Manju Rajan

Abhijit Das
email: abhijit.a.das@inria.fr

John Jose
email: johnjose@iitg.ac.in

LOKI: A Hardware Trojan Affecting Multiple Components of an SoC

Keywords: Hardware Trojan (HT), System-on-Chip(SoC), Network-on-Chip (NoC), Last-Level Cache (LLC)

Outsourcing Intellectual Properties (IPs) from vendors around the globe exposes System-on-Chip (SoC) designs to malicious implants like Hardware Trojans (HTs). Carefully crafted HTs with extremely rare trigger conditions evade conventional validation. While Machine Learning (ML) based validation increases detection accuracy, they themselves are vulnerable to Trojan attacks. Available detection and mitigation techniques fall short when an HT is capable of affecting multiple components of an SoC. This paper proposes an intermittent and robust HT that can attack the Network-on-Chip (NoC), the shared cache, and the cores, all at once. The proposed HT is mounted in the Network Interface (NI) of a malicious IP and can be triggered by specific inputs. Experimental evaluation shows that the proposed HT can increase packet latency by 3.44x (affecting the NoC), increase miss penalty by 15% (affecting the cache) and decrease system speedup by 10% (affecting the cores). Moreover, this paper also discusses why state-of-the-art defence mechanisms are insufficient to tackle the proposed HT and suggests better solutions.

I. INTRODUCTION

To reduce design costs and meet aggressive time-to-market constraints, System-on-Chip (SoC) manufacturers outsource Intellectual Properties (IPs) from different vendors around the globe. This supply-chain exposes SoC designs to malicious implants like Hardware Trojans (HTs). Typically, there are two critical parts in a Trojan, trigger and payload. An example Trojan in Figure 1 shows that a trigger with 2 logic gates is added to the original 4-input circuit. The trigger is usually created using one or more extremely subtle events (rare inputs, signals, transitions). Once triggered, the payload initiates the attack, like information leakage, Denial-of-Service (DoS), performance degradation, etc. In the example, out of the 16 (2 4 ) combination, only when the input is 1101 (unlucky 13), trigger is activated, and the payload inverts the original output.

The exponential growth of input combination space in modern SoCs coupled with carefully crafted HTs makes it infeasible for conventional simulation based validation to detect Trojans [START_REF] Lyu | Scalable Activation of Rare Triggers in Hardware Trojans by Repeated Maximal Clique Sampling[END_REF] [START_REF] Pan | Automated Test Generation for Hardware Trojan Detection using Reinforcement Learning[END_REF]. Machine Learning (ML) based validation offers better detection, but they are computationally expensive, and themselves are susceptible to Trojan attacks [START_REF] Pan | Design of AI Trojans for Evading Machine Learning-based Detection of Hardware Trojans[END_REF]. Moreover, if an HT is capable of attacking multiple components of an SoC, even the existing detection and mitigation techniques will fail to locate and neutralise it. To launch such an attack, the and payload (blue gate). Only when the input is 1101, the trigger is activated, and the payload inverts the original output.

Trojan must be inserted in a place that has access to multiple SoC components. This is the motivation for the proposed HT.

A. Threat Model

Due to the long and distributed supply-chain, HT like implants can be inserted into the Register-Transfer Level (RTL) or netlist of an IP from different access points. There are practical scenarios of Trojan insertion by Computer-Aided Design (CAD) tool, by designer or at the foundry by reverse engineering [START_REF] Areno | Supply Chain Threats Against Integrated Circuits[END_REF] [START_REF] Mishra | Network-on-Chip Security and Privacy[END_REF]. Network-on-Chip (NoC) facilitates communication between the IPs and has access to all the components of an SoC. Hence, it is more vulnerable to attacks, as a malicious IP can simply eavesdrop NoC packets to extract information without the need of hacking into individual IPs [START_REF] Charles | A Survey of Network-on-Chip Security Attacks and Countermeasures[END_REF]. This work considers that the proposed HT is mounted on the Network Interface (NI) of the malicious IP, which connects it to the NoC IP (refer Figure 3). Sitting on the NI, the Trojan is able to attack the NoC, the shared Last-Level Cache (LLC) and other core IPs, all at once. The proposed Trojan attacks the SoC for performance degradation; however, based on intentions, it can always be used for other attacks.

B. Research Contributions

The proposed HT is named as LOKI1 , which is very mischievous in the sense that it sits on one IP but affects multiple components of the SoC, without actually hacking them. Specifically, the major contributions of this work are:

1) LOKI selectively duplicates NoC control packets to attack three SoC components. Using duplicate control packets to attack multiple components without hacking into them is a first of its kind in NoC based SoCs.

2) We show that when the attacker triggers LOKI, packet latency, miss penalty and system speedup are severely affected thereby degrading the overall SoC performance. 3) When multiple components are attacked at the same time, state-of-the-art defence mechanisms fall short to locate and isolate LOKI. Towards the end, we discuss possible ways to tackle LOKI-like malicious implants.

II. RELATED WORK AND MOTIVATION

A. State-of-the-Art

Attackers typically use shared on-chip resources like LLC and NoC as a backdoor to gain access to the victim processes, applications and IPs. One of the earliest attacks on LLC called Prime+Probe tries to identify the cache line eviction pattern of a victim process by creating conflicts to steal sensitive information [START_REF] Osvik | Cache Attacks and Countermeasures: The Case of AES[END_REF]. Other popular attacks on LLC includes Flush+Reload [START_REF] Yarom | FLUSH+RELOAD: A High Resolution, Low Noise, L3 Cache Side-Channel Attack[END_REF], Flush+Flush [START_REF] Gruss | Flush+Flush: A Fast and Stealthy Cache Attack[END_REF], and Streamline [START_REF] Saileshwar | Streamline: A Fast, Flushless Cache Covert-Channel Attack by Enabling Asynchronous Collusion[END_REF]. Being the communication backbone, NoC's positional advantage makes it a prime target for attackers. Moreover, its distributed nature eases attack replication and amplification. For example, a Prime+Probe like side-channel attack is also proposed in NoC, where its infrastructure is used to monitor the contents of the shared LLC [START_REF] Reinbrecht | Side Channel Attack on NoC-based MPSoCs are Practical: NoC Prime+Probe Attack[END_REF]. There are a wide variety of Trojan based attacks launched on NoC based SoCs like, eavesdropping [START_REF] Charles | Lightweight Anonymous Routing in NoC based SoCs[END_REF][13], data integrity [START_REF] Charles | Lightweight and Trust-Aware Routing in NoC-based SoCs[END_REF], information leakage [START_REF] Ancajas | Fort-NoCs: Mitigating the Threat of a Compromised NoC[END_REF][16], DoS [START_REF] Boraten | Mitigation of Denial of Service Attack with Hardware Trojans in NoC Architectures[END_REF] [START_REF] Charles | Real-Time Detection and Localization of DoS Attacks in NoC based SoCs[END_REF], delay-of-service [START_REF] Manju | SECTAR: Secure NoC using Trojan Aware Routing[END_REF][20], performance degradation [START_REF] Kulkarni | Packet Header Attack by Hardware Trojan in NoC based TCMP and its Impact Analysis[END_REF] [START_REF] Khan | Dead Flit Attack on NoC by Hardware Trojan and its Impact Analysis[END_REF], etc. Except [START_REF] Raparti | Lightweight Mitigation of Hardware Trojan Attacks in NoC-based Manycore Computing[END_REF], all other works actively use NoC resources to launch their attacks on the SoC. [START_REF] Raparti | Lightweight Mitigation of Hardware Trojan Attacks in NoC-based Manycore Computing[END_REF] proposed an attack called SIM+THANOS, which mounts the HT on the NI of one IP and steals information for an accomplice thread hiding in another IP. The proposed Trojan LOKI is mounted on the NI of one IP and attacks multiple SoC components without other resources or accomplices, making it difficult to detect by state-of-the-art techniques.

B. Motivation

IPs communicate with each-other by exchanging messages, having a header and a payload 2 , as shown in Figure 2. The header contains necessary information, including source (SRC), destination (DEST), memory address (ADDR), message type (TYPE), etc., for the message traversal, whereas the payload carries data. There are two types of messages, control and data, and the payload remains empty in control messages as they are used to request data or send coherence messages. In an NoC based SoC, when a source (IP SRC ) wants to communicate with its destination (IP DEST ), it forwards the message to the NI (blue IP node), as shown in Figure 3. NI converts the message (yellow) into either a control or a data packet (brown) and forwards it to the router to travel through the NoC and reach destination. Similar steps in reverse are followed to receive the message at the destination (green IP node). Different techniques are proposed to encrypt (and decrypt) the messages and prevent data stealing in modern NoC based SoCs [START_REF] Sepúlveda | Towards Protected MPSoC Communication for Information Protection Against a Malicious NoC[END_REF] [START_REF] Charles | Securing Network-on-Chip using Incremental Cryptography[END_REF]. Usually, only the payload of the message (or packet) is encrypted as the header information is required for routing and arbitration decisions in the NoC. In other words, only the data packets are encrypted as control packets do not carry any payload. Our proposed Trojan LOKI exploits this vulnerability to duplicate control packets in the NI to attack the SoC. LOKI is carefully crafted to get triggered only with read request packets (refer Section III-A). The existing information leakage attack from NI, SIM+THANOS [START_REF] Raparti | Lightweight Mitigation of Hardware Trojan Attacks in NoC-based Manycore Computing[END_REF] ignores the possibility of encryption and duplicates data packets. To the best of our knowledge, this is the first attempt to use read request packets to attack multiple SoC components.

III. LOKI: DESIGN AND DEMONSTRATION

In this section, we first present the design of LOKI, including the circuit diagram of a possible way of inserting it into the NI. Then, we take multiple example scenarios to demonstrate how LOKI attacks and impacts multiple SoC components.

A. LOKI Design

As shown in Figure 3, NI is responsible for converting a message into a packet and vice-versa. Due to limited NoC channel width, a packet is divided into multiple smaller units called flits. A head flit carries the message header, and multiple body flits ended by the tail flit carries the payload. An NoC control and data packet can be represented as: As proposed in [START_REF] Boraten | Mitigation of Denial of Service Attack with Hardware Trojans in NoC Architectures[END_REF], a backdoor Kill Switch (KS) is used to trigger LOKI and initiate the attack. Packet Type (PT) provides the message type (TYPE from Figure 2), and Flit Type (FT) provides the type of flit (head, body or tail). We target read requests as they are control packets with just one head flit (refer Equation 1), thus less storage overhead to store a duplicate. LOKI uses a buffer of 1-flit size and can store only one duplicate read request packet at any given point of time. As shown in Figure 4, only when P T = READ, F T = F i Head and KS = EN 3 , LOKI gets triggered and copies a head flit (read request packet) from the Flit Generator sub-module into its buffer. LOKI then keeps inserting this duplicate flit into the Flit Queue until KS = DS. Please note that the duplicate flit is inserted only in the free locations to avoid interrupting the usual flow of inter IP communication.

P i CT RL = {F i Head } (1)
P i DAT A = {F i Head | F i Body0 | . . . | F i Bodyn-1 | F i T ail } (2)

B. LOKI Demonstration

As shown in Figure 5, let us consider an NoC based SoC with 2-levels of on-chip caching. L1 instruction (L1I) and data (L1D) caches are private to each IP core, whereas L2 is shared 3 READ = Read request, EN = Enable, and DS = Disable and distributed and is the Last-Level Cache (LLC). When an IP core encounters an L1 cache miss, it needs to communicate with the LLC to get the data block. Since LLC is distributed as multiple banks, the destination LLC bank could be anywhere, from the nearest to the farthest IP node. This is when the L1 Cache Controller (L1 CTLR) sends a request message to the NI intended for the destination LLC bank. Upon receiving such a request, the destination LLC bank Controller (LLC CTLR) sends a reply message with the corresponding data block.

Let us consider that LOKI is mounted on the NI of the IP node shown in blue in Figure 5, and is now triggered by the KS. We take two example scenarios to demonstrate how LOKI launches the attack on multiple SoC components at once. 1) Scenario 1: IP SRC1 (blue) requests a data block B 3 and encounters an L1 cache miss. The corresponding L1 CTLR forwards a read request message RQ 1 to the NI for the destination LLC bank at IP DEST (green) where B 3 is cached. The destination LLC CTLR sends the requested data block with a reply message RP 1 . When LOKI is active, it copies RQ 1 from the Flit Generator into its buffer and keeps inserting this duplicate request in free locations of the Flit Queue. These duplicate requests reach the destination, and the LLC CTLR treats them like genuine by replying with RP 1 . Since IP SRC1 and IP DEST are sufficiently spaced, the duplicate requests and replies (red) spread over the entire SoC. This kind of scenario increases contention in the routers and links, resulting in increased packet latency (affecting the NoC).

2) Scenario 2: While Scenario 1 (III-B1) is in progress, IP SRC2 (brown) sends a read request message RQ 2 to IP DEST for the data block B 7 . According to the mapping strategy (say modulo 4) employed in the destination LLC bank, B 3 and B 7 are in the same set. Now, due to frequent requests for B 3 by duplicate RQ 1 , B 7 could be evicted from the bank. In fact, the LLC CTLR enters a thrashing phase where useful blocks are evicted to service duplicate requests. Future requests for these B 7 -like evicted blocks encounter LLC miss, which increases the miss penalty (affecting the caches).

From the increase in packet latency and miss penalty, it is intuitive that sources like IP SRC2 will suffer from delayed instruction execution. It has a cascading effect since delayed execution means delayed commit and thus delayed issue of new instructions. This decreases the system speedup (affecting the core). Even though LOKI is mounted on a single NI, it is capable of affecting multiple components without directly intruding in them, thereby paralysing the entire SoC.

IV. EXPERIMENTAL ANALYSIS We consider the following two architectures for evaluation:

• Baseline: Without any Trojan.

• LOKI: With the proposed Trojan on NI of one IP node.

A. Simulation Setup and Workloads

Baseline and LOKI architectures are modelled on eventdriven gem5 simulator [START_REF] Binkert | The gem5 simulator[END_REF], and the system configuration is given in Table 2. We modify the GARNET [START_REF]GARNET: A Detailed On-Chip Network Model inside a Full-System Simulator[END_REF] interconnection module inside gem5 to model LOKI and mount it on the NI of IP core 5 of a 4×4 NoC based SoC (similar to Figure 5).

To evaluate and analyse the attack, we consider multiprogrammed SPEC CPU2006 benchmarks to mimic a modern NoC based SoC running multiple applications in parallel. We select benchmarks that show varying Misses Per Kilo Instructions (MPKIs) and categorise them as high (MPKI ≥ 40), medium (20 ≤ MPKI <40), and low (MPKI < 20). Table 1 presents the workload mixes, where M1 through M3 run 16 copies of the same benchmark on all the 16 cores (1×16: 16). Whereas M4 through M9 run a random combination of 4 different benchmarks with 4 copies each (4×4: 16). All the workloads are run with 5 different combinations (application to core mapping) and the average of each of them are reported. For a relative comparison of the evaluation metrics, all the results are normalised with respect to the baseline architecture.

B. Impact on NoC

The number of cycles required for a packet to reach from source to its destination is called packet latency. Figure 6 shows the normalised average packet latency when LOKI is active. Duplicate request and reply packets create NoC congestion and increase average packet latency by 3.44x.

SPEC CPU2006 Benchmark Mixes

C. Impact on Caches

Figure 7 shows the normalised LLC misses when LOKI is active. We observe that duplicate requests create an intermittent probing of the same data block in the LLC bank, which results in the eviction of the genuine blocks. Hence, LLC misses increase across all the workloads with an average of 7%. Significant increase of more than 15% is observed in workloads M5 and M6, as they are made of medium and low MPKIs. Due to low packet injection rate in M5 and M6, LOKI is able to inject more duplicate requests into the Flit Buffer. Workloads M2 and M3 also inject many duplicate requests, but the impact on LLC bank is less, as all the cores run the same benchmark with minimum interference (refer Table 1). The number of cycles required to service an L1 cache miss by bringing in the requested data block is called L1 cache miss penalty. With the increase in number of LLC misses, L1 cache miss penalty is bound to increase, as the missed data blocks are now fetched from the off-chip main memory. Figure 8 shows a maximum of up to 36% and an average of 15% increase in L1 cache miss penalty among the evaluated workloads.

SPEC CPU2006 Benchmark Mixes

D. Impact on Cores

An increase in packet latency and L1 cache miss penalty directly impacts instruction execution time. We use Instructions Per Cycle (IPC) to compare the system speedup between baseline and LOKI. A maximum of up to 20% and an average of 10% decrease in system speedup can be seen in Figure 9. It shows how LOKI is able to attack multiple SoC components indirectly and bring down the overall system performance.

V. SENSITIVITY AND OVERHEAD ANALYSIS A. LOKI vs An Existing Trojan

A recently proposed Trojan in NoC router alters the destination (DEST in Figure 2) in the header of packets to attack an SoC for performance degradation [START_REF] Kulkarni | Packet Header Attack by Hardware Trojan in NoC based TCMP and its Impact Analysis[END_REF]. For ease of reference, we call that work as Packet Header Attack Trojan (PHAT). Since they considered L1 cache miss penalty as one of the evaluation metrics, we compare LOKI and PHAT with the same. To have a fair comparison, we identify that cactusADM and hmmer benchmarks dominated their workloads and thus consider workload M6 for analysis. As shown in Figure 10, LOKI has a greater impact on the L1 cache miss penalty without any direct presence on the NoC or the shared cache.

Cores

B. LLC Misses vs L1 Cache Miss Penalty

To understand the relationship between LLC misses and L1 cache miss penalty, we choose to dissect workload M9, which performs the worst in system speedup (refer Figure 9). We show a core-by-core distribution of LLC misses and L1 cache miss penalty of M9 in Figure 11. Except in core 5, the relation between LLC misses and L1 cache miss penalty is almost uniform. The high spike in core 5 is due to the presence of LOKI in its NI. This is owing to the unnecessary delay by duplicate reply packets in the coherence protocol buffer.

C. LLC Misses vs Block Re-Reference

When an evicted LLC block is requested again in the near future, it is called block re-reference [START_REF] Das | Reducing Off-Chip Miss Penalty by Exploiting Underutilised On-Chip Router Buffers[END_REF]. Using the same workload M9, we conduct an analysis to understand how the increased LLC misses on genuine block requests affect the number of their re-references. Figure 12 shows that the number of block re-reference linearly increases across cores with the increase in LLC misses, with an average of 16%. This increase is relatively less in core 5, as the duplicate block requests from this core evict genuine blocks and not the other way around.

