Margaux Wiber

Elsa Maitre

Jean-Marc Poncet

Virginie Duchenet

Gandhi Damaj

Edouard Cornet

Xavier Troussard

A population-based study of hairy cell leukemia over a period of 20 years

Keywords: Hairy cell leukemia, HCL, epidemiology

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

Introduction

Hairy cell leukemia (HCL) is a rare and indolent B-cell chronic lymphoproliferative disorder that accounts for 2% of all leukemia. HCL is four to five times more frequent in men than women. At diagnosis, the median age of HCL patients is 55 years old Patients with HCL commonly present with splenomegaly, infections, or pancytopenia.

Abnormal hairy cells are characterized by the expression of CD103, CD123, CD25 and CD11c antigens, in addition to the pan-B-cell antigens CD19, CD20 or CD22 [START_REF] Matutes | Immunophenotyping and Differential Diagnosis of Hairy Cell Leukemia[END_REF].

In more than 80-90% of cases, the BRAF V600E mutation can be identified [START_REF] Tiacci | BRAF Mutations in Hairy-Cell Leukemia[END_REF]. Over the past few decades, HCL treatment has progressively changed over time. In the 1980s, splenectomy was the standard treatment. Interferon alpha (IFN-α) was subsequently introduced and used until the early 2000s [START_REF] Quesada | Alpha interferon for induction of remission in hairy-cell leukemia[END_REF]. Then the purine nucleoside analogues (PNAs) pentostatin (2'-deoxycoformycin) [START_REF] Spiers | Hairy-cell leukemia: induction of complete remission with pentostatin (2'-deoxycoformycin)[END_REF] and cladribine (2-chlorodeoxyadenosine) [START_REF] Piro | Lasting remissions in hairy-cell leukemia induced by a single infusion of 2-chlorodeoxyadenosine[END_REF] were introduced; these drugs are currently the first-line therapeutic option for symptomatic HCL patients [START_REF] Troussard | Hairy cell leukemia 2018: Update on diagnosis, riskstratification, and treatment[END_REF]. New drugs have recently emerged, especially BRAF inhibitors (BRAFi) (vemurafenib, dabrafenib), BRAFi associated with MEK inhibitors (trametinib, cobimetinib), CD22-targeted therapy and BCR inhibitors (BCRi) (ibrutinib). In all HCL cases, long-term follow-up is mandatory because of the risk of relapses and secondary malignancies.

The few available population-based studies of HCL are limited in scale [START_REF] Bernstein | Epidemiology of Hairy Cell Leukemia in Los Angeles County[END_REF][START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF][START_REF] Paltiel | A population-based study of hairy cell leukemia in Israel[END_REF][START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Chandran | Improved survival in hairy cell leukaemia over three decades: a SEER database analysis of prognostic factors[END_REF][START_REF] Teodorescu | Incidence, risk of infection and survival of hairy cell leukaemia in Denmark[END_REF][START_REF] Kristinsson | Epidemiology of hairy cell leukemia in Iceland[END_REF]. We analyzed the clinical and biological data of 123 new HCL cases recorded between 1996 and 2016 in the Regional Register of Hematological Malignancies of Western Normandy (RRHMNO). The main objectives of the study were to describe in the real life the clinical and biological characteristics of HCL patients; to establish the crude incidence rate and the overall age-standardized incidence ratio (SIR); to analyze the overall survival (OS), the time to next treatment (TNT), and also the risk of secondary malignancies.

Patients and methods

Patients.

The RRHMNO is a regional specialized registry in hematology, which actively records all incident cases of hematological malignant diseases (HM), including all HCL patients living in Western Normandy. Western Normandy is

HCL diagnosis.

We selected all HCL patients diagnosed between 1996 and 2016, with a follow-up by the national directory for the identification of natural persons (RNIPP) for vital statistics until September 15, 2018. Patients with the variant form of hairy cell leukemia (HCL-v) were excluded. HCL diagnosis was based on identification of hairy cells in the peripheral blood and/or bone marrow. In most cases, flow cytometry (FCM) was achieved in the peripheral blood and/or bone marrow. In addition, the identification of the BRAF V600E mutation was performed in the most recent cases. Symptomatic HCL was defined as a hemoglobin level less than 110 g/L, platelet count less than 100x10 9 /L or neutrophil count less than 1x10 9 /L. These are the limit values that determine the implementation of a drug treatment according to the recommendations [START_REF] Grever | Consensus guidelines for the diagnosis and management of patients with classic hairy cell leukemia[END_REF]. Secondary malignancies were defined as second neoplasms diagnosed after HCL diagnosis.

Assessment of response.

The definition of complete response (CR) required normalization of peripheral blood counts: hemoglobin > 11 g/dL without transfusion, platelets > 100,000/µL and an absolute neutrophil count >1500/µL with absence of morphologic evidence of HCL on both the peripheral blood smear and the bone marrow examination [START_REF] Xi | Both variant and IGHV4-34-expressing hairy cell leukemia lack the BRAF V600E mutation[END_REF]. In addition, patients were required to lack any palpable splenomegaly on physical examination and to have achieved full resolution of all symptoms related to the disease. The vast majority of our patients did not have a follow-up bone marrow examination, which is not mandatory outside of clinical trials according to French recommendations [START_REF] Cornet | French Society of Haematology, Recommendations of the SFH (French Society of Haematology) for the diagnosis, treatment and follow-up of hairy cell leukaemia[END_REF]. In our study, we defined hematological complete response (HCR) as recovery of blood counts and resolution of all clinical symptoms. Statistical analysis. Categorical variables were summarized with frequencies and percentages and compared using Fisher's exact test or the χ 2 test, depending on their distribution. Continuous variables were summarized with a median value and range and compared using the Mann-Whitney U test or the Kruskal-Wallis test. OS was defined as the time from the date of HCL diagnosis until death from any cause or the date of last observation. Time to next treatment (TNT) was defined as the time from start date of first-line treatment until start date of second-line treatment, death from any cause or date of last observation. OS and TNT were plotted using the Kaplan-Meier method and compared by a log-rank test. Univariate analysis was performed using the following variables: sex, diagnosis period and first-line therapy.

Multivariable analysis was not performed due to the low number of events. P-values were considered to indicate statistical significance when <0.05. All statistical analyses were performed using GraphPad Prism version 8.0.2 for Windows (GraphPad Software, La Jolla California USA, www.graphpad.com).

Concerning the description of the RRHMNO general data, the SIR of most hematological malignancies in Western Normandy was assessed between 1997 and 2016. For the reference population, we chose the median year of the period analyzed, 2007. The annual gross rate was calculated by dividing the headcount by the population of Lower Normandy in 2007 and was reported as the number per 100,000 inhabitants. The SIR was calculated by multiplying the annual gross ageclass rate by the 2007 world population for each age group. Then, the different standardized rates were added together and divided by the 2007 global population.

Results

Distribution of malignant hematological disorders.

Over the period 1996-2016, RRHMNO recorded 18.324 hematological malignancies, 9.898 cases (54%) in men and 8.426 (46%) in women. The crude incidence rate and the overall SIR for each malignant hematologic disorder are listed in Table 1. In men, the top three malignant hematologic disorders were myelodysplastic syndromes (1.446 patients), chronic lymphocytic leukemia (1.274 patients) and multiple myeloma/plasmacytoma (1.133 patients). In women, myelodysplastic syndromes (1,233 patients), myeloproliferative neoplasms (1.157 patients) and multiple myeloma/plasmacytoma (1.051 patients) were identified in the database.

Study population characteristics.

One hundred and twenty-three patients, 102 men (82.9%) with a median age at diagnosis of 63 years (33-92) and 21 women (17.1%) with a median age at diagnosis of 59 years , were included in the study. Only 2 patients (1.6%) were between 30 and 39 years old, 76 patients (61.8%) were between 40 and 69 years old, and 45 patients (36.6%) were ≥ 70 years old.

Patient characteristics are presented in Table 2. At diagnosis, 41 patients (33%) had splenomegaly, and 24 patients (19.5%) had infections, mostly lung infections (50%).

One patient presented atypical mycobacterial infection and two patients had lymph node tuberculosis. Eight patients (6.5%) had hemorrhagic manifestations. Almost all patients had at least one cytopenia with, in order of frequency, thrombocytopenia in 76 patients (62%), neutropenia in 66 patients (54%) and anemia in 47 patients (38%). Pancytopenia was observed in 25 patients (20.3%) (Table 2). Bone marrow aspiration showed medullary infiltration by hairy cells, associated with a decrease in marrow cells in 79.3% of cases. Bone marrow biopsy was performed in only 18.7% of cases. FCM was performed in 84/123 patients (68.3%), and the clonal nature of the cells by the isotypic restriction of the immunoglobulin light chains was confirmed in all cases. The expression of CD103, CD25, CD11c and CD123 markers was positive in 95% of cases (40/42 patients). The expression of only 3 of the 4 markers was observed in two patients: negative markers were either CD103 or CD123. The BRAF V600E mutation was demonstrated in all 40 recently tested patients.

