preparation of the nodes; 7) When all the nodes are properly prepared, the master node starts scheduling and executing tasks on them. At the beginning of each build, the chroot is uncompressed from a tar archive, to ensure that the build environment is always clean. The build log is stored locally until the end of the build, and is then copied to the NFS directory.

8) After all the tasks have been executed, all the nodes are given back to the batch scheduler. It is possible that, at the end of the rebuild, there are no remaining tasks to run on some nodes, which could therefore be freed. But the OAR batch scheduler does not allow releasing some nodes earlier than others, which can lead to a waste of resources in this case.

While NFS is not efficient over high-latency networks, it proved to be an easy way to push configuration files and scripts to the nodes. Also, we made sure not to use the NFS server for performance-critical steps during the process.

We also chose to use a standard deployment environment, instead of a customized one. This allows us to use an environment maintained by Grid'5000's system administrators, and available everywhere. After deployment, we install the necessary software packages, like sbuild (the Debian tool used to build packages in a chroot) and approx, a Debian mirror proxy. Installed on each node, it allows caching locally builddependencies that are frequently downloaded, and alleviate the load on the central Debian mirror.

Finally, our infrastructure has obvious reliability issues: both the master node and the static part of the infrastructure (NFS server, Debian mirror) are single points of failure. However, due to the length of full Debian rebuilds on Grid'5000 (less than 10 hours in practice), we do not consider this to be an important issue: if a grave problem occurs during a rebuild, it is still possible and relatively cheap to restart the whole rebuild. Regarding compute nodes, the script responsible of running the tasks on them tries to detect problems that might arise during a build. When they occur, the failed build is restarted on another node, and the compute node is removed from the list of nodes used in the rebuild.

IV. RESULTS

Using our architecture, we rebuilt all the packages in Debian lenny using 49 nodes of the azur Grid'5000 cluster in Sophia. Each compute node is a server with 2 Opteron 246 (2.0 GHz) CPUs, and 2 GB of RAM. It took a total of 9 hours and 20 mins, of which 13 minutes where spent deploying the infrastructure. The sum of the build time of all packages (sequential time) is 17 days and 4 hours. The logs generated by all builds use 2.0 GB on the NFS directory.

Figure 5 shows the distribution of the packages' build time. One can see that most packages take a very short time to build -62% take less than a minute, while 90% take less than 3 minutes. However, a few packages take a lot more time (table I). Those packages also are responsible for the majority of the build time (figure 6): the 5% longest packages account for 50% of the build time.

Looking at various system counters during the builds, we could determine that the tasks are both CPU-and I/O-bound. Memory usage generally stays quite low (but may vary greatly between packages). Network does not play an important role: common build-dependencies are cached on the node, and it is only used for control besides that. V. OPTIMIZATIONS Two objectives can be targeted when trying to improve the process:

• Reduce the makespan, possibly increasing the number of necessary machines. The main reason for this is that, if possible, we could use a lot more machines on Grid'5000: it is generally considered less disturbing to use more nodes during a shorter period of time, than to use less nodes during a longer period. To reduce the makespan, the main problem to address is the build time of the longest packages;

• Reduce the number of machines without increasing the makespan. This requires making the build process more efficient for all packages.

A. Scheduling of the tasks: longest-first

There are huge differences between the build time of all the packages. While most packages are extremely fast to build, a few packages take a very long time. To minimize the makespan, it is important to schedule those long packages early in the rebuild process: if we schedule them too late, we might reach a point where we all tasks are finished except one, and we are only waiting for that (long) task to finish.

A simple optimization is therefore, after we have determined the time taken to build each package, to schedule them starting with the longest packages.

Using this scheduling, and the results described in section IV, we can estimate that the optimal scheduling of the rebuild of all packages would take 7 h 33 m (time taken to build openoffice.org), using 55 compute nodes (this does not include the time needed to configure the environment at the start of the job): with more nodes, some nodes would be idle at the end of the process while we wait for openoffice.org; with less nodes, we would still have some tasks to process after openoffice.org is finished.

B. Adding parallel building support to long packages

The makespan is limited by the time taken by the longest packageopenoffice.org. An interesting way to reduce its build time is to make use of parallel building (often known as make -j). This consists in running several steps of the build process in parallel to make use of several CPUs or to allow to continue to perform CPU-intensive operations in some threads while other threads are blocked on I/O [START_REF] Cantrill | Real-world concurrency[END_REF].

Unfortunately, most Debian packages lack support for building using several threads. An interface for that was recently added to Debian's build system, and we worked together with some package maintainers to help them implement it. The results presented in section IV include results obtained with parallel builds for some packages, like openoffice.org (where only a small part of the build process can be done in parallel), linux-2.6 or latex-cjk-chinese-arphic.

C. Reducing the local I/O bottleneck

Building packages is I/O intensive, especially for small packages where the build time is dominated by the creation of the chroot, and the installation of build-dependencies. We investigated ways to alleviate this problem. First, the EXT3 file system used on the compute nodes issues a sync() every 5 seconds by default, to ensure that all the data and meta-data is written to disk. We modified that parameter by re-mounting the build partition with the commit=86400 option to delay syncs. Unfortunately, it seems that sync() system calls are also issued by some applications during the build process. As a consequence, we didn't notice any improvement.

Since the data written during the build is only used temporarily, we investigated another solution: building in memory, using Linux's tmpfs file system, which stores its content in virtual memory (RAM or swap). As our compute nodes have at least 2 GB of RAM, most packages could be built without ever swapping some memory pages to disk.

This approach has some drawbacks. Firstly, We needed to add more swap space to the compute nodes by adding a swap file, and creating such a file takes a long time during node preparation. We chose to create a 32 GB swap file, and this file is not allowed to contain holes -it cannot be a sparse file. Creating and writing a 32 GB file takes 12 minutes on our compute nodes -limited by the disk writing speed, since the file has to be filled with zeroes. It is possible that the new EXT4 file system will solve this problem by implementing the fallocate() system call.

Secondly, some packages failed to build on tmpfs, for various reasons that still need to be investigated. However, this approach is promising: the build time (when comparing only packages that built fine with both configurations) was reduced by 13%. But some packages took more time to build on tmpfs, as seen on figure 7. Also, it seems that this optimization mainly benefits packages that are quick to build, while packages that take a long time to build do not benefit as much.

D. Building several packages concurrently

Since most packages lack support for building using several parallel threads ("make -j"), another solution is to build several packages concurrently, on the same compute node: for example, the same compute node would build 4 different packages concurrently. This allows to reduce the total number of compute nodes used for the rebuild, without increasing the makespan. One problem with this approach, however, is that the individual packages take more time to build. While computing power can be shared equally between tasks, the concurrent tasks on the same node will be fighting for the I/O bandwidth. This is not a problem for small packages, but might be a problem for packages that already take a very long time to build: slowing down those packages would result in an increase of the makespan. We mitigated this issue by setting process priorities based on the duration of the build: long builds get an higher priority than short builds.

