H Aziza

H Ayari

S Onkaraiah

J-M Portal

M Moreau

M Bocquet

Oxide based Resistive RAM: ON/OFF Resistance Analysis versus Circuit Variability

Keywords: component, Resistive RAM, Oxide-based RAM (OxRRAM), variability I

A deeper understanding of the impact of variability on Oxide-based Resistive Random Access Memory (so-called OxRRAM) is needed to propose variability tolerant designs to ensure the robustness of the technology. Although research has taken steps to resolve this issue, variability remains an important characteristic for OxRRAMs. In this paper, impact of variability on OxRRAM circuit performances is analysed quantitatively at a circuit level through electrical simulations. Variability is introduced at the memory cell level but also at the peripheral circuitry level. The aim of this study is to determine the contribution of each component of an OxRRAM circuit on the ON/OFF resistance ratio.

INTRODUCTION

A typical Resistive RAM (RRAM) device consists of two metallic electrodes that sandwich a thin dielectric layer serving as the ion transport and storage medium. The exact mechanism differs significantly among the different materials being used, but the common link among all RRAM devices is an electric field or heat causes ionic movements and local structural changes in the storage medium, which in turn causes a measurable change of the device resistance [START_REF] Hutchby | Assessment of the Potential & Maturity of Selected Emerging Research Memory Technologies, ITRS -ERD/ERM Technology Work Groups Report on Emerging Research Memory Technologies[END_REF]. In RRAM, the data is stored as two or multiple resistance states of the resistive switching device and relies on a Metal/Insulator/Metal (MIM) stack that can be easily integrated into the Back-End Of Line (BEOL), paving the way for 3D technology.

Resistive switching in transition metal oxides was discovered in thin NiO films decades ago [START_REF] Seo | Reproducible resistance switching in polycrystalline NiO films[END_REF]. Since then, a large number of materials showing a resistive switching have been reported in the literature [START_REF] Nardi | Resistive switching by voltage-driven ion migration in bipolar RRAM Part I: Experimental study[END_REF][START_REF] Larentis | Resistive switching by voltage-driven ion migration in bipolar RRAM Part II: Modeling[END_REF]. Among them, metal oxides as HfO 2 , NiO, TiO 2 or Cu 2 O are promising candidates due to their compatibility with CMOS processes. Oxide-based RAM elements (OxRRAMs) present a lot of interesting features like high integration density, highspeed operations (write/erase/read) and satisfactory reliability performances in terms of retention and cycling [START_REF] Le | A fast, high-endurance and scalable non-volatile memory device made from asymmetric Ta(2)O(5-x)/TaO(2-x) bilayer structures[END_REF]. In OxRRAM memories, MIM structure are used as a single-bit memory cell, while the semiconductor transistor subsystem enables performing all the peripheral operations (input/output, coding/decoding, line driving, and sense amplification) [START_REF] Aziza | Bipolar OxRRAM memory array reliability evaluation based on fault injection[END_REF].

Although OxRRAM-based devices have shown encouraging properties, challenges remain, among which the device variability (or reproducibility) is the main. Indeed, the variance from switching cycle to cycle and from device to device can be very large. For example, it has been experimentally demonstrated that such variability is in the range 2×-10× for the ON resistance and 5×-100× for the OFF resistance in Cu 2 -O-based devices [START_REF] Chen | Variability of resistive switching memories and its impact on crossbar array performance[END_REF]. Besides, MOSFET mismatch in the transistor subsystem (digital and analog blocks) increases inherent variability of OxRRAM technology [START_REF] Joly | Matching degradation of threshold voltage and gate voltage of NMOSFET after Hot Carrier Injection stress[END_REF][START_REF] Joly | Active "multi-fingers": Test structure to improve MOSFET matching in sub-threshold area[END_REF]. On top of that, sensitivity to Single Event Effects (SEEs) caused by a single energetic particle is also investigated [START_REF] Castellani-Coulie | SPICE level analysis of Single Event Effects in an OxRRAM cell[END_REF][START_REF] Castellani-Coulie | Analysis of SEU parameters for the study of SRAM cells reliability under radiation[END_REF].

In the literature, unipolar, bipolar and non-polar electrical behaviors are reported [START_REF] Hutchby | Assessment of the Potential & Maturity of Selected Emerging Research Memory Technologies, ITRS -ERD/ERM Technology Work Groups Report on Emerging Research Memory Technologies[END_REF]. In the case of bipolar switching, addressed in this paper, bipolar voltage sweeps are required to switch the memory element (Fig. 1). In working conditions, after an initial electroforming process, the OxRRAM element may be reversibly switched between RESET (high resistance) and SET states (low resistance). Electroforming stage corresponds to a voltage-induced resistance switching from an initial very high resistance state (virgin state) to a conductive state. In Fig. 1, a typical I-V characteristic of a bipolar OxRRAM cell is presented. Resistive switching corresponds to an abrupt change between a High Resistance State (HRS or OFF state) and a Low Resistance State (LRS or ON state). This resistance change is achieved by applying specific voltage to the structure (i.e. V SET and V RES ). Based on the memory cell hysteresis presented in Fig. 1, in a first approximation, four OxRRAM critical reliability parameters can be considered: V SET , V RES , R HRS and R LRS . Indeed, any variations of any of these parameters, among the cells in a memory array may lead to a limitation in the overall performance of the memory. As a result of cell variability impact on OxRRAM cell parameters, circuit performance exhibits much wider variability [START_REF] Aziza | Evaluation of OxRAM cell variability impact on memory performances through electrical simulations[END_REF][START_REF] Aziza | Single-ended sense amplifier robustness evaluation for OxRRAM technology[END_REF]. This inherent drawback of the technology has to be investigated at a circuit level. In this context, the presented study proposes an evaluation of the impact of variability on the ON/OFF resistance ratio. Section II presents the simulation circuit while section III analyses the contribution of each component of an OxRRAM circuit on the ON/OFF resistance ratio. Section IV concludes the paper.

II. SIMULATION CIRCUIT

A. OxRRAM model

The proposed OxRRAM modeling approach relies on electric field-induced creation/destruction of oxygen vacancies within the switching layer. The model enables continuously accounting for both SET and RESET operations into a single master equation in which the resistance is controlled by the radius of the conduction pathways ( CF r ) [START_REF] Bocquet | Compact Modeling Solutions for Oxide-Based Resistive Switching Memories (OxRAM)[END_REF]:

( ) T k V q Ea CF T k V q Ea CF CF CF b cell ox dOx b cell red dOx e r e r r dt dr ⋅ ⋅ ⋅ + - ⋅ ⋅ ⋅ - - ⋅ ⋅ - ⋅ ⋅ - = α β α β Re Re 10 10 max (1)
where β RedOx is the nominal oxide reduction rate, E a is the activation energy, α red and α ox are the transfer coefficients (ranging between 0 and 1), k b is the Boltzmann constant, T is the temperature and V cell the voltage across the cell. Moreover, the model makes assumptions of a uniform radius of the conduction pathways, a uniform electric field in the cell and temperature triggered acceleration of the oxide reduction reactions ("redox"). Finally, the total current in the OxRRAM includes two components, i.e. one is related to the conductive species (I FC ) and the other to the conduction through the oxide (I OX ).

( ) ( )

OX CF OX CF CF x Cell CF r r L V I σ π σ σ π ⋅ ⋅ + - ⋅ ⋅ ⋅ = 2 max 2 (2) HRS x Cell Cell HRS OX L V S A I β ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ = (3)
where Lx is the oxide thickness, S Cell is the total area of the device, σ Ox the oxidation rate and σ CF the reduction rate. To take into account I OX trap assisted current (Poole-Frenkel, Schottky emission, Space Charge Limited Current (SCLC)), a power law between the cell current and the applied bias is considered with two parameters A HRS and β HRS . Finally, the total current flowing through the cell is:

OX CF Cell I I I + = (4)
I CF is the main contributor to LRS current (I LRS ) and I OX is the main contributor to HRS current (I HRS ). The memory cell compact model is calibrated on silicon. The model was confronted to quasi-static and dynamic experimental data before its implementation in electrical circuit simulators. As presented in Fig. 2a, after calibration, the model satisfactorily matches quasi-static and dynamic experimental data measured on actual HfO 2 -based memory elements (TiN/Ti/HfO x /TiN stack reported in [START_REF] Diokh | Investigation of the Impact of the Oxide Thickness and RESET conditions on Disturb in HfO2-RRAM integrated in a 65nm CMOS Technology[END_REF]). To program a bipolar OxRRAM cell, a voltage ramp is needed. In Fig. 2b, the evolution of SET voltages as a function of the ramp speed is presented. The model implementation focused on this dependence which is crucial for the model to be confidently implemented in circuit simulators. Lines: Simu. Symbols: Data [START_REF] Joly | Active "multi-fingers": Test structure to improve MOSFET matching in sub-threshold area[END_REF] ICell (A)

VCell (V)

Fig. 3 Measured and corresponding simulated I-V characteristic obtained from TiN/Ti/HfO2/TiN devices showing strong variation on R LHS and R HRS Due to the stochastic nature of the switching process in OxRRAMs, leading to large variability, the OxRRAM model features a variability dependency.