Standardized incidence ratio (SIR)

. HCL represented 0.7% of all malignant hematological disorders and 3.0% of all leukemia, 1.0% and 4.5% in men and 0.3% and 1.2% in women, respectively. The crude incidence rate was 0.71/100,000 in men and 0.15/100,000 in women. The overall SIR was 0.39/100,000 inhabitants in men and 0.09/100,000 inhabitants in women (Table 1).

Overall Survival (OS)

The median OS was over 15 years (188 months), with a 5year and 10-year survival rate of 84% and 70.5%, respectively (Figure 1). The characteristics and treatments were similar between men and women, and no significant difference in OS was observed (P-value=0.11).

Treatment. After a median follow-up of 60 months (0-264), 74 patients (60.2%) were alive, and 49 (39.8%) patients died. The median number of lines of treatment was 1.3 (0-5). Sixteen patients (13%) did not receive treatment. Out of the 16 patients without treatment, 5 symptomatic HCL patients died very shortly after diagnosis, 4 patients were over 75 years old and presented comorbidities, 6 patients were asymptomatic, and one patient declined the treatment. One hundred seven patients (88%) received first-line treatment, 33 patients (27%) at least 2 treatment lines and 10 patients (8%) received more than 2 lines. As first-line treatment, 47 patients received IFN-α (43.9%), 49 patients (45.8%) received cladribine and 11 patients (10.3%) received pentostatin. Hematological complete response (HCR) was observed in 97.5%, 92% and 90% of cases, respectively. Cladribine and pentostatin were combined in the same group we called PNAs for statistical analyses. Patient characteristics (age, sex ratio, clinical presentation, and blood count) according to first-line treatment were similar with the exception of the infection rate, which was higher in PNAs group (P-value=0.0008) (Tableau 3). The follow-up period was also statistically different with a median follow-up of 183 months (range, 0.01-264) in IFN-α group and only 87 months (range, 1-231) in PNAs group (P-value <0.0001). Time to next treatment (TNT) was compared according to first-line treatment. The median TNT was 147 months for PNAs and 84 months for IFN-α. However, the difference was not statistically significant (P-value=0.1481) (Figure 2). Overall survival (OS) was compared between patients, who received just only one line of treatment, either IFNα or PNAs. The difference was not statistically significant between both groups, with a median OS of 153 months for patients treated with IFN-α and not reached for PNAs (P-value=0,4763). However, a second-line treatment was required more often in patients treated in first line by IFN-α (20/47, 43%) compared to those treated by PNAs (13/60, 22%) (P-value=0,03408). Of the 20 patients who received IFN-α as first-line, 14 received PNAs as second line, 5 IFN-α and one patient was splenectomized. Of the 13 patients who received PNAs as first-line, 7 received PNAs again, of the same type as in first line in 5 out of 7 cases, 3 received rituximab, 2 received IFN-α and one received the combination of pentostatin plus rituximab. The mean number of treatment lines was 1.6 (range, 1-5) in the IFN-α group and 1.3 (range, 1-3) in the PNAs (P-value=0.0095).

The study was divided into 4 calendar periods : 1996-1999, 2000-2004, 2005-2009 and 2010-2016. The number of new HCL cases yearly remained stable over time, with a mean of 6 cases per year [START_REF] Quesada | Alpha interferon for induction of remission in hairy-cell leukemia[END_REF][START_REF] Spiers | Hairy-cell leukemia: induction of complete remission with pentostatin (2'-deoxycoformycin)[END_REF][START_REF] Piro | Lasting remissions in hairy-cell leukemia induced by a single infusion of 2-chlorodeoxyadenosine[END_REF][START_REF] Troussard | Hairy cell leukemia 2018: Update on diagnosis, riskstratification, and treatment[END_REF][START_REF] Bernstein | Epidemiology of Hairy Cell Leukemia in Los Angeles County[END_REF][START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF][START_REF] Paltiel | A population-based study of hairy cell leukemia in Israel[END_REF][START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Chandran | Improved survival in hairy cell leukaemia over three decades: a SEER database analysis of prognostic factors[END_REF][START_REF] Teodorescu | Incidence, risk of infection and survival of hairy cell leukaemia in Denmark[END_REF][START_REF] Kristinsson | Epidemiology of hairy cell leukemia in Iceland[END_REF]. The characteristics of the patients were also similar and did not change with time, with the exception of a smaller percentage of women over the period from 2005 to 2009 (sex ratio: 11.0). Regarding the management of HCL patients, IFN-α was gradually replaced by cladribine in first line. Some patients who received IFN-α in the first line, benefited from the introduction of PNAs as second line (n=14). The percentage of patients treated with pentostatin remained similar over time. Rituximab emerged in the therapeutic arsenal mainly from 2010, and was used in second line and more, either in monotherapy (n=6) or combination (n=2). In the univariate analysis, we did not observe a statistically significant difference in OS between the different periods analyzed (Figure 3). Furthermore, 4 malignancies were diagnosed concurrently with HCL: renal cell carcinoma, colorectal cancer, chronic lymphocytic leukemia, and follicular lymphoma.

Discussion

HCL is a rare hematologic disorder, and few population-based studies have been published [START_REF] Bernstein | Epidemiology of Hairy Cell Leukemia in Los Angeles County[END_REF][START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF][START_REF] Paltiel | A population-based study of hairy cell leukemia in Israel[END_REF][START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Chandran | Improved survival in hairy cell leukaemia over three decades: a SEER database analysis of prognostic factors[END_REF][START_REF] Teodorescu | Incidence, risk of infection and survival of hairy cell leukaemia in Denmark[END_REF][START_REF] Kristinsson | Epidemiology of hairy cell leukemia in Iceland[END_REF]. This study represents in real life the experience of HCL management in a single French center (Western Normandy) over a period of 20 years. HCL diagnosis was established, including clinical, biological, and molecular studies. The demographic characteristics are similar to those reported in the literature [START_REF] Bernstein | Epidemiology of Hairy Cell Leukemia in Los Angeles County[END_REF][START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF][START_REF] Paltiel | A population-based study of hairy cell leukemia in Israel[END_REF][START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Chandran | Improved survival in hairy cell leukaemia over three decades: a SEER database analysis of prognostic factors[END_REF][START_REF] Teodorescu | Incidence, risk of infection and survival of hairy cell leukaemia in Denmark[END_REF][START_REF] Kristinsson | Epidemiology of hairy cell leukemia in Iceland[END_REF][START_REF] Kraut | Clinical manifestations and infectious complications of hairy-cell leukaemia[END_REF]. Note that only one-third of patients presented splenomegaly, while most studies reported a rate of approximately two-thirds. We can explain the difference by an earlier diagnosis. Three patients presented mycobacterial infections, in line with the known particular susceptibility to this type of infections. The immunologic panel we used, included initially CD103 and has widened over time with other typical markers, CD25, CD11c and CD123. These markers are usually negative in other HCL-like disorders: HCL-v, splenic marginal zone lymphoma (SMZL) and splenic diffuse red pulp small B-cell lymphoma (SDRPL). In the current study, we found an immunological score greater than or equal to 3 in all cases. The BRAF V600E somatic mutation was initially described in 2011 [START_REF] Tiacci | BRAF Mutations in Hairy-Cell Leukemia[END_REF] and is now considered the molecular hallmark of the disease. The absence of the BRAF gene mutation was reported in up to 10% to 20% of patients with HCL and could constitute a subgroup of HCL patients with IGHV4-34 rearrangement and a poor prognosis [START_REF] Xi | Both variant and IGHV4-34-expressing hairy cell leukemia lack the BRAF V600E mutation[END_REF][START_REF] Arons | VH4-34+ hairy cell leukemia, a new variant with poor prognosis despite standard therapy[END_REF]. In particular, the BRAF V600E mutation must be searched for in cases of relapsed/refractory disease to rule out the diagnosis of HCL-v. Moreover, the presence of the mutation is necessary for the use of BRAFi. In our cohort, all 40 tested samples presented the BRAF V600E mutation.

The therapeutic management of the patients is in line with the main recommendations: PNAs remain the gold standard of HCL in first line treatment. The second line treatment is based on immunochemotherapy associating PNAs plus rituximab. The new drugs (BRAFi, BCRi, immunotoxins) [START_REF] Troussard | Hairy cell leukemia 2018: Update on diagnosis, riskstratification, and treatment[END_REF] introduced more recently are an option in cases of relapsed/refractory HCL: they were not still used in our cohort, with HCL diagnosis between 1996 and 2016.

