More Than 1700 Years of Word Equations

Geometry and Diophantine equations have been ever-present in mathematics. Diophantus of Alexandria was born in the 3rd century (as far as we know), but a systematic mathematical study of word equations began only in the 20th century. So, the title of the present article does not seem to be justified at all. However, a linear Diophantine equation can be viewed as a special case of a system of word equations over a unary alphabet, and, more importantly, a word equation can be viewed as a special case of a Diophantine equation. Hence, the problem WordEquations: "Is a given word equation solvable?" is intimately related to Hilbert's 10th problem on the solvability of Diophantine equations. This became clear to the Russian school of mathematics at the latest in the mid 1960s, after which a systematic study of that relation began. Here, we review some recent developments which led to an amazingly simple decision procedure for WordEquations, and to the description of the set of all solutions as an EDT0L language.Comment: The paper will appear as an invited address in the LNCS proceedings of CAI 2015, Stuttgart, Germany, September 1 - 4, 201

On the number of simple arrangements of five double pseudolines

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.Comment: 24 pages, 16 figures, 6 table

Solution sets for equations over free groups are EDT0L languages

© World Scientific Publishing Company. We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language characterization we give, as well as further questions about the existence or finiteness of solutions, follow from our explicit construction of a finite directed graph which encodes all the solutions. Our result incorporates the recently invented recompression technique of Jez, and a new way to integrate solutions of linear Diophantine equations into the process. As a byproduct of our techniques, we improve the complexity from quadratic nondeterministic space in previous works to NSPACE(n log n) here

Les phlébotomes (Diptera-Psychodidae) de l'île de Chypre.II - Presence de Leishmania (Leishmania) infantum Nicolle, 1908 (zymodeme MON 1) chez Phlebotomus (Larroussius) tobbi Adler et Theodor, 1930

Dans le foyer leishmanien cypriote, les auteurs ont disseque 2910 femelles de phlebotomes appartenant a 11 especes : Phlebotomus papatasi, P. sergenti, P. jacusieli, P. alexandri, P. tobbi, P. galilaeus, P. mascittii, P. economidesi, Sergentomyia fallax, S. minuta et S. azizi . Les deux larroussius (P. galilaeus et P. tobbi ) sont les especes les plus abondantes. Elles representent plus de 60 % des captures realisees avec des pieges CDC. Des promastigotes ont ete observees chez un seul specimen appartenant a l'espece P. tobbi . Elles ont ete mises en culture puis identifiees selon la methode isoenzymatique. La souche de Leishmania isolee appartient a l'espece Leishmania infantum , zymodeme MON 1. Le meme zymodeme a ete aussi isole et identifie chez quatre chiens de l'ile. En l'absence des vecteurs habituels de L. infantum dans l'est mediterraneen (P. neglectus ef P. syriacus) et en raison de sa repartition a Chypre, P. tobbi constitue vraisemblablement un bon vecteur local. Sa faible anthropophilie expliquerait peut-etre le tres faible nombre de cas humains. Le role de P. galilaeus dans la transmission de la leishmaniose a Chypre reste a preciser

Evidence of pseudoprogression in patients treated with PD1/ PDL1 antibodies across tumor types

Background: PD(L)1 antibodies (anti-PD(L)-1) have been a major breakthrough in several types of cancer. Novel patterns of response and progression have been described with anti-PD(L)-1. We aimed at characterizing pseudoprogression (PSPD) among patients with various solid tumor types treated by anti-PD(L)-1. Methods: All consecutive patients (pts) enrolled in phase 1 trials with advanced solid tumors and lymphomas treated in phase I clinical trials evaluating monotherapy by anti-PD(L)-1 at Gustave Roussy were analyzed. We aimed to assess prevalence and outcome of PSPD across tumor types. We also intended to describe potential clinical and pathological factors associated with PSPD. Results: A total of 169 patients treated with anti-PD(L)-1 were included in the study. Most frequent tumor types included melanoma (n = 57) and non-small cell lung cancer (n = 19). At first tumor evaluation 77 patients (46%) presented with immune unconfirmed progressive disease. Six patients (8%) experienced PSPD: 2 patients with partial response; 4 patients with stable disease. Increase in target lesions in the first CT-scan was more frequently associated to PSPD (67% vs 33%; P = .04). Patients with a PSPD had a superior survival when compared to patients progressing (median OS: 10.7 months vs 8.7 months; P = .07). Conclusions: A small subset of PSPD patients may experience response after an initial progression. Assessment of the current strategy for immune-related response evaluations may require further attention

Consistent lensing and clustering in a low-S8 Universe with BOSS, DES Year 3, HSC Year 1, and KiDS-1000

We evaluate the consistency between lensing and clustering based on measurements from BOSS combined with galaxy-galaxy lensing from DES-Y3, HSC-Y1, KiDS-1000. We find good agreement between these lensing datasets. We model the observations using the Dark Emulator and fit the data at two fixed cosmologies: Planck (S 8 = 0.83), and a Lensing cosmology (S 8 = 0.76). For a joint analysis limited to large scales, we find that both cosmologies provide an acceptable fit to the data. Full utilisation of the higher signal-to-noise small-scale measurements is hindered by uncertainty in the impact of baryon feedback and assembly bias, which we account for with a reasoned theoretical error budget. We incorporate a systematic inconsistency parameter for each redshift bin, A, that decouples the lensing and clustering. With a wide range of scales, we find different results for the consistency between the two cosmologies. Limiting the analysis to the bins for which the impact of the lens sample selection is expected to be minimal, for the Lensing cosmology, the measurements are consistent with A=1; A = 0.91 ± 0.04 (A = 0.97 ± 0.06) using DES+KiDS (HSC). For the Planck case, we find a discrepancy: A = 0.79 ± 0.03 (A = 0.84 ± 0.05) using DES+KiDS (HSC). We demonstrate that a kSZ-based estimate for baryonic effects alleviates some of the discrepancy in the Planck cosmology. This analysis demonstrates the statistical power of small-scale measurements, but caution is still warranted given modelling uncertainties and foreground sample selection effects

