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Suppose you have an uncomputable set $X$ and you want to find a set $A$, all of whose infinite subsets compute $X$. There are several ways to do this, but all of them seem to produce a set $A$ which is fairly sparse. We show that this is necessary in the following technical sense: if $X$ is uncomputable and $A$ is a set of positive lower density then $A$ has an infinite subset which does not compute $X$. We also prove an analogous result for PA degree: if $X$ is uncomputable and $A$ is a set of positive lower density then $A$ has an infinite subset which is not of PA degree. We will show that these theorems are sharp in certain senses and also prove a quantitative version formulated in terms of Kolmogorov complexity. Our results use a modified version of Mathias forcing and build on work by Seetapun, Liu, and others on the reverse math of Ramsey's theorem for pairs., Comment: 37 pages. Paper updated to fix typos

Dedicated neural network (NN) architectures have been designed to handle specific data types (such as CNN for images or RNN for text), which ranks them among state-of-the-art methods for dealing with these data. Unfortunately, no architecture has been found for dealing with tabular data yet, for which tree ensemble methods (tree boosting, random forests) usually show the best predictive performances. In this work, we propose a new sparse initialization technique for (potentially deep) multilayer perceptrons (MLP): we first train a tree-based procedure to detect feature interactions and use the resulting information to initialize the network, which is subsequently trained via standard stochastic gradient strategies. Numerical experiments on several tabular data sets show that this new, simple and easy-to-use method is a solid concurrent, both in terms of generalization capacity and computation time, to default MLP initialization and even to existing complex deep learning solutions. In fact, this wise MLP initialization raises the resulting NN methods to the level of a valid competitor to gradient boosting when dealing with tabular data. Besides, such initializations are able to preserve the sparsity of weights introduced in the first layers of the network through training. This fact suggests that this new initializer operates an implicit regularization during the NN training, and emphasizes that the first layers act as a sparse feature extractor (as for convolutional layers in CNN).

We describe a project to formalize Galois theory using the Lean theorem prover, which is part of a larger effort to formalize all of the standard undergraduate mathematics curriculum in Lean. We discuss some of the challenges we faced and the decisions we made in the course of this project. The main theorems we formalized are the primitive element theorem, the fundamental theorem of Galois theory, and the equivalence of several characterizations of finite degree Galois extensions., Comment: 15 pages

SCOPUS: le.j, info:eu-repo/semantics/published

SCOPUS: le.j, info:eu-repo/semantics/published

Despite advances in supportive therapy to prevent complications of sickle cell disease (SCD), access to care is not universal. Hematopoietic cell transplantation is, to date, the only curative therapy for SCD, but its application is limited by availability of a suitable HLA-matched donor and lack of awareness of the benefits of transplant. Included in this study are 1000 recipients of HLA-identical sibling transplants performed between 1986 and 2013 and reported to the European Society for Blood and Marrow Transplantation, Eurocord, and the Center for International Blood and Marrow Transplant Research. The primary endpoint was event-free survival, defined as being alive without graft failure; risk factors were studied using a Cox regression models. The median age at transplantation was 9 years, and the median follow-up was longer than 5 years. Most patients received a myeloablative conditioning regimen (n = 873; 87%); the remainder received reduced-intensity conditioning regimens (n = 125; 13%). Bone marrow was the predominant stem cell source (n = 839; 84%); peripheral blood and cord blood progenitors were used in 73 (7%) and 88 (9%) patients, respectively. The 5-year event-free survival and overall survival were 91.4% (95% confidence interval, 89.6%-93.3%) and 92.9% (95% confidence interval, 91.1%-94.6%), respectively. Event-free survival was lower with increasing age at transplantation (hazard ratio [HR], 1.09; P < .001) and higher for transplantations performed after 2006 (HR, 0.95; P = .013). Twenty-three patients experienced graft failure, and 70 patients (7%) died, with the most common cause of death being infection. The excellent outcome of a cohort transplanted over the course of 3 decades confirms the role of HLA-identical sibling transplantation for children and adults with SCD.

