Yorgos Rizopoulos
email: yorgos.rizopoulos@univ-paris-diderot.fr

Economic nationalism: Constrained and fragmented, if any?

Keywords:

In this contribution, the meaning of economic nationalism and the possibilities of pursuing nationalist policies in the context of increasingly interdependent economic processes are discussed. Economic nationalism need not solely be affiliated with statist protectionism, while very few states dispose the necessary economic, social, political and institutional conditions to influence economic policy given the long-term tendencies that undermine nationalist wills (empowerment of supranational bodies, internationalization of production, deindustrialization). Even these states are not monolithic and the pattern of business/government relations in different fields would have a critical influence.

Nationalist-type policies would probably be fragmented, followed in some specific domains under powerful constraints.

Introduction

"A spectre is rising", The Economist, February 5th, 2009.

Following the 2008 crisis, economic journals and specialized media repeatedly warn of the 'rising spectre' of economic nationalism. Indeed, trends of economic nationalism have crept into the economic policies and different states are taking measures supposed to promote the interests of national economies and to preserve their autonomy in an increasingly internationalized world. Such policies appearand are justifiedas a counter-movement to the unrestricted mobility of capital, goods, and services and, to a very lesser extent, labour. A widespread feeling is that globalization favours and legitimates the interests of big multinational firms and of wealthy international elites, against those of the majority. Many studiesincluding those of international organizations as the International Monetary Fund [START_REF] Imf | Globalization: A brief overview[END_REF] point out that globalization, financialization and neo-liberal policies have increased unemployment and inequality [START_REF] Dreher | Has globalization increased inequality?[END_REF][START_REF] Haskel | Globalization and U.S. wages: Modifying classic theory to explain recent facts[END_REF] to such a degree that it is slowing down economic growth. More, the operation of free markets has led to economic financial instability (Mendoza and Quadrini, 2010). Even in rich states, persistent and institutionalized forms of poverty have appeared [START_REF] Kiely | Globalization and poverty, and the poverty of globalization theory[END_REF].

National-interest oriented policies seem to be the answer and President Trump asserts that protection will lead to prosperity and strength (CNN Politics, 2017). But, does it make sense to talk about economic nationalism in the context of a world economy which is still heterogeneous but involves strong interdependencies between national economies? What could be its meaning, rational, forms and consequences?

As a first step, it is relevant to outline the conditions for pursuing comprehensive nationalist economic policies. Indeed, the definition and application of such policies imply some interlinked conditions. Among others, big and powerful countries with a high degree of sovereignty, a relative autonomy of national economic processes, social and political forces with strong bargaining power whose interests converge and crystallize at the national level, institutional arrangements enabling the coordination between the political and economic spheres, relevant administrative skills and a capacity for coherent action by the government. Very few countries meet these conditions and, even then, structural factors seem to greatly diminish the scope of nationalist policies. This inflicts to nuance the rhetoric concerning the "spectre" of generalized commercial wars. The current desire to rebalance relations with internationalized capital is probably the backlash to an unbridled laissez-faire period, more than the manifestation of wide-range nationalist economic strategies.

Concerning the meaning of economic nationalism, many scholars put into question its assimilation with protectionism and statism [START_REF] Cohen | Crossing frontiers: Explorations in International Political Economy[END_REF][START_REF] Shulman | Nationalist sources of international integration[END_REF][START_REF] Helleiner | Economic nationalism as a challenge to economic liberalism? Lessons from the 19th century[END_REF][START_REF] Helleiner | Economic nationalism in a globalizing world[END_REF][START_REF] Gonzalez | Between economic nationalism and economic liberalism: An alternative view[END_REF][START_REF] Clift | Economic patriotism: reinventing control over open markets[END_REF][START_REF] D'costa | Globalization and economic nationalism in Asia [Online[END_REF]. Liberal policies may be motivated by national interests and quite a few historical examples show that free trade and national quest of power can go hand in hand. So, if there is any economic nationalism, a finer and more rigorous representation of its very essence is needed.

Furthermore, states can no longer be considered as monolithic entities [START_REF] Rhodes | Understanding governance ten years on[END_REF] and the business/government interactions on which the adopted policies depend are sufficiently differentiated in each issue-area [START_REF] Brewer | An issue-area approach to the analysis of MNE-Government relations[END_REF][START_REF] Grosse | The bargaining view of government-business relations[END_REF][START_REF] Levy | Bargains old and new: Multinational corporations in global governance[END_REF][START_REF] Bonardi | Corporate political strategies for widely salient issues[END_REF][START_REF] Rizopoulos | MNEs and policy networks: Institutional embeddedness and strategic choice[END_REF] to generate diverse attitudes, or even inconsistencies, between policy-making domains. This means that ad hoc actions, depending on the ability of interest groups to highlight their specific concerns as national priorities, often substitute for economic policies serving a global project.

The paper is structured as follows. In the next section, the meaning of economic nationalism is briefly discussed based on the teachings of the academic literature. Next are presented the factors that undermine the sovereignty of countries and the impact of differentiated business/government relation patterns in various issue-areas is underlined.

It is argued that fragmented contingent measures are probably the current form of national-interest oriented policies. The last section draws some conclusions.

The Meaning of Economic Nationalism: Protectionist, Statist or Liberal?

"As American business and the American military move about the world, we are relearning the old wisdom that "business follows the flag.". Our efforts to build security and your efforts to build prosperity have become increasingly synergisticto the benefit of millions around the globe. When our diplomats and military forces combine to help create stability and security in a nation or region, that same stability and security attracts investment. That investment, in turn, generates prosperity."

Cohen, W. S., US Secretary of Defense, Remarks at Fortune 500 Forum Dinner Keynote. Pittsburgh, PA (October 16, 1998).

Generally speaking, economic nationalism is the pursuit of national interests through economic means and it "should be considered as a set of practices designed to create, bolster and protect national economies in the context of world markets" (Pryke, 2012, p. 285). Its crucial element is that national identities should determine economic policies. However, this term is usually used in a narrower sense to describe statism and mercantilist policies; Protectionism in the trade area (tariff and non-tariff barriers), industrial policy measures to subsidize key industries with either state finance or by using administrative measures and taxation, restrictions on entry of multinational corporations preventing domestic firms from foreign competition, but also political pressure on domestic firms and shaping of the conditions in which private capital and market mechanisms operate. In other words, defensive protectionism is deemed as nationalism, free trade not. This seems to be a bias.

When [START_REF] List | The national system of political economy (trans. S. Lloyd)[END_REF] -concerned with the interests of the (relatively weak) Germany -argues that protectionism ensures industrial development, that it has spillover effects throughout the economy as it is the basis of military power and, as a consequence, states should direct and protect the economy for the good of the nation, this is obviously considered as nationalism. The objective is to accumulate wealth and enhance power given that relative national gain is more important than mutual or aggregate gain. Conversely, when Smith and Ricardo advocate free trade, they stress the harmony of interests not the dominance of British industry over the rest of the world.

Laissez-faire appears as favoring mutual economic benefitat least from a static comparative advantage perspective -while List's protectionism or Fichte's "closed commercial State" imply that cost-benefit analysis becomes a secondary issue concerning economic policy. Priorities are defined by national identity, eventually by bearing short-term economic costs for the building of latecomer national states, and their search for power in international relations 1 . However, free trade and mobility of capital may serve the interests of some (powerful) States or, more precisely, the interests of their economic, political and military elites. Pax britannica and, later on, pax americana are clearly an expression of economic nationalism in the interest of the British Empire and the USA respectively, as the above quotation of the US Secretary of Defense clearly shows.

Generally, nationalism is assimilated to statism, protectionism and costly selfinterest attitudes, while free trade and capital movements are presented as liberal policies to enhance an open efficient world, bringing mutual benefits and wealth.

Nevertheless, even during the 19th century, different views have been developed. For instance, Hegel's economic nationalism (patriotism) also departs from economic 1 Debates concerning economic policy and the conditions of building the national State in the US focus also on free trade versus restriction of imports, and isolationism (peaceful nationalism) versus expansionism. More recently, quite successful protectionist East Asian policies during post World War-II period (including the discouragement of foreign direct investment) lend support to the idea that economic nationalism involves necessarily protectionism.

liberalism but involves international expansion and colonization/emigration (Nakano, 2004b;[START_REF] Plant | Hegel and political economy[END_REF]. Later on, Lenin's analysis of imperialism points out the tight link between national interests of advanced states and a, usually violent, international expansion at the expense of weaker nations.

So, the first point to clarify is that economic nationalism does not always join protectionism. Nowadays, the aim of promoting local industries can lead governments to lift certain trade barriers and encourage foreign direct investment. Since the early 1990s, China has evolved away from concerns about protecting the home market toward favouring the expansion of domestically and internationally competitive firms. The obligations of WTO membership have actually pushed China towards a more sophisticated form of economic nationalism. Some authors talk about "aggressive economic nationalism" (D'Costa, 2012) to signify policies encouraging national businesses abroad. Also, in view of the difficulties caused by capital movement liberalization, most Asian countries, apart from Malaysia, instead of seeking capital controls, they chose to build up reserves through current account surpluses [START_REF] Singh | Globalisation, openness and economic nationalism: Conceptual issues and Asian practice[END_REF]. Encouraging national businesses abroad and liberalization of the markets may aim to increase the power of the nation-state. Therefore, economic nationalism need not solely be affiliated with protectionism. Nationalist aspirations of autonomy, unity and identity can lead to both economic closure and openness [START_REF] Shulman | Nationalist sources of international integration[END_REF]. The crucial point is the reciprocal relationship between the political and economic power of the nation-state (Nakano, (2004a).