The variation is chosen to fit experimental data as presented in Fig. 3 (I-V characteristic in logarithmic scale). The model behavior (lines) is consistent with experimental data (symbols). HRS variation is generally larger than LRS variation for this technology. The manufacturing process of a TiN/Hf/HfO 2 /TiN stack is presented in [START_REF] Govoreanu | 10x10nm2 Hf/HfOx Crossbar Resistive RAM with Excellent Performance, Reliability and Low-Energy Operation[END_REF]. Statistical variations in the switching parameter metrics such as V SET , V RESET , R OFF and R ON have been examined in-depth in the recent past. The origin ("cause") of all these variations in resistive switching memory are the microscopic transport of oxygen ions/vacancies [START_REF] Degraeve | Dynamic 'hour glass' model for SET and RESET in HfO2RRAM[END_REF] and the different permutations of filamentary clusters [START_REF] Raghavan | RTN insight to filamentary instability and disturb immunity in ultra-low power switching HfOxand AlOxRRAM[END_REF] they form during different SET-RESET cycles.

The cell variability modeling is based on OxRRAM card model parameters variation. The variation is chosen to feet experimental data. Variability is introduced through specific model parameters (i.e. β RedOx and β HRS parameters presented respectively in Equ. 1 and Equ. 3).

B. OxRRAM elementary circuit

Fig. 4 presents the elementary array used for simulation which is constituted by a 3×3 1T/1R cell matrix, a row decoder, a column decoder and a sense amplifier for the read operation. The 1T/1R memory cell (one MOS transistor in series with one resistor) is seen as an effective alternative to replace embedded DRAM-based memory modules by substituting the capacitor by an OxRRAM resistor. The memory cell is modeled by the OxRRAM cell model presented in section II.A. The variability analysis is conducted through Monte Carlo simulations. Each Monte Carlo simulation targets specific elements of the circuit: the resistive element, the select transistor, the decoding blocs and the sense amplifier. As a result, R ON and R OFF distribution spreads are extracted. Thus, the contribution of each element in terms of memory performance degradation is demonstrated. The study is conducted using a 28-nm Fully Depleted Silicon-On-Insulator (FDSOI) technology [START_REF] Mazure | FDSOI: From substrate to devices and circuit applications[END_REF]. Memory array cells are first placed in a virgin state. Then, the memory array programming is done in 2 cycles. First, all memory cells are set (logical "1"), then the memory array is reset (logical "0"). R ON value is extracted after the SET operation and R OFF after the RESET operation for each Monte Carlo run. Variability introduced in the resistive element is chosen to feet experimental data (see Fig. 3) whereas variability of the transistor subsystem is given by the considered technology. In this study, 4 different configurations are considered: the "ALL" configuration considers variability in the memory cell (resistive element and select transistor) and the peripheral circuits. In the "CELL" configuration, variability affects only the resistive element. In the "SELECT" configuration, variability affects only the OxRRAM select transistor. In the "NO CELL" configuration, variability affects only the peripheral circuits (transistor subsystem, including the select transistor). In this study, the impact of the select transistor variability is subject to special attention. Indeed, the select transistor compliance allows the control of the maximum available current during the set transition, impacting directly the ON/OFF resistance. Table I Fig. 5 ON/OFF resistance distributions for the "ALL" configuration Fig. 6 presents the impact of variability on R OFF distributions (after RESET) for the 4 configurations. By comparing configuration "ALL" with configuration "CELL", it appears clearly that the impact of cell variability is more important than the impact of the transistor subsystem variability. The third and fourth configurations ("NO CELL" and "SELECT") shows that impact of transistors variability on R OFF is negligible. Besides, the contribution of the select transistor variability is dominant in the peripheral circuit elements. Table II proposes a synthesis of results obtained in Fig. 6 (mean values, standard deviation and standard deviation ratio, reported on maximum standard deviation value). Compared with Fig. 6, it appears clearly that the cell variability impact is less pronounced for low resistive states (LRS), which is a common feature of all OxRRAM technologies [START_REF] Boquet | Robust Compact Model for Bipolar Oxide-Based Resistive Switching Memories[END_REF][START_REF] Hamdioui | Memristor based memories: Technology, design and test[END_REF][START_REF] Haron | On defect oriented testing for hybrid CMOS/memristor memory[END_REF][START_REF] Haron | DfT schemes for resistive open defects in RRAMs[END_REF]. Moreover, the contribution of transistors variability is comparable to the contribution of the memory cell variability (see "CELL" and "NO CELL" configurations in Fig. 7). Once again, simulation results show that the impact of the select transistor is not negligible. Table III proposes a synthesis of results obtained in Fig. 7. Fig. 9 shows a comparison between R ON and R OFF distributions. Based on the considered technology, it is shown that resistance variability in RESET state is much more important than variability in the SET state. This variability is mainly due to the memory cell. In addition, the impact of the select transistor is non-negligible. This effect is visible in the SET state where the impact of the memory cell variability is much less important, making the select transistor variability critical. Variability in OxRRAM memories presents a major challenge for fabrication process and design engineers. In the proposed study, OxRRAM variability is evaluated based on an OxRRAM compact model included in an elementary memory array design. Simulation results show a signification impact of cell variability on the memory array ON/OFF resistances. Variability is introduced at the memory cell level but also at the peripheral circuitry level. The aim of this study is to determine the contribution of each component of an OxRRAM circuit on the ON/OFF resistance ratio. It has been demonstrated, based on a specific technology that variability in RESET state is mainly due to the memory cell. In SET state, impact of variability is less important, making the select transistor variability critical. This study underlines the need of variability tolerant designs to ensure the robustness of the technology.

Fig. 1

 1 Fig.1Typical I-V characteristic of a bipolar OxRRAM cell

  Fig.2 (a) I-V characteristic measured on HfO2-based devices [15] and corresponding simulation using a bipolar OxRRAM physical model. (b) Set voltage as a function of the programming ramp

  Fig.43×3 OxRRAM elementary memory array

Fig. 6

 6 Fig.6ROFF distributions

Fig. 7

 7 Fig. 7 presents the impact of variability on R ON distributions (after SET) for the 4 configurations.

Fig. 7

 7 Fig.7RON distributions

Fig. 8

 8 Fig.8RON/ROFF distributions

  summarizes the 4 configuration to simulate.

TABLE I

 I

	« ALL » configuration
	R ON	R OFF
			.	SIMULATED CONFIGURATIONS
		Configuration	RUNS	Elements under variability
		« ALL »	400	All circuit elements
		« CELL »	400	Resistive element
		« SELECT »	400	Select transistor
		« NO CELL »	400	All elements excluding the resistive element
		Fig 5 presents the impact of variability of the whole circuit
		elements (resistive element and transistor subsystem: "ALL"
		configuration) on R ON and R OFF distributions after 400 Monte
		Carlo simulations. Note that R OFF distribution is much larger
		than R ON distribution. In order to discriminate the contribution
		of each element of the circuit on ON/OFF resistances, a set of
		Monte Carlo simulations are performed with "CELL",
		"SELECT" and "NO CELL" configurations.

TABLE II .

 II ROFF DISTRIBUTION PARAMETERS

	Configuration	Mean (Ω)	σ (Ω)	σ (%)
	« ALL »	60200	5598	100
	« CELL »	60240	5617	99
	« NO CELL »	60004	598	9.6
	« SELECT »	59990	536	10.6

TABLE III .

 III RON DISTRIBUTION PARAMETERS

	Configuration	Mean (Ω)	σ (Ω)	σ (%)
	« ALL »	9674	724	100
	« CELL »	9679	513	70.8
	« NO CELL »	9642	550	78.7
	« SELECT »	9713	570	75.9


Raheel Qader

Gwénolé Lecorvé

Damien Lolive

Pascale Sébillot

Disfluency Insertion for Spontaneous TTS: Formalization and Proof of Concept

Keywords: Disfluencies, Spontaneous speech, Natural language generation

This paper presents an exploratory work to automatically insert disfluencies in text-to-speech (TTS) systems. The objective is to make TTS more spontaneous and expressive. To achieve this, we propose to focus on the linguistic level of speech through the insertion of pauses, repetitions and revisions. We formalize the problem as a theoretical process, where transformations are iteratively composed. This is a novel contribution since most of the previous work either focus on the detection or cleaning of linguistic disfluencies in speech transcripts, or solely concentrate on acoustic phenomena in TTS, especially pauses. We present a first implementation of the proposed process using conditional random fields and language models. The objective and perceptual evalation conducted on an English corpus of spontaneous speech show that our proposition is effective to generate disfluencies, and highlights perspectives for future improvements.

