Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

Tracking planar orientations of active MRI needles

Purpose: To determine and track the planar orientation of active interventional devices without using localizing RF microcoils. Materials and Methods: An image-based tracking method that determines a device's orientation using projection images was developed. An automated and a manual detection scheme were implemented. The method was demonstrated in an in vivo mesocaval puncture procedure in swine, which required accurate orientation of an active transvascular needle catheter. Results: The plane of the catheter was determined using two projection images. The scan plane was adjusted automatically to follow the catheter plane, and its orientation with respect to a previously acquired target plane was displayed. The algorithm facilitated navigation for a fast and accurate puncture. Conclusion: Using image-based techniques, with no mechanical design changes, the orientation of an active intravascular probe could be tracked. © 2007 Wiley-Liss, Inc

Magnetic control of large room-temperature polarization

Numerous authors have referred to room-temperature magnetic switching of large electric polarizations as The Holy Grail of magnetoelectricity.We report this long-sought effect using a new physical process of coupling between magnetic and ferroelectric relaxor nano-regions. Here we report magnetic switching between the normal ferroelectric state and the ferroelectric relaxor state. This gives both a new room-temperature, single-phase, multiferroic magnetoelectric, PbZr0.46Ti0.34Fe0.13W0.07O3, with polarization, loss (<4%), and resistivity (typically 108 -109 ohm.cm) equal to or superior to BiFeO3, and also a new and very large magnetoelectric effect: switching not from +Pr to negative Pr with applied H, but from Pr to zero with applied H of less than a Tesla. This switching of the polarization occurs not because of a conventional magnetically induced phase transition, but because of dynamic effects: Increasing H lengthens the relaxation time by x500 from 100 ?s, and it couples strongly the polarization relaxation and spin relaxations. The diverging polarization relaxation time accurately fits a modified Vogel-Fulcher Equation in which the freezing temperature Tf is replaced by a critical freezing field Hf that is 0.92 positive/negative 0.07 Tesla. This field dependence and the critical field Hc are derived analytically from the spherical random bond random field (SRBRF) model with no adjustable parameters and an E2H2 coupling. This device permits 3-state logic (+Pr,0,negative Pr) and a condenser with >5000% magnetic field change in its capacitance.Comment: 20 pages, 5 figure

Orexin receptors exert a neuroprotective effect in Alzheimer's disease (AD) via heterodimerization with GPR103

Orexins are neuropeptides that regulate the sleep-wake cycle and feeding behaviour. QRFP is a newly discovered neuropeptide which exerts similar orexigenic activity, thus playing an important role in energy homeostasis and regulation of appetite. The exact expression and signalling characteristics and physiological actions of QRFP and its receptor GPR103 are poorly understood. Alzheimerâ €™ s disease (AD) patients experience increased nocturnal activity, excessive daytime sleepiness, and weight loss. We hypothesised therefore that orexins and QRFP might be implicated in the pathophysiology of AD. We report that the down-regulation of hippocampal orexin receptors (OXRs) and GPR103 particularly in the cornu ammonis (CA) subfield from AD patients suffering from early onset familial AD (EOFAD) and late onset familial AD (LOAD). Using an in vitro model we demonstrate that this downregulation is due to to Aβ-plaque formation and tau hyper-phosphorylation. Transcriptomics revealed a neuroprotective role for both orexins and QRFP. Finally we provide conclusive evidence using BRET and FRET that OXRs and GPR103 form functional hetero-dimers to exert their effects involving activation of ERK 1/2. Pharmacological intervention directed at the orexigenic system may prove to be an attractive avenue towards the discovery of novel therapeutics for diseases such as AD and improving neuroprotective signalling pathways

Distortions of Subjective Time Perception Within and Across Senses

Background: The ability to estimate the passage of time is of fundamental importance for perceptual and cognitive processes. One experience of time is the perception of duration, which is not isomorphic to physical duration and can be distorted by a number of factors. Yet, the critical features generating these perceptual shifts in subjective duration are not understood. Methodology/Findings: We used prospective duration judgments within and across sensory modalities to examine the effect of stimulus predictability and feature change on the perception of duration. First, we found robust distortions of perceived duration in auditory, visual and auditory-visual presentations despite the predictability of the feature changes in the stimuli. For example, a looming disc embedded in a series of steady discs led to time dilation, whereas a steady disc embedded in a series of looming discs led to time compression. Second, we addressed whether visual (auditory) inputs could alter the perception of duration of auditory (visual) inputs. When participants were presented with incongruent audio-visual stimuli, the perceived duration of auditory events could be shortened or lengthened by the presence of conflicting visual information; however, the perceived duration of visual events was seldom distorted by the presence of auditory information and was never perceived shorter than their actual durations. Conclusions/Significance: These results support the existence of multisensory interactions in the perception of duration and, importantly, suggest that vision can modify auditory temporal perception in a pure timing task. Insofar as distortions in subjective duration can neither be accounted for by the unpredictability of an auditory, visual or auditory-visual event, we propose that it is the intrinsic features of the stimulus that critically affect subjective time distortions

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

A one-stop perineal clinic: our eleven-year experience.

INTRODUCTION AND HYPOTHESIS: The perineal clinic is a dedicated setting offering assessment for various childbirth-related presentations including obstetric anal sphincter injuries (OASIs), perineal wound complications, pelvic floor dysfunction and other conditions such as female genital mutilation(FGM). We describe the clinical presentation and outcomes of women from a tertiary perineal clinic based on data collected over an 11-year period. METHODS: This is a retrospective observational study. A one-stop outpatient service was offered to all women who sustained OASIs (postnatally and antenatally in a subsequent pregnancy), perineal complications (within 16 weeks postpartum), FGM and/or peripartum symptoms of urinary/anal incontinence or prolapse. Assessment included history with validated questionnaires, examination and anal manometry and endoanal ultrasound when appropriate. Outcomes were compared among different grades of OASIs. Management of each type of presentation was reported with outcomes. RESULTS: There were 3254 first attendance episodes between 2006 and 2016. The majority (58.1%) were for OASIs, followed by perineal wound complications. Compared to the lower grades, the higher grades of OASI were associated with poorer outcomes in terms of symptoms, investigations and complications. Women with OASIs had unrelated symptoms such as urinary incontinence, perineal pain and wound infections that needed further intervention. A high proportion(42%) of wound complications required further specialist management. CONCLUSION: We describe a dedicated, one-stop perineal clinic model for antenatal and postnatal women for management of perineal and pelvic floor disorders. This comprehensive and novel data will enable clinicians to better counsel women regarding of outcomes after OASI and focus training to minimize risks of morbidities

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe