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 Vam6 GEF controls TORC1 by activating the EGO complex

The target of rapamycin complex 1 (TORC1) is a central regulator of eukaryotic cell growth that is activated by a variety of hormones (e.g., insulin) and nutrients (e.g., amino acids) and is deregulated in various cancers. Here, we report that the yeast Rag GTPase homolog Gtr1, a component of the vacuolar-membrane-associated EGO complex (EGOC), interacts with and activates TORC1 in an amino-acid-sensitive manner. Expression of a constitutively active (GTP-bound) Gtr1GTP, which interacted strongly with TORC1, rendered TORC1 partially resistant to leucine deprivation, whereas expression of a growth inhibitory, GDP-bound Gtr1GDP, caused constitutively low TORC1 activity. We also show that the nucleotide-binding status of Gtr1 is regulated by the conserved guanine nucleotide exchange factor (GEF) Vam6. Thus, in addition to its regulatory role in homotypic vacuolar fusion and vacuole protein sorting within the HOPS complex, Vam6 also controls TORC1 function by activating the Gtr1 subunit of the EGO complex

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

Global Outcome Assessment Life-long after stroke in young adults initiative-the GOAL initiative : study protocol and rationale of a multicentre retrospective individual patient data meta-analysis

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.Peer reviewe

Sex differences in cerebral venous sinus thrombosis after adenoviral vaccination against COVID-19

Introduction: Cerebral venous sinus thrombosis associated with vaccine-induced immune thrombotic thrombocytopenia (CVST-VITT) is a severe disease with high mortality. There are few data on sex differences in CVST-VITT. The aim of our study was to investigate the differences in presentation, treatment, clinical course, complications, and outcome of CVST-VITT between women and men. Patients and methods: We used data from an ongoing international registry on CVST-VITT. VITT was diagnosed according to the Pavord criteria. We compared the characteristics of CVST-VITT in women and men. Results: Of 133 patients with possible, probable, or definite CVST-VITT, 102 (77%) were women. Women were slightly younger [median age 42 (IQR 28–54) vs 45 (28–56)], presented more often with coma (26% vs 10%) and had a lower platelet count at presentation [median (IQR) 50x109/L (28–79) vs 68 (30–125)] than men. The nadir platelet count was lower in women [median (IQR) 34 (19–62) vs 53 (20–92)]. More women received endovascular treatment than men (15% vs 6%). Rates of treatment with intravenous immunoglobulins were similar (63% vs 66%), as were new venous thromboembolic events (14% vs 14%) and major bleeding complications (30% vs 20%). Rates of good functional outcome (modified Rankin Scale 0-2, 42% vs 45%) and in-hospital death (39% vs 41%) did not differ. Discussion and conclusions: Three quarters of CVST-VITT patients in this study were women. Women were more severely affected at presentation, but clinical course and outcome did not differ between women and men. VITT-specific treatments were overall similar, but more women received endovascular treatment.</p

Sex differences in cerebral venous sinus thrombosis after adenoviral vaccination against COVID-19

Introduction: Cerebral venous sinus thrombosis associated with vaccine-induced immune thrombotic thrombocytopenia (CVST-VITT) is a severe disease with high mortality. There are few data on sex differences in CVST-VITT. The aim of our study was to investigate the differences in presentation, treatment, clinical course, complications, and outcome of CVST-VITT between women and men. Patients and methods: We used data from an ongoing international registry on CVST-VITT. VITT was diagnosed according to the Pavord criteria. We compared the characteristics of CVST-VITT in women and men. Results: Of 133 patients with possible, probable, or definite CVST-VITT, 102 (77%) were women. Women were slightly younger [median age 42 (IQR 28–54) vs 45 (28–56)], presented more often with coma (26% vs 10%) and had a lower platelet count at presentation [median (IQR) 50x109/L (28–79) vs 68 (30–125)] than men. The nadir platelet count was lower in women [median (IQR) 34 (19–62) vs 53 (20–92)]. More women received endovascular treatment than men (15% vs 6%). Rates of treatment with intravenous immunoglobulins were similar (63% vs 66%), as were new venous thromboembolic events (14% vs 14%) and major bleeding complications (30% vs 20%). Rates of good functional outcome (modified Rankin Scale 0-2, 42% vs 45%) and in-hospital death (39% vs 41%) did not differ. Discussion and conclusions: Three quarters of CVST-VITT patients in this study were women. Women were more severely affected at presentation, but clinical course and outcome did not differ between women and men. VITT-specific treatments were overall similar, but more women received endovascular treatment.</p

