Roman Bourgade
email: bourgade@irit.fr

Christine Rochange
email: rochange@irit.fr

Pascal Sainrat
email: sainrat@irit.fr

Predictable Two-Level Bus Arbitration for Heterogeneous Task Sets

Keywords: Real-time, multicore, bus arbitration, task mapping, task scheduling

In a multicore processor, arbitrating the shared resources so as to ensure predictable latencies for hard real-time tasks is challenging. In [1], we have introduced a two-level bus arbitration scheme that fits the needs of heterogeneous task sets, when some tasks have a higher demand to memory than others. In this paper, we show how this scheme can be used to optimise the overall utilisation of the cores while enforcing the schedulability of the whole task set. Our approach both configures the bus arbiter and maps the tasks onto the cores. Experimental results show that it reduces the global utilisation of the cores compared to the traditional round-robin scheme.

Introduction

Multicore processors (CMP or chip multiprocessors) are becoming essential in the design of constrained embedded systems due to their high performance and efficiency in terms of power consumption, thermal dissipation, cost. This efficiency is reached by sharing resources among the cores. For example, in a typical medium-scale multicore, the cores share a bus to the highest levels of the memory hierarchy.

Resource sharing engenders conflicts between cores trying to accessing the same resource simultaneously. A consequence is that the resource latency seen by each core is higher than it would have been in a single-core processor. In realtime systems, this can be acceptable if and only if a safe upper-bound of the latency is known: this bound is required to determine the worst-case execution times (WCETs) of critical tasks.

In this paper, we focus on shared buses. Several schemes have been studied in the past to perform time-predictable bus arbitration, i.e. arbitration that makes it possible to predict the worst-case bus latency seen by a core [START_REF] Paolieri | Hardware support for wcet analysis of hard real-time multicore systems[END_REF][3] [START_REF] Wandeler | Optimal tdma time slot and cycle length allocation for hard real-time systems[END_REF]. In a recent paper, we have introduced a two-level scheme that was specially designed to support heterogeneous task sets, in which tasks exhibit various levels of demands to the shared bus [START_REF] Bourgade | Predictable Bus Arbitration Schemes for Heterogeneous Time-Critical Workloads Running on Multicore Processors[END_REF]. With this scheme, the cores undergo different latencies, and the ones that see the shortest latencies should host the highest demanding tasks. In this paper, we propose an approach to exploit such a scheme, i.e. to select the best arbiter configuration and to map the tasks onto the cores, so that the overall core utilisation is minimised.

We report a reduction of the global utilisation of up to 29.1% compared to a solution with the traditional round-robin algorithm. In addition, we show that our two-level bus arbiter combined to our mapping approach may allow mapping a given task set on a smaller number of cores compared to round-robin.

The paper is organised as follows. Section 2 gives an overview of related work. Our bus arbiter is described in Section 3 and the mapping approach is introduced in Section 4. Section 5 reports experimental results. We conclude the paper in Section 6.

Related Work

A real-time aware bus arbiter allows computing the worst-case latency for a given core to be granted the bus. Several such schemes have been proposed in the last years. In [START_REF] Paolieri | Hardware support for wcet analysis of hard real-time multicore systems[END_REF], a round-robin algorithm is considered. Each core is granted the bus in turn, then the maximum delay it can undergo when requesting the bus is a linear function of the total number of cores. The worst-case latency is predictable and identical for all the cores. This approach fits homogeneous workloads. However, for heterogeneous task sets, it may be desirable to fasten the execution of high demanding tasks by granting them the bus more often than less demanding tasks. For parallel applications with inter-task dependencies, it may also be needed to accelerate the tasks on the critical path.

Time-Division Multiple Access (TDMA) policies allocate time slots for bus access to the cores. The bus schedule is determined off-line [3][4]. However, it may be hard to determine with enough accuracy whether an access to the bus falls within a slot allocated to the hosting core or not, at WCET analysis time. To predict latencies, the alignment of basic block time-stamps to the allocated bus slots may be analyzed [START_REF] Chattopadhyay | Modeling shared cache and bus in multi-cores for timing analysis[END_REF]. However, it makes the WCET analysis of one task dependent on the bus scheduling and thus on the co-running tasks. We instead aim at keeping the worst-case bus latencies for any task independent of the other tasks. This simplifies the analysis and favours timing composition.

Time-Predictable Bus Arbitration

A round-robin bus arbiter generates the same worst-case latency for each core in a shared-bus multicore: N × L, where N is the number of cores and L the latency of the longest bus transaction. This latency, computed by considering that each core is permanently requesting the bus, is generally overestimated but safe. This may be acceptable when all the tasks exhibit homogeneous bus demands. Otherwise, its impact might be negligible for low-demanding tasks but disastrous for high-demanding tasks. For this reason, we have introduced a new bus arbitration scheme that enforces different worst-case latencies for the cores: some cores see a low latency and should host the most-demanding tasks, while other cores undergo longer latencies and should run low-demanding tasks [START_REF] Bourgade | Predictable Bus Arbitration Schemes for Heterogeneous Time-Critical Workloads Running on Multicore Processors[END_REF].

Figure 1 gives an overview of our two-level arbiter. The cores are organised into groups, and the L1 arbiter grants permission to one group. Then the L2 arbiter selects one core in this group. The worst-case latency to be considered for the tasks running on a given core depends on: (a) the number of groups and the L1 arbitration policy; and (b) the number of cores in each group and the L2 arbitration policy.

Fig. 1. Two-level bus arbiter

For the sake of simplicity, we consider a round-robin algorithm in level L2. This means that the cores that belong to the same group see the same latency, which can be computed as: L c = n c × L g , where n c is the number of cores in the group and L g is the worst-case delay for the group to be selected by the L1 arbiter.

We consider two possible policies for the L1 arbiter: (a) the round-robin algorithm, and (b) an original scheme which we call Geometric Latencies. The resulting two-level schemes are denoted GRR and GGL, respectively.

For GRR, the worst-case bus latency for a group is given by L g = n g × L, where n g is the number of groups. As a result, the worst-case latency seen by one core is

L c = n c × n g × L.
The Geometric Latencies arbitration policy generates worst-case latencies that follow a geometric series: group G 0 sees a latency of 2 × L, group G 1 a latency of 4 × L, group G 2 a latency of 8 × L, etc. The two last groups have the same latency. In [START_REF] Bourgade | Predictable Bus Arbitration Schemes for Heterogeneous Time-Critical Workloads Running on Multicore Processors[END_REF], we provide a formal specification of the scheme that also describes its possible implementation in logic. The worst case latency of group G i (∀i < n g -1) is given by L gi = 2 i+1 × L, and L g (ng -1) = 2 ng-1 × L (see proof in [START_REF] Bourgade | Predictable bus arbitration schemes for heterogeneous time-critical workloads running on multicore processors[END_REF]).

With the GGL scheme, the latency to be considered for a task running on one core in group G i is then:

⎧ ⎨ ⎩ L c = n ci × 2 i+1 × L for 0 ≤ i < n g -1 L c = n ci × 2 ng-1 × L if i = n g -1 (1)
where n ci is the number of cores in group G i .

To summarise, the worst-case latency seen by one core depends on the number of cores in the same group in both schemes. In addition, it depends on the group's rank in GGL.

Configuring our two-level arbiter means mapping the cores to groups. The arbiter configuration impacts the bus latency seen by each core, and then the worst-case execution times of the tasks it runs. In next section, we introduce an algorithm to select an arbiter configuration together with a mapping of tasks to cores that both minimise the overall utilisation of cores while ensuring the schedulability of the whole task set.

Task Mapping Optimisation

The problem addressed in this section breaks down into: (a) determining the best configuration of our bus arbiter for a given task set; (b) finding out the best mapping of tasks to cores considering this configuration. Both should be solved simultaneously.

Algorithm 1. Computation of time/utilisation vectors

Preliminary Computations

The WCET of a task, and thus its core utilisation, depends on the bus latency seen by the core that hosts it, which in turn depends on the arbiter configuration. Algorithm 1 computes the WCET and utilisation of each task, considering each possible value of the bus latency (the possible values result from the various possible arbiter configurations). These results are later used to analyse the schedulability of the task set.

General Approach to Task Mapping

The problem of mapping tasks together with configuring the two-level arbiter exhibits several degrees of liberty: L1 arbitration policy (GRR or GGL), number of groups, number of cores, number of cores in each group, assignment of each task to a core. Only schedulable solutions should be retained.

Our approach is shown in Algorithm 2. To keep the problem resolution tractable, the problem is split into several sub-problems. Each sub-problem consists in finding out the best task mapping for a given arbiter configuration (line 5 ): our approach is explained in Section 4.3. If one solution is found, it is added to the set of possible solutions (line 7 ). The set of possible configurations is exhaustively scanned in the two outer loops (lines 2 and 4 ). As we will see, splitting the whole problem into sub-problems allows using Integer Linear Programming (ILP) techniques.

Task Mapping for a Given Arbiter Configuration

Overview. Algorithm 3 describes the process of searching the best task mapping for a given arbiter configuration. We consider the aggregated utilisation of the cores (i.e. the sum of the individual utilisations) as the primary criterion to estimate the quality of a particular mapping. A lower global utilisation leaves computing resources to run additional tasks. Now, to be acceptable, a task mapping must also be globally schedulable. In this paper, we consider a partitioned scheduling strategy. Then each subset of tasks assigned to one core must be shown schedulable on this core. In the following, we assume non-preemptive EDF scheduling and we use the related schedulability test [START_REF] Jeffay | On non-preemptive scheduling of periodic and sporadic tasks[END_REF].

