Laraaji is a musician, mystic and laughter meditation practitioner based in New York City. He began playing music on the streets in the 1970s, improvising trance-inducing jams on a modified autoharp processed through various electronic effects. Brian Eno saw him playing one night in Washington Square Park and invited him to record an album for his seminal Ambient series (Ambient 3: Day Of Radiance, released 1980). Laraaji went on to release a prolific series of albums for a wide variety of labels, many of which he recorded himself at home and sold as cassettes during his street performances. In recent years he has had his career celebrated extensively, with two All Saints/Warp retrospectives Celestial Music 1970–2011 and Two Sides of Laraaji – as well as reissues on Glitterbeat and Leaving Records/Stone Throw. He has also collaborated with a new generation of underground musicians such as Sun Araw, their new LP Professional Sunflow (Superior Viaduct) being the fruit of the live shows they played together in 2014. In September 2017 All Saints release a stunning pair of LPs of new studio recordings by the celestial music pioneer. Bring On The Sun is an epic double album that runs the full gamut of 'Laraaji music', from blissed-out percussive jams to reflective vocal hymnals to trance-inducing drones. A perfect Laraaji entry-point on his never-ending creative journey through inner light. The record is recorded by Davey Jewell (Peaking Lights/Flaming Lips) and mixed by Carlos Niño (Leaving Records). Sun Gong is a major new self-contained work experimenting with gong micro-tonalties processed through various electronic effects. The results are unlike any music he has made before – two side-long long-form pieces that evoke the sound of a shimmering metallic eternal wave.


The 145 rooms and suites at the Naoura Barriere are spacious and have modern facilities including free Wi-Fi, flat-screen TVs, bathrobes, DVD players and a private balcony or terrace boasting views to the pool, the Palm trees in the gardens or across the city to the Koutoubia Mosque.
There is a refined restaurant offering quality local cuisine using fresh market produce, a sports bar and a cocktail lounge. Other amenities include a large heated outdoor pool and a luxury spa offering a full range of treatments, two Moroccan Hammams and a fitness centre.
This luxury hotel, run by the exclusive Lucien Barriere Group, is the perfect destination for a refined holiday in the centre of the city, yet is a peaceful oasis away from the hustle and bustle of Marrakech.
There are more than a dozen golf courses around the city, each a little different from the others, so we can create a diverse golf itinerary to complement your holiday.


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A mum graduating from college said thank you with a breastfeeding photo
Jacci Sharkey at her graduation ceremony.
Image: USC / Facebook
By Jenni Ryall 2014-11-07 14:15:43 UTC
A photo of a student breastfeeding her child at her graduation ceremony has received resounding praise on Facebook.
Queensland mother Jacci Sharkey sent the photo to the University of the Sunshine Coast (USC) in early October, thanking the university for letting her complete her degree while giving birth to two babies, Ari and Alek (20 months old and 6 weeks old in the photo, respectively).
See also: Artist imagines life as her mother's best friend in beautiful photo series
The photo was snapped by her sister-in-law and shows the proud mum in her university robe feeding Alek.
"Just wanted to share a photo from the most recent graduation that I am proud of. I'm extremely proud that with the support of the Uni, during my degree I was able to have 2 babies and still finish my degree. Thanks USC!" 24-year-old Sharkey wrote, with the hashtag #itcanbedone.
Post by University of the Sunshine Coast.
The photo had received almost 300,000 Likes and nearly 10,000 shares at the time of writing. Sharkey's dedication to her family and studies was praised by commenters, a refreshing change of pace from most Internet comments.
"I can barely look after myself while studying... I couldn't imagine trying to do it while having two kids. Well done Jacci Sharkey," one commenter, who went by Danny Dan, wrote.
Another commenter, Nathan Czislowski, wrote: "The photo couldn't have made a better statement about supporting mothers and families reach their goals as well as setting a standard for the uni being supportive of real world commitments."
Not all comments were praiseworthy, however; those who denounce public breastfeeding were quick to jump on the bandwagon. But the majority of commenters saw past the hate and thanked the university for sharing the message.
"Beautiful photo, and well done to the University of the Sunshine Coast for supporting this student and sharing this image as, evidently, there's still a lot of immature people who need to be exposed to images... to be made aware of the realities of life," commenter Nikki Burrows wrote on the post.
Sharkey told the ABC she didn't expect the post to get so much attention, but was glad to show other mothers it was possible to get out of the house and achieve personal goals.
"I never expected it to go crazy. I thought I'd be really happy if it got 100 likes and then it's just gone out of control," she said. "There has been a sea of thank you messages from people. Some were saying they were really worried about starting university but that I've helped them through it."
She said the photo wasn't meant to be a statement on breastfeeding, and it was simply a thank you message to her university for allowing her to complete her degree.
"It was really a message of thanks and that other mums can do it as well. You don't have to give up the career to have kids and you don't have to give up kids to have the career ... you can have it all," she said.
Topics: Australia, Graduation, World

redpajama_set_name: RedPajamaCommonCrawl


Directions: Entering from Peking University's East Gate and take a right at the first intersection. Take the next right and then the next left. Go past the sports fields and see the traditionally styled Lee Shao Kee Humanities buildings on the left. Keep straight and Building 4 will be the second large building on the right.


Verein für Bewegungsspiele Stuttgart 1893 e. V., commonly known as VfB Stuttgart (German pronunciation: [faʊ̯ ʔɛf beː ˈʃtʊtɡaʁt]), is a German sports club based in Stuttgart, Baden-Württemberg. The club is best known for its football team which is part of Germany's first division Bundesliga, missing only two seasons of play since the top tier of the German football league system was established in 1963. VfB Stuttgart has won the national championship five times, most recently in 2006–07; the DFB-Pokal three times; and the UEFA Intertoto Cup a record three times. The football team plays its home games at the Mercedes-Benz Arena, in the Neckarpark which is located near the Cannstatter Wasen where the city's Oktoberfest celebration takes place. Second team side VfB Stuttgart II currently plays in the 3. Liga, which is the highest division allowed for a reserve team. The club's junior teams have won the national U19 championships a record ten times and the Under 17 Bundesliga six times. A membership-based club with 45,636 members (as of September 2011), VfB is the largest sports club in Baden-Württemberg and the fifth-largest in Germany. It has departments for fistball, hockey, track and field, table-tennis and football referees, all of which compete only at the amateur level. The club also maintains a social department, the VfB-Garde.
Description above from the Wikipedia article VfB Stuttgart, licenced under CC-BY-SA, full list of contributors on Wikipedia.


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Professor of Mathematical Biosciences Robert Beardmore
EPSRC Healthcare Technology Impact Fellow
Living Systems Institute T05.13
Living Systems Institute, University of Exeter, Stocker Road, Exeter, EX4 4QD
1998 SIAM Student Prize, presented Toronto 1999
2012 Lee Segel Prize (shared), presented Arizona 2013
EPSRC Leadership Fellow, 2010-2015
EPSRC Healthcare Technology Impact Fellow, 2016-2018
BSc (1st Class) Edinburgh University 1990-1994
MSc Nonlinear Mathematics, Bath University 1994-1995
PhD Engineering Mathematics, Bath University 1997-2000
Defence-related Project Engineer (satellite imaging), SEA Ltd, Beckington Castle, Frome, 1995-1996
Lecturer in Mathematics, Imperial College London, 2000-2005
Senior Lecturer in Mathematics, Imperial College London, 2005-2008
Reader in Mathematics, Imperial College London, 2008-2010
Professor Mathematical Biosciences, EPSRC Leadership Research Fellow 2010
EPSRC Healthcare Technology Impact Fellow 2016-2018
Microbes and Disease
Mathematical modelling of evolutionary datasets, particularly relating to antibiotic resistance
Mathematical analysis of differential-algebraic equations
Applications of mathematical analysis/computation to evolutionary biology and physics
Applying fluids DFT to understand the action and dose-dependence of antimicrobial peptides (with Laurie Frink)
Understanding complete viral (phage) resistance in E.coli (with Justin Meyer)
Using optimisation theory as a basis to model optimal antibiotic use (with Hinrich Schulenberg)
EPSRC-funded Mathematical Models and Experimental Microbial Systems (www.mmems.org)
2012 EPSRC
Developing Leaders award (value £315,000)
Creativity @ Home award (value £20,000)
Leadership Fellowship on the application of mathematical modelling to the study of antibiotic resistance evolution (value £1,139,110)
Cross-Disciplinary Enhancement to Leadership Fellowship: funding to take theoretical research into the lab (value £100,000)
2009 MRC
Discipline Hopping Fellowship: Applications of Control Theory to Optimal Antibiotic Deployment (value £110,000)
Funded Two PDRAs on the Invariant Manifolds of Differential-Algebraic Equations (value £123,000)
EPSRC-funded network: Mathematics and Microbes
Fuentes-Hernandez A, Plucain J, Gori F, Pena-Miller R, Reding C, Jansen G, Schulenburg H, Gudelj I, Beardmore R (2015). Using a sequential regimen to eliminate bacteria at sublethal antibiotic dosages. PLoS Biol, 13(4).
Using a sequential regimen to eliminate bacteria at sublethal antibiotic dosages.