Cerebral venous sinus thrombosis due to vaccine-induced immune thrombotic thrombocytopenia in middle-income countries

Background: Adenovirus-based COVID-19 vaccines are extensively used in low- and middle-income countries (LMICs). Remarkably, cases of cerebral venous sinus thrombosis due to vaccine-induced immune thrombotic thrombocytopenia (CVST-VITT) have rarely been reported from LMICs. Aims: We studied the frequency, manifestations, treatment, and outcomes of CVST-VITT in LMICs. Methods: We report data from an international registry on CVST after COVID-19 vaccination. VITT was classified according to the Pavord criteria. We compared CVST-VITT cases from LMICs to cases from high-income countries (HICs). Results: Until August 2022, 228 CVST cases were reported, of which 63 were from LMICs (all middle-income countries [MICs]: Brazil, China, India, Iran, Mexico, Pakistan, Turkey). Of these 63, 32 (51%) met the VITT criteria, compared to 103 of 165 (62%) from HICs. Only 5 of the 32 (16%) CVST-VITT cases from MICs had definite VITT, mostly because anti-platelet factor 4 antibodies were often not tested. The median age was 26 (interquartile range [IQR] 20–37) versus 47 (IQR 32–58) years, and the proportion of women was 25 of 32 (78%) versus 77 of 103 (75%) in MICs versus HICs, respectively. Patients from MICs were diagnosed later than patients from HICs (1/32 [3%] vs. 65/103 [63%] diagnosed before May 2021). Clinical manifestations, including intracranial hemorrhage, were largely similar as was intravenous immunoglobulin use. In-hospital mortality was lower in MICs (7/31 [23%, 95% confidence interval (CI) 11–40]) than in HICs (44/102 [43%, 95% CI 34–53], p = 0.039). Conclusions: The number of CVST-VITT cases reported from LMICs was small despite the widespread use of adenoviral vaccines. Clinical manifestations and treatment of CVST-VITT cases were largely similar in MICs and HICs, while mortality was lower in patients from MICs.</p

An acetylated form of histone H2A.Z regulates chromosome architecture in Schizosaccharomyces pombe

Histone variant H2A.Z has a conserved role in genome stability, although it remains unclear how this is mediated. Here we demonstrate that the fission yeast Swr1 ATPase inserts H2A.Z (Pht1) into chromatin and Kat5 acetyltransferase (Mst1) acetylates it. Deletion or an unacetylatable mutation of Pht1 leads to genome instability, primarily caused by chromosome entanglement and breakage at anaphase. This leads to the loss of telomere-proximal markers, though telomere protection and repeat length are unaffected by the absence of Pht1. Strikingly, the chromosome entanglement in pht1Delta anaphase cells can be rescued by forcing chromosome condensation before anaphase onset. We show that the condensin complex, required for the maintenance of anaphase chromosome condensation, prematurely dissociates from chromatin in the absence of Pht1. This and other findings suggest an important role for H2A.Z in the architecture of anaphase chromosomes

Effects of fluoxetine on functional outcomes after acute stroke (FOCUS): a pragmatic, double-blind, randomised, controlled trial

