Global Log Research Articles

On the global log canonical threshold of Fano complete intersections

We show that the global log canonical threshold of generic Fano complete intersections of index 1 and codimension k in \({\mathbb {P}}^{M+k}\) is equal to 1 if \(M\geqslant 3k+4\) and the highest degree of defining equations is at least 8. This improves the earlier result where the inequality \(M\geqslant 4k+1\) was required, so the class of Fano complete intersections covered by our theorem is considerably larger. The result implies, in particular, that the Fano complete intersections satisfying our assumptions admit a Kahler–Einstein metric. We also show the existence of Kahler–Einstein metrics for a new finite set of families of Fano complete intersections.

Log Canonical Thresholds of Complete Intersection Log Del Pezzo Surfaces

AbstractWe compute the global log canonical thresholds of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As a corollary we show the existence of orbifold Kähler—Einstein metrics on many of them.

Prognosis model for overall survival in locally advanced unresecable pancreatic carcinoma: An ancillary study of the LAP 07 trial.

235 Background: The management of locally advanced pancreatic cancer (LAPC) patients remains controversial and complex. Better discrimination for Overall Survival (OS) is needed to improve therapeutic decisions. We address this issue, with the largest Phase III cohort of LAPC, by establishing the first prognosis model for OS with the full spectrum of parameters currently available at diagnosis. Methods: We enrolled 442 LAPC patients recruited in LAP07, an international multicenter randomized phase III trial (NCT00634725). 30 baseline variables among demographic, cancer history, clinical, biological and radiological parameters were evaluated in univariate and multivariate analyses as prognostic factors for OS. The predictive value of the final model was evaluated with Harrell’s C index. This analysis was repeated 1,000 times with the use of bootstrap sample to derive 95%CI for the C. A prognostic score and nomogramm were then developed based on the identified prognostic factors in the final model. Results: Independent prognostic factors identified in multivariate analysis (n=370) for OS were: Age (HR= 1.01; 95%CI 1.00 - 1.03; p=0.0418), Pain (HR= 1.36 ; 95%CI 1.08 - 1.71; p=0.0094), Albumin (HR= 0.96; 95%CI 0.94 - 0.98; p=0.0001), and RECIST size (HR= 1.01; 95%CI 1.00 - 1.02; p=0.0033), Harrell’s C-statistic for the final model was 0.60 (95% bootstrap CI 0.56 0.63). A prognostic score between 0 and 4 was then calculated for each patient, based on the previous model. Three risk-groups for death could be identified: lower risk (n=17; median OS time = 18.8 months; group of reference); intermediate risk (n=166 ;median OS time = 13.4 months; HR=1.7); higher risk (n=187 ; median OS time = 11.8 months; HR=2.1); p = 0.0101 by the global log rank test. A score and nomogramm were also developped with the addition of CA19.9 information. Conclusions: Our results highlighted 4 OS’s independent pronostic factors among a broad spectrum of parameters at time of diagnosis. We identified 3 groups with different OS’s prognosis profile. The determination of this simple prognostic score allows risk stratification that may help guiding clinical management of patients and the design for future clinical trials.

Smoothness dependent stability in corrosion detection

We consider the stability issue for the determination of a linear corrosion in a conductor by a single electrostatic measurement. We established a global log–log type stability when the corroded boundary is simply Lipschitz. We also improve such a result obtaining a global log stability by assuming that the damaged boundary is C1,1-smooth.

Log canonical thresholds of del Pezzo surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár–Shokurov’s connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic 0. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than 4 are K-semistable.

CORFU

CORFU is a global log which clients can append-to and read-from over a network. Internally, CORFU is distributed over a cluster of machines in such a way that there is no single I/O bottleneck to either appends or reads. Data is fully replicated for fault tolerance, and a modest cluster of about 16--32 machines with SSD drives can sustain 1 million 4-KByte operations per second. The CORFU log enabled the construction of a variety of distributed applications that require strong consistency at high speeds, such as databases, transactional key-value stores, replicated state machines, and metadata services.