D. Timing and Area Overhead

We use ProNoC [START_REF] Monemi | ProNoC: A Low Latency Network-on-Chip based Many-Core System-on-Chip Prototyping Platform[END_REF], that facilitates prototyping of NoC based SoCs. The baseline and LOKI architectures are modelled in Verilog for which ProNoC generates the equivalent RTL. Vivado HLS 2020.2 webpack targeting Xilinx Kintex UltraScale FPGA board is used to synthesize the RTL. LOKI has a negligible increase of 0.29% LookUp Tables (LUTs) and 1.26% FlipFlops (FFs) while meeting the timing constraints.

VI. DISCUSSION ON DETECTION AND MITIGATION

The use of KS prevents logic testing from the accidental triggering of LOKI during the verification process [START_REF] Boraten | Mitigation of Denial of Service Attack with Hardware Trojans in NoC Architectures[END_REF]. As LOKI is intermittent and affects multiple SoC components indirectly, locating its position is difficult. For example, any existing detection technique employed in NoC, LLC or even the cores will not be effective [START_REF] Boraten | Mitigation of Denial of Service Attack with Hardware Trojans in NoC Architectures[END_REF][18] [START_REF] Manju | SECTAR: Secure NoC using Trojan Aware Routing[END_REF]. Prevention and mitigation techniques like obfuscation, encryption, anonymous routing, etc., work well with eavesdropping, data integrity and information leakage attacks, but not LOKI [15][12][13]. This is because LOKI uses control packets for the attack, and they are usually not modified, as the header information is required at every intermediate router for making routing and arbitration decisions. If a technique to mask the header is proposed, unmasking it at every router along the way will fall in the critical path of execution thereby increasing the packet latency.

The mitigation technique proposed in SIM+THANOS [START_REF] Raparti | Lightweight Mitigation of Hardware Trojan Attacks in NoC-based Manycore Computing[END_REF] can not directly tackle LOKI as the header information remain unchanged. However, a similar approach that involves generating a unique message identity between a pair of source and destination can be explored at the IP cores. In this direction, a Packet Leak Detection Unit (PLDU) [START_REF] Hussain | Packet Leak Detection on Hardware-Trojan Infected NoCs for MPSoC Systems[END_REF] that generates a unique tag for every packet can also be tried. A modified version of packet certification from [START_REF] Ancajas | Fort-NoCs: Mitigating the Threat of a Compromised NoC[END_REF] can be implemented to counteract LOKI. Another way of tackling LOKI and other SIM+THANOS-like Trojan attacks could be using something like a Miss Status Handling Register (MSHR) at the NI.

VII. CONCLUSION

This work introduces an HT that has minimal presence yet maximum impact in an NoC based SoC. In a first of its kind, the proposed Trojan uses control packets to attack the NoC, the shared cache and the core IPs to degrade overall system performance without directly intruding in any of them. Being selective and intermittent in nature, detection and mitigation of the Trojan pose unique challenges for future exploration.

Figure 1 :

 1 Figure 1: An example Hardware Trojan with trigger (red gates) and payload (blue gate). Only when the input is 1101, the trigger is activated, and the payload inverts the original output.

2Figure 2 :

 2 Figure 2: Structure of a message exchanged between IPs.

Figure 3 :

 3 Figure 3: Communication between IPs in an NoC based SoC.

1 KSFigure 4 :

 14 Figure 4: Insertion of the proposed Trojan LOKI in NI.

Figure 4

 4 Figure 4 shows a possible way of inserting the proposed Trojan LOKI into the NI of an IP node. Usually, NI employs the Packetiser and De-Packetiser modules for the source and destination IP nodes, respectively. LOKI is inserted in the Packetiser and hence we omit the details about the De-Packetiser module in Figure 4. When NI receives a message from the source IP core, the Packet Generator sub-module converts it into a packet. The Flit Generator sub-module then converts the packet into one or more flits and stores them in the circular Flit Queue. Stored flits are inserted into the NoC router to travel towards their respective destination IP nodes.As proposed in[START_REF] Boraten | Mitigation of Denial of Service Attack with Hardware Trojans in NoC Architectures[END_REF], a backdoor Kill Switch (KS) is used to trigger LOKI and initiate the attack. Packet Type (PT) provides the message type (TYPE from Figure2), and Flit Type (FT) provides the type of flit (head, body or tail). We target read requests as they are control packets with just one head flit (refer Equation1), thus less storage overhead to store a duplicate. LOKI uses a buffer of 1-flit size and can store only one duplicate read request packet at any given point of time. As shown in Figure4, only when P T = READ, F T = F i Head and KS = EN 3 , LOKI gets triggered and copies a head flit (read request packet) from the Flit Generator sub-module into its buffer. LOKI then keeps inserting this duplicate flit into the Flit Queue until KS = DS. Please note that the duplicate flit is inserted only in the free locations to avoid interrupting the usual flow of inter IP communication.

Figure 5 :

 5 Figure 5: Demonstration of the attack launched by LOKI.

Figure 6 :

 6 Figure 6: Normalised average packet latency

Figure 7 :

 7 Figure 7: Normalised LLC misses

Figure 8 :

 8 Figure 8: Normalised L1 cache miss penalty

Figure 9 :

 9 Figure 9: Normalised system speedup

Figure 10 :

 10 Figure 10: LOKI vs An Existing Trojan

Figure 11 :

 11 Figure 11: LLC Misses vs L1 Cache Miss Penalty

Figure 12 :

 12 Figure 12: LLC Misses vs Block Re-Reference

Table 1 :

 1 Workload mixes

	Mix Benchmarks	Copies	Characteristics
	M1	GemsFDTD		high MPKI
	M2	astar	1×16: 16	medium MPKI
	M3	cactusADM		low MPKI
	M4	GemsFDTD, lbm, xalancbmk, gobmk		100% high MPKI
	M5	astar, sjeng, omnetpp, sphinx		100% medium MPKI
	M6 M7	cactusADM, gromacs, perlbench, hmmer GemsFDTD, xalancbmk, astar, omnetpp	4×4: 16	100% low MPKI 50% high MPKI, 50% medium MPKI
	M8	astar, omnetpp, cactusADM, perlbench		50% medium MPKI, 50% low MPKI
	M9	cactusADM, perlbench, GemsFDTD, xalancbmk		50% low MPKI, 50% high MPKI
		Table 2: System configuration
	Processor 16 OoO x86 cores
	L1 Cache	16KB×16, 4-way, 64B blocks, private, split
	L2 Cache (LLC) 256KB×16, 8-way, 64B blocks, shared
		NoC 4×4 2D mesh, 4-VCs/port, 128-bit flit channel
	Routing	2-stage routers, X-Y dimension-order routing
	Packets 1-flit control packets, 5-flit data packets
	Benchmarks	SPEC CPU2006 (multi-programmed)

God of Mischief in Norse Mythology


domain: qfin shs

text:
Because most food processes are fossil fuel-based, many food markets are more or less connected to the oil market. Fishing technology in the high seas being energy-intensive, higher oil prices should aect the sh markets. This research looks at price transmission between Marine Diesel Oil and a global shery commodity, frozen Skipjack tuna (Katsuwonus pelamis ) through a time series analysis combining four dierent methods to look for possible structural breaks and regime shifts in the relationship (Bai-Perron, Lavielle, Gregory-Hansen, Markov-switching). Our results prove that the long-run equilibrium between both prices is weakening after the turn of the 2010s. Explaining the drivers of change is of great interest for short-term forecast but also to build long-term scenarios where both supply and demand variables are likely to aect tuna markets.

1

Introduction

In a world of uncertainty characterized by signicant environmental, economic and geopolitical changes, forecasting commodity prices remains a dicult though stimulating and necessary challenge for economists [START_REF] Asche | The spot-forward relationship in the atlantic salmon market[END_REF], [START_REF] Gordon | A short-run ardl-bounds model for forecasting and simulating the price of lobster[END_REF]]. Most food processes in the 21st century use energy-intensive technologies and bunker costs represent a major expense in sh supply chains. This is the case for high-seas shing targeting tuna species [Parker et al. (2015), [START_REF] Basurko | Fuel consumption of free-swimming school versus fad strategies in tropical tuna purse seine shing[END_REF]]. We should logically observe a high degree of transmission between oil rates and tuna prices [START_REF] Yahya | Temporal and spectral dependence between crude oil and agricultural commodities: A wavelet-based copula approach[END_REF].

Tuna prices are highly volatile in a globally integrated market [START_REF] Jiménez-Toribio | Global integration of european tuna markets[END_REF].

The historical volatility was estimated to 26% and the coecient of variation for tuna landings amounted to 76%, on the same range as salmon production [START_REF] Dahl | Fish price volatility[END_REF].

Tuna prices have more than trebled over the past two decades (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017) whereas the oil price has only doubled, but both products are passing through ups and downs. Tuna catches and trade are subject to many drivers and stressors, such as increasing shing eort, the use of Fish Aggregating Devices (FADs), ENSO events, trade policy changes, new shery management rules implemented by Regional Fisheries Management Organizations, exchange rate movements, demand shocks, population and economic growth in emerging countries, etc.