In Algorithm 3, a loop (line 5 ) iterates until a schedulable solution has been found or no other task mapping exists. In each iteration, an integer linear program is used to find a task mapping (line 6 ). If a solution is found, it is tested for schedulability on each core (line 10 ). When a subset assigned to one core is found schedulable, it is locked to this core (line 11 ). Otherwise, it is appended to the black list and the task mapping is invalidated (lines 13-14 ). In the next iteration, the integer linear program is enriched with information about the locked and black-listed subsets to search for another task mapping. Locking task subsets is a way to accelerate the mapping process, as we will see in Section 5. Basic ILP Formulation of the Task Mapping Problem. The mapping of a task set onto cores for a given arbiter configuration γ is described by the following set:

Algorithm 3. Mapping of tasks for a given arbiter configuration (F indSolution(γ, T ))

1 foreach k ∈ [1..n] do 2 B k ← ∅; L k ← ∅; 3 end 4 mappable
{μ τ,k |τ ∈ T, 0 ≤ k < n} with: μ τ,k = 1 if task τ is mapped to core k 0 otherwise
Let λ k,γ be the bus latency for core k considering configuration γ. The ILP formulation is the following:

min : U = n k=0 U k /* objective: minimising the global utilisation */ ∀k|0 ≤ k < n, U k = τ ∈T μ τ,k .u λ k,γ τ
/* utilisation of one core is the sum of the utilisations of the tasks it runs */ ∀k|0 ≤ k < n, U k ≤ 1 /* utilisation of one core cannot exceed 1*/ ∀τ ∈ T,

n-1 k=0 μ τ,k = 1
/* a task cannot be mapped on several cores */ Additional Constraints for Locked Task Subsets and Black Lists. These constraints are used to accelerate the search for a schedulable task mapping. They avoid exploring new possible tasks subsets when one schedulable subset has been found for a given core. In addition, they avoid considering subsets that have already been shown unschedulable.

∀k|0 ≤ k < n, ∀τ ∈ L k , μ τ,k = 1 /* locked task τ is mapped onto core k */ ∀k|0 ≤ k < n, ∀τ / ∈ L k , μ τ,k = 0 /* locked task τ is not mapped onto core k */ ∀k|0 ≤ k < n, τ ∈B k μ τ,k < |B k | /*
tasks in the blacklist for core k cannot be mapped together on core k */ 5 Experimental Results

Methodology

In the following, we consider an 8-core architecture, with in-order 2-way superscalar cores supporting the PowerPC ISA. Each core has a 2-Kbyte 2-way associative level-1 instruction cache with 16-byte cache lines. We consider a perfect level-1 data cache1 . We consider a 32-bit bus, with a bus latency of 1 cycle. The memory latency is 5 cycles for the first word of a cache line and one additional cycle for each subsequent word.

Our task set includes 32 tasks, that is four instances of each of the tasks described in Table 1. They belong to the Mälardalen Benchmark Suite [START_REF] Gustafsson | The Mälardalen WCET benchmarks -past, present and future[END_REF] (nsischneu and statemate), the SPEC95 suite 2 (compress) and the MiBench suite [START_REF] Guthaus | Mibench: A free, commercially representative embedded benchmark suite[END_REF] (susan). These tasks have been selected because of their heterogeneous demands to the bus. Figure 2 show the variability of the WCET for each of these tasks as a function of the bus latency. The reference value is the WCET found considering the 8-core round-robin scheme (that gives a 73-cycle latency). The latency values are those observed in various configurations of our arbiter, as will be shown later.

WCET sensitivity (%)

Fig. 2. Sensitivity of the tasks WCETs to the bus latency

For each task, considered as a real-time task, a period must be specified. In this paper, we consider a uniform core utilisation among the tasks. The utilisation of a task is computed as the ratio of its (worst-case) execution time to its period. To choose its value, we have performed some experiments considering a round-robin bus arbiter. We have observed that our task set is schedulable if the utilisation of tasks is not higher than 0.21. Since the schemes we propose aim at performing better than the round-robin algorithm, we have decided to use this value for the rest of the experiments. Then, the period of each task (used to decide on the task set schedulability) is computed as the ratio of its WCET to 0.21.

The worst-case execution times are analysed using our OTAWA/oRange toolset [10][11]. It implements static analysis techniques to build a representation of the binary code of the application (a Control Flow Graph), to determine flow facts (e.g. loop bounds), to derive the worst-case execution costs of basic blocks, and to determine the global WCET with the IPET technique [START_REF] Li | Performance analysis of embedded software using implicit path enumeration[END_REF]. The algorithms presented in this paper are implemented in Perl and the integer linear programs are solved with the CPLEX tool3 .

Results

Quantitative results for eight cores are provided in Table 2. For each configuration, described by the number of cores in each group (limited to three groups), it gives:

the latency seen by any core in each group; -the minimum global utilisation and the number of iterations needed to find it (see Algorithm 3), for both schemes (GRR and GGL).

When several configurations enforce the same values for bus latencies, only one of them has been considered. Doubles do not appear in the table, or with their latencies italicised. Configurations for which no schedulable mapping could be found are marked n.s.

Reference Value. The first configuration (all the eight cores in group G 0 ) enforces the same latency for each core; it is equivalent to the traditional roundrobin scheme. The corresponding minimum utilisation (6.72) will then be considered as our reference value.

Performance of the GRR and GGL Schemes. Our two-level schemes both help in lowering the global utilisation of the cores compared to the round-robin algorithm: GRR can reduce it by 25.1% and GGL by 29.1%. GGL configurations that have a low number of cores in the highest priority group (G 0 ) perform better than GRR.

In addition, our schemes may be able to map and schedule the task set on a smaller number of cores. For example, the task set considered in these experiments cannot be scheduled on six or seven cores with the round-robin scheme. But we can find schedulable mappings considering both GRR and GGL. They even exhibit slightly lower utilisations: 5.01 and 4.70, respectively, for seven cores.

Finally, both GRR and GGL have solutions for this task set considering an utilisation of up to 0.27 for each task. The global utilisation then reaches 6.8 for eight cores. On the contrary, the task set cannot be mapped and scheduled with the round-robin scheme if the individual task utilisation exceeds 0.21. Impact of Locking Schedulable Task Subsets. In Algorithm3, we have introduced task subsets locking as a way of making the computation faster: as soon as the mapping algorithm finds a solution with some of the task subsets being schedulable on their assigned core, these task subsets are locked on their core. Subsequent iterations of the loop, that may be necessary if some subsets are still not schedulable, consider the locked task subsets as a starting point and focus on mapping the remaining tasks only. Our experiments have shown that this drastically limits the number of needed iterations: without this feature, as many as 7 290 iterations are needed for some configurations; the maximum number of iterations with subsets locking is lowered down to 111.

Conclusion

Time-predictable resource sharing is a key feature that will allow using multicore architectures for hard real-time systems. In this paper, we propose an approach to efficiently use a time-predictable bus arbiter which was introduced in a recent paper [START_REF] Bourgade | Predictable Bus Arbitration Schemes for Heterogeneous Time-Critical Workloads Running on Multicore Processors[END_REF]. This arbiter enforces different worst-case bus latencies for the different cores in order to meet the requirements of heterogeneous workloads. The approach presented here determines the best arbiter configuration and mapping of the tasks to the cores. Experimental results show a reduction of the multicore utilisation by more than 29% compared to a round-robin bus arbiter.

1 3 Λn ← ∅; 4 foreach γ ∈ Γn do 5 Λn 6 end 7 foreach

 34567 for n ← 1 to num cores do 2 Γn ← P ossibleConf igurations(n); ← Λn ∪ P ossibleLatencies(γ); task τ ∈ T do 8 foreach λ ∈ Λn do 9 t λ τ ← W CET (τ, λ);

Algorithm 2 . 4 foreach γ ∈ Γn do 5 ( 6 if (schedulable) then 7 M

 24567 General approach to task mapping 1 M ← ∅; 2 for n ← 1 to num cores do 3 Γn ← P ossibleConf igurations(n); schedulable, m) ← F indSolution(γ, T ); ← M ∪ {γ, m};

12 else 13 B

← true; schedulable ← false; 5 while mappable && !schedulable do 6 (mappable, m) ← Map(n, T, B, L); 7 if mappable then 8 schedulable ← true; 9 foreach k ∈ [1..n] do 10 if IsSchedulable(m k ) then 11 L k ← m k ; k ← B k ∪ m k ; 14 schedulable ← false;

15 end 16 end 17 end 18 end 19 return

(schedulable, m);

Table 1 .

 1 Benchmark tasks

	Task name	Function
	nsischneu	Simulation of an extended Petri net
	statemate	Automatically generated code (STARC tool)
	compress	Data compression
	susan corners quick
	susan edges small
	susan principle	Image processing (SUSAN)
	edge draw
	corner draw

Table 2 .