Figure 8 describes the overall build time (number of compute nodes used, multiplied by walltime) when running several concurrent builds on the same compute nodes. Running one build per compute nodes, 14 days of compute time on Grid'5000 was used (which could translate into using 42 nodes for 8 hours, for example). Running 4 concurrent builds, the total time decreases to about 4 days (12 nodes for 8 hours). However, in practice, the slowdown caused by I/O concurrency is a major problem: even after having added processes priorities based on the duration of the build, the long packages still take more time when they are built concurrently with other packages (figure 9). A solution could be to schedule long packages alone on a compute nodes, while the shorter packages would be built concurrency with others. This has not been implemented yet.

VI. CONCLUSION

With this infrastructure, we performed several full rebuilds of Debian during the lenny development cycle, and reported more than 2300 critical bugs on packages that failed to build from source.

In addition to that, this work was the basis of a small shift in the Debian development processes: since it was easy to rebuild the Debian archive with a custom setup, we performed some builds with custom environments to evaluate the consequences of proposed changes to build tools. In the same spirit, several rebuilds were also performed with newer development versions of base software, like the GCC compiler: rebuilding all packages in Debian with a beta version of GCC allowed to find several important regressions that were fixed before the final GCC release. We think that there are other opportunities where such environments could be helpful for the free software community.

This work would not have been possible without the flexibility offered by Grid'5000. This application has very specific and demanding requirements, like the fact that a special environment has to be deployed on the nodes, and that root access is required for several steps. Despite being "experimental" in terms of software used, Grid'5000 proved reliable enough to fully automate the complex processes needed by this work.

Fig. 1 .

 1 Fig. 1. Distribution of the size of source packages: most packages are quite small.

Fig. 2 .

 2 Fig. 2. Distribution of the space used in the archive by packages: the few biggest packages account for a very large part of the archive's size.

Fig. 4 .

 4 Fig. 4. Software infrastructure

Fig. 5 .Fig. 6 .

 56 Fig. 5. Distribution of the build time of packages. Most packages are fast to build.

Fig. 7 .

 7 Fig.7. Distribution of the packages' build time on tmpfs. Most packages reduce their build time, but short builds benefit more than long builds.

  time (nb nodes * walltime) (days) Concurrent builds per compute node

Fig. 8 .

 8 Fig. 8. Overall build time when building several packages concurrently on the same node.

3 Fig. 9 .

 39 Fig.9. Build time for some packages that take a long time to build, when running several other builds concurrently on the same nodes.

TABLE I

 I

	PACKAGES THAT TAKE MORE THAN 2 HOURS TO BUILD
	Package	Time
	openoffice.org	7 h 33 m
	openjdk-6	5 h 42 m
	insighttoolkit	5 h 38 m
	gecode	4 h 51 m
	latex-cjk-chinese-arphic	4 h 38 m
	linux-2.6	4 h 33 m
	gcc-4.3	4 h 21 m
	gcc-4.2	3 h 38 m
	installation-guide	3 h 28 m
	qt4-x11	2 h 12 m


Guillaume Paulin

David Carpentier

Conductance correlations in a mesoscopic spin glass wire : a numerical Landauer study

In this letter we study the coherent electronic transport through a metallic nanowire with magnetic impurities. The spins of these impurities are considered as frozen to mimic a low temperature spin glass phase. The transport properties of the wire are derived from a numerical Landauer technique which provides the conductance of the wire as a function of the disorder configuration. We show that the correlation of conductance between two spin configurations provides a measure of the correlation between these spin configurations. This correlation corresponds to the mean field overlap in the absence of any spatial order between the spin configurations. Moreover, we find that these conductance correlations are sensitive to the spatial order between the two spin configurations, i.e whether the spin flips between them occur in a compact region or not.

Spin glasses have been a focus of continuous interest in condensed matter for more than three decades. In spite of the relative simplicity of the models describing their physics, a precise understanding of their properties remains elusive. Spectacular progress has been made in understanding their nature at the mean field level [1,[START_REF] Mézard | Spin Glass Theory and Beyond[END_REF], in characterizing their exotic aging properties in mean field models [START_REF] Cugliandolo | Lecture notes[END_REF], including a proper description of the violation of the fluctuation-dissipation theorem, and experimentally in characterizing their memory and rejuvenation effects (see [START_REF] Vincent | Wandering with Curiosity in Complex Landscapes[END_REF] for a recent review). However the applicability of mean field ideas in real samples remains debated [START_REF] Fisher | [END_REF], with alternative approaches stressing the importance of the nature of excitations, and their consequences on various out-of-equilibrium properties of the phase [6].

A crucial quantity to characterize this spin glass physics is the correlation between different states of spins { S (1) i } i and { S [START_REF] Mézard | Spin Glass Theory and Beyond[END_REF] i } i in a given sample corresponding e.g to two different times t 1 and t 2 in a same quench, or two different quenches. For a single spin i, this correlation is naturally given by the local overlap S (1) i . S [START_REF] Mézard | Spin Glass Theory and Beyond[END_REF] i . For a collection of spins, mean-field theory neglects any spatial correlation of this local overlap : the correlation between the two spin states is given by

Q 12 = 1 N N i=1 S (1)
i . S

i .

(

) 1
The distribution of this overlap between states reached after successive cooling in a sample plays a central role in the Parisi's mean field theory. Note however that this overlap (1), while perfectly adequate at the mean field level, does not contain any information on the geometry of the correlation. In the simplest case of Ising spins it simply counts the number of spin flips between the two spin states, without any information on whether these spin flips occur in a compact region or randomly in the sample. Information about the spatial structure of this spin states correlation would require a more refined function.

Recently, building on previous theoretical work on sensitivity of conductance fluctuations to perturbations like magnetic impurities [7] and pioneering experiments on conductance fluctuations in spin glasses [8,9,10], the study of magneto-conductance of spin glass nanowires was proposed as a unique probe of these correlations between spin glass configurations [11]. Indeed, the correlation between conductances for two different mean-field like spin states depends monotonously on the overlap between these two states. Hence measurement of this conductance correlation can give access to the corresponding overlap [11,12]. This proposal calls for experimental and numerical studies of the correlations of conductance in a spin glass metallic system. It is the purpose of this letter to develop a numerical study of these conductance correlations, and in particular to address the question of sensitivity of these conductance correlations to spatial order between the corresponding spin states, originating from e.g the nature of excitation in the spin glass (see [13] for an alternative numerical approach focused on the time evolution of conductance fluctuations). This question is naturally of crucial importance for experimental studies of quantum transport in spin glass nanowires. To address this question, we present a numerical Landauer approach allowing to accurately describe the weak localization regime of experimental relevance. This approach allows to go beyond the restrictions of analytical techniques and consider random spin states with spatial correlations between them.

