Nice Algorithm Research Articles

Order-Independent Algorithm for the Asymptotic Stability of Complex Polynomials

The Extended Routh Array (ERA) settles the asymptotic stability of complex polynomials. The ERA is a natural extension of the Routh Array which applies only to real polynomials. Although the ERA is a nice theoretical algorithm for stability testing, it has its limitations. Unfortunately, as the order of the polynomial increases, the size of calculations increases dramatically as will be shown below. In the current work, we offer an alternative algorithm which is basically equivalent to the ERA, but has the extra advantage of being simpler, more efficient, and easy to apply even to large order polynomials. In all the steps required in the construction of the new algorithm, only one single and simple algebraic operation is needed, which makes it a polynomial order-independent algorithm.

On detectability of probabilistic Boolean networks

This paper devotes to introducing and investigating the detectability of probabilistic Boolean networks (PBNs). Two types of detectability, weak detectability and strong detectability, are proposed to deal with different situations. Firstly, by resorting to the semi-tensor product (STP) of matrices, the equivalent algebraic expression of the PBN is converted into another kind of expression, which is called the data form. This data form can estimate the current state distribution from the corresponding output sequence. Then, using this data form constructs the detection form, based on which, two necessary and sufficient conditions are derived for checking weak detectability and strong detectability. Secondly, combining the STP and this detection form, a nice algorithm is established for checking wether a PBN is weak detectability. Finally, for better presentation, two numerical examples are shown to demonstrate the effectiveness of the theoretical results, and the diagnosis of tuberculosis is briefly analyzed.

A Large Set of Torus Obstructions and How They Were Discovered

We outline the progress made so far on the search for the complete set of torus obstructions and also consider practical algorithms for torus embedding and their implementations. We present the set of obstructions that are known to-date and give a brief history of how these graphs were found. We also describe a nice algorithm for embedding graphs on the torus which we used to verify previous results and add to the set of torus obstructions. Although it is still exponential in the order of the graph, the algorithm presented here is relatively simple to describe and implement and fast-in-practice for small graphs.It parallels the popular quadratic planar embedding algorithm of Demoucron, Malgrange, and Pertuiset.

A key distribution scheme for secure communication in acoustic sensor networks

Cryptographic key distribution is always a major problem in large scale wireless communications such as Acoustic Sensor Networks (ASNs) based on wireless sensors in an Internet of Things (IoT) environment. Because of the resource constraints of the nodes in such networks, the traditional cryptographic primitives are not suitable solutions. Our endeavor in this paper is to develop a new deterministic key distribution mechanism for such networks. In particular, we bring in a novel construction methodology from two-dimensional geometry by exploiting the properties of regular Hexagon. One advantage of using the proposed approach, as opposed to randomized distribution techniques, is that, the configurations have a compact and efficient algebraic description. This yields nice algorithm for shared-key discovery, in which very little information (or no information at all) needs to be broadcasted. Furthermore, it is shown that the security strength of the proposed approach outperforms well-known deterministic techniques in terms of resilience. Furthermore, the distribution technique ensures 100% connectivity (i.e., the probability that two nodes share a key is 1) and average key-path length is 1.

S58 Prospective Health Economic Evaluation Of Different Recommended Strategies For Tb Testing In A Contemporary Hiv Positive Cohort

Introduction The risk of active tuberculosis (TB) disease is estimated to be increased 40-fold in people with HIV (PHIV). Effective antiretroviral treatment (ART) may reduce this significantly. UK national guidance recommends using blood interferon gamma release assay (IGRA) +/- tuberculin skin testing (TST) for latent TB (LTBI) diagnosis but there are little supporting health economic data. We sought to evaluate the cost-effectiveness of different testing strategies using data from a prospective contemporary cohort. Methods Subjects receiving ambulatory HIV care were recruited by stratified selection within our HIV centre. TST, IGRA (TSpot. TB), frontal chest radiograph (CXR) and single induced sputum for mycobacterial culture were performed. The yield was used to model a screening programme that utilised current UK HIV demographics (Public Health England). Costs were based on the BNF, local costs or published literature (TST £16, IGRA £60, CXR £50, induced sputum £42, treatment for latent and active TB £786 and £7619 respectively). Uptake and LTBI treatment efficacy were both estimated at 65%. We assumed a lifetime reactivation rate with TST+/IGRA+ of 10% and TST+/IGRA- of 2%; and that all those with evidence of LTBI would be given treatment. Results Over 13 months, 211 people were recruited. 26% were female and 26% black African. LTBI rates amongst subjects from sub-Saharan Africa, medium and low TB incidence countries were 8/55 (15%), 2/31 (6%) and 4/125 (3%) respectively. One patient had a persistently indeterminate IGRA. Subclinical TB disease was diagnosed in two (1%) subjects. Using these data to model TB testing nationally, the British HIV Association (BHIVA) testing algorithm was the most cost-effective with an incremental cost effectiveness ratio (ICER) of £21,475. The NICE algorithm both cost more and prevented fewer cases of active TB (Table 1). More comprehensive strategies were associated with increasing cost. Conclusion Testing only those at highest risk of progression to active TB disease in an HIV population with high ART use was cost-effective, whilst most strategies testing all comers and for active TB cost considerably more than the £20–30,000/QALY gained threshold used in the UK.

