Some Faster Algorithms for Finding Large Prime Gaps

This paper investigates the problem of finding large prime gaps (the difference between two consecutive prime numbers, pi+1 – pi) and on the development of a small, efficient program for generating such large prime gaps for a single computer, a laptop or a workstation. In Wikipedia [1], one can find a table of all known record prime gaps less than 264, the record is a 20 decimal digit number. We wanted to go beyond 64 bit numbers and demonstrate algorithms that do not needed a huge number of computers in a grid to produce useful results. After some preliminary tests, we found that the Sieve of Eratosthenes, SE, from the year 250 BC was the fastest for finding prime numbers and it could also be made space efficient. Each odd number is represented by one bit and when storing 8 odd numbers in a single byte (representing 16 consecutive numbers ignoring the even numbers), we found that we should not make one long SE table, but instead divide the SE table into segments (called SE segments), each of length 108 or 109 and dynamically generate the necessary SE segments as to find prime numbers. First, we made a basic segment of all prime numbers < 108 (in less than a second). We also relied heavily on the old observation [2] that when using SE to find all prime numbers ?????, we cross out all numbers using the prime numbers ???? ? ?????, and that the first number crossed off when crossing out for prime number p is p2. When we want to find prime gaps, we first create one or more consecutive SE in that range, say starting on 274 and ending with the value M – initially these big segments are crossed out by our first basic set of primes < 108 , To find all prime number in these big segments, we next need the rest of prime numbers ???? ? ????? . These can be all be constructed by using our first set of prime numbers to generate segments of consecutive SE from 108. The primes in these segments are used to cross out in the big SE segment and can then be discarded (each prime used only once). Our most significant algorithm was to find a simple formula for using primes from a range 3 – 236 to cross out the non-primes in any SE segment without crossing out in all the numbers between 236 and 272. This leads to an exponential saving in both space and execution time. In addition to this, we created a small package Int3 to represent numbers > 264 by storing 8 decimal values in each of 3 integer variables together with the necessary mathematical operations. The Int3 package can handle numbers up to 24 decimal digits and is significantly faster than the BigInteger package in the Java library. We also created a faster algorithm for finding all record prime gaps. The results presented in this paper are some tables of prime gaps for primes significantly larger than 264 and data supporting an observation that big prime gaps in these segments are much more frequent than the ones we find in the Wikipedia table where the search starts at prime number 3. Our combined set of algorithms is also sufficiently fast to test every entry in the Wikipedia table in less than 5 minutes. We conclude by reflecting on the use of brute force (more computers) versus smarter algorithms

The Rho GDI Rdi1 regulates Rho GTPases by distinct mechanisms

© 2008 by The American Society for Cell Biology. Under the License and Publishing Agreement, authors grant to the general public, effective two months after publication of (i.e.,. the appearance of) the edited manuscript in an online issue of MBoC, the nonexclusive right to copy, distribute, or display the manuscript subject to the terms of the Creative Commons–Noncommercial–Share Alike 3.0 Unported license (http://creativecommons.org/licenses/by-nc-sa/3.0).The small guanosine triphosphate (GTP)-binding proteins of the Rho family are implicated in various cell functions, including establishment and maintenance of cell polarity. Activity of Rho guanosine triphosphatases (GTPases) is not only regulated by guanine nucleotide exchange factors and GTPase-activating proteins but also by guanine nucleotide dissociation inhibitors (GDIs). These proteins have the ability to extract Rho proteins from membranes and keep them in an inactive cytosolic complex. Here, we show that Rdi1, the sole Rho GDI of the yeast Saccharomyces cerevisiae, contributes to pseudohyphal growth and mitotic exit. Rdi1 interacts only with Cdc42, Rho1, and Rho4, and it regulates these Rho GTPases by distinct mechanisms. Binding between Rdi1 and Cdc42 as well as Rho1 is modulated by the Cdc42 effector and p21-activated kinase Cla4. After membrane extraction mediated by Rdi1, Rho4 is degraded by a novel mechanism, which includes the glycogen synthase kinase 3β homologue Ygk3, vacuolar proteases, and the proteasome. Together, these results indicate that Rdi1 uses distinct modes of regulation for different Rho GTPases.Deutsche Forschungsgemeinschaf

Spike frequency adaptation in primate lateral prefrontal cortex neurons results from interplay between intrinsic properties and circuit dynamics

Cortical neurons in brain slices display intrinsic spike frequency adaptation (I-SFA) to constant current inputs, while extracellular recordings show extrinsic SFA (E-SFA) during sustained visual stimulation. Inferring how I-SFA contributes to E-SFA during behavior is challenging due to the isolated nature of slice recordings. To address this, we recorded macaque lateral prefrontal cortex (LPFC) neurons in vivo during a visually guided saccade task and in vitro in brain slices. Broad-spiking (BS) putative pyramidal cells and narrow-spiking (NS) putative inhibitory interneurons exhibit both E-SFA and I-SFA. Developing a data-driven hybrid circuit model comprising NS model neurons receiving BS input reveals that NS model neurons exhibit longer SFA than observed in vivo; however, adding feedforward inhibition corrects this in a manner dependent on I-SFA. Identification of this circuit motif shaping E-SFA in LPFC highlights the roles of both intrinsic and network mechanisms in neural activity underlying behavior