Kähler–Einstein metrics on symmetric Fano [formula omitted]-varieties

We relate the global log canonical threshold of a variety with torus action to the global log canonical threshold of its quotient. We apply this to certain Fano varieties and use Tian’s criterion to prove the existence of Kähler–Einstein metrics on them. In particular, we obtain simple examples of Fano threefolds being Kähler–Einstein but admitting deformations without Kähler–Einstein metric.

Double non-global logarithms in-n-out of jets

We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto \Lambda due to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form \alpha_s^2 \ln^2(\Lambda/m_{1,2}) or \alpha_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambridge-Aachen algorithms. In addition to determining the full algorithmic and R dependence of the leading NGLs, we derive new relations among their coefficients. We also derive to all orders in \alpha_s a factorized form for the soft function S(k_L,k_R,\Lambda) in the cross section \sigma(m_1,m_2,\Lambda) in which dependence on each of the global logs of \mu/k_L, \mu/k_R and \mu/\Lambda determined by the renormalization group are separated from one another and from the non-global logs. The same kind of soft function, its associated non-global structure, and the algorithmic dependence we derive here will also arise in exclusive jet cross sections at hadron colliders, and must be understood and brought under control to achieve precise theoretical predictions.

Data analysis of the inactivation of foodborne microorganisms under high hydrostatic pressure to establish global kinetic parameters and influencing factors.

The inactivation rate of foodborne microorganisms under high hydrostatic pressure (HHP) is influenced by factors such as substrate, species, strain, temperature, pH, and stage of growth of the cell. In this study, 445 D(P)-values from previously published data were analyzed, including those from bacterial spores, vegetative cells, and yeasts. Three secondary linear inactivation models with pressure and/or temperature as process parameters were tested to estimate global log D(P)-, z(P)-, and z(T)-values, and the influence of these parameters and additional factors was assessed. The results show that significant differences in microbial resistance are mainly the result of temperature, highlighting the need for its inclusion as a process parameter. Perhaps due to the large number of data and very distinct factors, the remaining factors showed no significant differences in microbial resistance, except in the case of Clostridium spp. in soy milk, which showed decreased resistance in this substrate compared with its behavior in other products. These results serve to establish priorities among factors influencing HHP inactivation and to estimate global kinetic parameters as a basis for setting target levels of inactivation. Moreover, they can be used as a benchmark for comparison of microbial HHP inactivation data gathered in future studies.

An Approach for Orphan Detection

In distributed systems, node crashes [1] and abort processes may result orphan computations: computations are still active and its results are no longer needed [5]. Orphans are undesirable because they waste system resources [3] and may make inconsistent data [4]. In this paper we present a new approach called global log and monitor approach to cope up with orphan in a more effective way. By this method orphans can be killed immediately after the node crash or abort process happens. No need to wait until the nodes get rebooted as the other methods does. This approach deals with the problem of grand orphans [2] as well. The grand orphans are by orphans who make further RPCs. i.e., the grand orphans are the result of nested transactions.

Existence of the Kähler-Einstein metric on certain Fano complete intersections

For certain families of Fano complete intersections we prove an estimate from below for the global (log) canonical threshold, which implies the existence of Kahler-Einstein metric on generic varieties in these families.

Exceptional del Pezzo Hypersurfaces

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in ℙ(a0,a1,a2,a3). As a corollary we obtain the existence of orbifold Kahler-Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in ℙ(a0,a1,a2,a3).

Log canonical thresholds of three-dimensional Fano hypersurfaces

We study global log canonical thresholds of generic hypersurfaces in of degree that have at most terminal singularities.