Another interesting distinction made by the international economic relations literature is between protectionism which limits foreign presence in the domestic market and state interventionism which can merely provide aid to national companies without limiting foreign competition per se. In other words, conversely to the widespread idea that nationalist measures cannot occur in a liberalized market, economic nationalism should not be considered as a synonym of statism either. Indeed, some authors [START_REF] Clift | Economic patriotism: reinventing control over open markets[END_REF][START_REF] Helleiner | Economic nationalism as a challenge to economic liberalism? Lessons from the 19th century[END_REF] distinguish two main forms of economic nationalism; classic protectionism and liberal economic nationalism. In their perspective, state interventionism does not appear to be a distinctive feature of closed economies, as it occurs in liberal openness policies which involve sustained state intervention. Deregulation, national rescue packages, bank recapitalizations and selective industry bailouts can be implemented. State interventionism and economic liberalism are not mutually excluded. Others, as [START_REF] Cohen | Crossing frontiers: Explorations in International Political Economy[END_REF], distinguish 'malign' and 'benign' economic nationalism; Malign nationalism seeks national goals relentlessly, even at the expense of others; benign nationalism is prepared to compromise national policy priorities where necessary to accommodate the interests of others. Another difference between these two types of nationalism lies in the willingness of a country to identify its own national interest within the stability of the overall international system. Benign nationalism acknowledges a connection between self-interest and systemic interest; malign nationalism ignores or denies it. According to [START_REF] Helleiner | Economic nationalism in a globalizing world[END_REF] economic nationalism is a changing phenomenon. Discriminatory measures through making regulation stricter and liberalization of the markets could both be considered as indicators of economic nationalism if their motivation is to increase the power of the nation-state [START_REF] Gonzalez | Between economic nationalism and economic liberalism: An alternative view[END_REF].

In this context, two aspects appear to be particularly important in assessing the chances of comprehensive nationalist economic policies; the sovereignty of nationstates and the pattern of business/government relations.

Undermined Sovereignty, Specific Business/Government Relations and

Fragmented Policies

Commitment to the sovereignty of individual states is a necessary condition for economic nationalism which presupposes that a country has the will and the means to orient economic policy in a specific direction in order to realize a collective project, that it is democratically defined or not.

The International Political Economy school of thought [START_REF] Mayall | Nationalism and international society[END_REF][START_REF] Gilpin | Global political economy, understanding the international economic order[END_REF] argues that, in spite of globalization trends, the nation-state still remains a main player in the international political and economic order. This is what [START_REF] Gilpin | Global political economy, understanding the international economic order[END_REF] calls 'state-centric realism'. But, what could be the material base of nationalist economic policies today? By what strictly national means would it be possible to improve the position of a state in the international division of labour and in the international power games? Some long-term global tendencies clearly undermine nationalist wills. Since the 1980s, capital markets liberalization and dismantling of state controls over capital flows, jointly with increasing sovereign debts, have largely shrunk the possibilities of pursuing independent national economic policies. Also, various international economic organizations are empowered to impose economic deregulation on states, regardless of whether they consider the measures to be in their national interest or not (Washington Consensus). At the same time, internationalization of production makes national productive systems dependent to the world economy. More, the deindustrialization process in some rich countries weakens old national corporatism and favours the "internationalization of the State", according to the term used by [START_REF] Cox | Social forces, states and world orders: Beyond international relations theory[END_REF]. France is an example of this tendency. One interesting expression at the institutional level is that the ministries of labour and industry2 which had built up in the context of national corporatism are henceforth subordinated to the ministry of finance which is clearly world-economy oriented.

Are there still countries sufficiently autonomous, with the appropriate social forces and institutional settings enabling the definition and deployment of nationalist economic policies? Apparently, they are very few. Some powerful states or big emerging countries involved in industrialization processes where influential interest groups have arisen may be tempted by nationalist policies, of protectionist nature (Russia) or not (China). However, even in this case, they act under powerful constraints. President Trump's apparently aggressive positions strengthen the impression of a return to mercantilism and of imminent commercial wars. Meanwhile, if we suppose that the US administration ultimately imposes new tariffs unilaterally, ignoring the rules of the WTO, the cross border activities of many American corporations would suffer. Indeed, the USA is very dependent on global value chains and a great part of American imports are in reality intra-firm trade of American multinationals, especially for complex engineering products such as aircrafts and cars. Favouring companies operating in the USA and penalizing the imports through tariffs and taxation policy may increase employment of Americans in the short-term but will also harm US firms producing abroad (and repatriating profits!) and benefit foreign firms producing in the USA. In a context where the national identity of businesses is blurred, fine tuning by targeting some specific activities seems quite difficult to operate. The rise in tariffs for some products imported from China seems more like a way to create a position of strength in a global bargaining game.

Indeed, this policy is driven by geopolitical considerations, primarily the containment of the rapidly catching-up China, rather than an intention to isolate the economy of the USA. Given the central position that the USA still occupies in the world economy, such a priority will certainly have consequences on the structure of global value chains of the American multinational firms, implying relocations to some countries like Vietnam or India which are considered rivals of China. In addition, the repatriation of certain activities is likely, particularly if fiscal incentives are adopted, as was the case in 20183 . But even if these developments have a significant impact on the modalities of globalization and show that politics may still impose constraints to firms and their profit motives, this situation is by no means a generalized commercial war.

A related question concerns the economic and social forces that could agree on a nationalist political program. An underlying assumption of economic nationalism is that the people forming a nation-state have common interests which transcend social divisions. However, social structure generates significant inequalities derived from ownership of assets, insertion to social networks, access to jobs, type of employment and levels of skill. Some interest groups may have sufficient bargaining power to impose discretionary nationalist policies generating private profits, while the majority of citizens do not benefit equally from them. As an example, the state could assume the entrepreneurial risks and facilitate the prosperity of certain businesses which recover alone the profits without any spillover effects. Globalization has precisely accentuated social and economic differentiation [START_REF] Imf | Globalization: A brief overview[END_REF] and, as a consequence, social alliances to support comprehensive economic nationalism are generally weak.

Another critical point is that economic nationalism implies a strong coordination between economic and political actors and tight relations between firms and the state.

Generally, business/government relations rely on multiple interactions and interdependencies. Firms try to legitimize their goals and use the state's coercive power in order to benefit from market failures, shape the rules of the game and, whenever possible, make political priorities match their own objectives. They deploy political strategies in order to receive support by governments. In return, governments obtain otherwise inaccessible resources through relations with firms (employment, intangible assets, external economic influence…). Their links stand on this reciprocity balance and mutual resource dependency.

Many possibilities would exist between two polar situations. One is when the state acts as an autonomous actor and constraints the specific interests of the firms in the name of the national interest and the economic well-being for the majority, and the other when the state puts itself at the service of the interest groups by justifying it as being in the country's interest to do so. In all cases, there is interaction, negotiation or even conflict, and this bargaining game can be assimilated to a bilateral monopoly with uncertain outcomes depending on the stakeholders' evolving power.

An additional element has to be taken into account. States are not monolithic.

They become differentiated internally [START_REF] Rhodes | Understanding governance ten years on[END_REF], and business/government interactions are multifaceted [START_REF] Grosse | The bargaining view of government-business relations[END_REF] taking place at intermediate levels of government and policy networks [START_REF] Rizopoulos | MNEs and policy networks: Institutional embeddedness and strategic choice[END_REF]). Brewer's seminal work (1992) stresses the variety of business/government relationships across different issue-areas, [START_REF] Bonardi | Corporate political strategies for widely salient issues[END_REF] explain why interaction is situated at the issue level, while [START_REF] Levy | Bargains old and new: Multinational corporations in global governance[END_REF] underline the differences existing between the state's interventions in different domains. The understanding of eventually nationalist economic measures implies the analysis of such contingencies. 4 Interest groups, bureaucrats and politicians interact within several fields, with varying influence and evolving bargaining potential determined by the specific historical context, institutional trajectories, specific economic interests and social constraints. One can hereby predict a wide range of stakeholders' relational patterns inside a single country and, as a consequence, diverse economic policy-making outcomes or even incoherence in government actions.

An approach in terms of issue-areas seems to be also relevant concerning economic nationalism. Given its economic and geo-political situation, a country may be open in some areas and not in others. Economic nationalist-type measures are possible in some domains where even relatively weak states maintain a degree of sovereignty (because of their historical trajectory, institutional framework, etc.) and/or where powerful local actors with sufficient bargaining power succeed to legitimate their interests as being the national ones.

The recent evolution concerning attitudes related to foreign direct investment is an interesting example of the current forms of national-interest oriented policies.

According to UNCTAD (2018, p. 80), because "most countries continued to actively attract FDI in 2017, and the share of investment liberalization or promotion measures increased compared with 2016... the overall share of restrictive or regulatory investment policy measures has significantly increased in recent months and some countries have become more critical of foreign takeovers. Also, additional ways and means to strengthen investment screening mechanisms are under discussion, particularly in some developed countries… New investment restrictions or regulations for foreign investors were mainly based on considerations of national security, local producers' competitiveness or foreign ownership of land and natural resources". Parallel to this renewed will to control FDI -especially incoming mergers and acquisitionsnew models of Bilateral Investment Treaties (BIT) have been developed in order to provide greater protection for host countries and their ability to regulate multinational enterprises (MNEs), whereas previous treaties focused on the protection of MNEs. In particular, some countries have narrowed certain substantive protections of foreign investors, abandoned the umbrella clause and strengthened the essential security interest clause (which allows governments to disregard BIT commitments under certain circumstances).

Indeed, governments pay more attention to competing objectives and the consensus that all FDI is equally beneficial is changing as more governments consider (certain) mergers and acquisitions as less beneficial than greenfield investments. They may encourage more sustainable FDI, i.e. investment that makes a real contribution to economic, social and environmental development and takes place within mutually beneficial governance mechanisms while being commercially viable. Indeed, it is unclear how important BITs are to help attract FDI, while it is clear that they restrict the policy space of governments. States try to restore a certain balance in their relations with the MNEs in order to avoid the consequences of too much latitude on their part, whereas when economic activities involving national actors develop, the will to ensure the conditions of their growth can be reflected in the policies applied. Such evolutions may be interpreted as a kind of economic nationalism and political sensitivities or pressure from civil society may jeopardize some deals involving domains perceived as strategic at the national level. Meanwhile, investment liberalization is still among the prominent features of policy measures and there is no will that such decisions impede the flow of international investment. Even if we take the example of the restrictive policies related to foreign direct investment in some strategic sectors in Russia [START_REF] Balzer | The Putin thesis and Russian energy policy[END_REF],5 FDI inflows of this country remain at a high level in fast growing non-sensitive private consumption activities. Also big deals occur in sensitive sectors, when foreign firms acquire minority stakes.