 2 Minimum utilisation obtained for all the possible configurations (8 cores)

This assumption is only due to the fact that our WCET analysis does not completely handle data caches. We also have performed experiments considering no data cache, which are not reported here for the sake of clarity, and we have found similar conclusions to the ones drawn with perfect caches.

2 www.spec.org

www.ibm.com/software/integration/optimization/cplex-optimizer/


Firas Damak
email: damak@irit.fr

Karen Pinel-Sauvagnat

Guillaume Cabanac
email: cabanac@irit.fr

Mohand Boughanem
email: boughanem@irit.fr

Effectiveness of State-of-the-art Features for Microblog Search

Keywords: H.3.3 [Information Search and Retrieval]: Information Search and Retrieval-Retrieval models Information retrieval, Microblog search, Feature evaluation

We investigate in this paper information retrieval in microblogs exploiting different state-of-the-art features. Microbloggers, besides posting microblogs, search for fresh and relevant information related to their interests, by submitting a query to a microblog search engine. The majority of approaches that collect information from microblogs exploit features such as the recency of the microblog, the authority of his/her author. . . to improve the quality of their results. In this paper, we evaluated some of the state-of-theart features to determine those that discriminate relevant from irrelevant microblogs given an information need. Then, we used the selected features to learn models to determine their effectiveness in a microblog search task. We conducted a series of experiments using the dataset and topics of the TREC Microblog 2011 and 2012 tracks. Results show that content, hypertextuality, and recency are the best predictors of relevance. We also found that Naive Bayes was the most effective learning approach for this type of classification.

INTRODUCTION

Searching for real time information published in microblogging platforms has become a challenge for Information Retrieval (IR) systems. Since a huge number of microblogs are published and many queries are issued each day (200 mil-SAC'13 March 18-22, 2013, Coimbra, Portugal. lion tweets1 and over 1.6 million search queries2 in Twitter), this new type of media has become of high interest for information retrieval research. IR systems should be adapted to the specificities of microblogs and be effective to handle the relative exponential growth of information requests.

Microblogs have many specificities. On the one hand, people's motivations for microblog search are diverse [START_REF] Teevan | #twittersearch: a comparison of microblog search and web search[END_REF]: some are similar to those of web search (e.g., astronomy or science stuff), while others, regarding a need for timely (e.g., traffic jam, down services) or social information (e.g., people with similar interests), are relatively specific to microblog search. On the other hand, microblogs are different from ordinary web pages. Tweets (i.e., microblogs in Twitter), for example, cannot exceed 140 characters. They are usually composed of a single sentence. Users publish microblogs on a wide variety of topics in real time. Thus, the messages contain mistakes and some are written in netspeak. Besides, some microblogging platforms like Twitter use specific syntax (e.g., re-tweets, hashtags, mentions), that is likely to challenge conventional natural language processing techniques. Finally microblogs often point to external sources by including hyperlinks to documents or other contents on the web.

Having in mind all the aforementioned specificities, the literature mentions tailored IR approaches [START_REF] Ounis | Overview of the TREC-2011 Microblog Track[END_REF]. In addition to message content, relevance is evaluated by combining other factors to process these specificities. It may depend on the novelty of the information, the quality of the message, the author's authority, and the freshness of the message. These factors are taken into account by combining specific features into the relevance function used. For example, if we consider the author's authority factor in Twitter, the associated features could be the number of the tweets of the author and the number of his followers [START_REF] Nagmoti | Ranking approaches for microblog search[END_REF]. One may also consider the number of times a user has been referred to or the rank of the author according to a PageRank-like algorithm based on retweet relations [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF].

While the effectiveness of each system can be assessed as a whole, we failed to find any work probing the effectiveness of each underlying feature in the literature. In this paper, we aim at evaluating the features commonly exploited in microblog search approaches. More specifically, we attempt to select those most effective for microblogs search.

The paper is organized as follows. In Section 2 we discuss related works for microblog search using features. Our evaluation method is then presented in Section 3. Section 4 presents our results on two TREC test sets that are then discussed in Section 5.

RELATED WORK

Many approaches using features to extract information from microblogs have recently been introduced in the literature. Many of them have been evaluated using the TREC Microblog track. 3 The Microblog track, started in 2011, promotes search tasks and evaluation methodologies for information seeking behaviors in microblogging environments.

Among these approaches Duan et al. [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF] used features to search and to rank microblogs given a query. These authors relied on the Okapi BM25 model as a content relevance feature. Some features specific to Twitter (i.e., popularity of the tweet, retweet frequency, hashtags frequency, length of the tweet, URL presence, is-reply) and others were used to measure the importance of the authors (i.e., number of followers, number of mentions). A machine learning approach was then used to build the search model. Similarly, the approach described in [START_REF] Metzler | USC/ISI at TREC 2011: Microblog Track[END_REF], 1st ranked in TREC 2011 Microblog track, used a learning approach to rank tweets based on a set of features (i.e., text score, time difference score, hashtag presence, URL presence, length, is-reply and the percentage of terms in a tweet that are out of the English vocabulary).

Features have also been used as quality indicators of microblogs. To select the best message from a set of retweets, Massoudi et al. [START_REF] Massoudi | Incorporating query expansion and quality indicators in searching microblog posts[END_REF] defined various quality indicators, such as the presence of a URL, the number of followers of the user who rebroadcast the microblog, and the time elapsed before its republication. With the same purpose, authors in [START_REF] Vosecky | Searching for quality microblog posts: Filtering and ranking based on content analysis and implicit links[END_REF] used a machine learning model based on contentbased features (i.e., punctuation and spelling features, syntactic and semantic complexity and grammaticality), linkbased features (i.e., URL presence, is-retweet, number of mentions, hashtag presence, number of times a tweet has been retweeted, URL reputation, hashtag reputation) and temporal features (i.e., the recency of the tweet).

According to [START_REF] Ounis | Overview of the TREC-2011 Microblog Track[END_REF], apart from content, features may be classified (Table 1) according to two characteristics: External features use information outside the microblog dataset (e.g., Wikipedia or the Web). Future features use information that would not have been available to the system when the query was issued.

In this paper, we are only interested in realistic settings: we do not want to use any information that has been published after the timestamp of the queries. The features under study were scored using only the available information in the corpus used for this study (e.g., number of tweets for a user will not concern the number of his/her tweets in all Twitter, but only in the corpus used and before the timestamp of the query; or, the number of followers was not considered since we did not have required information in the corpus). Approaches using features marked as future in Table 1 are not necessary unrealistic: some approaches do not take into account the timestamps of queries. They thus relied on the 3 http://sites.google.com/site/trecmicroblogtrack/ +online version of Twitter. However, in our case, the same features are considered as unrealistic since we consider the query timestamps. The complete list of selected features we study in this paper are presented in the next section. We evaluated then the selected features to determine those that best reflect relevance. Finally, we used the relevant features to learn models to determine their effectiveness in a microblog search task.

METHOD

The corpus we used for our study was provided by the TREC evaluation campaign (TREC Microblog Track) and is based on Twitter. We describe it in section 3.2. Section 3.1 describes the features selected for analysis.

Selected Features

Most of the evaluated features are derived from state of the art. We evaluate these features in a context of information retrieval, i.e., the evaluation of the relevance of a tweet given a query. We use the following notations in the sequel: t is a tweet posted a timestamp tmp(t), q is the query, also known as a topic, which has a timestamp tmp(q), Cq is the corpus of tweets posted before the timestamp of the topic q. Tq is the set of tweets returned by a given search engine based only on the content of tweets. Tq ⊆ Cq.

The features are normalized to lie between 0 and 1.

Tweet popularity [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF]: estimates the popularity of tweet t in Tq. The similarity between a pair of tweets is calculated using the Lucene similarity function4 sim( t, t ). We denote the current tweet modelled as a vector t:

F1( t, q) = t = t sim( t, t ) |Tq| -1 (1)
Tweet length [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF]: instinctively, the longer a sentence is, the more information it is able to contain. We calculate this feature by counting the number of words in the tweet. We denote l(t) the number of words in tweet t. This feature is defined as:

F2(t, q) = l(t) max t ∈Tq l(t ) (2)
Exact term matching: promotes tweets that contain terms of the topic q. nb(t, q) denotes the number of common terms between t and q: F3(t, q) = nb(t, q) max t ∈Tq nb(t , q)

(3)

URL presence [START_REF] Nagmoti | Ranking approaches for microblog search[END_REF]. By sharing an URL, an author would confirm the information published in his tweet:

F4(t) = 1 if t contains at least one URL 0 otherwise (4)
URL frequency [START_REF] Zhao | A weighted multi-factor algorithm for microblog search[END_REF]: counts how many URLs are published in tweet t:

F5(t, q) = |{w ∈ t/isU RL(w)}| max t ∈Tq |{w ∈ t /isU RL(w)}| (5)
URL popularity: aims at calculating how important the URLs published in tweet t are in Cq. f req(url) denotes the number of time the URL appears in Cq:

F6(t, q) = url∈t f req(url) max t ∈Tq url∈t f req(url) (6)
Notice that different URLs may lead to the same document. Such URLs are not uniformed in this work. they are considered as different ones.

Hashtag presence [START_REF] Metzler | USC/ISI at TREC 2011: Microblog Track[END_REF]. The # symbol, called a hashtag, is used to mark a keyword or a topic in a tweet. Any user can categorize or follow topics with hashtags.