[ [START_REF] Miyake | Recent developments in the tuna industry: stocks, sheries, management, processing, trade and markets[END_REF], [START_REF] Maury | From shared socio-economic pathways (ssps) to oceanic system pathways (osps): Building policy-relevant scenarios for global oceanic ecosystems and sheries[END_REF], [START_REF] Scherrer | Regulation strength and technology creep play key roles in global long-term projections of wild capture sheries[END_REF], [START_REF] Bell | Pathways to sustaining tuna-dependent pacic island economies during climate change[END_REF]].

Economic knowledge about tuna markets improves gradually [START_REF] Herrick | Integration of united states, thailand and philippine canned tuna markets[END_REF], [START_REF] Squires | Price linkages in pacic tuna markets: implications for the south pacic tuna treaty and the western and central pacic region[END_REF], [START_REF] Jeon | Is there a global market for tuna? policy implications for tropical tuna sheries[END_REF], [START_REF] Guillotreau | Local, regional and global markets: what drives the tuna sheries?[END_REF], [START_REF] Sun | More landings for higher prot? inverse demand analysis of the bluen tuna auction price in japan and economic incentives in global bluen tuna sheries management[END_REF]], but is still far from being sucient to accurately forecast the future prices of tuna several months, years or even decades ahead. In particular, the linkage between the energy sector and the shing industry is overlooked in the existing literature, with a few rare exceptions [START_REF] Tyedmers | Fuel consumption and greenhouse gas emissions from global tuna sheries: A preliminary assessment[END_REF], Parker and Tyedmers (2015), [START_REF] Guillen | Oil for sh: an energy return on investment analysis of selected european union shing eets[END_REF]]. However, the existing literature deals more with the energy returns of shing than about the relationship between the cost of energy and the price of sh. This latter question is nonetheless important to understand the economic drivers of the shing eort and their impact on the dynamics of global sheries. In particular, long-run scenarios need to rely on simple but robust economic models to test for the long-term consequences of severe impacts aecting social and ecological systems [START_REF] Dueri | Food security or economic protability? projecting the eects of climate and socioeconomic changes on global skipjack tuna sheries under three management strategies[END_REF], [START_REF] Maury | From shared socio-economic pathways (ssps) to oceanic system pathways (osps): Building policy-relevant scenarios for global oceanic ecosystems and sheries[END_REF], [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF], [START_REF] Bell | Pathways to sustaining tuna-dependent pacic island economies during climate change[END_REF]]. For example, if lower catches cannot fully supply the growing market demand any longer, prices may increase proportionally, so as to leave the shers' income unchanged [START_REF] Sun | Fewer sh for higher prots? price response and economic incentives in global tuna sheries management[END_REF]?

Conversely, if the catch becomes lower with constant prices, an increasing energy cost may deter shers to maintain the same level of eort, hence relaxing the pressure on stocks. On a more theoretical ground, the relationship between the oil and sh markets is also interesting because the optimal exploitation rules of an exhaustible and renewable resource are dierent. The Hotelling rule applied to the optimal exploitation of exhaustible resources equalizes the growth rate of prices to the discount rate, under a nite time horizon. For a renewable resource like wild sh, the marginal productivity of stocks added to a marginal stock eect on the shing rent must be equal to the discount rate at the optimum level of exploitation over an innite time horizon. Any increase of the discount rate can have opposite eects on extraction rates, accelerating the exhaustion of oil reserves but preserving the renewable stocks at a higher level of biomass, hence resulting in higher catches and lower sh prices [START_REF] Hannesson | The eect of the discount rate on the optimal exploitation of renewable resources[END_REF]. Fish markets, whose demand is often found price-elastic, would therefore face a fast-growing price of oil energy beyond the peak oil, thus creating a potential price squeeze that would aect the prot margins of the shing industry.

Despite the intensive use of energy in many food production processes, research works analyzing the link between both markets are not very common [START_REF] Yahya | Temporal and spectral dependence between crude oil and agricultural commodities: A wavelet-based copula approach[END_REF], [START_REF] Dahl | Dynamics of volatility spillover in commodity markets: Linking crude oil to agriculture[END_REF]]. This is why our research contributes to the empirical literature by analyzing the co-evolution of energy and sh prices. In particular, we selected a procedure combining various time series techniques to determine possible break dates in the two markets separately, and in their relationship. Because the eorts of analysts attempting to predict the price of commodities several months ahead are rather concentrated on the oil market, the idea is to test for the long-run relationship between the price of Marine Diesel Oil (MDO) and the price of skipjack (Katsuwonus pelamis). If a long-run relationship can be found between the two markets, and according to the direction of the Granger causality, we could be in a position to predict condently the evolution of the skipjack price from the oil Futures market. More precisely, by looking at the relationship between both markets, we hope to learn whether any actual inuence of the oil price on the skipjack price is passing through the supply-side (energy being a major component of the marginal cost of shing) or the demand-side for these two global natural resources [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF], [START_REF] Maury | From shared socio-economic pathways (ssps) to oceanic system pathways (osps): Building policy-relevant scenarios for global oceanic ecosystems and sheries[END_REF]]. The oil market being global, just like the market for canned tuna through which skipjack is mostly traded, the dynamics of both prices might well be linked to the worldwide demand growth, just like many other food commodities [START_REF] Yahya | Temporal and spectral dependence between crude oil and agricultural commodities: A wavelet-based copula approach[END_REF], [START_REF] Dahl | Dynamics of volatility spillover in commodity markets: Linking crude oil to agriculture[END_REF]].

The following article is organized as follows. First we propose a literature review about the link between oil and commodity prices to show the importance of the issue at stake regarding tuna markets. Secondly, we developed a time series analysis combining dierent techniques on monthly prices between 2000 and 2020 to scrutinize the link between the sh and oil markets and look for possible breaks in the relationship. In a following section, we search for other candidate variables to introduce a possible regime shift explaining the dynamics of the skipjack market. Finally, we discuss the results in a last section with regard to the input requirements of holistic models dealing with the future of tuna sheries under global change scenarios.

Literature survey

An increasing number of research works attempts to model the global food demand scenarios for the 21 st century [START_REF] Valin | The future of food demand: understanding dierences in global economic models[END_REF], [START_REF] Bodirsky | Global food demand scenarios for the 21 st century[END_REF], [START_REF] Flies | Forecasting future global food demand: A systematic review and meta-analysis of model complexity[END_REF]]. In particular, the authors try to do so in order to assess the consequences of reference climate scenarios 1 on food production and consumption levels. Food models are inuenced by many dierent drivers such as real income and prices, but also trade policy changes, population growth and characteristics, the diet patterns, urbanization, and of course by the availability of commodities on the supply side [START_REF] Valin | The future of food demand: understanding dierences in global economic models[END_REF]. This is all the more true when it concerns wild and common resources such as shery products. Climate change is expected to transform profoundly the level of biomass and the spatial distribution of sh populations, justifying the interest of modelling global demand for shery products to better understand its long-run drivers [START_REF] Maury | From shared socio-economic pathways (ssps) to oceanic system pathways (osps): Building policy-relevant scenarios for global oceanic ecosystems and sheries[END_REF], [START_REF] Scherrer | Regulation strength and technology creep play key roles in global long-term projections of wild capture sheries[END_REF], [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF], [START_REF] Bell | Pathways to sustaining tuna-dependent pacic island economies during climate change[END_REF]].

Two classes of models are mostly used to forecast food demand: partial equilibrium models and computable general equilibrium (CGE) models. The latter models are based on utility functions being maximized under the budget constraint to derive the demand functions where households can substitute all types of consumption goods. Consequently, such models require a tremendous amount of data and often rely on strong assumptions regarding the consumption behavior of households. Partial equilibrium models apply reduced forms of demand functions to a limited set of goods [START_REF] Flies | Forecasting future global food demand: A systematic review and meta-analysis of model complexity[END_REF]. If the second class of models seems more limited in scope, it allows for greater details about the bundle of goods included in the model (e.g. several sh species), the substitutability between them and the set of determining factors [START_REF] Guillotreau | Local, regional and global markets: what drives the tuna sheries?[END_REF].

Beyond the interest of understanding food demand drivers, the modelling eorts concerning the demand for wild-caught sh show the interest of unveiling the exibility coecients which represent key market-incentives for shery management. The eort reduction which is required to adjust the shing capacity to the sustainable level is more likely to be accepted if the price response allows shers to earn more by catching less and conversely [START_REF] Sun | Fewer sh for higher prots? price response and economic incentives in global tuna sheries management[END_REF], [START_REF] Sun | More landings for higher prot? inverse demand analysis of the bluen tuna auction price in japan and economic incentives in global bluen tuna sheries management[END_REF]]. Tuna sheries oer a perfect illustration of a global commodity being harvested in the three oceans, supplying the canning industry with large quantity of raw materials, and being traded as a major source of sh proteins in many countries around the world [START_REF] Miyake | Recent developments in the tuna industry: stocks, sheries, management, processing, trade and markets[END_REF], [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF]]. The market is global and all regional markets are now quite well integrated under the leading role of the Bangkok market [START_REF] Jiménez-Toribio | Global integration of european tuna markets[END_REF], [START_REF] Sun | Fewer sh for higher prots? price response and economic incentives in global tuna sheries management[END_REF]]. This market presents the valuable advantage of its central position between two oceans and its vicinity to the most productive shing grounds in the world [START_REF] Miyake | Recent developments in the tuna industry: stocks, sheries, management, processing, trade and markets[END_REF].