Extremal metrics on del Pezzo threefolds

We prove the existence of Kähler-Einstein metrics on a nonsingular section of the Grassmannian Gr(2, 5) ⊂ ℙ9 by a linear subspace of codimension 3 and on the Fermat hypersurface of degree 6 in ℙ(1, 1, 1, 2, 3). We also show that a global log canonical threshold of the Mukai-Umemura variety is equal to 1/2.

On Singular Cubic Surfaces

We study global log canonical thresholds of cubic surfaces with canonical singularities, and we prove the existence of a Kahler-Einstein metric on two singular cubic surfaces.

Log Canonical Thresholds of Del Pezzo Surfaces

We study global log canonical thresholds of del Pezzo surfaces. All varieties are assumed to be defined over $${\mathbb{C}}$$ .

Market impacts of a multiyear mechanical fuel treatment program in the U.S.

We describe a two-stage model of global log and chip markets that evaluates the spatial and temporal economic effects of government-subsidized fire-related mechanical fuel treatment programs in the U.S. West and South. The first stage is a goal program that allocates subsidies according to fire risk and location priorities, given a budget and a feasible, market-clearing market solution. The second stage is a quadratic welfare maximization spatial equilibrium model of individual State and global product markets, subject to the fuel treatment allocation. Results show that the program enhances timber market welfare in regions where treatments occur and globally but has an overall negative economic impact, once fuel treatment program costs are included. The overall cost of a mechanical fuel treatment program, when considering timber market welfare, transport costs, treatment costs, and timber receipts, exceeds $1000 per acre, implying that the long run fire effects and ecosystem net benefits of a treatment program would need to exceed this figure in order to justify widespread implementation.

Fano varieties with many selfmaps

We study global log canonical thresholds of anticanonically embedded quasismooth weighted Fano threefold hypersurfaces having terminal quotient singularities to prove the existence of a Kähler–Einstein metric on most of them, and to produce examples of Fano varieties with infinite discrete groups of birational automorphisms.

The additive effect of p53 Arg72Pro and RNASEL Arg462Gln genotypes on age of disease onset in Lynch syndrome patients with pathogenic germline mutations in MSH2 or MLH1

p53 and the prostate-cancer-susceptibility gene RNASEL are tumour suppressor genes involved in apoptosis. We have previously reported that the common, functionally different variants Arg72Pro in p53 and Arg462Gln in RNASEL are associated with the age of disease onset of colorectal cancer in Lynch syndrome patients. To assess the combined effect of both variants, we screened 246 unrelated Lynch syndrome patients with a pathogenic germline mutation either in MSH2 ( n = 138) or in MLH1 ( n = 108) and colorectal cancer as first tumour, and 245 healthy controls. The global log rank test revealed significant differences in the age of disease onset for the genotypes of each variant ( p = 0.0176 for p53 and p = 0.0358 for RNASEL) and for the combined genotypes of both variants ( p = 0.0174). The highest difference in median age of disease onset was seen between homozygotes for the wild-types in both genes (42 years [range 22–75]) and homozygotes for the variant alleles in both genes (30 years [range 26–47]). A multivariate Cox regression model indicated that only the p53 and RNASEL genotypes had a significant influence on age of disease onset ( p = 0.016 for p53 and p = 0.014 for RNASEL) in an additive mode of inheritance, and that the effects of both variants are purely additive, which supports the notion that the p53 and RNaseL pathways do not interact. These findings may be relevant for preventive strategies in Lynch syndrome.

Concurrency control issues in Grid databases

Grid architecture is a fast evolving distributed computing architecture. The working of databases in the Grid architecture is not well understood. In view of changing distributed architecture we strongly feel that concurrency control issues should be revisited and reassessed for this new and evolving architecture. Implementing global lock table and global log records may not be practically possible in the Grid architecture due to the scalability issues. In this paper, we propose a correctness criterion and the Grid concurrency control protocol, which has the capability to deal with heterogeneity, autonomy, distribution and high volume of data in Grids. We then prove the correctness of the protocol followed by performance evaluation of the protocol.