F7(t) = 1 if t contains a hashtag 0 otherwise (7)
Hashtag popularity [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF]: f req(h) denotes the frequency of a hashtag h in the corpus Cq:

F8(t, q) = h∈t∧isHashtag(h) f req(h) max t ∈Tq h∈t f req(h) (8)
Topic as hashtags: calculates the number of terms of topic q that are present as hashtag in tweet t:

F9(t, q) = |{w ∈ q/#w ∈ t}| max t ∈Tq |{w ∈ q/#w ∈ t }| (9)
Number of tweets [START_REF] Nagmoti | Ranking approaches for microblog search[END_REF]. N (a(t)) is the number of tweets published by the author of the tweet t in Cq:

F10(t, q) = N (a(t)) max t ∈Tq N (a(t )) (10)
Mention [START_REF] Zhao | A weighted multi-factor algorithm for microblog search[END_REF]. M (a(t)) denotes how many times the author of the tweet t has been mentioned in Cq:

F11(t, q) = M (a(t)) max t ∈Tq M (a(t )) (11)
Is-reply [START_REF] Metzler | USC/ISI at TREC 2011: Microblog Track[END_REF]. If a user likes a tweet published by another user, he/she may comment and publish it again. In this case, the new message will be marked with RT (retweet).

F12(t) = 1 if t contains RT 0 otherwise (12)
Recency [START_REF] Magnani | Conversation retrieval for microblogging sites[END_REF]. The difference in time, measured in seconds, between the query q and the tweet t. tmp(t) is the timestamp in seconds of the tweet t.

F13(t, q) = tmp(q) -tmp(t) max t ∈Tq tmp(q) -tmp(t ) ( 13
)
Language quality [START_REF] Duan | An empirical study on learning to rank of tweets[END_REF]: is used to approximate the language quality of tweets. It calculates the proportion of existing words in a dictionary5 with respect to all the terms of the tweet t. dic(term) return a binary value: 1 if the term exists in the dictionary, 0 if not:

F14(t) = term∈t dic(term) l(t) (14)

Corpus

We used for our study the corpus of tweets provided to the 2011 and 2012 TREC Microblog Track participants. The collection is composed of 16 million tweets expressed in various languages and posted on Twitter between January 23, 2011 and February 8, 2011. Each tweet is characterized by its identifier (ID), author, and date of publication. Topics are composed of multiple tags. The title tag describes the user's information need expressed at a given time querytime: 49 topics of the 2011 track and 60 topics of the 2012 track. Relevance judgements were obtained from qrels of Microblog Track 2011 and 2012. The relevance of each tweet is ternary: irrelevant, relevant, and highly relevant. However, we did not differentiate between relevant and highly relevant in our evaluation.

Our study was conducted in two phases: we first evaluated the features using score distribution and some attribute selection approaches. We used in this case topics of TREC 2011. Different sets of features are obtained from this studies. Then, we evaluated the effectiveness of these features by applying the different outcome sets on learning techniques. We used for this second case the topics of TREC 2011 for learning and topics of TREC 2012 for the evaluation.

Preliminary Studies

We describe in this section the methodologies used to evaluate the effectiveness of the selected features. We conducted two different studies: one based on feature score distribution, and another using some attribute selection approaches.

Score Distribution Study

The assumption behind this study is that an effective feature discriminates the relevant tweets from irrelevant ones (i.e., effective features will not have the same distribution in relevant tweets compared to irrelevant tweets). To assess a feature, we looked at its score distribution within microblogs. We compared its scores between relevant and irrelevant microblogs. The set of tweets to analyse was formed as follows: for each topic having more than 100 relevant tweets 6 , we kept all the relevant tweets according to the qrels, and we added the same number of irrelevant tweets. Irrelevant tweets were selected according to their content score, i.e., we only kept the most relevant according to a search engine. We used Lucene7 as a search engine for this purpose. Resuls of all topics were merged together to plot scores for the overall distribution.

Attribute Selection Approaches Study

In a second study, we relied on some selection attribute algorithms to determine the best features to use in a microblog search information task. Attribute selection algorithms [START_REF] Hall | Benchmarking attribute selection techniques for discrete class data mining[END_REF] aim at identifying and removing as much of the irrelevant and redundant information as possible. We used Weka 8 for this experiment. It is a powerful open-source Java-based machine learning workbench that brings together many machine learning and selection attributes algorithm.

We proceeded thereby: the top 1,500 tweets for each topic were retrieved from Lucene. Then, all feature scores were calculated for each tweet. We identified the relevant and irrelevant tweets according to the qrels of the topics. The obtained tweet set contains 72,614 instances composed of 2,129 relevant tweets and 70,485 irrelevant tweets. One could observe that this collection has unbalanced relevance class distribution. This occurs when there are much more items in one class than in the other class of a training dataset. In this case, a classifier usually tends to predict samples from the majority class and completely ignore the minority class [START_REF] Yen | Under-sampling approaches for improving prediction of the minority class in an imbalanced dataset[END_REF]. For this reason we applied an under-sampling approach (reduce the number of samples which have the majority class) to generate an unbalanced collection composed of 2,129 relevant and 2,129 irrelevant tweets that were randomly selected. Finally, we applied the attribute selection algorithm on the whole set.

RESULTS OF ATTRIBUTE SELECTION

In this section, we present results of preliminary studies. Then, we compare and discuss our findings.

Score Distribution Study

Figure 1 shows the distribution of the scores of relevant tweets (Relevant) and irrelevant tweets (Not relevant) for our first study. The intervals were calculated with the Sturge's rule [START_REF] Sturges | The Choice of a Class Interval[END_REF]. One can observe that Tweet popularity (F1), Length (F2), Exact term matching (F3), URL presence (F4), URL frequency (F5), URL popularity (F6) and Recency (F13) are not distributed the same way compared to irrelevant tweets. These features have their best scores in relevant tweets and characterize more relevance. The difference of the two populations (relevant and irrelevant) is statistically significant according to Student's t test, bilateral and paired with p < 0.05.

Attribute Selection Approaches Study

Table 2 shows the features selected through selection attribute algorithms. Practically, features obtained from the score distribution study and most of the selection attribute approaches are the same (F1, F2, F3, F4, F5, F6, F13), which confirms the effectiveness of this set compared with the rest of features. We also conducted this analysis without sampling the dataset. We found that there is no effect of sampling on the outcome of attribute selection approaches.

Discussion

We found that the same features that emerge from the first study were selected by selection attribute approaches: content features (Tweet popularity, Length, Exact term matching), Hypertextuality features (URL presence, URL popularity, URL frequency) and time feature (Recency).

8 http://www.cs.waikato.ac.nz/ml Other features were selected by selection attribute algorithms, but less frequently: author authority features (Number of tweets, Mention, Topic as hashtags) and Language quality feature. Finally, the hashtag features (Hashtag popularity, Hashtag presence) were seldom selected and seem not to be effective for assessing relevance.

EFFECTIVENESS OF THE SELECTED FEATURES

In this section, we evaluate machine learning techniques with the set of effective features identified in the previous section. The aim is twofold: on the one hand we wondered whether the attribute selection really improves the results of a microblog search task. On the other hand, we intended to measure the performance of some learning algorithms in this type of classification.

Results

To evaluate the learned models, we used Lucene results of the 2011 TREC Microblog topics results as a learning set and the 2012 TREC Microblog topics results as a test set. Learned model predicts the relevance class (relevant or not relevant) for resulting tweets and give effectiveness classification scores. The non-relevant predicted tweets are then deleted and tweets predicted as relevant are ranked given the effectiveness classification scores. To evaluate our runs, we used the P@30 measure, since it was the official measure for the 2011 Microblog track of TREC.

We chose to experiment with three learning algorithms. This choice is explained by the fact that they are the most used in the short texts classification tasks and they have been shown to be effective for microblogs search in the past: SVM [START_REF] Vosecky | Searching for quality microblog posts: Filtering and ranking based on content analysis and implicit links[END_REF][START_REF] Duan | An empirical study on learning to rank of tweets[END_REF], J48 [START_REF] Yuan | Enhancing naive bayes with various smoothing methods for short text classification[END_REF] and Naive Bayes [START_REF] Yuan | Enhancing naive bayes with various smoothing methods for short text classification[END_REF].

Authors in [START_REF] Hall | Benchmarking attribute selection techniques for discrete class data mining[END_REF] studied the effectiveness of some selection attribute approaches with learning algorithms. Based on their study, we used the same combination of learning and attribute selection approaches applied on our own features:

• Naive Bayes and Wrapper Subset Evaluation (WRP) which uses a target learning algorithm to estimate the worth of attribute subsets. Thus, the features selected in this case were Lucene score, F3, F4, F5, F6.

• Naive Bayes and Correlation-based feature Selection (CFS) (Lucene, F1, F2, F3, F4, F5, F6, F12, F13).

• J48 and ReliefFAttribute Eval (RLF) (Lucene, F1, F2, F3, F5, F6, F9, F10, F11, F12, F13, F14).

• SVM and SVM Attribute Eval that assess attributes using the SVM classifier (Lucene, F1, F2, F3, F4, F5, F6, F9, F11, F12, F13, F14).

Table 3 shows results of the 3 learning approaches learned with score distribution outcome features, attribute selection approaches features, and with all features. Results were compared with the run called Lucene (baseline: only Lucene scores were used to rank tweets).

