Anne Roumier

Catherine Béchade

Luc Maroteaux

Serotonin and the immune system

The defense against pathogens is mediated by innate and adaptive immune mechanisms that act in periphery and central nervous system (CNS). Outside the CNS, serotonin is found in gastrointestinal tract and enteric nerves, in hematopoietic stem cells, and in particularly high abundance in platelets. Serotonin regulates inflammation and immunity by acting on serotonin receptors that are differentially expressed on immune cells, both in rodents and humans. Serotonin acts as a potent chemoattractant, recruiting innate immune cells to sites of inflammation. Serotonin also alters the production and release of cytokines and cell activation/proliferation. Some immune cells, including mast cells and T-lymphocytes, have the capacity to synthesize and release serotonin, expanding the range of tissues for serotonin signaling.

Introduction 1.1 How do immune cells encounter serotonin?

Although serotonin is largely studied as a neurotransmitter, enterochromaffin cells of the gut produce most of the body's serotonin. These cells express tryptophan hydroxylase TPH1, a rate-limiting enzyme for serotonin production [START_REF] Walther | 7-Hydroxytryptophan, a novel, specific, cytotoxic agent for carcinoids and other serotonin-producing tumors[END_REF]. A second TPH isoform, TPH2, synthesizes serotonin in CNS, and gut enteric nerves [START_REF] Walther | 7-Hydroxytryptophan, a novel, specific, cytotoxic agent for carcinoids and other serotonin-producing tumors[END_REF]. Serotonin concentrations in blood and tissues are normally low because of uptake by platelets (<1 nM). Immune cells, however, may encounter serotonin released from enterochromaffin cells in gut mucosa, or from platelets, that accumulate serotonin via the membrane serotonin transporter, SERT (SLC6A4), and then stored in dense granules via the vesicular transporter VMAT-2. In turn, platelets can release this stored serotonin at sites of injury and inflammation. Plateletderived serotonin is important for attracting innate immune cells such as neutrophils to inflamed tissue [START_REF] Duerschmied | Platelet serotonin promotes the recruitment of neutrophils to sites of acute inflammation in mice[END_REF]. In addition to platelets, dendritic cells (professional antigen-presenting cells) and B-lymphocytes express SERT and thus, can accumulate and release serotonin. Interestingly, recent studies indicate that some immune cells are capable of serotonin biosynthesis. Mast cells (tissue-resident-cells) in rodents and humans express TPH1 and levels of serotonin are elevated in patients with mastocytosis, who have greatly elevated mast-cell numbers [START_REF] Kushnir-Sukhov | Human mast cells are capable of serotonin synthesis and release[END_REF][START_REF] Nowak | Tryptophan hydroxylase-1 regulates immune tolerance and inflammation[END_REF]. Further, T-lymphocytes [START_REF] León-Ponte | Serotonin provides an accessory signal to enhance T-cell activation by signaling through the 5-HT7 receptor[END_REF][START_REF] O'connell | A novel form of immune signaling revealed by transmission of the inflammatory mediator serotonin between dendritic cells and T cells[END_REF][START_REF] Urbina | 5-HT7 receptors and tryptophan hydroxylase in lymphocytes of rats: mitogen activation, physical restraint or treatment with reserpine[END_REF] express TPH1 upon mitogen or T-cell receptor activation and can synthesize serotonin. Interestingly, expression of TPH1 and serotonin production is greater in CD8 + compared with CD4 + T-cells [START_REF] Chen | T lymphocytes possess the machinery for 5-HT synthesis, storage, degradation and release[END_REF].

Serotonin and hematopoiesis

It was proposed that serotonin acts at hematopoietic stem cell progenitors directly or via modulation of bone-marrow microenvironment [START_REF] Yang | Promoting effects of serotonin on hematopoiesis: ex vivo expansion of cord blood CD34+ stem/progenitor cells, proliferation of bone marrow stromal cells, and antiapoptosis[END_REF]. Mice deficient in peripheral serotonin (Tph1 -/-) display morphological and cellular features reminiscent of ineffective erythropoiesis [START_REF] Amireault | Ineffective erythropoiesis with reduced red blood cell survival in serotonin-deficient mice[END_REF]. Other data showed that bone-marrow composition of Htr 2B -/-mice displayed a significant increase in Cd11b+/Gr+ cells that represents granulocyte precursors. This is associated with a significant reduction in Cd11b-/Cd31+ population that corresponds to immature endothelial progenitor cells in 5-HT 2B -/mice [START_REF] Launay | Serotonin 5-HT2B receptors are required for bone-marrow contribution to pulmonary arterial hypertension[END_REF]. These observations support the hypothesis that serotonin signaling controls differentiation of myeloid precursor cells in the monocyte/macrophage lineages.

Serotonin and the immune tolerance

Acquired peripheral tolerance -defined as a functional state of immunological unresponsiveness to antigenic challenge -is a continuous process that prevents innocuous, nonself antigens from stimulating excessive immunity leading to tissue damage. Peripheral tolerance is established by a number of partly overlapping mechanisms that mostly involve control at the level of T cells, especially by differentiation of naïve CD4+ helper T cells into induced Treg cells, which give B cells the confirmatory signals they need in order to produce antibodies. One well-documented way to control immunity and tolerance is through regulation of nutrients in microenvironment of immune cells. Best described is tryptophan deficiency mediated by the catabolic enzyme indoleamine 2,3-dioxygenase (IDO), which locally depletes tryptophan and liberates immunoregulatory metabolites known as kynurenines. T-cell activation is exquisitely sensitive to local tryptophan catabolism, and thus IDO exerts profound protective effects in allo-fetal rejection, autoimmunity, and inflammation [START_REF] Munn | Indoleamine 2,3 dioxygenase and metabolic control of immune responses[END_REF]. Although IDO is thought to be the major tryptophancatabolizing enzyme outside of liver, TPH1 shares a similar K M (~20 µM) [START_REF] Mckinney | Different properties of the central and peripheral forms of human tryptophan hydroxylase[END_REF] and can also potentially exhaust tryptophan to regulate immune tolerance. Indeed, in models of skin allograft tolerance, tumor growth and experimental autoimmune encephalomyelitis (multiple sclerosis), Tph1 deficiency was shown to break allograft tolerance, to induce tumor remission, and to intensify neuroinflammation independent of downstream product, serotonin [START_REF] Nowak | Tryptophan hydroxylase-1 regulates immune tolerance and inflammation[END_REF].

Serotonin and the innate immune response

Innate immune system function involves monocytes, macrophages, dendritic cells, neutrophils, eosinophils, mast cells and natural killer cells that act immediately in the area of infection, leading to destruction of pathogens. Innate immunity is primarily responsible for recognizing and eradicating "non-self" molecules presented by pathogens, and is therefore confined to recognizing extracellular pathogens (bacteria vs. viruses). This response is nonspecific with respect to particular invaders, but provides immediate host defense against pathogens via pattern recognition by toll-like receptors (TLRs). Pathogen-associated molecular patterns (e.g. peptidoglycans, bacterial lipopolysaccharides-LPS, double-stranded viral RNAs) bind TLRs on antigen-presenting cells, namely, dendritic cells and macrophages. Antigen-presenting cells then phagocytose pathogens and display pathogen-derived peptides via the major histocompatibility complex (MHC) on their cell surface for recognition by leukocytes of the "adaptive" immune system. Antigen-presenting cells also secrete proinflammatory cytokines (e.g., IL1β, IL-6, TNFα), prostaglandins, and histamine, which further activate physiological responses, alerting the body to infection/invasion. In addition to cellular protective mechanisms, innate immunity also includes the complement system, activated by foreign substances, antigen-antibody complexes (classical pathway), and Gramnegative bacteria (alternative pathway). This system leads to cell lysis, increased vascular permeability (allowing antibodies, innate immune cells, and fluid to enter tissues), and chemotaxis. The complement system also helps to activate antigen-presenting cells, namely, dendritic cells and B-cells during specific immune responses. Innate immunity also functions to communicate the presence of pathogens to cells involved in adaptive immune responses [START_REF] Baganz | A dialogue between the immune system and brain, spoken in the language of serotonin[END_REF]. The local environment and the presence of stimulatory signals determine whether monocytes acquire dendritic cell or macrophage characteristics and functions. Serotonin receptors are expressed by a broad range of inflammatory cell types.

1 Serotonin and neutrophils

Neutrophils are the most abundant white blood cells and serve an essential role in innate immunity, particularly against bacteria. Duerschmied and colleagues (2013) reported that Tph1 -/-mice show mild leukocytosis, i.e. elevated white blood cells (WBC) numbers compared with wild-type (WT) mice, which is primarily driven by an elevated neutrophil count. Despite this, 50% fewer leukocytes rolled on unstimulated mesenteric venous endothelium of Tph1 -/-mice. After LPS treatment, diminished rolling in Tph1 -/-mice resulted in reduced firm adhesion of leukocytes and neutrophil extravasation into lung, peritoneum and skin wounds was also reduced. Serotonin alone did not induce neutrophil migration invitro, suggesting that endothelial adhesion was the primary deficit. Consequently, survival from LPS-induced endotoxic shock was improved in Tph1 -/-mice.

Acute fluoxetine treatment increased plasma serotonin concentrations and promoted leukocyte-endothelial interactions in-vivo, suggesting that serotonin participates in acute inflammation. E-selectin is a cell adhesion molecule expressed only on endothelial cells activated by cytokines, and plays an important part in inflammation. E-selectin is upregulated on endothelial cells in the presence of serotonin, possibly explaining the observed increase in leukocyte-endothelial interactions. Whether SSRI use in humans alters leukocyte recruitment remains to be investigated [START_REF] Herr | Acute fluoxetine treatment induces slow rolling of leukocytes on endothelium in mice[END_REF].

In conclusion, platelet serotonin promotes recruitment of neutrophils in acute inflammation; however, the nature of serotonin receptor(s) underlying these effects is unknown.

Serotonin and monocytes

Monocytes are the largest type of leukocyte and can differentiate into macrophages and myeloid lineage dendritic cells. In human monocytes ( CD14+), mRNA expression of 5-HT 1E , 5-HT 2A , 5-HT 3 , 5-HT 4 and 5-HT 7 receptors is detectable [START_REF] Dürk | 5-Hydroxytryptamine modulates cytokine and chemokine production in LPS-primed human monocytes via stimulation of different 5-HTR subtypes[END_REF]. In LPSstimulated human blood monocytes, serotonin modulates the release of IL-1β, IL-6, IL-8/CXCL8, IL-12p40 and TNF-α, but has no effect on the production of IL-18 and IFN-γ. Moreover, serotonin modulates mRNA levels of IL-6 and IL-8/CXCL8, but not of IL-1β and TNF-α. Interestingly, 5-HT 1E and 5-HT 2A receptor agonists do not modulate the LPS-induced cytokine production in human monocytes [START_REF] Dürk | 5-Hydroxytryptamine modulates cytokine and chemokine production in LPS-primed human monocytes via stimulation of different 5-HTR subtypes[END_REF]. Instead, serotonin modulates cytokine production via activation of 5-HT 3 , 5-HT 4 and 5-HT 7 receptors. Pharmacologic experiments suggested that signaling through the 5-HT 3 receptor up-regulates LPS-induced production of IL-1β, IL-6 and IL-8/CXCL8, but not that of TNF-α and IL-12p40. Furthermore, activation of the Gs-coupled 5-HT 4 and 5-HT 7 receptors increases secretion of IL-1β, IL-6, IL-12p40 and IL-8/CXCL8, but in contrast, inhibits LPS-induced TNF-α release.

Serotonin and monocyte to macrophage differentiation

Serotonin upregulates the activity of peritoneal macrophages, and increases the in-vitro activity of phagocytosis in a concentration-dependent manner via 5-HT 1A/7 receptors and nuclear factor κB (NF-κB) [START_REF] Freire-Garabal | Serotonin upregulates the activity of phagocytosis through 5-HT1A receptors[END_REF]. Gene expression profiling of proinflammatory M1 (GM-CSF) and anti-inflammatory M2 (M-CSF) macrophages revealed that 5-HT 2B and 5-HT 7 receptor mRNAs are preferentially expressed by M2 macrophages, whereas the 5-HT 7 receptor is the only serotonin receptor expressed in M1 macrophages (de Las [START_REF] De | Serotonin skews human macrophage polarization through HTR2B and HTR7[END_REF]. The 5-HT 2B receptor is preferentially expressed by antiinflammatory M2 macrophages, and is also detected in-vivo in liver Kupffer cells, and in tumor-associated macrophages. Expression of 5-HT 2C receptors also occurs in alveolar macrophages, where serotonin induces a rise in intracellular Ca 2+ concentration and an increased expression of CCL2 (MCP-1) mRNA [START_REF] Mikulski | Serotonin activates murine alveolar macrophages through 5-HT2C receptors[END_REF]. LPS, the archetypal macrophage-activating stimulus that signals via TLR4, was shown to regulate expression of 5-HT 2B receptors (20 fold over basal 24h after LPS) in mouse macrophages. 5-HT 2B receptor mRNA is increased 20-fold in murine thioglycollate-elicited peritoneal macrophages, compared to bone marrow macrophages [START_REF] Lattin | Expression analysis of G Protein-Coupled Receptors in mouse macrophages[END_REF]. Serotonin inhibits LPS-induced release of pro-inflammatory cytokines, upregulates expression of macrophage M2 polarization-associated genes and reduces expression of M1-associated genes. Only 5-HT 7 receptors mediate inhibitory action of serotonin on the release of pro-inflammatory cytokines. Both 5-HT 2B and 5-HT 7 receptors mediate the pro-M2 skewing effect of serotonin. Blockade of both receptors during in-vitro monocyte-to-macrophage differentiation preferentially modulates acquisition of M2 polarization markers (de Las [START_REF] De | Serotonin skews human macrophage polarization through HTR2B and HTR7[END_REF].

Natural killer cells are large lymphocytes with innate killing capacity. Addition of serotonin to mixtures of target-cells and CD56 + natural killer-enriched human mononuclear cells strongly augmented natural killer cell cytotoxicity via 5-HT 1A receptors. This effect was indirect and involved serotonin signaling at accessory monocytes. The cytotoxicityenhancing effect of serotonin was additive to that induced by IFN-α, IFN-γ, or IL 2, but not to histamine [START_REF] Hellstrand | Role of serotonin in the regulation of human natural killer cell cytotoxicity[END_REF].

Serotonin and microglia

In mice, it has been established that serotonin is an important regulator of microglia, the brain resident macrophages, which are derived from yolk sac hematopoietic stem cell precursors. In the presence of serotonin, microglial processes moved more rapidly towards a lesion, which is considered a chemotactic response. Similarly, chemotactic response of cultured microglia to ATP is enhanced by serotonin. Phagocytic activity determined by the uptake of microspheres reveals that serotonin application decreases phagocytic activity of amoeboid microglia. Expression of microglial 5-HT 2B , 5-HT 5A and 5-HT 7 receptors was shown by qPCR analysis of RNA isolated from primary cultured and acutely isolated adult microglia [START_REF] Krabbe | Activation of serotonin receptors promotes microglial injury-induced motility but attenuates phagocytic activity[END_REF][START_REF] Kolodziejczak | Serotonin Modulates Developmental Microglia via 5-HT2B Receptors: Potential Implication during Synaptic Refinement of Retinogeniculate Projections[END_REF]. The presence of functional serotonin receptors was confirmed by patch clamp experiments in cultured and amoeboid neonatal microglia. This was also recently established by two-photon microscopy, showing that microglial processes moved rapidly toward the source of serotonin via activation of the 5-HT 2B receptor [START_REF] Kolodziejczak | Serotonin Modulates Developmental Microglia via 5-HT2B Receptors: Potential Implication during Synaptic Refinement of Retinogeniculate Projections[END_REF]. Modulation of microglial functions like phagocytosis and migration is fundamental for CNS since microglia can influence the balance of synaptogenesis and neuronal death during development and in pathology.

In-vitro analyses revealed that stimulation of 5-HT 7 receptors in human microglial cell lines results in an increase in IL-6 expression in these cells, an effect blocked by antagonizing 5-HT 7 receptors [START_REF] Mahé | Serotonin 5-HT7 receptors coupled to induction of interleukin-6 in human microglial MC-3 cells[END_REF]. As mentioned previously, one of the major functions of microglia is to respond to disruptions in homeostatic states through the release of proinflammatory cytokines. In vitro studies using murine microglia cell line showed that microglia can release cytokines, including IL-1β, in exosomes by a process that is not yet fully understood [START_REF] Glebov | Serotonin stimulates secretion of exosomes from microglia cells[END_REF]. Serotonin also plays an important role in the ability of microglia to release exosomes, which is dependent on increases in cytosolic Ca 2+ elicited through 5-HT 2 and 5-HT 4 receptor activation [START_REF] Glebov | Serotonin stimulates secretion of exosomes from microglia cells[END_REF]. In this manner, serotonin may ultimately be able to regulate cytokine release and immune processes within the CNS similarly to immune function in the periphery. The release of these cytokines may then act in a concerted manner to modulate other aspects of serotonin neurotransmission, such as SERTmediated serotonin clearance or exocytotic serotonin release [START_REF] Robson | Immune System Activation and Depression: Roles of Serotonin in the Central Nervous System and Periphery[END_REF].

Microglia are implicated in pathogenesis of neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS; motoneuron disease; Lou Gehrig's or Charcot's disease). During neurodegeneration, microglial activation is accompanied by infiltration of circulating monocytes, leading to production of multiple inflammatory mediators in spinal cord. The 5-HT 2B receptor expressed in microglia, is upregulated in spinal cord of three different transgenic mouse models of ALS. In mutant SOD1 mice, this upregulation was restricted to cells positive for CD11b, a marker of mononuclear phagocytes. Ablation of 5-HT 2B receptor in transgenic ALS mice expressing mutant SOD1 resulted in increased degeneration of mononuclear phagocytes, as evidenced by fragmentation of Iba1-positive cellular processes [START_REF] El Oussini | Serotonin 2B receptor slows disease progression and prevents degeneration of spinal cord mononuclear phagocytes in amyotrophic lateral sclerosis[END_REF]. This was accompanied by decreased expression of key neuroinflammatory genes but also loss of expression of homeostatic microglial genes. Importantly, the dramatic effect on mononuclear phagocytes of 5-HT 2B -receptor ablation was associated with acceleration of disease progression. In a large cohort of ALS patients, the C allele of SNP rs10199752 in HTR2B was associated with longer survival. Moreover, patients carrying one copy of the C allele of SNP rs10199752 showed increased 5-HT 2B receptor mRNA expression in spinal cord and displayed less pronounced degeneration of Iba1 positive cells than patients carrying two copies of the more common A allele. Thus, the 5-HT 2B receptor is able to limit degeneration of spinal cord mononuclear phagocytes, most likely microglia, and slows disease progression in ALS [START_REF] El Oussini | Serotonin 2B receptor slows disease progression and prevents degeneration of spinal cord mononuclear phagocytes in amyotrophic lateral sclerosis[END_REF].

Serotonin and dendritic cells

Dendritic cells are potent antigen-presenting cells endowed with the unique ability to initiate adaptive immune responses upon inflammation. Inflammatory processes are often associated with an increased production of serotonin, which operates by activating specific receptors. However, functional role of serotonin receptors in regulation of dendritic cell functions is poorly understood. Platelet activation was reported in patients with various allergic disorders. Platelet-derived factors may influence monocytic differentiation into dendritic cells. Indeed, serotonin alters differentiation of monocytes into dendritic cells (triggered by granulocytemacrophage colony-stimulating factor (GM-CSF) and IL-4), leading to dendritic cells with reduced expression of co-stimulatory molecules and CD1a, and higher expression of CD14. These serotonin-triggered dendritic cells exhibit significantly reduced stimulatory activity toward allogenic T-cells. However, they show enhanced cytokine-producing capacity, including for IL-10 but not IL-12. Serotonin-induced alteration of dendritic cells phenotype and reduction in antigen-presenting capacity are mediated via 5-HT 1E /5-HT 7 receptors [START_REF] Katoh | Effect of serotonin on the differentiation of human monocytes into dendritic cells[END_REF].

Immature dendritic cells preferentially express mRNA for 5-HT 1B , 5-HT 1E and 5-HT 2A/2B receptors. The 5-HT 1B/1E and 5-HT 2A/2B receptor stimulation induces intracellular Ca 2+ mobilization via Gi/Gq proteins in immature, but not mature, dendritic cells. The mRNA expression level of ligand-gated cation channel 5-HT 3 and the GPCR 5-HT 2A receptors are not modified during maturation. Serotonin stimulates 5-HT 3 -dependent Ca 2+ influx in both immature and mature dendritic cells. Mature dendritic cells mostly express 5-HT 4 and 5-HT 7 receptors and their activation induces cAMP elevation. Functional studies indicate that activation of 5-HT 4 and 5-HT 7 receptors enhances the release of the cytokines IL-1β and IL-8, while reducing secretion of IL-12 and TNF-α in mature dendritic cells [START_REF] Idzko | The serotoninergic receptors of human dendritic cells: identification and coupling to cytokine release[END_REF]. Expression of 5-HT 7 receptor as well as its downstream effectors Cdc42 are upregulated in dendritic cells upon maturation. In addition, basal activity of 5-HT 7 receptors is required for proper expression of the chemokine receptor CCR7, which is a key factor that controls dendritic cell migration. 5-HT 7 receptor enhances chemotactic motility of dendritic cells in-vitro by modulating their directionality and migration velocity [START_REF] Holst | The serotonin receptor 5-HT₇R regulates the morphology and migratory properties of dendritic cells[END_REF].

Serotonin can induce oriented migration in immature but not in LPS-matured dendritic cells via activation of 5-HT 1B/1E and 5-HT 2A/2B receptors. Accordingly, serotonin also increases migration of pulmonary dendritic cells to draining lymph nodes in-vivo. By binding to 5-HT 3 , 5-HT 4 and 5-HT 7 receptors, serotonin up-regulates production of the proinflammatory cytokine IL-6. Additionally, serotonin influenced chemokine release by human monocyte-derived dendritic cells: production of the potent T-helper cells Th1 chemoattractant IP-10/CXCL10 was inhibited in mature dendritic cells, whereas CCL22/MDC secretion was up-regulated in both immature and mature dendritic cells. Furthermore, dendritic cells matured in the presence of serotonin switched to a high IL-10 and low IL-12p70 secreting phenotype. Consistently, serotonin favored the outcome of a Th2 immune response both in-vitro and in-vivo [START_REF] Müller | 5-hydroxytryptamine modulates migration, cytokine and chemokine release and T-cell priming capacity of dendritic cells in vitro and in vivo[END_REF]. A recent study using Htr 7 -/mice confirmed 5-HT 7 receptor expression in CD103 + CD11c + dendritic cells found in colon (and spleen), and its importance in immune activation and gut inflammation [START_REF] Kim | Targeted inhibition of serotonin type 7 (5-HT7) receptor function modulates immune responses and reduces the severity of intestinal inflammation[END_REF]. Lack of endogenous serotonin in-vitro and in-vivo was associated with an impaired Th2-priming capacity of bone marrow dendritic cells [START_REF] Dürk | Production of serotonin by tryptophan hydroxylase 1 and release via platelets contribute to allergic airway inflammation[END_REF].

Interestingly, like platelets, dendritic cells can take up serotonin from the microenvironment and the antidepressant, fluoxetine, inhibits this uptake. Expression of serotonin transporter (SERT) is regulated by dendritic cell maturation, exposure to microbial stimuli, and physical interactions with T-cells. Significantly, serotonin sequestered by dendritic cells is stored within LAMP-1+ vesicles and subsequently released via Ca 2+dependent exocytosis, as confirmed by amperometric recordings [START_REF] O'connell | A novel form of immune signaling revealed by transmission of the inflammatory mediator serotonin between dendritic cells and T cells[END_REF].

Serotonin and eosinophils

Asthma is an inflammatory disease of the lung characterized by airways hyperresponsiveness, inflammation, and mucus hyperproduction. Notably, allergic asthma is characterized by infiltration of eosinophils, and plasma levels of serotonin are elevated in symptomatic asthma patients. Serotonin levels are increased in bronchoalveolar lavage fluid of mice and people with asthma after allergen provocation. TPH1 deficiency and TPH1 inhibition reduced all cardinal features of allergic airway inflammation. Transfusion of platelets from wild type and TPH1-deficient mice revealed that only platelets containing serotonin enhanced allergic airway inflammation.

Serotonin is well known to be involved in lung inflammatory processes. There is solid evidence that serotonin contributes to this eosinophil recruitment. Indeed, serotonin alone can stimulate in-vitro migration of murine and human eosinophils [START_REF] Boehme | Cutting edge: serotonin is a chemotactic factor for eosinophils and functions additively with eotaxin[END_REF][START_REF] Kang | Regulation of serotonin-induced trafficking and migration of eosinophils[END_REF]. Although several serotonin receptor subtypes are expressed, 5-HT 2A is the most prominent, and 5-HT 2A receptor antagonists inhibit serotonin-induced, but not eotaxininduced migration. Further, eosinophils roll in response to serotonin in venules under conditions of physiological shear stress [START_REF] Boehme | Cutting edge: serotonin is a chemotactic factor for eosinophils and functions additively with eotaxin[END_REF][START_REF] Kang | Regulation of serotonin-induced trafficking and migration of eosinophils[END_REF]. Signaling via 5-HT 2A receptors is associated with changes in cell shape/morphology via activation of specific intracellular signaling molecules (ROCK, MAPK, PI3K and the PKC-calmodulin pathway) [START_REF] Kang | Regulation of serotonin-induced trafficking and migration of eosinophils[END_REF].

In the ovalbumin mouse model of allergic inflammation, inhalation of the 5-HT 2 receptor agonist (R)-DOI prevents the development of many key features of allergic asthma, including airways hyper-responsiveness, mucus hyperproduction, airways inflammation, and pulmonary eosinophil recruitment. The 5-HT 2A receptors participate thus in allergic airways disease [START_REF] Nau | Serotonin 5-HT₂ receptor activation prevents allergic asthma in a mouse model[END_REF].

Serotonin and mast cells

Mast-cells have the capacity to synthesize and accumulate serotonin [START_REF] Kushnir-Sukhov | Human mast cells are capable of serotonin synthesis and release[END_REF]. In turn, this stored serotonin can be released upon IgE cross-linking. Further, mast cells express mRNA for multiple serotonin receptors, including 5-HT 1A , 5-HT 1B , 5-HT 1D , 5-HT 2A , 5-HT 2B , 5-HT 6 , and 5-HT 7 receptors [START_REF] Kushnir-Sukhov | 5-hydroxytryptamine induces mast cell adhesion and migration[END_REF]. Serotonin can induce mast-cell adherence to fibronectin and stimulate cell migration. However, there is no evidence that serotonin degranulates mast cells or modulates their activation by IgE. Mast cells from 5-HT 1A receptor knockout mouse (Htr 1A -/-) do not respond to serotonin indicating a principal role for this receptor. Importantly, serotonin attracts mast cells to sites of inflammation; injection of serotonin into the skin enhances accumulation of mast cells in wild type but not in 5-HT 1A receptor-null mice.

Serotonin and adaptive immunity

The response of a second immune system division, termed adaptive, or specific, immune system, occurs within hours of an infection and involves antigen-specific recognition and destruction of pathogens by T and B-lymphocytes. The two components of adaptive immune system involve cell-mediated and humoral immunity. Cell-mediated immunity is carried out by T-cells located in thymus, lymph nodes, and circulation. Antigen presenting cells that migrate to lymph nodes will prime and educate T-cells as to the nature of the pathogen. Tcells then proliferate and differentiate into, for example, CD4 + T-helper inflammatory cells (Th1) that activate macrophages, CD4 + Th2 cells that aid antibody responses, or CD8 + cytotoxic cells that target-cells infected with intracellular microbes. The second component of adaptive immunity involves the contributions of B-cells, located in lymph tissue, spleen and in the circulation. Upon stimulation, B-cells become plasma cells (with or without the help of Th2) that produce and secrete antibodies (immunoglobulins). Memory T and B-cells recognize specific antigens and respond quickly. Thus, adaptive immune system is distinguished from innate immune system by its ability to identify, remember, and eliminate pathogens that have been designated as non-self. Adaptive immunity is triggered at the immune synapse, where peptide major histocompatibility complexes and co-stimulatory molecules expressed by dendritic cells are physically presented to T-cells [START_REF] Baganz | A dialogue between the immune system and brain, spoken in the language of serotonin[END_REF].

The mRNA expression of serotonin receptors in lymphoid tissues of the rat, ex-vivo isolated spleen, thymus, and peripheral blood lymphocytes includes that of 5-HT 1B , 5-HT 1F , 5-HT 2A , 5-HT 2B , 5-HT 6 and 5-HT 7 . Mitogen-stimulated spleen cells additionally express mRNA corresponding to the 5-HT 3 receptor [START_REF] Stefulj | mRNA expression of serotonin receptors in cells of the immune tissues of the rat[END_REF]. In rhesus macaque, SERT positive cells were found among CD4 + , CD3 + , and CD3 + CD4 + lymphocytes respectively [START_REF] Yang | Promoting effects of serotonin on hematopoiesis: ex vivo expansion of cord blood CD34+ stem/progenitor cells, proliferation of bone marrow stromal cells, and antiapoptosis[END_REF]. Fluoxetine significantly increases number of lymphocytes expressing SERT, and stimulates an enrichment of CD8 + T-cells, decreasing CD4 + /CD8 + ratio. Fluoxetine administration elevates the levels of IL-4 at 1, 2 and 3 weeks; and of IL-2, at 2 and 3 weeks. IL-4/IL-2 ratio is significantly increased in fluoxetine group respecting the controls and is similar during 3 weeks of treatment [START_REF] Fazzino | Fluoxetine treatment to rats modifies serotonin transporter and cAMP in lymphocytes, CD4+ and CD8+ subpopulations and interleukins 2 and 4[END_REF]. Therefore, serotonin may have multiple actions in lymphoid tissues.

Serotonin and T-lymphocytes

There is long standing evidence that serotonin can influence T-cell activation. Notably, mice treated with an irreversible inhibitor of TPH1, para-chlorophenylalanine, exhibit a reduction in the number of CD25-positive T-cells [START_REF] León-Ponte | Serotonin provides an accessory signal to enhance T-cell activation by signaling through the 5-HT7 receptor[END_REF][START_REF] Young | Stimulation of splenic T-lymphocyte function by endogenous serotonin and by low-dose exogenous serotonin[END_REF], suggesting that serotonin contributes physiologically to T-cell activation. T-cells have the capacity to synthesize serotonin and levels of TPH1 expression increase following T-cell activation [START_REF] Chen | T lymphocytes possess the machinery for 5-HT synthesis, storage, degradation and release[END_REF][START_REF] León-Ponte | Serotonin provides an accessory signal to enhance T-cell activation by signaling through the 5-HT7 receptor[END_REF][START_REF] O'connell | A novel form of immune signaling revealed by transmission of the inflammatory mediator serotonin between dendritic cells and T cells[END_REF][START_REF] Urbina | 5-HT7 receptors and tryptophan hydroxylase in lymphocytes of rats: mitogen activation, physical restraint or treatment with reserpine[END_REF]. Conceivably, TPH1 activity in T-cells could act to exhaust tryptophan as proposed for mast cells [START_REF] Nowak | Tryptophan hydroxylase-1 regulates immune tolerance and inflammation[END_REF]. On the other hand, serotonin produced by T-cells might act in an autocrine or paracrine manner. Indeed, T-cells express the type 1 vesicular monoamine transporter (VMAT1) responsible for vesicular storage of serotonin, and VMAT1 expression increases following T-cell activation concomitant with TPH1. Further, Ca 2+ elevations in Tcells can trigger secretion of serotonin. Interestingly, levels of TPH1 and monoamine oxidase A, the principal catabolic enzyme for serotonin are greater in CD8 + compared to CD4 + Tcells suggesting a specific biological role for serotonin synthesis in this T-cell subset [START_REF] Chen | T lymphocytes possess the machinery for 5-HT synthesis, storage, degradation and release[END_REF].

A screen for serotonin receptor subtypes in murine T-cells revealed expression of three subtypes; naïve T-cells selectively express 5-HT 7 receptors while following T-cell activation there is a strong upregulation of 5-HT 1B and 5-HT 2A receptors [START_REF] León-Ponte | Serotonin provides an accessory signal to enhance T-cell activation by signaling through the 5-HT7 receptor[END_REF]. Significantly, exogenous serotonin induces rapid phosphorylation of extracellular signal-regulated kinase-1 and -2 (ERK1/2) and IκBα in naive T-cells that is inhibited by preincubation with a selective 5-HT 7 -receptor antagonist. Thus, serotonin signaling via 5-HT 7 receptor may contribute to early T-cell activation. [START_REF] Yin | 5-HT(1B) receptors play a prominent role in the proliferation of T-lymphocytes[END_REF] showed that 5-HT 1B receptor antagonists impaired the proliferation of helper CD4+ T-cells in mouse and human. [START_REF] Inoue | Regulation of antigen-specific CTL and Th1 cell activation through 5-Hydroxytryptamine 2A receptor[END_REF] showed that a 5-HT 2A receptor agonist enhanced Concavalin-A induced activation of murine CD4 + and CD8 + T-cells, whereas a 5-HT 2A receptor antagonist blocked T-cell receptor mediated IL-2 and IFN-γ production. Consistent with these data, [START_REF] Akiyoshi | Induction of indefinite survival of fully mismatched cardiac allografts and generation of regulatory cells by sarpogrelate hydrochloride[END_REF] showed that treatment with a 5-HT 2A receptor antagonist enhanced the survival of cardiac allograft in mice. Thus, these mouse data strongly support involvement of a trio of serotonin receptors (5-HT 7 , 5-HT 1B and 5-HT 2A ) during early and late stage T-cell activation.

Interestingly, the 5-HT 2B receptor is expressed in human T-cells. Gene expression profiles during human CD4 + T-cell differentiation, identified the 5-HT 2B receptor with 10fold greater expression in CD3 high CD4 + CD8 -SP4 thymocytes over intrathymic T progenitor cells, CD3 -CD4 + CD8 + 'double positive' thymocytes (ITTP), CD3 + CD4 + CD8 - CD45RA + CD62L + 'naive' T-cells from cord blood (CB4) and CD3 + CD4 + CD8 - CD45RA + CD62L + 'naive' T-cells from adult blood (AB4) [START_REF] Lee | Gene expression profiles during human CD4+ T cell differentiation[END_REF]. Further, 5-HT 2B receptors are differentially expressed among Th subsets. In human umbilical cord blood, Th cells cultured in the presence of cytokines promoting Th2 differentiation were found to increase 5-HT 2B receptor expression along with 50 Th2 differentially expressed genes [START_REF] Aijö | An integrative computational systems biology approach identifies differentially regulated dynamic transcriptome signatures which drive the initiation of human T helper cell differentiation[END_REF].