The main fact is that the growth of FDI brings new players into the global markets, and their competition is not welcomed by traditional players. Some nationalistlike measures are simply favoured by economic groups in order to protect their interests. From a historical point of view, this is a quite usual phenomenon. Thus, various contributions in the 1980s and 1990s [START_REF] Bellon | L'interventionnisme libéral[END_REF][START_REF] Porter | The competitive advantage of nations[END_REF][START_REF] Reich | The work of nations: Preparing ourselves for 21st century capitalism, United States, Vintage Books A Division of Random[END_REF] attempt to account for the state's economic commitment to the competitiveness of domestic firms, justified by the process of internationalization.

The same goes for the strategic trade policies deployed in order to affect the outcome of interactions between firms in world oligopolistic markets (Brander and[START_REF] Brander | International R&D rivalry and industrial strategy[END_REF][START_REF] Brander | Export subsidies and international market share rivalry[END_REF]. At an applied micro level, [START_REF] Eden | Insiders and outsiders: Defining "Who is us?" in the North American auto industry[END_REF] analyse the strategies of the Big Three US car makers in order to influence political decisionmaking and reinforce their position as regards their Japanese competitors. Now, the only novelty is that considerations about 'sustainable' foreign investment are returning to the surface after more than two decades of laissez-faire and facilitation of international capital movements to the detriment of states' ability to influence the outcome of such movements. Some authors call this tendency "a paradigm shift from laissez-faire liberalism toward embedded liberalism… a model whereby liberalization is embedded within a wider framework that enables public regulation in the interest of domestic stability" [START_REF] Kalderimis | Investment treaties and public goods[END_REF][START_REF] Titi | EU investment agreements and the search for a new balance: A paradigm shift from laissez-faire liberalism toward embedded liberalism?[END_REF].

Conclusions

After October 2008, a number of states raised tariffs, but, compared to historical experiences as the duties imposed on imports by the USA consequently to the 1929 crisis and provoking retaliatory measures across the world,6 was not pronounced and systematic. Actually, the number of trade-restricting measures applied by governments has declined since 2009.

The calls of journalists, politicians and capitalists that there should be no return to protectionism are rhetorical rather than analysis based. The dominance of international over national capital, international interdependencies, the internationalization of production blurring national identity of businesses, the internationalization and fragmentation of the state bureaucracies within the major countries (including the ongoing crossover of personnel between high finance and public administration), the empowerment of supranational organizations, the lack of cohesion between social groups which suffer of the negative effects of globalizationand as a consequence, their lack of political powermake that even in countries which historically were strongly involved into policies driven by the national interests we observe a process of abandoning global voluntarist projects. Currently, the United States conduct policies guided by geopolitical considerations which can have significant consequences on the modalities of globalization. However, in general, the material base for classic protectionism is undermined and the probability of thorough nationalist policies is low, even if there are possibilities of:

-A more balanced approach between openness and maintaining some bargaining power at the countries' level.

-Strategic policies and selective nationalist-type measures in specific domains, when the pattern of links between business interests, civil society organizations and state bureaucracies makes it possible.

Such policies may attenuate some negative economic and social consequences of globalization and, in this sense, they are even desirable from a normative point of view [START_REF] Kobrin | The rise of nationalism, FDI and the multinational enterprise[END_REF]. Meanwhile, few states seem able to define and apply such policies. In the contemporary international context, economic nationalism, if any, would be fragmented, constrained, and probably liberal.

From 2017 there is no more ministry or state secretariat dedicated to the industry in this country.

In 2018, the large-scale repatriations of accumulated foreign earnings by United States MNEs, resulted in negative FDI outflows (UNCTAD, 2019).

For a stimulating analysis of this interactive process in Russia, see[START_REF] Yakovlev | The evolution of business-state interaction in Russia: From state capture to business capture?[END_REF]

In October 2005, Natural Resources Minister Trutnev stated that Russia should limit foreign participation in three main areas: scarce natural resources, large mineral deposits and fields close to military sites (reported inLiuhto, 2008, p. 3).

By 1939, almost half of world trade was restricted by tariffs[START_REF] Jones | Multinationals and global capitalism: From the nineteenth century to the twenty-first century[END_REF].


Adel Mesbah

Jai Prakash

Jessica C Beard

Christos D Malliakas

James A Ibers
email: ibers@chem.northwestern.edu

Syntheses and crystal structures of the Ba 7 UM 2 S 12.5 O 0.5 (M = Ti, Si/Fe) compounds

Keywords: Solid state chemistry, Crystal structure, X-ray techniques, Ba 7 UV 2 S 12.5 O 0.5 structure type

Black single crystals of the Ba 7 UM 2 S 12.5 O 0.5 (M = Ti, Si/Fe) compounds were obtained by standard solid-state chemistry method at 1123 K. Both compounds crystallize at 100 K in the Ba 7 UV 2 S 12.5 O 0.5 structure type in space group I4/mcm of the tetragonal system with a = 16.1451(3) Å and c = 9.5310(2) Å (Ba 7 UTi 2 S 12.5 O 0.5 ) and a = 16.1218(16) Å and c = 9.4103(11) Å (Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 ).

The crystal structures consist of infinite chains of U atoms octahedrally coordinated through the sharing of O/S corners along the c axis. The M atoms form isolated MS 4 tetrahedra aligned also along the c axis. The space between US 5 O and MS 4 polyhedra is filled by Ba atoms.

1.

Introduction.

Actinide chalcogenides (An =Th, U, Np; Q =S, Se, Te) form the basis for the study of interactions between the actinides (5f) and transition metals (3d). Although such An systems are well studied, those with Ak (Ak = alkaline-earth metal) are not. Examples of the latter were reported in a recent review [1]. Among them, the compounds Ba 7 UM 2 S 12.5 O 0.5 (M = Fe, V) [2] are particularly relevant to the present study. These show remarkable flexibility that allows the accommodation of two transition metals having different oxidation states in the structure. In fact V 4+ atoms are positioned in isolated VS 4 tetrahedra in the V compound, but in the Fe compound a short S-S bond leads to the formation of a Fe 2 S 8 species and charge balance of the compound. The V compound crystallizes in space group I4/mcm, whereas the Fe compound crystallizes in space group P4/mbm of the tetragonal system. Here we describe the syntheses and structural characterization of the two new compounds, Ba 7 UTi 2 S 12.5 O 0.5 and Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 . Both crystallize in space group I4/mcm in the Ba 7 UV 2 S 12.5 O 0.5 structure type.

Experimental section

Syntheses

The starting reactants were used as supplied: Ba (Johnson Matthey, 99.5%), S (Mallinckrodt, 99.6%), Ti (Aldrich, 99.7%), and Si (Aldrich, 99.99 %). Depleted U chips (IBI laboratories) were powdered by hydridization in a modification [3] of a previous literature protocol [4].

For each reaction, the weighed amounts of powders were loaded into a carbon-coated fused-silica 6 mm tube inside an Ar-filled dry box. The tube had been pre-baked and dried at 500 K. The tube was transferred with a special adapter to minimize oxygen or moisture contamination, then evacuated to 10 -4 Torr, and flame sealed. Finally the tube was placed in a computer-controlled furnace, heated to 1123 K in 48 h, held at that temperature for 96 h, then cooled to 673 K at 2.5 K/h before the furnace was turned off. Some crystals were selected and analyzed with an EDX-equipped Hitachi S-3400 SEM. Ba 7 UTi 2 S 12.5 O 0.5 . Black blocks of Ba 7 UTi 2 S 12.5 O 0.5 were obtained (yield  70%) in an attempt to synthesize the eventual quaternary compound Ba 3 TiUS 6 that crystallizes as a 2H hexagonal perovskite [5]. Therefore, the mixture consisted of U (20.23 mg, 0.084 mmol), Ti (14.00 mg, 0.255 mmol), Ba (35.01 mg, 0.255 mmol), and S (16.35 mg, 0.51 mmol). EDX analysis on black crystals revealed a molar ratio close to Ba:Ti:U:S ≈UOS [6] was detected as a byproduct. Other attempts were performed that led to the formation of a black powder. Black blocks were analyzed by EDX to reveal Ba:U:Si:Fe:S ≈The presence of Fe is probably a contamination from an earlier reaction that led to another compound (Ba 8 UFeSiS 14 [7]). A secondary phase was also detected with a U:S ratio of 1:1 and considered as UOS [6]. 

Structure determinations

Single-crystal X-ray diffraction data for the compounds Ba 7 UTi 2 S 12.5 O 0.5 and Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 were collected at 100(2) K with the use of the Bruker APEX2 diffractometer equipped with graphite-monochromatized MoKα radiation (λ = 0.71073 Å) [START_REF]5-1 Data Collection and Processing Software[END_REF]. The data collection strategy used the algorithm COSMO implemented in the APEX2 package with a series of 0.3 scans in ω and φ. The exposure time was 10 s/frame. The collection of intensity data as well as cell refinement and data reduction were carried out with the use of the program APEX2 [START_REF]5-1 Data Collection and Processing Software[END_REF]. Face-indexed absorption, incident beam, and decay corrections were performed with the use of the program SADABS [START_REF]SMART Version 5.054 Data Collection and SAINT-Plus Version 6.45a Data Processing Software for the SMART System[END_REF]. Both structures were solved and refined with the use of the SHELX14 programs [START_REF] Sheldrick | [END_REF]. As found previously, both structures contain oxygen; the O atoms were refined successfully. In addition the crystal structure of Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 was refined with Fe and Si occupying the same positions and having the same displacement parameters. Additional information is given in Table 1 and in Supplementary Material. (..m, m.., and m.., respectively), and also an O1/S4 mixed site (422). A general drawing of the structure is viewed in Fig. 1 along the c axis; metrical values are reported in Table 2. Each U atom is octahedrally coordinated to five S atoms and one O atom. These octahedra are connected through the sharing of O/S corners along the c axis to form infinite chains, as viewed in Fig. 2. The presence of the -U-S-U-O-sequence leads to a 50% disorder of the U atoms along the c direction (Fig. 2). The Ti or (Si/Fe) site is coordinated to four S atoms to form isolated tetrahedra aligned along the c axis. The space between US 5 O infinite chains and isolated MS 4 tetrahedra is filled by Ba atoms leading to the one-dimensional structure.