We need to find ways of enhancing the potency of existing antibiotics, and, with this in mind, we begin with an unusual question: how low can antibiotic dosages be and yet bacterial clearance still be observed? Seeking to optimise the simultaneous use of two antibiotics, we use the minimal dose at which clearance is observed in an in vitro experimental model of antibiotic treatment as a criterion to distinguish the best and worst treatments of a bacterium, Escherichia coli. Our aim is to compare a combination treatment consisting of two synergistic antibiotics to so-called sequential treatments in which the choice of antibiotic to administer can change with each round of treatment. Using mathematical predictions validated by the E. coli treatment model, we show that clearance of the bacterium can be achieved using sequential treatments at antibiotic dosages so low that the equivalent two-drug combination treatments are ineffective. Seeking to treat the bacterium in testing circumstances, we purposefully study an E. coli strain that has a multidrug pump encoded in its chromosome that effluxes both antibiotics. Genomic amplifications that increase the number of pumps expressed per cell can cause the failure of high-dose combination treatments, yet, as we show, sequentially treated populations can still collapse. However, dual resistance due to the pump means that the antibiotics must be carefully deployed and not all sublethal sequential treatments succeed. A screen of 136 96-h-long sequential treatments determined five of these that could clear the bacterium at sublethal dosages in all replicate populations, even though none had done so by 24 h. These successes can be attributed to a collateral sensitivity whereby cross-resistance due to the duplicated pump proves insufficient to stop a reduction in E. coli growth rate following drug exchanges, a reduction that proves large enough for appropriately chosen drug switches to clear the bacterium.
Beardmore RE, Pena-Miller R, Laehnemann D, Jansen G, Fuentes-Hernandez A, Rosenstiel P, Schulenburg H (2013). When the most potent combination of antibiotics selects for the greatest bacterial load: the Smile-Frown transition. PLoS Biology, 11(4), 1-13. Full text.
Peña-Miller R, Lähnemann D, Schulenburg H, Ackermann M, Beardmore R (2012). Selecting against antibiotic-resistant pathogens: optimal treatments in the presence of commensal bacteria. Bull Math Biol, 74(4), 908-934.
Selecting against antibiotic-resistant pathogens: optimal treatments in the presence of commensal bacteria.
Using optimal control theory as the basic theoretical tool, we investigate the efficacy of different antibiotic treatment protocols in the most exacting of circumstances, described as follows. Viewing a continuous culture device as a proxy for a much more complex host organism, we first inoculate the device with a single bacterial species and deem this the 'commensal' bacterium of our host. We then force the commensal to compete for a single carbon source with a rapidly evolving and fitter 'pathogenic bacterium', the latter so-named because we wish to use a bacteriostatic antibiotic to drive the pathogen toward low population densities. Constructing a mathematical model to mimic the biology, we do so in such a way that the commensal would be eventually excluded by the pathogen if no antibiotic treatment were given to the host or if the antibiotic were over-deployed. Indeed, in our model, all fixed-dose antibiotic treatment regimens will lead to the eventual loss of the commensal from the host proxy. Despite the obvious gravity of the situation for the commensal bacterium, we show by example that it is possible to design drug deployment protocols that support the commensal and reduce the pathogen load. This may be achieved by appropriately fluctuating the concentration of drug in the environment; a result that is to be anticipated from the theory optimal control where bang-bang solutions may be interpreted as intermittent periods of either maximal and minimal drug deployment. While such 'antibiotic pulsing' is near-optimal for a wide range of treatment objectives, we also use this model to evaluate the efficacy of different antibiotic usage strategies to show that dynamically changing antimicrobial therapies may be effective in clearing a bacterial infection even when every 'static monotherapy' fails.
Peña-Miller R, Lähnemann D, Schulenburg H, Ackermann M, Beardmore R (2012). The optimal deployment of synergistic antibiotics: a control-theoretic approach. J R Soc Interface, 9(75), 2488-2502.
The optimal deployment of synergistic antibiotics: a control-theoretic approach.
Medical and pharmacological communities have long searched for antimicrobial drugs that increase their effect when used in combination, an interaction known as synergism. These drug combinations, however, impose selective pressures in favour of multi-drug resistance and as a result, the benefit of synergy may be lost after only a few bacterial generations. Furthermore, there is experimental evidence that antibiotic treatment can disrupt colonization resistance by shifting the balance between enteropathogenic and commensal bacteria in favour of the pathogens, with the potential to increase the risk of infections. So, we ask, what is the best way of using synergistic drugs? We pose an evolutionary model of commensal and pathogenic bacteria competing in a continuous culture device for a single limiting carbon source under the effect of two bacteriostatic and synergistic antibiotics. This model allows us to evaluate the efficacy of different drug deployment strategies and, using ideas from optimal control theory, to understand whether there are circumstances in which other types of therapy might be favoured over those based on fixed-dose multi-drug combinations. Our main result can be stated thus: the optimal deployment of synergistic antibiotics to remove a pathogen in the presence of commensal bacteria in our model system occurs not in combination, but by deploying them sequentially.
Beardmore RE, Gudelj I, Lipson DA, Hurst LD (2011). Metabolic trade-offs and the maintenance of the fittest and the flattest. Nature, 472(7343), 342-346.
Metabolic trade-offs and the maintenance of the fittest and the flattest.
How is diversity maintained? Environmental heterogeneity is considered to be important, yet diversity in seemingly homogeneous environments is nonetheless observed. This, it is assumed, must either be owing to weak selection, mutational input or a fitness advantage to genotypes when rare. Here we demonstrate the possibility of a new general mechanism of stable diversity maintenance, one that stems from metabolic and physiological trade-offs. The model requires that such trade-offs translate into a fitness landscape in which the most fit has unfit near-mutational neighbours, and a lower fitness peak also exists that is more mutationally robust. The 'survival of the fittest' applies at low mutation rates, giving way to 'survival of the flattest' at high mutation rates. However, as a consequence of quasispecies-level negative frequency-dependent selection and differences in mutational robustness we observe a transition zone in which both fittest and flattest coexist. Although diversity maintenance is possible for simple organisms in simple environments, the more trade-offs there are, the wider the maintenance zone becomes. The principle may be applied to lineages within a species or species within a community, potentially explaining why competitive exclusion need not be observed in homogeneous environments. This principle predicts the enigmatic richness of metabolic strategies in clonal bacteria and questions the safety of lethal mutagenesis as an antimicrobial treatment.
Beardmore R, Webster K (2008). Normal forms, quasi-invariant manifolds, and bifurcations of nonlinear difference-algebraic equations. SIAM Journal on Mathematical Analysis, 40(1), 413-441.
Normal forms, quasi-invariant manifolds, and bifurcations of nonlinear difference-algebraic equations
We study the existence of quasi-invariant manifolds in a neighborhood of a fixed point of the difference-algebraic equation (ΔAE) F(zn, zn+1) = 0, where F : &Rdbl;2m → ℝm is a smooth map satisfying F(0, 0) = 0. We demonstrate the existence of quasi-invariant manifolds on which one can define forward and backward orbits of the ΔAE under mild assumptions on its linearization at the fixed point Z = 0. Indeed, by assuming this linearization to be a regular matrix pencil, one obtains a functional equation satisfied by invariant manifolds which can be solved using an extension of the contraction mapping to spaces that satisfy an interpolation property. If the ΔAE under study is permitted to depend smoothly on a parameter, we then obtain a Neimark-Sacker bifurcation theorem as a corollary that can be deduced from the existence of a normal form for nonlinear ΔAEs. © 2008 Society for Industrial and Applied Mathematics.
Reding C, Hewlett M, Bergmiller T, Gudelj I, Beardmore R (In Press). Fluorescence photography of patterns and waves of bacterial adaptation at high antibiotic doses.
Fluorescence photography of patterns and waves of bacterial adaptation at high antibiotic doses
Fisher suggested advantageous genes would spread through populations as a wave so we sought genetic waves in evolving populations, as follows. By fusing a fluorescent marker to a drug efflux protein (AcrB) whose expression provides Escherichia coli with resistance to some antibiotics, we quantified the evolution and spread of drug-resistant E. coli through spacetime using image analysis and quantitative PCR. As is done in hospitals routinely, we exposed the bacterium to a gradient of antibiotic in a 'disk diffusion' drug susceptibility test that we videoed. The videos show complex spatio-genomic patterns redolent of, yet more complex than, Fisher's predictions whereby a decelerating wave front of advantageous genes colonises towards the antibiotic source, forming bullseye patterns en route and leaving a wave back of bacterial sub-populations expressing AcrB at decreasing levels away from the drug source. qPCR data show that E. coli sited at rapidly-adapting spatial hotspots gain 2 additional copies of acr, the operon that encodes AcrB, within 24h and imaging data show resistant sub-populations thrive most near the antibiotic source due to non-monotone relationships between inhibition due to antibiotic and distance from the source. In the spirit of Fisher, we provide an explicitly spatial nonlinear diffusion equation that exhibits these properties too. Finally, linear diffusion theory quantifies how the spatial extent of bacterial killing scales with increases in antibiotic dosage, predicting that microbes can survive chemotherapies that have been escalated to 250× the clinical dosage if the antibiotic is diffusion-limited.
Barbosa C, Beardmore R, Schulenburg H, Jansen G (2018). Antibiotic combination efficacy (ACE) networks for a Pseudomonas aeruginosa model. PLoS Biol, 16(4).
Antibiotic combination efficacy (ACE) networks for a Pseudomonas aeruginosa model.