Introduction

Speech disfluencies can be defined as a phenomenon which interrupts the flow of speech and does not add any propositional content [START_REF] Tree | The effects of false starts and repetitions on the processing of subsequent words in spontaneous speech[END_REF]. Despite the lack of propositional content, disfluencies have several communicative values. They facilitate synchronization between addressees in conversations [START_REF] Clark | Speaking in time[END_REF]. They also improve listening comprehension by creating delays in speech and signaling the upcoming message complexity [START_REF] Rose | The communicative value of filled pauses in spontaneous speech[END_REF][START_REF] Tree | Listeners' uses ofum anduh in speech comprehension[END_REF] (cited by [START_REF] Adell | Production of filled pauses in concatenative speech synthesis based on the underlying fluent sentence[END_REF]). Despite this, current Text-To-Speech (TTS) systems only partially integrate disfluencies. They are thus inadequate to express a spontaneous style, and prevent from high user acceptability in some human-machine interactions (e.g. personnal assistants, avatars). To tackle the issue, this paper investigates the automatic insertion of disfluencies.

This paper proposes a novel formalization of the disfluency generation mechanism. This formalization enables controlling the nature and proportion of the disfluencies to be generated. Our proposal is supported by a proof of concept through a first implementation trained on an English corpus. This implementation relies on conditional random fields (CRFs) and language models (LMs) to experimentally demonstrate the ability of our approach to produce plausible disfluent utterances. As exploratory work, no synthesis experiment is carried out because integrating disfluencies in a TTS system requires adaptations on many aspects (underlying speech corpus, prosody prediction, etc.). Thus, the current work conducts the textual validation of the generated disfluent utterances.

In the remainder, Section 2 reviews the domain and presents our motivations. Then, Section 3 introduces the formalization of the problem while its implementation is given in Section 4. Finally, the validation of our work is provided in Section 5 through objective and perceptual evaluations.

Review of the Domain and Motivations

According to Shriberg [START_REF] Shriberg | Preliminaries to a theory of speech disfluencies[END_REF], disfluencies are characterized by 3 sections playing a specific role: the reparandum region (or RM) which is the sequence of erroneous words ; the repair region (RR), i.e. the sequence of corrected words for the RM region ; and finally the so-called interregnum section indicating the interruption in the speech stream. In this schema, the point between the reparandum and the interregnum is the interruption point (IP). Below is an example of disfluency:

I think RM she will ↑ IP IM I mean RR he will not come today. ( Example 1)
Several studies suggest to categorize disfluencies into three main types: pauses, repetitions, and revisions [START_REF] Shriberg | Phonetic consequences of speech disfluency[END_REF][START_REF] Tseng | Grammar, prosody and speech disfluencies in spoken dialogues[END_REF][START_REF] Boula De Mareüil | A quantitative study of disfluencies in french broadcast interviews[END_REF]. Pauses are useful to keep the conversation on while the speaker searches for a phrase. Pauses can be silent, filled (e.g., "uh" or "um") or discourse markers ("you know", "well", etc.). Repetitions can be used to gain time and recover the flow of the speech, intensify the effect of an expression, or signal an upcoming problem in the speech [START_REF] Tseng | Grammar, prosody and speech disfluencies in spoken dialogues[END_REF]. Finally, revisions occur when the speaker slightly fixes his speech after an error. False starts are an extreme case of revisions in which the speaker completely abandons the interrupted speech and starts a fresh one. Hence, revisions help the speaker monitoring his speech.

Most studies on disfluencies are for automatic speech recognition [START_REF] Stolcke | Statistical language modeling for speech disfluencies[END_REF][START_REF] Stolcke | Automatic detection of sentence boundaries and disfluencies based on recognized words[END_REF][START_REF] Liu | Enriching speech recognition with automatic detection of sentence boundaries and disfluencies[END_REF][START_REF] Kaushik | Automatic detection and removal of disfluencies from spontaneous speech[END_REF][START_REF] Hassan | Segmentation and disfluency removal for conversational speech translation[END_REF] where the main objective improve language modeling and produce disfluency-free transcripts. On the contrary, disfluency generation is still poorly studied in TTS. According to [START_REF] Adell | On the generation of synthetic disfluent speech: local prosodic modifications caused by the insertion of editing terms[END_REF], this is because, most of the time, speech databases for TTS systems do not contain any disfluencies, and linguistic processing pipelines in the front-end still badly integrate disfluent sentences, in spite of NLP progresses in the domain [START_REF] Honnibal | Joint incremental disfluency detection and dependency parsing[END_REF]. Among existing work, [START_REF] Sundaram | An empirical text transformation method for spontaneous speech synthesizers[END_REF][START_REF] Tomalin | A lattice-based approach to automatic filled pause insertion[END_REF] studied the automatic insertion of filled pauses (especially "uh", "um") using finite state acceptors or word lattices. Other studies like [START_REF] Adell | Filled pauses in speech synthesis: towards conversational speech[END_REF][START_REF] Dall | Investigating automatic & human filled pause insertion for speech synthesis[END_REF][START_REF] Andersson | Prediction and realisation of conversational characteristics by utilising spontaneous speech for unit selection[END_REF] have formalized the problem as searching for an IP using machine learning before selecting, among a set of possibilities, the best words to be inserted according to probabilities given by an LM. This approach is also adopted in our work. Although this approach relies on the reductive hypothesis that disfluencies are predictable based on shallow (non-psychological) cues (raw words, parts of speech, etc.) [START_REF] Dall | Investigating automatic & human filled pause insertion for speech synthesis[END_REF], the resulting disfluencies have shown to feign personality traits [START_REF] Wester | Artificial personality and disfluency[END_REF]. Likewise, recent work has studied the acoustic aspects of lengthenings and filled pauses w.r.t. the perception of uncertainty [START_REF] Székely | Synthesising uncertainty: the interplay of vocal effort and hesitation disfluencies[END_REF].

Among limitations, most of these studies concentrate on one type of disfluencies (mostly filled pauses). Recently, [START_REF] Betz | Micro-structure of disfluencies: Basics for conversational speech synthesis[END_REF] proposed to model several types of pauses. Following the same objective, we introduce a rich formalization, able to integrate repetitions and revisions in addition to pauses. Then, Shriberg's schema of disfluencies is useful to determine whether an utterance is disfluent or not, but it does not explain how to move from a fluent to a disfluent utterance, especially when disfluencies are interwinted. To solve this problem, we propose to decompose this schema such that it can be used to generate disfluencies in a deterministic way. Finally, it is worth noting that disfluency generation, as usually in natural language generation, is difficult to evaluate since several outputs are generally acceptable in these problems. This makes it particularly difficult to compute objective measures when data, as is the case in our work, contains only one reference to be compared with. This problem is discussed in Section 5.

Disfluency Generation Process

In this work, we propose a complete process for disfluency generation. The key idea is to compose disfluencies of elementary types. This section presents the whole process, each disfluency type, and the composition mechanism.

Main Principles

The proposed process considers a disfluency as the result of a transformation function on a fluent utterance. Hence, an utterance with multiple disfluencies results from successively composing transformation functions. In practice, one transformation function is defined for each disfluency type. That is, given a disfluency type T , the transformation function f T reads a sequence of n words w ∈ V n , where V denotes the vocabulary, and returns a sequence of m words, m > n. In practice, each function f T consists of two sub-functions: π T , which determines the IP position, and ω T which inserts the actual disfluent words using the result of π T . Mathematically, these two functions can be defined as below:

π T : V n → 0, n , (1)
and ω T :

V n × 0, n → V m . (2)
Thus, f T is simply calculated as ω T (w, π T (w)). Sub-functions have been chosen to be specific on disfluency types since IPs may not appear in the same context according to the type, and each type has its own structure, expressible through Shriberg's schema and described in the following.

Disfluency Functions

Pauses can syntactically be seen as a simple interruptions, without any RM nor RR, solely reduced to an IM. This IM can be instantiated by different pause tokens, in our work those present in the corpus used for the experiments: "<silence>", "uh", "um", "you know" "I mean" and "well". This list can obviously be extended in order to make the whole process richer. The following is an example of a pause transformation from a fluent utterance:

w : once you get to a certain degree of frustration,

f pause (w) : once you get to a certain degree of ↑ IP IM uh frustration. ( Example 2)
To make the link with the sub-functions presented earlier, the IP here is determined by the π pause function and the choice of the word(s) to be inserted is made by the ω pause function. Repetitions are duplications of one or few words, i.e., their RM and RR regions are identical. Due to the proposed composition mechanism, no IM is considered, as follows: Thus, all repetition are treated as the following example: (

A repetition with a pause in the middle is considered as 2 disfluencies. The scope of the repetition, i.e., length of RM and RR, is determined by the sub-function ω repetition . In a similar fashion, revisions do not include any IM, and ω revision determines the span of the RR region and generates the RM. As opposed to repetitions, the predicted RM differs from the RR region. An example of revision is given below:

w : that is so that if whoever would get it,

f revision (w) : that is so that RM if you ↑ IP RR
if whoever would get it.

(Example 4)

Fig. 1. Whole disfluency generation process.