The U-S distances are 2.648(1) Å and 2.667(2) Å (Ba 7 UTi 2 S 12.5 O 0.5 ) and 2.604(1) Å and 2.690(1) Å (Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 ). Similar U-S distances occur (2.627(1) Å and 2.679(1) Å) for Ba 7 V 2 US 12.5 O 0.5 and 2.596(1)-2.667(2) Å (U1), 2.598(1)-2.640(2) Å (U2) for Ba 7 UFe 2 S 12.5 O 0.5 [2]. Compare these distances with those of BaUS 3 [11] 2.668(1) to 2.696(1) Å, Ba 2 Cu 2 US 5 [12] 2.673(2) to 2.770(1) Å, and Li 2 US 3 [13] tetrahedra. The Ba1 and Ba2 atoms are coordinated to eight S atoms whereas each Ba3 atom is nine coordinated. Those values are reported in Table 2 and may be compared with those found in similar compounds, such as BaUS 3 [11], Ba 2 US 6 [16], Ba 3.69 US 6 [11], and BaU 2 S 5 [11].

Oxidation states

Because there are no short S-S distances, the assignment of formal oxidation states in the Ba 7 UTi 2 S 12.5 O 0.5 compound is straightforward with 7 Ba 2+ , 2 Ti 4+ , 1 U 4+ , 12.5 S 2-, 0.5 O 2-.

In the Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 the assumption of Fe 3+ with 7 Ba 2+ , 1.7 Si 4+ , 12.5 S 2-, 0.5 O 2-, leads to a mixed charge balance of U 4/5+ . U 4/5+ has previously been conjectured in the compounds Ba 3.69 US 6 [11], Ba 3.3 Rb 0.7 US 6 [17], and Ba 3.2 K 0.8 US 6 [17].

Conclusions

The

Ba 7 USi 1 . 7

 717 Fe 0.3 S 12.5 O 0.5 . This compound was obtained (yield  70%) in an attempt to synthesize the Ba 7 USi 2 S 12.5 O 0.5 compounds. The reaction mixture consisted of U (20 mg, 0.084 mmol), Ba (81.69 mg, 0.59 mmol), Si (4.76, 0.16 mmol), and S (35.43 mg, 1.11 mmol).

  The compounds Ba 7 UTi 2 S 12.5 O 0.5 and Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 crystallize in the Ba 7 UV 2 S 12.5 O 0.5[2] structure type in space group I4/mcm of the tetragonal system with four formula units in unit cells of dimensions a = 16.1451(3) Å and c = 9.5310(2) Å and a = 16.1218(16) Å and c = 9.4103(11) Å at 100 K, respectively. The asymmetric unit contains one disordered U1 atom (site symmetry 4..), one M (Ti or (0.85 Si + 0.15 Fe)) atom (m.2m), three Ba atoms Ba1, Ba2, Ba3 (.2., m.2m,-42m, respectively), three S positions S1, S2, S3

Fig. 1 :

 1 Fig. 1: View of the crystal structure of the Ba 7 UM 2 S 12.5 O 0.5 down the c axis.

Figure 2 :Fig 2 :

 22 Figure 2:

  2.603 to 2.677 Å. TiS 4[15]. In Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 the Si/Fe distances are 2.111(1) Å and 2.139(1) Å. The Si-S distances in Ba 8 USi 2 S 14 are 2.105(3)-2.127(2) Å and the Fe-S distances in Ba 8 USiFeS 14 are 2.154(1)-2.182 (1) Å [7]. The bond angles reported in Table 2 are typical for a US 5 O octahedra and MS 4

	The U1-O distances are 2.118(1) Å and 2.101(1) Å for Ba 7 UTi 2 S 12.5 O 0.5 and
	Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 , respectively.	In UP 4 O 12 distance is 2.136(1) Å [14]. In
	Ba 7 UTi 2 S 12.5 O 0.5 the Ti-S distances are 2.177(3) Å and 2.190(3) Å; these are 2.24(2) and
	2.29(1) in Tl 4

Table 1 . Crystal data and structure refinements for Ba 7 UTi 2 S 12.5 O 0.5 and Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5

 1 Ba 7 UM 2 S 12.5 O 0.5 (M = Ti, Si/Fe) compounds crystallize in Ba 7 V 2 US 12.5 O 0.5 structure type in space group I4/mcm of the tetragonal system. The crystal structure consists of US 5 O octahedra connected through the sharing of S/O corners to form infinite chains and isolated MS 4 tetrahedra, both aligned down the c axis. Ba atoms fill the space between US 5 O and MS 4 UTi 2 S 12.5 O 0.5 , 0.0091 for Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5  

	polyhedra.

a Space group = I4/mcm, T = 100(2) K, Z = 4, λ = 0.71073 Å. b

Table 2 Selected

 2 Interatomic Distances (Å) and bond angles (deg) for Ba 7 UTi 2 S 12.5 O 0.5 and Ba 7 UTi 1.7 Fe 0.3 S 12.5 O 0.5 . Ba 7 UTi 2 S 12.5 O 0.5 Ba 7 UTi 1.7 Fe 0.3 S 12.5 O 0.5

	U1-S4 × 4	2.667(2)	2.690(1)
	U1-S1	2.648(1)	2.604(1)
	U1-O1	2.118(1)	2.101(1)
	M1-S2 × 2	2.177(3)	2.111(1)
	M1-S3 × 2	2.190(3)	2.139(1)
	Ba1-S	3.032(2)-3.421(2)	3.027(1)-3.502(1)
	Ba2-S3 × 8	3.436(2)	3.378(1)
	Ba3-S	3.262(2)-3.461(2)	3.2628(7)-3.441(1)
	S1-U1-S1	180.0	180.0
	S1-U1-S4	95.71(2)	95.37(1)
	S2-Si1-S2	116.29(17)	117.57(7)
	S2-Si1-S3	106.67(4)	107.05(1)
	S3-Si1-S3	114.14(17)	111.08(8)

Acknowledgments

Use was made of the IMSERC X-ray Facility at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205); the State of Illinois, and International Institute for Nanotechnology (IIN).  Appendix. Supplementary data Data for Ba 7 UTi 2 S 12.5 O 0.5 (CCDC#1898481) and Ba 7 USi 1.7 Fe 0.3 S 12.5 O 0.5 (CCDC#1898480) may be obtained free of charge by contacting CCDC at (https://www.ccdc.cam.ac.uk).

Conflict of Interest None Declaration of Interest None


S Biswas

A Lemasson

M Rejmund

Y H Kim

A Navin

C Michelagnoli

I Stefan

R Banik

P Bednarczyk

S Bhattacharya

S Bhattacharyya

E Clément

H L Crawford

G De France

P Fallon

J Goupil

B Jacquot

H J Li

J Ljungvall

A O Macchiavelli

A Maj

L Ménager

V Morel

R Palit

R M Pérez-Vidal

J Ropert

C Schmitt

Spectroscopy of neutron-rich Sb isotopes using AGATA, VAMOS++ and EXOGAM

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

Introduction 132 Sn is one of the rare neutron-rich unstable nuclei, with classical doubly magic shell closures, that is experimentally accessible with the recent developments in accelerators and detectors. The study of the excited states and the transition probabilities in nuclei in its vicinity, with few particles or/and holes added to the inert core, are crucial for understanding the shell model theory and the relevant pp, pn and nn interactions in this mass A ∼ 130 region. Additionally, in this mass-region, there are presence of many seniority isomers in the range of ns to µs. When the lifetime of the isomer is of the order of µs's, an additional challenge appears in correlating the γ-ray transition feeding and depopulating these isomers. Therefore, these nuclei are often known either from their isomer decay or from their prompt γ spectroscopy. In the present work, the prompt-delayed spectroscopy of neutronrich Sb isotopes have been carried out by utilising the unique combination of AGATA, VA-MOS++ and EXOGAM detectors [1]. * Electronic address: biswas@ganil.fr

Experimental Details and Results

The neutron-rich 122-131 Sb fission fragments were populated using the inverse kinematics reaction, 9 Be( 238 U, f) at 6.2 MeV/u. The experimental setup included the AGATA array, VAMOS++ spectrometer and the EX-OGAM detectors. The prompt γ rays, emitted by the excited fission fragments, were detected using the AGATA γ-ray tracking array. The VAMOS++ spectrometer was used for the unambiguous identification of the neutronrich fission fragments on an event by event basis. The delayed γ rays were detected by the EXOGAM detectors, placed at the focal plane of VAMOS++. More details regarding the experimental setup are given in Ref. [2]. This setup enabled the correlation of the prompt and delayed γ rays in the time range of 100 ns -200 µs.

A systematic analysis of the prompt and delayed transitions for all the neutron-rich 122-131 Sb isotopes have been carried out. The already known isomers in the odd-A 123-131 Sb isotopes have been confirmed in the present analysis. In addition, several new prompt and delayed transitions for these isotopes have been identified. New isomers, prompt and delayed γ rays have been identified in the even-A Shell model calculations using the restricted model space, consisting of neutron d 3/2 , s 1/2 , h 1/2 and proton p 1/2 , g 9/2 , and g 7/2 orbitals have been carried out using the interaction used in Ref. [3]. The interaction has been improved so as to have a better agreement for the binding energies, excitation energies and the transition probabilities. Also, a systematic comparison of the isomers in Sb have been carried out with the corresponding isomers in 121-130 Sn isotopes, showing that the isomers in Sb dominantly arise due to a πg 7/2 particle coupled to the corresponding neutron configurations in the Sn isotopes. Though the energies of the excited states in the Sb isotopes seem to follow the seniority scheme, the transition probabilities do not. This could be probably due to the breaking of the neutron pairs in the h 11/2 orbital arising due to the πg 7/2 -νh 11/2 interaction.