The incidence of HCL remained stable over the period analyzed, with similar patient characteristics. We did not observe an improvement of the OS over time. Recent data [START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF] showed an improvement in the relative survival (RS) of patients only aged between 60 and 69 years and analyzed between 2001-2015, as compared to 1989-1993. However, the RS was similar between 1994-2000 and 2001-2015.

We found no statistically significant difference in OS between men and women. The median age at diagnosis was 59 years in women and 63 years in men. A recent Israeli study reported better outcomes in females than in males [START_REF] Inbar | Hairy Cell Leukemia: Retrospective Analysis of Demographic Data and Outcome of 203 Patients from 12 Medical Centers in Israel[END_REF]. A similar difference was also observed in patients with chronic lymphocytic leukemia (CLL), with women generally having an earlier disease stage at diagnosis and fewer comorbidities [START_REF] Molica | Sex differences in incidence and outcome of chronic lymphocytic leukemia patients[END_REF]. In non-Hodgkin lymphomas, women have a better prognosis than men due to a better response to immunochemotherapy [START_REF] Horesh | Does Gender Matter in Non-Hodgkin Lymphoma? Differences in Epidemiology, Clinical Behavior, and Therapy[END_REF]. In HCL, the life expectancy of patients being close to that of the general population [START_REF] Dinmohamed | Relative survival reaches a plateau in hairy cell leukemia: a population-based analysis in The Netherlands[END_REF], the better survival of women might simply reflect their better general longevity. In our study, we did not show statistically significant difference in OS between patients who received only one line of treatment by either IFN-α or PNA. This may be explained by the small number of patients in our cohort and by the difference of the follow-up time. It is important to note that OS is not probably a relevant indicator in a disease with a good long-term survival.

Most patients who received first-line PNA treatment did not need a second line compared to those treated with IFN-α. Moreover, the time to next treatment, even if it is not statistically demonstrated, seems to be longer in PNAs group (median TNT: 147 months) than in the IFN-α group (median TNT: 87 months), which suggests a longer duration of response to treatment. In addition, the modalities of taking cladribine over 5 consecutive days are less restrictive for the patient than those of IFN-α, which is administered subcutaneously three times weekly and produces frequent side effects. Indications for IFN-α are now more restricted in patients with severe febrile neutropenia (<0.2 G/L), active infection and in pregnant women [START_REF] Troussard | Hairy cell leukemia 2018: Update on diagnosis, riskstratification, and treatment[END_REF][START_REF] Grever | Consensus guidelines for the diagnosis and management of patients with classic hairy cell leukemia[END_REF].

The rate of secondary malignancies reported in our study was 7.3% is rather in the lower range of what we find in the literature (range,4-24%) [START_REF] Bernstein | Epidemiology of Hairy Cell Leukemia in Los Angeles County[END_REF][START_REF] Paltiel | A population-based study of hairy cell leukemia in Israel[END_REF][START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Kurzrock | Second cancer risk in hairy cell leukemia: analysis of 350 patients[END_REF][START_REF] Federico | Italian Cooperative Group for the Study of Hairy Cell Leukemia, Risk of second cancer in patients with hairy cell leukemia: long-term follow-up[END_REF][START_REF] Kampmeier | Increased incidence of second neoplasms in patients treated with interferon alpha 2b for hairy cell leukemia: a clinicopathologic assessment[END_REF][START_REF] Pawson | Second malignancy in hairy cell leukaemia: no evidence of increased incidence after treatment with interferon alpha[END_REF][START_REF] Cheson | Second malignancies as a consequence of nucleoside analog therapy for chronic lymphoid leukemias[END_REF][START_REF] Flinn | Long-term follow-up of remission duration, mortality, and second malignancies in hairy cell leukemia patients treated with pentostatin[END_REF][START_REF] Jacobs | Second malignancies in hairy cell leukemia[END_REF][START_REF] Au | Second malignancies in patients with hairy cell leukemia in british columbia: a 20-year experience[END_REF][START_REF] Saven | Long-term follow-up of patients with hairy cell leukemia after cladribine treatment[END_REF][START_REF] Goodman | Extended follow-up of patients with hairy cell leukemia after treatment with cladribine[END_REF][START_REF] Maloisel | Long-term outcome with pentostatin treatment in hairy cell leukemia patients. A French retrospective study of 238 patients[END_REF][START_REF] Troussard | Second cancer risk after interferon therapy?[END_REF][START_REF] Zheng | Second primary cancers in patients with acute lymphoblastic, chronic lymphocytic and hairy cell leukaemia[END_REF]. The differences in the incidence of secondary malignancies could depend on the type of cancer reported, the number of patients in the cohort and, importantly, the length of patient follow-up. Data in the literature are controversial concerning the link between HCL and the impact of the treatment and the increased risk of secondary malignancies. We showed in 2014 [START_REF] Cornet | the Société Française d'Hématologie, Long-term follow-up and second malignancies in 487 patients with hairy cell leukaemia[END_REF] an increased risk of secondary neoplasm, with SIR = 1.86 (95% CI, 1.34-2.51), independent of the type of treatment. Secondary malignancies would thus be linked to the pathology itself and probably to the intrinsic immune alterations induced by HCL that diminished antitumor defense [START_REF] Bourguin-Plonquet | Severe decrease in peripheral blood dendritic cells in hairy cell leukaemia[END_REF][START_REF] Netea | Defective interferon-gamma production in patients with hairy cell leukaemia[END_REF][START_REF] Bigda | Interleukin 2-and interferon alpha induced natural killer cell activity as a marker of progression in hairy cell leukemia[END_REF][START_REF] Van De Corput | Impaired expression of CD28 on T cells in hairy cell leukemia[END_REF]. If several types of cancers can occur, some studies report a particularly increased risk of developing non-Hodgkin B-cell lymphomas [START_REF] Hisada | Second cancer incidence and cause-specific mortality among 3104 patients with hairy cell leukemia: a population-based study[END_REF][START_REF] Zheng | Second primary cancers in patients with acute lymphoblastic, chronic lymphocytic and hairy cell leukaemia[END_REF][START_REF] Cornet | the Société Française d'Hématologie, Long-term follow-up and second malignancies in 487 patients with hairy cell leukaemia[END_REF] and skin tumors [START_REF] Zheng | Second primary cancers in patients with acute lymphoblastic, chronic lymphocytic and hairy cell leukaemia[END_REF][START_REF] Da Silva | Outcomes and second neoplasms in hairy cell leukemia: A retrospective cohort[END_REF][START_REF] Watts | Melanoma and non-melanoma skin cancers in hairy cell leukaemia: a Surveillance, Epidemiology and End Results population analysis and the 30-year experience at Memorial Sloan Kettering Cancer Center[END_REF].

In our study, we observed different types of tumors, including one skin tumor and 1 lymphoid disorder. The SIR could not be calculated for our cohort due to the low number of events.

In conclusion, we report data from the first French registry study spanning an extended period of 20 years. The demographic characteristics of the HCL cohort are similar to what is usually described in the literature, including the frequency of secondary malignancies. The need of a long-term follow-up is mandatory in HCL patients. We did not find any difference in OS over time or in terms of first-line treatment. The number of patients in our cohort is probably a limiting factor. PNAs, with or without the addition of rituximab, are now recommended in first line treatment; this approach will decrease the relapse rate. The new drugs may also be effective in relapsed/refractory patients and change the management of patients with relapsed/refractory HCL.

Funding statement: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

  composed of three departments, called La Manche, l'Orne and Le Calvados. The RRHMNO covers a population of 1,477,349 inhabitants, 693,679 inhabitants in Le Calvados, 498,362 inhabitants in La Manche and 285 308 inhabitants in l'Orne (INSEE estimates, January 2016). The RRHMNO belongs to the network France Cancer Incidence and Mortality (Francim), composed of general and specialized registers allowing the surveillance of approximately 8 million people corresponding to 13 to 14% of the French population. The WHO classification of tumours of the haematopoietic and lymphoid tissues (4 th edition) was used to classify the hematologic malignancies. Validated cases were registered in a database hosted on a secure server of the hospital of Caen, France. Recorded data focused on medical history, clinical presentation, biological results, treatment, and secondary neoplasms.

  Secondary malignancies. Nine (7.3%) secondary malignancies were diagnosed after HCL diagnosis. Eight patients developed solid tumors, and 1 developed hematological malignancy. The solid tumors comprised prostate cancers (n=4), lung cancers (n=2), a skin and facial tumor, and a pancreatic cancer. The hematological malignancy was an EBV-induced large B-cell lymphoma. The median time from HCL diagnosis to secondary malignancy was 76 (range, 12-258) months for solid tumors.The time from HCL diagnosis to the large B-cell lymphoma was 184 months.

