Solution of the Thirring model in thimble regularization

Thimble regularization of lattice field theories has been proposed as a solution to the infamous sign problem. It is conceptually very clean and powerful, but it is in practice limited by a potentially very serious issue: in general many thimbles can contribute to the computation of the functional integrals. Semiclassical arguments would suggest that the fundamental thimble could be sufficient to get the correct answer, but this hypothesis has been proven not to hold true in general. A first example of this failure has been put forward in the context of the Thirring model: the dominant thimble approximation is valid only in given regions of the parameter space of the theory. Since then a complete solution of this (simple) model in thimble regularization has been missing. In this paper we show that a full solution (taking the continuum limit) is indeed possible. It is possible thanks to a method we recently proposed which de facto evades the need to simulate on many thimbles

Taylor expansions and Padé approximations for Lefschetz thimbles and beyond

Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model. Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex µB plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration

Taylor expansions and Padé approximations for Lefschetz thimbles and beyond

Deforming the domain of integration after complexification of the field variables is an intriguing idea to tackle the sign problem. In thimble regularization the domain of integration is deformed into an union of manifolds called Lefschetz thimbles. On each thimble the imaginary part of the action stays constant and the sign problem disappears. A long standing issue of this approach is how to determine the relative weight to assign to each thimble contribution in the (multi)-thimble decomposition. Yet this is an issue one has to face, as previous work has shown that different theories exist for which the contributions coming from thimbles other than the dominant one cannot be neglected. Historically, one of the first examples of such theories is the one-dimensional Thirring model. Here we discuss how Taylor expansions can be used to by-pass the need for multi-thimble simulations. If multiple, disjoint regions can be found in the parameters space of the theory where only one thimble gives a relevant contribution, multiple Taylor expansions can be carried out in those regions to reach other regions by single thimble simulations. Better yet, these Taylor expansions can be bridged by Padé interpolants. Not only does this improve the convergence properties of the series, but it also gives access to information about the analytical structure of the observables. The true singularities of the observables can be recovered. We show that this program can be applied to the one-dimensional Thirring model and to a (simple) version of HDQCD. But the general idea behind our strategy can be helpful beyond thimble regularization itself, i.e. it could be valuable in studying the singularities of QCD in the complex µB plane. Indeed this is a program that is currently being carried out by the Bielefeld-Parma collaboration

One-thimble regularisation of lattice field theories: Is it only a dream?

Lefschetz thimbles regularisation of (lattice) field theories was put forward as a possible solution to the sign problem. Despite elegant and conceptually simple, it has many subtleties, a major one boiling down to a plain question: how many thimbles should we take into account? In the original formulation, a single thimble dominance hypothesis was put forward: in the thermodynamic limit, universality arguments could support a scenario in which the dominant thimble (associated to the global minimum of the action) captures the physical content of the field theory. We know by now many counterexamples and we have been pursuing multi-thimble simulations ourselves. Still, a single thimble regularisation would be the real breakthrough. We report on ongoing work aiming at a single thimble formulation of lattice field theories, in particular putting forward the proposal of performing Taylor expansions on the dominant thimble

Net-baryon number fluctuations

The appearance of large, none-Gaussian cumulants of the baryon number distribution is commonly discussed as a signal for the QCD critical point. We review the status of the Taylor expansion of cumulant ratios of baryon number fluctuations along the freeze-out line and also compare QCD results with the corresponding proton number fluctuations as measured by the STAR Collaboration at RHIC. To further constrain the location of a possible QCD critical point we discuss poles of the baryon number fluctuations in the complex plane. Here we use not only the Taylor coefficients obtained at zero chemical potential but perform also calculations of Taylor expansion coefficients of the pressure at purely imaginary chemical potentials.Comment: 10 pages, 5 figures, talk presented at the Workshop "Criticality in QCD and the Hadron Resonance Gas", 29-31 July 2020, Onlin

Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD

We present a calculation of the net baryon number density as a function of imaginary baryon number chemical potential, obtained with highly improved staggered quarks at temporal lattice extent of Nτ=4, 6. We construct various rational function approximations of the lattice data and discuss how poles in the complex plane can be determined from them. We compare our results of the singularities in the chemical potential plane to the theoretically expected positions of the Lee-Yang edge singularity in the vicinity of the Roberge-Weiss and chiral phase transitions. We find a temperature scaling that is in accordance with the expected power law behavior

Persistence of Natural Killer (NK) cell lymphocytosis with hyposplenism without development of leukaemia

BACKGROUND: Natural killer (NK) cell lymphocytosis usually has an indolent course and can progress into massive lymphocytosis with development of cytopenias and neoplastic diseases. NK-cells usually express one or more "NK-associated" antigens (CD16, CD56, CD57). Reactive expansions are seen in autoimmune diseases, viral infections, solid tumours and non-Hodgkin's lymphoma. CASE PRESENTATION: We report a lady with a benign clinical course over 10 years and persistent CD8+/CD3-/CD57+/CD16+ LGL proliferation with presence of Howell-Jolly bodies (functional hyposplenism), an association not previously described. CONCLUSION: We discuss the possible causes of clonal expansion and conclude that this may be part of the spectrum of immune dysregulation associated with NK-cell lymphocytosis

MATRix-RICE therapy and autologous haematopoietic stem-cell transplantation in diffuse large B-cell lymphoma with secondary CNS involvement (MARIETTA): an international, single-arm, phase 2 trial.