Discussion and limitations

Our fist aim for this study is to check if attribute selection improves effectiveness of learned models. SVM attribute Eval, WRP, CFS, and score distribution outcome features confirm the hypothesis. Apart from J48 learned with RLF selected feature, all results were improved compared to runs for which all features are used. One could also see also that apart from J48, machine learning approaches have better effectiveness with attribute selection approaches than when they are learned with our score distribution study features.

Our second aim was to find which machine learning approach is the more suitable for a microblog search task. We notice that only Naive Bayes model outperforms Lucene (+18% with CFS selected features and +16% with score distribution selected feature). The other learning approaches failed to improve effectiveness, leading us to conclude on the interest of Naive Bayes.

We compared the run obtained using Naive Bayes learned with CFS features with TREC 2011 Microblog participants. We learned and cross-validated Naive Bayes with CFS selected feature on TREC 2011 topics. We obtain an averaged P@30 of 0.3707. This result would have been ranked 5th among participants who did not use future evidences and submitted automatic runs. This precision is reduced by 9.4% when using the same model on TREC 2012 topics. In addition, machine learning approaches such as J48 and SVM have a gain of 80% of effectiveness when tested and cross-validated on TREC 2011 topics. However, they did not perform as intended on 2012 topics. All these observations raise the question whether the two track topics and qrels have been created in the same way.

In order to control this potential collection bias, we also merged 2011 and 2012 tracks topics and repeated the same steps. We obtained an averaged P@30 of 0.3435. This good result confirms that Naive Bayes learned with CFS selected features is the most suitable for this task.

Nonetheless, our work presents some limitations. First, machine learning certainly improves effectiveness of classifi- cation. However, the weight of features is not always accessible, neither how features were combined. Secondly, some features which are used in some approaches of microblog search (e.g., retweet frequency, number of followers of an author) could not be evaluated since the required data do not appear in the corpus we used for experimenting. An open access to Twitter would be necessary to evaluate them, which is not possible. Finally, concerning the TREC Microblog track, participating teams promoted microblogs published by popular, well-retweeted, with lots of mentions authors. However, it seems in reality that these features do not reflect relevance for our search task. Indeed, there are cases when people search for microblogs and find very relevant information from people who are not popular. Those people just happen to be in the right place and time to post the relevant and fresh information. One flaw of the track is that the tasks consist only in finding relevant microblogs given an information need. However, a microblogger could be interested in other entities like conversations, persons, trending topics . . . . The 2011 and 2012 tasks do not deal with such a broad range of search types.

CONCLUSION

In this paper, we analysed the effectiveness of a set of features commonly used in microblog search. We compared the distribution of scores between relevant and irrelevant microblogs for selected topics. We also used selection attribute approaches for the same purpose. We found almost the same results: tweet popularity, length, exact term matching, URL presence, URL popularity in the corpus, URL frequency in the microblog and the recency of the microblog are the features that best reflect relevance. We then tried to compare often-used learning approaches for microblog task and we found that only Naive bayes yields improvement in terms of effectiveness compared to our baseline. Regarding future work, we will try to improve recall by using query expansion and harnessing the content of URLs published in microblogs.

Figure 1 :

 1 Figure 1: Distribution of the scores of relevant versus irrelevant tweets

Table 1 :

 1

	External (E) and future (F) features
	Feature		E F
	Popularity of the tweet	[2]	-	-
	Topic tweet term matching	[1]	-	-
	Retweet frequency	[14, 4, 11, 2] -+
	Hashtags frequency	[2]	-	-
	Hashtags presence	[11, 6]	-	-
	Hashtag reputation	[11]	-+
	Length of the tweet	[14, 4, 6, 2]	-	-
	Url presence	[11, 5, 6, 2]	-	-
	Number of urls in the tweet [14]	-	-
	Url reputation	[11]	-+
	Is-reply	[11, 6, 2]	-	-
	Number of tweets of a user	[14]	-+
	Number of followers	[4, 5, 2, 14]	-+
	Number of mention	[11, 2]	-+
	Tweet time difference	[4, 11, 6]	-	-
	Language quality	[6]

Table 2 :

 2 Selected features with attribute selection approaches

	Algorithm	Lucene F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14
	Cfssubseteval	+	+	+	+	+	+	+						+	+
	ChisquaredAtt.Eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	FilteredAtt.Eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	FilteredSubsetEval	+	+	+	+	+	+	+							+
	Gain ration att eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	Info gain att eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	One att eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	ReliefFAttribute Eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	SVM Attribute Eval	+	+	+	+	+	+	+			+		+	+	+	+
	SymetricalUncertEval	+	+	+	+	+	+	+			+	+	+	+	+	+
	Consistency subset Eval	+	+	+	+	+	+	+			+	+	+	+	+	+
	Wrapper subset Eval	+			+	+	+	+
	LatentSymanticAnalysis	+	+	+	+
	Count	13	12 12 13 12 12 12	0	0	9	8	9	10	11	9

Table 3 :

 3 Results (P@30), results in bold indicate significant improvement over the baseline

	Lucene (Baseline)		0.2842
		Score distribution features Attribute selection features All features
	J48	0.1627	0.0983 (RLF)	0.1000
	Naive Bayes	0.3305	0.3311 (WRP) 0.3356 (CFS)	0.2372
	SVM	0.1689	0.1746 (SVM)	0.1729

http://blog.twitter.com/2011/06/200-million-tweets-perday.html

2 http://engineering.twitter.com/2011/05/engineeringbehind-twitters-new-search.html

http://lucene.apache.org/core/3 6 1/scoring.html

http://code.google.com/p/language-detection/

We only kept these topics to have a sufficient number of tweets to study. This corresponds to 9 topics (to be compared with the initial number of 49)

[START_REF] Nagmoti | Ranking approaches for microblog search[END_REF] http://lucene.apache.org/


Maximilien Bowen
email: maximilien.bowen@univ-smb.fr

Pierre Samozino

Mylène Vonderscher

Denys Dutykh

Baptiste Morel

Development of a force-endurance model able to describe the muscle fatigability in the severe domain and validation of the RACLET test

Keywords: muscle, fatigability, critical power

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Development of a force-endurance model able to describe the muscle fatigability

in the severe domain and validation of the RACLET test. ⋆

Introduction. Muscle fatigability corresponds to the decrease in the ability of muscles to generate force. The Critical Power (P c ) concept [START_REF] Monod | The work capacity of a synergic muscular group[END_REF] predicts the point at which fatigue develops, in such a way that the required constant intensity will no longer be sustainable (W ′ reserve is emptied). During all-out tests the power plateau reached at the end of the test and the work done above this value have been numerically and conceptually related to P c and W ′ , respectively. These two mathematical models, characterizing similar phenomena but based on very different exercises (steady state versus all-out) have not been directly linked. Thus, the aims of this study were to i) develop an integrative model of exercise fatigability and ii) propose a submaximal test based on this model to determine critical intensity.

Methods. From Mortons 3-parameters model [START_REF] Hugh | A 3-parameter critical power model[END_REF] one can make the assumption that fatigability is proportional to the impulse accumulation above the critical force (F c ) so:

F max (t) = - 1 τ t 0 (F (T ) -F c ) dT + F i (1)
Since the model can be applied to any exercise, a specific Ramp Above CriticaL Exhaustion Test (RACLET) was proposed. The test was designed so that the target intensity starts above the critical intensity and decreases below it, before exhaustion of W ′ , so before the exhaustion of the participant. It was tested for a cycling task with a 300s ramp test decreasing from 40% to 5% of initial force (F i ), where maximal capacities (F max ) were assessed every 30s from 6-pedal-strokes sprints. Twenty participants realized 5 experimental sessions: 2 RACLET and 3 time to exhaustion (TTE). A custom friction regulated instrumented cyclo-ergometer was developed to measure crank torque and velocity. Each F max was used to adjust the model's parameters. The model's reliability and validity were tested by determination of individual parameters F c and τ by adjusting the model to F max and time data from RACLET and TTE tests.

Results. The model's goodness of the fit on RACLET test experimental data was excellent (median adjusted R2 =0.95; RMSE=3.4%F i ). Mean±SD F c and τ were 29.6±7.2%F i and 22.7±13.9s, respectively. F c parameter in RACLET demonstrated good relative (ICC=0.9) and absolute reliability (SEM=4.5%). The comparison of F c between RACLET and reference TTE method was acceptable (R 2 =0.8, SEM=5.8%).

Discussion. The proposed model fits very well with the experimental data obtained during the RACLET. The latter showed very good test-retest reliability. Moreover, the fitted parameters were very similar to those obtained with the gold standard method TTE. The present results show that it is possible to determine individual model parameters (F i , F c , and τ ) from experimental data obtained from the proposed RACLET. As this test does not lead to the participants' exhaustion, it could be interesting for athletes monitoring training, or patients with pathologies that make it difficult to use traditional methods (TTE and all-out tests).