To describe the electronic transport in the low temperature phase of a spin glass metallic wire, we consider a tight-binding Anderson model with magnetic disorder :

H = <i,j>,s t ij c † j,s c i,s + i,s v i c † i,s c i,s + J i,s,s ′ S i . σ s,s ′ c † i,s c i,s ′ , ( 2
)
where t ij = t represents the hopping of an electron from site i to j, v i is the scalar random potential uniformly distributed in the interval [-W/2; W/2] and J is the intensity of the magnetic disorder which is typically smaller than W . The σ are Pauli matrices and s labels the spin state of the electron. The magnetic impurities of the spin glass contribute to two different random potentials: a scalar diffusive potential v i (originating in part from the random positions of the impurities) and a magnetic disorder originating from the random spins S i . In this description, all impurity spins S i are frozen and treated as classical spins. We choose the classical spins S i randomly in the sphere of radius S, and independent from each other. This amounts to neglect any spatial order in a given state, in agreement with neutron scattering experiments [START_REF] Mydosh | Spin Glasses, An Experimental Introduction[END_REF]. Going beyond this simple description by including more complex hidden spatial order goes beyond the scope of the present paper. Owing to the experimental findings of universal conductance fluctuations in the spin glass phase [8,9], we focus on the corresponding regime where the wire's length L x is comparable or smaller than the inelastic dephasing length L φ , which effectively includes contribution from free spins. Without loss of generality, we will restrict ourselves to a twodimensional ribbon of size (in units of lattice spacing)

L x × L y with L y ≪ L x .
For a given configuration of scalar disorder V ≡ {v i } i and spins { S i } i , we numerically determine the corresponding dimensionless conductance g = G × h/e 2 through the Landauer formula [START_REF] Landauer | [END_REF]: g = n,m |t nm | 2 , where n (resp. m) labels the propagating modes in the contacts and t nm the corresponding transmission amplitude. These transmission amplitudes are deduced from the electron's retarded Green's functions G R using the Fisher-Lee relation [16]. This Green's function G R for the system connected to two semi-infinite leads is obtained by a recursive method [17]. The Fermi Energy is chosen so that the total number of transverse propagating modes is equal to 2 × L y . In units of t = 1, the amplitude of scalar disorder is chosen as W = 0.6 , while the coupling J is varied from 0 (no magnetic disorder) to 0.4 ("strong" magnetic disorder). For fixed parameters, the conductance g is a random function of both disorders V and { S i } i . We focus on the weak localization regime, where the conductance g displays universal fluctuations of order 1. Experimentally, these fluctuations are measured as a function of a weak transverse magnetic flux, assuming the ergodic hypothesis (see [18] and [19] for a numerical analysis). The amplitude of magnetoconductance fluctuations in a spin glass sample is given by the variance of the distribution of g[V, { S i } i ] as V is varied. In the rest of the article, for each configuration of spins the corresponding distribution will be sampled by 5000 independent realizations of the scalar potential V .

We start by identifying the regime of weak localiza-

[V, { S (1) i }]-g[V, { S (2)
i }] as V is varied. The result for various pairs of mean-field like spin states are shown, parametrized by the corresponding overlap between these spin states. tion. In this regime, for a given random spin configuration, the variance of the above distribution of conductance (δg

) 2 = g[V, { S i } i ] -g[V, { S i } i ] 2
(where corresponds to an average over V ) is given in the 1D diffusive regime by

(δg) 2 = 1 4 F (0) + 3 4 F 2L x √ 3L m + 1 4 F 2L x L m + 1 4 F √ 2L x √ 3L m (3)
where we defined [20] F (x) = (6 + 6x 2 -6 cosh(2x) + 3x sinh x)/(x 4 sinh 2 x). The amplitude of these fluctuations extrapolate from 8/15 for L x ≪ L m (orthogonal class with spin-degenerate states) to 1/15 for L x ≫ L m (unitary class with double number of modes). The magnetic dephasing length L m depends in particular on the strength of magnetic disorder J. It is numerically determined through the use of formula [START_REF] Cugliandolo | Lecture notes[END_REF]. The inset of Fig. 2 shows the excellent agreement between the numerical data for this conductance fluctuations and weak localization formula (3) plotted as a function of x = L x /L m (J).

Having determined the weak localization regime, we now turn to the study of correlations of the conductance between two different spin configurations { S (1)

i } i and { S (2) i } i . We consider the distribution as V is var- ied of the difference g V, { S (1) i } -g V, { S (2)
i } . This distribution has naturally zero mean, and its variance encodes statistical correlations between the two conductances (δg 1 -δg 2 ) 2 = 2( (δg 1,2 ) 2 -δg 1 δg 2 ) where

g α = g V, { S (α) i } .
Similarly to the variance (3), they are parametrized by four dephasing lengths [7,11,21] as follows

δg 1 δg 2 = 1 4 F L x /L D,S m + 3 4 F L x /L D,T m + 1 4 F L x /L C,S m + 3 4 F L x /L C,T m (4)
with F (y) given in (3) and the L C/D,S/T m correspond to magnetic dephasing lengths for the Singlet/Triplet components of Diffuson/Cooperon contributions built between spin configurations 1 and 2. We will study these conductance correlations for different types of correlations between the spin configurations.

Mean-Field like excitations. First, we consider spin states with no spatial correlations between them. These configurations are generated as follows : we start from a configuration 1 where the orientations of spins are chosen randomly and independently from each other. From this first state, we generate other configurations by regenerating with a probability p the orientations of each spin. In this case, the overlap ( 1) is an adequate measure of the correlation between these states. In practice with this method we generated spin states with mutual overlap Q 12 from 10 -3 to 1. For these spin configurations, we find a very good agreement with analytical studies [11] : the correlation between the conductances is entirely parametrized by their overlap Q 12 . In Figure 1 we plot the probability density function (PDF) of the difference

g[V, { S (1) i }] -g[V, { S (2)
i }] as V is varied. The PDF for three different pairs of spin states with the same overlap Q 12 ≃ 0.91 (dots, squares and triangles) are identical with each other and different from the PDF for a pair with Q 12 = 0.98. These PDF are found to be reasonably well Gaussian, parametrized solely by the above second cumulant.

Then we compare the behaviour of this second cumulant with eq.( 4), using the analytical expressions to V -δg1δg2 V ) and the so-called Diffuson Singlet contribution F (0) -F (Lx/L D,S m ). This contribution is found to be dominant in the region Q12 ≃ 1. In the inset we plot this σ function for different value of overlap Q12 and for J = 0.1. Plain lines are theoretical fits allowing to determine L D,S m (Q12, J). System size is 40 × 1600.

order J 2 for the dephasing lengths [11] :

L D/C,S m = L m / √ 1 ∓ Q 12 and L D/C,T m = L m / 1 ± Q 12 /3.
We find a reasonable agreement between this prediction and numerical results, as shown in Fig. 2. Note that this comparison is done without any free parameter as the magnetic dephasing length L m was determined from (δg) 2 (see Fig. 3) The behaviour of this variance also explains the high sensitivity of P (g 1 -g 2 ≃ 0) on small departures from Q 12 = 1 as shown in the inset of Fig. 1. Indeed, the probability of similar conductances reads

P (0) = 1/ √ 2πσ with σ = 2( (δg) 2 V -δg 1 δg 2 V
). From the above analytical expressions for L C/D,S/T m for overlaps Q 12 ≃ 1 the only diverging magnetic length is found to be L D,S m . Thus in this regime the expression (4) is dominated by the corresponding contribution [21]. This allows for a direct determination of L D,S m from the L x -dependance of σ in the region Q 12 ≃ 1, as shown in Fig. 3. We find an excellent agreement between the corresponding dephasing rate 1/(L D,S m ) 2 and its perturbative analytical expression (1 -Q 12 )/(L m ) 2 as shown on Fig. 4.

