F R Éd

Éric Dias

Denys Dutykh
email: denys.dutykh@univ-savoie.fr

Laura O'brien

Emiliano Renzi
email: emiliano.renzi@ucd.ie

Themistoklis Stefanakis
email: stefanakis.themistoklis@gmail.com

ON THE MODELLING OF TSUNAMI GENERATION AND TSUNAMI INUNDATION

Keywords: tsunamis, run-up, landslides, tsunami generation, tsunami inundation

While the propagation of tsunamis is well understood and well simulated by numerical models, there are still a number of unanswered questions related to the generation of tsunamis or the subsequent inundation. We review some of the basic generation mechanisms as well as their simulation. In particular, we present a simple and computationally inexpensive model that describes the seabed displacement during an underwater earthquake. This model is based on the finite fault solution for the slip distribution under some assumptions on the kinematics of the rupturing process. We also consider an unusual source for tsunami generation: the sinking of a cruise ship. Then we review some aspects of tsunami run-up. In particular, we explain why the first wave of a tsunami is sometimes less devastating than the subsequent waves. A resonance effect can boost the waves that come later. We also look at a particular feature of the 11 March 2011 tsunami in Japanthe formation of macro-scale vortices -and show that these macro-scale vortices can be captured by the nonlinear shallow water equations.

1. Introduction the water surface is perturbed. There are three main types of disturbances: underwater earthquakes concentrated in zones where there is slipping or subduction of tectonic plates, submarine landslides which are often but not always triggered by earthquakes, and sudden earth surface movements adjacent to the ocean (volcanoes, rock falls, sub-aerial landslides, ship sinking). In the generation of tsunamis by earthquakes the key point is to predict the displacement of the sea bottom, and then to understand the energy transfer to the water column. The generation of tsunamis by submarine landslides is even more challenging for various reasons: lack of data, coupling between fluid and solid motions, longer duration, more physical parameters. The modeling of sudden earth surface movements adjacent to the ocean has not been much studied, the reason being that such movements are quite rare.

The propagation of tsunamis is now well understood and operational codes can easily propagate tsunamis across a whole ocean (see for example the various simulations of the megatsunamis of 2004 in the Indian Ocean and of 2011 in the Pacific Ocean).

Wave run-up (maximum vertical extent of wave uprush on a beach above still water level) and wave inundation (maximum horizontal extent) have been studied during the last sixty years, but continue to be a challenging problem. A high level of mesh refinement as well as high resolution bathymetric and topographic data are required to describe local wave run-up.

Our group has developed a novel tool for tsunami wave modelling. This tool has the potential of being used for operational purposes: indeed, the numerical code VOLNA is able to handle the complete life-cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. A detailed description of the finite volume scheme implemented in the code as well as the numerical treatment of the wet/dry transition can be found in [START_REF] Dutykh | The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation[END_REF].

In Section 2, we review some of the basic generation mechanisms as well as their simulation. In particular, we present a simple and computationally inexpensive model that describes the seabed displacement during an underwater earthquake. This model is based on the finite fault solution for the slip distribution under some assumptions on the kinematics of the rupturing process. We also consider an unusual source for tsunami generation: the sinking of a cruise ship. In Section 3, we review some aspects of tsunami run-up. In particular, we explain why the first wave of a tsunami is sometimes less devastating than the subsequent waves. A resonance effect can boost the waves that come later. We also look at a particular feature of the 11 March 2011 tsunami in Japan -the formation of macro-scale vortices -and show that these macro-scale vortices can be captured by the nonlinear shallow water equations.

Tsunami generation

The modelling of tsunami generation was initiated in the early 1960's by the prominent work of Kajiura [14], who proposed the static approach which is still widely used by the tsunami wave modelling community: the static sea bed displacement is translated towards the free surface as an initial condition. The most classical solution for the co-seismic sea bed displacements is the celebrated Okada solution [START_REF] Okada | Surface deformation due to shear and tensile faults in a half-space[END_REF]. The kinematics of earthquakes is relatively well understood. The maximum bottom deformation is achieved during a finite time known as the rise time. For example the rise time was 8 seconds for the July 17, 2006 Java event simulated by Dutykh et al. [6]. In the next subsection, we will show how kinematics can be taken into account in tsunami generation.

However, modelling tsunamis generated by landslides is far more complicated. Firstly, the kinematics of underwater landslides is not well understood. Also the time scale over which they occur is longer than for an earthquake, so simply transferring the sea bed deformation directly to the free surface does not accurately model the landslide. For onedimensional landslides, Liu et al. [15] showed that the free-surface elevation is significantly different from the bottom motion by using an anlytical technique developed by Tuck & Hwang [35]. Sammarco & Renzi [START_REF] Ezersky | Physical simulation of resonant wave run-up on a beach[END_REF] extended the results to two-dimensional landslides (see also [START_REF] Renzi | Landslide tsunamis propagating around a conical island[END_REF]27]). Sarri et al.

[29] used the Sammarco & Renzi model to build a statistical emulator.

Mass movements on dry land can be put into a number of different categories. Rotational slides, translational slides, block slides, falls, topples, debris flows, debris avalanches, earthflows, creep and lateral spreads each have their own characteristic kinematics of motion. However, when considering landslides that are in contact with water, our knowledge of the kinematics in this environment is lacking. This is due to lack of data, in particular lack of bathymetry data prior to large tsunamigenic events.

A recent review of submarine mass movements [16] shows that they can consist of soil and rock, and similar to dry land movements they can take the form of slides, spreads, flows, topples or falls, but in addition they can develop into turbidity currents. They can move up to to 50 km/h, reach distances over 1000 km and volumes can be enormous, the largest known being the Storegga slide at approximately 2500 km 3 . Underwater mass movements pose a threat to coastal communities and infrastructures both onshore and offshore. The main triggers are seismic shaking, overloading gas hydrate dissolution and excess pore pressure, wave loading, erosion and human activities such as coastal construction. The 1998 Papua New Guinea tsunami generated a renewed interest in tsunamigenic landslides.

Although generally landslide tsunamis occur over a much smaller scale than earthquakes (O(1km) vs O(100km)), they can cause very large run-up values. Gutenberg [11] was one of the first to suggest that tsunamis can be caused by submarine landslides. He goes so far as to say that they can be considered as one of the chief causes of tsunamis. He reported that co-seismic landslides possibly triggered large waves in Ceram in 1899, Assam in 1897 and caused cable breaks in Greece in the 19th century. More recently, in 1979, a part of the Nice harbour extension slumped into the Mediterranean and was followed by a small tsunami [START_REF] Assier-Rzadkieaicz | Numerical Modelling of a Landslide-generated Tsunami: The 1979 Nice Event[END_REF].

The Storegga slide is one of the largest known submarine landslides (2500 -3500 km 3 ) and occurred off the west coast of Norway generating a huge tsunami 8200 years ago [2]. In 1929 an earthquake at the edge of Grand Banks, Canada, triggered a large submarine slope failure (200 km 3 ) generating a tsunami with run-up heights up to 13 m that propagated as far as Portugal and the Azores Islands [START_REF] Fine | The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling[END_REF]. A tsunami generated by a 0.03 km 3 of rock falling from 914 m into Lituya Bay, Alaska, in 1958 is dubbed the world's largest tsunami at 524 m. Plafker [START_REF] Plafker | Tectonic Deformation Associated with the 1964 Alaska Earthquake: The earthquake of 27 March 1964 resulted in observable crustal deformation of unprecedented areal extent[END_REF] points out numerous major landslides that were triggered during the 1964 Alaska Earthquake.

There is debate about the triggering of the 1946 Aleutian tsunami that destroyed Scotch Cap's lighthouse. Freyer et al. [10] argue the possible involvement of a submarine slump that caused nearsource damage. Similarly, landslides have been suggested as a possible cause of amplification of the 1992 Flores Island tsunami [12]. Ma et al. [START_REF] Ma | Mechanism of the 1975 Kalapana, Hawaii, earthquake inferred from tsunami data[END_REF] demonstrate large scale slumping combined with faulting as a good model for the 1975 Kalapana, Hawaii tsunami.

Seafloor mapping has begun to open up the research of submarine landslides. Evidence of several underwater slides in the St. Lawrence estuary, Canada, have been identified through seafloor mapping [25].

The scale of the 1998 Papua New Guinea tsunami was a "wake-up call" for tsunami scientists. Although there was much controversy initially over the main trigger of the tsunami, the magnitude 7.1 earthquake was relatively small compared to the 10 -15 m tsunami that devastated the coast. Synolakis et al. [START_REF] Synolakis | The slump origin of the 1998 Papua New Guinea Tsunami[END_REF] presented high resolution bathymetric data combined with hydrodynamic modelling indicating a large underwater slump in the area. Subsequent research of this event has contributed to new and improved models of tsunamis due to submarine mass failure and it is now accepted by most scientists that the source of this event was a submarine slump [32].

There is also strong evidence that Island volcanoes such as Stromboli, Italy [START_REF] Chiocci | Morphologic resilience and depositional processes due to the rapid evolution of the submerged Sciara del Fuoco (Stromboli Island) after the December 2002 submarine slide and tsunami[END_REF], Ritter Island, Papau New Guinea [37] and the Hawaiian Islands [START_REF] Moore | Giant Hawaiian landslides[END_REF] Landslides have the potential to cause more destructive tsunamis than originally thought. They may be seismic triggered landslides amplifying waves originally generated from earthquakes, large scale collapsing of volcanoes into the sea, or rock falls from mountainous regions into restricted bays. In Section 2.2, we will consider a special case of tsunami, generated by the sinking of a cruise ship.

Finite fault.

Here we review some recent advances in seismology and show how to reconstruct better co-seismic displacements of a tsunamigenic earthquake. More precisely, we use the so-called finite fault solution developed by Ji and his collaborators [13], based on static and seismic data inversion. This solution provides multiple fault segments of variable local slip, rake angle and several other parameters. By applying Okada's solution to each subfault, the sea bed displacement is reconstructed with higher resolution. Since Okada's solution consists of relatively simple closed-form analytical expressions, all computations can be done efficiently enough so that they can be used in a real-time Tsunami Warning System. Seabed displacements are then coupled with a water wave model. Further details can be found in [6]. This approach was recently extended to include horizontal displacements as well [5]. Figure 1 shows snapshots of the free surface elevation for the July 17, 2006 tsunami generation. The x-axis is the longitude while the y-axis is the latitude. The times are in seconds. The water elevation is in meters.

2.2. Costa Concordia. This is the first application of the VOLNA code presented in this paper. A second one will be presented below. The Costa Concordia has been balancing nearly horizontally on its side since she partially sank on the night of 13 January 2012 on rocks beside the island of Giglio, Italy (see Figures 2 and3). The local bathymetry in the area contains a steep drop from approximately 20 m depth to over 100 m (see Figures 4 and5). Before the ship is stabilised, it is possible that she may slide into deeper waters and create waves that would travel along the island and possibly head towards the Italian mainland. If this were to happen, could a tsunami be generated?

A similar incident occurred off the Greek island of Santorini in 2007 with the MS Sea Diamond when she ran aground on a volcanic reef. The ship was towed off the rocks and stabilised, but the ship sank some 15 hours after it initially struck rocks. The bathymetry in the area is a caldera (cauldron-like volcanic feature) and so the shore is almost vertical. The stern now sits in about 180 m of water and the bow in about 60m (information obtained through Wikipedia). It was feared the wreck would slide deeper into the caldera below.

We consider here estimates taken from [START_REF] Miloh | Tsunamis effects at coastal sites due to offshore faulting[END_REF], Equation (2.1) and [23], Equation (2.2) for wave heights generated by displacements in the bathymetry:

η 1 = 8α ρ s ρ w ℓh L v c 1/2 (2.1)
and

η 2 (x, t) = h L v 2 2c exp (-k(x + ct) 2 ) -exp (-k(ξ + cτ ) 2 ) c + v + exp (-k(x -ct) 2 ) -exp (-k(ξ -cτ ) 2 ) c -v , (2.2)
where ξ = x -vT and τ = t -T . In these expressions, η denotes the free-surface elevation (maximum only for η 1 and space and time distribution for η 2 ). α is the transfer coefficient (only a portion of the landslide momentum is imparted on the water column), ρ s is the solid density, ρ w is the water density, w and ℓ are the two horizontal dimensions of the landslide, h L is the height of the landslide, v is the landslide velocity, c is the long wave velocity ( √ gh) with h the water depth, T is the duration of the landslide and k is a coefficient. The dimensions of the ship are 291 x 52 x 38 m 3 . Assuming that she is lying completely on her side, a rough geometry is shown in Figure 6. The following assumptions are used: the width parallel to the shore is w = 291 m, the height is h L = 38 m, the length is ℓ = 52 m, the distance from the top of the ship to the still water line is ≈ 38/2 = 19 m, the depth h is ≈ 38/2 = 19 m, and the slope of the shore is ≈ 80/400 = 0.2. We also assume that ρ s = ρ w = 1000 kg/m 3 , α = 0.01 and k = 18/ℓ 2 . Then the only missing parameter is the velocity v, which of course is difficult to estimate. Some sources say that the Titanic sank at approximately 15 m/s once she was completely submerged (information obtained through National Geographic). However, her stern lifted high into the air as the ship pivoted down into the water and she may have broken in two before she sank completely.

Although the Costa Concordia is of the same scale as the Titanic (she is actually bigger) Applying the above parameters to Equation (2.1) from [START_REF] Miloh | Tsunamis effects at coastal sites due to offshore faulting[END_REF] gives

η 1 = (8)(0.01)(1) (52)(38)v (9.8)(19) 1/2 = (11.6v) 1/2 m.
Sinking speeds of v = [0.001, 0.1, 1] m/s will give wave heights of η = [0.108, 1.08, 3.41] m. Therefore, the speed that the ship goes down at is an important parameter to get right.

Okal & Synolakis [23] model the free surface propagation due to an underwater gaussian slump source by Equation (2.2). With the above parameters for the Costa Concordia together with a total travel time T = 100 s and a velocity v = 1 m/s, the maximum occurs at x = 0, t = 0. The free-surface elevation at this point is η 2 (0, 0) = 0.2052 m. For v = 0.1 m/s, η 2 (0, 0) = 0.002 m and v = 10 m/s gives η 2 (0, 0) = 44.08 m. Again the velocity is an important parameter.

Simulations of the sinking of the Costa Concordia were carried out using the VOLNA code. A gaussian shaped slide with the same volume as above (291 x 52 x 38 m 3 ) was used as a model of the ship and three simulations were carried out with sinking speeds v = (0.5, 1, 10) m/s. The geometry is shown in Figure 7.

An unstructured triangular mesh was implemented over an area of 8.1 x 16 km 2 with a distance of 100 m behind the shoreline x = 0. The control volumes were of the order of 100 m, but refined to the order of 5 m in a 600 x 300 m 2 region near the ship (see Figure 8).

Each simulation was run for 300 seconds. The free surface plots for each simulation are shown at t = 75 s, t = 150 s and t = 300 s in Figures 9, 10 and 11 respectively.

Wave gauges were recorded at three points for each simulation: at the shore where the ship sinks (x, y) = (0, 0), on the shore line far from the slide (x, y) = (0, 400) and far offshore from the ship at (x, y) = (1000, 0). Figure 12 shows the free surface at (x, y) = (0, 0) from the time the ship leaves the shore and is completely submerged. The free surface values before this time are not applicable because the water depth is zero. For v = 10 m/s the maximum run-up value is 5.2 m, for v = 1 m/s the maximum run-up is 0.52 m and for v = 0.5 m/s there is no run-up for t < 300 s.

Figure 13 shows the wave gauge on the shore line far from the slide at (x, y) = (0, 400). Clearly the free surface amplitude for v = 10 m/s is much larger than for v = 1 m/s and v = 0.5 m/s. The maximum run-up for v = 10 m/s is 2 m, and negligible for the other two velocities.

Figure 14 shows the wave gauge far offshore from the ship at (x, y) = (1000, 0). The maximum run-up values for v = 10, 1 and 0.5 m/s are 3.32, 0.12 and 0.05 m respectively. Once again these results demonstrate the effect of the sinking velocity. If the ship were to sink slowly then a wave of only a few centimeters would be generated, however if it were to slide quickly down the steep slope it lies on, waves of a few meters could threaten not only the immediate coast, but the Italian mainland and the coastline on the island north and south of the ship. In particular, a wave entering the nearby port south of the Costa Concordia could be reflected and amplified. Since the sinking velocity is an important factor in determining the size of the waves, it is important to know the average density of the ship. Reports on the weight of the Costa Concordia vary. She has a dead weight of 10, 000 t but some reports suggest that she has an actual weight of 45, 000 t, not including luggage or water inside. If the ship is half filled with water then the mass of the water is 2.88 x 10 8 kg and adding this to 45, 000 t would give the ship a density of 579 kg/m 3 . This would give ρ s /ρ w < 1. However, if the ship was filled with water then ρ s = 1078 kg/m 3 and ρ s /ρ w ≈ 1. Also air pockets within the ship would effect the sinking kinematics.

In conclusion, if the Costa Concordia were to suddenly and quickly slip down the steep slope she lies on then large waves could be generated and pose a danger to the immediate, far field and offshore coastlines. However, given that this is a ship and not a solid mass it is likely that the sinking kinematics would not be straight forward. It is difficult to determine the density of the ship and how air pockets may effect the way in which she would sink.

Tsunami inundation

When it comes to tsunami inundation, one could simply say: rely on the wisdom of ancient people. In Japan, for example, hundreds of stone tablets warn citizen about the dangers of a tsunami. For example, one tablet in Aneyoshi, a small coastal town, reads: "High dwellings are the peace and harmony of our descendants. Remember the calamity of the great tsunami. Do not build any homes below this point." As the ancient warnings in stone attest, tsunamis are not new to this vulnerable part of Japan. In 1896, during the Meiji Period, a tsunami killed at least 22,000 people on the same Sanriku Coast -a death toll chillingly close to the recent 2011 disaster which left an estimated 23,000 dead or missing.