Rheumatoid arthritis is a chronic disease that results in a disabling and painful condition as it progresses to destruction of the articular cartilage and ankylosis of the joints. Although the cause of the disease is still unknown, evidence argues that autoimmunity plays an important part. There are increasing but contradictory views regarding serotonin being associated with activation of immuno-inflammatory pathways and the onset of autoimmune reactions. Studies have shown that platelets can have a role in rheumatic diseases. In patients with rheumatoid arthritis, IL-1-containing platelet-derived vesicles called microparticles are abundant in arthritic joint fluid. Platelets also serve as a source of prostaglandins that contribute to synovial inflammation. Furthermore, serotonin released by platelets helps drive persistent vascular permeability that characterizes the microvasculature of inflamed synovium. Therefore, platelets have a distinct role in autoimmunity [START_REF] Boilard | Platelets: active players in the pathogenesis of arthritis and SLE[END_REF]. In mice, induction of arthritis triggers a robust increase in serotonin content in the paws combined with low inflammation. In Tph1 -/-mice with arthritis, a significant increase in osteoclast differentiation and bone resorption was observed with an increase in IL-17 levels in the paws and in Th17 lymphocytes in draining lymph nodes, whereas T-regulatory cells were dampened. Ex-vivo serotonin and agonists of 5-HT 2A/2B receptors restored IL-17 secretion from splenocytes and Th17 cell differentiation in Tph1 -/-mice. Serotonin plays thus a fundamental role in arthritis through regulation of Th17/T-regulatory cell balance and osteoclastogenesis [START_REF] Chabbi-Achengli | Serotonin Is Involved in Autoimmune Arthritis through Th17 Immunity and Bone Resorption[END_REF].

Serotonin may also modulate migration of human T-cells. Human, but not mouse Tcells, express functional 5-HT 3 receptors. 5-HT 3 receptor agonists selectively decrease T-cell migration towards gradients of the chemokine CXCL12, but not to other chemokines such as CCL2 and CCL5. Interestingly, CXCL12 is highly expressed on vascular endothelium and inhibits T-cell migration across endothelium and extravasation. In transmigration experiments, 5-HT 3 -receptor stimulation reverses this effect of endothelial-bound CXCL12 on T-cell migration [START_REF] Magrini | Serotonin-mediated tuning of human helper T cell responsiveness to the chemokine CXCL12[END_REF]. These data suggest that serotonin can stimulate trafficking of T-cells from blood to tissues.

Serotonin and B-lymphocytes

B-lymphocytes have the capacity to sense and take up serotonin. Serotonin increases mitogen-stimulated CD19 + B-lymphocyte proliferation in a concentration-and timedependent manner. These effects are reproduced by a 5-HT 1A -receptor agonist. Serotonininduced increases in proliferation are blocked by 5-HT 1A receptor antagonists. Moreover, LPS-activated mouse spleen cells express specific binding sites for 5-HT 1A receptor, suggesting that serotonin upregulates mitogen-stimulated B-lymphocyte proliferation through 5-HT 1A receptors [START_REF] Iken | Serotonin upregulates mitogen-stimulated B lymphocyte proliferation through 5-HT1A receptors[END_REF]. Further, mitogen-activated B-lymphocytes express higher levels of 5-HT 1A receptor mRNA and protein than resting cells. This upregulation is seemingly dependent upon NF-κB transcription factors, as specific inhibitors of this pathway prevent the increase in mRNA expression for the 5-HT 1A receptor [START_REF] Abdouh | Transcriptional mechanisms for induction of 5-HT1A receptor mRNA and protein in activated B and T lymphocytes[END_REF]. B-lymphocytes express SERT and uptake of serotonin leads to apoptosis of Burkitt lymphoma cells [START_REF] Serafeim | 5-Hydroxytryptamine drives apoptosis in biopsylike Burkitt lymphoma cells: reversal by selective serotonin reuptake inhibitors[END_REF]. Serotonin may induce apoptosis via intracellular serotonylation-signaling pathway. Further, long-term treatment with SSRIs in humans leads to enhanced (~30%) numbers of B-lymphocytes [START_REF] Hernandez | Evaluation of the effect of selective serotonin-reuptake inhibitors on lymphocyte subsets in patients with a major depressive disorder[END_REF]. Interestingly, higher doses of SSRIs directly promote apoptosis of Burkitt lymphoma cells by inhibiting DNA synthesis, whereas normal peripheral and tonsillar B-cells are relatively resistant to SSRI-induced apoptosis [START_REF] Serafeim | 5-Hydroxytryptamine drives apoptosis in biopsylike Burkitt lymphoma cells: reversal by selective serotonin reuptake inhibitors[END_REF]. SERT has been detected in a variety of Bcell lines [START_REF] Meredith | The serotonin transporter (SLC6A4) is present in B-cell clones of diverse malignant origin: probing a potential anti-tumor target for psychotropics[END_REF], revealing SERT as a potential target for a broad range of Bcell malignancies.

Concluding remarks

Serotonin regulates inflammation and immunity by acting on serotonin receptors that are differentially expressed on immune cells, both in rodents and humans. Serotonin acts as a potent chemoattractant, recruiting innate immune cells to sites of inflammation. Serotonin also alters production and release of cytokines and cell activation/proliferation. Some immune cells, including mast cells and T-lymphocytes, have the capacity to synthesize and release serotonin, expanding the range of tissues for serotonin signaling.

Figure1-Relationships between hematopoietic cells and serotonin system. Cells of the hematopoietic system are depicted, with arrows indicating lineage relatedness with in blue the serotonin markers SERT and TPH1 and in red the distribution of receptors.


Siti Mutmainah
email: siti.mutmainah@uin-suka.ac.id

Samir Hachour

Frédéric Pichon

David Mercier

On learning evidential contextual corrections from soft labels using a measure of discrepancy between contour functions

Keywords: Belief functions, Contextual corrections, Learning, Soft labels

In this paper, a proposition is made to learn the parameters of evidential contextual correction mechanisms from a learning set composed of soft labelled data, that is data where the true class of each object is only partially known. The method consists in optimizing a measure of discrepancy between the values of the corrected contour function and the ground truth also represented by a contour function. The advantages of this method are illustrated by tests on synthetic and real data.

Introduction

In Dempster-Shafer theory [START_REF] Shafer | A mathematical theory of evidence[END_REF][START_REF] Smets | The Transferable Belief Model[END_REF], the correction of a source of information, a sensor for example, is classically done using the discounting operation introduced by Shafer [START_REF] Shafer | A mathematical theory of evidence[END_REF], but also by so-called contextual correction mechanisms [START_REF] Mercier | Refined Modeling of Sensor Reliability in the Belief Function Framework Using Contextual Discounting[END_REF][START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF] taking into account more refined knowledge about the quality of a source.

These mechanisms, called contextual discounting, negating and reinforcement [START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF], can be derived from the notions of reliability (or relevance), which concerns the competence of a source to answer the question of interest, and truthfulness [START_REF] Pichon | Relevance and truthfulness in information correction and fusion[END_REF][START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF] indicating the source's ability to say what it knows (it may also be linked with the notion of bias of a source). The contextual discounting is an extension of the discounting operation, which corresponds to a partially reliable and totally truthful source. The contextual negating is an extension of the negating operation [START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF][START_REF] Pichon | Relevance and truthfulness in information correction and fusion[END_REF], which corresponds to the case of a totally reliable but partially truthful source, the extreme case being the negation of a source [START_REF] Dubois | A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets[END_REF]. At last, the contextual reinforcement is an extension of the reinforcement, a dual operation of the discounting [START_REF] Mercier | Belief functions contextual discounting and canonical decompositions[END_REF][START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF].

In this paper, the problem of learning the parameters of these correction mechanisms from soft labels, meaning partially labelled data, is tackled. More specifically, in our case, soft labels indicate the true class of each object in an imprecise manner through a contour function.