The spread of antibiotic resistance is always a consequence of evolutionary processes. The consideration of evolution is thus key to the development of sustainable therapy. Two main factors were recently proposed to enhance long-term effectiveness of drug combinations: evolved collateral sensitivities between the drugs in a pair and antagonistic drug interactions. We systematically assessed these factors by performing over 1,600 evolution experiments with the opportunistic nosocomial pathogen Pseudomonas aeruginosa in single- and multidrug environments. Based on the growth dynamics during these experiments, we reconstructed antibiotic combination efficacy (ACE) networks as a new tool for characterizing the ability of the tested drug combinations to constrain bacterial survival as well as drug resistance evolution across time. Subsequent statistical analysis of the influence of the factors on ACE network characteristics revealed that (i) synergistic drug interactions increased the likelihood of bacterial population extinction-irrespective of whether combinations were compared at the same level of inhibition or not-while (ii) the potential for evolved collateral sensitivities between 2 drugs accounted for a reduction in bacterial adaptation rates. In sum, our systematic experimental analysis allowed us to pinpoint 2 complementary determinants of combination efficacy and to identify specific drug pairs with high ACE scores. Our findings can guide attempts to further improve the sustainability of antibiotic therapy by simultaneously reducing pathogen load and resistance evolution.
Schuetz P, Beardmore RE (2018). Antibiotic strategies in critical care: back to square one?. Lancet Infect Dis, 18(4), 360-361. Author URL.
Beardmore RE, Cook E, Nilsson S, Smith AR, Tillmann A, Esquivel BD, Haynes K, Gow NAR, Brown AJP, White TC, et al (2018). Drug-mediated metabolic tipping between antibiotic resistant states in a mixed-species community. Nat Ecol Evol, 2(8), 1312-1320.
Drug-mediated metabolic tipping between antibiotic resistant states in a mixed-species community.
Microbes rarely exist in isolation, rather, they form intricate multi-species communities that colonize our bodies and inserted medical devices. However, the efficacy of antimicrobials is measured in clinical laboratories exclusively using microbial monocultures. Here, to determine how multi-species interactions mediate selection for resistance during antibiotic treatment, particularly following drug withdrawal, we study a laboratory community consisting of two microbial pathogens. Single-species dose responses are a poor predictor of community dynamics during treatment so, to better understand those dynamics, we introduce the concept of a dose-response mosaic, a multi-dimensional map that indicates how species' abundance is affected by changes in abiotic conditions. We study the dose-response mosaic of a two-species community with a 'Gene × Gene × Environment × Environment' ecological interaction whereby Candida glabrata, which is resistant to the antifungal drug fluconazole, competes for survival with Candida albicans, which is susceptible to fluconazole. The mosaic comprises several zones that delineate abiotic conditions where each species dominates. Zones are separated by loci of bifurcations and tipping points that identify what environmental changes can trigger the loss of either species. Observations of the laboratory communities corroborated theory, showing that changes in both antibiotic concentration and nutrient availability can push populations beyond tipping points, thus creating irreversible shifts in community composition from drug-sensitive to drug-resistant species. This has an important consequence: resistant species can increase in frequency even if an antibiotic is withdrawn because, unwittingly, a tipping point was passed during treatment.
Beardmore RE, Cook E, Nilsson S, Smith AR, Tillmann A, Esquivel BD, Haynes K, Gow NAR, Brown AJP, White TC, et al (2018). Erratum to: Drug-mediated metabolic tipping between antibiotic resistant states in a mixed-species community (Nature Ecology & Evolution, (2018), 2, 8, (1312-1320), 10.1038/s41559-018-0582-7). Nature Ecology and Evolution, 2(11).
Erratum to: Drug-mediated metabolic tipping between antibiotic resistant states in a mixed-species community (Nature Ecology & Evolution, (2018), 2, 8, (1312-1320), 10.1038/s41559-018-0582-7)
© 2018, Springer Nature Limited. In the version of this Article originally published, the following sentence was missing from the Acknowledgements: "R.E.B. is an EPSRC Healthcare Technologies Impact Fellow EP/N033671/1; I.G. is funded by ERC Consolidator grant 647292 MathModExp; A.J.P.B. N.A.R.G. and A.T. were funded by BBSRC grant BB/F00513X/1; K.H. I.G. S.N. and E.C. were funded by BBSRC grant BB/F005210/2." This text has now been added.
Barbosa C, Trebosc V, Kemmer C, Rosenstiel P, Beardmore R, Schulenburg H, Jansen G (2017). Alternative Evolutionary Paths to Bacterial Antibiotic Resistance Cause Distinct Collateral Effects. Mol Biol Evol, 34(9), 2229-2244.
Alternative Evolutionary Paths to Bacterial Antibiotic Resistance Cause Distinct Collateral Effects.
When bacteria evolve resistance against a particular antibiotic, they may simultaneously gain increased sensitivity against a second one. Such collateral sensitivity may be exploited to develop novel, sustainable antibiotic treatment strategies aimed at containing the current, dramatic spread of drug resistance. To date, the presence and molecular basis of collateral sensitivity has only been studied in few bacterial species and is unknown for opportunistic human pathogens such as Pseudomonas aeruginosa. In the present study, we assessed patterns of collateral effects by experimentally evolving 160 independent populations of P. aeruginosa to high levels of resistance against eight commonly used antibiotics. The bacteria evolved resistance rapidly and expressed both collateral sensitivity and cross-resistance. The pattern of such collateral effects differed to those previously reported for other bacterial species, suggesting interspecific differences in the underlying evolutionary trade-offs. Intriguingly, we also identified contrasting patterns of collateral sensitivity and cross-resistance among the replicate populations adapted to the same drug. Whole-genome sequencing of 81 independently evolved populations revealed distinct evolutionary paths of resistance to the selective drug, which determined whether bacteria became cross-resistant or collaterally sensitive towards others. Based on genomic and functional genetic analysis, we demonstrate that collateral sensitivity can result from resistance mutations in regulatory genes such as nalC or mexZ, which mediate aminoglycoside sensitivity in β-lactam-adapted populations, or the two-component regulatory system gene pmrB, which enhances penicillin sensitivity in gentamicin-resistant populations. Our findings highlight substantial variation in the evolved collateral effects among replicates, which in turn determine their potential in antibiotic therapy.
Beardmore RE, Peña-Miller R, Gori F, Iredell J (2017). Antibiotic Cycling and Antibiotic Mixing: Which One Best Mitigates Antibiotic Resistance?. Mol Biol Evol, 34(4), 802-817.
Antibiotic Cycling and Antibiotic Mixing: Which One Best Mitigates Antibiotic Resistance?
Can we exploit our burgeoning understanding of molecular evolution to slow the progress of drug resistance? One role of an infection clinician is exactly that: to foresee trajectories to resistance during antibiotic treatment and to hinder that evolutionary course. But can this be done at a hospital-wide scale? Clinicians and theoreticians tried to when they proposed two conflicting behavioral strategies that are expected to curb resistance evolution in the clinic, these are known as "antibiotic cycling" and "antibiotic mixing." However, the accumulated data from clinical trials, now approaching 4 million patient days of treatment, is too variable for cycling or mixing to be deemed successful. The former implements the restriction and prioritization of different antibiotics at different times in hospitals in a manner said to "cycle" between them. In antibiotic mixing, appropriate antibiotics are allocated to patients but randomly. Mixing results in no correlation, in time or across patients, in the drugs used for treatment which is why theorists saw this as an optimal behavioral strategy. So while cycling and mixing were proposed as ways of controlling evolution, we show there is good reason why clinical datasets cannot choose between them: by re-examining the theoretical literature we show prior support for the theoretical optimality of mixing was misplaced. Our analysis is consistent with a pattern emerging in data: neither cycling or mixing is a priori better than the other at mitigating selection for antibiotic resistance in the clinic. Key words: : antibiotic cycling, antibiotic mixing, optimal control, stochastic models.
Reding-Roman C, Hewlett M, Duxbury S, Gori F, Gudelj I, Beardmore R (2017). The unconstrained evolution of fast and efficient antibiotic-resistant bacterial genomes. Nature Ecology & Evolution, 1(3). Full text.
Rashkov P, Barrett IP, Beardmore RE, Bendtsen C, Gudelj I (2016). Kinase Inhibition Leads to Hormesis in a Dual Phosphorylation-Dephosphorylation Cycle. PLoS Comput Biol, 12(11).
Kinase Inhibition Leads to Hormesis in a Dual Phosphorylation-Dephosphorylation Cycle.
Many antimicrobial and anti-tumour drugs elicit hormetic responses characterised by low-dose stimulation and high-dose inhibition. While this can have profound consequences for human health, with low drug concentrations actually stimulating pathogen or tumour growth, the mechanistic understanding behind such responses is still lacking. We propose a novel, simple but general mechanism that could give rise to hormesis in systems where an inhibitor acts on an enzyme. At its core is one of the basic building blocks in intracellular signalling, the dual phosphorylation-dephosphorylation motif, found in diverse regulatory processes including control of cell proliferation and programmed cell death. Our analytically-derived conditions for observing hormesis provide clues as to why this mechanism has not been previously identified. Current mathematical models regularly make simplifying assumptions that lack empirical support but inadvertently preclude the observation of hormesis. In addition, due to the inherent population heterogeneities, the presence of hormesis is likely to be masked in empirical population-level studies. Therefore, examining hormetic responses at single-cell level coupled with improved mathematical models could substantially enhance detection and mechanistic understanding of hormesis.