3.1. Run-up amplification. Until recently the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. Stefanakis et al.

[30] performed one-dimensional numerical simulations in the framework of the NSWE to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, were used as forcing conditions to the BVP. Resonant phenomena between the incident wavelength and the beach slope were found to occur, which result in enhanced run-up of non-leading waves (these resonances are different from edge-wave resonances and from bay resonances, which are two-dimensional phenomena). Run-up amplification occurs for both leading elevation and depression waves. Figure 15 shows the maximum run-up amplification ratio as a function of non-dimensional frequency and non-dimensional wavelength for two beach lengths, namely L = 12.5 m and 4000 m. Here η 0 is the incoming wave amplitude, ω the frequency, g the acceleration due to gravity, θ the beach slope, λ 0 the incoming wavelength. The classical formula based on linear theory for a constant slope reads (see for example [18])

R η 0 = 2 √ π Lω 2 g tan θ 1/4 . ( 3.1)
Even though these results are in an ideal setting (plane beach, incoming sinusoidal wave) they have been shown to persist in more realistic situations (arbitrary bathymetry, complex wave signal). The effects of dispersion have been studied as well: dispersion reduces slightly the amplification ratio. An experimental confirmation of the theoretical results of Stefanakis et al. 3.2. Whirlpool like effect in tsunamis. We conclude this paper by investigating an intriguing phenomenon observed during the 11th March 2011 tsunami in Japan. The behaviour of the tsunami in Oarai port was picked up by reporters as it seemed to create a whirlpool like effect within the bounds of the harbour walls (see Figure 16). In an attempt to understand this phenomenon better, the VOLNA code was run on a simplified geometry of the harbour, inputting a tsunami from the right hand side of the domain. The harbour was given a depth of 5 m at the shore with a gently sloping seafloor with slope 1/300. These values are based on rough values from Google Earth, as the depth is 5 m just outside the harbour and it drops off to 15 m over approximately 3 km. See Figures 17 and18 for a comparison of the real and simplified geometry. The tsunami was modelled by a sine wave with amplitude 1 m and period 10.5 minutes η = -sin(0.01t), at x = 7000 m.

An unstructured triangular mesh was generated over an approximate area of 7 x 5.5 km 2 . The mesh contained approximately 320 x 10 3 elements of order 100 m outside the harbour and refined to 5 m within the harbour area as shown in Figure 19.

The free surface results between 7 and 18 minutes are shown in Figure 20. Once the wave hits the first harbour wall, it is reflected and refracted. When the wave hits the subsequent boundaries a swirling type motion starts to appear (see Figure 21 for a close up of this effect between 13 and 16 minutes). This motion is dramatic for a few minutes, however even sometime later a depression in the harbour is maintained (see Figure 22). It

Conclusion

This paper shows that there are still a number of poorly explored topics related to tsunami science, especially when it comes to tsunami generation or to tsunami run-up.

  have experienced lateral flank collapses in the distant past which potentially could have caused large scale tsunamis. On the 30 th December 2002 part of the western flank of the Stromboli volcano slid into the sea initiating two tsunamis seven minutes apart [16]. This gave Tinti et al. [34] and Chiocci et al. [3] the unique opportunity to observe and model both the submarine and subaerial morphological changes thanks to a previous multibeam survey of the area. Recently, scientists have become concerned that a section of the Cumbre Vieja volcano, La Palma in the Canary Islands, may experience failure and generate a megatsunami [4, 36].

Figure 1 .

 1 Figure 1. Generation of the July 17, 2006 tsunami in Java. Snapshots of the free surface elevation computed with a water wave model. The waves are generated by dynamic co-seismic bottom displacements reconstructed using the corresponding finite fault solution.

Figure 2 .Figure 3 .

 23 Figure 2. Location of the Costa Concordia at time of submission from http://www.marinetraffic.com (17/05/12)

Figure 4 .FigureFigure 6 .

 46 Figure 4. Bathymetric chart from the Italian Hydrographic Institute. The Costa Concordia is near Gabbianara (north of Giglio Porto on the map)

Figure 7 .

 7 Figure 7. Geometry used for the VOLNA simulation of the Costa Concordia on sloping sea floor, from above.

Figure 8 .

 8 Figure 8. Mesh used for the VOLNA simulation of the Costa Concordia.

Figure 9 .

 9 Figure 9. VOLNA simulations of the Costa Concordia sinking: free surface at t = 75 s.

  Figure 10. VOLNA simulations of the Costa Concordia sinking: free surface at t = 150 s.

Figure 11 .Figure 12 .

 1112 Figure 11. VOLNA simulations of the Costa Concordia sinking: free surface at t = 300 s.

Figure 13 .Figure 14 .

 1314 Figure 13. Wave gauge at (x, y) = (0, 400) for VOLNA simulations of the Costa Concordia sinking: (a) v = 0.5 m/s, v = 1 m/s and v = 10 m/s; (b) close up of v = 0.5 m/s and v = 1 m/s .

  [30] was recently published by Ezersky et al. [8].

Figure 15 .

 15 Figure 15. Maximum run-up amplification ratio as a function of nondimensional angular frequency (top) and non-dimensional wavelength (bottom) for two beach lengths, namely L = 12.5 m and 4000 m (from [30]).

Figure 16 .Figure 17 .

 1617 Figure 16. Image of Oarai Harbour on a Japanese news channel when the tsunami hit. Source: http://www.youtube.com/watch?v=Qgp1jq6Og4k (screenshot 10/08/11)

Figure 18 .

 18 Figure 18. Simplified bathymetry used for Oarai harbour simulation, the tsunami is generated at the right boundary and travels from right to left, all other boundaries are wall boundaries.

Figure 19 .

 19 Figure 19. Unstructured triangular mesh used for Oarai harbour simulation. There are approximately 320 x 10 3 elements of order 100 m, refined to 5 m within the harbour area.

Figure 20 .

 20 Figure 20. Snapshots of the free surface between 7 and 18 minutes.

  Figure 21. Free-surface close up between 13 and 16 minutes.

Figure 22 .

 22 Figure 22. Free-surface close up at later times.

Acknowledgements 18 References 18 Acknowledgements This work was funded by IRCSET under the Postgraduate Research Scholarship Scheme, ERC under the research project ERC-2011-AdG 290562-MULTIWAVE and SFI under the programme ERC Starter Grant -Top Up, Grant 12/ERC/E2227.


T S Stefanakis

F Dias

& D Dutykh

Resonant Long-Wave Run-Up On A Plane Beach

Keywords: Long wave, run-up, resonance

 underlined the importance of resonant long wave interactions during run-up and run-down. In the current paper we provide additional results with the use of one-dimensional numerical simulations in the framework of the nonlinear shallow water equations with boundary forcing for plane and nontrivial beaches. Several wave profiles are used as forcing conditions to the boundary value problem. Resonant interactions between incident and receding waves are found to occur, depending on the beach slope and the wavelength, and result in enhanced run-up of non-leading waves.

INTRODUCTION

From a mathematical standpoint, wave run-up, which is the maximum vertical extent of wave uprush on a beach above still water level (Sorensen, 1997), has an intrinsic difficulty: the moving shoreline. The no-slip condition applied at the initial shoreline for the solution of the Navier-Stokes equations, implies that the shoreline should remain stationary, which of course is not the case. Despite this difficulty, major progress to the solution of the initial value problem in one propagation direction was achieved with the introduction of the Carrier and Greenspan (CG) transformation (1958), which allows the reduction of the two nonlinear shallow water equations (NSWE) into a single linear equation and the transformation of the moving wet/dry interface to a stationary point. Further important advances on the subject were achieved by Keller and Keller (1964), [START_REF] Carrier | On the Solitary Wave Paradigm for Tsunamis[END_REF] and [START_REF] Synolakis | The Runup of Solitary Waves[END_REF], with the latter deriving an analytical expression for the run-up of solitary waves. The solitary wave together with the N-wave [START_REF] Tadepalli | The Run-up of N-Waves on Sloping Beaches[END_REF] are the two predominant conceptual wave profiles in tsunami literature, even though more recent studies [START_REF] Carrier | On the Solitary Wave Paradigm for Tsunamis[END_REF]Shaffer, 2010) question them and propose more geophysically relevant paradigms. Expressions for long wave run-up that are independent of the incident wave profile were derived by Didenkulova and Pelinovsky (2008). All the above studies dealt with the initial value problem (IVP). [START_REF] Antuono | The Boundary Value Problem for the Nonlinear Shallow Water Equations[END_REF] solved the boundary value problem (BVP) for the NSWE, using the CG transformation, and applied a perturbation approach by assuming small amplitude incoming waves at the seaward boundary. Later, the same authors (2010) solved the BVP in physical space without use of the CG transformation.

The only ones who addressed the two-dimensional problem were [START_REF] Brocchini | Integral Flow Properties of the Swash Zone and Averaging[END_REF]. They used a transformation to relate the longshore coordinate to the time variable. This operation allowed the derivation of an expression for the horizontal velocity, which reduced the dimensions and transformed their problem into the already solved one-dimensional canonical problem. However, their solution is only valid for mild angles of incidence. Almost all of the aforementioned studies focus on the value of maximum wave run-up. Nevertheless, none of these theoretical models is able to capture extreme values such as those observed during the Java 2006 tsunami (Fritz et al., 2007). Moreover, despite the fact that solitary waves or N-waves might be appropriate as models for the leading tsunami waves, DART buoy measurements reveal a sequence of waves reaching the shore. Furthermore, it has been reported that in some cases it is not the leading wave that caused the maximum damage. Scientists explain this phenomenon by assuming that the amplification is due to reflection and refraction effects from nearshore topographic features [START_REF] Neetu | Trapped Waves of the 27 November 1945 Makran Tsunami: Observations and Numerical Modeling[END_REF] or due to earthquakegenerated local submarine landslides. It is found that bathymetric changes may lead to wave resonance (Kajiura, 1977;[START_REF] Agnon | Trapping and Resonance of Long Shelf Waves due to Groups of Short Waves[END_REF]Grataloup and Mei, 2003). In addition, shelf resonance [START_REF] Munk | Long Waves on the Continental Shelf: An Experiment to Separate Trapped and Leaky Modes[END_REF][START_REF] Rabinovich | Influence of Seiche Oscillations on the Formation of the Long-Wave Spectrum Near the Coast of the Southern Kuriles[END_REF], responsible for wave amplification phenomena, is caused due to trapping of long waves on the continental shelf region, which requires the existence of a shelf break (i.e. abrupt change of bathymetry). This type of resonance is observed when the incident wavelength is four times larger than the continental shelf and is found to affect tides as well as tsunamis. However, shelf resonance, as stated above, mainly describes wave amplification and not run-up amplification. In the present study we shed light on the run-up amplification phenomenon by non-leading long waves with the use of one-dimensional numerical simulations of the NSWE for the boundary value problem. Our solver uses a Finite Volume Characteristic Flux scheme with a UNO2 type of reconstruction for higher order terms and a third order Runge-Kutta time discretization. The model is described in detail and validated by Dutykh et al. (2011a).

