Curve Counting Research Articles

Elliptic curves over a finite field and the trace formula

We prove formulas for power moments for point counts of elliptic curves over a finite field $k$ such that the groups of $k$-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$. As our main technical input we prove an Eichler-Selberg trace formula for a family of congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$ which include as special cases the groups $\Gamma_1(N)$ and $\Gamma(N)$. Our formulas generalize results of Birch and Ihara (the case of the trivial subgroup, and the full modular group), and previous work of the authors (the subgroups $\mathbb{Z}/2\mathbb{Z}$ and $(\mathbb{Z}/2\mathbb{Z})^2$ and congruence subgroups $\Gamma_0(2),\Gamma_0(4)$). We use these formulas to answer statistical questions about point counts for elliptic curves over a fixed finite field, generalizing results of Vl\v{a}du\c{t}, Gekeler, Howe, and others.

Counting spinning dyons in maximal supergravity: the Hodge-elliptic genus for tori

We consider $M$-theory compactified on $T^4 \times T^2$ and describe the count of spinning $1/8$-BPS states. This refines the classic count of Maldacena-Moore-Strominger in the physics literature and the recent mathematical work of Bryan-Oberdieck-Pandharipande-Yin, which studied reduced Donaldson-Thomas invariants of abelian surfaces and threefolds. As in previous work on $K3 \times T^2$ compactification, we track angular momenta under both the $SU(2)_L$ and $SU(2)_R$ factors in the 5d little group, providing predictions for the relevant motivic curve counts.

PET Imaging Stability Measurements During Simultaneous Pulsing of Aggressive MR Sequences on the SIGNA PET/MR System.

The recent introduction of simultaneous whole-body PET/MR scanners has enabled new research taking advantage of the complementary information obtainable with PET and MRI. One such application is kinetic modeling, which requires high levels of PET quantitative stability. To accomplish the required PET stability levels, the PET subsystem must be sufficiently isolated from the effects of MR activity. Performance measurements have previously been published, demonstrating sufficient PET stability in the presence of MR pulsing for typical clinical use; however, PET stability during radiofrequency (RF)-intensive and gradient-intensive sequences has not previously been evaluated for a clinical whole-body scanner. In this work, PET stability of the GE SIGNA PET/MR was examined during simultaneous scanning of aggressive MR pulse sequences. Methods: PET performance tests were acquired with MR idle and during simultaneous MR pulsing. Recent system improvements mitigating RF interference and gain variation were used. A fast recovery fast spin echo MR sequence was selected for high RF power, and an echo planar imaging sequence was selected for its high heat-inducing gradients. Measurements were performed to determine PET stability under varying MR conditions using the following metrics: sensitivity, scatter fraction, contrast recovery, uniformity, count rate performance, and image quantitation. A final PET quantitative stability assessment for simultaneous PET scanning during functional MRI studies was performed with a spiral in-and-out gradient echo sequence. Results: Quantitation stability of a 68Ge flood phantom was demonstrated within 0.34%. Normalized sensitivity was stable during simultaneous scanning within 0.3%. Scatter fraction measured with a 68Ge line source in the scatter phantom was stable within the range of 40.4%-40.6%. Contrast recovery and uniformity were comparable for PET images acquired simultaneously with multiple MR conditions. Peak noise equivalent count rate was 224 kcps at an effective activity concentration of 18.6 kBq/mL, and the count rate curves and scatter fraction curve were consistent for the alternating MR pulsing states. A final test demonstrated quantitative stability during a spiral functional MRI sequence. Conclusion: PET stability metrics demonstrated that PET quantitation was not affected during simultaneous aggressive MRI. This stability enables demanding applications such as kinetic modeling.

The Hodge-Elliptic Genus, Spinning BPS States, and Black Holes

We perform a refined count of BPS states in the compactification of M-theory on $K3 \times T^2$, keeping track of the information provided by both the $SU(2)_L$ and $SU(2)_R$ angular momenta in the $SO(4)$ little group. Mathematically, this four variable counting function may be expressed via the motivic Donaldson-Thomas counts of $K3 \times T^2$, simultaneously refining Katz, Klemm, and Pandharipande's motivic Donaldson-Thomas counts on $K3$ and Oberdieck-Pandharipande's Gromov-Witten counts on $K3 \times T^2$. This provides the first full answer for motivic curve counts of a compact Calabi-Yau threefold. Along the way, we develop a Hodge-elliptic genus for Calabi-Yau manifolds -- a new counting function for BPS states that interpolates between the Hodge polynomial and the elliptic genus of a Calabi-Yau.