FIG. 1 :

 1 FIG. 1: (a) The prompt γ-ray spectrum (γP ) in coincidence with already known delayed 247 keV γ-ray (γD) in 127 Sb. (b) The γD in coincidence with newly identified 1195 keV prompt γ-ray in 128 Sb. The newly observed delayed transitions have been marked with an asterisk.

Acknowledgments

The authors would like to thank the entire AGATA Collaboration and the important technical contributions of the GANIL accelerator staff for the successful running of the experiment. PB and AM acknowledge support from National Science Centre under Contract No. 2013/08/M/ST2/00257 and the French LEA COPIGAL project. SB, RB, SB, SB and RP acknowledge support from CEFIPRA project No. 5604-4 and the LIA France-India agreement. HLC, PF and AOM acknowledge support from the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Contract No. DE-AC02-05CH11231 (LBNL).


Laure-Hélène Canette

Nathalie Bedoin

Philippe Lalitte

Emmanuel Bigand

Barbara Tillmann

The Regularity of Rhythmic Primes In6luences Syntax Processing in Adults

Keywords: Rhythmic priming, syntax, music, temporal attention, inter-individual differences

Recent research has shown that auditory rhythmic stimulation improves subsequent syntax processing of speech in children with and without developmental language disorders. Sensitivity to grammatical errors is enhanced after regular rhythmic primes in comparison to irregular ones. Our present study investigated this rhythmic priming effect in healthy adults by using subtle grammatical errors as targets, aiming to \it with the high linguistic level of the participants. We also assessed whether participants' sensitivity to rhythmic priming on syntax processing was related to self-reported rhythmic skills and musical habits. Participants listened to rhythmic regular or irregular primes followed by blocks of six grammatically correct or incorrect sentences. Participants provided grammaticality judgments on each of the sentences, and response accuracy was analyzed. Furthermore, participants \illed out a questionnaire about their musical skills, listening habits and music experience. Results revealed better grammaticality processing after regular rhythmic primes in comparison to irregular ones in healthy adults. Moreover, self-reported individual characteristics related to (1) rhythmic processing and synchronization, (2) amount of daily exposure to music, and (3) social bonding, contributed to signi\icantly predict the rhythmic priming effect. Our \indings con\irm the in\luence of temporal regularities of musical primes on subsequent syntax processing, even when syntax processing is automatized (as in healthy young adults), and they point to inter-individual differences modulating the strength of this priming effect. We discuss results within the framework of the Dynamic Attending Theory suggesting that regular rhythms orient attentional resources over time, improving the processing of event structures, including for speech.

INTRODUCTION

Rhythm has been de\ined as the temporal patterning of event durations in an auditory sequence (e.g., [START_REF] Large | Perceiving temporal regularity in music[END_REF]. In music, the rhythmic patterns allow for the abstraction of an underlying beat (i.e., a regular isochronous pulse). These temporal regularities facilitate the processing of musical events: rhythms with regular temporal structures (i.e., beat-based or metric rhythms) are better discriminated and reproduced than are irregular rhythms (i.e., non-metric rhythms) [START_REF] Essens | Metrical and nonmetrical representations of temporal patterns[END_REF][START_REF] Grahn | See what I hear? Beat perception in auditory and visual rhythms[END_REF][START_REF] Grahn | Rhythm and beat perception in motor areas of the brain[END_REF][START_REF] Grahn | Individual differences in rhythmic ability: Behavioral and neuroimaging investigations[END_REF]. Similarly, in language, temporal regularities in the speech signal in\luence syntax processing: a rhythmically regular sentence facilitates syntactic ambiguity processing (Roncaglia-Denissen, Schmidt-Kassow, & Kotz, 2013) and temporal intervals modulate the latency of syntactic error processing [START_REF] Schmidt-Kassow | Entrainment of syntactic processing? ERP-responses to predictable time intervals during syntactic reanalysis[END_REF].

As music and speech signals have temporal regularities, it has been suggested that music and speech processing share cognitive resources and mechanisms (e.g., [START_REF] Patel | Music, language and the brain[END_REF]. Several studies have reported a link between rhythmic musical abilities and linguistic abilities in children, notably related to grammar skills [START_REF] Gordon | Musical rhythm discrimination explains individual differences in grammar skills in children[END_REF], phonological awareness [START_REF] Woodruff Carr | Beat synchronization predicts neural speech encoding and reading readiness in preschoolers[END_REF] and reading skills [START_REF] Flaugnacco | Rhythm perception and production predict reading abilities in developmental dyslexia[END_REF]. The links between rhythmic musical and linguistic processing have been observed both in case of de\icits and expertise. For instance, children with developmental language disorders (i.e., dyslexia and Speci\ic Language Impairment) have been shown to present also impaired rhythmic processing of non-speech material, and these impaired performance levels are related to language performance levels [START_REF] Colling | Neural entrainment and sensorimotor synchronization to the beat in children with developmental dyslexia: An EEG study[END_REF][START_REF] Corriveau | Rhythmic motor entrainment in children with speech and language impairments: Tapping to the beat[END_REF][START_REF] Thomson | Rhythmic processing in children with developmental dyslexia: Auditory and motor rhythms link to reading and spelling[END_REF]). For healthy individuals, numerous studies have shown enhanced speech processing for musicians compared to non-musicians (e.g., syntax processing: [START_REF] Jentschke | Musical training modulates the development of syntax processing in children[END_REF]; early sensory encoding of speech: [START_REF] Musacchia | Musicians have enhanced subcortical auditory and audiovisual processing of speech and music[END_REF]. Converging evidence has been provided by musical training studies focusing on rhythmic processing. Experimentally implemented musical training programs improved not only rhythmic abilities, but also phonological and reading skills in dyslexic children [START_REF] Flaugnacco | Music training increases phonological awareness and reading skills in developmental dyslexia: A randomized control trial[END_REF][START_REF] Overy | Dyslexia, temporal processing and music: The potential of music as an early learning aid for dyslexic children[END_REF].

Beyond mid-and long-term effects of musical or rhythmic training on language processing, the link between rhythm and speech processing has been shown with short-term rhythmic priming studies, which also allows for studying pathological populations and open for perspectives of training and rehabilitation. Listening to a musical sequence with a strongly regular underlying beat improves syntax processing for subsequently presented sentences in typically developing children as well as children with developmental language disorders [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF][START_REF] Canette | Rhythmic and textural musical sequences differently in\luence syntax and semantic processing in children[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF]. Rhythmic priming studies have also been conducted in adult patients with basal ganglia lesions or Parkinson's disease while measuring EEG. Listening to a rhythmically regular stimulus before listening to sentences restored the late positivity in response to grammatical violations (i.e., the P600) [START_REF] Kotz | Can rhythmic auditory cuing remediate language-related de\icits in Parkinson's disease?[END_REF][START_REF] Kotz | The basal ganglia are receptive to rhythmic compensating during auditory syntactic processing: ERP patient data[END_REF], which had been reported previously as missing in basal ganglia patients [START_REF] Kotz | Syntactic language processing: ERP lesion data on the role of the basal ganglia[END_REF]. It also increased the P600 amplitude in response to grammatical errors listened by dyslexic and non-dyslexic adults (Canette et al., 2020a).

These studies can be understood within the framework of the Dynamic Attending Theory [START_REF] Jones | Time, our lost dimension: Toward a new theory of perception, attention and memory[END_REF][START_REF] Jones | Time will tell: A theory of dynamic attending[END_REF][START_REF] Jones | Dynamic attending and responses to time[END_REF]. According to this framework, internal oscillators (i.e., internal attending rhythms; [START_REF] Drake | The development of rhythmic attending in auditory sequences: Attunement, referent period, focal attending[END_REF] tend to synchronize with external regularities. Thanks to this synchronization, perceivers develop expectations about the temporal occurrence of next events, which then facilitates processing, segmentation and integration. At a neural level, cerebral rhythms have been shown to entrain with the temporal regularities of external stimuli and in\luence event processing (e.g., [START_REF] Ding | Cortical entrainment to continuous speech: Functional roles and interpretations[END_REF][START_REF] Fujioka | Internalized timing of isochronous sounds is represented in neuromagnetic beta oscillations[END_REF][START_REF] Giraud | Cortical oscillations and speech processing: Emerging computational principles and operations[END_REF][START_REF] Large | Pulse and meter as neural resonance[END_REF]. Dynamic attending can be applied both to music [START_REF] Large | Neural networks for beat perception in musical rhythm[END_REF][START_REF] Large | Perceiving temporal regularity in music[END_REF] and speech perception [START_REF] Kotz | Cortical speech processing unplugged: A timely subcorticocortical framework[END_REF]; framed as the "Attentional Bounce Hypothesis" by [START_REF] Pitt | The use of rhythm in attending to speech[END_REF]. For example, listeners are more accurate in judging the pitch of rhythmically expected tones than unexpected ones [START_REF] Jones | Temporal aspects of stimulusdriven attending in dynamic arrays[END_REF], and more accurate in spoken word perception when presented with a regular than an irregular inter-stress interval [START_REF] Quené | Effects of timing regularity and metrical expectancy on spokenword perception[END_REF]. In the rhythmic priming paradigm, the hypothesis is that the regular events in the musical prime entrain internal oscillators. After the musical prime, this then facilitates entrainment to the less regular speech signal, and consequently favors the processing of the speech signal and its syntactic structure [START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF][START_REF] Schön | Short-and long-term rhythmic interventions: Perspectives for language rehabilitation[END_REF].

Previous research has shown that rhythmic abilities vary strongly between healthy individuals [START_REF] Repp | Sensorimotor synchronization and perception of timing: Effects of music training and task experience[END_REF][START_REF] Sowinski | Poor synchronization to the beat may result from de\icient auditory-motor mapping[END_REF] and are in\luenced by musical training [START_REF] Grahn | Individual differences in rhythmic ability: Behavioral and neuroimaging investigations[END_REF][START_REF] Repp | Sensorimotor synchronization and perception of timing: Effects of music training and task experience[END_REF]. Interestingly, inter-individual variabilities in rhythmic skills have been shown to contribute to explain the variability in the ef\icacy of a rhythmic intervention for patients with Parkinson's disease (i.e., gait improvement via rhythmic auditory stimulation) (Dalla Bella et al., 2017a). These \indings outline the need for considering individual differences also in rhythmic priming studies for syntax processing.

