On nonlinear models of markets with finite liquidity: Some cautionary notes

The recent financial crisis and related liquidity issues have illuminated an urgent need for a better understanding of the effects of limited liquidity on all aspects of the financial system. This paper considers such effects on the Black-Scholes-Merton financial model, which for the most part result in highly nonlinear partial differential equations (PDEs). We investigate in detail a model studied by Schönbucher and Wilmott (2000) which incorporates the price impact of option hedging strategies. First, we consider a first-order feedback model, which leads to the exceptional case of a linear PDE. Numerical results, and more particularly an asymptotic approach close to option expiry, reveal subtle differences from the Black-Scholes-Merton model. Second, we go on to consider a full-feedback model in which price impact is fully incorporated into the model. Here, standard numerical techniques lead to spurious results in even the simplest cases. An asymptotic approach, valid close to expiry, is mounted, and a robust numerical procedure, valid for all times, is developed, revealing two distinct classes of behavior. The first may be attributed to the infinite second derivative associated with standard option payoff conditions, for which it is necessary to admit solutions with discontinuous first derivatives; perhaps even more disturbingly, negative option values are a frequent occurrence. The second failure (applicable to smoothed payoff functions) is caused by a singularity in the coefficient of the diffusion term in the option-pricing equation. Our conclusion is that several classes of model in the literature involving permanent price impact irretrievably break down (i.e., there is insufficient "financial modeling" in the pricing equation). Our analysis should provide the information necessary to avoid such pitfalls in the future. © 2010 Society for Industrial and Applied Mathematics

Unique Changes in Mitochondrial Genomes Associated with Reversions of S-Type Cytoplasmic Male Sterility in Maizemar

Cytoplasmic male sterility (CMS) in plants is usually associated with the expression of specific chimeric regions within rearranged mitochondrial genomes. Maize CMS-S plants express high amounts of a 1.6-kb mitochondrial RNA during microspore maturation, which is associated with the observed pollen abortion. This transcript carries two chimeric open reading frames, orf355 and orf77, both unique to CMS-S. CMS-S mitochondria also contain free linear DNA plasmids bearing terminal inverted repeats (TIRs). These TIRs recombine with TIR-homologous sequences that precede orf355/orf77 within the main mitochondrial genome to produce linear ends. Transcription of the 1.6-kb RNA is initiated from a promoter within the TIRs only when they are at linear ends. Reversions of CMS-S to fertility occur in certain nuclear backgrounds and are usually associated with loss of the S plasmids and/or the sterility-associated region. We describe an unusual set of independently recovered revertants from a single maternal lineage that retain both the S plasmids and an intact orf355/orf77 region but which do not produce the 1.6-kb RNA. A 7.3-kb inversion resulting from illegitmate recombination between 14-bp microrepeats has separated the genomic TIR sequences from the CMS-associated region. Although RNAs containing orf355/orf77 can still be detected in the revertants, they are not highly expressed during pollen development and they are no longer initiated from the TIR promoter at a protein-stabilized linear end. They appear instead to be co-transcribed with cytochrome oxidase subunit 2. The 7.3-kb inversion was not detected in CMS-S or in other fertile revertants. Therefore, this inversion appears to be a de novo mutation that has continued to sort out within a single maternal lineage, giving rise to fertile progeny in successive generations

‘It's good to talk’ – judicial allocation decision making and the Family Court

This article focuses on the opportunities and potential benefits of collaborative judicial working and social processes within the new Family Court. To illustrate this, findings from a recent evaluation by the authors of the Greater Manchester Gatekeeping and Allocation – Care Proceedings Pilot (the Manchester Pilot) will be presented. In the Manchester Pilot, the allocation of care cases to a particular level of court became a collaborative judicial decision, to be achieved through consensual decision making. The social processes of face-to-face communication, negotiation, knowing and learning from each other in this new procedure, provide the main area of analysis in this article. Findings from our evaluation illustrate issues and opportunities for the lower courts under the new allocation arrangements within the Family Court, and may in some respects reflect aspects of other research of social processes such as Paterson's studies in the appellate courts

Erratum: Correction: Kujawski et al. Autonomic and Cognitive Function Response to Normobaric Hyperoxia Exposure in Healthy Subjects. Preliminary Study. Medicina 2020, 56, 172 (Medicina (Kaunas, Lithuania) (2020) 56 4 PII: 255)

There was an error in the original publication [...]