WAVES ON A PLANE BEACH

Monochromatic Waves

The maximum wave run-up for the geometry of Fig. 1 was first studied for three different beach slopes, namely, tan = 0.13, 0.26, and 0.3, using incident monochromatic waves at the seaward boundary (x = -L) of the form:

(L, t) = ± 0 sin(t), / g tan( ) / L (0, 6.29) (1)

where (x,t) is the free-surface elevation, is the angular frequency, is the beach angle and g is the gravitational acceleration. At the seaward boundary, we only prescribe the free-surface elevation and not the velocity because boundary velocity is actually a result of the BVP as pointed out by [START_REF] Antuono | Solving the Nonlinear Shallow-Water Equations in Physical Space[END_REF]. However, in our opinion, the realistic implementation of the seaward boundary conditions still remains a open question and one should also keep in mind that the NSWE are an approximate model. The maximum run-up was found to depend on the incident wavelength, the beach slope as well as the beach length (Fig. 2). For a given slope, maximum run-up is highest when the non-dimensional wavelength 0 /L 5.1 (i.e. at L = 1000 m offshore, the resonant wavelength is 0 = 5100 m) for which resonance is observed. Here 0 denotes the wavelength of the incident wave:

0 = 2 gL tan( ) (2)
The maximum run-up increases with increasing slope and with increasing beach length and the run-up amplification reaches values that are extremely high (R max / 0 60). Increasing the beach length leads to an observation of a secondary resonant regime at 0 /L = 1.5 (Fig. 2). Resonant amplification is apparent in both leading elevation and leading depression waves. Adding dispersion to the system (Dutykh et al., 2011a) results in reduced amplification values, though without qualitatively changing the overall picture, as the resonant frequencies remain the same. The resonant maximum run-up values are not achieved by the first incident wave, as is the case for 0 /L > 10, but by subsequent ones (Fig. 3), which strengthens the assumption of the existence of a resonant mechanism between incident and receding waves. Linear theory [START_REF] Pelinovsky | Exact Analytical Solutions of Nonlinear Problems of Tsunami Wave Run-up on Slopes with Different Profiles[END_REF] does not predict resonant regimes, according to which R max / 0 = 2 (2L/ 0 ) 1/2 . Our numerical results are in close agreement with linear theory for nonresonant regimes (Fig. 2). Fig. 3: Run-up timeseries for two different angular frequencies, namely = 0.4 s -1 , which is the resonant frequency when tan = 0.13 and = 0.6 s -1 , which is a non-resonant frequency for the same slope (L = 12.5 m).

In Fig. 3 we can observe that waves with both resonant and nonresonant frequencies reach a quasiperiodic state of equilibrium, although non-resonant frequencies reach this state faster. A differentiating point is the existence of a single peak (trough) [run-up (run-down)] at the quasiperiodic state of the resonant frequency, while the non-resonant frequencies show multiple peaks (troughs). This difference indicates the synchronization between the incident and reflected waves on the run-up and run-down process in the resonant regime.

The spatiotemporal behaviour of the non-dimensional horizontal velocity is shown in Fig. 4. From this figure we can observe that during the resonant run-up (Fig. 4a) in one location there is an abrupt change from negative to high positive values of the velocity, which clearly states the creation of a wave front. On the other hand, the run-down process is much smoother but during it the wave assumes higher absolute velocities than during the run-up. In the same figure it can be seen that the velocity in inundated areas does not go to zero as the shoreline recedes. This is due to the presence of a very thin layer of fluid (h/ 0 < 10 -2 ) which recedes very slowly and is not considered in the computation of the shoreline position. The non-resonant regime exhibits velocities that do not vary as much over time and are lower than the equivalent resonant ones (Fig. 4b).

E P = 1 2 g 2 dx x
(3)

E K = 1 2 u 2 h dx x dz (4)
The energy evolution for the resonant regime when tan = 0.3 is depicted in Fig. 5. Both maximum potential and kinetic energies increase over time until a quasiperiodic state is reached. potential energy takes its maximum value at the instance of maximum run-up, when the kinetic energy is minimum. Moreover, the maximum potential energy is approximately 5 times larger than the equivalent kinetic energy. The extreme oscillations in the total energy are due to the large volumetric changes (inflow-outflow) during run-up and rundown (Fig. 6), which actually affect the limits of integration in the energy equations. Since the volume of fluid inside the computational domain is changing, the current resonant mechanism should not be confused with wavemaker resonance (inside a laboratory flume the volume remains constant).

Bichromatic Waves

In order to further explore whether there is more physics carried out by modal interactions in the resonant run-up amplification phenomenon, we investigated waves of bichromatic modal structure. In order to make direct comparisons with the monochromatic case, each mode had half the amplitude of the equivalent monochromatic wave ( 0 /2). According to our simulations (Fig. 7) no important new interactions are found to occur. When one of the two frequencies is in the resonant regime, the run-up is dominated by this frequency, while the second (non-resonant) frequency does not interfere in the dynamics. When both frequencies are resonant, there is a little enhancement of the run-up but it is not very significant. Nevertheless, an important finding is that the resonant mechanism is not restricted to the monochromatic wave case.

Cnoidal Waves

Cnoidal wave profiles were also investigated as boundary forcing:

(L, t) = 0 H sn 2 kc t 2 , m kc = 3g mh (5) H = mK K E
where sn is a Jacobian elliptic function with parameter m (0<m<1), and K=K(m) and E=E(m) are the complete elliptic integrals of the first and second kind, respectively [START_REF] Abramowitz | Handbook of Mathematical Functions[END_REF]. The parameter m controls both the wave profile and the wavelength. Small m values result in high frequency sinusoidal waves, whereas high m values tend to solitary-like wave profiles. These cnoidal waves are exact solutions to the nonlinear Serre equations [START_REF] Serre | Contribution à l' Etude des Ecoulements Permanents et Variables Dans les Canaux[END_REF]Dias and Milewski, 2010). Varying the parameter m, the maximum run-up shows a more complex behaviour (Fig. 8) compared to monochromatic waves. Multiple resonant regimes, interrupted by "calmer" ones, are observed, the severity of which grows with increasing m. The run-up amplification reaches the value R max / 0 = 27 which clearly is considerably high.

Single Wave With Tail

All previous simulations dealt with idealized wave conditions. However, we wanted to explore whether similar resonant phenomena can occur during a real tsunami. For this reason, a simulation was run for the 25 October 2010 Mentawai Islands tsunami. A virtual wave gauge was placed at Lon = 100.24 o E, Lat = -3.4 o N which recorded the free-surface elevation timeseries for the first 10,800 s of the tsunami (Fig. 9a). At the wave gauge location, the depth is approximately 120 m. Therefore the mean actual slope to the closest shore is tan = 0.03. Using this slope and by setting the first 2000 s of the gauge recordings as boundary forcing, we computed the evolution of the shoreline elevation (Fig. 9b). We can observe the run-up of three waves at t = 720 s, t = 1320 s, and t = 1860 s. It is clear that the first wave does not lead to the highest run-up, even though it has the highest amplitude, as recorded by the wave gauge. Therefore, local resonant tsunami run-up amplification might give an explanation to why it is not always the leading higher wave that causes the maximum damage.

WAVES ON A NON-TRIVIAL BEACH

Driven by our curiosity to see whether our results can be extended to real bathymetries, we ran simulations of monochromatic waves over a transect of the real Mentawai bathymetry (Fig 10a). The existence of multiple resonant peaks may be observed in Fig. 10b. However, the run-up amplification is not as high as in the plane beach case. Nevertheless, the existence of several resonant regimes implies that in nature this phenomenon might not be rare.

CONCLUSIONS

In summary, we discovered local resonant run-up amplification phenomena demonstrated in the context of the one-dimensional BVP of NSWE on a plane beach. The resonance occurs due to the interaction between incoming and reflected waves, and the actual amplification ratio depends on the beach slope and beach length for the case of monochromatic waves. Resonant wave interactions are apparent for various idealized wave profiles, such as dichromatic and cnoidal waves. These phenomena can explain why it is not always the first wave that results in the highest run-up. More realistic wave profiles, which are typical of tsunamis can also exhibit resonant behaviour, explaining why the tail of a single wave may produce leading-order run-up values.

