A Multiscale Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficients

In this paper, we propose a multiscale data-driven stochastic method (MsDSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. This method combines the advantages of the recently developed multiscale model reduction method [M. L. Ci, T. Y. Hou, and Z. Shi, ESAIM Math. Model. Numer. Anal., 48 (2014), pp. 449--474] and the data-driven stochastic method (DSM) [M. L. Cheng et al., SIAM/ASA J. Uncertain. Quantif., 1 (2013), pp. 452--493]. Our method consists of offline and online stages. In the offline stage, we decompose the harmonic coordinate into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Based on the Karhunen--Loève (KL) expansion of the smooth parts and oscillatory parts of the harmonic coordinates, we can derive an effective stochastic equation that can be well-resolved on a coarse grid. We then apply the DSM to the effective stochastic equation to construct a data-driven stochastic basis under which the stochastic solutions enjoy a compact representation for a broad range of forcing functions. In the online stage, we expand the SPDE solution using the data-driven stochastic basis and solve a small number of coupled deterministic partial differential equations (PDEs) to obtain the expansion coefficients. The MsDSM reduces both the stochastic and the physical dimensions of the solution. We have performed complexity analysis which shows that the MsDSM offers considerable savings over not only traditional methods but also DSM in solving multiscale SPDEs. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation

A two-stage mechanism of viral RNA compaction revealed by single molecule fluorescence

Long RNAs often exist as multiple conformers in equilibrium. For the genomes of single-stranded RNA viruses, one of these conformers must include a compacted state allowing the RNA to be confined within the virion. We have used single molecule fluorescence correlation spectroscopy to monitor the conformations of viral genomes and sub-fragments in the absence and presence of coat proteins. Cognate RNA-coat protein interactions in two model viruses cause a rapid collapse in the hydrodynamic radii of their respective RNAs. This is caused by protein binding at multiple sites on the RNA that facilitate additional protein-protein contacts. The collapsed species recruit further coat proteins to complete capsid assembly with great efficiency and fidelity. The specificity in RNA-coat protein interactions seen at single-molecule concentrations reflects the packaging selectivity seen for such viruses in vivo. This contrasts with many in vitro reassembly measurements performed at much higher concentrations. RNA compaction by coat protein or polycation binding are distinct processes, implying that defined RNA-coat protein contacts are required for assembly

Changes in and predictors of length of stay in hospital after surgery for breast cancer between 1997/98 and 2004/05 in two regions of England: a population-based

BACKGROUND Decreases in length of stay (LOS) in hospital after breast cancer surgery can be partly attributed to the change to less radical surgery, but many other factors are operating at the patient, surgeon and hospital levels. This study aimed to describe the changes in and predictors of length of stay (LOS) in hospital after surgery for breast cancer between 1997/98 and 2004/05 in two regions of England. METHODS Cases of female invasive breast cancer diagnosed in two English cancer registry regions were linked to Hospital Episode Statistics data for the period 1st April 1997 to 31st March 2005. A subset of records where women underwent mastectomy or breast conserving surgery (BCS) was extracted (n = 44,877). Variations in LOS over the study period were investigated. A multilevel model with patients clustered within surgical teams and NHS Trusts was used to examine associations between LOS and a range of factors. RESULTS Over the study period the proportion of women having a mastectomy reduced from 58% to 52%. The proportion varied from 14% to 80% according to NHS Trust. LOS decreased by 21% from 1997/98 to 2004/05 (LOSratio = 0.79, 95%CI 0.77-0.80). BCS was associated with 33% shorter hospital stays compared to mastectomy (LOSratio = 0.67, 95%CI 0.66-0.68). Older age, advanced disease, presence of comorbidities, lymph node excision and reconstructive surgery were associated with increased LOS. Significant variation remained amongst Trusts and surgical teams. CONCLUSION The number of days spent in hospital after breast cancer surgery has continued to decline for several decades. The change from mastectomy to BCS accounts for only 9% of the overall decrease in LOS. Other explanations include the adoption of new techniques and practices, such as sentinel lymph node biopsy and early discharge. This study has identified wide variation in practice with substantial cost implications for the NHS. Further work is required to explain this variation

Deletion of the GABAA α2-subunit does not alter self dministration of cocaine or reinstatement of cocaine seeking

