Elliptic curves and explicit enumeration of irreducible polynomials with two coefficients prescribed

Let $F_q$ be a finite field of characteristic $p=2,3$. We give the number of irreducible polynomials x^m+a_{m-1}x^{m-1}+...+a_0\in\F_q[x] with $a_{m-1}$ and $a_{m-3}$ prescribed for any given $m$ if $p=2$, and with $a_{m-1}$ and $a_1$ prescribed for $m=1,...,10$ if $p=2,3$.Comment: 17 pages, Part of the results was presented at the Polynomials over Finite Fields and Applications workshop at Banff International Research Station, Canad

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which a viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the escape times scale with polymer length, $\tau \sim N^\alpha$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha = 1.33$, which is close to $\alpha = 1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha = 1.25$ and $1.21$ for $\rho = 0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha = 1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho \gtrapprox 0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.Comment: 10 pages, 6 figure

Automatic construction of rule-based ICD-9-CM coding systems

Background: In this paper we focus on the problem of automatically constructing ICD-9-CM coding systems for radiology reports. ICD-9-CM codes are used for billing purposes by health institutes and are assigned to clinical records manually following clinical treatment. Since this labeling task requires expert knowledge in the field of medicine, the process itself is costly and is prone to errors as human annotators have to consider thousands of possible codes when assigning the right ICD-9-CM labels to a document. In this study we use the datasets made available for training and testing automated ICD-9-CM coding systems by the organisers of an International Challenge on Classifying Clinical Free Text Using Natural Language Processing in spring 2007. The challenge itself was dominated by entirely or partly rule-based systems that solve the coding task using a set of hand crafted expert rules. Since the feasibility of the construction of such systems for thousands of ICD codes is indeed questionable, we decided to examine the problem of automatically constructing similar rule sets that turned out to achieve a remarkable accuracy in the shared task challenge. Results: Our results are very promising in the sense that we managed to achieve comparable results with purely hand-crafted ICD-9-CM classifiers. Our best model got a 90.26 % F measure on the training dataset and an 88.93 % F measure on the challenge test dataset, using the micro-averaged Fβ=1 measure, the official evaluatio

High-Resolution Confocal Fluorescence Imaging of Serine Hydrolase Activity in Cryosections - Application to Glioma Brain Unveils Activity Hotspots Originating from Tumor-Associated Neutrophils

Background Serine hydrolases (SHs) are a functionally diverse family of enzymes playing pivotal roles in health and disease and have emerged as important therapeutic targets in many clinical conditions. Activity-based protein profiling (ABPP) using fluorophosphonate (FP) probes has been a powerful chemoproteomic approach in studies unveiling roles of SHs in various biological systems. ABPP utilizes cell/tissue proteomes and features the FP-warhead, linked to a fluorescent reporter for in-gel fluorescence imaging or a biotin tag for streptavidin enrichment and LC-MS/MS-based target identification. Existing ABPP approaches characterize global SH activity based on mobility in gel or MS-based target identification and cannot reveal the identity of the cell-type responsible for an individual SH activity originating from complex proteomes. Results Here, by using an activity probe with broad reactivity towards the SH family, we advance the ABPP methodology to glioma brain cryosections, enabling for the first time high-resolution confocal fluorescence imaging of global SH activity in the tumor microenvironment. Tumor-associated cell types were identified by extensive immunohistochemistry on activity probe-labeled sections. Tissue-ABPP indicated heightened SH activity in glioma vs. normal brain and unveiled activity hotspots originating from tumor-associated neutrophils (TANs), rather than tumor-associated macrophages (TAMs). Thorough optimization and validation was provided by parallel gel-based ABPP combined with LC-MS/MS-based target verification. Conclusions Our study advances the ABPP methodology to tissue sections, enabling high-resolution confocal fluorescence imaging of global SH activity in anatomically preserved complex native cellular environment. To achieve global portrait of SH activity throughout the section, a probe with broad reactivity towards the SH family members was employed. As ABPP requires no a priori knowledge of the identity of the target, we envisage no imaginable reason why the presently described approach would not work for sections regardless of species and tissue source.Peer reviewe