Figure 1 .

 1 Figure 1. Overall survival (OS) for all patients (n=123).

Figure 2 .

 2 Figure 2. Time to next treatment (TNT) according to first-line therapy.

Figure 3 .

 3 Figure 3. Overall survival (OS) according to the period of diagnosis.

Table 1 .

 1 Incidence of hematological malignancies in Western Normandy.

		Men (N) Western Normandy 1996-2016	Crude incidence rate/100,000	Standardized incidence rate (SIR) /100,000	Women (N) Western Normandy 1996-2016	Crude rate/100,000 incidence	Standardized incidence rate (SIR) /100,000
	Acute leukemia	838	5.92	4.24	801	5.31	3.67
	Myeloproliferative disorder	1120	7.91	4.31	1157	7.67	4.01
	Myelodysplastic syndrome	1446	10.22	4.10	1233	8.18	3.04
	Chronic myelomonocytic leukemia	182	1.29	0.51	119	0.79	0.30
	B-cell lymphoma including :	2444	17.27	9.24	2111	14.00	7.01
	Diffuse large B-cell lymphoma	1014	7.17	3.94	931	6.17	3.07
	Follicular lymphoma	473	3.34	1.97	468	3.10	1.73
	Marginal zone lymphoma	342	2.42	1.20	303	2.01	0.98
	Mantle cell lymphoma	232	1.64	0.73	102	0.68	0.29
	Other B-cell lymphomas	383	2.71	1.41	307	2.04	0.94
	Mature B-cell lymphoproliferative disorder including:	1704	12.04	5.72	1155	7.66	3.43
	Chronic lymphocytic leukemia	1274	9.00	4.29	943	6.25	2.81
	Waldenstrom macroglobulinemia	321	2.27	1.01	182	1.21	0.51
	Hairy cell leukemia	102	0.71	0.39	21	0.15	0.09
	Prolymphocytic leukemia	9	0.06	0.03	8	0.05	0.02
	Myeloma and plasmacytoma	1133	8.01	3.85	1051	6.97	3.18
	Hodgkin lymphoma	443	3.13	2.96	345	2.29	2.44
	T-cell lymphoma	388	2.74	1.73	270	1.79	1.20
	Mature T-cell lymphoproliferative disorder	107	0.76	0.40	106	0.70	0.36
	Other lymphomas	72	0.51	0.25	58	0.38	0.14
	Histiocytosis	21	0.15	0.15	20	0.13	0.18
	TOTAL	9898	69.95	37.45	8426	55.88	28.96

Table 2 .

 2 Patient characteristics (n=123).

	n=123

Table 3 .

 3 Comparison of patient characteristics according to first-line treatment.

		Purin analogs (n=60)	Interferon (n=47)	P-value
	Median age at diagnosis, years (range)	60 (33-89)	65 (41-84)	0.0997
	Male:female ratio	6,5	4,2	0.4369
	Follow-up (months), median (range)	87 (1-231)	183 (0-264)	<0,0001
	Splenomegaly, n (%)	23 (38%)	15 (32%)	0.5453
	Alteration of the general state, n (%)	17 (28%)	9 (19%)	0.3644
	Infections, n (%)	18 (30%)	2 (9%)	0.0008
	Neutrophil count (x10 9 /L), median (range)	0.78 (0.18-4.40) 1.00 (0.16-2.02)	0.2962
	Hemoglobin (g/L), median (range)	12.1 (4.9-15.5) 11.4 (4.4-15.2)	0.0921
	Platelet count (x10 9 /L), median (range)	83 (17-320)	87 (21-494)	0.6625


Eric Innocenti
email: eric.innocenti@univ-corse.fr

Claudio Detotto

Corinne Idda

Dawn Cassandra Parker

Dominique Prunetti

An iterative process to construct an interdisciplinary ABM using MR POTATOHEAD: An application to Housing Market Models in touristic areas

Keywords: Complex systems, ABM/LUCC, MR POTATOHEAD, Conceptual Modeling, NetLogo pattern

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

Introduction

In the last few years, Agent-Based Models (ABM) have sought to address questions of economics in the field of Land Use and Cover Change [START_REF] Parker | An economic perspective on agent-based models of land use and land cover change[END_REF]. For land market models in particular, Agent-Based Models of Land Use and Cover Change (ABM/LUCC) provide modeling paradigms and formalisms that are more and more acknowledged for their effectiveness to produce modular and scalable computer models for virtual experimentation. They supply engineering concepts, methods and IT techniques that provide a new way to overcome the inherent difficulty of spatial land-use planning models that describe economic development and land competition. ABM/LUCC computer models facilitate the behavior of highly heterogeneous economic agents in very diverse areas and biotopes. While corresponding classic economic models are generally analytically intractable, the ABM/LUCC make it possible to simulate heterogeneous behaviors integrating many interacting components. Conceptual formalisms based on Agent-Based Models (ABM) are a prerequisite to effectively carry out the interdisciplinary labor that is needed to development computer code.

However, the path from the verbal and mathematical model descriptions traditionally employed by economists to the detailed specifications required to create a computer model is not transparent.

The methods and formalisms coming from Modeling & Simulation computer science (M&S) can dictate a formal modeling process that can assist in this process.

In this paper, we present a method to build an ABM/LUCC of land and housing market using Design Patterns. We highlight benefits offered by this software engineering technique to design reusable, extensible and scalable code for economic models. Design patterns couple recurrent problems and their solutions to overcome the difficulties raised when designing software components.

They are usually employed by modelers experienced in Object Oriented Programming (O.O.P.).

The use of Design Patterns in M&S is fairly new and seems to be promising -especially in ABM design [START_REF] Torres | More design patterns for multi-agent systems[END_REF][START_REF] Alexander | A pattern language: towns, buildings, construction[END_REF]. Design patterns provide solutions for modelers to design and write computer models that are accessible to all researchers community members.

Hence, design patterns improve the modeling process in multidisciplinary contexts, such as our case study. We show how design patterns can be used in the modeling process: from the conceptualization and description of the real-world problem, to design of the computer model, to implementation of the programming model. Our contribution also aims to increase uptake of design patterns used at all stages of the modeling process by a larger audience of researchers in M&S. To this end, we use textual specification and graphics formalisms, the MR POTATOHEAD: Property Market Edition to develop a conceptual model representing the different points of view and behaviour of system actors, for our real world case study. The exercise provides an example of an interdisciplinary process modeling involving economists and computer scientists to formulate an ABM/LUCC computer model, which describes the organization of computer code. By means of the ABM/LUCC formalisms, we built our ABM/LUCC for a tourist area that faces an intense residential development leading to a huge pressure on land prices as well as to land-use conflicts.

The rest of the paper is organized as follows. In section 2, we present the use of design pattern in computer simulation and describe the MR POTATOHEAD conceptual design pattern specifically used for describing ABM/LUCC. A short review of ABM/LUCC literature regarding the main papers used to formulate the structure, the behavior algorithms as well as the simulation rules governing the ABM/LUCC agents follows. In section 3, we present how we apply the methodology based on MR POTATOHEAD Property Market Edition standardization [START_REF] Parker | MR POTATOHEAD: Property Market Edition-Development of a Common Description Template and Code Base for Agent-Based Land Market Models[END_REF] in the context of our case study and the construction of the computer modeling process (Parker et al., 2008a,b;[START_REF] Parker | An economic perspective on agent-based models of land use and land cover change[END_REF]. We conclude and draw research perspectives in Section 4.

From the real world to the model

The modeling process

Computer simulation is a developing science that works to understand natural or artificial phenomena of our environment. For that purpose, simulation modelers have developed software tools based on conceptual computer models aiming at producing simulation data. Computer simulation has profited from recent progress in computer science in terms of concepts (paradigms, formalisms, norms, standards, algorithms, etc.), technologies (programming languages, structures, objects, components, etc.), and hardware (CPU, memory, GPGPU, networks, etc.). The modeling process has also been the subject of much recent literature discussion [START_REF] Chwif | A framework for specifying a discreteevent simulation conceptual model[END_REF][START_REF] Balci | How to successfully conduct large-scale modeling and simulation projects[END_REF][START_REF] Mitroff | On managing science in the systems age: two schemas for the study of science as a whole systems phenomenon[END_REF]. In the area of economic research, computer simulation science has the potential to improve our understanding capacity to investigate real economic complex systems [START_REF] Arthur | Complexity and the Economy[END_REF][START_REF] Tesfatsion | Modeling economic systems as locally-constructive sequential games[END_REF]. These systems are composed of a large number of heterogeneous entities and consequently, behavioral descriptions result from multiples entities' interactions. The process of modeling such systems principally includes formulations of conceptual and computer models that are carried out by modelers in charge of a simulation project.