Interuniversity laboratory in Biology of Movement, Savoie-Mont Banc University

LAboratoire de MAthématiques, Savoie-Mont Banc University

⋆ This work was supported by French National Research Agency [ANR-22-CE14-0073]


E M Neeman
email: elias.neeman@univ-lille.fr

N Osseiran

T R Huet

The gas-phase structure determination of α-pinene oxide: an endocyclic epoxide of atmospheric interest

Gas-phase rotational spectra of α-pinene oxide have been recorded using a chirped-pulse Fourier transform microwave spectrometers in the 6-18 GHz frequency range. Parent species and all heavy atom isotopologues 13 C and 18 O have been observed in their natural abundance. The experimental rotational constants of all isotopic species observed have been determined and used to obtain the substitution (𝑟 𝑠 ) and the effective (𝑟 0 ) structures of the most stable conformer of α-pinene oxide. Calculations using the density functional theory B3LYP, M06-2X and MN15-L as well as the ab initio method MP2 level of theory were carried out to check their performance against experimental results. The structure of the heavy atom's skeleton of α-pinene oxide has been compared to α-pinene and has shown that epoxidation does not affect overmuch the structure of the bicycle, validating its robustness. Furthermore, structural features have been compared to other bicyclic molecules nopinone and β-pinene.

Introduction

Monoterpenes (C 10 H 16 ) are biogenic organic volatile compounds (BVOC) emitted in the atmosphere from vegetation and represent a major source of reactive biogenic species. On a global scale, plants emit the equivalent to 10 14 g.yr -1 of monoterpenes which represent 11% of the total BVOCs emission. 1,2 Those can react rapidly with other atmospheric oxidants such as O 3 , OH and NO x radicals to form low volatile compounds making them among the most important class of secondary organic aerosols (SOA) precursors. SOA represent a source of uncertainty for climate simulations since their formation and evolution mechanisms remain poorly understood and deserve more attention. 3 They play an important role in the global climate [START_REF] Kanakidou | Organic Aerosol and Global Climate Modelling: A Review[END_REF] and regional air quality since they degrade visibility by absorbing and reflecting solar radiation, or by modifying cloud formation. [START_REF] Zhang | [END_REF] They affect human health. 6,7 α-pinene is the most abundant monoterpene in the atmosphere and its oxidation leads to the formation of different class 8 of oxygenated monoterpenoids that are involved in the formation of atmospheric SOA. Among the formed species is α-pinene oxide, 9 which is formed in high yield from the direct reaction of ozone with α-pinene. 10,11 Recently, studies have shown that the reaction of epoxides with sulfuric acid is kinetically preferred over the reaction of alcohols with sulfuric acid for the formation of organosulfates. 12 α-pinene oxide (APO), C 10 H 16 O, 2,7,7-Trimethyl-3-oxatricyclo[4. 1.1.02,4]octane is an endo-cyclic epoxide which has been observed to participate in the formation of organosulfates under atmospheric conditions. 12 Apart their role in atmospheric chemistry, terpenes and their oxidation products are also the essential building blocks in the food flavour, pharmaceutical and fragrance industries. 13 For that reason α-pinene This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909 oxide is used to produce several compound highly valuable fragrance and/or pharmaceutical ingredients via an acid-catalysed mechanism. 14 Recent microwave studies supported by quantum chemical calculations on bicyclic monoterpenes [15][16][17][18][19] have shown the structural characteristics between similar bicyclic molecules with different functional group. For example, the structure of β-pinene is quasi-unchanged upon oxidation to nopinone (Figure 1). 16 The introduction of high-resolution broadband microwave spectroscopy 20,21 (CP-FTMW) permitted an efficient search for different species present in the supersonic jet. This technique allows the collection at once of a large portion of the rotational spectrum of a molecule. In other words, every frequency element of the whole acquired spectrum is collected in every shot of the spectrometer. Consequently, it facilitates the identification of spectral patterns and reduces acquisition time.

In this study, we used a new CP-FTMW spectrometer recently constructed at Lille. The recorded spectra, of parent and isotopologue species of APO, have been analyzed and the rotational molecular parameters have been obtained. Their values have been used to determine the structure of the heavy atom skeleton using substitution (𝑟 𝑠 ) and ground state (𝑟 0 ) methods. A

Methods

Quantum chemical calculations

Quantum chemical calculations were performed using the Gaussian 16 software package. 22 The structures of APO have been optimised using Møller-Plesset second order perturbation theory (MP2) 23 and the DFT method B3LYP, 24,25 M06-2X, 26 and MN0-L15. 27 Pople split-valence triplezeta basis set augmented with diffuse and polarization functions on all atoms basis set (6-311++G(d,p)) were used. 28 The set of equilibrium molecular parameters has been obtained from the structure, such as rotational constants (A, B, C), quartic centrifugal distortion parameters (D J , D JK , D K , d 1 , d 2 ) and permanent electric dipole moment components ( a ,  b ,  c ).

Experimental

The jet-cooled pure rotational spectra (6-18 GHz) of APO were recorded on the recently developed CP-FTMW spectrometer, in Lille. [START_REF] Osseiran | 26th Int. Conf. High Resolut. Mol. Spectrosc[END_REF] A 65 GSa/s arbitrary waveform generator (AWG, Keysight M8195A) generates a fast chirp microwave pulse spanning 1-5 μs and varying linearly in frequency sweep. A 300 W traveling wave tube amplifier (Instruments for Industry, GT186-300) amplifies the microwave pulse in the 6-18 GHz region. It is coupled into a vacuum chamber via a standard horn antenna (ATM 650-442-C3), where it polarizes all transitions in the molecular sample produced with up to three pulsed valves (Parker IOTA ONE). A second horn antenna is used to detect the free induction decay signals (FIDs) emitted by the molecular ensemble as This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. APO (98%) was purchased as liquid sample from Merck and was used without any further purification. The sample was placed inside the reservoir of a pulsed nozzle and heated to about 363 K and mixed with a carrier gas (Ne or Ar) at stagnation pressure of 2 bar. The sample was then injected inside the vacuum chamber at a repetition rate of 2 Hz. A molecular pulse of about 900 µs is used to create the supersonic jet expansion. Chirp microwave pulses of 4 µs were applied with a delay of about 400-500 µs with respect to the start of the molecular pulse. Up to 8 FIDs per gas pulse were collected for 20 µs using the digital oscilloscope and then Fouriertransformed in the Kaiser-Bessel windows function. As microwave radiation is perpendicular to the supersonic jet in our setup, the FWHM of the observed lines is estimated to be ∼100 kHz in the present spectra. In addition to the CP-FTMW spectra, we performed a few measurements for This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909 6 the APO 18 O isotopologue to record more lines by using the Lille Fabry-Pérot (FP) cavity. This experimental set-up has been described in details elsewhere. 15,[START_REF] Tudorie | [END_REF]

Results

Calculated structures

The only degree of freedom in APO is the position of the epoxide in the molecule. It leads to two possible configurations, presented in Figure 2. The calculated rotational parameters of the lowest energy structure are reported in Table I. The second conformer is very high in energy (≈18 kJ/mol, ≈ 15 kJ/mol, 20 kJ/mol at the MP2/6-311++G(d,p)) and is not detectable in the supersonic expansion. Its rotational parameters are given in the supplementary materials, together with the Cartesian coordinates of the two conformers.

Broadband spectrum

The broadband rotational spectrum of APO is shown in Figure 3. It is very dense and shows a series of intense lines with many weaker lines.

According to theoretical calculations, APO is an asymmetric prolate rotor with a Ray's asymmetry This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. The values of the rotational constants obtained from the fit for the parent species are reported in Table I. After cleaning the rotational spectra from the assigned lines of APO small lines were identified as belonging to the ten possible 13 C isotopologues in their natural abundance (1.1%) and about four very small lines were assigned to 18 O isotopologue in its natural abundance (0.2%).

PLEASE CITE THIS ARTICLE AS

Further experiments were performed using the FP-FTMW spectrometer of Lille to record more line transitions for the isotopologue 18 O in its natural abundance. The corresponding rotational constants are reported in Table II.

Molecular structure

The tricyclic structure of APO seems very rigid, as reflected by the small values of the centrifugal distortion parameters. As in the case of similar molecules, 15,16,18 no evidence of splitting due to internal rotation of the methyl group was observed in the rotational spectrum. Further theoretical calculations at the B3LYP/6-311++(d,p) level have been performed to calculate the barrier height of the three methyl groups in APO. Those barrier heights were found to be very high (875 cm -1 for C 10 , 860 cm -1 for C 9 , 1040 cm -1 for C 8 ) similar to those calculated for αpinene, 15 β-pinene and nopinone. 14 The obtained molecular parameters for the parent species and all isotopologues, allows the determination of an experimental gas phase structure of the heavy atom's skeleton of APO.

Indeed since the rotational constants are linked to the atomic distribution in the molecule it is possible to calculate an experimental structure of the heavy atom skeleton using the substitution structure (𝑟 𝑠 ) based on Kraitchman's equations, 33 and by estimate their Costain uncertainties 34 from vibration-rotation effects. Structural parameters from the 𝑟 𝑠 structure, are given in Table III.

The determined 𝑟 𝑠 coordinates are reported along with their calculated uncertainties in electronic supplementary materials.

It was also possible to determine the ground state effective geometry ( 𝑟 0 ) of heavy atom substitution by fitting the molecular geometry directly to all observed moments of inertia, and by taking CH bond lengths and CCH angles from the ab initio MP2 calculations which gives the better agreement with experimental rotational constants. The obtained results are also presented in the Table III. The experimental structure of the skeleton atoms is also compared to the two best theoretical MP2/6-311++G(d,p) and M06-2X/6-311++G(d,p) calculations.