Composition of Disfluency Functions

Composition is the only way to generate all disfluency regions and several disfluencies. For instance, an utterance containing a revision and a pause can be seen as the result of f revision • f pause . However, this may be also the result of f pause • f revision . To minimize such ambiguities and make the process deterministic, the following precedence order is defined:

revision ≺ repetition ≺ pause . (3)
Thus, for the given example, the composition f pause • f revision is forbidden. This order is justified by the fact that knowing where revisions and repetitions are can be useful to determine where to insert pauses. Technically, it is also easier to insert a pause in between repeated words than inserting repeated words around one or several pause tokens. Likewise, inserting revisions after repetitions would break repetitions, whereas repetitions applied on top of revisions may help strengthening revisions. Following this precedence order, the generation process is as given in Figure 1. Starting from a fluent utterance, and in the respect of , each type of disfluency can be applied zero, one or several times. Below is an example of consecutive transformations:

I have to go. These hierarchized iterative compositions can easily be formulated as an actual algorithm and implemented, as described in the next section.

Implementation

This section presents one way to implement the disfluency generation process. The objective of this implementation is to validate the approach before studying input : OriginalUtt: a fluent utterance output: input utterance with added disfluencies richer and more efficient implementations in the future. For this reason, we limit this study to pauses and repetitions, and set aside the more difficult case of revisions. This configuration is minimal but functionnal since it enables testing the composition mechanism.

For each disfluency type T , the IP prediction function π T is treated as a labeling task achieved using a CRF, while the word insertion function ω T is the selection of the best phrase among a set of automatically built candidates, the selection criterion relying on an LM. In short, the whole process is built on 2 CRFs and 2 LMs. We describe the main algorithm, then these models.

Main Algorithm

Algorithm 1 presents how to transform an input utterance to a disfluent one. Each type T is examined in a same manner, following the precedence order. The algorithm tries to determine a potential IP (line 8). If this IP is accepted according to a stopping criterion (l. 9), a new disfluency of type T is added to the current version of the utterance being transformed (l. 10). Then, a next IP proposal is computed (l. 11). As soon as an IP is rejected by the stopping criterion, the algorithm moves to the next disfluency type (l. 7) or, if none anymore, returns the transformed utterance (l. 12). The stopping criterion stops insertions as soon as, for the current type T , the proportion of disfluencies of this type in the transformed utterance reaches a maximum threshold fixed by the user. In practice, these thresholds have been set to 1 % and 12 %, respectively for repetitions and pauses, as observed on average in the training corpus.

IP Prediction

IP prediction is carried out by a CRF on an input (fluent or disfluent) sequence of words and potentially associated features. This CRF is trained to categorize successive words under two labels: words that are followed by an IP, and the others. At runtime, the CRF produces a list of IPs which are examined in turn until finding out one which has not been exploited yet. This requirement for fresh IPs at each iteration prevents the method from indefinitely adding disfluencies at the sole best place deemed by the CRF. If no new IP is found, the main algorithm moves to the next disfluency type. The examined IPs are those returned for each labelling hypothesis in the N-best list of the CRF. They are sorted by descending posterior probability. Falling back on N-best lists ensures a very large choice of IPs, delegating the termination decision to the stopping criterion.

Insertion of New Words

Given a chosen IP, the word insertion step seeks to produce a disfluency that best integrates into the utterance. The proposed implementation of ω T constructs a set of possible word sequences, centered on the IP, and then determines the most probable w.r.t. type T . For repetitions, candidates are RM/RR pairs of various lengths. As for pauses, 6 candidates are proposed, one for each considered pause tokens able to fill the IM. Candidate sequences are descriminated by comparing their probability within their local contexts (±3 words around the IP). The probability for type T is computed by an n-gram LM trained on T -specific disfluent data. For an IP at position i in a sequence of words w

= [w 1 • • • w N ], let a disfluent section under examination d = [d 1 • • • d D ]
, and the left/right surrounding words w

( ) = [w i-W +1 • • • w i ] and w (r) = [w i+1 • • • w i+W ] respectively.
The proper integration of d within w can be measured through either the average probability per word or the global probability conditionned on d , respectively defined as:

Pr(w ( ) dw (r) ) 2W + D (4)
and Pr(w

( ) dw (r) |d) = Pr(w ( ) dw (r) ) Pr(d) (5)
Since utterances are processed independently, the first measure favors overinsertion of the most frequent tokens from the training corpus. On the contrary, the second disregards the prior probability of the disfluent tokens and solely focuses on how the final word sequence flows well. As a consequence, it leads to over-generating rare tokens. In this paper, a linear interpolation with equal weights associated to each measure is chosen.

Experimental Validation

The proposed implementation has been tested on 20 h from the Buckeye corpus [START_REF] Pitt | The Buckeye corpus of conversational speech: labeling conventions and a test of transcriber reliability[END_REF], an American English conversational speech corpus made of individual interviews with 20 speakers. Manual transcripts (150K words) are annotated with 2, 714 repetitions and 20, 264 pauses. For each type of disfluencies, a dedicated version of the corpus is derived where utterances with no disfluency of that type were filtered out. To be consistent with precedence order, all pauses were removed from the repetition-specific corpus. An entirely cleaned (fluent) version of the corpus was also built. Data is divided into 3 sets: one to train the models (train, 60% of the utterances), another to tune hyper-parameters (development, 20%), and a set for evaluation (test, 20%). CRFs were trained using Wapiti3 and LMs are trigrams trained with SRILM 4 . The remainder presents the different evaluations conducted to validate the proposed approach.

Objective Evaluation

IP predictions are examined through precision, recall and F1-score compared to the reference from our corpus, i.e., a predicted IP is a true positive if it is placed at the exact same position as an IP of the reference utterance. In the absence of multiple references, these measurements are difficult to interpret. Thus, we also propose to introduce the Interruption Rate Ratio (IRR) between the predictions and the reference, i.e., the scale factor between the average number of IPs per sentence in our hypotheses and in the reference. For example, IRR with value 1 indicates an equal proportion of IPs, 0.6 means an under-prediction of 40 %, and 2.2 an over-prediction of 120 %. Word insertion is evaluated by the LM perplexity given to the generated sequences. Since LMs are also used to select disfluency candidates, this measure is biased but it is primary used to understand the general behavior of the proposition. Disfluent sentences are expected to get lower perplexities than fluent sentences. Different CRF training settings were studied in preliminary experiments on the development set for IP prediction. Two factors have been studied and adjusted: the optimal set of features and the size of contextual information for each word, i.e., the size of the observed neighborhood window. As a result, it turns out that our best results are obtained with very few attributes, namely raw words and part of speech (POS). As for the neighborhood, a window of a few words (2 in the final experiments) around the word being examined is beneficial.

On the test set, the compared configurations are: the cleaned utterances (cl.), their disfluent reference (ref.), and utterances produced by our models with the previously exposed features. Regarding pause insertion, an extra feature is introduced to tell the CRF whether a word under study comes from the original fluent sentence or has been added along iterations. This intents to integrate dependencies across transformations, as for instance desired to insert a pause in a repetition. We remind that the reference for repetitions do not contain any pause, whereas the cleaned version for pauses can include repetitions.

Tables 1 and2 show the results obtained for the repetitions (R) and pauses (P). First, the results are globally low, especially for repetitions. These results can be explained by the relatively small amount of learning data and the uniqueness of our reference. IRRs show that generated utterances have always fewer disfluencies than the reference, because of the adopted stopping criterion. To our knowledge, no comparative work exists for repetitions, and considering a wide range of pause tokens (not only "uh" and "um") is rather difficult [START_REF] Tomalin | A lattice-based approach to automatic filled pause insertion[END_REF].

Hence, these results are acceptable for a first implementation. In terms of perplexity, the generated disfluencies are rather close to the reference. Moreover, perplexities and IRRs on pauses highlight, as expected, that a high proportion of pauses brings a low perplexity. Finally, information about previous iterations of the algorithm, i.e., knowing which words are inserted (disfluent) words, seems beneficial, as shown in particular by the increase of about 2 percentage points of the F1-score (P B vs. P C ).

Perceptual Tests

Two series of perceptual tests were conducted on 24 participants. The first series separately studies the effects of repetitions and pauses, while the second seeks to measure their combined effects. Based on a displayed fluent text, testers had to imagine how it could be uttered during a spontaneous conversation, and gave their opinion on several proposals, ranging from 0 (impossible utterance) to 10 (perfectly possible). A same set of 40 utterances from the test set is used for all experiments (4-25 words, all selected so that their disfluent reference contains a mixture of repetitions and pauses, not necessarily interleaved). Mean opinion scores (MOSs, confidence interval α = 0.05) are reported in Figure 2 for the first series of tests. System labels are the same as in Tables 1 and2. First, these results are close from one configuration to another, and differences are generally insignificant, even between the cleaned and reference utterances. This seems to show that the perception of disfluencies is a difficult task, at least when presented in a textual form. On repetitions, it appears that configurations with no or few repetitions (R cl. and R A ) are preferred to those containing more (R ref. and R B ). This can be explained by the absence of pauses in the middle of the presented repetitions. Then, the results on pauses seem Fig. 2. MOS on repetitions (left) and pauses (right). System labels are as in Table 1. Fig. 3. MOS for mixed repetitions (R) and pauses (P). System labels are as in Table 2.

correlated with the proportion of pauses (see IRRs in Table 2), although significance is not proven. On the whole, these two tests show that the automatically generated utterances do not denote w.r.t. the reference.

The incidences of the disfluency proportions, and of combining repetitions and pauses are studied in the second series of experiments. For each type, three insertion levels are considered by modulating the stopping criterion threshold (see Algorithm 1): zero means no disfluency of the considered type ; medium, a proportion consistent with the training set ; or high, 3 times more disfluencies than in the corpus. MOSs of these tests are in Figure 3. Again, the results are all very similar. Nevertheless, the absence of low scores means that the disfluency composition mechanism produces plausible utterances, which is the first motivation of these tests. Then, two trends emerge: first, the absence of pause or their strong presence are badly perceived compared to the intermediate setting (B, E, H), then the most disfluent utterances (I) get the lowest MOS.

As a conclusion, the perceptual tests show that the utterances produced by our method are acceptable in comparison to clean ones and to disfluent ones as uttered in real situations. This tends to validate the proof-of-concept im-plementation and the underlying proposed formalization. The small differences between configurations however encourage one to improve this implementation and to think about more discriminating ways to conduct perceptual tests.

Conclusion

In this paper, we have presented an innovative formalization for the automatic insertion of disfluencies in texts. The ultimate goal of this work is to make synthetic speech signals more spontaneous, and thus more acceptable in some human-machine interactions. We have introduced a theoretical process of disfluency composition and provided a first implementation based on CRFs and LMs. The experiments conducted on this implementation show that the proposed process is functional, although perfectible.

A first perspective is now the extension to revisions. Since the validation in this paper, this work has been achieved. The word insertion part, which is the difficult part, has been implemented by altering words from the RR with linguistically similar ones, i.e., words with the same POS and geometrically close in a lexical embedding space. Evaluation will be conducted in the near future. Among other perspectives, more complex models could be tested, for instance to enable including broader, non-lexical, considerations (phonetic confusion, speaker intention, etc.). However, collecting training data is an obstacle here. Finally, evaluation is a challenge. The best improvement track on this point seems to us to provide natural realizations of all the tested utterances. This would avoid bypass the unsuitability of current TTS systems but it requires recording people.

w

  : and I think this happens to a lot of people, this happens to a lot of people.

  f revision [I want to I have to] revision go. • f repetition I want [to to] repetition I have to revision go. • f pause I want [to to] repetition [uh] pause I have to revision go. • f pause I want [to to] repetition [uh] pause [I mean] pause I have to revision go. (Example 5)

1 data: 2

 12 Types: list of disfluency types 3 OutputUtt: sequence of words 4 IP: integer 5 Types ← [ repetition, pause ] 6 OutputUtt ← OriginalUtt 7 for each T ∈ Types do 8 IP ← πT (OutputUtt) 9 while ¬ StoppingCriterion(T, OutputUtt, IP) do 10 OutputUtt ← ωT (OutputUtt, IP) 11 IP ← πT (OutputUtt) 12 return OutputUtt Algorithm 1. Main algorithm for disfluency generation.

Table 1 .

 1 Objective evaluation of repetitions on the test set.

		Features Window?	Recall	Prec.	F1	IRR	PPL
	(R cl. )	Fluent (cleaned) utterance			0.0	241
	(R ref. ) Disfluent reference utterances			1.0	236
	(R A )	Words	no	0.8%	3.8%	1.3	0.1	236
	(R B )	+ POS	yes	6.2%	17.1%	9.2	0.4	231

Table 2 .

 2 Objective evaluation of pauses on the test set.

		Features	Window?	Recall	Prec.	F1	IRR	PPL
	(P cl. )	Fluent (cleaned) utterances				0.0	242
	(P ref. ) Disfluent reference utterances			1.0	172
	(P A )	Words	no	8.2%	29.4%	12.8	0.5	209
	(P B )	+ POS	yes	17.9%	33.6%	23.3	0.7	191
	(P C )	+ prev. disfl.	yes	19.8% 34.5% 25.1	0.7	188

http://wapiti.limsi.fr/

http://www.speech.sri.com/projects/srilm/

This study has been realized under the ANR (French National Research Agency) project SynPaFlex ANR-15-CE23-0015.


Alexandre Nicolas

Santiago Ibáñez

Marcelo N Kuperman

Sebastián Bouzat

A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: Can 'more' escape faster?

Dense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We use simulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contactaverse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians.

Introduction

Clogs rank high on the list of nightmares of grain silo managers and crowd managers alike. Every year, grain entrapment still claims the lives of dozens of workers who crawled inside bins or silos to knock down clogs and speed up the outpour. For instance, in the United States, it was at the origin of 11 fatalities and 18 non-fatal injuries in 2016 [START_REF] Issa | 2016 summary of u.s. agricultural confined space-related injuries and fatalities[END_REF], while in France [START_REF] Barpi | Accidentologie silos bois et céréales depuis[END_REF] and in Argentina [START_REF]Superintendencia de Riesgos del Trabajo, Informe anual de accidentabilidad laboral 2015[END_REF] fatal accidents occur every few years. Concurrently, crowd disasters due to massive rushes towards an exit in situations of emergency hit the headlines on a yearly basis.

From a fundamental perspective, recent works have shed light on similarities in the clogging and unclogging dynamics across a wide variety of systems, from vibrated granular flows to pedestrian flows through a bottleneck [START_REF] Zuriguel | Clogging transition of many-particle systems flowing through bottlenecks[END_REF]. In the study of granular flows through a silo or a hopper, different strategies have been investigated to avoid or destroy clogs. On account of the sensitivity of the flow to the size of the outlet, enlarging the latter is an intuitive and efficient strategy, but researchers have also studied the effect of vibrating the setup vertically [START_REF] Mankoc | Role of vibrations in the jamming and unjamming of grains discharging from a silo[END_REF][START_REF] Lozano | Breaking arches with vibrations: the role of defects[END_REF] or making the exit oscillate in the horizontal plane [START_REF] To | Flow and clog in a silo with oscillating exit[END_REF]. Placing an obstacle in front of the exit was also found to enhance the flow in specific conditions [START_REF] Zuriguel | Silo clogging reduction by the presence of an obstacle[END_REF][START_REF] Endo | Obstacle-shape effect in a two-dimensional granular silo flow field[END_REF]. The latter strategy may also be efficient to facilitate the evacuation of living beings, such as sheep and mice, but the results seem to strongly depend on the position of the obstacle [START_REF] Zuriguel | Effect of obstacle position in the flow of sheep through a narrow door[END_REF] and the geometry of the setup [START_REF] Lin | An experimental study of the impact of an obstacle on the escape efficiency by using mice under high competition[END_REF], and it has not been demontrated yet that this method also applies to real pedestrian crowds [START_REF] Yano | Effect of form of obstacle on speed of crowd evacuation[END_REF]. In contrast, an aspect that is known to considerably affect pedestrian flow rates is the motivation or eagerness to escape. In a first regime, a crowd that is more eager to escape will effectively evacuate faster [START_REF] Nicolas | Pedestrian flows through a narrow doorway: Effect of individual behaviours on the global flow and microscopic dynamics[END_REF]. However, beyond a certain level of competitiveness, further increasing the eagerness to egress results in the build-up of higher pressure at the bottleneck, due to physical contacts, which stabilises clogs and thus delays the evacuation [START_REF] Parisi | Why 'faster-is-slower' in evacuation process[END_REF][START_REF] Pastor | Experimental proof of faster-isslower in systems of frictional particles flowing through constrictions[END_REF]. This is the well-known 'faster-is-slower' effect, first evidenced in numerical simulations [START_REF] Helbing | Simulating dynamical features of escape panic[END_REF] (note that similar effects are observed when increasing the effective gravity in granular hopper flows [START_REF] Zuriguel | Clogging transition of many-particle systems flowing through bottlenecks[END_REF]). Pedestrian flow is thus enhanced by maintaining the crowd's competitiveness in-between these two regimes, where the exit capacity reaches its peak value. Previous numerical studies of evacuation dynamics have also considered crowds with heterogeneous behaviours [START_REF] Heliövaara | Patient and impatient pedestrians in a spatial game for egress congestion[END_REF][START_REF] Parisi | Human-ant behavior in evacuation dynamics[END_REF][START_REF] Nicolas | Statistical fluctuations in pedestrian evacuation times and the effect of social contagion[END_REF]. These behaviours are split into two categories: cooperative vs non-cooperative ‡. Non-cooperative behaviour was found to limit the evacuation efficiency owing to the formation of clogs and jams, but purely cooperative behaviour was also suboptimal, because of the placidity of the agents. The fastest evacuations were achieved by mixed crowds, with an optimal mixture of agents.

In this contribution, we examine a somehow counter-intuitive way to accelerate bottleneck flows of highly competitive crowds and grains prone to clogging: Instead of varying the fraction of cooperators within a crowd, we consider a given homogeneous non-cooperative population and bring in more entities. Naïvely, one might expect that the evacuation will then always take longer, because the assembly is larger. However, given that clogs are due to force-bearing contacts at the bottleneck, the injection of entities (pedestrians or grains) that shun contacts may actually limit these clogs. We ‡ The behaviours are called 'patient' and 'impatient' in [START_REF] Heliövaara | Patient and impatient pedestrians in a spatial game for egress congestion[END_REF], while ant-like vs human-like strategies are considered in [START_REF] Parisi | Human-ant behavior in evacuation dynamics[END_REF].

show that such dilution among contact-averse entities can effectively lead to a quicker evacuation of the original system, even though overall more entities need to escape. We start by exposing some theoretical arguments to support the possible occurrence of this paradoxical effect in Sec. 2. Then, we test it in a cellular automaton model for pedestrian evacuation through a bottleneck in Sec. 3 and a related agent-based model (operating in continuous space) in Sec. 4. Finally, in Sec. 5, we report on granular hopper flow experiments with a mix of magnetic and neutral (non magnetic) disks, in which the magnetic disks play the role of contact-averse entities.

Theoretical principle

The theoretical idea underlying the method proposed is easy to grasp. Consider an assembly of N discrete bodies (e.g., pedestrians), n of which are prone to contact (that is, highly competitive in the case of pedestrians) while the remaining m = N -n are not. Let T (n, m) be the total time needed for evacuation through a bottleneck of width w. For a large crowd (N ≫ 1), in the absence of macroscopic segregation, it is fair to approximate T as

T (n, m) ≈ n + m J m m+n
, where J(c m ) is the steady-state flow rate for a well-mixed assembly made of a fraction c m = m m+n ∈ [0, 1] of contact-averse bodies. For crowds, the experimentally observed 'faster-is-slower' effect [START_REF] Pastor | Experimental proof of faster-isslower in systems of frictional particles flowing through constrictions[END_REF] suggests that J may increase with rising c m near c m = 0 §. Therefore, the minimum evacuation time T at fixed n will not necessarily be reached for m = 0. Taking the continuous limit m ∈ R, one can write

∂T ∂m n = J (c m ) -(1 -c m ) J ′ (c m ) J 2 (c m ) .
Any extremum of T reached for c m ∈ (0, 1) should obey

J (c m ) -(1 -c m ) J ′ (c m ) = 0. d dc m [(1 -c m ) J(c m )] = 0
It follows that the evacuation time of the contact-prone entities will be extremised at c m > 0, i.e., in the presence of other people, if the partial flow rate (1 -c m ) J(c m ) is non-monotonic. For instance, should J(c m ) be strongly reduced due to clogs when c m → 0, this condition will be met.

This raises two questions. First, beyond its theoretical possibility, can such reduction of delays at bottlenecks through 'dilution' actually occur in realistic settings? Secondly, can the proposed mechanism be implemented concretely for practical applications? The following sections address the first question, while the second issue will be touched upon in the conclusion.

To address the problem quantitatively, in addition to the global evacuation time T and flow rate J, we will inspect the series of exit times t i , with i ∈ [1, N ], and compute the time gaps τ i = t i -t i-1 between successive egresses, where i ∈ [2, N ], as well as the time gaps θ j = t σ(j+1) -t σ(j) between egresses of contact-prone entities, where σ(j) is the egress rank of the j-th such entity and j ∈ [2, n]. Note that the global evacuation time is given by

T (n, m) = t 1 + N i=2 τ i = t σ(1) + n j=2 θ j ,
so, for large n, the mean evacuation time per contact-prone (competitive) entity is given by θ ≃ T (n,m) n .

Cellular automaton model for pedestrian evacuation through a bottleneck

We start by exploring the validity of the idea exposed in the previous section with a cellular automaton developed by some of us [START_REF] Nicolas | Statistical fluctuations in pedestrian evacuation times and the effect of social contagion[END_REF]. The model was shown to semiquantitatively reproduce the experimental pedestrian-scale dynamics [START_REF] Pastor | Experimental proof of faster-isslower in systems of frictional particles flowing through constrictions[END_REF] of pedestrian flows through a narrow door, notably the statistics of time gaps between escapes.

Here, we consider a crowd of n highly competitive (impatient) pedestrians and m patient agents, all of whom wish to evacuate through a door of width L d . Patient and impatient agents are characterised by a propensity to cooperate Π that is uniformly distributed in the intervals (0.8, 1) and (0, 0.2), respectively.

Brief description of the cellular automaton model

To make the paper self-contained, we briefly recall the main features of the model. Space is discretised into a square lattice with at most one agent per site. At each time step, (1) each agent behaves either cooperatively (with probability Π) or competitively (with probability 1 -Π);

(2) all agents select a target site among the four adjacent sites (von Neumann neighbourhood) plus the current one, with probabilities that depend on the proximity of the sites to the exit and a strong preference for empty sites. The probability to select the current site, i.e., to choose to stay on site, is strongly reduced if the agent behaves competitively. (3a) if the target site is occupied, the agent just waits; (3b) otherwise, he/she moves to it, unless other agents are competing for it (in which case no one moves).

(4) Following this first round of motion, some sites have been freshly vacated, which may allow waiting pedestrians to move to their target site. Steps (3) are iterated until all possibilities of motion have been exhausted.

The iterative rule (3) allows the formation of files of moving pedestrians, without voids. Note that agents cannot move more than once during a time step and that rule (3b) corresponds to the limit of strong friction, where any competition for a site is counterproductive.

Results

We consider a crowd of N = n + m agents, where n = 6, 000 will be kept fixed while m will be varied, and simulate its evacuation through a door of the width of two agents, i.e., L d = 2.

Figure 1(a) shows that the mean evacuation time per competitive agent θ increases with m for L d = 2. This implies that the simulated evacuation lasts longer as more patient agents are inserted. Thus, the dilution strategy fails to substantially fluidise the flow. It may be worth mentioning that we had come to a similar conclusion in previously published controlled experiments in which a mixed crowd made of polite and selfish agents evacuated through a narrow door. Indeed, the outflow was found to slow down as the fraction c m of polite participants in the crowd increased [START_REF] Nicolas | Pedestrian flows through a narrow doorway: Effect of individual behaviours on the global flow and microscopic dynamics[END_REF]. This observation should be put in parallel with the absence of long-lasting clogs in the evacuation of the purely selfish crowd (c m = 0): For the chosen door width, as a result of the safety prescriptions, the participants did not behave competitively enough to make the evacuation dynamics strongly intermittent.

In our simulations, the delay induced by the addition of m patient agents in the crowd is confirmed by plotting the complementary cumulative distribution function (CCDF) P > (θ) = ´∞ θ p(θ ′ ) dθ ′ , where p(θ) is the probability density function of time gaps between competitive agents. Note that θ can be deduced from the CCDF via θ = ´∞ 0 P > (θ ′ ) dθ ′ . As can be seen in Fig. 1(b), larger time gaps θ become more frequent as the fraction of patient agents c m = m N increases. In light of the failure of the fluidisation strategy for L d = 2, we consider an even narrower door, L d = 1, which should lead to even more clogging. This narrowing considerably affects the results. The evacuation time θ per competitive agent then seems to be reduced as patient agents are introduced in the crowd and reaches its minimal value for a fraction c m > 0 [Fig. 2(a)]. However, despite the large crowd (N > 6, 000), very large fluctuations occur between realisations under the same conditions, typical of clogged flows, which hampers a clear appraisal of the evolution of θ with c m . Here, the seemingly erratic outliers at surprisingly large values of θ originate in the fortuitous encounter of extremely competitive agents (Π → 0) at the door. Therefore, we turn to an inspection of the CCDF P > (θ) in Fig. 2(b). While the addition of patient agents (larger c m ) still increases the overall frequency of moderate to long time gaps θ between competitors (θ > 10), it results in rarer very long clogs (leading to θ > 30), as the doorway is less likely to be blocked by an encounter between extremely competitive agents. Even though such clogs are rare events, they are so long that they significantly reduce the flow rate. The strategy of introduction of patient agents thus succeeds in fluidising the competitors' flow via the alleviation of these long clogs.

Agent-based model for pedestrian dynamics

Brief description of the model

In the previous section, flow enhancement through the incorporation of polite agents was proven possible within a lattice-based model, which had been calibrated for the evacuation of homogeneous crowds. To test the robustness of these predictions, we now investigate a second model for pedestrian evacuation dynamics. This model, introduced in [START_REF] Dossetti | Behavioral effects in room evacuation models[END_REF], operates in discrete time and continuous space, and it also considers the influence of different individual attitudes. Agents are modelled as hard disks of diameter d = 1 and continuously make decisions about how to move in a changing environment. When possible, they step into free space but, if little space is available, they adopt a behaviour that is either patient (cooperative strategy) or impatient (competitive strategy). Patient agents will only attempt a move if some distance µ = µ m , with 0 < µ m < 1 is available in the desired direction, whereas their impatient counterparts will try to move as soon as they see a distance µ = µ n in this direction, with 0 < µ n ≪ µ m . We will vary µ n while keeping µ m = 0.6 fixed. The desired direction is drawn randomly within a window of angular width η around the direction towards the exit or, if it is obstructed, one of the two perpendicular directions.