Correlated excitations. We now consider the influence of spatial correlation between two spin configurations. Generation of correlated spin configurations is obtained as follows: from an initial spin configuration we generate a configuration n by reversing spins preferably inside a box of size L (n)

x ×L y in the middle of the sample. We consider boxes of increases length L

(n) x = nL (1)
x , such that all states have the same overlap Q with the initial configuration, but their spatial correlations with this initial configuration decreases with n (the larger the box, the smaller the probability that a given spin inside the box m ) for mean-field like, spin wave (dash dot), and boxed excitations. The overlap is 0.9 for all of them, and the size is 40 × 1600. The linear dependance corresponds to the analytical expression 1/(L D,S m ) 2 = (1 -Q12)/(L 2 m ), valid in the absence of spatial correlations between the spin states. These results show the clear departure from this behavior for strong spatial correlations, and the absence of any effective overlap. Right: same evolution for random configurations and for spin wave with two different spatial periods corresponding to the same overlap (Q = 0.54). The stronger correlation (longer period) corresponds to the larger deviation from the linear law. is modified). We also generated spin wave like excitations: from the same initial spin configuration, each spin is rotated by δφ(x, y) = xδφ 0 around the z-axis (axis perpendicular to the planar sample). δφ 0 determines the period of the spin wave, and thus the overlap between both configurations. For the different pairs of correlated spin configurations, we repeat the previous analysis of conductance correlations. In particular, we determine the Diffuson Singlet length L D,S m for different values of magnetic disorder amplitude J in the region Q 12 ≃ 1. The result is shown in the left part of Fig. 4 for the overlap Q 12 = 0.9. We find clear deviation from the behavior 1/(L D,S m ) 2 = (1 -Q 12 )/(L m ) 2 which is valid in the absence of spatial correlations (Fig. 3). The deviation from this linear behavior is largest for the strongest spatial correlations between spin states, i.e for the smallest box excitations (n = 1) and the spin wave excitations. We also consider two spin wave excitations with different period but the same overlap with an initial spin state (Fig. 4). Here again, the resulting Diffuson Singlet magnetic length is smaller for the strongest spatial correlation between the two spin states, corresponding to the largest period. These results demonstrate the sensitivity of the magnetic dephasing length L D,S m on spatial correlations between the magnetic disorder configurations, and thus the influence of the geometry of random spin excitations on the associated correlation of conductances. Note that these results of Fig. 4 can in principle be tested experimentally by varying the density of magnetic impurities while working at fixed T /T SG , allowing for an unprecedented test of e.g the nature of excitations in a spin glass state.

In this letter we presented a numerical Landauer analysis of transport in a mesoscopic metallic wire in the presence of frozen magnetic impurities. We have found that statistical properties of conductance correlations between two mean-field like spin configurations depend only on the corresponding spin overlap, in agreement with theoretical analysis. These results open the route to direct spin state correlations in mesoscopic spin glasses. We have also shown the crucial importance of spatial correlations between spin configurations in the electronic dephasing process. Studying these correlations along the lines of Fig. 4 could be experimentally achieved by varying the electronic density in diluted magnetic semiconductors. Unfortunately this would also modify the couplings between the impurity spins, and hence the spin configuration. A more promising route consists in exploring other multi-terminal geometries along the lines of [8].

FIG. 1 :

 1 FIG. 1: Probability Density Function of the difference g[V, { S

FIG. 2 :

 2 FIG.2: Conductance correlations as a function of spin configurations overlap for different longitudinal sizes, and normalized by their value for Q12 = 1. In the inset, the conductance fluctuations (Q12 = 1) are plotted as a function of Lx/Lm.

FIG. 3 :

 3 FIG.3: Comparison between the correlation between conductances σ = 2( (δg)2 V -δg1δg2 V ) and the so-called Diffuson Singlet contribution F (0) -F (Lx/L D,S m ). This contribution is found to be dominant in the region Q12 ≃ 1. In the inset we plot this σ function for different value of overlap Q12 and for J = 0.1. Plain lines are theoretical fits allowing to determine L D,S m (Q12, J). System size is 40 × 1600.

2 FIG. 4 :

 24 FIG.4: Left: evolution of the Diffuson Singlet dephasing rate of 1/(L D,S m ) 2 as a function of the electronic dephasing rate 1/(L 2 m ) for mean-field like, spin wave (dash dot), and boxed excitations. The overlap is 0.9 for all of them, and the size is 40 × 1600. The linear dependance corresponds to the analytical expression 1/(L D,S m ) 2 = (1 -Q12)/(L 2 m ), valid in the absence of spatial correlations between the spin states. These results show the clear departure from this behavior for strong spatial correlations, and the absence of any effective overlap. Right: same evolution for random configurations and for spin wave with two different spatial periods corresponding to the same overlap (Q = 0.54). The stronger correlation (longer period) corresponds to the larger deviation from the linear law.

We thank T. Capron for a much informative discussion concerning possible experimental test of our results. This work was supported by the ANR grants QuSpins and Mesoglass. All numerical calculations were performed on the computing facilities of the ENS-Lyon calculation center (PSMN).


PhD Catherine Fiévet
email: catherine.fievet@pasteur-lille.fr

Bart Staels
email: bart.staels@pasteur-lille.fr

Combination therapy of statins and fibrates in the management of cardiovascular risk

Keywords: Cardiovascular risk factors, residual risk, statins, fibrates, dyslipoproteinemia

Purpose of review

Despite that statin treatment substantially reduces cardiovascular morbidity and mortality, many treated patients still experience a high residual risk. Statins lower LDL-cholesterol (LDL-C), with limited effects on other lipid parameters. Fibrates improve atherogenic dyslipidemia characterized by high triglyceride and/or low HDL-C levels and elevated concentrations of small dense LDL particles, with or without high LDL-C levels. Fibrates decrease cardiovascular morbidity especially in patients with the metabolic syndrome. The purpose of this review is to provide a rationale for the combined use of statins and fibrates in the management of patients with high residual cardiovascular risk related to atherogenic dyslipidemia and persisting after single therapy.