Discussion

Based on data from all isotopologues, both 𝑟 s and 𝑟 0 structures have been determined and compared with theoretical values and those of a few related species such as α-pinene, β-pinene and nopinone. By comparing the obtained structures, some of molecular parameters obtained This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. from 𝑟 s differ with those obtained from 𝑟 0 and theoretical values. Those parameters involve atoms that are close to the principal axis. Kraitchman's method provides the absolute values of coordinates for the substituted atoms, in the center of mass system for the parent species, using differences in moments of inertia for the parent and singly substituted molecules. The accuracy of these coordinates is significantly reduced and the uncertainties in atom coordinates are typically magnified when the substituted atom lies close to a principal axis or the center of mass. This is the case for example of the C1 atom and therefore molecular parameters involving C1 are affected. For that reason, and to compare the structures of related bicyclic molecules we use the

PLEASE CITE THIS ARTICLE AS

𝑟 0 structures.
The structure of APO is very similar to the structure of α-pinene, meanwhile a few features can be noticed from the comparison of their 𝑟 0 structures. The main difference involves the bond length C 3 C 2 which is double bond in the α-pinene and consequently shorter than in the APO.

Concerning the angles, their values in both molecules are very similar. In the case of dihedral is very similar in both molecules. This demonstrates once again the rigidity of this type of bicyclic molecules despite the fact of epoxidation and the presence of a third cycle, α-pinene oxide conserves a similar structure to α-pinene.

The gas phase structure of APO can be compared also with the two other similar molecules such as the pinene isomer β-pinene and its oxidation product nopinone. The bond lengths are very close in the three molecules and again except for C 3 C 2 induced by the presence of the epoxide group. We could note, from the comparison of the 𝑟 0 structures, significant differences in their

Conclusions

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The broadband rotational spectra of -pinene oxide has been recorded using the Lille CP-FTMW spectrometer in the 6-18 GHz range. 13 C and 18 O isotopologues were observed in their natural abundances allowing the determination of an experimental structure of the heavy atom skeleton using the ground-state (𝑟 0 ) substitution (𝑟 𝑠 ) methods. Theoretical calculations using density functional and ab initio methods have been performed to obtain the equilibrium structure, and to guide the spectral analysis.

The gas-phase structure of APO has been compared to related molecules such as -pinene, βpinene and nopinone. Their structures were found to be very similar in particular between -

Figure 1 .

 1 Figure 1. 3-D structures of the four molecules α-pinene oxide, α-pinene, β -pinene and nopinone

  DOI: 10.1063/5.0147909 response to the microwave excitation. A pin diode limiter (AMS/COBHAM ACLM-4537) protects the detection branch of the electronics from accidental damage. Then the collected FIDs are further amplified by a low noise amplifier (MITEQ amplifier JS42-06001 800-20-10P). A digital oscilloscope (160 GSa/s, 63 GHz hardware bandwidth, Keysight DSOZ634A) collects the amplified rotational FIDs in the time domain. A microwave single-pole single-throw switch (SPST, ATM S1517D) is used to protect the oscilloscope. To enable a coherent system all the electronic components are phase-locked to the same 10 MHz rubidium frequency standard clock (SRS FS725). A digital pulse delay generator (Berkeley Nucleonics Corp Model 577) manages the sequences. The FIDs can then be coadded, and the final molecular FID transformed on the computer to the frequency domain using a program written in Python and including different window function options such as Kaiser-Bessel, Bartlett or Hann.

Figure 2 .

 2 Figure 2. Equilibrium structure, of the possible conformer of α-pinene oxide with the numbering of carbons skeleton (left), and of the less stable conformer (right). They differ by the position of the epoxide group. E is relative electronic energy in kJ.mol -1 calculated at MP2; M06-2X; B3LYP; MN15-L levels

  parameter (κ = (2B -A -C)/(A -C)) value equal to -0.67. The main component of the dipole moment lies along the a-inertial axis. A set of intense lines was observed in the recorded broadband spectrum and identified as a-type R-branch. Indeed (𝐽 + 1) 0,𝐽+1 ← 𝐽 0,𝐽 and (𝐽 + 1) 1,𝐽+1 ← 𝐽 1,𝐽 lines spaced approximately by B + C were easily identified. Following iterative fittings and predictions, c-type and b-type R-branches and Q-branches transitions were then

Figure 3 .

 3 Figure 3. The broadband spectrum of α-pinene oxide recorded in the 8-18 GHz frequency

  DOI: 10.1063/5.0147909 identified in the spectrum. A total of 567 transitions were fitted together using SPFIT/SPCAT suite of program 31 with a Watson's semi-rigid rotor Hamiltonian 32 in the 𝐼 𝑟 representation and in the 𝑆-reduction. All the observed lines of APO are available in the supplementary material.

  DOI: 10.1063/5.0147909

  angles, C 4 C 3 C 2 C 1 and C 2 C 3 C 4 C 5 are close to 0° in both cases. The other dihedral angles have relativity very close values. The main differences involve C 10 C 2 C 3 C 1 and C 10 C 2 C 3 C 4 dihedral angles that are close to 180° in the case of α-pinene, and the value decrease of about 30° in the APO molecule. This is due to the presence of the epoxide functional group linked to the C 3 and C 2 atoms. This also could be observed in the value of the C 2 C 1 C 6 angle which is bigger in the case of APO than in the α-pinene by about 4°. The presence of the epoxide forces the 5-members ring to open further reshaping its structure. The other structure parameters of APO are close to their corresponding parameters in the α-pinene suggesting that the overall structure in the gas phase This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909

  dihedral angles. It can be observed that the C 2 C 3 C 4 C 5 , C 4 C 3 C 2 C 1 and C 3 C 4 C 5 C 7 dihedral angles are smaller in the case of APO than in the β-pinene and nopinone. The C 3 C 4 C 5 C 6 and C 3 C 4 C 5 C 7 dihedral angles are bigger in the APO than in β-pinene and nopinone. Surprisingly, the C 10 C 2 C 3 C 4 dihedral angle is closer to β-pinene than to α-pinene, but again C 10 C 1 C 2 C 3 is completely different from βpinene. The presence of the epoxide tilts the structure of this C 10 C 1 C 2 C 3 dihedral angle of about 30°. Table III. Comparison of the geometrical parameters (lengths/Å and angles/°) values determined experimentally and theoretically for the heavy atoms of α-pinene oxide, and with those of other related molecules α-pinene, β-pinene and nopinone.

  pinene oxide and -pinene. As in the case of β-pinene/nopinone, the oxidation of -pinene does not affect too much the structure even with the formation of a tricyclic APO molecule the main structural difference involves the dihedral angle C 10 C 1 C 2 C 3 . With the β-pinene and nopinone more structural features could be observed and mainly in the dihedral angles C 2 C 3 C 4 C 5 , C 4 C 3 C 2 C 1 , C 3 C 4 C 5 C 7 , C 3 C 4 C 5 C 6 and C 3 C 4 C 5 C 7 . Those structural changes are associated with the presence of epoxide functional group, which tilts the five ring atoms. α-pinene oxide α-pinene β-pinene nopinone Accepted to J. Chem. Phys. 10.1063/5

Table I .

 I Experimental spectroscopic parameters for the ground state of α-pinene oxide compared with those predicted from quantum chemical calculations. A, B, C are the rotational constants given in MHz; D J , D Jk , D k , d 1 and d 2 are the quartic centrifugal distortion given in kHz; b  a ,  b ,  c are the components of the electric dipole moment in D;

				Parent species
		Experimental	MP2 e	B3LYP e	M06-2X e	MN15-L e
	A a B a	1726.71952(16) 1092.35191(11)	1730.1 (-0.2%) 1096.3 (-0.4%)	1722.6 (-0.2%) 1080.6 (1.1%)	1735.1 (-0.5%) 1100.4 (-0.7%)	1710.9 (0.9%) 1088.9 (0.3%)
	C a	968.23479(12)	971.5 (-0.3%)	959.0 (1.0%)	974.6 (-0.7%)	962.4 (0.6%)
	D J a D K a D JK a d 1 a d 2 a │µ a │ b │µ b │ b │µ c │ b N c σ d	0.03793(68) 0.05316(72) -0.01782(63) 0.006077(79) 0.0254(13) Observed Observed Observed 567 11	0.0363 0.0556 -0.0191 0.00613 0.0272 1.6 0.9 1.1 --	0.0363 0.0560 -0.0182 0.00619 0.0250 1.5 0.9 1.1 --	0.0361 0.0569 -0.0201 0.00629 0.0271 1.5 1.0 1.1 --	0.0338 0.0541 -0.0177 0.00526 0.0265 1.4 0.8 1.0 --

a c Number of fitted transitions; d rms deviation of the fit in kHz; e 6-311++G(d,p) basis set. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909

To benchmark the performance of theoretical calculation, we compared the experimental rotational constants with those predicted from theory using density functional theory, with the B3LYP, M06-2X and MN15-L functionals, and ab initio calculations at MP2 level of theory all used with Pople's 6-311G++(d,p) basis set. From the data in Table

I

, all methods predict very close rotational constants. Meanwhile, the best agreement with the experimental rotational constants is provided by calculations at the MP2/6-311++G(d,p) level which is better than 0.4%.