Pediatric supracondylar fractures of the distal humerus

Supracondylar fractures of the humerus are a common pediatric elbow injury that are historically associated with morbidity due to malunion, neurovascular complications, and compartment syndrome. True anteroposterior and lateral radiographs are essential not only for an accurate diagnosis, but also for creating a treatment plan for these injuries. A staging system (based on the lateral radiograph) for classifying the severity of the fracture helps guide definitive management. Nondisplaced fractures are treated initially with a posterior splint, followed by a long-arm casting. Closed reduction and percutaneous pinning is the preferred treatment for displaced or unstable fractures. If there is any question about fracture stability, patients should be seen within 5 days postoperatively for repeat radiographs to ensure that the reduction and pin fixation has been maintained. Understanding the anatomy, radiographic findings, management options, and complications associated with this fracture allow physicians to limit the morbidity associated with this relatively common pediatric injury

Identification of a small molecule yeast TORC1 inhibitor with a flow cytometry-based multiplex screen

TOR (target of rapamycin) is a serine/threonine kinase, evolutionarily conserved from yeast to human, which functions as a fundamental controller of cell growth. The moderate clinical benefit of rapamycin in mTOR-based therapy of many cancers favors the development of new TOR inhibitors. Here we report a high throughput flow cytometry multiplexed screen using five GFPtagged yeast clones that represent the readouts of four branches of the TORC1 signaling pathway in budding yeast. Each GFP-tagged clone was differentially color-coded and the GFP signal of each clone was measured simultaneously by flow cytometry, which allows rapid prioritization of compounds that likely act through direct modulation of TORC1 or proximal signaling components. A total of 255 compounds were confirmed in dose-response analysis to alter GFP expression in one or more clones. To validate the concept of the high throughput screen, we have characterized CID 3528206, a small molecule most likely to act on TORC1 as it alters GFP expression in all five GFP clones in an analogous manner to rapamycin. We have shown that CID 3528206 inhibited yeast cell growth, and that CID 3528206 inhibited TORC1 activity both in vitro and in vivo with EC50s of 150 nM and 3.9 μM, respectively. The results of microarray analysis and yeast GFP collection screen further support the notion that CID 3528206 and rapamycin modulate similar cellular pathways. Together, these results indicate that the HTS has identified a potentially useful small molecule for further development of TOR inhibitors

Remission of Behcet's disease with anti-tumor necrosis factor monoclonal antibody therapy: a case report

BACKGROUND: Behcet's disease (BD) is a chronic relapsing multisystem inflammatory disorder with mucocutaneous, ocular, articular, vascular, gastrointestinal and central nervous system manifestations. Tumor necrosis factor (TNF)-alpha is believed to play a pivotal role in BD. Therapeutic blockade of the activity of TNF has been successfully given in a short course of therapy with favorable effects in patients with BD refractory to conventional immunosuppressive drugs. We aimed to find out whether a 12-month treatment with infliximab, a chimeric monoclonal antibody to TNF-alpha, had any beneficial effect in reducing relapses of a patient with long-standing BD refractory to conventional immunosuppressive drugs. CASE PRESENTATION: A 54 year-old-woman with a 35-year history of BD with orogenital ulcerations, arthritis in the right knee and retinal lesions compatible with vasculitis received infliximab, 5 mg/kg by a two-hour intravenous infusion. Symptoms improved within 24 hours and eight days later the genital and oral ulcers healed as well as the arthritis in the right knee subsided. The retinal infiltrates completely resolved within 10 days. The infusions were repeated at weeks 2, 6, 14, 22 and then every 8 weeks. The patient was able to return to her domestic daily life. No exacerbation of the mucocutaneous ocular or arthritic symptoms occurred during the treatment period. CONCLUSIONS: Previous studies have suggested that infliximab given in a short course of treatment is effective in inducing remission of severe mucocutaneous, gastrointestinal and ocular manifestations of BD. Our patient received a 12-month infliximab treatment showing a favorable effect on remission of BD manifestations. The long-term infliximab treatment appears as a new therapeutic option for patients with active BD who failed to respond to conventional immunosuppressive agents

Coexpression of epidermal growth factor receptor with related factors is associated with a poor prognosis in non-small-cell lung cancer

