Finding and verifying all solutions of a system of nonlinear equations using public domain software: Working paper series--02-14

Economic models are often stated as systems of nonlinear equations, for example general equilibrium models, game theory models, and macroeconomic models. The existence and uniqueness of solutions to the model are critical issues. Interval arithmetic is an arithmetic that operates on interval values rather than point values. It can be used to find all solutions of a system of nonlinear equations over a specified region and to determine if a solution is unique. We present arguments demonstrating that this arithmetic is capable of determining existence and uniqueness. We then use a public domain software package to find all roots of several simple economic example problems

Uniform Diagonalization Theorem for Complexity Classes of Promise Problems including Randomized and Quantum Classes

Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform Diagonalization Theorem allows the construction of problems outside complexity classes while still being reducible to a specific decision problem. This paper provides a generalization of the Uniform Diagonalization Theorem by extending it to promise problems and the complexity classes they form, e.g. randomized and quantum complexity classes. The theorem requires from the underlying computing model not only the decidability of its acceptance and rejection behaviour but also of its promise-contradicting indifferent behaviour - a property that we will introduce as "total decidability" of promise problems. Implications of the Uniform Diagonalization Theorem are mainly of two kinds: 1. Existence of intermediate problems (e.g. between BQP and QMA) - also known as Ladner's Theorem - and 2. Undecidability if a problem of a complexity class is contained in a subclass (e.g. membership of a QMA-problem in BQP). Like the original Uniform Diagonalization Theorem the extension applies besides BQP and QMA to a large variety of complexity class pairs, including combinations from deterministic, randomized and quantum classes.Comment: 15 page

The Role of Legal Services in the Antipoverty Program

Large-scale adaptive radiations might explain the runaway success of a minority of extant vertebrate clades. This hypothesis predicts, among other things, rapid rates of morphological evolution during the early history of major groups, as lineages invade disparate ecological niches. However, few studies of adaptive radiation have included deep time data, so the links between extant diversity and major extinct radiations are unclear. The intensively studied Mesozoic dinosaur record provides a model system for such investigation, representing an ecologically diverse group that dominated terrestrial ecosystems for 170 million years. Furthermore, with 10,000 species, extant dinosaurs (birds) are the most speciose living tetrapod clade. We assembled composite trees of 614-622 Mesozoic dinosaurs/birds, and a comprehensive body mass dataset using the scaling relationship of limb bone robustness. Maximum-likelihood modelling and the node height test reveal rapid evolutionary rates and a predominance of rapid shifts among size classes in early (Triassic) dinosaurs. This indicates an early burst niche-filling pattern and contrasts with previous studies that favoured gradualistic rates. Subsequently, rates declined in most lineages, which rarely exploited new ecological niches. However, feathered maniraptoran dinosaurs (including Mesozoic birds) sustained rapid evolution from at least the Middle Jurassic, suggesting that these taxa evaded the effects of niche saturation. This indicates that a long evolutionary history of continuing ecological innovation paved the way for a second great radiation of dinosaurs, in birds. We therefore demonstrate links between the predominantly extinct deep time adaptive radiation of non-avian dinosaurs and the phenomenal diversification of birds, via continuing rapid rates of evolution along the phylogenetic stem lineage. This raises the possibility that the uneven distribution of biodiversity results not just from large-scale extrapolation of the process of adaptive radiation in a few extant clades, but also from the maintenance of evolvability on vast time scales across the history of life, in key lineages

Active tuning of high-Q dielectric metasurfaces

We demonstrate the active tuning of all-dielectric metasurfaces exhibiting high-quality factor (high-Q) resonances. The active control is provided by embedding the asymmetric silicon meta-atoms with liquid crystals, which allows the relative index of refraction to be controlled through heating. It is found that high quality factor resonances ($Q=270\pm30$) can be tuned over more than three resonance widths. Our results demonstrate the feasibility of using all-dielectric metasurfaces to construct tunable narrow-band filters.Comment: 4 pages, 6 figure

effect of calcipotriol on etanercept partial responder psoriasis vulgaris and psoriatic arthritis patients