Our present study investigated the effect of listening to regular rhythmic primes (in comparison to irregular primes) on subsequent syntax processing in healthy young adults. Our aim was to test whether the fully mature syntax processing system still bene\its from the regularity of musical primes, and to assess the potential inter-individual differences in the strength of the rhythmic priming effect. In contrast to previous studies in children, we used more subtle and varied grammatical errors adapted to the linguistic and educational level of the participants, as well as a larger set of musical primes (not just one pair as in [START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF]. Based on the results reported for children [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF], we predicted better performance in the grammaticality judgment task after regular primes than after irregular primes. Using questionnaires, we further investigated whether inter-individual differences related to musical skills, listening habits and music experience might in\luence the strength of the rhythmic priming effect on syntax processing in young healthy adults. Music and dance experience as well as self-reported rhythmic processing skills were expected to in\luence participants' potential sensitivity to the rhythmic regularity of the prime, as shown by differences in grammaticality judgments after regular and irregular primes.

MATERIALS AND METHODS

Participants

Twenty-\ive native French-speaking adults participated in the study (mean = 21.2 years, SD = 1.76, range = 19-26). The study was performed in an educational context, in which students took part in a noninvasive laboratory experiment in exchange for course credit. They participated naïvely, and after the recording of the data, they could ask the experimenter about the purpose of the study to further their understanding of experimental psychology. Informed verbal consent was obtained from all participants prior to taking part in the experiment. The study was anonymous and fully respected the Helsinki Declaration, Convention of the Council of Europe on Human Rights and Biomedicine.

Material

Musical Stimuli

Four rhythmically regular sequences and four irregular sequences were used. The four regular sequences were constructed on the basis of a 4/4 meter and a 120 BPM tempo, that is with an underlying inter-beat-interval of 500 ms (i.e., 2 Hz). These sequences were formed by 4 layers of rhythmic patterns, each based on different inter-beat-intervals, leading to a four-level rhythmic hierarchy. To vary and characterize the sequences in timbres, each layer was played by one (sometime two) percussion instrument(s) (i.e., bass drum, snare drum, tom-tom, and cymbal). All sequences were based on MIDI VST instruments timbres. Four of the sequences also contained some samples of electronic sounds. Each sequence was composed of one cycle of 16 beats that was repeated identically four times, thus leading to a duration of 32 seconds. To create a feeling of completion at the end of the sequence, the \irst beat of the cycle was added again at the end, thus extending the sequence for 2 seconds with a short reverberation effect, leading to the total duration of 34 seconds. Note that a short rhythmic pattern or a percussion sound was added at the end of a cycle to reinforce the sensation of formal periodicity.

The four rhythmically irregular sequences were derived from the four rhythmically regular ones. The layers, the percussion sounds, the total duration as well as the duration of each event were identical. In each layer, the number of percussive events was the same as for the regular sequences, but reordered to obtain a maximum of rhythmic irregularity. In this way, it was impossible to extract perceptively an underlying pulse or a regular metric. In addition, the process of reordering the percussive impacts was made across the entire sequence. Thus, the rhythmically irregular sequences were not characterized by repeated cycles of 16 beats.

All sequences were recorded with Cubase 4 and Kontakt 3 VST instruments. They were exported in 16 bits/48 000 Hz mono wav \iles and normalized in loudness (dBA). See supplemental material for examples.

Linguistic Stimuli

The linguistic material was composed of 96 sentences, which were either grammatically correct (48) or not (48) (see Appendix A). We \irst created 48 correct sentences and derived an incorrect sentence from each correct sentence. Incorrect sentences contained subtle morpho-syntactic errors (aiming to avoid ceiling performance) covering errors regarding tense, prepositions, and person agreement. Sentences were separated into two lists (List A and List B) of 48 sentences (24 correct sentences and 24 incorrect sentences) to avoid participants listening to a same sentence in its correct and incorrect versions. Each correct sentence of List A was matched in number of words, number of syllables, and word's lexical frequency (Lexique 3; [START_REF] New | Une base de données lexicales du français contemporain sur internet: LEXIQUE TM[END_REF] to a correct sentence of List B. The mean number of words per sentence was 10.33 (SD = 1.83, range = 6 to 15) in list A and 10.35 (SD = 1.80, range = 6 to 15) in list B. The mean number of syllables was 13.67 (SD = 1.75, range = 10 to 18) in list A and 13.75 (SD = 1.72, range = 10 to 17) in list B. Half of the participants heard the correct sentences of List A and the incorrect sentences of List B, and the reverse was done for the other half of the participants. Overall the 96 sentences, the mean number of words per sentence was 10.34 (SD = 1.81, range = 6 to 15) and the mean number of syllables per sentence was 13.71 (SD = 1.73, range = 10 to 18). Sentences were spoken by a female native speaker of French at a natural speed of production, and were normalized in loudness. The mean duration of sentences was 2574 ms (SD = 379, range = 1676 to 3466), with 2569 ms (SD = 403, range = 1825 to 3466) in list A and 2579 ms (SD = 359, range = 1676 to 3389) in list B.

Procedure

The 48 sentences were presented by blocks of six sentences (three grammatical sentences, three ungrammatical sentences). Sentence distribution in the blocks and sentence order in each block were randomized for each participant. The experiment consisted in 8 blocks, each preceded by a musical prime. Half of the blocks were preceded by a regular prime and half by an irregular prime. Primes were arranged in a pseudo-randomized order. Two consecutive blocks were presented with the same rhythmic prime type (regular or irregular), but with two different musical prime sequences. Then, the two following blocks changed to the other priming condition. A given prime did not follow its matched regular or irregular version. Half of the participants started with regular rhythmic primes and half with irregular primes.

Participants were asked to listen to the music and to perform the grammaticality judgment task on each sentence. They triggered each prime and each sentence by pressing the space bar and judged each sentence for grammaticality by pressing one of two response buttons. Response choices were indicated on the keyboard as well as on the computer screen by the words "grammatical" and "ungrammatical" associated with the colors green and red. There was a break in the middle of the experiment. Participants were tested individually in a testing room. The experiment was run using the software OpenSesame [START_REF] Mathôt | OpenSesame: An open-source, graphical experiment builder for the social sciences[END_REF], and stimuli were presented via headphones at a comfortable loudness level, which could be adapted if requested by the participant.

At the end of the experimental session, participants completed a questionnaire about their musical skills and listening habits. This questionnaire was partly based on [START_REF] Peretz | On-line identi\ication of congenital amusia[END_REF] and was composed of various items investigating music and dance practice as well as music in everyday life (i.e., open questions, yes/no questions and \ive-point scales). Participants also completed the BMRQ (Barcelona Music Reward Questionnaire) (Mas-Herrero, Marco-Pallares, Lorenzo-Seva, Zatorre, & Rodriguez-Fornells, 2013; see [START_REF] Saliba | French validation of the Barcelona music reward questionnaire[END_REF] for the French version used here). The BMRQ investigates \ive main facets of musical reward experience in individuals: musical seeking, emotion evocation, mood regulation, social reward and sensory-motor. For a total of 20 questions, it contains four items for each of the \ive facets. Participants indicated the level of agreement with each item by using a \ive-point scale ranging from "fully disagree" (1) to "fully agree" (5).

Data Analyses

Performance was analyzed with signal detection theory calculating discrimination sensitivity with d' and response bias with c for each participant and for each prime condition . Based on 1 previous data leading to predict better performance after regular primes, performance (d') was analyzed by one-sided paired t-tests, with either participants (t1) or sentences (t 2 ) as the random variable. In addition, potential differences in response bias c were assessed with twosided paired t-tests and participants as the random variable. We reported effect sizes in terms of dz or d using G*Power software [START_REF] Faul | G*power 3: A \lexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF], with the following proposed categories for interpretation: small = 0.20, medium = 0.50, large = 0.80 [START_REF] Cohen | Statistical power analysis for the behavioral sciences[END_REF].

These analyses are based on the proportions of hits (i.e., proportion of correct responses for 1 ungrammatical sentences, p[hits]) and false alarms (i.e., errors for grammatical sentences, p[FAs]) after regular and irregular primes. D' is de\ined as z(p[hits]) -z(p[FAs]), and response bias c as -0.5[z(p[hits]) + z(p[FAs])]; see [START_REF] Macmillan | Detection theory: A user's guide[END_REF] for more details. The correction of the d' and c measures used 0.01 for cases without false alarms and 0.99 for the maximum number of hits.

Aiming to predict the difference between performance (d') after regular primes and performance after irregular primes, we ran multiple regression analyses (forward stepwise) with participants' responses in the questionnaire as predictors. The questions were separated into three subsets (see Appendix B) and analyzed with three regression analyses: (1) number of years of music training and of dance training (i.e., two questions), (2) 17 questions about "music in everyday life" related to pitch and rhythm processing as well as to musical exposure, and (3) items of the BMRQ (i.e., 20 questions). We performed supplementary regression analyses on each of the \ive BMRQ subscales (i.e., four questions each) aiming to con\irm results of the regression on all BMRQ items.

RESULTS

Grammaticality Judgments

Participants' performance was better after regular primes (mean d' = 2.42, SD = 0.76) than after irregular primes (mean d' = 2.08, SD = 0.86), t1(24) = -1.82, p = .041, dz = 0.37. Analysis on sentences con\irmed this signi\icant difference, t 2 (47) = -1.97, p = .027, dz = 0.28.

Bias c did not differ between the two prime conditions, p = .397. Response bias c was signi\icantly above 0 (i.e., bias to respond "grammatical") for both the regular condition (mean c = 0.54, SD = 0.45), t(24) = 15.91, p < .001, d = 1.14, and the irregular condition (mean c = 0.45, SD = 0.42), t(24) = 12.10, p < .001, d = 0.97.