Recent findings

A meta-analysis from 14 randomised trials conducted in high-risk patients reported that statin therapy is effective in reducing the proportional risk for major vascular events by 21% for each mmol/L lowering of LDL-C. However, on average 14% of patients still experienced an event despite being allocated to statin. Beyond LDL-C, other factors, including triglycerides, non-HDL-C, HDL-C and apolipoprotein B, have been identified as factors determining residual risk, and normalization of these parameters may further decrease cardiovascular disease in patients treated with statins. Data from fibrate trials indicate that these drugs are particularly effective in reducing cardiovascular morbidity in patients with atherogenic dyslipidemia.

Summary

Reducing the residual cardiovascular risk in patients treated with statins requires addressing multiple lipid goals. In this context, future therapeutic interventions based on combination therapy, such as statins and fibrates, appears particularly promising.

Introduction

An elevated low-density lipoprotein cholesterol (LDL-C) level is a major risk factor for cardiovascular disease (CVD), and several randomised clinical trials have shown that lowering LDL-C levels with statins results in a substantial reduced CVD morbidity and mortality [1,2 • ,3]. However, a significant number of treated patients continue to experience events, despite targeting LDL-C levels according to current guidelines [START_REF] Kearney | Efficacy of cholesterol-lowering therapy in 18,686 people with diabetes in 14 randomised trials of statins: a meta-analysis[END_REF][START_REF] Delahoy | The relationship between reduction in lowdensity lipoprotein cholesterol by statins and reduction in risk of cardiovascular outcomes: an updated meta-analysis[END_REF]. Moreover, even upon high doses of statins, a substantial residual risk remains [START_REF] Cannon | Meta-analysis of cardiovascular outcomes trials comparing intensive versus moderate statin therapy[END_REF][START_REF] Afilalo | Intensive statin therapy in acute coronary syndromes and stable coronary heart disease: a comparative meta-analysis of randomised controlled trials[END_REF].

Data from the INTERHEART study indicated that dyslipidemia is responsible for more than 50% of population-attributable vascular risk [START_REF] Yusuf | Effect of potentially modifiable risk factors associated with myocardial infarction in 52 countries (the INTERHEART study): casecontrol study[END_REF]. Within this context, more and more attention is now being paid to atherogenic dyslipidemia which is characterized by elevated triglyceride (TG) and low HDL-C levels, a preponderance of small, dense LDL particles, and an accumulation of cholesterol-rich remnant particles with high levels of apolipoprotein (apo) B.

These lipoprotein abnormalities are frequently found in patients with high vascular risk, including patients with the metabolic syndrome (MS) or type 2 diabetes mellitus (T2DM) [START_REF] Carr | Abdominal obesity and dyslipidemia in the metabolic syndrome: importance of type 2 diabetes and familial combined hyperlipidemia in coronary artery disease risk[END_REF][START_REF] Tenenbaum | Which is the best lipid-modifying strategy in metabolic syndrome and diabetes: fibrates, statins or both?[END_REF]. Although the primary goal to reduce the cardiovascular risk in these patients is LDL-C lowering [START_REF] Grundy | Implications of recent clinical trials for the National Cholesterol Education Program Adult Treatment Panel III guidelines[END_REF], current treatment guidelines emphasize the relevance of considering the other lipoprotein abnormalities, but also non-lipid risk factors (such as tobacco consumption, blood pressure, physical activity, weight management….) that contribute to global risk [START_REF] Smith | AHA/ACC guidelines for secondary prevention for patients with coronary and other atherosclerotic vascular disease: 2006 update: endorsed by the National Heart, Lung, and Blood Institute[END_REF][START_REF] Buse | Primary prevention of cardiovascular diseases in people with diabetes mellitus: a scientific statement from the American Heart Association and the American Diabetes Association[END_REF][START_REF] Graham | European guidelines on cardiovascular disease prevention in clinical practice: executive summary[END_REF].

Statins and fibrates are both lipid-lowering drugs. Statins are hydroxymethylglutarylcoenzyme A reductase inhibitors, inhibiting the synthesis of cholesterol, and are primarily LDL-C-lowering agents. Fibrates activate the peroxisome proliferator-activated receptor α (PPARα), a transcription factor that regulates the expression of a number of genes involved in multiple metabolic pathways including lipid metabolism, ultimately reducing plasma TG concentrations and enhancing HDL levels [14 • ]. Fibrates have a beneficial action on the atherogenic dyslipidemia. The differences in action mechanisms of statins and fibrates, resulting in distinct pharmacological effects and an improvement of different components of the lipid profile, provide a rationale for their use in combination in patients with high residual cardiovascular risk related to atherogenic dyslipidemia and persisting after single therapy, such as patients with the MS or T2DM.

Besides their effects on lipid metabolism, fibrates and statins display other pleiotropic effects, such as an improvement of endothelial function, a reduced inflammation at both vascular and systemic levels, an increased stability of atherosclerotic plaques, and a decreased thrombogenic response. Evidence suggests that, at least for statins, these pleiotropic effects may play a role in the reduction of cardiovascular morbidity and mortality [15,16 Pleiotropic effects of fenofibrate might explain the positive effects of fenofibrate on microvascular complications of T2DM, and a potential benefit on the CVD risk [START_REF] Ansquer | Fibrates and microvascular complications in diabetes--insight from the FIELD study[END_REF].

However, whether combination statin-fibrate therapy is more effective on inflammatory markers than either form of monotherapy requires further investigation [START_REF] Koh | Additive beneficial effects of fenofibrate combined with atorvastatin in the treatment of combined hyperlipidemia[END_REF][START_REF] Muhlestein | The reduction of inflammatory biomarkers by statin, fibrate, and combination therapy among diabetic patients with mixed dyslipidemia: the DIACOR (Diabetes and Combined Lipid Therapy Regimen) study[END_REF].

Patients treated with statins still experience a residual cardiovascular risk

A meta-analysis from 14 randomized secondary and/or primary prevention trials studied the efficacity of cholesterol-lowering therapy by statin therapy in patients with pre-existing coronary heart disease (CHD), history of diabetes or hypertension, i.e in a wide range of highrisk patients, having variable baseline lipid profile [START_REF] Baigent | Efficacy and safety of cholesterol-lowering treatment: prospective meta-analysis of data from 90,056 participants in 14 randomised trials of statins[END_REF]. This analysis reported that statin therapy efficaciously reduces the risk for vascular events (defined as the composite outcome of myocardial infarction (MI) or coronary death, stroke, or coronary revascularisation) by 21% for each mmol/L lowering of LDL-C (relative risk (RR), 0.79 ; 95% confidence interval (CI), 0.77-0.81 ; p<0.0001) [START_REF] Baigent | Efficacy and safety of cholesterol-lowering treatment: prospective meta-analysis of data from 90,056 participants in 14 randomised trials of statins[END_REF]. Despite this, treated patients are left with a substantial relative residual risk, and 1 in 7 patients experienced events over a 5-year period. More recently, analyses of the diabetic patients in these studies showed that statin therapy results in a proportionally similar reduction in vascular events irrespective of whether diabetes was present (0.79 ; 0.72-0.86 ; p<0.0001 with diabetes versus 0.79 ; 0.76-0.82 ; p<0.001 without diabetes) [START_REF] Kearney | Efficacy of cholesterol-lowering therapy in 18,686 people with diabetes in 14 randomised trials of statins: a meta-analysis[END_REF]. However, among the diabetic patients, the presence of low HDL-C and/or elevated TG limits the reduction in vascular events, even if patients achieve LDL-C levels below current targets [START_REF] Kearney | Efficacy of cholesterol-lowering therapy in 18,686 people with diabetes in 14 randomised trials of statins: a meta-analysis[END_REF].