Table II .

 II Experimental rotational constants for the13 C and18 O isotopologues of APO-I. The numbering of carbon atoms refers to Figure1.

		13 C1	13 C2	13 C3	13 C4	13 C5	13 C6
	A (MHz) a 1720.4015(49) 1724.9625(10) 1721.4047(14)	1707.049(15)	1717.803(25)	1709.9532(43)
	B (MHz) 1090.16193(47) 1089.02183(56) 1086.35389(42) 1089.47355(69) 1090.13622(79) 1088.07344(70)
	C (MHz) 967.95785(42) 965.28418(37) 964.32972(31) 964.06316(66) 963.81451(62) 965.52835(67) 14.0 13.7 14.0 9.9 11.1 11.2 σ (kHz) b N c 22 22 26 15 14 13
		13 C7	13 C8		13 C9	13 C10	18 O d
	A (MHz) a	1726.1856(16)	1708.2239(10)	1723.6656(51)	1706.8298(40)	1720.6760(39)
	B (MHz)	1088.32659(49)	1084.53754(90)	1074.93691(67)	1084.34373(79)	1071.56547(11)
	C (MHz) σ (kHz) b N c	964.92859(43) 14.4 32	963.02249(71) 13.1 19	954.49869(56) 14.7 18	955.88732(43) 10.9 13	951.22344(10) 1.3 12

a A, B, C are the rotational constants given in MHz; the quartic centrifugal distortion constants were kept fixed to the parent species values; b rms deviation of the fit in kHz; c Number of fitted transitions; d Line transitions from FP-FTMW were fitted together. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909 Accepted to J.

Chem. Phys. 10.1063/5.0147909 10

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. Ref.15 ; b Ref.16 ; c calculated using 6-311++G(d,p) basis set.

		r(C 1 C 7 )	1.641(29) 1.576(14)	1.569	1.571 1.567(12)	1.561(15)	1.564(18)
		r(C 2 C 10 )	1.514(3)	1.511(6)	1.503	1.504 1.500(6)	1.339(5)	-
		r(C 6 C 5 )	1.557(10) 1.551(11)	1.548	1.551 1.554(12)	1.563(13)	1.559(13)
		r(C 7 C 8 )	1.557(16) 1.537(18)	1.526	1.526 1.527(13)	1.538(16)	1.539(18)
		r(C 7 C 9 )	1.523(8)	1.530(11)	1.529	1.530 1.538(8)	1.526(9)	1.526(10)
		r(C 1 C 2 )	1.413(30) 1.507(13)	1.526	1.523 1.512(16)	1.491(13)	1.499(13)
		r(C 1 C 6 )	1.577(10) 1.557(8)	1.546	1.549 1.565(7)	1.556(8)	1.554(8)
		r(C 2 O) r(C 3 O)	1.442(3) 1.442(4)	1.445(7) 1.445(6)	1.427 1.426	1.450 -1.448 -	--	--
	PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0147909	117.2(2) 111.4(2) 112.3(5) 85.5(5) 121.7(4) 109.5(3) 117.4(11) 118.2(13) 117.6(3) 111.6(2) 111.6(6) 85.4(7) 121.5(8) 109.2(4) 116.4(14) 112.8(14) 116.8(3) 117.5(7) 107.0(5) 107.7(7) 117.0(6) 119.4(6) 112.7(5) 112.0(8) 87.8(4) 86.5(3) 86.4(8) 86.9(9) 113.5(12) 110.3(7) 116.3(4) 114.7(4) 109.8(6) 109.2(8) 83.0(12) 86.7(7) 59.6(2) 59.3(4) 59.6(2) 59.3(4) 60.9(3) 61.4(5) 114.3(1) 114.7(3) 115.0(5) 116.1(7) 117.8(2) 117.8(4) -1.4(9) ∠(C 2 C 3 C 4 C 5 ) -1.0(4) ∠(C 2 C 3 C 4 ) ∠(C 5 C 4 C 3 ) ∠(C 4 C 5 C 7 ) ∠(C 1 C 7 C 5 ) ∠(C 10 C 2 C 3 ) ∠(C 6 C 5 C 4 ) ∠(C 8 C 7 C 5 ) ∠(C 9 C 7 C 1 ) ∠(C 10 C 2 C 1 ) ∠(C 8 C 7 C 9 ) ∠(C 8 C 7 C 1 ) ∠(C 9 C 7 C 5 ) ∠(C 5 C 6 C 1 ) ∠(C 6 C 5 C 7 ) ∠(C 2 C 1 C 6 ) ∠(C 1 C 2 C 3 ) ∠(C 2 C 1 C 7 ) ∠(C 6 C 1 C 7 ) ∠(OC 2 C 3 ) ∠(OC 3 C 2 ) ∠(C 2 OC 3 ) ∠(OC 2 C 10 ) ∠(OC 2 C 1 ) ∠(OC 3 C 4 ) -0.8(9) ∠(C 4 C 3 C 2 C 1 ) -2.9(8) 81.5(10) ∠(C 4 C 5 C 7 C 1 ) 78.9(11) -45.2(10) ∠(C 3 C 4 C 5 C 7 ) -45.2(8) 49.1(4) ∠(C 3 C 4 C 5 C 6 ) 49.0(3) ∠(C 4 C 5 C 7 C 9 ) -164.3(9) -165.7(10) -39.6(8) ∠(C 4 C 5 C 7 C 8 ) -39.3(7) ∠(C 10 C 2 C 3 C 4 ) 150.7(3) 150.5(5) 152.5(14) ∠(C 10 C 1 C 2 C 3 ) 154.9(9) ∠(C 3 OC 2 C 1 ) -107.0(7) -104.5(7) σ fit /(uÅ 2 ) -0.0088	117.8 111.3 111.4 85.1 122.1 109.2 118.8 111.9 117.1 108.1 119.6 111.8 86.4 87.6 109.6 114.2 108.8 87.6 59.0 58.9 62.1 115.5 116.1 118.1 -1.1 -0.7 82.7 -46.1 49.0 -165.7 -38.6 149.7 152.0 -103.7 -	117.9 119.5(4) 111.3 110.4(3) 111.4 110.7(6) 85.2 85.4(6) 122.1 123.7(12) 109.2 108.0(6) 118.9 119.4(10) 111.8 111.6(8) 117.2 119.4(11) 108.2 108.1(6) 119.7 119.1(5) 111.7 111.9(7) 86.4 85.6(3) 87.5 87.8(6) 109.7 106.5(7) 114.2 116.9(5) 108.6 110.2(10) 87.4 87.1(6) 59.4 -59.6 -61.1 -114.9 -116.0 -117.8 --1.5 1.9(18) -0.5 -1.3(24) 82.6 80.6(7) -45.7 -48.5(10) 49.3 46.1(7) -165.9 -168.0(9) -38.8 -40.3(7) 150.5 177.8(13) 152.5 179.1(35) -104.0 --0.0087	113.4(2) 111.3(3) 110.8(6) 85.7(5) 122.5(5) 108.9(5) 119.6(8) 111.3(10) 123.3(6) 108.7(6) 118.0(5) 112.0(6) 86.3(4) 88.1(6) 109.3(6) 114.2(4) 108.9(6) 87.0(5) ------21.6(9) 23.7(10) 82.7(8) -58.6(9) 36.6(5) 165.3(6) -37.2(7) 155.8(8) 179.5(5) -0.0080	114.1(2) 111.5(4) 111.9(10) 86.6(8) -108.4(6) 118.8(12) 112.1(13) -108.0(8) 117.5(6) 112.7(9) 86.5(4) 87.5(9) 108.8(8) 115.0(4) 108.2(3) 86.9(7) ------16.1(9) -18.8(11) 83.8(7) -55.5(8) 40.1(5) -165.3(8) -36.0(7) ---0.0079
		r(C 3 C 2 )	1.461(6)	1.475(12)	1.471	c MP2 c 1.472 1.349(15) 𝑟 0	𝑟 0 1.513(10)	𝑟 0 1.525(10)
		r(C 4 C 3 )	1.533(5)	1.521(8)	1.521	1.519 1.509(7)	1.546(7)	1.544(8)
		r(C 4 C 5 )	1.518(8)	1.536(10)	1.534	1.535 1.545(8)	1.530(12)	1.533(13)
		r(C 5 C 7 )	1.560(5)	1.571(11)	1.564	1.566 1.558(10)	1.546(10)	1.545(11)

a

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Acknowledgements

The present work was funded by the French ANR Labex CaPPA through the PIA under contract ANR-11-LABX-0005-01, by the Regional Council Hauts-de-France and by the European Funds for Regional Economic Development (FEDER), and by the CPER CLIMIBIO and CPER P4S. E. M. N. would like to thank the CNRS for a researcher contract. Accepted to J. Chem. Phys. 10.1063/5.0147909 Accepted to J. Chem. Phys. 10.1063/5.0147909

SUPPLEMENTARY MATERIAL

The Supplementary Material contains calculated parameters of the APO at MP2/6-311++G(d,p), the fitted lines for the main species and monosubstituted isotopologues of APO. It contains also the obtained coordinates, 𝑟 𝑠 , and their associated uncertainties.

Conflicts of interest

There are no conflicts to declare This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

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