Like for any other ocean-wide shery, tuna shing and trade are highly dependent on energyconsuming industrial eets, particularly because of an increasing distance from ports to shing grounds [START_REF] Tickler | Far from home: Distance patterns of global shing eets[END_REF]. The conventional index assessing the high level of catch dependence to energy is the Fuel Use Intensity (FUI) measuring the ratio of consumed oil Litres per tonne of landed sh. Across a great number of species and world regions, the mean FUI found by Parker and Tyedmers (2015) since 1990 was 706 L * t -1 . A study reported an average FUI value of 368 L * t -1 for the global purse-seine eet targeting skipjack and yellown tuna (Parker et al., 2015). Two more recent and accurate research works based on vessel data looked at the FUI of the European purse-seine eet shing tuna in the Indian Ocean showed a variable FUI value, oscillating between 390 and 680 L * t -1 since 2015 according to the level of catches, shing eort (quantitatively and qualitatively) and vessel size [START_REF] Chassot | Fuel consumption and air emissions in one of the world largest commercial sheries[END_REF], [START_REF] Basurko | Fuel consumption of free-swimming school versus fad strategies in tropical tuna purse seine shing[END_REF]]. Keeping in mind an average marine diesel oil price of $554 t -1 between January 2018 and October 2020 and a conversion factor of 0.72 kg per Litre, the fuel cost would reach nearly $200 per tonne of sh with a 500L * t -1 FUI.

The average price of frozen skipjack being $1468 per tonne for the same period 2 , the energy cost would represent 14% of the ex-vessel price of frozen tuna. Bunker costs are undoubtedly an important component of expenses for purse-seiners targeting skipjack tuna. The share of energy costs is estimated between 20% and 30% of operating costs, depending on the level of oil rates [START_REF] Miyake | Recent developments in the tuna industry: stocks, sheries, management, processing, trade and markets[END_REF]. This proportion could even rise up to 50% (Parker and Tyedmers, 2015) or more in case of extremely high prices on the oil market as it happened in September 2008 when the crude oil barrel skyrocketed at $147 per barrel, just before the nancial crash [START_REF] Tyedmers | Fuel consumption and greenhouse gas emissions from global tuna sheries: A preliminary assessment[END_REF].

The high share of fuel expenses in operating costs legitimates the issue of price transmission between oil and food markets [START_REF] Avalos | Do oil prices drive food prices? the tale of a structural break[END_REF], [START_REF] Dillon | Global oil prices and local food prices: Evidence from east africa[END_REF], [START_REF] Su | Do oil prices drive agricultural commodity prices? further evidence in a global bio-energy context[END_REF]].

Oil prices and food prices can interact through at least two channels: directly through the trade-o between biofuel energy and agricultural markets, indirectly through oil energy as major input for most food products [START_REF] Su | Do oil prices drive agricultural commodity prices? further evidence in a global bio-energy context[END_REF]. The relationship is not straightforward because of this dual inuence and some articles bring evidence with a VECM and impulseresponse models that oil prices may even adjust to the long-run relationship with corn prices rather than the expected opposite causality [START_REF] Avalos | Do oil prices drive food prices? the tale of a structural break[END_REF]. Interestingly, in this study, the relationship has become narrower after that a US Energy Policy Act has made ethanol the only allowed standard additive of gasoline, thus creating a dependence between the oil price and the ethanol (hence corn) price.

However, using Partial Equilibrium frameworks may overlook the macroeconomic eects of oil prices on food markets. Using a global CGE model, some authors have shown that energy prices have also an impact on real income and trade balances [START_REF] Gohin | The long-run impact of energy prices on world agricultural markets: The role of macro-economic linkages[END_REF].

The eect would be positive for crude-oil producing countries, but negative for oil importing countries. The authors simulated a 20% reduction shock in world oil reserves and found evidence of a negative relationship between world food and energy prices, countervailing the cost-push eect of an oil price change to food prices. However, one could turn the macroeconomic eect upside down and also hypothesize that an increasing oil price is the result of global economic growth which could somehow benet to food prices in general, and sh prices in particular. Whatever the channel of pass-through from oil prices to skipjack tuna prices, either as a marginal cost-push mechanism, or a demand-pull process aecting both oil and sh markets, we believe that the relationship deserves a thorough analysis through time series and through a variety of empirical models based on cointegration theory [START_REF] Johansen | Statistical analysis of cointegration vectors[END_REF]. First of all, a positive correlation and causality found between oil rates and sh prices, if ever demonstrated, could be used to forecast the tuna price as input for canneries with the underlying support of Futures oil market contracts, as proved in other global sh markets like the salmon market [START_REF] Asche | The spot-forward relationship in the atlantic salmon market[END_REF]. Secondly, a long-term linkage between oil prices and tuna prices may also be an interesting contribution to a more prospective analysis of global food demand with respect to the peak oil and climate-driven scenarios. What can be the future of the large-scale tuna sheries if high shing costs and price elasticity of nal demand hamper the protability of purse-seine vessels and canneries [START_REF] Sala | The economics of shing the high seas[END_REF]?

Thirdly, if the relationship appears not to be robust enough in the long term, it might reveal some structural changes and regime shifts that could be meaningful to better understand the price formation on the global tuna markets. Besides the inuential status of oil for many food commodities, what is the role of landings or substitute species in the shery markets, keeping in mind that the world is facing a maximum supply of 80 or 90 million tonnes of wild-caught sh for more than three decades, this supply being now threatened by the global warming process going on and the lack of stringent regulation [START_REF] Scherrer | Regulation strength and technology creep play key roles in global long-term projections of wild capture sheries[END_REF].

In parallel, the world population is still growing with a higher level of income per capita and requires an increasing amount and diversity of food proteins. What we propose in this research is to reconcile the partial and general equilibrium hypotheses about the link between energy and sh markets by applying a parsimonious cointegration model of price transmission between the oil and sh markets. To that end, we adopt an original procedure combining various structural break searching techniques. First, we check the existence of a long-term equilibrium relation between the marine diesel oil price and the skipjack tuna price. Secondly, we look for structural break dates in the two markets separately, and then jointly by dierent econometric means. By doing so, we expect more robust outcomes and condence about the identication of break dates. Thirdly, we investigate the supply or demand-sided nature of the long-term relationship between the two prices by considering other factors aecting the tuna market.

3 Relationship between the prices of skipjack and marine diesel oil First of all, we check that all series are I(1), in particular for Pmdo and Pskj. This is the case from ADF, ADF-GLS and KPSS tests 6 . Seasonal unit roots needed also to be scrutinized in the following equation suggested by [START_REF] Miron | The economics of seasonal cycles[END_REF]:

y t -y t-1 = µ 1 D 1 + µ 2 D 2 + ... + µ 12 D 12 + t (1)
where y t is the time series under investigation, and D is a (monthly) seasonal dummy variable. In the case where the residual term does not contain any information on seasonality, we may consider the Fisher test and the R 2 value associated to each regression as giving an indication about the deterministic seasonality. For the price of skipjack series, this R 2 value is close to 0.10 and even found lower for the price of marine diesel oil (0.05). We can conclude that there is no deterministic seasonality nor deterministic trend in the series [START_REF] Franses | Seasonality, non-stationarity and the forecasting of monthly time series[END_REF], [START_REF] Beaulieu | Seasonal unit roots in aggregate us data[END_REF]].

The price of skipjack looks also quite volatile. Looking at the annualized standard deviation of log price returns between February 2012 and September 2020 gave a historical volatility of 0.26, which is exactly the same value found in [START_REF] Dahl | Fish price volatility[END_REF] over the period January 1990-December 2012. This volatility of skipjack tuna monthly prices is comparable to that of the farm-bred Norwegian salmon export price in USD per kilogram (source IMF)

between February 2012 and September 2020, i.e. 0.29. The long-term relationship was then tested in a second step but without any success. The null of no cointegration could not be rejected (p-value=0.35) over the whole sample. We assumed that the relationship between the two market prices could have been distorted in the course of time. The cointegration equation including a break in July 2004 was then successfully tested with a price transmission elasticity of 0.41, and an increasing intercept after July 2004 (R 2 = 0.64). This is in line with the result obtained on a truncated sample of the same monthly data (from 2000:02 to 2015:02) by [START_REF] Nadzon | Consommation d'énergie et politique de pré vention de la pollution liée aux activités maritimes[END_REF], who found an elasticity of 0.64 and a R 2 = 0.73 with a Fully-Modied Least Square method [START_REF] Nadzon | Consommation d'énergie et politique de pré vention de la pollution liée aux activités maritimes[END_REF]. However, the structural change could also concerned a shift in the slope of the relation. A Gregory-Hansen test was therefore performed to look for the right specication [START_REF] Gregory | Residual-based tests for cointegration in models with regime shifts[END_REF]. Such models allow to determine when the unknown breakpoints occur (looking at the stationarity of the residuals through the minimum value of the ADF statistic corresponding to the date), and if the latter aects the constant, the trend or the slope in the regression model, thus explaining the absence of cointegration. Their model (4) was selected as the best one, with a shift in both the constant and the slope with no trend [START_REF] Gregory | Residual-based tests for cointegration in models with regime shifts[END_REF]:

l Pskj,t = α 0 + α 1 × I(t > τ ) + β 1 × l P mdo,t + β 2 × l P mdo,t , ×I(t > τ ) + µ t (2)
The ADF test procedure gave a breakpoint in September 2010 (t -stat = -5.171 with The τ -stat of the ADF test for µ t was -5.12 (p=0.000), proving the long-term relationship (cointegration) between the two variables. However, the dierence between the two prices increased and the price transmission elasticity fell signicantly from 0.52 to 0.32 after the breakpoint, meaning that the MDO price is less well transmitted to the tuna price after this date. The worldwide economy increased again after two years of crisis, boosting the crude oil price between September 2010 and April 2011. On the tuna market side, this coincided with a period of stable catches (around 2.5 million tonnes between 2006 and 2011), hence lower imports of frozen skipjack in Thailand and higher prices. An error-correction model (VECM) was also tested. The coecient of the cointegrating vector for lPmdo is 0.530 and the adjustment vector shows a weak exogeneity on the MDO market side, as expected. The skipjack price dierence equation of the VECM can be written as follows:

∆ Lpskj t = -0.118 To summarize the results of this section, the dynamics of skipjack prices alone has changed in February 2007. The pattern of the MDO price has changed several times over the period, but particularly in July 2004 which has modied the trajectory of its inuence on skipjack tuna prices (intercept of the cointegration relation). Finally, another major break was found in September 2010, changing even more deeply the long-run equilibrium between the two prices (constant and slope of the relation). It seems important to investigate what could be the changes on the two markets and the factors aecting the long-run relationship between both markets.

A weak prediction of the skipjack price

From the cointegration model and the VECM, we try to simulate the price of skipjack from the single mdo price variable to see whether the latter could represent a trustful predictor of tuna prices. To this end, we generate random errors of the VECM from a normal distribution ût ∼ N (0, σ2 u ) to rst simulate the ∆lP skj from Eq.( 4). Since we know for each time step lP mdo t-1 , lP skj t-1 , and µ t-1 , we can simulate the level of lpskj (= lP skj t-1 + ∆lP skj)

from the current and following periods. The skipjack price is simulated from April 2000 to September 2020 and displayed in Fig. 2, along with the actual skipjack price and with the break of September 2010.

Insert here Fig. After the introduction of the lagged quantity variable, the oil price became non-signicant, as if the Bangkok tuna price was responding more to the past level of landings than to the oil input price. Unfortunately, the own-price exibility coecient did not show the expected sign, i.e. normally negative and unitary as found in previous studies [START_REF] Sun | Fewer sh for higher prots? price response and economic incentives in global tuna sheries management[END_REF], presumably because of an identication problem. The level of catch and landings is also possibly aected by the oil rate itself, because the lQskj equation of the VAR system had a very signicant parameter estimate for the lagged lPmdo variable. The level of landings could certainly be aected by the energy cost of shing beyond a threshold, but there may be some other explanation behind the degraded correlation after the breakpoint and the alternate periods of good and bad connections between the two markets. This needed to be scrutinised with potential regime shifts between some sub-periods. In a preliminary conclusion, we consider that the oil price, although inuential for the skipjack price, is not a good predictor of skipjack prices for every period.

4

Introducing a regime shift in the oil-tuna price relation

The previous analysis of structural breaks emphasizes the changes aecting the long-run relationship between the skipjack price and the fuel price. We are therefore looking for other possible candidates to explain the evolution of skipjack prices along with the oil price. In particular, the leading role played by a substitute species (yellown tuna, Thunnus albacares)

was pointed out by another study about price cointegration [START_REF] Jiménez-Toribio | Global integration of european tuna markets[END_REF].

The correlation between the two prices is clearly observed in Fig. 3, with a higher price of the big yellown, hence more targeted by purse-seiners, because of a better yield of raw materials per sh for canneries.

Insert here Fig. 3 Skipjack and yellown tuna prices in the Bangkok market (in USD/t) It was therefore decided to test for the relationship between the prices of the two major cannery-grade tuna species before including them in a Markov chain model which allows two regimes of price relationship between the fuel and the skipjack prices, assuming that the change may not be permanent but shifting between two regimes as observed in other sh market studies [START_REF] Asche | Regime shifts in the sh meal/soybean meal price ratio[END_REF].

Conrming the results of the 2010 study, which was based on a sample between January 1995and December 2006[START_REF] Jiménez-Toribio | Global integration of european tuna markets[END_REF], a cointegration relation was easily found between the two I(1) series of the logarithmic prices of skipjack and yellown 8 . A VECM model proved the weak exogeneity of the yellown price, the skipjack price reverting back to its long-run relationship with the price of the other species (with a speed of adjustement of -0.1317, signicant at the 1% level) while the former one is signicant but positive, thus not moving back to the long-run relation. We also assumed that the transition probabilities between the two regimes are depending on the skipjack landings, since the quantity of skipjack, which is prevailing in the Bangkok market [START_REF] Sun | Fewer sh for higher prots? price response and economic incentives in global tuna sheries management[END_REF], showed some kind of inuence over the skipjack price in the previous VAR equation.

The two regimes shown were then estimated on a sample 2000m1-2020m9 with Eviews 11 (full results in Appendix):

Regime 1: Clearly, the inuence of the marine diesel oil price on the skipjack price is weaker during the second regime, the elasticity of price transmission decreasing from 24.1 to 5.2% while the fundamentals of the tuna market (catches and substitute species) are more present in Regime 2. Looking at Fig. 4 gives an insight to the periods under Regime 1 (Regime 2 is easily deducted when the probability of Regime 1 is null). dominates:

lPskj t = 0.
Insert here Fig. 4 The two regimes of the relation between oil and skipjack tuna prices between January 2000 and September 2020

We can see that the two regimes alternate, although the higher probabilities of being in Regime 1 at each time step are rather found during the rst decade, the second decade being more characterized by the second regime of price transmission, with a few exceptions around 2015 and 2019. We can therefore better understand the gaps between the actual and simulated price of skipjack shown in Fig. 2. The periods of Regime#1 of higher transmission between oil and tuna prices are rather found at the beginning of the sample period, i.e. prior to the nancial crisis and when the economic growth rates were quite high. At the turn of the decade, landings stagnated for several years, creating shortages on the growing canned tuna market. After the crisis, the increasing spread between the two prices could therefore be explained by a more important role of landings upon the skipjack quotations. We can have a more specic understanding about the role of skipjack landings by looking at the parameters of the transition matrix:

P t =    P 11,t P 12,t P 21,t P 22,t    (8)
From the results of the MS model (Table 4 in Appendix), the probabilities of transition between the two regimes can be written as a logistic function of lQskj:

       P 11,t = 1 1+e -0.216 * lQskj t P 21,t = 1 1+e -(-0.284 * lQskj t ) (9)
Using the min and max values of Qskj in Table 1 helps to interpret the two transition probabilities of Eq.( 9). In a month where the landings in Bangkok are low (15,164 tonnes), the probability of remaining in regime #1 is 89%, hence 11% of shifting to the second regime.

Whenever the landings reach a maximum value (90,435 t), the likelihood of shifting to regime #2 is 3 points lower. In other words, the high level of price transmission between the MDO price and the skipjack price is more likely to occur when the tuna market is not under the stress of low landings and when the tension is rather on the oil market. However, in case of shortage on the tuna market and if the tension on the oil market is relaxed, the role of tuna landings prevail and oil is no longer a dominating driver of tuna prices.

5

Discussion of the results

The relationship between the oil price and the price of food commodities might be overlooked by economists although most food industrial processes are fossil fuel-based, particularly in sheries [Parker and Tyedmers (2015), Parker et al. (2015)]. The fuel use intensity of an industrial purse-seine eet is estimated around 500 Litres per tonne of caught sh, but it can reach nearly 700 Litres in some cases and varies according to the shing technique [START_REF] Chassot | Fuel consumption and air emissions in one of the world largest commercial sheries[END_REF], [START_REF] Basurko | Fuel consumption of free-swimming school versus fad strategies in tropical tuna purse seine shing[END_REF]]. Consequently, marine diesel oil represents a substantial share of costs, between 20 and 30% of total shing costs for high-seas eets, although the tuna purse-seine eet is considered more ecient than others in terms of energy return on investment indicator, and even when it is compared to many agricultural production activities [START_REF] Guillen | Oil for sh: an energy return on investment analysis of selected european union shing eets[END_REF].

We hypothesized that such an important energy input should be somehow visible in the price of skipjack tuna which is valued around USD1280 per tonne at the Bangkok market (sample mean between 2000 and 2020), major international marketplace in the world by the volume of trade (nearly 600, 000mt were imported by Thailand in 2019). A strong relationship would allow to predict future tuna prices, helping both shing and canning companies to plan their economic results and investment. On this particular expectation, our rst results from a price transmission model applied to the relationship between marine diesel oil and skipjack tuna prices between January 2000 and September 2020 were quite disapointing because no cointegration relation could be found. However, searching for structural breaks with dierent econometric procedures [START_REF] Lavielle | Using penalized contrasts for the change-point problem[END_REF], [START_REF] Bai | Computation and analysis of multiple structural change models[END_REF], [START_REF] Gregory | Residual-based tests for cointegration in models with regime shifts[END_REF]] allowed to identify at least two possible breakpoints in July 2004 and September 2010. The rst date concerned mainly the oil market. The period starting in 2004 has been characterized by a sharp increase of crude oil prices. Between July 2004 and July 2008, the average USD price per barrel has grown by 258% because of the tremendous demand from fast growing economies like China and south-East Asian countries, thus creating supply shortages, locally and globally [START_REF] Casamassima | The impact of oil prices uctuactions on transport and its related sectors[END_REF]. This could explain the rst breakpoint found in the P mdo series, followed by several other successive changes marking the booms and busts of the worldwide conjuncture.