Intensive statin therapy with high-dose statins, resulting in LDL-C levels that are maximally reduced below currently optimal thresholds for treatment of very high-risk patients (i.e <70 mg/dL), provides an additional and significant cardiovascular benefit in patients with recent acute coronary syndromes (ACS) and stable CHD over standard-dose therapy [START_REF] Cannon | Meta-analysis of cardiovascular outcomes trials comparing intensive versus moderate statin therapy[END_REF][START_REF] Afilalo | Intensive statin therapy in acute coronary syndromes and stable coronary heart disease: a comparative meta-analysis of randomised controlled trials[END_REF]. However, despite this, patients were still at very high residual risk, and although the combined analysis from 4 large trials yielded a 16% relative reduction of coronary death or any cardiovascular event (defined as MI, stroke, hospitalization for unstable angina, or revascularization) (p<0.0001), 28.8% of patients still experienced events [START_REF] Cannon | Meta-analysis of cardiovascular outcomes trials comparing intensive versus moderate statin therapy[END_REF]. More recently, pooled data from 6 trials, analysing separately recent ACS and stable CHD, showed that intensive statin therapy is associated with a reduction of 14 and 18% in cardiovascular death, ACS, or stroke, but is still leaving respectively 1 in 4 and 10 patients at risk, depending on their clinical subcategory [START_REF] Afilalo | Intensive statin therapy in acute coronary syndromes and stable coronary heart disease: a comparative meta-analysis of randomised controlled trials[END_REF]. Whether further increasing statin doses in monotherapy to further enhance LDL-C lowering is an appropriate strategy is a matter of debate for different reasons. First, because of the flattening of the dose-response curve at higher doses, the therapeutic benefit of dose increases likely becomes smaller, and recent data indicated that ACS patients with the lowest LDL-C levels have only modest clinical benefits after intensive statin therapy [START_REF] Giraldez | Baseline low-density lipoprotein cholesterol is an important predictor of the benefit of intensive lipid-lowering therapy: a PROVE IT-TIMI 22 (Pravastatin or Atorvastatin Evaluation and Infection Therapy-Thrombolysis In Myocardial Infarction 22) analysis[END_REF]. Second, increasing the statin dose occurs at the expense of increased risk for adverse events such as myalgia and/or elevations in liver or muscle enzymes. Third, the optimal target for LDL-C remains unknown and a large randomized trial is underway to examine whether the addition of ezetimibe to simvastatin, resulting in further decreased LDL-C as compared to changes obtained after simvastatin alone, translates into clinical benefit on cardiovascular events in patients with ACS [21 • ]. Finally, beyond LDL-C other additional lipid, especially those associated with atherogenic dyslipidemia, and non-lipid factors determine the cardiovascular risk. Therefore it cannot be determined whether benefits of intensive statin therapy are due to high-dose statins resulting in effects on other factors than solely LDL-C, or solely due to LDL-C level lowering. Interestingly, it has been recently demonstrated that statin-treatment decreases cardiovascular event rates even in asymptomatic subjects with normal LDL-C concentrations but with evidence of inflammation as assessed by increased levels of the inflammatory biomarker high-sensitive C-reactive protein (hsCRP) [16

Other lipoprotein parameters beyond LDL-C determine the CVD risk

Post-hoc analysis of 4S trial showed that patients with combined dyslipidemia at baseline, i.e elevated LDL-C, low HDL-C, and elevated TGs, had increased morbidity and an increased major coronary event (death, MI) rate on placebo [START_REF] Ballantyne | Influence of low high-density lipoprotein cholesterol and elevated triglyceride on coronary heart disease events and response to simvastatin therapy in 4S[END_REF]. Moreover, patients with T2DM experience higher rates of cardiovascular events with decreasing HDL-C and increasing TG concentrations, and an increasing LDL/HDL ratio [START_REF] Kearney | Efficacy of cholesterol-lowering therapy in 18,686 people with diabetes in 14 randomised trials of statins: a meta-analysis[END_REF]. Finally, retrospective analyses demonstrate that the achievement of combined lipid values, rather than solely reducing LDL-C, is associated with a reduced risk of cardiovascular events [START_REF] Cziraky | The impact of residual CVD risk in the managed care setting[END_REF].

The residual cardiovascular risk that remains after statin treatment is of multifactorial origin, and recent post-hoc analyses from clinical trials suggests an important contribution of lipid parameters other than LDL-C. It has long been established that HDL-C levels are a strong, independent inverse predictor of CVD [START_REF] Gordon | High density lipoprotein as a protective factor against coronary heart disease. The Framingham Study[END_REF]. Accordingly, post-hoc analyses showed that the risk of CVD events was inversely related to HDL-C levels in individuals with CVD who achieved LDL-C levels <70mg/dL upon statin treatment [START_REF] Barter | HDL cholesterol, very low levels of LDL cholesterol, and cardiovascular events[END_REF][START_REF] Degoma | Clinical significance of high-density lipoprotein cholesterol in patients with low low-density lipoprotein cholesterol[END_REF]. A pooled analysis of 4 statin trials showed that a moderate increase in HDL-C (7.5%) correlated with atheroma regression [START_REF] Nicholls | Statins, high-density lipoprotein cholesterol, and regression of coronary atherosclerosis[END_REF]. Finally, from the BIP study, post-hoc extended analysis showed that HDL-C increments during bezafibrate therapy are inversely correlated with cardiovascular risk [29 • ], and longterm follow-up reported long-term reduction in mortality [START_REF] Goldenberg | Long-term benefit of high-density lipoprotein cholesterol-raising therapy with bezafibrate: 16-year mortality follow-up of the bezafibrate infarction prevention trial[END_REF].