Functional regression method for whole genome eQTL epistasis analysis with sequencing data

BackgroundEpistasis plays an essential rule in understanding the regulation mechanisms and is an essential component of the genetic architecture of the gene expressions. However, interaction analysis of gene expressions remains fundamentally unexplored due to great computational challenges and data availability. Due to variation in splicing, transcription start sites, polyadenylation sites, post-transcriptional RNA editing across the entire gene, and transcription rates of the cells, RNA-seq measurements generate large expression variability and collectively create the observed position level read count curves. A single number for measuring gene expression which is widely used for microarray measured gene expression analysis is highly unlikely to sufficiently account for large expression variation across the gene. Simultaneously analyzing epistatic architecture using the RNA-seq and whole genome sequencing (WGS) data poses enormous challenges.MethodsWe develop a nonlinear functional regression model (FRGM) with functional responses where the position-level read counts within a gene are taken as a function of genomic position, and functional predictors where genotype profiles are viewed as a function of genomic position, for epistasis analysis with RNA-seq data. Instead of testing the interaction of all possible pair-wises SNPs, the FRGM takes a gene as a basic unit for epistasis analysis, which tests for the interaction of all possible pairs of genes and use all the information that can be accessed to collectively test interaction between all possible pairs of SNPs within two genome regions.ResultsBy large-scale simulations, we demonstrate that the proposed FRGM for epistasis analysis can achieve the correct type 1 error and has higher power to detect the interactions between genes than the existing methods. The proposed methods are applied to the RNA-seq and WGS data from the 1000 Genome Project. The numbers of pairs of significantly interacting genes after Bonferroni correction identified using FRGM, RPKM and DESeq were 16,2361, 260 and 51, respectively, from the 350 European samples.ConclusionsThe proposed FRGM for epistasis analysis of RNA-seq can capture isoform and position-level information and will have a broad application. Both simulations and real data analysis highlight the potential for the FRGM to be a good choice of the epistatic analysis with sequencing data.

Mixed mode fracture properties of GFRP-adhesive interfaces based on video gauge and acoustic emission measurements from specimens with adherend fibres normal to the interfaces

Mixed-mode bending tests were performed on fifty-three GFRP-adhesive-GFRP specimens. In each specimen the pre-crack was located near the GFRP adherend with fibres normal to the GFRP-adhesive interface, so as to encourage crack propagation along this interface rather than through the GFRP. The other GFRP adherend contained fibres parallel to the interface, leading to asymmetry of GFRP material (but not of specimen geometry) with respect to the adhesive layer in each specimen. This switching, across the adhesive layer, between normal and parallel fibres in the adherends, reflects a T-joint detail considered for a wave energy device. All tests used a video gauge system to measure crack propagation. Some tests also employed an acoustic emission (AE) system. Comparisons between the AE results and the video gauge-based crack propagation data strongly suggest that the AE energy vs time curve is a much clearer indication of crack initiation than is the widely used AE hit count vs time curve. Increase in Mode II ratio during the tests led to fewer but larger post-peak load drops. Williams's approach, based on beam theory for asymmetric sections with correction factors for large displacements and shear deformation included, led to fracture toughness (G(c)) values in the range 0.3-2.8 kJ/m(2), with a trend of increasing Gc values as pure Mode II is approached. The ASTM approach, developed only for symmetric specimens, gave much lower Gc values. (C) 2017 Elsevier Ltd. All rights reserved.

Value of platelet count in the early diagnosis of nosocomial invasive fungal infections in premature infants