Resonant mechanisms are not limited to the plane beach paradigm but can be observed in more complex bathymetries, as well, thus suggesting that local run-up amplification is not a rare event. However, when the bathymetry is non-trivial, we cannot draw firm conclusions on what extent resonance is attributed to wave trapping and generation of harmonics. Moreover, further research should be conducted on the relevance of the run-up amplification mechanism to the continental shelf resonance [START_REF] Munk | Long Waves on the Continental Shelf: An Experiment to Separate Trapped and Leaky Modes[END_REF][START_REF] Rabinovich | Influence of Seiche Oscillations on the Formation of the Long-Wave Spectrum Near the Coast of the Southern Kuriles[END_REF]. We will also investigate resonant long-wave run-up on two-dimensional bathymetry, with the VOLNA code (Dutykh et al., 2011b).

Mentawai Bathymetry

Fig. 1 :

 1 Fig. 1: Schematic of run-up problem geometry.

Fig. 2 :

 2 Fig. 2: Maximum run-up amplification factor as a function of nondimensional angular frequency (top) and non-dimensional wavelength (bottom) for two beach lengths (L = 12.5 m and 4000 m).

  Spatiotemporal behaviour of non-dimensional horizontal velocity u / (g tan L) 1/2 in the resonant regime (a) and non-resonant regime (b). The black line describes the evolution of the shoreline position in time. In both cases tan = 0.13 and L = 12.5 m. The resonant run-up mechanism is now examined in terms of energy. The potential and kinetic energy are respectively (Dutykh and Dias, 2009):

Fig. 5 :Fig. 6 :

 56 Fig. 5: Energy evolution for the resonant regime ( = 0.6 s -1 ) when tan = 0.3 and L = 12.5 .

Fig. 7 :

 7 Fig. 7: Maximum run-up of a dichromatic wave as a function of nondimensional frequency when tan = 0.13 and L = 12.5 .

Fig. 8 :

 8 Fig. 8: Cnoidal run-up amplification as a function of parameter m.

  Fig. 9: (a) Virtual wave gauge recordings (Lon = 100.24 o E, Lat = -3.4 o N) for the 25 October 2010 Mentawai Islands tsunami. (b) Evolution of the shoreline elevation for the first 2000 s.

  Lef t Boundary :9 9 .8333 o E -3.2333 o N Right Boundary :1 0 0 .2333 o E -2.8167 o N : (a) Transect of the Mentawai bathymetry. (b) Amplification ratio as a function of non-dimensional wavelength.

ACKNOWLEDGEMENTS We would like to acknowledge Professors C. C. Mei and C. E. Synolakis for insightful discussions. This work has been partially supported by the Strategic and Major Initiatives scheme of University College Dublin and by the Framework Program for Research, Technological Development, and Innovation of the Cyprus Research Promotion Foundation under the Project ATI/0308(BE)/05.

J Fluid Mech, Vol 24, pp 641-659. Carrier, GF and Greenspan, HP (1958). "Water Waves of Finite Amplitude on a Sloping Beach," J Fluid Mech, Vol 4, pp 97-109. Dias, F and Milewski, P (2010). "On the Fully-Nonlinear Shallow Water Generalized Serre Equations," Phys Lett A, Vol 374, pp 1049-1053. Didenkulova, I and Pelinovsky, E (2008) "Run-up of Long Waves on a Beach: The Influence of the Incident Wave Form," Oceanology, Vol 48, pp 1-6. Dutykh, D and Dias, F (2009). "Energy of Tsunami Waves Generated by Bottom Motion," Proc R Soc A, Vol 465, pp 725-744. Dutykh, D, Katsaounis, T and Mitsotakis, D (2011a). "Finite Volume Schemes for Dispersive Wave Propagation and Runup," J Comput Phys, Vol 230, pp 3035-3061. Dutykh, D, Poncet, R and Dias, F (2011b). "The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation," Eur J Mech B/Fluids, Vol 30, pp 598-615. Fritz, HM, Kongko, W, Moore, A, McAdoo, B, Goff, J, Harbitz, C, Uslu, B, Kalligeris, N, Suteja, D, Kalsum, K, Titov, VV, Gusman, A, and Latief, H, Santoso, E, Sujoko, S, Djulkarnaen, D, Sunendar, H and Synolakis, C (2007). "Extreme Runup from the 17 July 2006 Java Tsunami," Geophys Res Lett, Vol 34, L12602. Grataloup, GL and Mei, CC (2003). "Localization of Harmonics Generated in Nonlinear Shallow Water Waves," Phys Rev E, Vol 68, pp 026314. Kajiura, K (1977) "Local Behaviour of Tsunamis," in Waves on Water of Variable Depth, Lecture Notes in Physics Vol. 64, pp 72-79 Keller, J and Keller, H (1964). "Water Wave Run-up on a Beach," ONR Research Report Contract No. NONR-3828(00). Madsen, PA and Schaffer, HA (2010). "Analytical Solutions for Tsunami Runup on a Plane Beach: Single Waves, N-Waves and Transient Waves," J Fluid Mech, Vol 645, pp 27-57.


Yannick Schwartz
email: yannick.schwartz@inria.fr

Gaël Varoquaux

Bertrand Thirion

On spatial selectivity and prediction across conditions with fMRI

Keywords: Machine learning, fMRI, feature selection, regions

Researchers in functional neuroimaging mostly use activation coordinates to formulate their hypotheses. Instead, we propose to use the full statistical images to define regions of interest (ROIs). This paper presents two machine learning approaches, transfer learning and selection transfer, that are compared upon their ability to identify the common patterns between brain activation maps related to two functional tasks. We provide some preliminary quantification of these similarities, and show that selection transfer makes it possible to set a spatial scale yielding ROIs that are more specific to the context of interest than with transfer learning. In particular, selection transfer outlines well known regions such as the Visual Word Form Area when discriminating between different visual tasks.

I. INTRODUCTION

Functional neuroimaging data are currently routinely used to better understand cognitive processes. They rely heavily on previous findings to formulate hypotheses and narrow the search space to regions of interest (ROIs), most often reported as coordinates of activation peaks [START_REF] Yarkoni | Large-scale automated synthesis of human functional neuroimaging data[END_REF], or from coordinate databases such as BrainMap [START_REF] Laird | Brainmap[END_REF]. However, understanding the literature is increasingly difficult, so that there is a need for more systematic methods, which use the images themselves to characterize the functional specificity of brain regions [START_REF] Sutton | Methods for metaanalysis in medical research[END_REF]. Transfer learning is a method that trains a classifier to learn a discriminant model on a source task, and then generalizes on a target task without further training. It can yield insights on some brain mechanisms if the tasks share specific common effects in some brain regions [START_REF] Knops | Recruitment of an area involved in eye movements during mental arithmetic[END_REF]. The goal of this work is to investigate the power of transfer learning procedures applied to pairs of cognitive contrasts, where the discrimination ability of the classifier quantifies the information shared between brain maps, and thus characterizes at which spatial scale functional contrasts can be jointly classified. We show that in many cases, transfer learning gives poor results in terms of spatial selectivity. To address this limitation, we introduce selection transfer, i.e. classification of brain states on the target task following the canonical procedure [START_REF] Mourão-Miranda | Classifying brain states and determining the discriminating activation patterns: Support vector machine on functional MRI data[END_REF], but using regions defined on the source task.

II. METHODS

Problem setting:

We start from a database holding several studies, each of them containing different functional contrast images, acquired over multiple subjects. We consider two sets of tasks, the source tasks and the target tasks, each composed of pairs of contrast images. Given n contrasts pairs of k voxel each, we call X ∈ R n,k the images of the source tasks, and y the label denoting the functional contrast under study. The target images and labels are defined likewise: X ∈ R n,k and y . The source and the target share a similar functional spatial pattern, and we are interested in finding the common ROIs, as well as the differences, using a machine learning approach. Note that a common pitfall in neuroimaging classification-based data processing is a successful prediction cannot guarantee that the information used by the classifier is specific to the cognitive process of interest.

Regions selection: Feature selection is an important step of brain activity decoding procedures. Full brain decoding approaches are efficient but require a careful methodology to recover the contribution of different brain regions in the classification. To test the involvement of a particular brain region, researchers typically use ROIs from an atlas, or derived from the literature. Another option is to use methods such as the searchlight algorithm, in order to evaluate and extract spatially relevant voxels across the whole brain [START_REF] Kriegeskorte | Informationbased functional brain mapping[END_REF]. We choose to use a one-way ANOVA procedure [START_REF] Cox | Functional magnetic resonance imaging (fMRI) "brain reading": detecting and classifying distributed patterns of fMRI activity in human visual cortex[END_REF], that yields a selection based on the functional activations elicited by a task, rather than using purely spatial information. We consider different fractions of the brain voxels that are most correlated to the functional contrast and perform the learning procedure on these voxels. We vary the percentiles of selected voxels with a cubic scale, from roughly 150 voxels to the full brain. This way we can control the spatial specificity against the prediction performance, and attempt to find an optimal set of regions.

Transfer learning: This consists in learning discriminative models on a source functional task (X, y) in order to capture information that should be predictive for a target task (X , y ). The general assumption is that if a transfer occurs, the two experiments share at least some common cognitive circuity. Here, we train a linear classifier on the source task, and we predict the labels of the target without any additional training. The features are selected with a oneway ANOVA on the source task, which makes it possible to compare region-based transfer learning with full brain transfer learning.

Selection transfer: This consists in building a predictive model for the target task based on information extracted from the source task. However, here the transfer occurs on feature selection: we perform the ANOVA procedure on (X, y) to select the most relevant voxels, then we train a linear classifier on (X , y ), and predict on the same task with the voxels selected from the source. Consequently, the transfer is not a generalization of a classifier as in transfer learning, but rather an evaluation of the significance of features from a task to another. We use the same linear classifier as the one used for transfer learning.

III. EXPERIMENTS AND RESULTS

A. FRMI dataset

We use data from two fMRI studies for this work. The first one [START_REF] Pinel | Fast reproducible identification and large-scale databasing of individual functional cognitive networks[END_REF] is composed of 322 subjects and was designed to assess the inter-subject variability in some language, visual, calculation, and sensorimotor tasks. The second study is similar to the first one in terms of stimuli, but the data were acquired on 35 pairs of twin subjects. The two studies were pre-processed and analyzed with the standard fMRI analysis software SPM5. The data used for this work are a subset of the 90 different statistical images resulting from the intrasubject analyses. The raw images were acquired on a 3T SIEMENS Trio and a 3T Brucker scanner for the first study, and on a 1.5T GE Signa for the second one. Table I presents the list of contrasts pairs used for this analysis.

B. Experimental results for transfer learning

We are interested in transfer learning: we learn a discriminative model on the source task with a univariate feature selection, and predict the labels on the target task.

The analysis presents two phases: we first train a linear classifier on a source task, and then re-use the discriminative model on the target task to perform the transfer learning; this is repeated on 6 different sub-samples of the source task to estimate the uncertainty on transfer accuracy. We use two kinds of linear classifiers: a SVC (Support Vector Classifier) and a Logistic Regression with 2 penalization. The penalization is set by nested 6-fold cross-validation for each classifier. We find that the two methods yield very close results, and thus report only results using the SVC classifier. We also train and then test the classifier on the target task and call this procedure inline learning. In Figure 1, we show the performance τ t p of transfer learning, relative to inline learning τ i p , varying the percentile p of features selected in a cubic scale. In general, for any given p, τ i p can remain significantly higher than τ t p . For this reason, we use a heuristic to select the scale parameter (see also Figure 1): the scale that yields the minimal τ i p -τ t p difference. We consider that at this scale, the maps associated with the two tasks share a maximal amount of common information. However, the voxels selected with this method are either too few to give an accurate prediction, or too many to yield identifiable regions. The transfers do not behave the same way on both directions: in general, one direction is more sensitive but less specific, and the other direction shows the opposite behaviour. This comes from tasks-related foci being more spatially focused for some contrasts. Because of this lack of specificity, we do not find contained regions that overlap with the Fusiform Face Area (FFA) [START_REF] Kanwisher | The fusiform face area: a module in human extrastriate cortex specialized for face perception[END_REF], the Parahippocampal Place Area (PPA) [START_REF] Epstein | A cortical representation of the local visual environment[END_REF] or the Visual Word Form Area (VWFA) [START_REF] Cohen | Specialization within the ventral stream: the case for the visual word form area[END_REF], regions respectively involved in face recognition, object visual processing, and reading.

C. Experimental results for selection transfer

We are interested in selection transfer: we do not perform transfer learning, instead, we use the univariate feature selection performed on the source task, to learn a discriminative model and predict the labels in the target task.

We use the same machine learning tools as the transfer learning: we train and test a linear classifier with a 6-fold cross validation test on the target task. For this method the SVC and the Logistic Regression with 2 penalization also give very close results. As with transfer learning, we also perform an inline learning on the target task, with features selected on the same images.

On Figure 2, we show the performance τ s p of selection transfer against inline learning τ i p , and how the performance varies with the percentile p of the brain recruited for the learning process. In comparison to transfer learning, two things happen: i) the selection transfer is more symmetric, ii) τ i p is not significantly higher than τ s p for every p. We can therefore use a t-test to define the selected scale (Figure 2) as the first one with non significant difference between the curves. This enables us to control the amount of information to include in the prediction problem, and have both a good performance and an improved specificity of the regions selected for the two tasks. In practical terms, the selected scale makes it possible to identify the smallest fraction of the brain that yields overlapping regions in the two tasks, and consequently an accurate prediction. Although the selected regions have no guarantee of optimality, they are specific enough to overlap with the FFA, the PPA and the VWFA. We can also use the area under the p-values curve from the t-test as a measure of similarity between the tasks. While, it is not possible to interpret this measure absolutely, we can use it to compare one task versus others. For the example on Figure 2, we can see that the area between face and word is smaller than between face and house. This indicates that the face task is closer to the word task than the house task, which is consistent with previous findings [START_REF] Dehaene | How learning to read changes the cortical networks for vision and language[END_REF].

Limitations: Selection transfer captures voxels that generalize well in terms of prediction from one task to another. However, a classifier may require very few voxels to perform well, in which case this method misses some regions involved in the cognitive process of interest. This effect is represented by the values in Table I, where selection transfer requires only a small p fraction of the brain to obtain a τ s p , which is not significantly lower than τ i p (e.g., V comp./sent → A motor/sent.). In order to retrieve optimal regions when this is the case, a standard analysis, based either on contrast addition or conjunction [START_REF] Nichols | Valid conjunction inference with the minimum statistic[END_REF], would be sensitive enough to detect the common active regions for both tasks.

IV. CONCLUSION

In this contribution, we investigate the ability of transfer learning and selection transfer to characterize the spatial scale at which functional contrasts can be jointly classified. The objective is to find a systematic procedure to extract ROIs that define common information between two functional tasks, instead of relying on activation coordinates from the literature. We show that transfer learning does not provide control on the regions size it uses to classify the tasks. Instead we use a selection transfer procedure that seems to better characterize which fraction of the brain yields discriminant information. Our results suggest that transfer learning requires to be used in a carefully designed study, as it is difficult to control the spatial selectivity of this method. Another interesting result is that selection transfer is not symmetric (i.e., source and target tasks are not inversible), as opposed to contrast conjunction. In the future, we would like use such methods in meta-analysis, in order to leverage large databases of functional images.

  SELECTED SCALES AND AREA UNDER THE P-VALUES CURVE FOR BOTH TRANSFER LEARNING AND SELECTION TRANSFER. TRANS.= TRANSFER LEARNING; SEL.= SELECTION TRANSFER; V= VISUAL STIMULI; A= AUDITORY STIMULI.

	Contrasts Names	Selected Scale	Area under p-curve	Description
		trans.	sel.	trans.	sel.
	house/scramble → face/scramble	68.11	3.25	22.73	4.51	house/scramble = house image versus scrambled image
	face/scramble → house/scramble	0.40	2.67	16.22	2.71	face/scramble = face image versus scrambled image
	word/scramble → face/scramble	23.77	4.63	10.36	2.88	word/scramble = word image versus scrambled image
	face/scramble → word/scramble	1.36	0.79	11.15	2.29	face/scramble = face image versus scrambled image
	French/sound → Korean/sound	0.40	0.02	3.57	4.61	French/sound = French listening versus unstructured sound
	Korean/sound → French/sound	0.27	0.00	14.59	1.21	Korean/sound = Korean listening versus unstructured sound
	V comp./sent. → A comp./sent.	11.01	0.00	2.62	1.76	V comp./sent. = computation versus sentences reading
	A comp./sent. → V comp./sent.	0.01	6.36	4.75	3.10	A comp./sent. = computation versus sentences listening
	V motor/sent. → A motor/sent.	0.10	0.00	11.84	1.85	V motor/sent. = button press action versus sentences reading
	A motor/sent. → V motor/sent.	7.37	0.00	4.45	2.11	A motor/sent. = button press action versus sentences listening
					Table I
	SOURCE AND TARGET TASKS:

V. ACKNOWLEDGEMENTS

This work was supported by the ANR grants BrainPedia ANR-10-JCJC 1408-01 and IRMGroup ANR-10-BLAN-0126-02.

The two prediction curves do converge, so that the difference becomes non-significant as soon as a relatively small fraction of the voxels are included: the spatial scale is defined here as the point where the curves can no longer be distinguished. It corresponds to more symmetric and meaningful brain maps than those obtained with transfer learning.


Sophie Cliquet

Julien Despreaux

Kashif Zeeshan

Denis De La Broise

Gavin Ash

Characterization of aggregates produced by the potential mycoherbistat Plectosporium alismatis in submerged culture: germination, UV-radiation tolerance and infectivity

Keywords: bioherbistat, aggregates, air-drying, UVradiation

Plectosporium alismatis, a potential mycoherbistat of Alismatacae spp., has been previously shown to produce aggregates which contain chlamydospores in liquid culture.

In this study we evaluated the impact of medium composition on the formation and composition of aggregates. In shake flasks cultures using 5.74 gL -1 sodium nitrate, 8.8 gL -1 malt extract or glucose and 0.1% Tween 80, P. alismatis formed small, uniform (diameter of 75% aggregates <720µm), dense, melanised aggregates containing 10 4 conidia and 10 3 chlamydospores, these numbers remained unchanged during growth. One hundred percent of 7-day-old aggregates exposed to desiccation or/ and UV-radiation germinated. In bioassays using leaf discs of Alisma plantago-aquatica, P.

alismatis aggregates caused necrosis, regardless of whether aggregates had been exposed to desiccation and/or UVradiations prior to application on leaf discs, whereas other propagules (10 3 propagules disc -1 ) exposed to drying and UV-radiation stress were unable to cause necrosis. This preliminary research shows the potential of aggregates to be used as part of a formulation of biocontrol agents, provided adequate conditions for optimal aggregate yields are found.

