Monotone and fast computation of Euler’s constant

Abstract We construct sequences of finite sums ( l ˜ n ) n ≥ 0 $(\tilde{l}_{n})_{n\geq 0}$ and ( u ˜ n ) n ≥ 0 $(\tilde{u}_{n})_{n\geq 0}$ converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for 2 γ $2^{\gamma }$ converging in a monotone and fast way at the same time. We use a probabilistic approach based on a differentiation formula for the gamma process

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hat pp$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p$ tends to $0$, and which guarantee that, for any $p$ in $(0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $r$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $r$ tends to infinity when $a=b$.Comment: 4 figure

The TALE Class Homeobox Gene Smed-prep Defines the Anterior Compartment for Head Regeneration

Planaria continue to blossom as a model system for understanding all aspects of regeneration. They provide an opportunity to understand how the replacement of missing tissues from preexisting adult tissue is orchestrated at the molecular level. When amputated along any plane, planaria are capable of regenerating all missing tissue and rescaling all structures to the new size of the animal. Recently, rapid progress has been made in understanding the developmental pathways that control planarian regeneration. In particular Wnt/beta-catenin signaling is central in promoting posterior fates and inhibiting anterior identity. Currently the mechanisms that actively promote anterior identity remain unknown. Here, Smed-prep, encoding a TALE class homeodomain, is described as the first gene necessary for correct anterior fate and patterning during planarian regeneration. Smed-prep is expressed at high levels in the anterior portion of whole animals, and Smed-prep(RNAi) leads to loss of the whole brain during anterior regeneration, but not during lateral regeneration or homeostasis in intact worms. Expression of markers of different anterior fated cells are greatly reduced or lost in Smed-prep(RNAi) animals. We find that the ectopic anterior structures induced by abrogation of Wnt signaling also require Smed-prep to form. We use double knockdown experiments with the S. mediterranea ortholog of nou-darake (that when knocked down induces ectopic brain formation) to show that Smed-prep defines an anterior fated compartment within which stem cells are permitted to assume brain fate, but is not required directly for this differentiation process. Smed-prep is the first gene clearly implicated as being necessary for promoting anterior fate and the first homeobox gene implicated in establishing positional identity during regeneration. Together our results suggest that Smed-prep is required in stem cell progeny as they form the anterior regenerative blastema and is required for specifying anterior cell fates and correct patterning

Evagination of Cells Controls Bio-Silica Formation and Maturation during Spicule Formation in Sponges

The enzymatic-silicatein mediated formation of the skeletal elements, the spicules of siliceous sponges starts intracellularly and is completed extracellularly. With Suberites domuncula we show that the axial growth of the spicules proceeds in three phases: (I) formation of an axial canal; (II) evagination of a cell process into the axial canal, and (III) assembly of the axial filament composed of silicatein. During these phases the core part of the spicule is synthesized. Silicatein and its substrate silicate are stored in silicasomes, found both inside and outside of the cellular extension within the axial canal, as well as all around the spicule. The membranes of the silicasomes are interspersed by pores of ≈2 nm that are likely associated with aquaporin channels which are implicated in the hardening of the initial bio-silica products formed by silicatein. We can summarize the sequence of events that govern spicule formation as follows: differential genetic readout (of silicatein) → fractal association of the silicateins → evagination of cells by hydro-mechanical forces into the axial canal → and finally processive bio-silica polycondensation around the axial canal. We termed this process, occurring sequentially or in parallel, bio-inorganic self-organization

The activation of eco-driving mental models: can text messages prime drivers to use their existing knowledge and skills?

Eco-driving campaigns have traditionally assumed that drivers lack the necessary knowledge and skills and that this is something that needs rectifying. Therefore, many support systems have been designed to closely guide drivers and fine-tune their proficiency. However, research suggests that drivers already possess a substantial amount of the necessary knowledge and skills regarding eco-driving. In previous studies, participants used these effectively when they were explicitly asked to drive fuel-efficiently. In contrast, they used their safe driving skills when they were instructed to drive as they would normally. Hence, it is assumed that many drivers choose not to engage purposefully in eco-driving in their everyday lives. The aim of the current study was to investigate the effect of simple, periodic text messages (nine messages in 2 weeks) on drivers’ eco- and safe driving performance. It was hypothesised that provision of eco-driving primes and advice would encourage the activation of their eco-driving mental models and that comparable safety primes increase driving safety. For this purpose, a driving simulator experiment was conducted. All participants performed a pre-test drive and were then randomly divided into four groups, which received different interventions. For a period of 2 weeks, one group received text messages with eco-driving primes and another group received safety primes. A third group received advice messages on how to eco-drive. The fourth group were instructed by the experimenter to drive fuel-efficiently, immediately before driving, with no text message intervention. A post-test drive measured behavioural changes in scenarios deemed relevant to eco- and safe driving. The results suggest that the eco-driving prime and advice text messages did not have the desired effect. In comparison, asking drivers to drive fuel-efficiently led to eco-driving behaviours. These outcomes demonstrate the difficulty in changing ingrained habits. Future research is needed to strengthen such messages or activate existing knowledge and skills in other ways, so driver behaviour can be changed in cost-efficient ways

Modeling Planarian Regeneration: A Primer for Reverse-Engineering the Worm

A mechanistic understanding of robust self-assembly and repair capabilities of complex systems would have enormous implications for basic evolutionary developmental biology as well as for transformative applications in regenerative biomedicine and the engineering of highly fault-tolerant cybernetic systems. Molecular biologists are working to identify the pathways underlying the remarkable regenerative abilities of model species that perfectly regenerate limbs, brains, and other complex body parts. However, a profound disconnect remains between the deluge of high-resolution genetic and protein data on pathways required for regeneration, and the desired spatial, algorithmic models that show how self-monitoring and growth control arise from the synthesis of cellular activities. This barrier to progress in the understanding of morphogenetic controls may be breached by powerful techniques from the computational sciences—using non-traditional modeling approaches to reverse-engineer systems such as planaria: flatworms with a complex bodyplan and nervous system that are able to regenerate any body part after traumatic injury. Currently, the involvement of experts from outside of molecular genetics is hampered by the specialist literature of molecular developmental biology: impactful collaborations across such different fields require that review literature be available that presents the key functional capabilities of important biological model systems while abstracting away from the often irrelevant and confusing details of specific genes and proteins. To facilitate modeling efforts by computer scientists, physicists, engineers, and mathematicians, we present a different kind of review of planarian regeneration. Focusing on the main patterning properties of this system, we review what is known about the signal exchanges that occur during regenerative repair in planaria and the cellular mechanisms that are thought to underlie them. By establishing an engineering-like style for reviews of the molecular developmental biology of biomedically important model systems, significant fresh insights and quantitative computational models will be developed by new collaborations between biology and the information sciences

Serotonin synthesis, release and reuptake in terminals: a mathematical model

<p>Abstract</p> <p>Background</p> <p>Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system.</p> <p>Methods</p> <p>We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data.</p> <p>Results</p> <p>We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct <it>in silico </it>experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine.</p> <p>Conclusions</p> <p>Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.</p