The aim of this study was to investigate the value of a platelet count (PLT) in the early diagnosis of nosocomial invasive fungal infections in premature infants. Based on clinical diagnosis combined with blood culture results, 72 premature infants of 5354 pediatric patients who were hospitalized in the neonatal ward of our hospital between September 2009 and February 2013 were diagnosed with nosocomial invasive fungal infections (fungal infection group). There were 58 premature infants diagnosed with bacterial infections during the same period (bacterial infection group). The control group included 74 premature infants without nosocomial infections who were hospitalized during the same period. Receiver operating characteristic (ROC) curves were used to analyze the sensitivity, specificity, and diagnostic efficacy of the PLT and white blood cell (WBC) counts and C-reactive protein (CRP) level in the diagnosis of fungal infections in premature infants. The risk factors for invasive fungal infections included birth weight < 2000 g, gestational age < 32 weeks, peripherally inserted central catheter (PICC), oxygen inhalation therapy, intravenous nutrition, and administration of antibiotics (p < 0.05). Compared with the control group, the WBC and PLT counts in the fungal infection group decreased in the early and acute stages of infection (p < 0.01), while the CRP level increased (p < 0.01). The PLT count in the bacterial infection group decreased in the early and acute stages of infection (p < 0.01) and the CRP level increased (p < 0.05). Moreover, the decrease in the PLT count in the fungal infection group was more significant than the bacterial infection group (p < 0.01) and the CRP level increased more in the fungal infection group in the early stage of infection (p < 0.01); however, there were no significant differences in the PLT count and CRP level between the fungal and bacterial infection groups in the acute stage of infection (p > 0.05). ROC curve analysis of the WBC and PLT counts and the CRP level in the early diagnosis of fungal infections showed that the area under the curve of the PLT count was 0.912 (95% confidence interval:0.863–0.961), thus indicating a high accuracy with a cutoff PLT count of 157.0 × 109/L. The corresponding sensitivity and specificity were 77.8% and 94.6%, respectively. We conclude that the PLT count is a convenient, economical, and effective predictor of invasive fungal infections in premature infants and has potential in the early diagnosis of fungal infections.

Three Dimensional Tropical Correspondence Formula

A tropical curve in $\mathbb R^{3}$ contributes to Gromov-Witten invariants in all genus. Nevertheless, we present a simple formula for how a given tropical curve contributes to Gromov-Witten invariants when we encode these invariants in a generating function with exponents of $\lambda$ recording Euler characteristic. Our main modification from the known tropical correspondence formula for rational curves is as follows: a trivalent vertex, which before contributed a factor of $n$ to the count of zero-genus holomorphic curves, contributes a factor of $2\sin(n\lambda/2)$. We explain how to calculate relative Gromov-Witten invariants using this tropical correspondence formula, and how to obtain the absolute Gromov-Witten and Donaldson-Thomas invariants of some $3$-dimensional toric manifolds including $\mathbb CP^{3}$. The tropical correspondence formula counting Donaldson-Thomas invariants replaces $n$ by $i^{-(1+n)}q^{n/2}+i^{1+n}q^{-n/2}$.

Qualitative aspects of counting real rational curves on real K3 surfaces

We study qualitative aspects of the Welschinger-like $\mathbb Z$-valued count of real rational curves on primitively polarized real $K3$ surfaces. In particular, we prove that with respect to the degree of the polarization, at logarithmic scale, the rate of growth of the number of such real rational curves is, up to a constant factor, the rate of growth of the number of complex rational curves. We indicate a few instances when the lower bound for the number of real rational curves provided by our count is sharp. In addition, we exhibit various congruences between real and complex counts.

Image-derived input function estimation on a TOF-enabled PET/MR for cerebral blood flow mapping

15O-H2O PET imaging is an accurate method to measure cerebral blood flow (CBF) but it requires an arterial input function (AIF). Historically, image-derived AIF estimation suffers from low temporal resolution, spill-in, and spill-over problems. Here, we optimized tracer dose on a time-of-flight PET/MR according to the acquisition-specific noise-equivalent count rate curve. An optimized dose of 850 MBq of 15O-H2O was determined, which allowed sufficient counts to reconstruct a short time-frame PET angiogram (PETA) during the arterial phase. This PETA enabled the measurement of the extent of spill-over, while an MR angiogram was used to measure the true arterial volume for AIF estimation. A segment of the high cervical arteries outside the brain was chosen, where the measured spill-in effects were minimal. CBF studies were performed twice with separate [15O]-H2O injections in 10 healthy subjects, yielding values of 88 ± 16, 44 ± 9, and 58 ± 11 mL/min/100 g for gray matter, white matter, and whole brain, with intra-subject CBF differences of 5.0 ± 4.0%, 4.1 ± 3.3%, and 4.5 ± 3.7%, respectively. A third CBF measurement after the administration of 1 g of acetazolamide showed 35 ± 23%, 29 ± 20%, and 33 ± 22% increase in gray matter, white matter, and whole brain, respectively. Based on these findings, the proposed noninvasive AIF method provides robust CBF measurement with 15O-H2O PET.

Counting curves on surfaces

We consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology: for a compact surface [Formula: see text], with a finite set of points [Formula: see text] fixed on its boundary, how many configurations of disjoint arcs are there on [Formula: see text] whose boundary is [Formula: see text]? We find that this enumerative problem, counting curves on surfaces, has a rich structure. We show that such curve counts obey an effective recursion, in the general spirit of topological recursion, and exhibit quasi-polynomial behavior. This “elementary curve-counting” is in fact related to a more advanced notion of “curve-counting” from algebraic geometry or symplectic geometry. The asymptotics of this enumerative problem are closely related to the asymptotics of volumes of moduli spaces of curves, and the quasi-polynomials governing the enumerative problem encode intersection numbers on moduli spaces. Among several other results, we show that generating functions and differential forms for these curve counts exhibit structure that is reminiscent of the mathematical physics of free energies, partition functions and quantum curves.

基于蒙特卡罗方法的密度测井薄层影响分析

薄层是影响密度测井的重要因素，利用蒙特卡罗方法对密度测井进行数值模拟，获取密度测井对薄层的响应资料，用于研究薄层对密度测井的影响，确定密度测井记录点及计数率曲线变化规律。研究表明，对于低密度薄层，随着薄层纵向位置的移动，计数率先增大后减少，曲线形态对称，极大值点为记录点；对于高密度薄层，随着薄层纵向位置的移动，计数率先减少后增大，曲线形态近似对称，极小值点为记录点。同时针对密度测井最小纵向分辨率进行了讨论。 Thin layer was an important factor influencing the density logging. Monte Carlo method was ap-plied to simulate the density logging and get the data of density logging response of thin layer, by which the influence of thin layer on the density logging was studied to determine the density log-ging record point and the change rules of the counting rate curve. The research indicates that the counting rate of low density thin layer increases initially and then decreases with the longitudinal movement of the thin layer. The shape of the curve is approximately symmetrical and the maximum point is a recorded point, while for the high density thin layer, the counting rate decreases first and then increases with vertical movement of the thin layer, the shape of the curve is also approximately symmetrical and the minimum point is the recorded point. Meanwhile, the minimum vertical resolution of density logging is discussed in this paper.

Tropical count of curves on abelian varieties

We investigate the problem of counting tropical genus g curves in g-dimensional tropical abelian varieties. For g = 2, 3, we prove that the tropical count matches the count provided by Gottsche, Bryan-Leung, and Lange-Sernesi in the complex setting.

Equivariant K3 invariants

In this note, we describe a connection between the enumerative geometry of curves in K3 surfaces and the chiral ring of an auxiliary superconformai field theory. We consider the invariants calculated by Yau-Zaslow (capturing the Euler characters of the moduli spaces of D2-branes on curves of given genus), together with their refinements to carry additional quantum numbers by Katz-Klemm-Vafa (KKV), and Katz-Klemm-Pandharipande (KKP). We observe that these invariants can be reproduced by studying the Ramond ground states of an auxiliary chiral superconformal field theory which has recently been used to establish mock modular moonshine for a variety of sporadic simple groups that are subgroups of Conway's group. This observation leads us to conjectural descriptions of equivariant versions of the KKV and KKP invariants. A K3 sigma model is specified by a choice of 4-plane in the K3 D-brane charge lattice. Symmetries of K3 sigma models are naturally identified with 4-plane preserving subgroups of the Conway group, according to the work of Gaberdiel-Hohenegger-Volpato, and one may consider corresponding equivariant refined K3 Gopakumar-Vafa invariants. The same symmetries naturally arise in the auxiliary CFT state space, affording a suggestive alternative view of the same computation. We comment on a lift of this story to the generating function of elliptic genera of symmetric products of K3 surfaces, and the connection to work of Oberdieck-Pandharipande on curve counts for the product of a K3 surface with an elliptic curve.

Models to Estimate Lactation Curves of Milk Yield and Somatic Cell Count in Dairy Cows at the Herd Level for the Use in Simulations and Predictive Models.