Despite advances in supportive therapy to prevent complications of sickle cell disease (SCD), access to care is not universal. Hematopoietic cell transplantation is, to date, the only curative therapy for SCD, but its application is limited by availability of a suitable HLA-matched donor and lack of awareness of the benefits of transplant. Included in this study are 1000 recipients of HLA-identical sibling transplants performed between 1986 and 2013 and reported to the European Society for Blood and Marrow Transplantation, Eurocord, and the Center for International Blood and Marrow Transplant Research. The primary endpoint was event-free survival, defined as being alive without graft failure; risk factors were studied using a Cox regression models. The median age at transplantation was 9 years, and the median follow-up was longer than 5 years. Most patients received a myeloablative conditioning regimen (n = 873; 87%); the remainder received reduced-intensity conditioning regimens (n = 125; 13%). Bone marrow was the predominant stem cell source (n = 839; 84%); peripheral blood and cord blood progenitors were used in 73 (7%) and 88 (9%) patients, respectively. The 5-year event-free survival and overall survival were 91.4% (95% confidence interval, 89.6%-93.3%) and 92.9% (95% confidence interval, 91.1%-94.6%), respectively. Event-free survival was lower with increasing age at transplantation (hazard ratio [HR], 1.09; < .001) and higher for transplantations performed after 2006 (HR, 0.95; = .013). Twenty-three patients experienced graft failure, and 70 patients (7%) died, with the most common cause of death being infection. The excellent outcome of a cohort transplanted over the course of 3 decades confirms the role of HLA-identical sibling transplantation for children and adults with SCD.

The most frequent germline mutations responsible for non syndromic congenital sideroblastic anemia are identified in ALAS2 and SLC25A38 genes. Iron overload is a key issue and optimal chelation therapy should be used to limit its adverse effects on the development of children. Our multicentre retrospective descriptive study compared the strategies for diagnosis and management of congenital sideroblastic anemia during the follow-up of six patients with an ALAS2 mutation and seven patients with an SLC25A38 mutation. We described in depth the clinical, biological and radiological phenotype of these patients at diagnosis and during follow-up and highlighted our results with a review of available evidence and data on the management strategies for congenital sideroblastic anemia. This report confirms the considerable variability in manifestations among patients with ALAS2 or SLC25A38 mutations and draws attention to differences in the assessment and the monitoring of iron overload and its complications. The use of an international registry would certainly help defining recommendations for the management of these rare disorders to improve patient outcome.

Despite advances in supportive therapy to prevent complications of sickle cell disease (SCD), access to care is not universal. Hematopoietic cell transplantation is, to date, the only curative therapy for SCD, but its application is limited by availability of a suitable HLA-matched donor and lack of awareness of the benefits of transplant. Included in this study are 1000 recipients of HLA-identical sibling transplants performed between 1986 and 2013 and reported to the European Society for Blood and Marrow Transplantation, Eurocord, and the Center for International Blood and Marrow Transplant Research. The primary endpoint was event-free survival, defined as being alive without graft failure; risk factors were studied using a Cox regression models. The median age at transplantation was 9 years, and the median follow-up was longer than 5 years. Most patients received a myeloablative conditioning regimen (n = 873; 87%); the remainder received reduced-intensity conditioning regimens (n = 125; 13%). Bone marrow was the predominant stem cell source (n = 839; 84%); peripheral blood and cord blood progenitors were used in 73 (7%) and 88 (9%) patients, respectively. The 5-year event-free survival and overall survival were 91.4% (95% confidence interval, 89.6%-93.3%) and 92.9% (95% confidence interval, 91.1%-94.6%), respectively. Event-free survival was lower with increasing age at transplantation (hazard ratio [HR], 1.09; P < .001) and higher for transplantations performed after 2006 (HR, 0.95; P = .013). Twenty-three patients experienced graft failure, and 70 patients (7%) died, with the most common cause of death being infection. The excellent outcome of a cohort transplanted over the course of 3 decades confirms the role of HLA-identical sibling transplantation for children and adults with SCD.

Asparaginase is an essential component of combination chemotherapy for childhood acute lymphoblastic leukemia and non-Hodgkin lymphoma. The value of asparaginase was further addressed in a group of non-very high-risk patients by comparing prolonged (long-asparaginase) versus standard (short-asparaginase) native E. coli asparaginase treatment in a randomized part of the phase III 58951 trial of the European Organization for Research and Treatment of Cancer Children’s Leukemia Group. The main endpoint was disease-free survival. Overall, 1,552 patients were randomly assigned to long-asparaginase (775 patients) or short-asparaginase (777 patients). Patients with grade ≥2 allergy to native E. coli asparaginase were switched to equivalent doses of Erwinia or pegylated E. coli asparaginase. The 8-year disease-free survival rate (±standard error) was 87.0±1.3% in the long-asparaginase group and 84.4±1.4% in the short-asparaginase group (hazard ratio: 0.87; P=0.33) and the 8-year overall survival rate was 92.6±1.0% and 91.3±1.2% respectively (hazard ratio: 0.89; P=0.53). An exploratory analysis suggested that the impact of long-asparaginase was beneficial in the National Cancer Institute standard-risk group with regards to disease-free survival (hazard ratio: 0.70; P=0.057), but far less so with regards to overall survival (hazard ratio: 0.89). The incidences of grade 3-4 infection during consolidation (25.2% versus 14.4%) and late intensification (22.6% versus 15.9%) and the incidence of grade 2-4 allergy were higher in the long-asparaginase arm (30% versus 21%). Prolonged native E. coli asparaginase therapy in consolidation and late intensification for our non-very high-risk patients did not improve overall outcome but led to an increase in infections and allergy., SCOPUS: ar.j, info:eu-repo/semantics/published