The second date was more interesting because it could potentially aect the two time series and their relation. [START_REF] Gregory | Residual-based tests for cointegration in models with regime shifts[END_REF] indicated that both intercept (i.e. the spread or margin) and slope (the elasticity of price transmission) were modied after the break. The spread has increased after the 2010 breakpoint but, more importantly, the elasticity of price transmission has been reduced from 0.516 to 0.316 between the two periods, meaning that the pass-through of oil prices to skipjack tuna prices has been degraded. Whenever the oil price increases by 10%, the tuna price only increases by 3% in the last decade, instead of +5% a decade ago. Other inuences had to be searched for.

This was done through the introduction of a substitute price (i.e. the leading price of another tuna species sold on the same market, yellown tuna or T. albacares), and the monthly quantity of skipjack imports in Thailand, in a Markov-switching model. With this approach, a clear regime shift appeared signicant throughout the two decades: the quality of price transmission between oil and tuna prices alternates between phases of high and low passthrough. In particular, prior to the nancial crisis or so, the rst regime of high transmission between the two markets prevails, while the second regime of lower transmission dominates the past decade. In the meantime, the oil market has experienced a high volatility period with spectacular ups and downs and the tuna market, after decades of steady growth, is increasingly stretched by an imbalance between the increasing worldwide demand and tuna catches reaching a ceiling after a long period of expansion [START_REF] Miyake | Recent developments in the tuna industry: stocks, sheries, management, processing, trade and markets[END_REF], [START_REF] Dueri | Food security or economic protability? projecting the eects of climate and socioeconomic changes on global skipjack tuna sheries under three management strategies[END_REF], [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF], [START_REF] Scherrer | Regulation strength and technology creep play key roles in global long-term projections of wild capture sheries[END_REF]]. In the estimated model outcome, we reported a regime shift at the turn of the 2010s: a rst regime where the tuna price responds quite well to the oil market shocks, and a second regime where other variables related to the tuna market become more inuential. Interestingly, the likelihood of Regime #1 (better pass-through between Pmdo and Pskj) is related to higher quantities sold on the tuna market, whereas the relationship between the two markets is aected by the market pressure of low landings or higher demand for sh. This result is similar to those found in other studies about the contrasted inuence of an oil price increase according to the phase of the economic cycle [START_REF] Raymond | Oil and the macroeconomy: A markov stateswitching approach[END_REF], [START_REF] Yahya | Temporal and spectral dependence between crude oil and agricultural commodities: A wavelet-based copula approach[END_REF], [START_REF] Dahl | Dynamics of volatility spillover in commodity markets: Linking crude oil to agriculture[END_REF]]. In the rst cited study, using a Markov-switching model, the authors showed that an increase of oil prices during the boom periods had little impact on the economy, but tends to aect more deeply the results during slow-growing phases. Yahya, Oglend andDahl (2019, 2020) found similar results with wavelet and copula methods applied to the crude oil price connected to agricultural prices on Futures markets: the spillover and dependence parameter between energy and ten agricultural markets decline during period of economic prosperity and spike during economic turmoil periods such as the 2008 global nancial crisis [START_REF] Dahl | Dynamics of volatility spillover in commodity markets: Linking crude oil to agriculture[END_REF].

In a closer case study to our own results, [START_REF] Asche | Regime shifts in the sh meal/soybean meal price ratio[END_REF] also found two Markov discrete regimes in the relationship between the shmeal and the soybean markets, both supplying aquaculture and terrestrial animals feed markets. Their interpretation is the following one:

whenever the shmeal market faces a shortage because of a climatic event like a strong El Niño Southern Oscillation, then the two markets are disconnected with a more volatile and higher relative price of shmeal [START_REF] Asche | Regime shifts in the sh meal/soybean meal price ratio[END_REF]. In this regard, structural breaks or regime shifts observed in commodity markets can help signalling more global changes such as environmental events [START_REF] Smith | Seafood prices reveal impacts of a major ecological disturbance[END_REF].

What lessons can be drawn from this study? It is clear that the years and decades to come will see higher tensions on the oil market, ending the ourishing expansion of the high-seas purse-seine eet targeting tropical tuna species since the early 1950s, and which is highly energy-consuming [Parker and Tyedmers (2015), [START_REF] Tickler | Far from home: Distance patterns of global shing eets[END_REF], [START_REF] Sala | The economics of shing the high seas[END_REF], [START_REF] Chassot | Fuel consumption and air emissions in one of the world largest commercial sheries[END_REF], [START_REF] Basurko | Fuel consumption of free-swimming school versus fad strategies in tropical tuna purse seine shing[END_REF]]. The most predictable scenarios for oceanic sheries of large pelagic are darker with respect to global changes [START_REF] Maury | From shared socio-economic pathways (ssps) to oceanic system pathways (osps): Building policy-relevant scenarios for global oceanic ecosystems and sheries[END_REF], [START_REF] Scherrer | Regulation strength and technology creep play key roles in global long-term projections of wild capture sheries[END_REF], [START_REF] Bell | Pathways to sustaining tuna-dependent pacic island economies during climate change[END_REF]], and the food requirements of the growing population will put pressure on the tuna market, thus creating a squeeze between a declining supply and an increasing demand [START_REF] Mullon | Exploring future scenarios for the global supply chain of tuna[END_REF]. The regime#2 of the MS model is more likely to be the new standard, relaxing the inuence of oil rates on tuna prices and moving back to the fundamentals of the market (GDP per capita and price of substitutes).

Consequently, we recommend tuna traders not to use the oil price on Futures markets as a reliable predictor of tuna prices in the short and mid-terms for their hedging operations [START_REF] Dillon | Global oil prices and local food prices: Evidence from east africa[END_REF], [START_REF] Su | Do oil prices drive agricultural commodity prices? further evidence in a global bio-energy context[END_REF]]. However, energy remains a powerful driver of the industry, as shown by the long-term relationship between the oil and tuna prices, and as such modellers must integrate this fact in their predictive models of global food demand scenarios for the 21 st century [START_REF] Bodirsky | Global food demand scenarios for the 21 st century[END_REF], [START_REF] Flies | Forecasting future global food demand: A systematic review and meta-analysis of model complexity[END_REF]].

  monthly price of skipjack (Pskj) is extracted from the FFA Fisheries Development Division using the Thailandese customs database from January 2000 to September 2020 (249 obs.) 3 . The price of Marine Diesel Oil (Pmdo) in Singapore is also supplied by the FFA Fisheries Development Division with data published by Bunkerworld 4 from January 2000 to May 2018. Between June 2018 and September 2020, the series is complemented by the estimated price obtained from a robust long-term relationship existing between the MDO in Singapore the New York Harbor No. 2 Heating Oil Future Contract 4 5 . Both series are transformed by their logarithm to test for the quality of price transmission in the long run (Fig. 1 and Table 1

  monthly) series running throughout several decades can be aected by disrupting events, as observed in other sh markets[START_REF] Asche | Regime shifts in the sh meal/soybean meal price ratio[END_REF],[START_REF] Smith | Seafood prices reveal impacts of a major ecological disturbance[END_REF]]. Consequently, we suspected the relationship between the price of skipjack and that of MDO to have been modied during the sampled period. To search for structural breaks, we rst used the Lavielle segmentation procedure based on the maximum likelihood criteria with the Rpackage segclust2d[START_REF] Lavielle | Using penalized contrasts for the change-point problem[END_REF],[START_REF] Patin | Package segclust2d[END_REF]]. With a L min of 24 months (minimum length of a segment) and K max = 7 (maximum number of breaks), we tested the two series separately. For the oil price, the optimal number of breaks was 3, hence 4 segments (breakpoints: July 2004, December 2010 and November 2014). For the price of Skipjack alone, only one break was found in February 2007 7 . However, the break dates did not match between the two series. A joint segmentation was then performed with the two series simultaneously and gave one single breakpoint (i.e. 2 segments) in July 2004. According to the International Energy Agency, demand for oil grew at its strongest pace in almost three decades in 2004, mainly driven by supply bottleneck and strong economic growth in Asia and America. The market was also tense because of uncertainty about the security of oil supplies during the second Gulf war (ECB monthly Bulletin, May 2005).