BACKGROUND Secondary CNS lymphoma is a rare but potentially lethal event in patients with diffuse large B-cell lymphoma. We aimed to assess the activity and safety of an intensive, CNS-directed chemoimmunotherapy consolidated by autologous haematopoietic stem-cell transplantation (HSCT) in patients with secondary CNS lymphoma. METHODS This international, single-arm, phase 2 trial was done in 24 hospitals in Italy, the UK, the Netherlands, and Switzerland. Adults (aged 18-70 years) with histologically diagnosed diffuse large B-cell lymphoma and CNS involvement at the time of primary diagnosis or at relapse and Eastern Cooperative Oncology Group Performance Status of 3 or less were enrolled and received three courses of MATRix (rituximab 375 mg/m2, intravenous infusion, day 0; methotrexate 3·5 g/m2, the first 0·5 g/m2 in 15 min followed by 3 g/m2 in a 3 h intravenous infusion, day 1; cytarabine 2 g/m2 every 12 h, in 1 h intravenous infusions, days 2 and 3; thiotepa 30 mg/m2, 30 min intravenous infusion, day 4) followed by three courses of RICE (rituximab 375 mg/m2, day 1; etoposide 100 mg/m2 per day in 500-1000 mL over a 60 min intravenous infusion, days 1, 2, and 3; ifosfamide 5 g/m2 in 1000 mL in a 24 h intravenous infusion with mesna support, day 2; carboplatin area under the curve of 5 in 500 mL in a 1 h intravenous infusion, day 2) and carmustine-thiotepa and autologous HSCT (carmustine 400 mg/m2 in 500 mL glucose 5% solution in a 1-2 h infusion, day -6; thiotepa 5 mg/kg in saline solution in a 2 h infusion every 12 h, days -5 and -4). The primary endpoint was progression-free survival at 1 year. Overall and complete response rates before autologous HSCT, duration of response, overall survival, and safety were the secondary endpoints. Analyses were in the modified intention-to-treat population. This study is registered with ClinicalTrials.gov, NCT02329080. The trial ended after accrual completion; the database lock was Dec 31, 2019. FINDINGS Between March 30, 2015, and Aug 3, 2018, 79 patients were enrolled. 75 patients were assessable. 319 (71%) of the 450 planned courses were delivered. At 1 year from enrolment the primary endpoint was met, 42 patients were progression free (progression-free survival 58%; 95% CI 55-61). 49 patients (65%; 95% CI 54-76) had an objective response after MATRix-RICE, 29 (39%) of whom had a complete response. 37 patients who responded had autologous HSCT. At the end of the programme, 46 patients (61%; 95% CI 51-71) had an objective response, with a median duration of objective response of 26 months (IQR 16-37). At a median follow-up of 29 months (IQR 20-40), 35 patients were progression-free and 33 were alive, with a 2-year overall survival of 46% (95% CI 39-53). Grade 3-4 toxicity was most commonly haematological: neutropenia in 46 (61%) of 75 patients, thrombocytopenia in 45 (60%), and anaemia in 26 (35%). 79 serious adverse events were recorded in 42 (56%) patients; four (5%) of those 79 were lethal due to sepsis caused by Gram-negative bacteria (treatment-related mortality 5%; 95% CI 0·07-9·93). INTERPRETATION MATRix-RICE plus autologous HSCT was active in this population of patients with very poor prognosis, and had an acceptable toxicity profile. FUNDING Stand Up To Cancer Campaign for Cancer Research UK, the Swiss Cancer Research foundation, and the Swiss Cancer League

HS1, a Lyn Kinase Substrate, Is Abnormally Expressed in B-Chronic Lymphocytic Leukemia and Correlates with Response to Fludarabine-Based Regimen

In B-Chronic Lymphocytic Leukemia (B-CLL) kinase Lyn is overexpressed, active, abnormally distributed, and part of a cytosolic complex involving hematopoietic lineage cell-specific protein 1 (HS1). These aberrant properties of Lyn could partially explain leukemic cells’ defective apoptosis, directly or through its substrates, for example, HS1 that has been associated to apoptosis in different cell types. To verify the hypothesis of HS1 involvement in Lyn-mediated leukemic cell survival, we investigated HS1 protein in 71 untreated B-CLL patients and 26 healthy controls. We found HS1 overexpressed in leukemic as compared to normal B lymphocytes (1.38±0.54 vs 0.86±0.29, p<0.01), and when HS1 levels were correlated to clinical parameters we found a higher expression of HS1 in poor-prognosis patients. Moreover, HS1 levels significantly decreased in ex vivo leukemic cells of patients responding to a fludarabine-containing regimen. We also observed that HS1 is partially localized in the nucleus of neoplastic B cells. All these data add new information on HS1 study, hypothesizing a pivotal role of HS1 in Lyn-mediated modulation of leukemic cells’ survival and focusing, one more time, the attention on the BCR-Lyn axis as a putative target for new therapeutic strategies in this disorder