To further investigate whether the priming effect changed across the experimental session, performance was calculated separately for the \irst part and for the second part of the experiment (i.e., before and after the break in the middle of the experiment). In the \irst part of the experiment, the difference between the two prime conditions did not reach signi\icance (mean regular d' = 2.23, mean irregular d' = 2.14), p = .358. In the second part of the experiment, performance was better after regular primes (mean d' = 3.00) than after irregular primes (mean d' = 2.50), t1(24) = -2.26, p = .017, dz = 0.45. Performance for irregular primes did not differ signi\icantly between the two parts of the experiment (mean d' difference = 0.36), p = .152, whereas performance after regular primes improved signi\icantly in the second part (mean d' difference = 0.77), t1(24) = -3.30, p = .003, dz = 0.67.

Regression Analyses

The \irst regression analysis with number of years of music and dance training did not result in a signi\icant regression model (no predictor ended up in the regression equation).

The second regression analysis with questions about "music in everyday life" resulted in a signi\icant regression model, R2 = 0.46, F(4, 20) = 4.31, p = .011. The item about the amount of music listening ("How many hours do you listen to music per day?") was a signi\icant positive predictor (beta = 0.30, t(20) = 2.28, p = .033). The item about the incapacity to follow music rhythm ("Indicate whether this sentence applies to you: I don't manage to follow music rhythm") just fell short of signi\icance as a negative predictor (beta = -0.88, t(20) = -1.89, p = .074).

The third regression analysis with all items of the BMRQ led to a signi\icant regression model , R 2 = .74, F(6, 17) = 8.17, p < .001. Two BMRQ items predicted positively the priming 2 effect: "When I hear a tune I like a lot I can't help tapping or moving to its beat" (beta = 0.57, t(17) = 3.82, p = .001) and "Music makes me bond with other people" (beta = 0.44, t(17) = Note that for this analysis we removed one participant who used one scale incongruently with 3.54, p = .003). Moreover, two BMRQ items predicted negatively the priming effect: "I sometimes feel chills when I hear a melody that I like" (beta = -0.37, t(17) = -3.06, p = .007), and "I can't help humming or singing along to music that I like" (beta = -0.40, t(17) = -2.37, p = .030). Finally, the BMRQ item "In my free time I hardly listen to music" just fell short of signi\icance (beta = 0.34, t(17) = 2.01, p = .060), but was not signi\icant in the additional regression model run separately on the subscale musical seeking (regression model was not signi\icant, no predictor ended up in the regression equation). In contrast, the other four items were con\irmed as signi\icant predictors in the regressions focusing on their respective subscales (sensory-motor, social reward, emotion evocation). See Table 1 for more details.

Table 1. Mean, standard deviation, minimum and maximum for each signi\icant question in the regression analyses. Items 1 and 2 are in the second regression analysis, items 3 to 7 are in the third regression analysis.

DISCUSSION

Previous behavioral studies conducted in children [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF] and electrophysiological studies in adult patients (Basal ganglia lesions: [START_REF] Kotz | The basal ganglia are receptive to rhythmic compensating during auditory syntactic processing: ERP patient data[END_REF]; Parkinson disease: Kotz & Gunter, 2015; dyslexia in adults: Canette et al., 2020a) have reported a bene\icial effect of a regular rhythm on subsequent syntax processing. Our study extends this \inding to healthy adults by measuring their performance in a grammaticality judgment task with a dif\iculty level adapted to their linguistic and educational level (University students). The results suggest that the auditory perception of rhythmic regularities immediately before speech perception can be ef\icient even in the case of highly automatized and non-impaired linguistic skills, at least regarding syntax processing in healthy young adults. Moreover, additional analyses showed that the bene\it of the regular rhythmic prime built up over the experimental session (see below for further discussion).

The rhythmic priming effect can be interpreted within the framework of the Dynamic Attending Theory [START_REF] Jones | Time, our lost dimension: Toward a new theory of perception, attention and memory[END_REF][START_REF] Jones | Time will tell: A theory of dynamic attending[END_REF][START_REF] Jones | Dynamic attending and responses to time[END_REF]. The regular events in the musical prime provide predictable cues that may allow boosting and entraining internal oscillators. Temporal expectations are assumed to develop over time following the strong metrical structure of the primes. This ongoing entrainment might then bene\it to the entrainment to the subsequent speech signal and in particular its syntax processing, notably as speech and syntax processing also requires entrainment and temporal attention [START_REF] Gordon | Perspectives on the rhythmgrammar link and its implications for typical and atypical language development[END_REF][START_REF] Kotz | Cortical speech processing unplugged: A timely subcorticocortical framework[END_REF][START_REF] Port | Meter and speech[END_REF][START_REF] Quené | Effects of timing regularity and metrical expectancy on spokenword perception[END_REF][START_REF] Schmidt-Kassow | Entrainment of syntactic processing? ERP-responses to predictable time intervals during syntactic reanalysis[END_REF]. The present results showed that even the healthy adult brain can bene\it from the modulation of temporal attention by regular rhythmic primes. It is relevant to note that the used tempo of 2 Hz for the regular rhythmic primes corresponds approximately to the rate of stressed syllables in speech [START_REF] Arvaniti | Rhythm, timing and the timing of rhythm[END_REF][START_REF] Dauer | Stress-timing and syllable-timing reanalyzed[END_REF], and is close to the preferred spontaneous tempo in young adults [START_REF] Mcauley | The time of our lives: Life span development of timing and event tracking[END_REF]. Future research should now investigate how speci\ic the effect is to the 2 Hz rate related to either the speech rate or the preferred tempo, and/or how \lexible it is to extend to slower or faster tempi as well as to potential mismatch between speech rate and preferred tempo.

In contrast to an explanation in terms of dynamic attending and rhythmic processing, it might be argued that the bene\icial effect of the rhythmic regular prime could operate via increased arousal level and the induction of positive mood, as suggested by the arousal-andmood-hypothesis (e.g., [START_REF] Schellenberg | Music and cognitive abilities[END_REF]. This hypothesis would suggest that the rhythmic priming effect is a general effect rather than a speci\ic effect on sequencing or syntax processing in particular. However, recent studies have reported that the rhythmic priming effect does not extend to tasks that do not require sequencing and segmentation, such as nonlinguistic control tasks requiring mathematical and visuo-spatial processing [START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF], as well as a semantic evocation task, for which textural sound sequences (judged as sadder than regular sequences) were more ef\icient [START_REF] Canette | Rhythmic and textural musical sequences differently in\luence syntax and semantic processing in children[END_REF]. While these studies were conducted with children, it seems plausible to expect a similar pattern in adults, even though future research needs to further investigate this.

In the present study, the comparison between regular and irregular sequences shows a relative facilitation effect, and it does not yet allow for disentangling whether the difference is due to a bene\it of the regular prime or a cost of the irregular prime (or both). The comparison of regular and irregular rhythmic sequences is a \irst step in priming approaches, which has then been followed by the investigation of costs and bene\its (despite the dif\iculty of de\ining appropriate baseline conditions) in psycholinguistics (see [START_REF] Jonides | On the cost and bene\it of cost and bene\it[END_REF], music cognition (see [START_REF] Tillmann | The costs and bene\its of tonal centers for chord processing[END_REF] as well as in the investigation of the rhythmic priming effect on syntax processing in children. For this later one, the \irst studies only compared regular versus irregular primes [START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF] and subsequent studies have provided evidence for the bene\it of the regular prime over more neutral baseline primes or a silent condition [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF][START_REF] Canette | Rhythmic and textural musical sequences differently in\luence syntax and semantic processing in children[END_REF]. Future research needs now to further investigate this more speci\ic comparison also in adult listeners, but our additional analyses over the course of the experimental session provide some \irst response in favor of a bene\icial effect of the regular prime.

The rhythmic priming effect (i.e., the difference between regular and irregular primes) became stronger in the second part of the experiment, mainly because performance after regular primes increased from the \irst to the second part of the experiment. This result is in agreement with the interpretation of a bene\icial effect of regular primes rather than a disturbing effect of irregular primes. It is also in agreement with previous rhythmic priming studies in children, showing a bene\it provided by regular rhythmic primes on syntax processing in comparison to neutral baseline conditions (environmental sounds: [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF]textural sounds and silence: Canette et al., 2020b), therefore excluding an alternative explanation solely invoking a cost of processing due to irregular primes. In the present study, participants bene\ited more strongly from regular primes over the time course of the experiment, possibly also because the increased familiarity with the musical sequences might have helped extracting the underlying 2 Hz beat and synchronizing to the primes. To explore this hypothesis, future research could investigate whether a familiarization phase before the experiment could reinforce the priming effect. For example, participants could listen to the primes or synchronize to them with externalized tapping, as it has been shown that body movement facilitates the extraction of temporal structures and pulse (e.g., [START_REF] Su | Body movement enhances the extraction of temporal structures in auditory sequences[END_REF]. A general musical rhythmic training session could also be proposed before the experiment (as for example in [START_REF] Hidalgo | Speak on time! Effects of a musical rhythmic training on children with hearing loss[END_REF], with hearing-impaired children), aiming to strengthen the priming effect. These future extensions of the rhythmic priming implementation in adults are particularly interesting as the effect size measured for the entire experiment does not seem to be as strong as previously reported effect sizes for typically developing children as well as dyslexic and SLI children [START_REF] Bedoin | Temporally regular musical primes facilitate subsequent syntax processing in children with Speci\ic Language Impairment[END_REF][START_REF] Chern | New evidence of a rhythmic priming effect that enhances grammaticality judgments in children[END_REF][START_REF] Przybylski | Rhythmic auditory stimulation in\luences syntactic processing in children with developmental language disorders[END_REF] . Interestingly, for the adults, the effect emerged over the 3 experimental session. These \indings suggest that the here implemented rhythmic priming effect for syntax might be more ef\icient in a developmental or a pathological context, and/or with increased familiarization to the material .