Meyer JR, Gudelj I, Beardmore R (2015). Biophysical mechanisms that maintain biodiversity through trade-offs. Nat Commun, 6
Biophysical mechanisms that maintain biodiversity through trade-offs.
Trade-offs are thought to arise from inevitable, biophysical limitations that prevent organisms from optimizing multiple traits simultaneously. A leading explanation for biodiversity maintenance is a theory that if the shape, or geometry, of a trade-off is right, then multiple species can coexist. Testing this theory, however, is difficult as trait data is usually too noisy to discern shape, or trade-offs necessary for the theory are not observed in vivo. To address this, we infer geometry directly from the biophysical mechanisms that cause trade-offs, deriving the geometry of two by studying nutrient uptake and metabolic properties common to all living cells. To test for their presence in vivo we isolated Escherichia coli mutants that vary in a nutrient transporter, LamB, and found evidence for both trade-offs. Consistent with data, population genetics models incorporating the trade-offs successfully predict the co-maintenance of three distinct genetic lineages, demonstrating that trade-off geometry can be deduced from fundamental principles of living cells and used to predict stable genetic polymorphisms.
Roemhild R, Barbosa C, Beardmore RE, Jansen G, Schulenburg H (2015). Temporal variation in antibiotic environments slows down resistance evolution in pathogenic Pseudomonas aeruginosa. Evolutionary Applications
Temporal variation in antibiotic environments slows down resistance evolution in pathogenic Pseudomonas aeruginosa
Antibiotic resistance is a growing concern to public health. New treatment strategies may alleviate the situation by slowing down the evolution of resistance. Here, we evaluated sequential treatment protocols using two fully independent laboratory-controlled evolution experiments with the human pathogen Pseudomonas aeruginosa PA14 and two pairs of clinically relevant antibiotics (doripenem/ciprofloxacin and cefsulodin/gentamicin). Our results consistently show that the sequential application of two antibiotics decelerates resistance evolution relative to monotherapy. Sequential treatment enhanced population extinction although we applied antibiotics at sublethal dosage. In both experiments, we identified an order effect of the antibiotics used in the sequential protocol, leading to significant variation in the long-term efficacy of the tested protocols. These variations appear to be caused by asymmetric evolutionary constraints, whereby adaptation to one drug slowed down adaptation to the other drug, but not vice versa. An understanding of such asymmetric constraints may help future development of evolutionary robust treatments against infectious disease.
Roemhild R, Barbosa C, Beardmore RE, Jansen G, Schulenburg H (2015). Temporal variation in antibiotic environments slows down resistance evolution in pathogenic Pseudomonas aeruginosa. Evolutionary Applications, 8(10), 945-955.
© 2015 John Wiley. &. Sons Ltd. Antibiotic resistance is a growing concern to public health. New treatment strategies may alleviate the situation by slowing down the evolution of resistance. Here, we evaluated sequential treatment protocols using two fully independent laboratory-controlled evolution experiments with the human pathogen Pseudomonas aeruginosa PA14 and two pairs of clinically relevant antibiotics (doripenem/ciprofloxacin and cefsulodin/gentamicin). Our results consistently show that the sequential application of two antibiotics decelerates resistance evolution relative to monotherapy. Sequential treatment enhanced population extinction although we applied antibiotics at sublethal dosage. In both experiments, we identified an order effect of the antibiotics used in the sequential protocol, leading to significant variation in the long-term efficacy of the tested protocols. These variations appear to be caused by asymmetric evolutionary constraints, whereby adaptation to one drug slowed down adaptation to the other drug, but not vice versa. An understanding of such asymmetric constraints may help future development of evolutionary robust treatments against infectious disease.
Arnoldini M, Vizcarra IA, Peña-Miller R, Stocker N, Diard M, Vogel V, Beardmore RE, Hardt W-D, Ackermann M (2014). Bistable expression of virulence genes in salmonella leads to the formation of an antibiotic-tolerant subpopulation. PLoS Biol, 12(8).
Bistable expression of virulence genes in salmonella leads to the formation of an antibiotic-tolerant subpopulation.
Phenotypic heterogeneity can confer clonal groups of organisms with new functionality. A paradigmatic example is the bistable expression of virulence genes in Salmonella typhimurium, which leads to phenotypically virulent and phenotypically avirulent subpopulations. The two subpopulations have been shown to divide labor during S. typhimurium infections. Here, we show that heterogeneous virulence gene expression in this organism also promotes survival against exposure to antibiotics through a bet-hedging mechanism. Using microfluidic devices in combination with fluorescence time-lapse microscopy and quantitative image analysis, we analyzed the expression of virulence genes at the single cell level and related it to survival when exposed to antibiotics. We found that, across different types of antibiotics and under concentrations that are clinically relevant, the subpopulation of bacterial cells that express virulence genes shows increased survival after exposure to antibiotics. Intriguingly, there is an interplay between the two consequences of phenotypic heterogeneity. The bet-hedging effect that arises through heterogeneity in virulence gene expression can protect clonal populations against avirulent mutants that exploit and subvert the division of labor within these populations. We conclude that bet-hedging and the division of labor can arise through variation in a single trait and interact with each other. This reveals a new degree of functional complexity of phenotypic heterogeneity. In addition, our results suggest a general principle of how pathogens can evade antibiotics: Expression of virulence factors often entails metabolic costs and the resulting growth retardation could generally increase tolerance against antibiotics and thus compromise treatment.
Laehnemann D, Peña-Miller R, Rosenstiel P, Beardmore R, Jansen G, Schulenburg H (2014). Genomics of rapid adaptation to antibiotics: convergent evolution and scalable sequence amplification. Genome Biol Evol, 6(6), 1287-1301.
Genomics of rapid adaptation to antibiotics: convergent evolution and scalable sequence amplification.
Evolutionary adaptation can be extremely fast, especially in response to high selection intensities. A prime example is the surge of antibiotic resistance in bacteria. The genomic underpinnings of such rapid changes may provide information on the genetic processes that enhance fast responses and the particular trait functions under selection. Here, we use experimentally evolved Escherichia coli for a detailed dissection of the genomics of rapid antibiotic resistance evolution. Our new analyses demonstrate that amplification of a sequence region containing several known antibiotic resistance genes represents a fast genomic response mechanism under high antibiotic stress, here exerted by drug combination. In particular, higher dosage of such antibiotic combinations coincided with higher copy number of the sequence region. The amplification appears to be evolutionarily costly, because amplification levels rapidly dropped after removal of the drugs. Our results suggest that amplification is a scalable process, as copy number rapidly changes in response to the selective pressure encountered. Moreover, repeated patterns of convergent evolution were found across the experimentally evolved bacterial populations, including those with lower antibiotic selection intensities. Intriguingly, convergent evolution was identified on different organizational levels, ranging from the above sequence amplification, high variant frequencies in specific genes, prevalence of individual nonsynonymous mutations to the unusual repeated occurrence of a particular synonymous mutation in Glycine codons. We conclude that constrained evolutionary trajectories underlie rapid adaptation to antibiotics. of the identified genomic changes, sequence amplification seems to represent the most potent, albeit costly genomic response mechanism to high antibiotic stress.
Peña-Miller R, Fuentes-Hernandez A, Reding C, Gudelj I, Beardmore R (2014). Testing the optimality properties of a dual antibiotic treatment in a two-locus, two-allele model. J R Soc Interface, 11(96).
Testing the optimality properties of a dual antibiotic treatment in a two-locus, two-allele model.
Mathematically speaking, it is self-evident that the optimal control of complex, dynamical systems with many interacting components cannot be achieved with 'non-responsive' control strategies that are constant through time. Although there are notable exceptions, this is usually how we design treatments with antimicrobial drugs when we give the same dose and the same antibiotic combination each day. Here, we use a frequency- and density-dependent pharmacogenetics mathematical model based on a standard, two-locus, two-allele representation of how bacteria resist antibiotics to probe the question of whether optimal antibiotic treatments might, in fact, be constant through time. The model describes the ecological and evolutionary dynamics of different sub-populations of the bacterium Escherichia coli that compete for a single limiting resource in a two-drug environment. We use in vitro evolutionary experiments to calibrate and test the model and show that antibiotic environments can support dynamically changing and heterogeneous population structures. We then demonstrate, theoretically and empirically, that the best treatment strategies should adapt through time and constant strategies are not optimal.
Maharjan R, Nilsson S, Sung J, Haynes K, Beardmore RE, Hurst LD, Ferenci T, Gudelj I (2013). The form of a trade-off determines the response to competition. Ecology Letters, 16(10), 1267-1276.
The form of a trade-off determines the response to competition
Understanding how populations and communities respond to competition is a central concern of ecology. A seminal theoretical solution first formalised by Levins (and re-derived in multiple fields) showed that, in theory, the form of a trade-off should determine the outcome of competition. While this has become a central postulate in ecology it has evaded experimental verification, not least because of substantial technical obstacles. We here solve the experimental problems by employing synthetic ecology. We engineer strains of Escherichia coli with fixed resource allocations enabling accurate measurement of trade-off shapes between bacterial survival and multiplication in multiple environments. A mathematical chemostat model predicts different, and experimentally verified, trajectories of gene frequency changes as a function of condition-specific trade-offs. The results support Levins' postulate and demonstrates that otherwise paradoxical alternative outcomes witnessed in subtly different conditions are predictable. © 2013 John Wiley & Sons Ltd/CNRS.