Extensive evidence supports elevated TG levels, predominantly in the post-prandial state, as a predictor for CVD [START_REF] Bansal | Fasting compared with nonfasting triglycerides and risk of cardiovascular events in women[END_REF][START_REF] Mcbride | Triglycerides and risk for coronary heart disease[END_REF], and a recently published meta-analysis of 29 prospective studies An accurate management of cardiovascular risk requires assessment of all atherogenic lipoprotein particles, not only LDL. Non-HDL-C levels correspond to the mass of cholesterol within all atherogenic lipoprotein particles, and apoB and/or LDL particle number provides an estimate of atherogenic particle concentrations. Although it has been shown that non-HDL-C is an important target of therapy for non-fatal MI and coronary death [START_REF] Robinson | Meta-analysis of the relationship between nonhigh-density lipoprotein cholesterol reduction and coronary heart disease risk[END_REF], whether it may further reduce excessive residual CVD risk along with LDL-C still remains open [START_REF] Ray | Prognostic utility of apoB/AI, total cholesterol/HDL, non-HDL cholesterol, or hs-CRP as predictors of clinical risk in patients receiving statin therapy after acute coronary syndromes: results from PROVE IT-TIMI 22[END_REF][START_REF] Kastelein | Lipids, apolipoproteins, and their ratios in relation to cardiovascular events with statin treatment[END_REF].

Studies reporting both measurement of LDL particles by nuclear magnetic resonance and/or apoB, and LDL-C have consistently found that total LDL particle number is a better predictor of CVD risk than LDL-C with the objective to reduce this risk [39,40,41 • ], particularly in patients with the MS [42 • ].

Mechanistic rationale for statin and fibrate combination therapy

Statins primarily lower LDL-C and have only limited effects on TGs and HDL-C at commonly used doses and in patients without marked hypertriglyceridemia. Moreover they do not normalize the LDL size-distribution pattern. Fibrate treatment results in reduced plasma TG, non-HDL-C, and apoB. Fibrates also positively influence HDL metabolism, through an increase in the PPARα-mediated transcription of apoAI and apoAII, the two major apolipoproteins of HDL, and stimulate reverse cholesterol transport by modulating macrophage cholesterol efflux and cholesterol transport, resulting in raised levels of HDL with absolute changes that depend on the fibrate. The effect of fibrates on LDL-C is variable, ranging from a small decrease to essentially no changes or even a slight increase in highly hypertriglyceridemic patients. Moreover, fibrates increase LDL particle size and modify LDL subclass distribution from small, dense particles to large buoyant LDL particles, and reduce the number of small LDL particles in patients with hypertriglyceridemia and the MS [43, [START_REF] Filippatos | Treatment of hyperlipidaemia with fenofibrate and related fibrates[END_REF][START_REF] Rosenson | Fenofibrate therapy ameliorates fasting and postprandial lipoproteinemia, oxidative stress, and the inflammatory response in subjects with hypertriglyceridemia and the metabolic syndrome[END_REF]. In vivo kinetic experiments showed that atorvastatin or fenofibrate treatment of patients with T2DM or the MS and hypertriglyceridemia, results in a similar decrease of plasma TG levels probably due to comparable effects on VLDL-apoCIII kinetics [START_REF] Chan | Atorvastatin and fenofibrate have comparable effects on VLDL-apolipoprotein C-III kinetics in men with the metabolic syndrome[END_REF], and distinct but favourable effects on apoB-containing lipoproteins with apoB100 and apoB48 metabolism [START_REF] Hogue | Differential effect of fenofibrate and atorvastatin on in vivo kinetics of apolipoproteins B-100 and B-48 in subjects with type 2 diabetes mellitus with marked hypertriglyceridemia[END_REF]. By contrast to atorvastatin, fenofibrate displayed significant effects on apoAI metabolism in HDL [START_REF] Watts | Differential regulation of lipoprotein kinetics by atorvastatin and fenofibrate in subjects with the metabolic syndrome[END_REF]. All these observations provide the rationale for the use of fibrate-statin combination therapy to optimally control dyslipoproteinemia in patients with T2DM or the MS.

Fibrates reduce CVD in patients with atherogenic dyslipidemia

A number of angiographic and intervention trials have shown that fibrates can slow the progression of atherosclerotic disease and decrease CVD morbidity [14 •• ]. However, most of the large prospective trials have been disappointing with respect to the primary endpoints, and meta-analysis suggest that fibrates do not influence overall mortality [START_REF] Saha | Fibrates in the prevention of cardiovascular disease in patients with type 2 diabetes mellitus -A pooled meta-analysis of randomized placebo-controlled clinical trials[END_REF]. It is likely that these fibrate trials produced mixed results due to the large differences in study populations. Indeed, post-hoc or follow-up analyses have consistently demonstrated that fibrates are more effective at reducing macrovascular events among patients with the MS. The HHS was a primary prevention trial testing gemfibrozil as active agent in men with primary dyslipidemia (non-HDL-C > 200mg/dL). An 18-year mortality follow-up analysis showed that patients with a body mass index and TG concentrations in the highest tertile had significantly lower rates of CHD mortality (71% lower relative risk) and all-cause mortality (33% lower relative risk) compared with those in the original placebo group [START_REF] Tenkanen | Gemfibrozil in the treatment of dyslipidemia: an 18-year mortality follow-up of the Helsinki Heart Study[END_REF]. The VA-HIT trial randomized men with low HDL-C, and LDL-C concentrations nearly at goal (<100 mg/dL) at baseline, to treatment with gemfibrozil or placebo. Participants with T2DM or those without T2DM but with insulinemia in the highest fasting plasma insulin quartile benefited from a higher reduction in the RR for major cardiovascular events (a composite of CHD death, stroke, and non-fatal MI) than in the entire study population (RR of 32, 35 and 24% respectively) [START_REF] Rubins | Diabetes, plasma insulin, and cardiovascular disease: subgroup analysis from the Department of Veterans Affairs high-density lipoprotein intervention trial (VA-HIT)[END_REF] after fibrate therapy. In the BIP study, bezafibrate treatment failed to achieve significance of the primary end point (a composite of fatal or non-fatal MI or sudden death) in patients with elevated LDL-C, low HDL-C and TG<150mg/dL. However, a post-hoc analysis showed significantly reduced event rates in patients with elevated TG levels [START_REF]Secondary prevention by raising HDL cholesterol and reducing triglycerides in patients with coronary artery disease: the Bezafibrate Infarction Prevention (BIP) study[END_REF]. More recently, a further post-hoc analysis confirmed that bezafibrate is more effective at reducing cardiovascular events among patients with the MS, with a more pronounced reduction in cardiac mortality depending on the number of MS features [START_REF] Tenenbaum | Bezafibrate for the secondary prevention of myocardial infarction in patients with metabolic syndrome[END_REF]. Finally, the FIELD study investigated the effects of fenofibrate on CVD morbidity and mortality in patients with earlystage, well-controlled T2DM. Although after 5 years of treatment there was not a significant risk reduction in the primary end point (CVD death or nonfatal MI), there was a significant reduction of total CVD events, particularly nonfatal MI and coronary revascularization. One potential problem in the study was the higher rate of statin therapy drop-in in the placebo group, which might have masked treatment benefit. Nevertheless, further subgroup analyses demonstrated that in the cohort with the most dyslipidemic profile, i.e low HDL-C and/or elevated TG levels, fenofibrate was significantly more efficacious (27% RR reduction) [35

Statin and fibrate combination therapy may be an appropriate therapeutic approach to reduce the global cardiovascular risk in patients with atherogenic or combined dyslipidemia

The distinct mechanisms of action, resulting in different clinical effects, of statins and fibrates provide a rationale for combined use in the treatment of patients with dyslipidemia and high residual cardiovascular risk persisting after single therapy.