Characteristic mTOR activity in Hodgkin-lymphomas offers a potential therapeutic target in high risk disease – a combined tissue microarray, in vitro and in vivo study

BACKGROUND: Targeting signaling pathways is an attractive approach in many malignancies. The PI3K/Akt/mTOR pathway is activated in a number of human neoplasms, accompanied by lower overall and/or disease free survival. mTOR kinase inhibitors have been introduced in the therapy of renal cell carcinoma and mantle cell lymphoma, and several trials are currently underway. However, the pathological characterization of mTOR activity in lymphomas is still incomplete. METHODS: mTOR activity and the elements of mTOR complexes were investigated by immunohistochemistry on tissue microarrays representing different human non-Hodgkin-lymphomas (81 cases) and Hodgkin-lymphomas (87 cases). The expression of phospho-mTOR, phospho-4EBP1, phospho-p70S6K, phospho-S6, Rictor, Raptor and Bcl-2, Bcl-xL, Survivin and NF-kappaB-p50 were evaluated, and mTOR activity was statistically analyzed along with 5-year survival data. The in vitro and in vivo effect of the mTOR inhibitor rapamycin was also examined in human Hodgkin-lymphoma cell lines. RESULTS: The majority (>50%) of mantle cell lymphoma, Burkitt lymphoma, diffuse large B-cell lymphoma, anaplastic large-cell lymphoma and Hodgkin-lymphoma cases showed higher mTOR activity compared to normal lymphoid tissues. Hodgkin-lymphoma was characterized by high mTOR activity in 93% of the cases, and Bcl-xL and NF-kappaB expression correlated with this mTOR activity. High mTOR activity was observed in the case of both favorable and unfavorable clinical response. Low mTOR activity was accompanied by complete remission and at least 5-year disease free survival in Hodgkin-lymphoma patients. However, statistical analysis did not identify correlation beetween mTOR activity and different clinical data of HL patients, such as survival. We also found that Rictor (mTORC2) was not overexpressed in Hodgkin-lymphoma biopsies and cell lines. Rapamycin inhibited proliferation and induced apoptosis in Hodgkin-lymphoma cells both in vitro and in vivo, moreover, it increased the apoptotic effect of chemotherapeutic agents. CONCLUSIONS: Targeting mTOR activity may be a potential therapeutic tool in lymphomas. The presence of mTOR activity probably indicates that the inclusion of mTOR inhibition in the therapy of Hodgkin-lymphomas may be feasible and beneficial, especially when standard protocols are ineffective, and it may also allow dose reduction in order to decrease late treatment toxicity. Most likely, the combination of mTOR inhibitors with other agents will offer the highest efficiency for achieving the best clinical response

Building an Efficient Cluster Cosmology Software Package for Modeling Cluster Counts and Lensing

We introduce a software suite developed for galaxy cluster cosmological analysis with the Dark Energy Survey Data. Cosmological analyses based on galaxy cluster number counts and weak-lensing measurements need efficient software infrastructure to explore an increasingly large parameter space, and account for various cosmological and astrophysical effects. Our software package is designed to model the cluster observables in a wide-field optical survey, including galaxy cluster counts, their averaged weak-lensing masses, or the cluster's averaged weak-lensing radial signals. To ensure maximum efficiency, this software package is developed in C++ in the CosmoSIS software framework, making use of the CUBA integration library. We also implement a testing and validation scheme to ensure the quality of the package. We demonstrate the effectiveness of this development by applying the software to the Dark Energy Survey Year 1 galaxy cluster cosmological data sets, and acquired cosmological constraints that are consistent with the fiducial Dark Energy Survey analysis

Performance status is the most powerful risk factor for early death among patients with advanced soft tissue sarcoma The European Organisation for Research and Treatment of Cancer – Soft Tissue and Bone Sarcoma Group (STBSG) and French Sarcoma Group (FSG) study

BACKGROUND: We investigated prognostic factors (PFs) for 90-day mortality in a large cohort of advanced/metastatic soft tissue sarcoma (STS) patients treated with first-line chemotherapy. METHODS: The PFs were identified by both logistic regression analysis and probability tree analysis in patients captured in the Soft Tissue and Bone Sarcoma Group (STBSG) database (3002 patients). Scores derived from the logistic regression analysis and algorithms derived from probability tree analysis were subsequently validated in an independent study cohort from the French Sarcoma Group (FSG) database (404 patients). RESULTS: The 90-day mortality rate was 8.6 and 4.5% in both cohorts. The logistic regression analysis retained performance status (PS; odds ratio (OR) = 3.83 if PS = 1, OR = 12.00 if PS >= 2), presence of liver metastasis (OR = 2.37) and rare site metastasis (OR = 2.00) as PFs for early death. The CHAID analysis retained PS as a major discriminator followed by histological grade (only for patients with PS >= 2). In both models, PS was the most powerful PF for 90-day mortality. CONCLUSION: Performance status has to be taken into account in the design of further clinical trials and is one of the most important parameters to guide patient management. For those patients with poor PS, expected benefits from therapy should be weighed up carefully against the anticipated toxicities. British Journal of Cancer (2011) 104, 1544-1550. doi: 10.1038/bjc.2011.136 www.bjcancer.com Published online 19 April 2011 (C) 2011 Cancer Research U