Rationale GABAA receptors containing α2-subunits are highly represented in brain areas that are involved in motivation and reward, and have been associated with addiction to several drugs, including cocaine. We have shown previously that a deletion of the α2-subunit results in an absence of sensitisation to cocaine. Objective We investigated the reinforcing properties of cocaine in GABAA α2-subunit knockout (KO) mice using an intravenous self-administration procedure. Methods α2-subunit wildtype (WT), heterozygous (HT) and KO mice were trained to lever press for a 30 % condensed milk solution. After implantation with a jugular catheter, mice were trained to lever press for cocaine (0.5 mg/kg/infusion) during ten daily sessions. Responding was extinguished and the mice tested for cue- and cocaine-primed reinstatement. Separate groups of mice were trained to respond for decreasing doses of cocaine (0.25, 0.125, 0.06 and 0.03 mg/kg). Results No differences were found in acquisition of lever pressing for milk. All genotypes acquired self-administration of cocaine and did not differ in rates of self-administration, dose dependency or reinstatement. However, whilst WT and HT mice showed a dose-dependent increase in lever pressing during the cue presentation, KO mice did not. Conclusions Despite a reported absence of sensitisation, motivation to obtain cocaine remains unchanged in KO and HT mice. Reinstatement of cocaine seeking by cocaine and cocaine-paired cues is also unaffected. We postulate that whilst not directly involved in reward perception, the α2-subunit may be involved in modulating the “energising” aspect of cocaine’s effects on reward-seeking

Memory consolidation in the cerebellar cortex

Several forms of learning, including classical conditioning of the eyeblink, depend upon the cerebellum. In examining mechanisms of eyeblink conditioning in rabbits, reversible inactivations of the control circuitry have begun to dissociate aspects of cerebellar cortical and nuclear function in memory consolidation. It was previously shown that post-training cerebellar cortical, but not nuclear, inactivations with the GABA(A) agonist muscimol prevented consolidation but these findings left open the question as to how final memory storage was partitioned across cortical and nuclear levels. Memory consolidation might be essentially cortical and directly disturbed by actions of the muscimol, or it might be nuclear, and sensitive to the raised excitability of the nuclear neurons following the loss of cortical inhibition. To resolve this question, we simultaneously inactivated cerebellar cortical lobule HVI and the anterior interpositus nucleus of rabbits during the post-training period, so protecting the nuclei from disinhibitory effects of cortical inactivation. Consolidation was impaired by these simultaneous inactivations. Because direct application of muscimol to the nuclei alone has no impact upon consolidation, we can conclude that post-training, consolidation processes and memory storage for eyeblink conditioning have critical cerebellar cortical components. The findings are consistent with a recent model that suggests the distribution of learning-related plasticity across cortical and nuclear levels is task-dependent. There can be transfer to nuclear or brainstem levels for control of high-frequency responses but learning with lower frequency response components, such as in eyeblink conditioning, remains mainly dependent upon cortical memory storage

Gain control network conditions in early sensory coding

Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models

Recurrent Modification of a Conserved Cis-Regulatory Element Underlies Fruit Fly Pigmentation Diversity

The development of morphological traits occurs through the collective action of networks of genes connected at the level of gene expression. As any node in a network may be a target of evolutionary change, the recurrent targeting of the same node would indicate that the path of evolution is biased for the relevant trait and network. Although examples of parallel evolution have implicated recurrent modification of the same gene and cis-regulatory element (CRE), little is known about the mutational and molecular paths of parallel CRE evolution. In Drosophila melanogaster fruit flies, the Bric-à-brac (Bab) transcription factors control the development of a suite of sexually dimorphic traits on the posterior abdomen. Female-specific Bab expression is regulated by the dimorphic element, a CRE that possesses direct inputs from body plan (ABD-B) and sex-determination (DSX) transcription factors. Here, we find that the recurrent evolutionary modification of this CRE underlies both intraspecific and interspecific variation in female pigmentation in the melanogaster species group. By reconstructing the sequence and regulatory activity of the ancestral Drosophila melanogaster dimorphic element, we demonstrate that a handful of mutations were sufficient to create independent CRE alleles with differing activities. Moreover, intraspecific and interspecific dimorphic element evolution proceeded with little to no alterations to the known body plan and sex-determination regulatory linkages. Collectively, our findings represent an example where the paths of evolution appear biased to a specific CRE, and drastic changes in function were accompanied by deep conservation of key regulatory linkages. © 2013 Rogers et al

Morphology and Anatomy of Foliar Nectaries and Associated Leaves in Mallotus (Euphorbiaceae)

The morphology and anatomy of the foliar nectaries and associated leaves offour species of Mallotus (Euphorbiaceae) were studied. Light microscopic observations of paraffin- and plastic-embedded specimens were complemented with scanning electron micrographs. Leaf anatomy of the four species is typical of large mesophytic plants. Aattened foliar nectaries are shown to be composed of specialized epidermal cells. The nonvascularized nectaries consist of narrow columnar cells each with a large nucleus, numerous vacuoles, and dense cytoplasm. Subglandular parenchyma cells have more pronounced nuclei, more vacuoles and denser cytoplasm than do typical laminar parenchyma. Structurally, these nectaries are similar to those found in other taxa of Euphorbiaceae and in other families of flowering plants. Brief field observations confirmed that ants are readily attracted to the nectar and probably function in a mutualistic relationship with the plants. The actual mechanism of nectar secretion was not studied