A recent post-hoc analysis of the BIP study using bezafibrate showed that in patients with low HDL-C and moderately elevated LDL-C, the clinical benefit of HDL-C and TG modification in terms of cardiac events (nonfatal MI or death) is inversely related with baseline levels of LDL-C, demonstrating enhanced benefit in patients with low LDL-C, whereas the benefit of LDL-C modification is more prominent in patients with increased LDL-C [54 • ]. Hence, combined assessment of LDL-C, HDL-C and TGs as therapeutic targets for lipid modification using lipid-lowering drugs may provide an incremental benefit on top of approaches based solely on LDL-C modification. Hence, a statin combination therapy with fibrates or other drugs that would enhance HDL-C and decrease TGs is recommended in such patients [START_REF] Grundy | Implications of recent clinical trials for the National Cholesterol Education Program Adult Treatment Panel III guidelines[END_REF]. Short-term clinical studies have shown that combined therapy with statin and fenofibrate is more effective in controlling atherogenic dyslipidemia in patients with T2DM, the MS or combined dyslipidemia than the administration of either drug alone [18,55,56,57,58 • ].

Accordingly, it has been calculated that atorvastatin-fenofibrate combination therapy for 24 weeks to patients with T2DM, free of CVD at entry, would reduce the estimated risk for MI within the next 10 years from 21.6 to 4.2% [55]. Fenofibrate is an ester of fenofibric acid and requires first pass metabolism to form the active metabolite, fenofibric acid. ABT-335, the choline salt of fenofibric acid, is more hydrophilic than fenofibrate. This compound dissociates to form the free acid in the gastrointestinal tract, and fenofibric acid is rapidly absorbed without requiring first-pass metabolism. Recently, a large phase III clinical trial evaluating ABT-335 in combination with simvastatin, atorvastatin or rosuvastatin in patients with mixed dyslipidemia (TG>150mg/dL, HDL-C<40mg/dL for men and <50mg/dL for women, LDL-C>130mg/dL) demonstrated that combination results in a more effective control of lipid parameters than either monotherapy alone [59 • ,60 Thus, from these data, it is evident that the combination of statin and fibrates results in an improved control of the atherogenic lipid profile often found in high-cardiovascular risk patients. However, whether this beneficial effect translates into risk reduction is not yet known. This will be answered by the lipid-lowering arm of the ongoing ACCORD study [62 •• ]. The ACCORD trial is a randomized clinical trial aimed at determining the effects on CVD of intensive glycemic control in combination with strategies for lipid and/or blood pressure management in patients with T2DM. In February 2008, the glycemic control study was halted due to the finding of an increased rate of mortality in the intensive arm compared with the standard arm. The blood pressure and lipid studies are still ongoing. The lipid arm tests the hypothesis whether, in the context of good glycemic control, adding fenofibrate to simvastatin will reduce the rate of CVD events compared to statin plus placebo.

Despite the potential benefit of fibrate statin combination therapy on the lipid profile, case reports of severe myopathy and rhabdomyolysis have raised concerns regarding safety of this coadministration. However, the absolute risk is low. Moreover, differences exist due to differences in pharmacokinetics and drug-drug interactions [START_REF] Jones | Reporting rate of rhabdomyolysis with fenofibrate + statin versus gemfibrozil + any statin[END_REF]. Pharmacokinetic data on the interactions between statins and fibrates suggest that gemfibrozil inhibits statin glucuronidation and its hepatic metabolism, inducing therefore higher statin concentrations, whereas other fibrates, such as fenofibrate, have a relatively low potential for interaction with statin metabolism [START_REF] Prueksaritanont | Effects of fibrates on metabolism of statins in human hepatocytes[END_REF]. Indeed, the combination of ABT-335 and rosuvastatin did not alter fenofibric acid pharmacokinetics, nor the rosuvastatin AUC, indicating that ABT-335 does not have a clinically significant pharmacokinetic interaction with rosuvastatin in humans [START_REF] Zhu | ABT-335, the choline salt of fenofibric acid, does not have a clinically significant pharmacokinetic interaction with rosuvastatin in humans[END_REF].

Hence, current guidelines recommend fenofibrate as the fibrate of choice for high-risk statintreated patients with atherogenic dyslipidemia [START_REF] Grundy | Clinical management of metabolic syndrome: report of the American Heart Association/National Heart, Lung, and Blood Institute/American Diabetes Association conference on scientific issues related to management[END_REF].

Conclusion and future perspectives

Although statins reduce cardiovascular morbidity and mortality owing, in part, to reduced LDL-C, a number of treated patients still face a very high cardiovascular risk. In fact, significant proportions of such patients are not reaching lipid goals. Generally they suffer from an atherogenic dyslipidemia associated to T2DM or the MS, which is not adequately corrected by statin therapy. Therefore, beyond a further decrease in LDL-C which could be achieved through the addition of other cholesterol-lowering agents, such as intestinal cholesterol absorption inhibitors (ezetimibe), other therapeutical approaches have to be developed for these dyslipidemic patients. Indeed, current guidelines recommend the addition of other drugs to achieve multiple lipid goals after LDL-C targets have been reached by statin therapy. Among these drugs, fibrates present a great interest because of its effects to reduce TG levels, improve LDL particle size and number, and increase HDL-C concentrations. Other drugs, such as niacin, merit also further investigation since these compounds increase HDL-C even more pronouncedly.

  (262,525 participants, 10,158 with CHD confirmed this association, showing independence from other risk factors, including HDL-C[START_REF] Sarwar | Triglycerides and the risk of coronary heart disease: 10,158 incident cases among 262,525 participants in 29 Western prospective studies[END_REF]. Post-hoc analysis of the PROVE-IT TIMI-22 trial showed that among patients with ACS treated with statins, on-treatment TG>150mg/d was associated with a higher risk of recurrent CVD events independently of the level of LDL-C [34•• ]. Finally, a post-hoc analysis of the FIELD study showed that the largest effects of fenofibrate to reduce CVD risk is obtained in individuals with the MS and hypertriglyceridemia or combined dyslipidemia (defined as TG levels >2.3 mmol/L alone or with a low HDL-C level, respectively)[35 •• ]. The absolute risk reduction in the presence of marked dyslipidemia was 4.3% compared with 0.8% in its absence, corresponding to a number needed to treat of 23 compared with 143, respectively.

  •• ], and that clinical benefits are maximised when both LDL-C and hsCRP are reduced [22

  •• ]. These studies demonstrate the need for considering markers of inflammation beyond LDL-C in the management of CVD.