Maharjan R, Nilsson S, Sung J, Haynes K, Beardmore RE, Hurst LD, Ferenci T, Gudelj I (2013). The form of a trade-off determines the response to competition. Ecol Lett, 16(10), 1267-1276.
The form of a trade-off determines the response to competition.
Understanding how populations and communities respond to competition is a central concern of ecology. A seminal theoretical solution first formalised by Levins (and re-derived in multiple fields) showed that, in theory, the form of a trade-off should determine the outcome of competition. While this has become a central postulate in ecology it has evaded experimental verification, not least because of substantial technical obstacles. We here solve the experimental problems by employing synthetic ecology. We engineer strains of Escherichia coli with fixed resource allocations enabling accurate measurement of trade-off shapes between bacterial survival and multiplication in multiple environments. A mathematical chemostat model predicts different, and experimentally verified, trajectories of gene frequency changes as a function of condition-specific trade-offs. The results support Levins' postulate and demonstrates that otherwise paradoxical alternative outcomes witnessed in subtly different conditions are predictable.
Beardmore RE, Pena-Miller R (2010). Antibiotic cycling versus mixing: the difficulty of using mathematical models to definitively quantify their relative merits. Math Biosci Eng, 7(4), 923-933.
Antibiotic cycling versus mixing: the difficulty of using mathematical models to definitively quantify their relative merits.
We ask the question Which antibiotic deployment protocols select best against drug-resistant microbes: mixing or periodic cycling? and demonstrate that the statistical distribution of the performances of both sets of protocols, mixing and periodic cycling, must have overlapping supports. In other words, it is a general, mathematical result that there must be mixing policies that outperform cycling policies and vice versa. As a result, we agree with the tenet of Bonhoefer et al. [1] that one should not apply the results of [2] to conclude that an antibiotic cycling policy that implements cycles of drug restriction and prioritisation on an ad-hoc basis can select against drug-resistant microbial pathogens in a clinical setting any better than random drug use. However, nor should we conclude that a random, per-patient drug-assignment protocol is the de facto optimal method for allocating antibiotics to patients in any general sense.
Peters R, Beckett N, Beardmore R, Peña-Miller R, Rockwood K, Mitnitski A, Mt-Isa S, Bulpitt C (2010). Modelling cognitive decline in the Hypertension in the Very Elderly Trial [HYVET] and proposed risk tables for population use. PLoS One, 5(7).
Modelling cognitive decline in the Hypertension in the Very Elderly Trial [HYVET] and proposed risk tables for population use.
INTRODUCTION: Although, on average, cognition declines with age, cognition in older adults is a dynamic process. Hypertension is associated with greater decline in cognition with age, but whether treatment of hypertension affects this is uncertain. Here, we modelled dynamics of cognition in relation to the treatment of hypertension, to see if treatment effects might better be discerned by a model that included baseline measures of cognition and consequent mortality METHODOLOGY/PRINCIPAL FINDINGS: This is a secondary analysis of the Hypertension in the Very Elderly Trial (HYVET), a double blind, placebo controlled trial of indapamide, with or without perindopril, in people aged 80+ years at enrollment. Cognitive states were defined in relation to errors on the Mini-Mental State Examination, with more errors signifying worse cognition. Change in cognitive state was evaluated using a dynamic model of cognitive transition. In the model, the probabilities of transitions between cognitive states is represented by a Poisson distribution, with the Poisson mean dependent on the baseline cognitive state. The dynamic model of cognitive transition was good (R(2) = 0.74) both for those on placebo and (0.86) for those on active treatment. The probability of maintaining cognitive function, based on baseline function, was slightly higher in the actively treated group (e.g. for those with the fewest baseline errors, the chance of staying in that state was 63% for those on treatment, compared with 60% for those on placebo). Outcomes at two and four years could be predicted based on the initial state and treatment. CONCLUSIONS/SIGNIFICANCE: a dynamic model of cognition that allows all outcomes (cognitive worsening, stability improvement or death) to be categorized simultaneously detected small but consistent differences between treatment and control groups (in favour of treatment) amongst very elderly people treated for hypertension. The model showed good fit, and suggests that most change in cognition in very elderly people is small, and depends on their baseline state and on treatment. Additional work is needed to understand whether this modelling approach is well suited to the valuation of small effects, especially in the face of mortality differences between treatment groups. TRIAL REGISTRATION: ClinicalTrials.gov NCT0012281.
Beardmore RE, Peña-Miller R (2010). Rotating antibiotics selects optimally against antibiotic resistance, in theory. Math Biosci Eng, 7(3), 527-552.
Rotating antibiotics selects optimally against antibiotic resistance, in theory.
The purpose of this paper is to use mathematical models to investigate the claim made in the medical literature over a decade ago that the routine rotation of antibiotics in an intensive care unit (ICU) will select against the evolution and spread of antibiotic-resistant pathogens. In contrast, previous theoretical studies addressing this question have demonstrated that routinely changing the drug of choice for a given pathogenic infection may in fact lead to a greater incidence of drug resistance in comparison to the random deployment of different drugs. Using mathematical models that do not explicitly incorporate the spatial dynamics of pathogen transmission within the ICU or hospital and assuming the antibiotics are from distinct functional groups, we use a control theoretic-approach to prove that one can relax the medical notion of what constitutes an antibiotic rotation and so obtain protocols that are arbitrarily close to the optimum. Finally, we show that theoretical feedback control measures that rotate between different antibiotics motivated directly by the outcome of clinical studies can be deployed to good effect to reduce the prevalence of antibiotic resistance below what can be achieved with random antibiotic use.
Forde SE, Beardmore RE, Gudelj I, Arkin SS, Thompson JN, Hurst LD (2008). Understanding the limits to generalizability of experimental evolutionary models. Nature, 455(7210), 220-223.
Understanding the limits to generalizability of experimental evolutionary models.
Given the difficulty of testing evolutionary and ecological theory in situ, in vitro model systems are attractive alternatives; however, can we appraise whether an experimental result is particular to the in vitro model, and, if so, characterize the systems likely to behave differently and understand why? Here we examine these issues using the relationship between phenotypic diversity and resource input in the T7-Escherichia coli co-evolving system as a case history. We establish a mathematical model of this interaction, framed as one instance of a super-class of host-parasite co-evolutionary models, and show that it captures experimental results. By tuning this model, we then ask how diversity as a function of resource input could behave for alternative co-evolving partners (for example, E. coli with lambda bacteriophages). In contrast to populations lacking bacteriophages, variation in diversity with differences in resources is always found for co-evolving populations, supporting the geographic mosaic theory of co-evolution. The form of this variation is not, however, universal. Details of infectivity are pivotal: in T7-E. coli with a modified gene-for-gene interaction, diversity is low at high resource input, whereas, for matching-allele interactions, maximal diversity is found at high resource input. A combination of in vitro systems and appropriately configured mathematical models is an effective means to isolate results particular to the in vitro system, to characterize systems likely to behave differently and to understand the biology underpinning those alternatives.
Beardmore RE, Peplow A (2007). A bifurcation analysis of the Ornstein-Zernike equation with hypernetted chain closure. Journal of Mathematical Analysis and Applications, 333(2), 919-942.
A bifurcation analysis of the Ornstein-Zernike equation with hypernetted chain closure
Motivated by the large number of solutions obtained when applying bifurcation algorithms to the Ornstein-Zernike (OZ) equation with the hypernetted chain (HNC) closure from liquid state theory, we provide existence and bifurcation results for a computationally-motivated version of the problem. We first establish the natural result that if the potential satisfies a short-range condition then a low-density branch of smooth solutions exists. We then consider the so-called truncated OZ HNC equation that is obtained when truncating the region occupied by the fluid in the original OZ equation to a finite ball, as is often done in the physics literature before applying a numerical technique. On physical grounds one expects to find one or two solution branches corresponding to vapour and liquid phases of the fluid. However, we are able to demonstrate the existence of infinitely many solution branches and bifurcation points at very low temperatures for the truncated one-dimensional problem provided that the potential is purely repulsive and homogeneous. © 2006 Elsevier Inc. All rights reserved.
Beardmore RE, Peplow AT, Bresme F (2007). A numerical bifurcation analysis of the ornstein-zernike equation with hypernetted chain closure. SIAM Journal on Scientific Computing, 29(6), 2442-2463.
A numerical bifurcation analysis of the ornstein-zernike equation with hypernetted chain closure
We study the codimension-one and -two bifurcations of the Ornstein-Zernike equation with hypernetted chain (HNC) closure with Lennard-Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation for the codimension-one case and a Newton-GMRES method for the codimension-two case. Through careful consideration of the results of our computations, an argument is formulated which shows that spinodal isothermal solution branches arising in this model cannot be reproduced numerically. Furthermore, we show that the existence of an upper bound on the density that can be realized on a vapor isothermal solution branch, which must be present at a spinodal, causes the existence of at least one fold bifurcation along that vapor branch when density is used as the bifurcation parameter. This provides an explanation for previous inconclusive attempts to compute solutions using Newton-Picard methods that are popular in the physical chemistry literature. © 2007 Society for Industrial and Applied Mathematics.
Gudelj I, Beardmore RE, Arkin SS, MacLean RC (2007). Constraints on microbial metabolism drive evolutionary diversification in homogeneous environments. J Evol Biol, 20(5), 1882-1889.
Constraints on microbial metabolism drive evolutionary diversification in homogeneous environments.