Patients who respond only partially to etanercept may require additional treatments that act synergistically to improve their therapeutic response while at the same time reducing the dose required and the risk of side-effects. The aim of this study was to evaluate the effectiveness of topical calcipotriol in etanercept partial responder patients. We enrolled 120 patients affected by psoriasis vulgaris and psoriatic arthritis. A 50 mg dose of etanercept was administered twice weekly for the first 12 weeks, followed by a 25 mg dose twice weekly for an additional 12 weeks. At week 12, for 45 patients who had not achieved PASI 50, calcipotriol cream was also prescribed twice daily for 4 weeks and then once daily for a further 8 weeks. At week 24, of the 45 patients in the group treated with etanercept plus calcipotriol,14 (31.1%) had achieved PASI 75, and 23 PASI 50, while 8 (17.7%) had dropped out of therapy; of the 75 patients who continued etanercept in monotherapy with a 25 mg dose twice weekly for another 12 weeks, 71 (94.6%) had achieved PASI 50 and 57 (76.0%) PASI 75. The application of calcipotriol in etanercept partial responder patients had therefore helped 37 out of 120 patients (31 %) achieve at least PASI 50. This is the first report about the controlled combination of topical calcipotriol and etanercept in a large group of psoriatic patients. The efficacy and cost-effectiveness of the combined treatment is evidenced by the good response shown at week 24 by a group of etanercept low-responder patients using drugs sparingly and limiting likely toxicity

Real-time optical manipulation of cardiac conduction in intact hearts

Optogenetics has provided new insights in cardiovascular research, leading to new methods for cardiac pacing, resynchronization therapy and cardioversion. Although these interventions have clearly demonstrated the feasibility of cardiac manipulation, current optical stimulation strategies do not take into account cardiac wave dynamics in real time. Here, we developed an all‐optical platform complemented by integrated, newly developed software to monitor and control electrical activity in intact mouse hearts. The system combined a wide‐field mesoscope with a digital projector for optogenetic activation. Cardiac functionality could be manipulated either in free‐run mode with submillisecond temporal resolution or in a closed‐loop fashion: a tailored hardware and software platform allowed real‐time intervention capable of reacting within 2 ms. The methodology was applied to restore normal electrical activity after atrioventricular block, by triggering the ventricle in response to optically mapped atrial activity with appropriate timing. Real‐time intraventricular manipulation of the propagating electrical wavefront was also demonstrated, opening the prospect for real‐time resynchronization therapy and cardiac defibrillation. Furthermore, the closed‐loop approach was applied to simulate a re‐entrant circuit across the ventricle demonstrating the capability of our system to manipulate heart conduction with high versatility even in arrhythmogenic conditions. The development of this innovative optical methodology provides the first proof‐of‐concept that a real‐time optically based stimulation can control cardiac rhythm in normal and abnormal conditions, promising a new approach for the investigation of the (patho)physiology of the heart

A three-dimensional approach to visualize pairwise morphological variation and its application to fragmentary palaeontological specimens

Classifying isolated vertebrate bones to a high level of taxonomic precision can be difficult. Many of Australia's Cretaceous terrestrial vertebrate fossil-bearing deposits, for example, produce large numbers of isolated bones and very few associated or articulated skeletons. Identifying these often fragmentary remains beyond high-level taxonomic ranks, such as Ornithopoda or Theropoda, is difficult and those classified to lower taxonomic levels are often debated. The ever-increasing accessibility to 3D-based comparative techniques has allowed palaeontologists to undertake a variety of shape analyses, such as geometric morphometrics, that although powerful and often ideal, require the recognition of diagnostic landmarks and the generation of sufficiently large data sets to detect clusters and accurately describe major components of morphological variation. As a result, such approaches are often outside the scope of basic palaeontological research that aims to simply identify fragmentary specimens. Herein we present a workflow in which pairwise comparisons between fragmentary fossils and better known exemplars are digitally achieved through three-dimensional mapping of their surface profiles and the iterative closest point (ICP) algorithm. To showcase this methodology, we compared a fragmentary theropod ungual (NMV P186153) from Victoria, Australia, identified as a neovenatorid, with the manual unguals of the megaraptoran Australovenator wintonensis (AODF604). We discovered that NMV P186153 was a near identical match to AODF604 manual ungual II-3, differing only in size, which, given their 10–15Ma age difference, suggests stasis in megaraptoran ungual morphology throughout this interval. Although useful, our approach is not free of subjectivity; care must be taken to eliminate the effects of broken and incomplete surfaces and identify the human errors incurred during scaling, such as through replication. Nevertheless, this approach will help to evaluate and identify fragmentary remains, adding a quantitative perspective to an otherwise qualitative endeavour

Basal cell carcinoma: A comprehensive review

Basal cell carcinoma (BCC) is the most common type of carcinoma worldwide. BCC development is the result of a complex interaction between environmental, phenotypic and genetic factors. However, despite the progress in the field, BCC biology and mechanisms of resistance against systemic treatments have been poorly investigated. The aim of the present review is to provide a revision of BCC histological and molecular features, including microRNA (miRNA) dysregulation, with a specific focus on the molecular basis of BCC systemic therapies. Papers from the last ten years regarding BCC genetic and phenotypic alterations, as well as the mechanism of resistance against hedgehog pathway inhibitors vismodegib and sonidegib were included. The involvement of miRNAs in BCC resistance to systemic therapies is emerging as a new field of knowledge