Introduction

The endemic fungus Plectosporium alismatis (Oudem) W. M. Pitt, W. Gams & U. Braun (synonym Rhynchosporium alismatis, Spermosporina alismatis) has the potential to be used as a biological control agent of weeds species of Alismataceae [START_REF] Cother | Efficacy of a potential mycoherbicide for control of Alisma lanceolatum and Damasonium minus in Australian rice crops[END_REF]Pitt, Goodwin, Ash, Cother and Cother 2004). The fungus reduces the biomass of the weed (Fox, Cother and Ash 1999), especially when used with low rates of the herbicide Londax (Jahromi, van de Ven, Cother and Ash 2006).

With the goal of developing a low-cost, submerged culture production process that yields high concentrations of viable, virulent P. alismatis propagules, we are currently evaluating how culture conditions may impact P. alismatis's growth and morphology in liquid culture.

Recent studies have shown that high P. alismatis conidial numbers and dry weight accumulation can be easily produced in media that contain an organic nitrogen source (such as casamino-acids, yeast extract, or tryptone [START_REF] Cliquet | Impact of nutritional conditions on yields, germination rate and shelf-life of Plectosporium alismatis conidia and chlamydospores as potential candidates for the development of a mycoherbicide of weeds in rice crops[END_REF]). In contrast, in a liquid culture medium based on the Czapex Dox composition, in which nitrogen is provided by sodium nitrate, P. alismatis produces low conidial yields and interestingly, chlamydospores [START_REF] Cliquet | Conidial and chlamydospore production of Rhynchosporium alismatis in submerged culture[END_REF], which make ideal candidates for the development of a stable mycoherbicide (Jackson and Schisler 2002). alismatis Aggregates may represent promising microgranules for the development of a stable and effective bioherbicide to be applied directly in rice fields.

Therefore, the objective of this study was to determine the yield, size and composition of P. alismatis aggregates produced in liquid culture. They were then compared to conidia and chlamydospores for their ability to survive drying or/and UV-radiation exposure, and for their ability to cause necroses on Alisma plantago-aquatica leaf discs.

Materials & Methods

Liquid culture experiments

Plectosporium alismatis DAR 73154 was obtained from the culture collection of the New South Wales Plant Pathology Herbarium held by NSW Department of Primary Industries, Orange, Australia. The fungal pathogen was originally isolated from Damasonium minus (R.Br) Buch and maintained as a single conidium culture at -80°C as previously described (Texier et al., 2009).

Stock solutions were stored as single spore cultures grown on PDA (Difco, Detroit, MI, USA), cut into plugs and stored at -80°C. A suspension of frozen cultures was inoculated onto a PDA plate, incubated for 2-3 weeks at 25°C until profuse sporulation occurred and renewed every month.

Plates were gently washed with 3 mL sterile distilled water and conidial suspension (approx. 1 x 10 7 conidia mL -1 ) stored at -80°C. Frozen conidial suspensions were inoculated (4x 10 3 conidia mL -1 ) into shake flaks for liquid culture.

Liquid cultures were based on a mineral composition as follows: K 2 HPO 4 , 1 g; MgSO 4 7H 2 0, 0.1 g; KCl, 0.5 g; Fe 2 SO 4 7H 2 O, 0.018 g; deionized water: 1 L. For chlamydospore and aggregate production, malt extract (Difco Laboratories, Detroit, MI, USA, 8.8 g L -1 ) or glucose.H 2 0 (3.68 g C L -1 ) and sodium nitrate (Sigma Chemicals, St Louis, MO, USA, 5.74 g L -1 ) were added to the mineral medium as the sole carbon and nitrogen sources (respectively 3.68 g C L -1 and 1g N L -1 ; [START_REF] Cliquet | Conidial and chlamydospore production of Rhynchosporium alismatis in submerged culture[END_REF]). Flasks containing the malt extract, sodium nitrate medium (100 mL medium in 250 mL flasks) were inoculated with conidia (4 x 10 3 conidia mL -1 ).

Cultures were incubated at 25°C on a rotary shaker incubator (Infors HT Bottmingen, Switzerland). Cultures were hand-shaken daily to prevent the formation of a mycelium ring on the flask wall.

In

Drying experiments

Whole cultures (2 flasks) were homogenised to release propa gules, vacuum-filtered on cellulose filters and placed in a pan at room temperature until dry mats reached a constant weight (12 h).

Whole cultures (2 flasks) containing aggregates were vacuum-filtered on cellulose filters and placed in a pan on the bench top, at room temperature, until constant weight (12h). The moisture content of dried whole cultures measured using a halogen moisture analyzer (Ohaus, MB 45)

was equal to 6.5%.

Chlamydospore, conidial and aggregate viability

Seven-day old cultures harvested from 2 duplicate flasks were homogenised. Propagule suspensions were rinsed and adjusted with sterile distilled water to 5 x 10 6 propagules mL -1 . Serial dilutions were sprayed on the surface of PDA plates. Plates were incubated at 25°C for 5 days and colony forming units (c.f.u.) were counted. For the determination of dry propagule viability, aliquots from homogenised dry mats on cellulose filters were gently rehydrated with sterile distilled water and adjusted to 5 x 10 6 propagules mL -1 . Serial dilutions were sprayed on PDA and colony forming units determined, as previously mentioned.

Exposure of propagules and aggregates to UV-radiation

Irradiation experiments were conducted in a dark cabinet as previously described (Texier et al. 2009). Triplicate 200-µL droplets of freshly-harvested, homogenised suspension ( 5x 10 6 propagules mL -1 ), or from homogenised rehydrated dry fungal mats (5 x 10 6 propagules mL -1 ) were placed in a petri or +1 (chlorotic/ necrotic area) was selected.

Statistical analysis

All experiments were repeated at least once.

Aggregate diameter and circularity frequency distribution were performed using Statgraphics Plus V.4. (Toulouse, France).

Anova analysis and Duncan mean separation tests (P < 0.05)

based on mean values for propagule and aggregate yields, were performed using Statgraphics. For data not suitable for ANOVA, standard errors values were estimated as a measure of variance.

Results and discussion

In media supplemented with nitrate, (providing 100% N in glucose-based medium; providing 85% N in malt extract-based medium, 15% being provided by malt extract), P. alismatis produced non-uniform, melanized, dense aggregates ranging in size from a few micrometers to more than one millimeter diameter (Table 1) whereas no hyphal suspension was observed in cultures. Nitrate has been shown to be a nonpreferred nitrogen source, partially utilized by P.

alismatis [START_REF] Cliquet | Impact of nutritional conditions on yields, germination rate and shelf-life of Plectosporium alismatis conidia and chlamydospores as potential candidates for the development of a mycoherbicide of weeds in rice crops[END_REF] which, in these nitrogen limiting, stressful conditions, produces low dry weight accumulation and low aggregate yields (Table 1).

Further homogenization and microscopic observation of the three 7-day-old cultures showed that all aggregates contained chlamydospores (1 x 10 3 chlamydospores aggregate -

1

)as previously reported [START_REF] Cliquet | Impact of nutritional conditions on yields, germination rate and shelf-life of Plectosporium alismatis conidia and chlamydospores as potential candidates for the development of a mycoherbicide of weeds in rice crops[END_REF] and conidia (1 x 10 4 conidia aggregate -1 ; Table 1). Although aggregate yields were low (1.9 x 10 5 L -1 ), the addition of Tween 80 in the liquid culture and enhanced agitation speed resulted in approximatively 10% increase in aggregate yields (Table 1). Moreover, aggregates produced under these conditions were small, spherical (circularity = 0.9, data not shown) and uniform (aggregate diameter uniformity, expressed as relative frequency distribution : 75% aggregate diameter < 720 µm, Table 1). Fungal aggregates were observed from day 2 (Table 2), becoming little nodes visible by naked eye at seven days growth (680 µm average diameter, Table 2) and eventually turning dark which were visible as dark pin-point to pin-head size bodies (Fig. 1).

In Tween 80 added to a slurry of Metarhizium anisopliae cells in water has been shown to induce cell aggregation, which is the first phase in the process of developing carrierfree granulates for combating pests and treating plants [START_REF] Andersch | Self-supporting carrier-free granulates for combating pests and treating plants[END_REF] Microscopic observation of 7-day old cultures showed that aggregates in their final form were composed of hairy compact, microsclerotia-like masses (Fig. 2A) containing chlamydospores (Fig. 2B). Other studies related to submerged liquid culture fermentation have demonstrated that, in specific nutritional conditions, plant pathogenic fungi produce melanized aggregates that happen to be microsclerotia (Jackson and Schisler 1995;Shearer andJackson 2003, 2006). The microsclerotia stability and effectiveness in soil and in aquatic environment have been reported as having potential for use as bioherbicides [START_REF] Boyette | Sesbania exaltata biocontrol with Colletotrichum truncatum microsclerotia formulated in "Pesta" granules[END_REF]Shearer and Jackson 2006). aggregates) exposed to stress (Table 3). Seven-day-old propagule germination expressed as [(% c.f.u. at 5d incubation/total c.f.u.) x 100] was significantly reduced (more than 80% suppression) after drying and subsequent UVradiation exposure (Table 3). Similarly, a drastic drop in conidial germination due to drying and subsequent UVradiation exposure has been simulated at the laboratory and previously reported (Texier et al. 2009).