Acute lymphoblastic leukemia of T cell lineage (T-ALL) is an aggressive malignant disease which accounts for 15 % of childhood ALL. T(11;14) is the more frequent chromosomal abnormality in childhood T-ALL, but its prognostic value remained controversial. Our aim was to analyze the outcome of childhood T-ALL with t(11;14) to know if the presence of this translocation is associated with a poor prognosis. We conducted a retrospective study from a series of 20 patients with t(11;14), treated in two consecutive trials from the European Organization for Research and Treatment of Cancer Children Leukemia Group over a 19-year period from 1989 to 2008. There were no significant differences between the 2 consecutive groups of patients with t(11;14) regarding the clinical and biological features at diagnosis. Among 19 patients who reached complete remission, 9 patients relapsed. We noticed 7 deaths all relapse- or failure-related. In the 58881 study, a presence of t(11;14) was associated with a poor outcome with an event-free survival at 5 years at 22.2 % versus 65.1 % for the non-t(11;14) T-ALL (p = 0.0004). In the more recent protocol, the outcome of T-ALL with t(11;14) reached that of non-t(11;14) T-ALL with an event-free survival at 5 years at 65.5 versus 74.9 % (p = 0.93). The presence of t(11;14) appeared as a poor prognostic feature in the 58881 trial whereas this abnormality no longer affected the outcome in the 58951 study. This difference is probably explained by the more intensive chemotherapy in the latest trial., info:eu-repo/semantics/published

Dexamethasone could be more effective than prednisolone at similar anti-inflammatory doses in the treatment of childhood acute lymphoblastic leukemia. In order to check if this "superiority" of dexamethasone might be dose-dependent, we conducted a randomized phase III trial comparing dexamethasone (6 mg/m(2)/day) to prednisolone (60 mg/m(2)/day) in induction therapy. All newly diagnosed children and adolescents with acute lymphoblastic leukemia in the 58951 EORTC trial were randomized on prephase day 1 or day 8. The main endpoint was event-free survival; secondary endpoints were overall survival and toxicity. A total of 1947 patients with acute lymphoblastic leukemia were randomized. At a median follow-up of 6.9 years, the 8-year event-free survival rate was 81.5% in the dexamethasone arm and 81.2% in the prednisolone arm; the 8-year overall survival rates were 87.2% and 89.0% respectively. The 8-year incidences of isolated or combined central nervous system relapse were 2.9% and 4.5% in the dexamethasone and prednisolone arms, respectively. The incidence of grade 3-4 toxicities during induction and the frequency of osteonecrosis were similar in the two arms. In conclusion, dexamethasone and prednisolone, used respectively at the doses of 6 and 60 mg/m(2)/day during induction, were equally effective and had a similar toxicity profile. Dexamethasone decreased the 8-year central nervous system relapse incidence by 1.6%. This trial was registered at www.clinicaltrials.gov as, SCOPUS: ar.j, info:eu-repo/semantics/published

The aim of our study was to analyze the factors contributing to heterogeneity of prognosis in patients with hyperdiploidy>50 chromosomes (HD>50), a group of B-cell precursor acute lymphoblastic leukemia with favorable outcome. The 541 HD>50 patients registered prospectively in the 58951 European Organisation for Research and Treatment of Cancer (EORTC) Children's Leukemia Group (CLG) trial, identified by karyotype (446 patients) and by DNA index (DI) (490 patients), had a 6-year event-free survival (EFS) of 89.0% (standard error [SE] = 1.5%) and a 6-year overall survival (OS) of 95.9% (SE = 0.9%). The strongest prognostic factor was the modal number of chromosomes (MNC): the 6-year EFS of 51-53, 54-57, and 58-66 MNC groups were 80%, 89%, and 99%, respectively (P < .0001). Ploidy assessed by DI was also a favorable factor: the higher the DI, the better the outcome. The 6-year EFS of the 3 subgroups of DI < 1.16/≥1.16-<1.24/≥1.24 were 83%, 90%, and 95%, respectively (P = .009). All usual combinations of trisomies (chromosomes 4, 10, 17, 18) were significant favorable factors but had lower EFS when MNC was lower than 58. In multivariate analysis, MNC remained the strongest factor. Consequently, the best indicator for excellent outcome was ploidy assessed by karyotype because patients with 58-66 chromosomes stood every chance of being cured (OS of 100% at 6-year follow-up) with less-intensive therapy. This trial was registered at www.clinicaltrials.gov as, Journal Article, Research Support, Non-U.S. Gov't, SCOPUS: ar.j, info:eu-repo/semantics/published