The concept of model is first and foremost, the representation of the complex system under study in the form of an abstraction (reality simplification). The abstraction should clearly articulate parts of the complex system in a set of components. These components must be formulated using carefully chosen criteria and according to a relevant point of view for the study. In the literature, numerous authors have pointed out to that a model must remain sufficiently "simple" regarding component's formulations [START_REF] Tesfatsion | Modeling economic systems as locally-constructive sequential games[END_REF]. Indeed, refined descriptions of components may considerably slow down the modeling process, generate unnecessary complexity, and provides both wrong simulation and questionable results. In computer simulation science, it is now understood that every rigorous modeling process needs prior to describe a first abstraction of the complex system: the conceptual model. The conceptual model is the first representation of the complex system. This first representation is developed according to a layered descriptive process. Historically, mathematics initiated the abstraction process, giving the first abstractions methods for complex systems. In computer simulation, the modeling process corresponds to the use of methods describing sets of sequential transformation (generic if possible) working to move the initial math abstraction from its continuous universe (problem's universe) to the discrete universe of the computer science (model's universe).

Thus, the conceptual model constitutes a prerequisite for writing computer models describing the computer code organization that finally runs on the computers [START_REF] Chwif | A framework for specifying a discreteevent simulation conceptual model[END_REF].

Economics has had a long tradition of conceptual model description via formal closed-form mathematics, accompanied by sparse verbal descriptions. Such a conceptual model suffices for non-complex systems -those for which analytical mathematics can be applied to describe the system and fully characterize its behavior. However, agent-based models of economic systems need to move beyond such mathematical conceptual representations, because they are simulated, potentially nonequilibrium systems. Thus a further challenge is created -how to create a conceptual design pattern that can move from a traditional economic model description to the full detail needed to implement a computer simulation.

A brief history of design patterns

The concept of a design pattern comes from [START_REF] Alexander | A pattern language: towns, buildings, construction[END_REF], whose authors worked in the 1970's on architectural design. They defined the notion of pattern, as follows: "Each pattern describes a problem which occurs over and over again in our environment, and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing it the same way twice.". This sentence has been the source of Design Pattern concept, i.e. formulation of a recurrent issue, and it solution in a precise context. Later, Designs Patterns were introduced into computer science, thanks to O.O.P. with the Model-View-Controller (MVC) pattern1 [START_REF] Buck | Les design patterns de Cocoa[END_REF]. Towards the end of 1980's, the works of Reid Smith also contributed to the use of design patterns in computer science [START_REF] Smith | Panel on design methodology[END_REF]. [START_REF] Beck | Using pattern languages for object-oriented programs[END_REF] proposed adapting the pattern language to O.O.P, through five compositions for user interfaces design. In 1995, the use of design patterns accelerated thanks to the "GoF" ("Gang of Four"): Erich Gamma, Richard Helm, Ralph Johnson and John Vlisides [START_REF] Gamma | Design patterns: elements of reusable object-oriented software[END_REF]. In this book, the design patterns are described under an accurate terminology for developing reusable software components with O.O.P. languages. These patterns are well-known solutions to classic design problems of software components encountered in a given programming context. For that, when its possible they must appears in the computer model. They must be used to enhance simulation code explanations and reproducibility.

As it is noted in modeling literature, the production of a computer model is therefore the result of prior formalization work (conceptual model). Such prior formalization makes it possible to avoid constraining the modelers' thinking within the constraints of the technical considerations of M&S. In addition, the computer model aims to produce modular, scalable and interoperable computer code (the programming model) (cf. Figure 1). In M&S, with the complexity of conceptual models, there is a need to develop methodologies to correctly and efficiently explain computer model components and their interconnections. These methodologies must ease production of object simulation code in a modular, extensible, and scalable form, and they also make best use of the modern computers multi-task and parallel hardware [START_REF] Touraille | A model-driven software environment for modeling, simulation and analysis of complex systems[END_REF]. Hence, they must capitalize knowledge and know-how within the simulation researchers community, which use O.O.P. as a modeling framework [START_REF] Rovere | Practical points for the software development of an agent-based model of a coupled human-natural system[END_REF][START_REF] Innocenti | A software framework for fine grain paral-lelization of cellular models with Openmp: Application to fire spread[END_REF]. While design patterns have the potential to solve these challenges, today, despite their many benefits, they are still rarely used in computer simulation. In this paper, through illustration of the role of design patterns in our model development, we hope to make design patterns more accessible to modelers in charge of computer simulations.

The MR POTATOHEAD conceptual design pattern

The path from real-world description to conceptual model to computer/programming code presents an infinity of choices available for simplifying assumptions, corresponding to an infinity of formal abstractions, and following from them, many very different computer models, obtained via different process, but for a same complex system. This fact is well sum-up by [START_REF] Robinson | A tutorial on conceptual modeling for simulation[END_REF] through the quote "conceptual modeling is more an art than a science", p.1826. Agent-based modeling of land-use and land-cover change (ABM/LUCC) illustrate this phenomena. While their development has grown exponentially over the last 20 years, modelers developing case-study models in different locations, from different disciplinary perspectives, and with different resources, have developed a small universe of similar, but different ABM/LUCC. This trend is no less evident even in the smaller sub-field of agent-based land market models (ABM/LMM), where even collaborators sharing similar disciplinary backgrounds have developed divergent models of almost identical systems.

Concurrently, agent-based modeling of complex systems has acquired increasing rigor and formal methods [START_REF] Wilensky | An introduction to agent-based modeling: modeling natural, social, and engineered complex systems with NetLogo[END_REF][START_REF] Railsback | Agent-based and individual-based modeling: a practical introduction[END_REF], and can be now considered as a science in its own right, providing today a plethora of concepts, formalisms and methods aiming at considerably streamling the modeler's job. The conceptual design pattern and conceptual modeling framework MR POTATOHEAD presented in this paper follow this trend, striving to bring harmonized formalization and standardization to the cacophony of ABM/LUCC and ABM/LMM.

The need for systematize the information on ABM for bridging the gap between social scientists and computer scientist has led to attempts to develop a common language, e.g., the Agent-Based Model Canvas presented in [START_REF] Garibay | The agent-based model canvas: A modeling lingua franca for computational social science[END_REF]. The need for harmonized formalization and standardization in specific fields like ABM/LUCC and ABM/LMM requires more specific tools. MR POTATOHEAD was developed specifically to counter the problem described in general here: a multiplicity of slightly different conceptual, formal, and programming models developed for exactly the same real-world systems.

The MR POTATOHEAD conceptual design pattern (CDP) was developed by Parker et al. (2008a) as a generic standardized template for describing agent-based models of land-use and land-cover change. The CDP takes the form of a hierarchical ontology, which describes key components of and ABM/LUCC and their potential sub-instances, taking an object-oriented design approach. The CDP was designed to address challenges not addressed by standardized model description protocols such as ODD [START_REF] Grimm | The ODD protocol: A review and first update[END_REF] and UML [START_REF] Ambler | The elements of UML (TM) 2.0 style[END_REF]. These forms were found to be too generic, and to lack sufficient detail, to ensure full model transparency and replicability. Further, they could not be used to show how different model implementations were instances of a more general meta-model. Most significantly from the perspective of this paper, there is not a clear and direct linkage between the structure of a protocol such as ODD and the structure of a software design pattern (discuss below), which is one of the issues and challenges of ODD [START_REF] Grimm | The odd protocol for describing agent-based and other simulation models: A second update to improve clarity, replication, and structural realism[END_REF]. MR POTATOHEAD has been demonstrated to overcome some of these deficits. The CDP has been used to describe five different models (Parker et al., 2008a), to compare ABM/LUCC of frontier regions (Parker et al., 2008b), and to develop an interdisciplinary survey of the behaviour of residential land owners. Its formulation has proven to be an effective documentation protocol for the ABM/LUCC modeling process, facilitating better model communication and comparisons.

Here, we demonstrate that it can also be used to facilitate development of a computer model and its incrementation.

The computer model

The computer model describes in an appropriate modeling language the constituting element assembly of the complex system and their interactions, in a hierarchical manner in the model's universe. The computer model is often referred in literature as a composition, hierarchical or multi-component model. The computer model expresses with a modeling language, components and interactions coming from the descriptive elements of the conceptual model. Subsequently, the programming model describes the implementation of the computer model in a programming language, in accordance with the structural and behavioral entities defined in the computer model.