4

Our results further revealed that inter-individual differences regarding self-reported musical skills and listening habits contributed to the strength of the rhythmic priming effect. Speci\ically, multiple regression analyses showed that items related to (1) rhythmic processing and synchronization, (2) amount of daily exposure to music, and (3) feeling of social bonding through music, contributed to predict the rhythmic priming effect.

Although beat tracking and synchronization skills are general human characteristics, they vary across the general population [START_REF] Repp | Sensorimotor synchronization and perception of timing: Effects of music training and task experience[END_REF][START_REF] Sowinski | Poor synchronization to the beat may result from de\icient auditory-motor mapping[END_REF]. Using regression analyses, we pointed out a link between the rhythmic priming effect on syntax processing and self-reported rhythmic interest and abilities: the desire to move and synchronize with music predicted positively the rhythmic priming effect, and the incapacity to follow musical rhythm tended to be a negative predictor of the rhythmic priming effect. In other words, the more the participants reported to be sensitive to rhythm, the more strongly the difference between the two priming conditions favored regular primes over irregular primes. The item about the desire to move and to synchronize with music can be linked to the concept of "groove". It has been de\ined as a cognitive temporal phenomenon characterized by beat perception and synchronized body responses [START_REF] Pressing | Black atlantic rhythm: Its computational and transcultural foundations[END_REF] and also by the desire to move with music [START_REF] Madison | Experiencing groove induced by music: Consistency and phenomenology[END_REF]. Some studies have shown that synchronization performance is enhanced by high beat saliency [START_REF] Tranchant | Keeping the beat: A large sample study of bouncing and clapping to music[END_REF] and more generally by high-groove music [START_REF] Leow | Individual differences in beat perception affect gait responses to low-and high-groove music[END_REF]. Various musical features, such as repetitive rhythm, syncopation, and beat salience have been proposed to contribute to groove [START_REF] Stupacher | Audio features underlying perceived groove and sensorimotor synchronization in music[END_REF]. The regular rhythmic primes in the present experiment included these various musical features contributing to groove and improving synchronization. The synchronization might favor signal sequencing and anticipation, which are central for syntax processing. To further understand the potential link between rhythmic abilities and the rhythmic priming effect, future research should go beyond self-reported responses and measure inter-individual differences in beat perception and synchronization with objective evaluation tools for perception (e.g., Beat Alignment Test, [START_REF] Iversen | The Beat Alignment Test (BAT): Surveying beat processing abilities in the general population[END_REF]Pro\ile of Music Perception Skills, Law & Zentner, 2012) and production (e.g., Battery for the Assessment of Auditory Sensorimotor and Timing Abilities, Dalla Bella et al., 2017b).

For children, the following effect sizes have been reported: Chern et al.: d = 0.57;Przybylski et al.: 3 partial eta2 = 0.34 and 0.14 for SLI and dyslexia children, respectively; Bedoin et al.: partial eta2 = 0.14. Power analyses con\irmed that the effect was weaker for healthy adults than for children. Indeed, in

In contrast to questionnaire items relative to rhythm processing, items relative to pitch processing and those that have been reported as indicative for congenital amusia (Peretz et 5 al., 2008) did not emerge as positive predictors for the rhythmic priming effect. This speci\ic predictive capacity of rhythm-related items in comparison to pitch-related items is in agreement with a recent rhythmic priming study measuring Evoked Related Potentials (ERPs) for words with a stress pattern that either matched or mismatched the preceding prime (Fotidzis, Moon, Steel, & Magne, 2018). Beyond observing an increased negativity for words with mismatching stress pattern, this study reported a correlation between speech rhythm sensitivity (i.e., the ERP difference between match and mismatch conditions) and musical rhythm aptitude, but failed to found any correlation with tonal abilities (both rhythmic and tonal abilities were objectively assessed with a comparison task on melody pairs). Converging evidence can also be found in the bene\icial effect of rhythmic cues on gait in patients with Parkinson disease: even though patients show an overall bene\icial effect of the rhythmic cue on gait, inter-individual differences in the extent of the effect of the rhythmic stimulation were reported (Dalla Bella, Dotov, Bardy, & Cochen de Cock, 2018). One explanation for these differences was related to inter-individual differences in rhythmic skills: relatively spared abilities to track the beat favored a positive response to rhythmic cueing (Cochen de Cock et al., 2018;Dalla Bella et al., 2017a, 2018).

Beyond the items related to rhythmic processing and synchronization, our analyses revealed that an item about social bonding (i.e., considering music as a way to create social links) was a positive predictor for the rhythmic priming effect. Relations between social bonding and temporal processing have been documented previously: experimental studies showed that joint music making, singing and dancing enhance prosocial behavior in children [START_REF] Kirschner | Joint music making promotes prosocial behavior in 4year-old children[END_REF], and that moving together in synchrony increases cooperation and af\iliation between adults [START_REF] Hove | It's all in the timing: Interpersonal synchrony increases af\iliation[END_REF][START_REF] Valdesolo | The rhythm of joint action: Synchrony promotes cooperative ability[END_REF][START_REF] Wiltermuth | Synchrony and cooperation[END_REF].

Finally, our analyses also revealed the amount of self-reported daily exposure to music as a positive predictor for the rhythmic priming effect. In contrast, we did not \ind a signi\icant contribution of music and dance training as measured by years of formal training. This might be linked to the fact that the range of music and dance training in our study was not systematically manipulated; we tested a mixed group of students and did not select highly trained musicians or dancers, for example. A more intense practice of music and dance (i.e., as professional musicians or dancers) or the age at beginning of musical practice (early trained musicians are better at reproducing the temporal structure or rhythms; Bailey & Penhune, 2010) could be considered in future studies.

While the rhythmic priming effects and the regression results discussed up to here have been rather expected based on previously reported \indings, our analyses revealed two less-expected results: two items related to emotion and singing predicted negatively the rhythmic priming effect on syntax processing. A possible explanation is that the tendency to engage in a listening attitude mostly guided by emotion or oriented to emotional aspects as well as focusing on the pitch dimension when listening to the musical primes could have disturbed the bene\it of the regular rhythm and its effect on sequencing and segmentation, which are required in syntax processing. There are different forms of musical engagement during listening, and two networks have been distinguished: a network for external engagement (e.g., rhythm processing) and a network for internal engagement (e.g., emotional processes) [START_REF] Janata | Music and the self[END_REF]. Even though both networks are involved in music listening, it might be that listeners differ in the potential asymmetry of the involvement of these networks. Assigning disproportionate importance to pitch and/or emotional processing might draw For example: I hardly recognize tunes without the help of lyrics; I rarely detect when someone signs attention away from the prime rhythm and meter and contribute to also reduce the potential in\luence of the rhythmic regularity of the prime.

CONCLUSION

Our study has shown that auditory rhythmic stimulation of syntax processing can be observed in healthy adults required to judge subtle grammatical manipulations. This result shows that syntax processing can be improved via previously heard musical regularities, even when it is an unimpaired and automatized capacity. Furthermore, our results suggest that the strength of the rhythmic priming effect might be related to some individual characteristics about rhythmic synchronization, social bonding in musical contexts, and daily exposure to music. Taken together, they provide perspectives to potentially increase rhythmic priming effects via rhythmic training, enhanced music listening or motor synchronization activities in both healthy and clinical populations. (2) Questions about "music in everyday life", related to pitch, rhythm, musical exposure and amusia

Item

Response options 1. Do you sing in private? (in the car, in the shower, etc.).

From 1 (never) to 5 (very often)

2. Do you sing in public? (with friends, karaoke, etc.) From 1 (never) to 5 (very often)

3. Do you think you sing in tune? Yes/No 4. I have dif\iculties recognizing a song without lyrics. From 1 (fully disagree) to 5 (fully agree) 5. I am rarely able to notice when someone sings out of tune.

From 1 (fully disagree) to 5 (fully agree)

6. Do you dance? From 1 (never) to 5 (very often) 7. Do you intentionally listen to music? From 1 (never) to 5 (very often) 8. How many hours do you listen to music per day?

9. Do you think you have the "sense of rhythm"? From 1 (not at all) to 5 (a lot) 10. Is it easy for you to follow the rhythm of a song? From 1 (not easy) to 5 (very easy)

  of years of music training and of dance training 1. Do you play or have you ever played (a) music instrument(s)? If yes, what kind of music instrument and for how long? 2. Do you take or have you ever taken dancing classes? If yes, what kind of dance and for how long?

  Indicate whether this sentence applies to you: 12. A relative, a friend or a teacher told me that I do not have a musical ear. 13. I don't manage to follow music rhythm. 14. I have dif\iculties reproducing by singing tones played on the piano. 15. For me, music is like noise. 16. Music is like speech in a foreign language. 17. I \ind most music irritating.

	11. Could you notice when someone produces a wrong	Yes/No
	note?
		Yes/No
		Yes/No
		Yes/No
		Yes/No
		Yes/No
		Yes/No

another response (she indicated listening rarely to music with 1 -out of 5 -while indicating 6 hours of daily music listening in the open question).

[START_REF] Canette | Rhythmic and textural musical sequences differently in\luence syntax and semantic processing in children[END_REF] for example, with N = 16 and dz = 0.62, the power was 0.76, and in the present study with N = 25 and dz = 0.37, we reached a power of 0.56 (with alpha = 0.05, one-tailed tests). For a power of 0.80, with the same effect size (dz = 0.37), 47 participants would be needed (calculated with G*Power).

out-of-tune.

BLes parents nourrissent leur enfant et lui apprennent à marcher / Les parents nourrissent et apprennent à marcher à leur enfant.

ACKNOWLEDGMENTS

We thank Audrey Sara\ian for help in running participants, Isabelle Peretz for sharing her questionnaire with us and Anna Fiveash for discussions and additional material analyses. The team "Auditory cognition and psychoacoustics" is part of the LabEx CeLyA ("Centre Lyonnais d' Acoustique", ANR-10-LABX-60) and L-HC is supported by a post-doctoral grant of the LabEx CeLyA.

DISCLOSURE STATEMENT

The authors declare that there is no con\lict of interest.

APPENDIX A