The epidermal growth factor receptor (EGFR) is commonly expressed in non-small-cell lung cancer (NSCLC) and promotes a host of mechanisms involved in tumorigenesis. However, EGFR expression does not reliably predict prognosis or response to EGFR-targeted therapies. The data from two previous studies of a series of 181 consecutive surgically resected stage I-IIIA NSCLC patients who had survived in excess of 60 days were explored. Of these patients, tissue was available for evaluation of EGFR in 179 patients, carbonic anhydrase (CA) IX in 177 patients and matrix metalloproteinase-9 (MMP-9) in 169 patients. We have previously reported an association between EGFR expression and MMP-9 expression. We have also reported that MMP-9 (P=0.001) and perinuclear (p)CA IX (P=0.03) but not EGFR expression were associated with a poor prognosis. Perinuclear CA IX expression was also associated with EGFR expression (P<0.001). Multivariate analysis demonstrated that coexpression of MMP-9 with EGFR conferred a worse prognosis than the expression of MMP-9 alone (P<0.001) and coexpression of EGFR and pCA IX conferred a worse prognosis than pCA IX alone (P=0.05). A model was then developed where the study population was divided into three groups: group 1 had expression of EGFR without coexpression of MMP-9 or pCA IX (number=21); group 2 had no expression of EGFR (number=75); and group 3 had coexpression of EGFR with pCA IX or MMP-9 or both (number=70). Group 3 had a worse prognosis than either groups 1 or 2 (P=0.0003 and 0.027, respectively) and group 1 had a better prognosis than group 2 (P=0.036). These data identify two cohorts of EGFR-positive patients with diametrically opposite prognoses. The group expressing either EGFR and or both MMP-9 and pCA IX may identify a group of patients with activated EGFR, which is of clinical relevance with the advent of EGFR-targeted therapies. © 2004 Cancer Research UK

BMJ Open

INTRODUCTION: Worldwide, 2 million patients aged 18-50 years suffer a stroke each year, and this number is increasing. Knowledge about global distribution of risk factors and aetiologies, and information about prognosis and optimal secondary prevention in young stroke patients are limited. This limits evidence-based treatment and hampers the provision of appropriate information regarding the causes of stroke, risk factors and prognosis of young stroke patients. METHODS AND ANALYSIS: The Global Outcome Assessment Life-long after stroke in young adults (GOAL) initiative aims to perform a global individual patient data meta-analysis with existing data from young stroke cohorts worldwide. All patients aged 18-50 years with ischaemic stroke or intracerebral haemorrhage will be included. Outcomes will be the distribution of stroke aetiology and (vascular) risk factors, functional outcome after stroke, risk of recurrent vascular events and death and finally the use of secondary prevention. Subgroup analyses will be made based on age, gender, aetiology, ethnicity and climate of residence. ETHICS AND DISSEMINATION: Ethical approval for the GOAL study has already been obtained from the Medical Review Ethics Committee region Arnhem-Nijmegen. Additionally and when necessary, approval will also be obtained from national or local institutional review boards in the participating centres. When needed, a standardised data transfer agreement will be provided for participating centres. We plan dissemination of our results in peer-reviewed international scientific journals and through conference presentations. We expect that the results of this unique study will lead to better understanding of worldwide differences in risk factors, causes and outcome of young stroke patients

Multisite Phosphorylation of the Guanine Nucleotide Exchange Factor Cdc24 during Yeast Cell Polarization

BACKGROUND:Cell polarization is essential for processes such as cell migration and asymmetric cell division. A common regulator of cell polarization in most eukaryotic cells is the conserved Rho GTPase, Cdc42. In budding yeast, Cdc42 is activated by a single guanine nucleotide exchange factor, Cdc24. The mechanistic details of Cdc24 activation at the onset of yeast cell polarization are unclear. Previous studies have suggested an important role for phosphorylation of Cdc24, which may regulate activity or function of the protein, representing a key step in the symmetry breaking process. METHODOLOGY/PRINCIPAL FINDINGS:Here, we directly ask whether multisite phosphorylation of Cdc24 plays a role in its regulation. We identify through mass spectrometry analysis over thirty putative in vivo phosphorylation sites. We first focus on sites matching consensus sequences for cyclin-dependent and p21-activated kinases, two kinase families that have been previously shown to phosphorylate Cdc24. Through site-directed mutagenesis, yeast genetics, and light and fluorescence microscopy, we show that nonphosphorylatable mutations of these consensus sites do not lead to any detectable consequences on growth rate, morphology, kinetics of polarization, or localization of the mutant protein. We do, however, observe a change in the mobility shift of mutant Cdc24 proteins on SDS-PAGE, suggesting that we have indeed perturbed its phosphorylation. Finally, we show that mutation of all identified phosphorylation sites does not cause observable defects in growth rate or morphology. CONCLUSIONS/SIGNIFICANCE:We conclude that lack of phosphorylation on Cdc24 has no overt functional consequences in budding yeast. Yeast cell polarization may be more tightly regulated by inactivation of Cdc42 by GTPase activating proteins or by alternative methods of Cdc24 regulation, such as conformational changes or oligomerization