While programming model materializes in a programming language (usually an object oriented programming language), the computer model of the complex system, initially considered in the form of a conceptual model (cf. Figure 1). In computer simulation science, scientific credibility of an interdisciplinary modeling work requires presentation of a clear and precise computer model.

The chosen concepts should be rigorously expressed with a modeling language, and materialized at end of the modeling process, using a programming language. Numerous works have striven to define standards for this process [START_REF] Cervenka | The Agent Modeling Language-AML: A Comprehensive Approach to Modeling Multi-Agent Systems[END_REF].

For our case study, this process was iterative. In fact, the programming model results from successive refinements from the problem universe to the model's universe. This iterative process allowed us to check both algorithms and data structures of the computer model's components, while refining the conceptual model, and thereby improving programming model's quality of implementation [START_REF] Corum | Using Pattern Oriented Modeling to Design and Validate Spatial Models: A Case Study in Agent-Based Modeling[END_REF]. Furthermore, our iterative modeling process also facilitated modularity, extensibility and reproducibility, as we worked to create a computer model and programming model that could be extended for future work, and for related case studies. Figure 1

Agent-Based Land Market modeling

An ABM is a data structure for computer simulation relying on a formalism applying the concept of Multi-Agent Systems (MAS) [START_REF] Klügl | Agent-based modeling and simulation[END_REF]. The ABM consists in an abstract representation of a complex system, in which many entities clearly identified, called agents, interact with each other, and with an environment in accordance with a set of precise rules [START_REF] Clarke | Cellular automata and agent-based models[END_REF][START_REF] Ferber | Multi-agent systems: an introduction to distributed artificial intelligence[END_REF]. All of these entities constitute an Agent-Based System (ABS), for example ABMs parallel Individual-based models developed for ecological applications [START_REF] Grimm | Agent-based models in ecology: patterns and alternative theories of adaptive behaviour[END_REF]. Using the ABM formalism, the modeling process consists of formalizing the details of the agents, their interactions, and their environment (cf. Figure 2).

In the context of economics, ABM complements more the traditional approaches to economic modeling to better link the micro and the macro [START_REF] Hamill | Agent-based modelling in economics[END_REF]. In recent years, computer simulations of ABM/LUCC have evolved in terms of theories, concepts and computer hardware developments, encouraging modelers to develop ever more complex conceptual models [START_REF] Grignard | Gama 1.6: Advancing the art of complex agent-based modeling and simulation[END_REF]. [START_REF] Parker | A conceptual design for a bilateral agent-based land market with heterogeneous economic agents[END_REF] argue that such models should also include representations of land and housing markets, arguing that ABM/LMM can capture the complexity that traditional economic analytical models can not.

An illustrative example: Our case study model

This section presents the use of the methodology based on MR POTATOHEAD (Property Market Edition) for our case study model. After presenting the foundations of our economic conceptual model and the specificities of MR POTATOHEAD: Property Market Edition, we describe each step of model abstraction: development of the conceptual design pattern via MR POTATOHEAD, computer model design, and programming model design.

Case-study model foundations

The ABM has various advantages for the development of models more closely to real-world data. Notably, these models allow consideration of heterogeneous agents, spatial and agent interactions and non-equilibrium dynamics. The model developed by Parker and Filatova in Filatova et al. (2009a) includes interactions between multiple agent types, the process of bid and ask price formation, and agent decision models combining deductive optimization with inductive models of price expectation formation.

Building from this strand of research, in this paper we propose an economic model based on two markets, one for land and the other for residences. The households' utility maximization program is based on [START_REF] Parker | A conceptual design for a bilateral agent-based land market with heterogeneous economic agents[END_REF], Filatova et al. (2009a) and Filatova et al. (2009b). We also take inspiration from other pieces of work, especially when modeling developers, and when modeling the agricultural landowners' willingness to accept (WTA) functions. This literature generally refers to Magliocca and his co-authors in CHALMS models [START_REF] Magliocca | An economic agent-based model of coupled housing and land markets (CHALMS)[END_REF][START_REF] Magliocca | Zoning on the urban fringe: Results from a new approach to modeling land and housing markets[END_REF][START_REF] Magliocca | Exploring sprawl: Results from an economic agentbased model of land and housing markets[END_REF]. Finally, two new types of economic agents are introduced in our model in order to better represent the specific context of tourist areas characterized by an intense residential development. On one hand, "non-agricultural landowners" exhibit substantively different behavior than "agricultural landowners". On the other hand, an "Investor" agent is also included. The latter seeks to make money by buying residences and transforming them into tourist rental investments.

MR POTATOHEAD: Property Market Edition

As described in greater detail in [START_REF] Parker | MR POTATOHEAD: Property Market Edition-Development of a Common Description Template and Code Base for Agent-Based Land Market Models[END_REF], MR POTATOHEAD has recently been updated and modified to specifically describe land market models. The authors, along with many other collaborators, are working to develop a simple common programming code base for agentbased land market models, which will nest all of our models, implemented in different languages with slightly different assumptions, into a common code base. This code base will allow us to directly compare the implications of different models assumptions, as well as to easily create new hybrid model instances combining model assumptions. As a first step towards this goal, we held two international workshops, during which land-market-specific versions of the MR POTATOHEAD agent decision model, land exchange, and landscape classes were created. These descriptions were successively refined by the authors, to translate the verbal and mathematical economic conceptual model (See Figure 1, upper right) into a detailed and complete description that would support development of the computer and programming models.

We found MR POTATOHEAD to be an effective tool to facilitate dialog and communication between the economists and the computer scientist, especially as it highlighted details that were required for the model, but not standard in economic descriptions. Through the iterative process of discussion and model formulation, we further refined MR POTATOHEAD to streamline and better move towards the structure of a potential computer model implementation. Note that, in contrast to the description above, agent decision model description templates are implemented for each agent type in each different role (buyer or seller). Many additional details required for code development are also included in the templates.

Our case study is characterized by an intense residential development, consisting of two markets: a land market and a real estate market. On the former market, two types of landowners (agricultural landowners and non-agricultural landowners) and one type of buyers (developers) are considered.

On the latter market, after building a given type of house on a given parcel of land the developer transforms themself from buyer to seller. The house is then supplied on the market populated by only two different types of buyers: households and the investor. The overall structure of our economic model is described in Figure 3 and the behavior of the various economic agents and their interactions are described using traditional economic formalism2 . We use templates to detail all elements of our economic conceptual model. Eight templates are realized3 : one for each market and one by agent based on their role (buyer or seller). The templates corresponding to our economic conceptual model are illustrated in Figure 4. Two examples of the templates are provided hereafter4 : one agent decision template (for the developer buyer on the land market) and one exchange class template (for the house market). (d) What will be built (developer land buyer): There are M developers, each of them buy a parcel and build a house of type m, with m = 1, ..., M .

(e) Willingness to Pay: They determine these WTP by requiring that the selling price allow them to generate a margin π m on the total cost of the house built on the parcel of land i (sum of the price paid for buying the parcel of land i and the construction cost to build a house) They build only one house by parcel. The WTP for a developer m for a given parcel with the vector characteristics z i , is given by the following expression:

W T P m,t (z i ) = P H,i,t-1 (zi,hm) 1+πm -C m,t (h m ) (f) Bid price: It is equal to the WTP.
(g) Information sources (i.e. Realtor, listings, neighbours): They have information about the past prices of parcel and houses built on a parcel sold as a common knowledge.

(h) Constraints: Developers have a building capacity constraint which means that they can only build n houses during a period t. Thus, one developer m will only bid on n m = n -σ m parcels of land, where σ m is the number of construction sites in progress for this developer.

2. P -Decision to participate in the market (become active as a buyer, seller, investor, or renter) (a) Decision to participate in the market as a buyer: They are active in market if they are below their building capacity constraint. (e) Negotiation strategy:

The negotiation power for the parcel of land i holded by landowner of type q (q = {1, 2})

depends on the number of potential demands N D i for i, i.e. for which: W T P m (z i )

W T A q i,t (•) ; N D i χ
Where χ is the number of developers, for which n m 0, with m = {1, ..., χ}.

(f) Rules if you don't succeed to purchase i. Stay in the market. (2) all households have a house, (3) there is no more transaction, (4) End time periods.

MR POTATOHEAD Real Estate

Computer modeling process

We detail in this part the construction of the MR POTATOHEAD computer model designed for our case study and it programming model counterpart.

MR POTATOHEAD computer model

For the prototype programming model now in development, we are writing our model on the Netlogo platform proposed by Uri Wilensky [START_REF] Wilensky | Netlogo[END_REF]. Thus, our computer model relies on the NetLogo Design Pattern (cf. Figure 5). Although NetLogo has some technical limitations, it is more likely to be used by others, and contributed to, as a meta design pattern, than a code base in another language. We perceive it as having has relatively low barriers to entry, compared to other languages, providing an easy entry point for new modelers, especially those lacking prior computer science training. As discussed by [START_REF] Railsback | Agent-based and individual-based modeling: a practical introduction[END_REF], NetLogo can also be used for large-scale scientific applications.