Typically, central milk recording data from dairy herds are recorded less than monthly. Over-fitting early in lactation periods is a challenge, which we explored in different ways by reducing the number of parameters needed to describe the milk yield and somatic cell count of individual cows. Furthermore, we investigated how the parameters of lactation models correlate between parities and from dam to offspring. The aim of the study was to provide simple and robust models for cow level milk yield and somatic cell count for fitting to sparse data to parameterize herd- and cow-specific simulation of dairy herds. Data from 610 Danish Holstein herds were used to determine parity traits in milk production regarding milk yield and somatic cell count of individual cows. Parity was stratified in first, second, and third and higher for milk, and first to sixth and higher for somatic cell count. Fitting of herd level parameters allowed for cow level lactation curves with three, two, or one parameters per lactation. Correlations of milk yield and somatic cell count were estimated between lactations and between dam and offspring. The shape of the lactation curves varied markedly between farms. The correlation between lactations for milk yield and somatic cell count was 0.2–0.6 and significant on more than 95% of farms. The variation in the daily milk yield was observed to be a source of variation to the somatic cell count, and the total somatic cell count was less correlated with the milk production than somatic cells per milliliter. A positive correlation was found between relative levels of the total somatic cell count and the milk yield. The variation of lactation and somatic cell count curves between farms highlights the importance of a herd level approach. The one-parameter per cow model using a herd level curve allows for estimating the cow production level from first the recording in the parity, while a two-parameter model requires more recordings for a credible estimate, but may more precisely predict persistence, and given the independence of parameters, these can be easily drawn for use in simulation models. We also conclude that using total somatic cell count may stabilize models, and therefore, the dilution factor is of importance in Danish Holstein.

Increased Short-Term Mortality in Patients with Spontaneous Intracerebral Hemorrhage and its Association with Admission Glucose Levels and Leukocytosis

Spontaneous intracerebral hemorrhage (ICH) can be a devastating event. An increased glucose level in patients with ICH is known to be related to poor outcomes, including acute leukocytosis, which is a well-established response to ICH. The purpose of this study was to evaluate the association between admission laboratory factors and 3-month mortality in patients with spontaneous supratentorial ICH. We performed a Kaplan-Meier analysis to evaluate the risk factors for 3-month mortality in patients with ICH. We used univariate and multivariate Cox regression analyses to calculate hazard ratios with 95% confidence intervals for short-term mortality based on clinical and laboratory factors. The area under the receiver operating characteristic curve was used to determine the laboratory risk factors that predicted mortality. In total, 538 patients from our hospital admitted with primary spontaneous supratentorial ICH over an 8-year period were enrolled in this study. Higher leukocyte counts (hazard ratio, 1.019; 95% confidence interval, 1.012-1.027; P < 0.001) and glucose levels on admission were associated with higher 3-month mortality. The receiver operating characteristic curve analysis showed that the areas under the curve of ICH volume, glucose, and leukocyte counts were 0.696 (cutoff value, 41.63), 0.687 (cutoff value, 134), and 0.642 (cutoff value, 9.4), respectively. Higher admission white blood cell counts and glucose levels were associated with higher 3-month mortality in patients with spontaneous ICH. These data show that an altered glucose metabolism and inflammatory state after ICH may be related to early deterioration after an ICH.

Number of Daily Steps to Discriminate Abdominal Obesity in a Sample of Brazilian Children and Adolescents.

Weight status-referenced pedometer step-count guidelines for young people have been developed for populations from high-income countries and may not be applicable to middle- and low-income countries. The objectives of this study were 1) to develop cut-off points for pedometer-determined step count in young Brazilians using waist circumference (WC) as a reference criterion, and 2) to analyze the capacity of previous recommendations to discriminate abdominal obesity in the sample studied. A cross-sectional study was conducted on 1,044 schoolchildren (456 boys) aged 6-17 years from Northeastern Brazil. WC was measured and daily step counts were determined with a pedometer. The area under the curve (AUC) of step count was significant for boys (AUC = 0.55; 95%CI: 0.50-0.59) and girls (AUC = 0.57; 95%CI: 0.53-0.61). Our cut-off points (14,414 and 11,355 steps for boys and girls, respectively) were more balanced in terms of sensitivity and specificity compared with previous recommendations. The use of previous guidelines to classify step count in the sample provided very low sensitivity or specificity and wide variation in the prevalence of insufficient physical activity (39.3-77.0%). A universal step-count recommendation for young people may not be adequate and specific guidelines seem to be necessary for different countries or regions.