The aim of our study was to analyze the factors contributing to heterogeneity of prognosis in patients with hyperdiploidy>50 chromosomes (HD>50), a group of B-cell precursor acute lymphoblastic leukemia with favorable outcome. The 541 HD>50 patients registered prospectively in the 58951 European Organisation for Research and Treatment of Cancer (EORTC) Children's Leukemia Group (CLG) trial, identified by karyotype (446 patients) and by DNA index (DI) (490 patients), had a 6-year event-free survival (EFS) of 89.0% (standard error [SE] = 1.5%) and a 6-year overall survival (OS) of 95.9% (SE = 0.9%). The strongest prognostic factor was the modal number of chromosomes (MNC): the 6-year EFS of 51-53, 54-57, and 58-66 MNC groups were 80%, 89%, and 99%, respectively (P < .0001). Ploidy assessed by DI was also a favorable factor: the higher the DI, the better the outcome. The 6-year EFS of the 3 subgroups of DI < 1.16/≥1.16-<1.24/≥1.24 were 83%, 90%, and 95%, respectively (P = .009). All usual combinations of trisomies (chromosomes 4, 10, 17, 18) were significant favorable factors but had lower EFS when MNC was lower than 58. In multivariate analysis, MNC remained the strongest factor. Consequently, the best indicator for excellent outcome was ploidy assessed by karyotype because patients with 58-66 chromosomes stood every chance of being cured (OS of 100% at 6-year follow-up) with less-intensive therapy. This trial was registered at www.clinicaltrials.gov as, Journal Article, Research Support, Non-U.S. Gov't, SCOPUS: ar.j, info:eu-repo/semantics/published

The molecular mechanisms that underlie T-cell quiescence are poorly understood. In the present study, we report a primary immunodeficiency phenotype associated with MST1 deficiency and primarily characterized by a progressive loss of naive T cells. The in vivo consequences include recurrent bacterial and viral infections and autoimmune manifestations. MST1-deficient T cells poorly expressed the transcription factor FOXO1, the IL-7 receptor, and BCL2. Conversely, FAS expression and the FAS-mediating apoptotic pathway were up-regulated. These abnormalities suggest that increased cell death of naive and proliferating T cells is the main mechanism underlying this novel immunodeficiency. Our results characterize a new mechanism in primary T-cell immunodeficiencies and highlight a role of the MST1/FOXO1 pathway in controlling the death of human naive T cells.

Allogeneic bone marrow transplantation (BMT) from HLA-identical siblings is an accepted treatment for both thalassemia and sickle cell disease (SCD). However, it is associated with decided risk of both transplant-related mortality (TRM) and chronic graft-versus-host disease (GVHD). We analyzed 44 patients (median age, 5 years; range, 1-20 years) given an allogeneic related cord blood transplant for either thalassemia (n = 33) or SCD (n = 11). Thirty children were given cyclosporin A (CsA) alone as GVHD prophylaxis, 10 received CsA and methotrexate (MTX), and 4 patients received other combinations of immunosuppressive drugs. The median number of nucleated cells infused was 4.0 x 10(7)/kg (range, 1.2-10 x 10(7)/kg). No patient died and 36 of 44 children remain free of disease, with a median follow-up of 24 months (range, 4-76 months). Only one patient with SCD did not have sustained donor engraftment as compared with 7 of the 33 patients with thalassemia. Three of these 8 patients had sustained donor engraftment after BMT from the same donor. Four patients experienced grade 2 acute GVHD; only 2 of the 36 patients at risk developed limited chronic GVHD. The 2-year probability of event-free survival is 79% and 90% for patients with thalassemia and SCD, respectively. Use of MTX for GVHD prophylaxis was associated with a greater risk of treatment failure. Related CBT for hemoglobinopathies offers a good probability of success and is associated with a low risk of GVHD. Optimization of transplantation strategies could further improve these results.