A Clifford algebra associated to generalized Fibonacci quaternions

In this paper, using the construction of Clifford algebras, we associate to the set of generalized Fibonacci quaternions a quaternion algebra A (i.e., a Clifford algebra of dimension four). Indeed, for the generalized quaternion algebra , denoting , if , therefore the algebra A is split. If , then the algebra A is a division algebra. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice versa. MSC:11E88, 11B39.

44 Are We Using BNP Wisely? Audit of the Utility of Natriuretic Peptide Testing (NT-Probnp) in Banes, Wiltshire and Somerset for Patients with Suspected Heart Failure

IntroductionThe NICE guidelines on Chronic Heart Failure 2010 recommend the use of natriuretic peptide (NP) testing in patients with suspected heart failure without previous myocardial infarction (MI). NP testing is...

139 Clinical outcomes of patients excluded from cardiac investigation in the NICE guidelines for chest pain of recent onset

IntroductionNICE guidance for the investigation of chest pain of recent onset1 recommends clinical assessment and risk stratification within a diagnostic algorithm. Patients with pain considered “non-anginal”, and those with atypical/typical...

Validation of the NICE algorithm for managing children with a non-blanching rash

Validation of the NICE algorithm for managing children with a non-blanching rash

Almanac 2011: Stable coronary artery disease. An editorial overview of selected research that has driven recent advances in clinical cardiology

### Diagnostic strategies The widespread application of specialist clinics for early evaluation of patients with chest pain has focused attention on the effectiveness of diagnostic testing. In a study of nearly 400 000 patients with suspected coronary artery disease, the diagnostic yield of cardiac catheterisation was only 37.6%, leading to calls for better strategies for risk stratification.1 As pointed out in correspondence, the low yield was probably due to verification bias, itself a consequence of basing referral decisions in low- risk populations on non-invasive tests such as exercise ECG.2 Similar considerations prompted the NICE guideline group to recommend a more selective approach to non-invasive testing based on a careful clinical assessment of disease probability in patients presenting with stable chest pain.3 For those, with unequivocal histories at the extremes of diagnostic probability ( 90%) no diagnostic tests were considered necessary, while for patients with a high probability of disease (60–90%) invasive angiography without prior ischaemia testing was recommended. The NICE call for CT calcium scoring in patients with a low (10–30%) probability of disease generated greatest concern, particularly after a report that 19% of patients without coronary calcification—who would have been ruled out for angina in the NICE algorithm—had obstructive (>50% stenosis) disease.4 However, the population referred for angiography in this study had a high pre-test probability of disease and in lower-risk populations CT calcium scoring retains a high diagnostic sensitivity.5 NICE recommendations were driven largely by cost-effectiveness analysis but whether they will improve the diagnostic yield of cardiac catheterisation remains to be seen. ### Circulating biomarkers in stable angina The clinical role of circulating biomarkers for diagnosis of obstructive coronary artery disease in patients with suspected angina has yet to be defined. In one study, blood samples for the N-terminal fragment of the prohormone brain natriuretic peptide (NT-proBNP) and various inflammatory markers were …

P54 Do the NICE new entrant TB screening guidelines under-diagnose cases of latent TB infection?

IntroductionIn 2006, 72% of active TB cases in the UK occurred in people born overseas (HPA 2008). 48% of new entrants with TB were diagnosed within 5 years of entering...

Guest editors' introduction: special section on mining and searching the web

Guest editors' introduction: special section on mining and searching the web

Partitioning chordal graphs into independent sets and cliques

We consider the following generalization of split graphs: A graph is said to be a ( k,ℓ)-graph if its vertex set can be partitioned into k independent sets and ℓ cliques. (Split graphs are obtained by setting k=ℓ=1.) Much of the appeal of split graphs is due to the fact that they are chordal, a property not shared by ( k,ℓ)-graphs in general. (For instance, being a ( k,0)-graph is equivalent to being k-colourable.) However, if we keep the assumption of chordality, nice algorithms and characterization theorems are possible. Indeed, our main result is a forbidden subgraph characterization of chordal ( k,ℓ)-graphs. We also give an O( n( m+ n)) recognition algorithm for chordal ( k,ℓ)-graphs. When k=1, our algorithm runs in time O( m+ n). In particular, we obtain a new simple and efficient greedy algorithm for the recognition of split graphs, from which it is easy to derive the well known forbidden subgraph characterization of split graphs. The algorithm and the characterization extend, in a natural way, to the ‘list’ (or ‘pre-colouring extension’) version of the split partition problem—given a graph with some vertices pre-assigned to the independent set, or to the clique, is there a split partition extending this pre-assignment? Another way to think of our main result is the following min–max property of chordal graphs: for each integer r⩾1, the maximum number of independent K r 's (i.e., of vertex disjoint subgraphs of G, each isomorphic to K r , with no edges joining two of the subgraphs) equals the minimum number of cliques of G that meet all the K r 's of G.