As it relies on the standard NetLogo pattern, the MR POTATOHEAD computer model should also be accessible to a majority of modelers in building ABM/LUCC computer simulations, and facilitate conceptual model cross-model comparisons for the modelers community working or not with NetLogo.

NetLogo Design pattern

The MR POTATOHEAD computer model is built upon the NetLogo pattern. This pattern allows efficient description of the ABM in the light of four groups of generic agents: Observer, Patch, Turtle and Link. The Observer is a unique agent which observes the environment and may give order to other agents.

Patches are agents that model fixed locations of plan. For example, they can represent cell's abstractions encountered in Cellular Automata Models (CAM) [START_REF] Innocenti | A multicomponent modeling approach for fishery simulations[END_REF]. Turtles are mobile agents where locations match with patches agents on which they are placed, i.e. a location of the cellular space. Turtles can move, and there may be several turtle agents on a same patch agent. Links are very special agents that allow to link two turtles agents with each other. As seen in Figure 5, turtle agents will be specialized in the context of the study using the inheritance mechanism of O.O.P. -instantiated as "Breeds" in Netlogo.

Using the MR POTATOHEAD conceptual model, we describe the computer model, integrating the economic agents described in the previous part. Note that while the MR POTATOHEAD conceptual model specifies different conceptual descriptions for agent types in buyers and seller roles, as Figure 5 shows, buyers and sellers are unified in single land-market-actor type turtle breeds in the computer model. Because Netlogo cannot implement sub-types, we use Boolean switches to activate (or suppress) buyer and seller roles for turtle breeds.

For the land market:

-LandownerAgr (Sellers).

-LandownerNonAgr (Sellers). For the house market:

-Investor (unique -Buyer).

-Household (Buyers).

Land and House market:

-Developer (Buyers on the land market and sellers on the house market).

-Property (Land parcel history).

The interactions of the agents are summarized Figure 6.

The Property agent's role is crucial in our model. These agents are placed on each land parcel of the world (Patches). They are used to implement land parcel evolution over time from a basic state to the building state which correspond to the last state of the house market. They are made up of several real estates properties. In short, use of the Property agents in Netlogo efficiently facilitates one-to-many patch to property relationships (such as an apartment building on a single land parcel), and many-to-one relationships between properties and land actor agents (such as an investor or developer who owns multiple properties). This type of agent remains fixed and has no behavioral rules, although they inherit characteristics of land-actor Turtles agents. Their task is limited information storage for the market process. At t = 0, several agents are placed on the world constituting the initial conditions of the simulation. Property agents are placed on the land parcels of the world.

Conclusions

In this paper, we have detailed a new generic multidisciplinary method to build ABM/LUCC of land and housing market aiming at simulate and evaluate territorial planning policies.

Our method is based on both conceptual modeling and Design Patterns software engineering techniques. Design Patterns inspire all stages of the modeling process proposed and help to formulate efficient and lasting software solutions in multidisciplinary contexts. As example, we detail the construction of an ABM/LUCC from its conceptual model to its computer model counterpart.

We use the MR POTATOHEAD Property Market Edition as a Conceptual Design Pattern for building a conceptual ABM/LUCC. The MR POTATOHEAD ontology provides a structured way to "decompose that system into the relevant parts, their properties, and the relationships between them" and to separate model design from model construction, as recommended by [START_REF] Smaldino | How to translate a verbal theory into a formal model[END_REF], line 303, as best practices for translation of verbal models to computer code. Moreover, the method help us to bridge the gap between economic descriptions and computer model/programming model.

The NetLogo software is used to implement the resulting programming model throw the generic NetLogo Design Pattern. Our method permits us to efficiently integrate the spatial aspect of ABM/LUCC.

The preliminary results show the method facilitates the ABM/LUCC formulation and one-to-many and many-to-one relationships between physical land parcels and properties descriptions.

The Netlogo design pattern helps in our particular case study that we had one team member who had a deep understanding of both economic and agent-based models, as well as rudimentary understanding of computer science and programming concepts. This method allowed us to build a prototype of the economic conceptual model on NetLogo providing a generic virtual laboratory. We also think that this method could be of interest to the readers of this journal who are expanding models on biocomplexity in the environment to individual based modelling, as they would normally have a similar formal mathematical presentation of their models to the economics norm.

This model will now be applied to Corsica (France), which represents an ideal framework for analysis because of its specificities: islands with a high expansion of population and tourists and high demand for accommodation. Policymakers could benefit from the empirical evidence provided by our study through the greater understanding of agents' behaviour and interactions. In a future work, we will employ real data in order to parametrize and calibrate the ABM/LUCC. The data (PERVAL) will come from an original dataset -filled by notaries -containing all real estate transactions in Corsica in last 15 years. By means of standard and spatial econometric procedures, in order to take into account space-time effects, we will be able to identify all the main parameters of the ABM/LUCC and perform simulation analysis.

Figure 1 :

 1 Figure 1: The Iterative Modeling process.

  illustrates the iterative modeling process used in this work. Our operational schema is in part inspired by the seminal work of Siegfried (2014); Chwif et al. (2013); Robinson (2013).

Figure 2 :

 2 Figure 2: Multi-Agent process modeling

Figure 3 :

 3 Figure 3: Economic Conceptual Model, after Filatova et al. (2009a).

Figure 4 :

 4 Figure 4: Economic Conceptual Model Templates.

  3. P -Participate in the market as a buyer (a) Which properties are evaluated (searching strategy) : All properties are evaluated. (b) WTP -call from above (c) Bid price -call from above (d) Which property(s) to bid on? i. Multiple per buyer: By respect of their building capacity constraints.

  unique products are being bought and sold? (a) Generic grid, uniform tessellation (Netlogo default) (b) Number of container types: one per parcel. amenities (example, sea view index) G. Neighbourhood disamenities (example, flood risk) ii. Number of different unit categories in the container: one by container iii. Unit category descriptions: Rules for buyers who did not find a home (call to ADM functions): Buyers who did not find properties stay in the market and continue to bid on next time step. (e) Identify active buyers and sellers for next round 8. What are your stopping rules for market activity? (a) Process stops when: (1) all houses are sold;

Figure 5 :

 5 Figure 5: The MR POTATOHEAD computer model.

Figure 6 :

 6 Figure 6: Agent's interactions of our MR POTATOHEAD computer model.

The MVC pattern is used in a software engineering to separate the components in charge of logic (model), data (GIS, database, etc.) and views (screen, print, etc.) into three distinct categories of software components.

The mathematical model is provided by the authors as Supplementary Material (Appendix A) and will be posted online.

The full templates are provided by the authors as Supplementary Material (Appendix B) and will be posted online.

Templates based on the MR POTATOHEAD are designed to be sufficiently modular to deal exhaustively with the different ABM/LUCC. Below, in the two examples, we only provide the relevant parts of the corresponding templates for our economic conceptual model. Others parts are present in the Online Supplementary Material (Appendix B).

Acknowledgment This work supports one of the research themes of the ESTATE Project (Etude de la SouTen-Abilité des recompositions TErritoriales de la Corse) funded by the Collectivity of Corsica (Cullettività di Corsica). We would like to thank the University of Corsica for funding the hosting of Professor Dawn Cassandra Parker as a visiting professor through its International Visiting Chair program; the Waterloo Institute for Complexity and Innovation, the University of Waterloo International Research Partnership Grant programme, the Oxford Institute for New Economic Thinking for workshop support; and all participants in the 2018 model template development workshops.

(d) How is the transaction price defined? i. The negotiation power for the house µ built on parcel of land i depends on the number of demands N D µ from households for whom this house corresponds to the maximal utility and from the investor if her WTP is higher than the WTA of the developer, N D µ ≤ C + 1. The individual ν who has the highest WTP buys the house. The transaction price is fixed as follow:


Frédéric Galliano
email: frederic.galliano@cea.fr

Dustpedia Collaboration

Cosmic dust evolution: the challenges for NIKA2

I summarize a recent study aimed at constraining dust evolution timescales in nearby galaxies. We were able to quantify the efficiency of dust condensation in SN II ejecta, grain growth in the ISM and dust destruction by SN II blast waves. Around Solar metallicity, our results are consistent with what we know in the Milky Way, that is dust production is dominated by grain growth. We however show that this changes with metallicity. The dust content in very-low-metallicity systems is dominated by grains that have formed in SN II ejecta. I end this article with a discussion about the potential of NIKA2 to study dust evolution in galaxies.