More precisely, at the beginning of the evacuation, N pedestrians are randomly distributed (without overlaps) in a square room of size L, with an exit in the middle of one of the walls. At each time step, (1) every agent considers a move towards the exit, with a small random angular fluctuation of standard deviation η = π/8 around the direction of the exit; (2a) if the gap distance D to the nearest obstacle (e.g., another agent) along the desired direction is larger than µ (which depends on the strategy), the agent attempts a forward step of size min(1, D ); (2b) otherwise, the agent considers a lateral move to the right or to the left, within η of the perpendicular to the exit direction; (2c) if the gap distance D ⊥ to the nearest obstacle along that direction is larger than µ, the agent attempts a lateral step of size min(1, D ⊥ );

(3) Once all individuals have defined their desired moves, conflicts may arise if these moves lead to collisions; they are settled by randomly selecting a winner among the rivals and letting her move.

(4) all agents move to their new positions. The update dynamics are synchronous.

Results

Let us first consider a purely competitive population with N = n = 1000 agents (while m = 0), and on the other hand a purely cooperative population with N = m = 1000 (n = 0). Figure 3(a) shows that, as expected, the addition of x agents of the same type as the original ones to either of these populations lengthens the evacuation: T (1000 + x, 0) and T (0, 1000 + x) grow monotonically with x. In contrast, when x cooperative agents are inserted amidst the competitive population, the evacuation time T (1000, x) is found to decrease for small x and reaches a minimum close to x = m ⋆ ≈ 50. For x > m ⋆ , the delay associated with the egress of the cooperators is no longer compensated by the higher flow rate, and the evacuation time increases with x. The effect is better shown in Fig. 3(b), where we plot the evacuation time per competitive agent θ ≡ T (n, m)/n as a function of m for fixed n = 1000. The effect holds for the three different values of the minimal distance µ n that we have tested.

Figure 4 shows how the fluidising effect of cooperators depends on the door width L d .

The effect disappears for a door wider than 3 agents, which is rather similar to our findings with the cellular automaton (where the effect disappeared for a door width L d = 2). Conversely, the peak reduction in evacuation time, relative to the situation without cooperators, is enhanced from 1% to 2% (approximately) when the door is reduced from L d = 2 to 1.75. The main reason for this trend is the strong increase in the propensity for clogs when the door narrows down [note, in particular, the related increase for m = 0].

Finally, the dependence of θ ≃ T (n, m)/n on the number n of competitive agents to be evacuated is studied in Fig. 5. The relative reduction in evacuation time seems to be enhanced for larger crowds (larger n).

All in all, the agent-based model corroborates the results obtained with the cellular automaton.

Hopper flow experiments with magnetic and non-magnetic disks

Having validated the proposed speeding-up method in two distinct models for pedestrian dynamics, we now test it in a granular hopper flow experiment.

We studied the flow of mixed magnetic and neutral (non magnetic) disks through a two dimensional (2D) vibrated hopper, sketched in Fig. 6. The setup was previously used in [START_REF] Nicolas | Influence of selfish and polite behaviours on a pedestrian evacuation through a narrow exit: A quantitative characterisation[END_REF]. The magnetic disks have parallel magnetic moments so that they repel each other and thus act as contact-averse entities; their magnetic interactions become very small (compared to friction) for distances larger than 1 disk diameter and practically negligible beyond 3 or 4 diameters. In contrast, neutral disks interact purely mechanically and have a stronger tendency to clogging.

As a matter of fact, the study of the hopper flow of magnetic and non-magnetic disks is a topic worthy of interest per se. Surprisingly, these systems have never been investigated. Some pioneering studies bore on magnetic grains in a silo [START_REF] Lumay | Controlled flow of smart powders[END_REF], or the hopper flow of only magnetic disks [START_REF] Lumay | Flow of magnetic repelling grains in a two-dimensional silo[END_REF][START_REF] Hernández-Enríquez | Discharge of repulsive grains from a silo: experiments and simulations[END_REF]. In the latter case, however, no vibrations were applied to the setup and permanent clogs were observed.

Beyond the intrinsic relevance of the granular system, it is interesting to recall the analogy that has been pointed out between granular hopper flows and pedestrian evacuations [START_REF] Zuriguel | Clogging transition of many-particle systems flowing through bottlenecks[END_REF][START_REF] Nicolas | Influence of selfish and polite behaviours on a pedestrian evacuation through a narrow exit: A quantitative characterisation[END_REF]. In fact, in our experiment, magnetic disks mimick patient or polite pedestrians (due to their tendency to avoid frictional contacts), while neutral disks resemble competitive pedestrians. A subtle difference between the granular and pedestrian systems is that magnetic disks will not be repelled by neutral ones. Therefore, in some sense, they are less cooperative than polite pedestrians. Apart from this subtlety, the analogy between pedestrian and granular flows gains practical relevance if one calls to mind the risk associated with conducting pedestrian experiments under conditions that favour large delays at bottlenecks such as those observed in highly competitive crowds .

Experimental setup and data analysis

We start by describing the setup in detail. Magnetic disks are about 1 mm-thick and consist of a circular plastic cap of 13 mm of diameter, mounted on a commercial Neodyme magnet of smaller diameter; they weigh 0.55g ± 0.01g. For the neutral disks, the magnet is replaced by a bronze washer and the total weight is 0.58g ± 0.01g ¶.

During the experiments, disks are confined between a tilted chipwood panel (at the bottom) and a transparent plastic sheet. Thin plastic bars between the panel and the sheet define a hopper geometry by delimiting a 2D funnel-like region, with an aperture of width w =3 cm (i.e., 2.3 disk diameters) and an opening angle of 58 • (see Fig. 6).

The setup is subjected to (in-plane) vibrations, with an amplitude of about 3-6 mm and a frequency of around 10 Hz. To this end, a motor equipped with an unbalanced helix was tied underneath the panel. The latter was carefully polished and varnished to reduce the friction coefficient and make it as homogeneous as possible. The static friction coefficient between disks and panel was about µ s ≃ 0.32, which corresponds to an angle of friction ψ = tan -1 (µ s ) ≃ 18 • ; the plane of the hopper is tilted by an angle roughly equal to (but slightly smaller) than, µ s . Still, since vibrations tend to suppress friction, sliding is possible. At the beginning of each experiment, n neutral (non-magnetic) disks and m magnetic ones (with typically N ≡ m + n of order 300) are inserted from the top of the funnel, in random order, and the setup is vibrated for ten seconds before the start. The error in the number of inserted disks is generally lower than 2%, i.e., 1-6 disks out of 300.

Experiments are filmed with a 60 Hz camera placed above the aperture + . Egresses of disks through the aperture are detected manually with the help of a computer-aided routine (similar to that used in [START_REF] Nicolas | Influence of selfish and polite behaviours on a pedestrian evacuation through a narrow exit: A quantitative characterisation[END_REF][START_REF] Nicolas | Pedestrian flows through a narrow doorway: Effect of individual behaviours on the global flow and microscopic dynamics[END_REF], following [START_REF] Garcimartín | Experimental evidence of the faster is slower effect[END_REF][START_REF] Pastor | Experimental proof of faster-isslower in systems of frictional particles flowing through constrictions[END_REF]), which constructs time frames of escapes by extracting a line of pixels just past the exit from every frame of the video and stitching these lines together (an example of such a time frame is shown in Fig. 6(c)). The analysis gives access to the series of exit times t i , i ∈ [1, N ], and to the time gaps τ i and time gaps θ i between the egresses of neutral disks.

The granular flows observed experimentally display highly intermittent dynamics, as shown in Fig. 7, with broadly distributed time gaps τ . In particular, long halts due to clogs are observed. To avoid excessive delays, we artificially destroy clogs of duration τ > 15 s, by introducing a plastic bar in the setup. This procedure does not affect the distribution of time gaps p(τ ), nor the CCDF P > (τ ) = ´∞ τ p(τ ′ ) dτ ′ , for τ < 15 s, but it has an impact on the global flow rate J = ´∞ 0 P > (τ ) dτ -1 . Accordingly, we define the capped time gaps between egresses of disks, τ i = min(15 s, τ i ), or neutral

Examples include some emergency evacuations [START_REF] New | Terrific tragedy in chile; two thousand five hundred persons roasted to death in a church[END_REF] as well as the huge clog formed at the gate of a stadium in the 2013 running of the bulls in Pamplona. ¶ The slightly smaller weight of the magnetic disks may be thought of as an additional sign of cooperativeness, as it results in a slightly smaller sliding speed (on average) than that of the neutral disks, in the absence of collective interactions. + Videos are provided as Supplemental Material; in particular, they show how magnetic interactions can help to break the clogging arches.

disks only, θ j = min(15 s, θ j ). The corresponding capped global and neutral flow rates read

J = N -1 n i=2 τ i and J n = n -1 n j=2 θ j . (1)
These capped flow rates are unaffected by our manual destructions of clogs and, were there no clogs that last longer than 15 s, they would match their bona fide counterparts, i.e., J = J.