On generalized split graphs

Abstract Abstract We prove that in a chordal graph the maximum number of independent (i.e., disjoint and nonadjacent) K r 's equals the minumum number of cliques that meet all K r 's. When r = 1, this implies that chordal graphs are perfect. When r = 2, it contains a well known forbidden subgraph characterization of split graphs. We also discuss algorithms for both these problems. In particular, we illustrate the techniques by giving a new simple recognition algorithm for split graphs. We apply these results to the following generalization of split graphs: A graph is said to be a ( k, l )-graph if its vertex set can be partitioned into k independent sets and l cliques. Much of the appeal of split graphs is due to the fact that they are chordal, a property not shared by ( k, l )-graphs in general. (For instance, being a ( k , 0)-graph is equivalent to being k -colourable.) However, if we keep the assumption of chordality, nice algorithms and characterization theorems are possible. Indeed, our result gives a forbidden subgraph characterization of (and a polynomial time recognition algorithm for) chordal ( k, l )-graphs.

Diagnosis and Psychopharmacology of Childhood and Adolescent Disorders, 2nd ed.

Diagnosis and Psychopharmacology of Childhood and Adolescent Disorders, 2nd ed.

On the calculation of transitive reduction—closure of orders

Computations of transitive closure and reduction of directed acyclic graphs are mainly considered in this paper. Classes of directed acyclic graphs for which such problems can be solved in linear time complexity (in accordance with the number of arcs) are proposed, namely: generalized N-free graphs, graphs such that the external or internal degree of any vertex is bounded in the transitive reduction, and bounded decomposition width orders, strongly W-free orders. For this purpose, we study the worst-case complexity of a nice algorithm. This algorithm is due to Goralcikova and Koubek (1979) and already studied by Mehlhorn (1984) and Simon (1988). Furthermore, two new classes of orders (generalized N-free and strongly W-free) which seem to have nice computational properties, are proposed and studied.

A Conjecture on the Hall Topology for the Free Group

The Hall topology for the free group is the coarsest topology such that every group morphism from the free group onto a finite discrete group is continuous. It was shown by M. Hall Jr. that every finitely generated subgroup of the free group is closed for this topology. We conjecture that if H1, H2, ..., Hn are finitely generated subgroups of the free group, then the product H1H2... Hn is closed. We discuss some consequences of this conjecture. First, it would give a nice and simple algorithm to compute the closure of a given rational subset of the free group. Next, it implies a similar conjecture for the free monoid, which, in turn, is equivalent to a deep conjecture on finite semigroup, for the solution of which J. Rhodes has offered $100. We hope that our new conjecture will shed some light on the Rhodes's conjecture.

Towers of hanoi problem with arbitraryk≧3 pages

The Towers of Hanoi problem with arbitrary k≧3pegs is an extension of the standard one. In this paper we present a nice recursive algorithm for this extended problem and then analyze its complexity. The analysis is based on a group of integer sequences which are closely related to the complexity of the algorithm and which are also independently significant because they possess some elegant combinatorial properties.

Computational-geometric methods for polygonal approximations of a curve

In cartography, computer graphics, pattern recognition, etc., we often encounter the problem of approximating a given finer piecewise linear curve by another coarser piecewise linear curve consisting of fewer line segments. In connection with this problem, a number of papers have been published, but it seems that the problem itself has not been well modelled from the standpoint of specific applications, nor has a nice algorithm, nice from the computational-geometric viewpoint, been proposed. In the present paper, we first consider (i) the problem of approximating a piecewise linear curve by another whose vertices are a subset of the vertices of the former, and show that an optimum solution of this problem can be found in a polynomial time. We also mention recent results on related problems by several researchers including the authors themselves. We then pose (ii) a problem of covering a sequence of n points by a minimum number of rectangles with a given width, and present an O(n long n)-time algorithm by making use of some fundamental established techniques in computational geometry. Furthermore, an O(mn(logn)2)-time algorithm is presented for finding the minimum width w such that a sequence of n points can be covered by at most m rectangles with width w. Finally, (iii) several related problems are discussed.

More on Subtraction Without Borrowing

In the March 1980 issue of the Mathe- matics Teacher, Bruce Colton presents a very nice algorithm in “Subtraction without Borrowing.”