A method for learning these corrections from labelled data (hard labels), where the truth is perfectly known for each element of the learning set, has already been introduced in [START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF]. It consists in minimizing a measure of discrepancy between the corrected contour functions and the ground truths over elements of a learning set. In this paper, it is shown that this same measure can be used to learn from soft labels, and tests on synthetic and real data illustrate its advantages to 1) improve a classifier even if the data is only partially labelled; and 2) obtain better performances than learning these corrections from approximate hard labels approaching the only available soft labels.

This paper is organized as follows. In Section 2, the basic concepts and notations used in this paper are presented. Then, in Section 3, the three applied contextual corrections as well as their learning from hard labels are exposed. The proposition to extend this method to soft labels is introduced. Tests of this method on synthetic and real data are presented in Section 4. At last, a discussion and future works are given in Section 5.

Belief functions: basic concepts used

Only the basic concepts used are presented in this section (See for example [START_REF] Shafer | A mathematical theory of evidence[END_REF][START_REF] Smets | The Transferable Belief Model[END_REF][START_REF] Denoeux | Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence[END_REF] for further details on the belief function framework).

From a frame of discernment Ω = {ω 1 , ..., ω K }, a mass function (MF), noted m Ω or m if no ambiguity, is defined from 2 Ω to [0, 1], and verify A⊆Ω m Ω (A) = 1.

The focal elements of a MF m are the subsets A of Ω such that m(A) > 0.

A MF m is in one-to-one correspondence with a plausibility function P l defined for all A ⊆ Ω by

P l(A) = B∩A =∅ m(B). (1)
The contour function pl of a MF m is defined for all ω ∈ Ω by

pl : Ω → [0, 1] ω → pl(ω) = P l({ω}) . (2)
It is the restriction of the plausibility function to all the singletons of Ω.

The knowledge of the reliability of a source is classically taken into account by the operation called discounting [START_REF] Shafer | A mathematical theory of evidence[END_REF][START_REF] Smets | Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem[END_REF]. Let us suppose a source S provides a piece of information represented by a MF m S . With β ∈ [0, 1] the degree of belief of the reliability of the source, the discounting of m S is defined by the MF m s.t.

m(A) = β m S (A) + (1 -β)m Ω (A) , (3)
for all A ⊆ Ω, where m Ω represents the total ignorance, i.e. the MF defined by m Ω (Ω) = 1.

Several justifications for this mechanism can be found in [START_REF] Smets | Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem[END_REF][START_REF] Mercier | Refined Modeling of Sensor Reliability in the Belief Function Framework Using Contextual Discounting[END_REF][START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF].

The contour function of the MF m resulting from the discounting (3) is defined for all ω ∈ Ω by (see for example [START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF]Prop. 11])

pl(ω) = 1 -(1 -pl S (ω))β , (4)
with pl S the contour function of m S .

Contextual corrections and learning from labelled data

In this Section, the contextual corrections we used are first exposed, then their learning from hard labels. The proposition to extend this method to soft labels is then introduced.

Contextual corrections of a mass function

For the sake of simplicity, we only recall here the contour functions expressions resulting from the applications of contextual discounting, reinforcement and negating mechanisms in the case of K contexts where K is the number of elements in Ω.

It is shown in [START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF] that these expressions are rich enough to minimize the discrepancy measure used to learn the parameters of these corrections, this measure being presented in Section 3.2.

Let us suppose a source S providing a piece of information m S .

The contour function resulting from the contextual discounting (CD) of m S and a set of contexts composed of the singletons of Ω is given by

pl(ω) = 1 -(1 -pl S (ω))β {ω} , (5)
for all ω ∈ Ω, with the K parameters β {ω} which may vary in [0, 1].

For the contextual reinforcement (CR) and the contextual negating (CN), the contour functions are respectively given, from a set of contexts composed of the complementary of each singleton of Ω, by

pl(ω) = pl S (ω)β {ω} , (6)
and pl(ω) = 0.5 + (pl S (ω) -0.5)(2β {ω} -1) ,

for all ω ∈ Ω, with the K parameters β {ω} able to vary in [0, 1].

Learning from hard labels

Let us suppose a source of information providing a MF m S concerning the true class of an object among a set of possible classes Ω.

If we have a learning set composed of n instances (or objects) the true values of which are known, we can learn the parameters of a correction by minimizing a discrepancy measure between the output of the classifier which is corrected (a correction is applied to m S ) and the ground truth [START_REF] Elouedi | The Evaluation of Sensors Reliability and Their Tuning for Multisensor Data Fusion within the Transferable Belief Model[END_REF][START_REF] Mercier | Refined Modeling of Sensor Reliability in the Belief Function Framework Using Contextual Discounting[END_REF][START_REF] Pichon | Proposition and learning of some belief function contextual correction mechanisms[END_REF].

Introduced in [START_REF] Mercier | Refined Modeling of Sensor Reliability in the Belief Function Framework Using Contextual Discounting[END_REF], the following measure E pl yields a simple optimization problem (a linear least-squares optimization problem, see [13, Prop. 12, 14 et 16]) to learn the vectors β CD , β CR and β CN composed of the K parameters of corrections CD, CR and CN:

E pl (β) = n i=1 K k=1 (pl i (ω k ) -δ i,k ) 2 , ( 8
)
where pl i is the contour function regarding the class of the instance i resulting from a contextual correction (CD, CR or CN) of the MF provided by the source for this instance, and δ i,k is the indicator function of the truth of all the instances i ∈ {1, . . . , n}, i.e. δ i,k = 1 if the class of the instance i is ω k , otherwise δ i,k = 0.

Learning from soft labels

In this paper, we consider the case where the truth is no longer given precisely by the values δ i,k , but only in an imprecise manner by a contour function δi s.t.

δi : Ω → [0, 1] ω k → δi (ω k ) = δi,k . (9)
The contour function δi gives information about the true class in Ω of the instance i.

Knowing then the truth only partially, we propose to learn the corrections parameters using the following discrepancy measure Ẽpl , extending directly (8):

Ẽpl (β) = n i=1 K k=1 (pl i (ω k ) -δi,k ) 2 . ( 10
)
The discrepancy measure Ẽpl also yields, for each correction (CD, CR et CN), a linear least-squares optimization problem. For example, for CD, Ẽpl can be written by

Ẽpl (β) = Qβ -d 2 (11)
with

Q =    diag(pl 1 -1) . . . diag(pl n -1)    , d =    δ1 -1 . . . δn -1    (12)
where diag(v) is a square diagonal matrix whose diagonal is composed of the elements of the vector v, and where for all i ∈ {1, . . . , n}, δi is the column vector composed of the values of the contour function δi , meaning δi = ( δi,1 , . . . , δi,K ) T . In the following, this learning proposition is tested with generated and real data.

Tests on generated and real data

We first expose how soft labels can be generated from hard labels to make the tests exposed afterwards on synthetic and real data.

Generating soft labels from hard labels

It is not easy to find partially labelled data in the literature. Thus, as in [START_REF] Côme | Learning from partially supervised data using mixture models and belief functions[END_REF][START_REF] Quost | Parametric classification with soft labels using the evidential EM algorithm: linear discriminant analysis versus logistic regression[END_REF][START_REF] Kanjanatarakul | An Evidential K-Nearest Neighbor Classifier Based on Contextual Discounting and Likelihood Maximization[END_REF][START_REF] Kanjanatarakul | A New Evidential K-Nearest Neighbor Rule based on Contextual Discounting with Partially Supervised learning[END_REF], we have built our partially labelled data sets (soft labels) from perfect truths (hard labels) using the procedure described in Algorithm 1 (where Bêta, B, and U means respectively Bêta, Bernoulli and uniform distributions).