Stationarity of the flow

To examine the stationarity of the flow, we compare the CCDF P > (τ ) computed for subparts of each experiment, namely, for the first, second, and third N/4 grains, where N = n + m is the total number of grains. For experiments with c m < 0.5, no significant difference is seen between these moving averages. If one discards the last 15% of grains, the flow can be regarded as stationary, even though the number of grains in the hopper varies during the experiment. Consistently with Beverloo's law for non-vibrated systems [START_REF] Beverloo | The flow of granular solids through orifices[END_REF], the flow rate is indeed independent of the column height (as long as it is a couple of times larger than the width). In contrast, for c m = 1, the flow is smoother (less intermittent); it is strongly non-stationary and monotonically decreases with time, as the height of the granular layer declines. Indeed, (frictional) force chains are absent in this purely magnetic case, and the pressure at the bottom thus continuously decreases during the experiment. In the following, we restrict our attention to situations with c m < 0.5, in which quasi-stationarity is achieved. For the same reason, the last 50-52 disks of each realisation will be discarded. Table 1. Capped total and neutral flow rates, J and Jn, for different fractions cm. For the sake of exhaustiveness, we also report the associated mean (capped) time intervals between egresses of disks ( τ ) or neutral disks ( θ ). in our pedestrian crowd models (see previous sections). This observation may be associated with our remark that magnetic disks are 'less polite' than their pedestrian counterparts, because they do not spontaneously avoid contact with neutral disks.

Analysis of the results

These results were obtained by comparing experiments at different fractions c m in which the same total number of disks, N , is discharged. Similar conclusions are reached if one chooses to compare segments of the experiments corresponding to the discharge of a given number of neutral disks n (while discarding the initial and final transients, i.e., the first 70 grains and the last 50 ones, approximately). The neutral CCDFs thus obtained are plotted in Fig. 9(b).

The capped neutral flow rates J n shown in Table 1 confirm the significant speed-up of the neutral flow J n (c m ) for c m = 0.4, viz., J n (0.4) > J n (0.2) ≈ J n (0), both at fixed N and at fixed n.

Summary and outlook

In summary, we have studied a strategy to enhance the efficiency of pedestrian evacuations through a narrow door, prone to clogging, by introducing contact-averse particles in the system. This strategy is somewhat counterintuitive insofar as more agents then need to escape to complete the evacuation of the original system. Still, using two distinct models for the evacuation dynamics of pedestrian crowds, one based on a lattice and the other one operating in continuous space, we found that the positive effect of the reduction of long clogs (caused by the encounter of competitive agents) could prevail over the negative effect due to the increase of the crowd size, when the door is very narrow. Moderate reductions in the evacuation times were then observed. On the other hand, for wider doors, the strategy is not operational: It heavily relies on the propensity to clogging displayed by the original system.

On the basis of the established similarities between competitive pedestrian evacuations and granular hopper flows, we then turned to an experimental test of the proposed strategy. The role of contact-averse agents was played by magnetic disks, which interact repulsively with each other, while the original system was made of neutral disks flowing through a two-dimensional hopper subjected to vibrations. When a fraction of around 40% of magnetic disks was introduced, we observed a faster decay of the distribution of time gaps between consecutive egresses of neutral disks, hinting at an effective enhancement of the flow of the original system. This effect was above the level of experimental noise and robust to variations in the total number of disks.

Having summarised our findings and shown the technical validity of the proposed strategy, we now wonder about their practical relevance. Regarding granular systems, one of the drawbacks of the method is that it cannot directly be transposed to three dimensions, where magnetic interactions would not be only repulsive. But one could contemplate the incorporation of soft frictionless particles, which are much less prone to clogging than their hard frictional counterparts [START_REF] Hong | Clogging of soft particles in two-dimensional hoppers[END_REF], instead of magnetic disks.

Turning to crowds, it should be borne in mind that our study is based on simplistic models: Any extrapolation to real crowds, though sensible, is speculative. Besides, in practice it is not possible to introduce polite pedestrians at the last moment, should an emergency occur. Nonetheless, our findings tentatively suggest that the presence of a small number of attendants trained to keep calm during emergencies (such as safety officers), despite making the crowd slightly larger, might be beneficial in terms of evacuation efficiency even if these agents do not modify the behaviour of the rest of the attendants.

Figure 1 .

 1 Figure 1. (Colour online) Pedestrian bottleneck flow through a door of size L d = 2 simulated with a cellular automaton. (a) Variation of the mean escape time θ = T /n per competitive agent with the fraction of cm. Each cross corresponds to one realisation of an evacuation of n = 6, 000 competitive agents. (b) Survival function (CCDF) P>(θ) of time intervals θ between competitive agents for different fractions cm.

Figure 2 .

 2 Figure 2. (Colour online) Pedestrian bottleneck flow through a door of size L d = 1 simulated with a cellular automaton. (a) Variation of θ with cm. Each cross corresponds to one realisation of an evacuation of n = 6, 000 competitive agents. (b) Survival function P>(θ) for different fractions cm.

Figure 3 .

 3 Figure 3. Evacuations of N pedestrians through a door of size L d = 2d in the agent-based model. (a) Global evacuation times for a purely competitive crowd (N = n = 1000 + x), a purely cooperative one (N = m = 1000 + x) and a mixed one, (N = n + m, n = 1000 and m = x). Here µn = 10 -4 and µm = 0.6 (b) Evacuation times per competitive agent for a mixed crowd composed of 1,000 competitive agents and m cooperative ones, as a function of m, for distinct minimal distances µn.

Figure 4 .Figure 5 .

 45 Figure 4. Dependence on the door width L d of the evacuation times per competitive agent θ ≃ T /n for a crowd composed of 1,000 competitive agents (µn = 10 -4 ) and m cooperative ones, as a function of m, in the agent-based model.

Figure 8 (

 8 Figure 8(a) presents CCDFs P > (τ ) of all time gaps τ (irrespective of the nature of the disks) for the 3 realisations performed for each fraction of magnetic disks: c m = 0, c m = 0.2, and c m = 0.4. The experimental data are noisy, but what clearly appears above the noise level is that the CCDFs for c m = 0.4 decay faster than those for c m = 0.2, which decay faster than those at c m = 0. The difference appears more clearly if data from realisations under the same conditions are aggregated [Fig. 8(b)].However, we are not interested in the total flow rate, but only in enhancing the flow of the neutral disks. Therefore, we now discard the magnetic disks and consider the time gaps θ n between consecutive neutral disks; the CCDFs of the corresponding aggregated data are plotted in Fig.9(a) with envelopes containing all values of P > found in the different realizations (from the lowest one to the largest one). One can see that the neutral CCDFs decay faster for c m = 0.4 than for c m = 0; results for c m = 0.2 (not shown) are virtually indistinguishable from those obtained for c m = 0, within the experimental error bars. Thus, introducing 40% of magnetic grains reduces the time gaps between egresses of the neutral grains and, as a consequence, speeds up the outflow of the latter. This confirms the validity of our fluidisation strategy in granular hopper flows. It is interesting to note that the fraction c m of magnetic ('polite') particles leading to neutral flow enhancement is larger than what we found

Figure 6 .

 6 Figure 6. (Color online) Experimental setup and video analysis. (a) Sketch of the setup. (b) Snapshot taken during the discharge of the hopper, close to the aperture. (c) Time frame obtained by stitching lines of pixels extracted from successive video frames (this line is marked in orange in panel b), as described in the main text, and manual tagging of the image.

Figure 7 .

 7 Figure 7. Time series of the time gaps τ i between successive egresses, labelled by their order of egress i, for (a) cm = 0 and (b) cm = 0.4. Note that the time gaps τ i which reach the upper bound of the window (15 s) correspond to long-lived clogs that were eventually destroyed manually.

Figure 8 .

 8 Figure 8. (Colour online) Survival functions of the time gaps τ between successive egresses (a) for every independent realisation. (b) for the aggregated data, grouped according to the fraction cm.

Figure 9 .

 9 Figure 9. (Colour online) Survival functions of time gaps θ between the egresses of consecutive neutral disks. (Data corresponding to realisations under the same conditions have been aggregated.) (a) For the 3 fractions cm of magnetic disks under study. (b) For cm = 0 and cm = 0.4, with envelopes (hatched regions) stretching from the lowest value of P>(θ) obtained over the set of realisations to the largest one, for every θ (three realisations for each condition). (c) Same as panel (b), but this time the analysis is performed over the time window associated with the discharge of a fixed number of neutral disks, n = 180, instead of a fixed total number of disks, N = 300.

§ Videos of the clogs obtained in this limit can be found on the internet, e.g. at https://www.youtube.com/watch?v=OCKO0c6lihU