In contrast, it is interesting to note that less than 5% of the 7-day old, dried aggregates exposed to UV-radiation failed to germinate after 18h on PDA (Table 3). Considering the 7-day-old propagule concentration per aggregate (approx. 10 4 conidia and 10 3 chlamydospores aggregate -1 , Table 2), we suggest that a significant number of propagules survive stress and germinate. Moreover, although the drying process at room temperature is similar for both propagules and aggregates, drying rate in the aggregate center is probably slower than drying speed of exposed, homogenised propagules, resulting in differences in viability as reported elsewhere [START_REF] Cliquet | Comparison of Air-Drying Methods for Evaluating the Desiccation Tolerance of Liquid Culture Produced Paecilomyces fumosoroseus spores[END_REF].

In addition, internal cells are likely protected from UVradiations by the aggregate external layers.

While chlamydospores and mycelial structures such as microsclerotia are mentioned as overwintering structures, literature on the impact of environmental effects on fungal structures is scarce. Surprisingly, viability of dried, UVexposed aggregates was higher (97±8%) compared to viability of freshly-harvested, UV-exposed aggregates (70±6%).

Although the detrimental impact of desiccation or UVradiation exposure experimented as one-factor at-a-time is widely reported, interactions between these environmental factors can impact significantly fungal viability (Texier and Cliquet, 2009). Because moisture level (Shabana, Baka and Abdel-Fattah 1997), and UV-radiation (Ghajar et al. 2006) are among the most constraining factors for the development of mycoherbistats, the impact of these factors and of their interaction on the viability of potential mycoherbistats deserve more attention.

A. plantago-aquatica leaf discs inoculated with freshlyharvested propagules (conidia and chlamydospores) developed a primary infection, expressed by necrosis at inoculation site after 5 d incubation compared to healthy water controls. Similarly, freshly-harvested aggregates infected A. plantago-aquatica leaf discs (Table 4). These results demonstrate that the sodium nitrate, malt extract medium supplemented with Tween 80 supports production of propagules and aggregates able to incite disease in Alisma plantago-aquatica. However, thresholds of 10 2 freshly harvested propagules disc -1 , and 10 3 freshly-harvested, UVexposed propagules disc -1 were required in order to induce leaf infectivity, whereas dry propagules were not able to cause disease, regardless of whether they were exposed to UV-radiation prior to pathogenicity tests or not (Table 4).

These data indicate that drying is likely more stressful than UV-radiation in the infectivity process. This contrasts with the observation that the drying process of propagules was less detrimental than UV-radiation exposure on germination (49% and 30% propagule germination, respectively, P. alismatis was grown in medium containing 0.1% Twin 80 and supplemented with 8.8 g L -1 malt extract, 5.74 g L -1 sodium nitrate. Flasks were shaken at 25 0 C and 120 rpm and pH maintained daily at 7.

b Aggregate circularity range 0-1, 0: irregular aggregates; 1: spherical aggregates.

c Total counts after whole culture homogenisation d in whole culture e calculated from difference between total counts and free counts and related to aggregates f standard error (SE) After desiccation e 49 ± 5 16 ± 4.2 100 ± 10 97 ± 8

  In our sodium nitrate, malt extract based medium, chlamydospores are found mostly inside non-uniform, dense, brown, melanized aggregates (Moulay, Cliquet, Zeeshan, Ash and Cother 2008; Cliquet and Zeeshan 2008). Homogenization of cultures is required in order to release chlamydospores. Chlamydospores are promising propagules showing viability after 4 months storage at 25°C (Moulay et al. 2008; Cliquet and Zeeshan 2008) and tolerance to UV-radiation exposure (Texier, Davy and Cliquet 2009). These findings indicate that chlamydospores may be viable from September to November, the period of rice sowing in New South Wales, Australia (Lanoiselet, Cother, Ash and van de Ven 2001). However, homogenization of aggregate-producing cultures in order to release chlamydospores represents an additional step in the development of the mycoherbistat, which is incompatible with the development of an economical, largescale mass production method. On the other hand, some plant pathogenic fungi of weedy plants produce conidia or other forms of propagules, including microsclerotia (Jackson and Schisler 1995; Boyette, Jackson, Bryson, Hoagland, Connick and Daigle 2007), which can be variously formulated -drying has been reported (Shearer and Jackson 2006), demonstrating the ability of microsclerotia to act as potential biocontrol agents for weeds. P.

  dish (89 mm diameter) (Greiner Bio-one 34/15 with vents, Courtaboeuf, France) covered with plastic lid, at prespecified position at a distance of 30 cm under the UVlamp, and droplets of propagule suspensions were simultaneously placed in a dark cabinet with no lamp (controls). Temperature and relative humidity in the dark cabinets remained constant (21°C, RH = 75%) during aggregates, were placed in a Petri dish and exposed to UV-radiation under the same irradiation parameters to those applied to propagules. In order to prevent dehydration, distilled water was placed beneath the plates. Preliminary experiments (data not shown) indicated that 30% propagules and 70% aggregates germinated following UV-radiation exposure of 45 min. This exposure time to UVradiation (UV-B dose = 3.6 kJm -2 ; UV-A dose = 0.72 kJm -2 ) is compatible with doses given for full-spectrum sunlight (Ghajar, Holford, Cother and Beattie 2006) and was selected for further studies. At the end of UV-radiation exposure, 100-µL were taken from the 200-µL propagule droplet, sprayed onto water agar plates and cfu counts determined after 4 days incubation at 25°C. Aggregates were placed on PDA plates and microscopical observation of hyphal germination performed after 18h incubation at 25°C. Duplicate flasks were used for propagule and aggregate UV-exposure experiments. Infectivity on leaf discs Alisma plantago-aquatica is naturally infected by P. alismatis (Lanoiselet et al. 2001) and has been recently found to grow naturally in La Retenue de Moulin-Neuf, moulin de Kerbenoc'h, Plonéour-Lanvern, Brittany, France. Leaves were surface sterilized with 1% chlorine and rinsed with sterile distilled water. Leaf discs were cut with a 10 mm diameter cork borer and placed on the surface of 1.5% water granulated agar (Difco) containing 1 µg mL -1 of benzylaminopurine (Acros Organics N.V., Thermo Fischer Scientific, Belgium) in plastic Petri dishes. Four replicate discs were inoculated with 0.2 mL of the appropriate dilutions of a propagule suspension taken from a seven-day-old homogenised culture, ranging from 10 1 to 10 3 propagules per disc, or with aggregates collected from cellulose filters (1 or 10 aggregates per disc). Two discs were inoculated with sterile distilled water. The entire experiment was repeated once. Leaf discs affected by necrosis and chlorosis were examined 5 d after inoculation. As different methods of inoculation were used (either with a propagule suspension or by placing an aggregate directly onto the leaf surface, the use of either the percentage of necrotic/chlorotic leaf disc or an ordinal scale in the range 0-10 (no symptom-entire disc chlorotic/necrotic, Cother and van de Ven (1999)), was not considered relevant. Instead, a simple score (no symptom)

  Figure 1B

(

  conidia and chlamydospores) and aggregates produced in submerged culture a Propagule( conidia and chlamydospores) germination: [c.f.u. / c.f.u. freshly-harvested propagules]x100 b Hundred aggregates were sprinkled on PDA and hyphal germination evaluated microscopically after 20h at 25°C c transmission of UV-B and UV-A radiations d %germination ± s.e. e propagules and aggregates were dried overnight at room temperature Propagule germination

Table 3

 3

	). UV-radiation may induce microcycle

Table 1 .

 1 The impact of the medium composition on propagule and aggregate production by Plectosporium alismatis in submerged culture

Table 2 .

 2 Growth of Plectosporium alismatis in a malt extract,

	sodium nitrate medium supplemented with 0.1% Tween 80
	Table 3. The impact of UV-radiation exposure on the germination
	rate	of	Plectosporium	alismatis	propagules	(conidia	and
	chlamydospores) and aggregates produced in submerged culture
	Table 4. The impact of propagule or pellet UV-radiation exposure
	and/or dessiccation on the disease caused by Plectosporium
	alismatis on Alisma plantago-aquatica leaf discs

Table 1 .

 1 The impact of the medium composition on propagule and aggregate production by Plectosporium alismatis in Volume calculated from each class midpoint; for x>1440µm, a mean value = 2000µm was selected

	submerged culture
	Growth conditions	Propagules b

a P. alismatis was grown in flasks containing 100 mL liquid medium and shaken for 7 days at 25°C, with pH daily ajusted to 7. b Production of conidia and chlamydospores during growth evaluated after homogenisation of whole culture, including aggregates.

c

Table 2 .

 2 Growth of Plectosporium alismatis in a malt extract, sodium nitrate medium supplemented with 0.1% Tween 80

	Culture	Dry	Aggregate production	Conidia
	age a	weights
	(days)

Table 3 .

 3 The impact of UV-radiation exposure on the germination rate of Plectosporium alismatis propagules

Acknowledgements

We are thankful to Claire Pichon and Saliha Berchiche for their excellent technical work. This work was supported by a PhD studentship from Higher Education Commission, Pakistan, and by the French Minister of Research.

appressorium formation by fungi with potential as mycoherbistats", Biocontrol Science and Technology, 16, 451-469. Gibbs, P.A., Seviour, R.J., and Schmid, F. (2000), "Growth of filamentous fungi in submerged culture: problems and possible solutions", Critical Reviews in Biotechnology, 20, 17-48. Jackson, M.A., and Schisler, D.A. (1995)