Introduction

Interstellar dust is a key physical ingredient of galaxies, obscuring star formation, regulating the heating and cooling of the gas, and building-up chemical complexity. Its properties are however difficult to estimate, as there are important uncertainties about the constitution of the grain mixture in the diffuse Interstellar Medium (ISM) of the Milky Way, where dust models are calibrated. In addition, dust properties are known to drastically evolve as a function of their local physical conditions (gas density, radiation field, shocks) and as a function of the history of the galaxy (enrichment of the ISM by successive waves of star formation). It is thus crucial to quantify this evolution.

Cosmic dust evolution models attempt to account for the balance between the main dust evolution processes, in a global way (cf. [1] for a review). They however rely on simple descriptions of the evolution mechanisms and depend on the value of uncertain tuning parameters, such as sticking coefficients, binding energies, sputtering yields, etc. We have attempted to provide an empirical estimate of these tuning parameters, using a sample of 800 nearby galaxies.

Galaxy sample and SED Modeling

In order to constrain a dust evolution model, we need to estimate the following global quantities, for a large sample of galaxies: the dust mass, M dust , the gas mass, M gas , the stellar mass, M , the metallicity, Z, and the Star Formation-Rate (SFR). We have used the DustPedia sample [2]. It provides homogeneous multi-wavelength photometry [3], with ancillary H i and CO observations. The stellar mass and SFR have been derived by [4], using ultraviolet-tomm Spectral Energy Distribution (SED) fitting. The metallicity have been estimated with a consistent calibration by [5].

One of the limitations of DustPedia is its selection of objects larger than 10 , excluding most local dwarf galaxies. Yet, the latter are crucial to constrain dust evolution, as they sample the low-metallicity regime corresponding to the early stages of the dust build-up. To overcome this deficiency, we have added to our sample the sources from the Dwarf Galaxy Survey (DGS, [6][7][8][9]). In total we have 800 objects covering a large metallicity range. The Skewed Uncertainty Ellipses (SUEs) represent the observed dustiness, as a function of metallicity, of each galaxy in our sample, color-coded according to its type [10]. The yellow-to-red density contours in the background represent the posterior probability density of our dust evolution model, inferred from the observations of galaxies (i.e. the SUEs). We have highlighted the three main dust production regimes in magenta.

Dust condensation in

We have performed infrared SED modeling of the observed photometry, using the hierachical Bayesian code HerBIE [11]. This model provides a rigorous account of the different sources of uncertainties and is efficient at recovering the intrinsic scatter and correlations of the studied parameters. We have used the properties of the THEMIS dust model [12]. The results are the Skewed Uncertainty Ellipses (SUEs) in figure 1 [10]. We have displayed the relation between the metallicity and the dustiness (i.e. the dust-to-gas mass ratio).

Constraining dust evolution timescales

The estimated M dust , M gas , M , Z and SFR of each galaxy are then used to constrain the parameters of our cosmic dust evolution model. This model, for a given Star Formation History (SFH), computes the evolution, as a function of time, of the masses of stars, gas, heavy elements and dust. At each time step, new stars are formed, depleting the gas. At the end of their lifetime (which depends on their initial mass), these stars return to the ISM a fraction of their gas, newly-formed elements, and dust seeds. The three dust evolution processes we account for (on top of astration, which is straightforward) are: the condensation of grain seeds in SN II ejecta, grain growth in the ISM and dust destruction by SN II blast waves. The efficiency of these different processes are vigorously debated in the literature and they can vary by more than one order of magnitude, depending on the study. We fit our dust evolution models to our observed estimates in a hierarchical Bayesian way, assuming that each galaxy has a particular SFH (parameterized by its timescale, amplitude, age, infall and outlfow rates), but that the dust evolution efficiencies are universal (i.e. they have the same value for each galaxy). The posterior probability distribution of our dust evolution model is represented as contours in figure 1.

From our inferred dust evolution efficiencies, we can derive dust evolution timescales. These are shown in figure 2. Although we only have one estimate of the three efficiencies for our whole sample, each galaxy has its own set of evolution timescales, because these depend also on the SFR, M gas , Z, etc. The most important conclusions from these trends are the following.

At very low metallicity, the timescale for dust condensation in SN II is shorter than that of grain growth in the ISM. This is because grain growth is inefficient when the abundance of heavy elements in the gas is low. Grains in these young systems are thus mainly stardust. SN II production is rather inefficient. This is the reason why, in figure 1, very low-metallicity galaxies, lie on the low-dustiness branch of the trend.

At low metallicity, there is a transition between two regimes. The dustiness rises steeply as grain growth in the ISM becomes rapidly more efficient. We are around what [13] have called the critical metallicity. Now, there are enough heavy element atoms in the gas to accrete onto grain surfaces.

At normal metallicity, the dust production is dominated by grain growth in the ISM, with a high efficiency. Although we did not use the constraints provided by the Milky Way, our timescales are consistent with the Galactic ones.

This study also provides methodological insights. First, it demonstrates the instrumental role of dwarf galaxies in understanding dust evolution. These objects indeed sample a metallicity range characterized by a dust production regime different from Solar-metallicity systems. The constraint on the low efficiency of dust production by SN II ( 0.03 M /SN in our article) relies entirely on dwarfs. Second, our work is the first rigorous fit of individual dust evolution models to actual observations of galaxies. Most studies before us were simply overlaying dust evolution tracks on top of observed scaling relations. Yet, such a visual comparison is inconsistent in many cases, as it permits interpreting two different quantities of a galaxy with two different ages. Lastly, our results emphasize that grain growth is fast, provided the metallicity is high enough (Z 0.4 Z ). It thus provides a natural mechanism to explain the existence of dusty objects at very high redshifts (z 6), only a few 100 Myrs after reionization.

Prospective: the potential of NIKA2

The dust evolution study we have just presented was limited because we analyzed galaxies as a whole. The dustiness we estimated for each galaxy was representative of their average conditions, but we know that local grain evolution, at the scale of molecular clouds, is important. Spatially-resolved studies are thus the necessary next step to constrain local dust evolution, that will provide empirical constraints on the effects of gas density and radiation field intensity on the grain properties.

NIKA2 is an instrument providing unprecedentedly deep images of nearby galaxies, at 1.2 and 2 mm, with angular resolutions 12 and 18 , respectively. It provides unique constraints on the grain properties at spatial scales of a few hundreds of parsecs, close to the size of giant molecular complexes. Figure 3 represents the typical SED of a nearby star-forming galaxy. We see that NIKA2 samples an important spectral domain, where the following physical processes can be probed.

Thermal dust emission, at long-wavelengths, is poorly constrained. Yet, it is crucial to properly estimate dust masses, as it is dominated by cold, massive regions. We have represented the potential presence of a "submm excess", which is likely the result of the inaccuracy of contemporary dust models (cf. [1] for a review). The detailed characterization of dust emission will likely account for this excess. NIKA2 might be instrumental in addressing the origin of this enigmatic effect.

The Anomalous Microwave Emission (AME) is the cm emission shown in red. It originates in fastly spinning small grains [14]. The exact nature of the carriers of this process is still debated. NIKA2 observations provide the data to properly constrain the baseline required to quantify the AME. NIKA2 data will thus open the possibility to make maps of AME intensity in external galaxies and understand how it correlates with other dust properties, which should give us clues about the nature of its carriers.

The consortium of the NIKA2 guaranteed program, IMEGIN, is currently tackling these challenges (cf. [START_REF] Ejlali | Dust Emission in Galaxies at Millimeter Wavelengths. Cooling of star forming regions in NGC6946[END_REF] and [START_REF] Katsioli | Exploring the millimetre emission in nearby galaxies: analysis of the edge-on galaxy NGC 891[END_REF] in this volume).

Figure 1 .

 1 Figure1. The Skewed Uncertainty Ellipses (SUEs) represent the observed dustiness, as a function of metallicity, of each galaxy in our sample, color-coded according to its type[10]. The yellow-to-red density contours in the background represent the posterior probability density of our dust evolution model, inferred from the observations of galaxies (i.e. the SUEs). We have highlighted the three main dust production regimes in magenta.

Figure 2 .

 2 Figure2. In each panel, the SUEs represent the inferred dust evolution timescales of the galaxies for which all constraints are available, as a function of metallicity[10]. Panel (a) shows the timescale of dust condensation in SN II ejecta, panel (b), the timescale of grain growth in the ISM, and panel (c), the timescale of dust destruction by SN II blast waves.

Figure 3 .

 3 Figure 3. We display the physical processes probed by NIKA2, in the nearby Universe (panel a), and at high redshift (panel b). We have represented the tpyical SED of a star-forming galaxy[1].