Background Results of small trials indicate that fluoxetine might improve functional outcomes after stroke. The FOCUS trial aimed to provide a precise estimate of these effects. Methods FOCUS was a pragmatic, multicentre, parallel group, double-blind, randomised, placebo-controlled trial done at 103 hospitals in the UK. Patients were eligible if they were aged 18 years or older, had a clinical stroke diagnosis, were enrolled and randomly assigned between 2 days and 15 days after onset, and had focal neurological deficits. Patients were randomly allocated fluoxetine 20 mg or matching placebo orally once daily for 6 months via a web-based system by use of a minimisation algorithm. The primary outcome was functional status, measured with the modified Rankin Scale (mRS), at 6 months. Patients, carers, health-care staff, and the trial team were masked to treatment allocation. Functional status was assessed at 6 months and 12 months after randomisation. Patients were analysed according to their treatment allocation. This trial is registered with the ISRCTN registry, number ISRCTN83290762. Findings Between Sept 10, 2012, and March 31, 2017, 3127 patients were recruited. 1564 patients were allocated fluoxetine and 1563 allocated placebo. mRS data at 6 months were available for 1553 (99·3%) patients in each treatment group. The distribution across mRS categories at 6 months was similar in the fluoxetine and placebo groups (common odds ratio adjusted for minimisation variables 0·951 [95% CI 0·839–1·079]; p=0·439). Patients allocated fluoxetine were less likely than those allocated placebo to develop new depression by 6 months (210 [13·43%] patients vs 269 [17·21%]; difference 3·78% [95% CI 1·26–6·30]; p=0·0033), but they had more bone fractures (45 [2·88%] vs 23 [1·47%]; difference 1·41% [95% CI 0·38–2·43]; p=0·0070). There were no significant differences in any other event at 6 or 12 months. Interpretation Fluoxetine 20 mg given daily for 6 months after acute stroke does not seem to improve functional outcomes. Although the treatment reduced the occurrence of depression, it increased the frequency of bone fractures. These results do not support the routine use of fluoxetine either for the prevention of post-stroke depression or to promote recovery of function. Funding UK Stroke Association and NIHR Health Technology Assessment Programme

Optimalisering av primtallsgenerering, og generering av primtallsørkener over 64 bit

Denne masteroppgaven baserer seg på teori fra allerede kjente algoritmer, samt noen nye algoritmer for å finne primtall og primtallsørkener. En primtallsørken er avstanden fra et primtall til neste påfølgende primtall. For å finne store primtallsørkener vil oppgaven se på primtallsørkener for primtall over 64 bit. I oppgaven er det benyttet kjente metoder for å finne primtall, slik som Eratosthenes sil, Sundarams sil, divisjonsmetoden, Mersenne primtall og ”Miller Rabin primality test”. For å finne primtallsørkener kreves minst 2 primtall i serie. Av de nevnte metodene, er det Eratosthenes sil, Sundarams sil og divisjonsmetoden som innfrir dette kriteriet. Oppgaven baserer seg mest på Eratosthenes sil, Sundarams sil og divisjonsmetoden, og ser på tidsforbruket til de ulike metodene til å finne primtall. Primtallene som jeg finner blir deretter brukt for å finne primtallsørkener. For å representere heltall over 64 bit, trengs det en datastruktur for dette. I denne oppgaven er det laget en datastruktur som kan utføre de nødvendigste regneoperasjonene for å finne primtall over 64 bit. I tillegg har det vært en oppgave å se på mulige metoder for å lagre mange primtall. Ved å se på tidsforbruket til de ulike algoritmene for å finne primtall, samt modifikasjoner av de, konkluderer oppgaven med hvilke metoder som er raskest for å finne primtall. Videre ser oppgaven på ulike metoder for å finne store primtallsørkener. En metode for å finne primtallsørkener er å finne alle primtallene i et gitt intervall. Dette kan gjøres ved hjelp av divisjonsmetoden for å finne primtallene, for å deretter se på avstanden mellom primtallene. Oppgaven tar også for seg en annen metode, der en kun finner de nødvendigste primtallene for å finne primtallsørkener ved hjelp av avstandshopp. Til slutt i oppgaven vil jeg komme inn på en løsning med å finne primtallsørkener basert på å finne alle primtallene i et intervall med glidende Eratosthenes sil. I oppgaven vil jeg sammenligne de ulike alternativene for å finne primtallsørkener og konkludere med glidende Eratosthenes sil som den raskeste metoden for å finne primtall over 64 bit, og store primtallsørkener bestående av primtall større enn 64 bit. Glidende Eratosthenes sil fant primtallsørkener med primtall over 64 bit raskt. En primtallsørken med lengde 834 som startet på primtallet 18 446 744 081 169 869 483 ble funnet på kun 2,3 minutter. Etter 14 timer og 26,1 minutter ble det funnet primtallsørken større enn 1000, i dette tilfellet 1062 som er etterfulgt av primtallet 18 446 747 749 629 047 369. Ved å se på primtallsørkener bestående av primtall større enn 70 bit, ble det funnet flere store primtallsørkener raskere. Etter 2 timer og 35,2 minutter ble det funnet to primtallsørkener over 1000. Den største primtallsørkenen som ble funnet har lengde 1134, som begynner på primtallet 1 180 591 621 421 105 449 327. Denne ble funnet etter 9 timer og 11,5 minutter