Understanding the evolution of microbial diversity is an important and current problem in evolutionary ecology. In this paper, we investigated the role of two established biochemical trade-offs in microbial diversification using a model that connects ecological and evolutionary processes with fundamental aspects of biochemistry. The trade-offs that we investigated are as follows:(1) a trade-off between the rate and affinity of substrate transport; and (2) a trade-off between the rate and yield of ATP production. Our model shows that these biochemical trade-offs can drive evolutionary diversification under the simplest possible ecological conditions: a homogeneous environment containing a single limiting resource. We argue that the results of a number of microbial selection experiments are consistent with the predictions of our model.
Peplow AT, Beardmore RE, Bresme F (2006). Algorithms for the computation of solutions of the Ornstein-Zernike equation. Phys Rev E Stat Nonlin Soft Matter Phys, 74(4 Pt 2).
Algorithms for the computation of solutions of the Ornstein-Zernike equation.
We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.
Gudelj I, Coman CD, Beardmore RE (2006). Classifying the role of trade-offs in the evolutionary diversity of pathogens. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462(2065), 97-116.
Classifying the role of trade-offs in the evolutionary diversity of pathogens
In this paper we use a system of non-local reaction-diffusion equations to study the effect of host heterogeneity on the phenotypic evolution of a pathogen population. The evolving phenotype is taken to be the transmission rate of the pathogen on the different hosts, and in our system there are two host populations present. The central feature of our model is a trade-off relationship between the transmission rates on these hosts, which means that an increase in the pathogen transmission on one host will lead to a decrease in the pathogen transmission on the other. The purpose of the paper is to develop a classification of phenotypic diversity as a function of the shape of the trade-off relationship and this is achieved by determining the maximum number of phenotypes a pathogen population can support in the long term, for a given form of the trade-off. Our findings are then compared with results obtained by applying classical theory from evolutionary ecology and the more recent adaptive dynamics method to the same host-pathogen system. We find our work to be in good agreement with these two approaches. © 2005 the Royal Society.
Beardmore RE, Peletier MA, Budd CJ, Wadee MA (2005). Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in reversible differential equations. SIAM Journal on Mathematical Analysis, 36(5), 1461-1488.
Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in reversible differential equations
This is a study of the existence of bifurcation branches for the problem of finding even, periodic solutions in fourth-order, reversible Hamiltonian systems such that the Hamiltonian evaluates to zero along each solution on the branch. The class considered here is a generalization of both the Swift-Hohenberg and extended Fisher-Kolmogorov equations that have been studied in several recent papers. We obtain the existence of local bifurcations from a trivial solution under mild restrictions on the nonlinearity and obtain existence and disjointness results regarding the global nature of the resulting bifurcating continua for the case where the Hamiltonian has a single-well potential. The local results rest on two abstract bifurcation theorems which also have applications to sixth-order problems and which show that the curves of zero-Hamiltonian solutions are contained within two-dimensional manifolds of solutions of both negative and positive Hamiltonian. © 2005 Society for Industrial and Applied Mathematics.
Laister R, Peplow AT, Beardmore RE (2004). Finite time extinction in nonlinear diffusion equations. Applied Mathematics Letters, 17(6), 561-567.
Finite time extinction in nonlinear diffusion equations
We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction follows by comparison with newly constructed finite travelling waves connecting two stable equilibria. © 2004 Elsevier Ltd. All rights reserved.
Beardmore RE, Laister R (2004). Sequential and continuum bifurcations in degenerate elliptic equations. Proceedings of the American Mathematical Society, 132(1), 165-174.
Sequential and continuum bifurcations in degenerate elliptic equations
We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations.
Beardmore RE, Laister R, Peplow A (2004). Trajectories of a DAE near a pseudo-equilibrium. Nonlinearity, 17(1), 253-279.
Trajectories of a DAE near a pseudo-equilibrium
We consider a class of differential-algebraic equations (DAEs) defined by analytic nonlinearities and study its singular solutions. The main assumption used is that the linearization of the DAE represents a Kronecker index-2 matrix pencil and that the constraint manifold has a quadratic fold along its singularity. From these assumptions we obtain a normal form for the DAE where the presence of the singularity and its effects on the dynamics of the problem are made explicit in the form of a quasi-linear differential equation. Subsequently, two distinct types of singular points are identified through which there pass exactly two analytic solutions: pseudo-nodes and pseudo-saddles. We also demonstrate that a singular point called a pseudo-node supports an uncountable infinity of solutions which are not analytic in general. Moreover, akin to known results in the literature for DAEs with singular equilibria, a degenerate singularity is found through which there passes one analytic solution such that the singular point in question is contained within a quasi-invariant manifold of solutions. We call this type of singularity a pseudo-centre and it provides not only a manifold of solutions which intersects the singularity, but also a local flow on that manifold which solves the DAE.
Beardmore RE, Laister R (2003). The flow of a DAE near a singular equilibrium. SIAM Journal on Matrix Analysis and Applications, 24(1), 106-120.
The flow of a DAE near a singular equilibrium
We extend the differential-algebraic equation (DAE) taxonomy by assuming that the linearization of a DAE about a singular equilibrium has a particular index-2 Kronecker normal form. A Lyapunov-Schmidt procedure is used to reduce the DAE to a quasilinear normal form which is shown to posses quasi-invariant manifolds which intersect the singularity. In turn, this provides solutions of the DAE which pass through the singularity.
Beardmore I, Beardmore R (2003). The global structure of a spatial model of infectious disease. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 459(2034), 1427-1448.
The global structure of a spatial model of infectious disease
In this paper we study an SI model of infectious diseases that takes into account spatial inhomogeneities, resulting in a system of reaction-convection- diffusion equations on a bounded domain. The convection process is included to account for social interaction, as modelled by the location of a focal point or den where the population will tend to aggregate. We show that a vertical bifurcation of steady-state solutions occurs in this model when birth rate is taken as the bifurcation parameter, from which emanates a global secondary branch, which then bifurcates at infinity. Subsequently, we use singular perturbation techniques to give a description of the limiting spatial structure along this branch in large and small parameter limits. Finally, the results are illustrated numerically on some biologically relevant cases.
Laister R, Beardmore RE (2003). Transversality and separation of zeros in second order differential equations. Proceedings of the American Mathematical Society, 131(1), 209-218.
Transversality and separation of zeros in second order differential equations
Sufficient conditions on the non-linearity f are given which ensure that non-trivial solutions of second order differential equations of the form Lu = f(t, u) have a finite number of transverse zeros in a given finite time interval. We also obtain a priori lower bounds on the separation of zeros of solutions. In particular our results apply to non-Lipschitz non-linearities. Applications to non-linear porous medium equations are considered, yielding information on the existence and strict positivity of equilibrium solutions in some important classes of equations.
Beardmore RE (2002). The singularity-induced bifurcation and its Kronecker normal form. SIAM Journal on Matrix Analysis and Applications, 23(1), 126-137.
The singularity-induced bifurcation and its Kronecker normal form
It is shown that the singularity-induced bifurcation theorem due to Venkatasubramanian, Schattler, and Zaborszky [Proceedings of the IEEE. 83 (1995), pp. 1530-1558] can be expressed as the perturbation of an infinite eigenvalue of a particular class of parameterized index-1 matrix pencil, denoted (M, L(λ)). It is shown that the matrix pencil at the singularity-induced bifurcation point, (M, L(λ0)), has Kronecker index-2. It is also shown that a two-parameter unfolding of a singularity-induced bifurcation point results in a locus of index-0 pencils, denoted (M(ε), L(λ(ε))), which has two purely imaginary eigenvalues near infinity.
Beardmore RE (2001). A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 457(2010), 1295-1305.
A singularity-induced bifurcation theorem for infinite-dimensional implicit dynamical systems
In this note we study a class of partial differential equations whose formal structure resembles the semi-explicit, index-1 form from the theory of differential-algebraic equations. It is known from the theory of such problems that one can encounter simple poles in the eigenvalue loci of parameter-dependent linearizations, leading to the loss of linear stability without the presence of steady-state bifurcations. We demonstrate how this carries over to implicitly defined problems on a Hilbert space.
Beardmore RE (2000). Double singularity-induced bifurcation points and singular Hopf bifurcations. Dynamical Systems, 15(4), 319-342.
Double singularity-induced bifurcation points and singular Hopf bifurcations
The singularity-induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arise when Newton's laws are coupled to Kirchhoff's laws are explored. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential-algebraic equation (DAE) or a singularly perturbed ordinary differential equation (ODE). As a consequence of the debate in the engineering literature as to which class of system is the 'true' representation of power systems, a discussion is included of the consequences of the power engineer's 'load-flow singularity' for both ODE and DAE.
Beardmore RE, Song YH (1998). Differential-algebraic equations: a tutorial review. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 8(7), 1399-1411.
Differential-algebraic equations: a tutorial review
This article1 explores some introductory principles of differential-algebraic equations (DAEs) and makes a connection with the theory of dynamical systems. Some results which are new in the field of DAEs are also surveyed. Most treatments on DAE emphasize the differences that exist when compared with the ODE case. Here we seek to underline the similarities so that readers with a very basic knowledge of nonlinear dynamics can understand some of their consequences in this more general context.
Beardmore RE (1998). Stability and bifurcation properties of index-1 DAEs. Numerical Algorithms, 19(1-4), 43-53.