Algorithm 1 Soft labels generation

Input: hard labels δi with i ∈ {1, . . . , n}, where for each i, the integer k ∈ {1, . . . , K} s.t. δ i,k = 1 is denoted by ki.

Output: soft labels δi with i ∈ {1, . . . , n}. 1: procedure HARDTOSOFTLABELS 2:

for each instance i do 3:

Draw pi ∼ Bêta(µ = .5, v = .04) 4:

Draw bi ∼ B(pi) 5:

if bi = 1 then 6:

Draw ki ∼ U {1,...,K}

7: δi,k i ← 1 8: δi,k ← pi for all k = ki
Algorithm 1 allows one to obtain soft labels that are all the more imprecise as the most plausible class is false.

Tests performed

The chosen evidential classifier used as a source of information is the eviential k-nearest neighbor classifier (EkNN) introduced by Denoeux in [START_REF] Denoeux | A k-nearest neighbor classification rule based on Dempster-Shafer theory[END_REF] with k = 3. We could have chosen another one with other settings, it can be seen as a black box.

The first test set we consider is composed of synthetic data composed of 3 classes built from 3 bivariate normal distributions with respective means µ ω1 = (1, 2), µ ω2 = (2, 1) and µ ω3 = (0, 0), and a common covariance matrix Σ s.t.

Σ = 1 0.5 0.5 1 . ( 13
)
For each class, 100 instances have been generated. They are illustrated in Figure 1. We have then considered several real data sets from the UCI database [START_REF] Dua | UCI Machine Learning Repository[END_REF] composed of numerical attributes as the EkNN classifier is used. Theses data sets are described in Table 1. For each dataset, a 10-repeated 10-fold cross validation has been undertaken as follows:

the group containing one tenth of the data is considered as the test set (the instances labels being made imprecise using Algorithm 1), the other 9 groups form the learning set, which is randomly divided into two groups of equal size:

• one group to learn the EkNN classifier (learnt from hard truths),

• one group to learn the parameters of the correction mechanisms from soft labels (the labels of the dataset are made imprecise using Algorithm 1).

For learning the parameters of contextual corrections, two strategies are compared.

1. In the first strategy, we use the optimization of Equation ( 8) from the closest hard truths from the soft truths (the most plausible class is chosen). Corrections with this strategy are denoted by CD, CR and CN. 2. In the second strategy, Equation ( 10) is directly optimized from soft labels (cf Section 3.3). The resulting corrections using this second strategy are denoted by CDsl, CRsl and CNsl.

The performances of the systems (the classifier alone and the corrections -CD, CR or CN -of this classifier according to the two strategies described above) are measured using Ẽpl [START_REF] Mercier | Refined Modeling of Sensor Reliability in the Belief Function Framework Using Contextual Discounting[END_REF], where δ represents the partially known truth. This measure corresponds to the sum over the test instances of the differences, in the least squares sense, between the truths being sought and the system outputs.

The performances Ẽpl (10) obtained from UCI and generated data for the classifier and its corrections are summed up in Table 2 for each type of correction. Standard deviations are indicated in brackets.

From the results presented in Table 2, we can remark that, for CD, the second strategy (CDsl) consisting in learning directly from the soft labels, allows one to obtain lower differences Ẽpl from the truth on the test set than the first strategy (CD) where the correction parameters are learnt from approximate hard labels. We can also remark that this strategy yields lower differences Ẽpl than the classifier alone, illustrating, in these experiments, the usefulness of soft labels even if hard labels are not available, which can be interesting in some applications.

The same conclusions can be drawn for CN.

For CR, the second strategy is also better than the first one but we can note that unlike the other corrections, there is no improvement for the first strategy in comparison to the classifier alone (the second strategy having also some close performances to the classifier alone).

Discussion and future works

We have shown that contextual corrections may lead to improved performances in the sense of measure Ẽpl , which relies on the plausibility values returned by the systems for each class for each instance. We also note that by using the same experiments as those in Section 4.2 but evaluating the performances using a simple 0-1 error criterion, where for each instance the most plausible class is compared to the true class, the performances remain globally identical for the classifier alone as well as all the corrections (the most plausible class being often the same for the classifier and each correction).

For future works, we are considering the use of other performance measures, which would also take fully into account the uncertainty and the imprecision of the outputs. For example, we would like to study those introduced by Zaffalon et al. [START_REF] Zafallon | Evaluating credal classifiers by utility-discounted predictive accuracy[END_REF].

It would also be possible to test other classifiers than the EkNN. We could also test the advantage of these correction mechanisms in classifiers fusion problems.

At last, we also intend to investigate the learning from soft labels using another measure than Ẽpl and in particular the evidential likelihood introduced by Denoeux [START_REF] Denoeux | Maximum likelihood estimation from uncertain data in the belief function framework[END_REF] and already used to develop a CD-based EkNN [START_REF] Kanjanatarakul | A New Evidential K-Nearest Neighbor Rule based on Contextual Discounting with Partially Supervised learning[END_REF].

Mrs. Mutmainah's research is supported by the overseas 5000 Doctors program of Indonesian Religious Affairs Ministry (MORA French Scholarship)

Fig. 1 .

 1 Fig. 1. Illustration of the generated dataset (3 classes, 2 attributes).

Table 1 .

 1 Characteristics of the UCI dataset used (number of instances without missing data, number of classes, number of numerical attributes used)

	Data	# Instances # Classes # Attributes
	Ionosphere	350	2	34
	Iris	150	3	4
	Sonar	208	2	60
	Vowel	990	11	9
	Wine	178	3	13

Table 2 .

 2 Performances Ẽpl obtained for the classifier alone and the classifier corrected with CD, CR and CN using both strategies. Standard deviations are indicated in brackets.

	Data	EkNN	CD	CDsl	CR	CRsl	CN	CNsl
	Generated Data 23.8 (3.8) 16.6 (2.8) 7.9 (1.5) 26.8 (3.0) 23.5 (3.7) 11.5 (1.6) 9.8 (0.6)
	Ionosphere 16.2 (2.5) 9.6 (2.2) 5.3 (1.0) 17.2 (1.9) 15.9 (2.3) 9.3 (1.3) 8.4 (0.9)
	Iris	12.5 (2.4) 8.4 (2.1) 3.3 (0.9) 13.1 (2.0) 12.3 (2.2) 6.7 (1.5) 4.8 (0.5)
	Sonar	7.8 (2.0) 6.3 (1.9) 3.5 (0.9) 9.0 (1.6) 7.7 (1.9) 5.1 (0.8) 5.0 (0.9)
	Vowel	279 (24) 278 (23) 62 (5) 310 (21) 279 (24) 240 (21) 65 (5)
	Wine	13.3 (2.6) 10.4 (2.3) 4.3 (1.0) 15.0 (2.1) 13.3 (2.5) 7.2 (1.6) 5.7 (0.6)

Acknowledgement

The authors would like to thank the anonymous reviewers for their helpful and constructive comments, which have helped them to improve the quality of the paper and to consider new paths for future research.