  AR lag = 2), while the Phillips procedure pointed at a breakpoint in March 2007 with z t = -4.986 and z a = -45.343. Including either break date in the model, the two series became cointegrated. However, the Gregory-Hansen model (4) showed no signicant parameter estimates for the break of March 2007 on the constant term or the slope, unlike the break of September 2010. Consequently, only the rst breakpoint of the ADF procedure (i.e. September 2010) was considered and tested in the following cointegration model: value in brackets; τ (129) = September 2010)

Figure 1 :

 1 Figure 1: Prices of skipjack in Bangkok and MDO in Singapore (USD/t) Source: FFA Fisheries Development Division

Figure 2 :Figure 3 :

 23 Figure 2: Prediction of the skipjack price (in USD/t) (blue line = actual price, red line = simulated price from the VECM since April 2000, green vertical line = structural break of September 2010, right axis)

  2 Prediction of the skipjack price (in USD/t) As seen in Fig.2, if oil rates may represent reasonable predictors of current skipjack price at the beginning of the period, the gap between actual and simulated prices increases for some periods, and particularly after the break of September 2010. This would indicate that the long-run relation evidenced by the cointegration model does not hold tightly for every period. Presumably, a growing demand in the mid-2000s on the oil market resulting in a steady price increase before the crash of August 2008 combined with a stagnation of skipjack catches may have aected the long-run relationship between the two prices. In order to clarify this assumption, additional information needed to be included in the model, in particular to account for the supply of the tuna market. Thailandese imports of frozen skipjack were collected on a monthly basis since this country represents nearly half of worldwide imports reported by FAO and one fth of global catches of skipjack. The series was found I(0)

	lPskj t = 0.172 (0.692)	+ 0.877 (20.860)	lP skj * * * t-1 + 0.034 (1.620)	lP mdo t-1 + 0.045 (2.217)	lQskj * * t-1
				+0.036 (1.671)	× I(t > 129) * + u t	(5)
	T = 248 R2 = 0.93 F (1, 243) = 4.919 σ = 0.101

but more importantly, a Zivot-Andrews unit root test detected several breaks in the series.

Consequently a VAR model with one lag, according to the AIC, BIC and Hannan-Quinn criteria, was tested and gave the following results for the rst equation with lPskj as the dependent variable: * , * * , * * * , signicant at 1%,5%,10% levels, t-stat in brackets.

  As far as the cannery-grade tuna market is concerned, the global catches stagnated for several years between 2007 and 2012 around 2.5 million tonnes after a continuous increase over the past decades (the average annual growth rate of landings being +5% since 1950 according to the FAO FishstatJ data). During this 6-year period, the demand kept on increasing at the steady rate of +3 -4%, corresponding to the average growth rate of frozen skipjack imports since 1976, thus creating a shortage eect on the market and higher prices. The monthly growth rate of skipjack prices over the dataset sample (Jan. 2000-Sep.

2020) being less than 1% on average, it grew by nearly +4% between February 2007 and August 2008, when the nancial crisis stopped the upward trend. The twofold shock of stable catches and the economic downturn of the late 2000s has deeply aected the long-run equilibrium between oil and tuna prices. A structural change model

Table 1

 1 : FFA Disheries Development Division and https://www.customs.go.th/ Monthly prices are in USD per tonne and the monthly quantity Qskj is in tonnes

	Stat	Pmdo	: Main statistics Pskj Pyft	Qskj
	Min	154.3	419.7	691.0 15,164
	1st Qu.	357.1	899.9 1210.5 33,691
	Median	536.5 1263.0 1615.0 43,701
	Mean	552.8 1278.3 1604.5 43,839
	s.d.	252.4	463.7	464.8 13,895
	3rd Qu.	693.3 1590.4 1922.5 54,460
	Max	1256.0 2230.0 2607.0 90,435

Source

4 www.bunkerworld.com/prices/port/sg/sin/ 5 www.eia.gov. (lP mdo = 0.972 × lP nyhf o) 6 The ADF test values of the unit root test for lmdo were -2.08 and -1.82 with C and with C+T, resp. The ADF stat in rst dierence was -10.77 * * * and the KPSS test value was 5.178 * * * . The series is therefore I(1). For lpskj, the ADF values in levels were -2.65 * and -3.09, respectively, but the ADF-GLS (-0.478) and KPSS (2.71 * * * ) concluded that the series was also I(1) DS. 7 The dates were conrmed by a Bai-Perron test procedure under the BIC and RSS criteria [START_REF] Bai | Estimation of a change point in multiple regression models[END_REF], [START_REF] Bai | Computation and analysis of multiple structural change models[END_REF] 8 The cointegration equation had the following form: lP skj -1.2748×lP yf t * * * +2.2704 * * * .

Results of the Markov-Switching regression between oil and tuna prices 652


Marie-Charlotte Picard

Pascal Perrier

Yohan Payan

MODEL-BASED SIMULATIONS OF THE INSERTION OF TENSOR THREADS IN PATIENT-SPECIFIC FACE: A PROOF OF CONCEPT

Introduction

Facial paralysis is associated with the loss of motricity of facial muscles, inducing face sagging under the effect of gravity, with aesthetic and functional consequences. In order to compensate for the sagging, surgeons have proposed a clinical procedure consisting of inserting and anchoring biodegradable tensor threads under the skin of the face, in order to restore tension to the sagging areas. This study allowed the realization of a proof of concept of a software tool that uses simulations with a Finite Element (FE) biomechanical model of the face [START_REF] Nazari | Shaping by stiffening: a modeling study for lips[END_REF] in order for the surgeons to (1) predict the behavior of the face after addition of tensor threads and (2) visualize preoperatively in real-time the postoperative aesthetic appearance of the patient's face using reduced order models (ROM) [START_REF] Cueto | Real time simulation for computational surgery: a review[END_REF].

Materials and Methods

Patient-specific FE face models are generated by registrating a reference Face model using the Elastix library (fig. 1). The mesh is composed of four layers, which represent skin, dermis, hypodermis and muscles, modeled by hyperelastic materials. An FE replica of the thread is inserted in the third layer of the FE face model and contacts between thread (that includes a set of hollow cones) and facial tissue are modeled. Nodal forces are then applied at the tip of the thread to simulate its traction (fig. 1) and the lifting of facial tissue. A ROM is then built from a set of selected FE simulations of the impact of the applied force on the facial tissue shape, using the StaticRomBuilder software of Ansys®.

Results

A interactive software has been developed using the CamiTK library (camitk.imag.fr), in order for the clinician to (1) build the patientspecific biomechanical face model, (2) insert the tensor thread (position and rotation) in the model, (3) generate the corresponding ROM and (4) test and display in real-time the shape of the face resulting from tractions with the tensor threads (fig. 2).

Discussion and Conclusions

We have demonstrated the feasibility of a software that allows surgeons to evaluate for each patient the extent to which the position of the threads can compensate for facial lifting.

Figure 1 :

 1 Figure 1: Patient-specific mesh generation

Figure 2 :

 2 Figure 2: Simulated face appearance after tensile wire traction of two forces imposed by the user.


Nathanaël Connesson

Yohan Payan

Noémie Briot

Pierre-Alain Barraud

Nathanael Connesson
email: nathanael.connesson@univ-grenoble-alpes.fr

Noemie Briot

In vivo bi-layer material Young muduli identification under small deformation using only suction

Introduction

In vivo, patient specific and non-invasive mechanical characterisation of biological soft tissue is challenging, even under moderate quasi-static loading and small deformations. Among other technical solutions, suction-based devices enable the acquisition of experimental data under relatively well controlled boundary and loading situations. However, (i) the usual aspiration head design constraints drastically limit the number of used aspiration aperture diameter [1], (ii) the underlying tissues are often assumed to be homogeneous during inverse identification, and (iii) inverse identifications usually imply time-consuming postprocessing that hinders any clinical application. An original suction system and method is implemented as a step toward dealing with these limitations.

Materials and Methods

An original suction system is proposed based on volume measurements [2], which enable extreme customisation of the suction aperture shape and diameter. Cyclic partial vacuum (repeatability) was applied under small deformation using 9 suction cups of aperture diameters ranging from 4 to 30 mm both on silicone reference phantoms (with different upper layer thicknesses) and in vivo on the abdominal tissue of a healthy volunteer. Each cup extract tissue mechanical behaviour information integrated over about one diameter depth [3]. The tissue in-depth heterogeneity thus differently affects the pressure-tissue volume curves depending on the suction diameter. A cost function was built to minimize the squared distance between the 9 experimental pressure-tissue volume curves with their simulated counterparts assuming a bilayer structure (two Neo Hookean layers) defined by three main parameters: the upper and lower layer Young's Moduli and the upper layer thickness. A real time evaluation of the simulated pressure volume curves was implemented by interpolating a Finite Elements database so that these three parameters, including the upper layer thickness, minimizing the cost function were identified in less than one minute. The parameter identifiability was also evaluated. The silicone reference mechanical properties were characterized during classical tensile tests. The silicone upper layers thicknesses were measured by annexe destructive measurement. The reference skin thickness of abdomen was measured using Bmode ultrasound imaging (natural contrast between the epidermis and fat).

Results

On a bilayer controlled silicone phantoms with superficial upper layer thickness of 3 mm, Young's moduli identified by suction and uniaxial tension presented a relative difference lower than 10%. Preliminary tests on in vivo abdomen tissue provided the skin and underlying adipose tissue Young's Moduli at 54±1 kPa and 4.8±0.1 kPa respectively. The skin upper thickness was of 2.21±0.033 mm using Bmode ultrasound and 2.15±0.05 mm using only suction data.

Discussion and Conclusions

The whole process results on controlled silicone phantoms were considered fully satisfactory. The identified Young moduli of skin and fat are in good accordance with literature data.