Stability and bifurcation properties of index-1 DAEs
It is well known that an equilibrium of a semi-explicit, index-1 differential-algebraic equation under a parameter variation may encounter the singularity manifold. It is a generic property of this encounter that one eigenvalue of the linear stability mapping associated with the equilibrium will pass from one half of the complex plane to the other without passing through the imaginary axis. This is known as singularity-induced bifurcation and an equivalent result is proven in this paper. While this property is generic, it is shown how more than one eigenvalue can diverge in an analogous manner, with applications in electrical power systems.
Beardmore R, Webster K (2008). A Hopf bifurcation theorem for singular differential-algebraic equations.
A Hopf bifurcation theorem for singular differential-algebraic equations
Laister R, Beardmore RE (2005). Bifurcations in degenerate elliptic equations. Author URL.
Rob_Beardmore Details from cache as at 2020-01-22 13:31:56
Member of EPSRC College
2011 EPSRC Leadership Fellows Sift and Interview Panels
2013 EPSRC Doctoral Training Centres Panel
Reviewer for EPSRC, NSERC (Canada), Portuguese Foundation for Science and Technology (FCT), ETH Zurich Collaborative Highly Interdisciplinary Research Projects (interdisciplinary research programme) and others...
2008 NESCent Research Meeting, April 7-10, Duke University Campus
2008 Bifurcation Theoretic Computations for 1-d DFTs, June 24th, Imperial College
2008 17th Annual Scottish Computational Mathematics Symposium, September 10th, Heriot-Watt University, Edinburgh
2008 IEEE Seminar, Devry Institute, New Brunswick, New Jersey, US.
2009 PIMS Lecture Series (University of Alberta and UBC, Vancouver), February
2009 Analyse des Systemes et Biometrie, March, Montpellier, France
2009 One-week postgraduate lecture course: Phase Transition Tracking for Classical Density Functional Theory, April, University Carlos III, Madrid
2009 ESA, Special Session on Microbial Evolution in Ecology, June, Albuquerque, New Mexico, US
2009 Epidemiology Seminar Series, Department of Zoology, University of Oxford, October
2010 Optimal control theory & rotating or mixing antibiotics, Yale, Connecticut, US, Jan
2010 Coevolution - Rapid Reciprocal Adaptation and its Genetic Basis, `Phenotypic diversity versus resource supply for GxE and GxGxE interactions in the chemostat,' Kiel, Feb
2010 Centre for Evolutionary Genetics Seminar, September, Kiel University,
2010 Basque Center for Applied Mathematics (BCAM), December, Bilboa, Spain
2011 Centre for Evolutionary Genetics Seminar, Kiel University, September
2011 Maths for Microbes session; Society for General Microbiology, Spring Conference, Harrogate, April
2011 Departmental Seminar, Engineering Mathematics, Bristol University, December
2011 H. Lee Moffitt Cancer Center, IMO seminar, December
2012 Seminar, Harvard Medical School (Kishony Lab), Boston US, February
2012 OEB `Special Seminar' Harvard Systems Biology Seminar, Boston US, February
2012 International Conference of Numerical Analysis and Applied Mathematics, Halkidiki, Greece, September; plenary symposium on the applications of numerical analysis and scientific computation in mathematical biology
2012 Department of Systems Biology, Novo Nordisk Foundation Center for Biosustainability, Copenhagen, December
2013 Colloquium (Optimisation in Biology) ETH Zurich in Basel, January
2013 Cavendish Laboratory Seminar Series, Cambridge, February
2013 Thematic Programme on Mathematical Biology, Lyon, March, plenary talk, mathbio2013.sciencesconf.org/
2013 Departmental Seminar (Mathematical Medicine), Nottingham, October
2013 Agents against Infectious Diseases, plenary talk, University Wurzburg, November
2006-2009: Imperial organiser of M4 Corridor PG Days in Numerical Analysis with Oxford, Brunel, Reading, Bath and Cardiff
2008 Bifurcation-Theoretic Computations and Classical Density Functional Theory, 24th June, Imperial College, London, approximately 20 attendees
2010 Organised the Mathematics of Microbes: Biophysical Details of the Evolving Cell, April, Imperial College, London, approximately 50 attendees
2013 Quantitative Evolutionary Dynamics (QED): microbes from cells to populations in their natural environments, April, Shaldon near Exeter University, UK, approximately 50 attendees
Dr Ayari Fuentes-Hernandez
Dr Fabio Gori
Dr Jessica Plucain
Mark Hewlett
Bogna Pawlowska
Carlos Reding
Cyrielle Tonneau
Dr Sinan Arkin former PhD student
Dr Rafael Pena-Miller former PhD student & EPSRC-funded post-doc
Dr Andrew Peplow former EPSRC-funded PDRA
Dr Kevin Webster former EPSRC-funded PDRA


Week 393 — Go Free Range.
There's been a distinct lack of week notes for the past 10 weeks or so (since week 383). We managed to miss a few weeks and then found that it became harder to motivate ourselves to write any at all. I'd like to think we'll fill in the gaps (some of them have already been written) but in the meantime I'm going to try to write about week 393 while it's fresh(ish) in my mind.
James and I finished working on Smart Answers on Thursday. Or finished working on Smart Answers at Aviation House, at least. There are a couple of small things we want to finish but we'll do those remotely over the coming week. It's possible we'll be back to help out in future but we haven't agreed to anything yet.
We spent most of our time either preparing for or taking part in a number of handover meetings with various people in the team. These meetings took quite a lot of time away from normal development so I really hope that were useful! This was a slightly different style of handover to what we've done in the past but it felt like a pragmatic approach. Particularly given the amount we wanted to discuss, the number of people involved and the relatively short time in which we had to do it.
We did manage to fit a little bit of development in amongst the various handover meetings. James managed to tidy up a spike of some work that should help the Content Designers work with, and edit the content of, Smart Answers. There was a positive response after demoing it last week so James was keen to finish it so that people could start using it. James also updated our regression test task so that it renders question pages as text instead of html. The content tools development team has recently been joined by a front end designer, Anika. Making this change should hopefully make Anika's life easier as she improves the neglected front end of Smart Answers.
I spent some time pairing with Pablo to finish some refactoring work we'd started on overseas-passports. We'd started the work a week or so ago so it was really good to get it finished before James and I left.
We headed to the Seven Stars for our GFR monthly drinks on Wednesday. It was my first of 2016 (having returned from my travels on the 1st July) and we had an enjoyable evening stood outside in the warm (albeit occasionally a little damp) weather.
I met with Andrew Pavord at FilmFixer on Friday morning (we originally met back in week 336 and have kept in touch since). It was good to catch up and hear how they've been getting on with their software development. It's always interesting talking to Andrew and learning more about the fascinating world of the film industry.
I spent some time talking to our accountant, Paul, on Friday afternoon. We're still trying to get our annual accounts submitted and I'd been tasked with checking the accounts that had been produced. I couldn't quite understand where some of the figures had come from and Paul very patiently answered all my questions and explained how various numbers had been calculated. Paul was particularly good at communicating over the phone: making it easy for me to ensure we were both looking at the same data. This process reminded me of remote pairing in that you need to be much more explicit about what you're doing than when you're sitting next to someone.
I think that's about all for now. Let's see whether this helps unblocks our weeknote backlog!


text:
newlifeoutlook
Rheumatoid Arthritis by the Numbers: Facts and Statistics
Rheumatoid Arthritis Facts and Statistics
Rheumatoid arthritis (RA) is one of the most common forms of arthritis. It can affect anyone of any age or background.
RA affects 1.3 million American adults, this according to the American College of Rheumatology. Worldwide, RA prevalence is up to 1%, this according to the World Health Organization (WHO).
Prevalence of RA
The average onset of RA is between the ages of 30 and 60, but RA can strike at any age. Even children can develop the disease. According to the Mayo Clinic, the lifetime risk of developing RA is 3.6% for women and 1.7% for men.
Women tend to develop RA much earlier in life, during their 30s and 40s. The course of the disease also differs between the genders.
Research shows women report more symptoms than men and their symptoms tend to be worse. Further, women may not respond to treatment as well as men do.
If you are a woman with RA, you are less likely to achieve remission, which is a period where you no longer experience symptoms and pain.
Women with RA may also develop fibromyalgia, which makes RA symptoms even worse. In fact, 5%-20% of people with RA also have fibromyalgia, this according to researchers from The Royal Wolverhampton Hospital, Wolverhampton, United Kingdom.
Researchers think hormones play a role in the development of RA, which may explain as to why more women are affected. Women tend to develop the disease at times when their hormones are unstable, such as after pregnancy or around menopause.
RA in Children and Older Adults
According to the Arthritis Foundation, at least 300,000 children under the age of 16 have arthritis or a rheumatic condition. Just like adult RA, juvenile rheumatoid arthritis (JRA) is caused by the immune system attacking its healthy tissues because it perceives them as foreign invaders.
Researchers believe children with JRA have the same genetic triggers as adults in the development of JRA. Moreover, children with JRA experience some of the same symptoms seen in adult RA.
The prevalence of RA in adults over age 60 is 2%. Treating RA in the elderly population can be challenging.
One of the problems older adults with RA face is sensitivity to RA medications. Taking other medications and having other diseases can also result in drug interactions, medication side effects, and even an advanced form of the disease.
RA Rheumatology Treatment
RA Treatment Therapy
RA Medication Side Effects
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RA does affect certain races and ethnicities more than others – not just in prevalence, but also in disease severity.
One report from Arthritis Research & Therapy finds Native Americans are at the highest risk for developing RA, which is up to 4 times higher than Europeans. Genetic factors are likely to blame for higher incidences related to race and ethnicity.
People of Afro-Caribbean origin are at the lowest for developing RA. In the United States, African Americans, European-Americans and Chinese Americans appear to have lower incidences of RA while those of South African origin tend to have higher RA incidence rates.
One 2013 report in the American Journal of Medicine finds significant differences in disease activity across ethnic and racial groups, with the lowest levels of disease activity in whites. Moreover, remission rates are highest in whites and lowest in African Americans.
Globally, the highest mortality rates associated with RA are in are the African Continent. The countries with the highest rates of RA are in Europe, with Finland having the most cases of RA.
Next page: Learn about the risk factors of RA and what you can do to decrease your risk.
Risk Factors of RA
Experts don't know what causes RA, but research seems to suggest that you are at a higher risk for developing RA if you are:
Genetically disposed to RA
Exposed to harmful chemicals, including smoking
Experienced significant hormonal imbalances
An imbalance of intestinal microbes, resulting from infection or other illness
The genetics involved in the development of RA are complex, but from what researchers know, heritability increases your risk for RA by 60% and a having an HLA gene (one genetic risk factor for RA) increases your risk from 11 to 37%, this according to a 2013 report in Clinical Reviews in Allergy & Immunology.
While having a close family member with RA increases your risk, RA is not an inherited disease, your predisposition to it is.
An exact link between nicotine and RA is unknown, but researchers confirm prolonged smoking can lead to an increased rheumatoid factor, the main antibody (protein) responsible for the development of RA. The presence of a rheumatoid factor indicates your immune system is not functioning properly.
One 2013 study published in Arthritis Research and Therapy finds that even light smoking can increase your risk for RA. Moreover, a woman's risk is doubled by smoking.
If you quit smoking, your chances of developing RA decrease and continue to decrease over time. Smoking is also associated with higher disease activity and quitting can improve symptoms and reduce your risk for complications.
Hormonal Imbalances
The fact more women get RA suggests hormones are at play in the development of the disease. The idea is supported by the idea that RA gets better during pregnancy and worsens following childbirth.
There is also evidence that irregular periods and early menopause may increase a women's risk of developing RA. Researchers also think natural hormone fluctuations, hormone medications, and birth control are additional disease triggers.
Low testosterone levels in men may also increase the risk for the development of RA later in life, this according to researchers from the Lund University in Sweden.
Infections and Microbe Imbalances
In recent years, researchers have been looking at connections between bacterial and viral infections and development of RA. Many believe specific infections may be linked to RA, including chronic hepatitis C and gingivitis.
Moreover, a person's microbes (good and bad microorganisms located throughout the body) may promote the development of RA.
More research is needed to confirm any specific connections between infection, microbes and RA development.
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Disease Severity
The same risk factors for RA also affect the severity of the disease. Doctors access the severity of the disease as mild, moderate or severe.
Your doctor will determine disease severity based on:
How active the disease is
How much functional impairment there is
Any physical damage
There is little research and clinical evidence on disease severity types and prevalence of severity types. It seems, however, the worst cases of RA are in people who have a progressive and more severe form of the disease.
Progressive RA advances and causes persistent inflammation and worsening pain. It requires aggressive treatment and is largely dependent on it the risk factors leading to the development of the disease.
Next page: What are the complications of RA? Continue to learn more about what this means for you.
What Are the Complications of RA?
RA increases your risk for more serious conditions, including heart disease and stroke. In fact, the risk of cardiac death is up 50% higher for people with RA, compared to the rest of the population.
RA patients are also hospitalized at a greater rate than people without RA.
One 2013 report from the Mayo Clinic looked at 799 patients with RA and 797 patients without RA in Olmsted County, Minnesota. The patients with RA experienced 2968 hospitalizations while those without it experienced 2069 hospitalizations.
The RA patients in the Mayo Clinic study were mostly hospitalized for depression and diabetes at much higher rates than patients who had these conditions, but not RA. There were no differences amongst the sexes, specific age groups, or based on the time of the year.
Disease activity appeared to play a role in the higher rates of hospitalization, as people with severe RA tend to have more complications.
RA isn't fatal, but its complications can shorten your life. Infection deaths are more common in people with RA at 36%, compared to the 26% of people without RA, this according to researchers from Helsinki University Central Hospital in Finland.
Disease progress and severity vary from person to person. People with specific disease factors will have a more progressive and severe form of RA, while those that do not have these factors will have a mild to moderate form of the disease.
Many people are living with RA who are in their 80s and 90s, so having RA doesn't necessarily mean you won't have a long life. It means you need to work with your doctor to treat RA aggressively and make healthy lifestyle choices (eating well, exercising, avoiding smoking, etc.) to avoid complications that may affect your quality of life or shorten it.
Current research data shows drug-free remission from RA ranges from 3.6 to 22 %. Certain factors increase your chances of remission, including having a milder form of the disease, early diagnosis, and aggressive treatment.
Men seem to have higher remission rates than women. One study from 2012 reported in Arthritis Care & Research found men have a 38% higher chance of remission than women and can sustain that during the first two years.
What Does All This Mean for You?
Currently, there is no cure for RA. There have been many advances in the last 30 years for treating RA, but none of them will cure you.
The goal of RA treatment is to lower inflammation, reduce pain, prevent joint damage, slow down the disease and prevent complications.
Rheumatoid arthritis facts and statistics are important to understanding how RA works and progresses and apply to groups of people from where these numbers were gathered. They may also be helpful to your doctor in developing a treatment plan.
But you and your RA are unique, and these statistics only offer guidance to many possible scenarios and outcomes. They cannot tell you how you will be affected personally by RA and what your health outcomes will be.
You can improve your outcomes by practicing healthy habits and adhering to your treatment plan. Successful management of RA will enhance your quality of life, reduce pain and symptoms, and promote better emotional and mental health.
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American College of Rheumatology (Prevalence Statistics)
National Institutes of Health (The lifetime risk of adult-onset rheumatoid arthritis and other inflammatory autoimmune rheumatic diseases)
Science Daily (Women with rheumatoid arthritis have significantly higher risk of mortality)
National Institutes of Health (Prevalence of rheumatoid arthritis in persons 60 years of age and older in the United States: effect of different methods of case classification)
Fibromyalgia: Open Access (Fibromyalgia in the Context of Rheumatoid Arthritis: A Review)
National Institutes of Health (Racial and Ethnic Disparities in Disease Activity in Rheumatoid Arthritis Patients)
National Institutes of Health (Risk for rheumatic disease in relation to ethnicity and admixture)
Health Grove (Global Statistics: Rheumatoid Arthritis)
National Institutes of Health (Genetics of Rheumatoid Arthritis — A Comprehensive Review)
National Institutes for Health (Hospitalization Rates and Utilization among Patients with Rheumatoid Arthritis: a Population-Based Study from 1987 to 2012 in Olmsted County, Minnesota)
Arthritis Research & Therapy (Cigarette smoking and risk of rheumatoid arthritis: a dose-response meta-analysis)
Annals of Rheumatic Diseases (Association between testosterone levels and risk of future rheumatoid arthritis in men: a population-based case–control study)
National Institutes of Health (Infectious causes of death in patients with rheumatoid arthritis: an autopsy study)
Arthritis Research & Therapy (Sustained biologic-free and drug-free remission in rheumatoid arthritis, where are we now?)
National Institutes of Health (Significance of Sex in Achieving Sustained Remission in the Consortium of Rheumatology Researchers of North America (CORRONA) Cohort of Rheumatoid Arthritis Patients)
National Institutes for Health (Cardiovascular complications of Rheumatoid Arthritis – Assessment, prevention and treatment)
Lana Barhum
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text:
How Many Logical Channel in LTE ?
The following control logical channels have been defined by the 3GPP:
BCCH, Broadcast Control Channel, used for the transmission of system control information. A UE needs to decode it before requesting a connection.
PCCH, Paging Control Channel, is a downlink channel that transfers paging information and system information change notifications. This channel is used for paging when the network does not know the location cell of the UE.
CCCH, Common Control Channel is a channel for transmitting control information between UEs and network. This channel is used for UEs having no RRC connection with the network.
DCCH, Dedicated Control Channel is a point-to-point bi-directional channel that transmits dedicated control information between a UE and the network. Used by UEs having an RRC connection.
MCCH, Multicast Control Channel is a point-to-multipoint downlink channel used for transmitting MBMS control information from the network to the UE, for one or several MTCHs. This channel is only used by UEs that receive MBMS.
The following traffic logical channels have been defined by the 3GPP:
DTCH, Dedicated Traffic Channel, is a point-to-point channel, dedicated to one UE, for the transfer of user information. A DTCH can exist both in uplink and downlink.
MTCH, Multicast Traffic Channel is a point-to-multipoint downlink channel for transmitting traffic data from the network to the UE. This channel is only used by UEs that receive MBMS.
Complete List at Here :
How MAC Protocol Work In LTE?
Radio Link Control (RLC) protocol services in LTE
State of RRC in LTE
Establishment and Maintenance of the RRC connection in LTE
Radio Resource Connection (RRC) protocol in LTE
From the Transport to the Physical Channel in LTE
DL & UL Physical Channel in LTE
QoS Parameters of LTE
Traffic Operation Overview in LTE
UE categories in LTE
« How Channel Architecture in LTE?
How Transport Channel Work in LTE? »