Rapid processing of PET list-mode data for efficient uncertainty estimation and data analysis

In this technical note we propose a rapid and scalable software solution for the processing of PET list-mode data, which allows the efficient integration of list mode data processing into the workflow of image reconstruction and analysis. All processing is performed on the graphics processing unit (GPU), making use of streamed and concurrent kernel execution together with data transfers between disk and CPU memory as well as CPU and GPU memory. This approach leads to fast generation of multiple bootstrap realisations, and when combined with fast image reconstruction and analysis, it enables assessment of uncertainties of any image statistic and of any component of the image generation process (e.g. random correction, image processing) within reasonable time frames (e.g. within five minutes per realisation). This is of particular value when handling complex chains of image generation and processing.The software outputs the following: (1) estimate of expected random event data for noise reduction; (2) dynamic prompt and random sinograms of span-1 and span-11 and (3) variance estimates based on multiple bootstrap realisations of (1) and (2) assuming reasonable count levels for acceptable accuracy. In addition, the software produces statistics and visualisations for immediate quality control and crude motion detection, such as: (1) count rate curves; (2) centre of mass plots of the radiodistribution for motion detection; (3) video of dynamic projection views for fast visual list-mode skimming and inspection; (4) full normalisation factor sinograms. To demonstrate the software, we present an example of the above processing for fast uncertainty estimation of regional SUVR (standard uptake value ratio) calculation for a single PET scan of 18F-florbetapir using the Siemens Biograph mMR scanner.

MAC 2 binding protein gi for the prediction of posthepatectomy liver failure in hepatocellular carcinoma patients

Introduction: Posthepatectomy liver failure (PHLF) is a serious postoperative state, and the precise prediction of PHLF is essential. Recently, Mac 2 binding protein Gi (M2BPGi) has been reported as a useful predictor of liver fibrosis. We aimed to evaluate the usefulness of M2BPGi in predicting PHLF in hepatocellular carcinoma (HCC) patients. Methods: We retrospectively collected and analyzed the data of liver function tests, fibrotic markers, shear wave velocity (SWV) by acoustic radiation force impulse imaging, and resection rate (RR) of 138 patients with HCC who underwent liver resection. M2BPGi values were measured using frozen serum samples. RR was calculated by computed tomography volumetry. PHLF was diagnosed based on the International Study Group of Liver Surgery definition. Results: PHLF grade≧B occurred in 19 patients (13.7%: grade B, n = 14; grade C, n = 5). The area under the receiver operating characteristic curve (AUROC) of M2BPGi, SWV and platelet count (Plt) in predicting PHLF grade≧B was high (0.705, 0.769 and 0.720, respectively). Multivariate analysis identified M2BPGi (odds ratio [OR]: 2.08, 95% confidence interval [CI]: 1.28 to 3.55, p < 0.01), Plt (OR: 0.39, 95% CI: 0.18 to 0.80, p = 0.02) and RR (OR: 2.71, 95% CI: 1.46 to 5.40, p < 0.01) as the significant factors associated with PHLF grade≧B, and the logistic model that included these factors resulted in an AUROC of 0.81. Conclusion: In HCC patients, M2BPGi was useful in predicting PHLF, and the predictive power was improved in combination with Plt and RR.

Iatrogenic Coagulopathy and the Development of Posterior Reversible Encephalopathy Syndrome after L-asparaginase Chemotherapy

Posterior reversible encephalopathy syndrome (PRES) is a clinical and radiological syndrome mostly related to hypertension, eclampsia, renal failure, or to chemotherapy and/or immunosuppressive drugs. Although the PRES pathophysiology is multifactorial, hypertension and endothelial dysfunction are hypothesized to be the pivotal factors. Here we report a case of PRES in an adult patient after chemotherapy (Escherichia coli L-asparaginase [L-ASP], daunorubicin, vincristine, and intrathecal methotrexate) for acute lymphoblastic leukemia. The development of the PRES was strictly associated with an iatrogenic coagulopathy induced by L-ASP, which inhibits the biosynthesis of hepatic coagulation factors. The nadir of platelet count, antithrombin III (ATIII) and fibrinogen curve was coincident with the onset of the PRES neurological picture; subsequently, the normalization of the ATIII and fibrinogen levels seemed to parallel the good clinical evolution. This case seems to provide new insights into the PRES pathophysiological mechanisms.