Predictive feedback control and Fitts' law

Fitts’ law is a well established empirical formula, known for encapsulating the “speed-accuracy trade-off”. For discrete, manual movements from a starting location to a target, Fitts’ law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts’ law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts’ law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed-loop response can be separated into a time delay and rational function whereas a non- predictive controller retains a state delay within feedback loop which is not consistent with Fitts’ law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts’ law. However, such high-order, “non-parametric” controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts’ law. The implication is that prediction is an inherent part of the “speed-accuracy trade-off”

Biomechanical properties of a buzz-pollinated flower

Approximately half of all bee species use vibrations to remove pollen from plants with diverse floral morphologies. In many buzz-pollinated flowers, these mechanical vibrations generated by bees are transmitted through floral tissues, principally pollen-containing anthers, causing pollen to be ejected from small openings (pores or slits) at the tip of the stamen. Despite the importance of substrate-borne vibrations for both bees and plants, few studies to date have characterised the transmission properties of floral vibrations. In this study, we use contactless laser vibrometry to evaluate the transmission of vibrations in the corolla and anthers of buzz- pollinated flowers of Solanum rostratum, and measured vibrations in three spatial axes. We found that floral vibrations conserve their dominant frequency (300Hz) as they are transmitted throughout the flower. We also found that vibration amplitude at anthers and petals can be up to >400% higher than input amplitude applied at the receptacle at the base of the flowe , and that anthers vibrate with a higher amplitude velocity than petals. Together, these results suggest that vibrations travel differently through floral structures and across different spatial axes. As pollen release is a function of vibration amplitude, we conjecture that bees might benefit from applying vibrations in the axes associated with higher vibration amplification

The interpretative value of transformed tephra sequences

Financial support was provided by the National Science Foundation of America through grants 1202692 and 1249313, the Carnegie Trust for the Universities of Scotland through a grant to RTS, and the NERC Doctoral Training Partnership PhD studentship NE/L002558/1 to PT.We explore developments in tephra science that consider more than chronology, using case studies. Volcanic processes and prevailing weather conditions determine the distribution of tephra deposits immediately after an eruption, but as these freshly fallen tephra become part of the stratigraphic record, the thickness, morphology and definition of the layers they form changes, reflecting the interplay of the tephra, Earth surface processes, topography and vegetation structure, plus direct or indirect modification caused by people and animals. Once part of the stratigraphic record, further diagnostic changes can happen to the morphology of tephra layers, such as the creation of over folds by cryoturbation. Thus, tephra layers may contain proxy evidence of both past surface environments and subsurface processes. Transformations of tephra deposits can complicate the reconstruction of past volcanic processes and make the application of classical tephrochronology as pioneered by Thorarinsson (Sigurður Þórarinsson in Icelandic) challenging. However, as Thorarinsson also noted, novel sources of environmental data can exist within transformed tephra sequences that include the spread or removal of tephra, variations in layer thickness and internal structures, the nature of contact surfaces and the orientation of layers.PostprintPeer reviewe

The role for osmotic agents in children with acute encephalopathies: a systematic review

Background: Raised intracranial pressure (ICP) is known to complicate both traumatic and non-traumatic encephalopathies. It impairs cerebral perfusion and may cause death due to global ischaemia and intracranial herniation. Osmotic agents are widely used to control ICP. In children, guidelines for their use are mainly guided by adult studies. We conducted this review to determine the current evidence of the effectiveness of osmotic agents and their effect on resolution of coma and outcome in children with acute encephalopathy.Methods: We searched several databases for published and unpublished studies in English and French languages, between January 1966 and March 2009. We considered studies on the use of osmotic agents in children aged between 0 and 16 years with acute encephalopathies. We examined reduction in intracranial pressure, time to resolution of coma, and occurrence of neurological sequelae and death.Results: We identified four randomized controlled trials, three prospective studies, two retrospective studies and one case report. Hypertonic saline (HS) achieved greater reduction in intracranial pressure (ICP) compared to mannitol and other fluids; normal saline or ringer's lactate. This effect was sustained for longer when it was given as continuous infusion. Boluses of glycerol and mannitol achieved transient reduction in ICP. Oral glycerol was associated with lower mortality and neurological sequelae when compared to placebo in children with acute bacterial meningitis. HS was associated with lower mortality when compared to mannitol in children with non-traumatic encephalopathies.Conclusion: HS appears to achieve a greater reduction in ICP than other osmotic agents. Oral glycerol seems to improve outcome among children with acute bacterial meningitis. A sustained reduction in ICP is desirable and could be achieved by modifying the modes and rates of administration of these osmotic agents, but these factors need further investigation

Trading or coercion? Variation in male mating strategies between two communities of East African chimpanzees

Across taxa, males employ a variety of mating strategies, including sexual coercion and the provision, or trading, of resources. Biological Market theory (BMT) predicts that trading of commodities for mating opportunities should exist only when males cannot monopolise access to females and/or obtain mating by force, in situations where power differentials between males are low; both coercion and trading have been reported for chimpanzees (Pan troglodytes). Here, we investigate whether the choice of strategy depends on the variation in male power differentials, using data from two wild communities of East African chimpanzees (P.t. schweinfurthii): the structurally despotic Sonso community (Budongo, Uganda) and the structurally egalitarian M-group (Mahale, Tanzania). We found evidence of sexual coercion by male Sonso chimpanzees, and of trading—of grooming for mating—by M-group males; females traded sex for neither meat nor protection from male aggression. Our results suggest that the despotism–egalitarian axis influences strategy choice: male chimpanzees appear to pursue sexual coercion when power differentials are large and trading when power differentials are small and coercion consequently ineffective. Our findings demonstrate that trading and coercive strategies are not restricted to particular chimpanzee subspecies; instead, their occurrence is consistent with BMT predictions. Our study raises interesting, and as yet unanswered, questions regarding female chimpanzees’ willingness to trade sex for grooming, if doing so represents a compromise to their fundamentally promiscuous mating strategy. It highlights the importance of within-species cross-group comparisons and the need for further study of the relationship between mating strategy and dominance steepness

Threat-sensitive anti-predator defence in precocial wader, the northern lapwing Vanellus vanellus

Birds exhibit various forms of anti-predator behaviours to avoid reproductive failure, with mobbing—observation, approach and usually harassment of a predator—being one of the most commonly observed. Here, we investigate patterns of temporal variation in the mobbing response exhibited by a precocial species, the northern lapwing (Vanellus vanellus). We test whether brood age and self-reliance, or the perceived risk posed by various predators, affect mobbing response of lapwings. We quantified aggressive interactions between lapwings and their natural avian predators and used generalized additive models to test how timing and predator species identity are related to the mobbing response of lapwings. Lapwings diversified mobbing response within the breeding season and depending on predator species. Raven Corvus corax, hooded crow Corvus cornix and harriers evoked the strongest response, while common buzzard Buteo buteo, white stork Ciconia ciconia, black-headed gull Chroicocephalus ridibundus and rook Corvus frugilegus were less frequently attacked. Lapwings increased their mobbing response against raven, common buzzard, white stork and rook throughout the breeding season, while defence against hooded crow, harriers and black-headed gull did not exhibit clear temporal patterns. Mobbing behaviour of lapwings apparently constitutes a flexible anti-predator strategy. The anti-predator response depends on predator species, which may suggest that lapwings distinguish between predator types and match mobbing response to the perceived hazard at different stages of the breeding cycle. We conclude that a single species may exhibit various patterns of temporal variation in anti-predator defence, which may correspond with various hypotheses derived from parental investment theory