An integer programming Model for the Hospitals/Residents Problem with Couples

The Hospitals/Residents problem with Couples (hrc) is a generalisation of the classical Hospitals/Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc. Further, we present an Integer Programming (IP) model for hrc and extend it the case where preference lists can include ties. Further, we describe an empirical study of an IP model for HRC and its extension to the case where preference lists can include ties. This model was applied to randomly generated instances and also real-world instances arising from previous matching runs of the Scottish Foundation Allocation Scheme, used to allocate junior doctors to hospitals in Scotland

Titina (Je Cherche Apres Titine)

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The efficacy of optometric vision training for altering eye movement patterns--A literature review

It has been shown that people who exhibit inadequate reading performance often have deficient eye movement skills. Inefficient readers may demonstrate poor fixations, regressions, saccades or any combination of these factors. Can eye movements be altered or improved by instituting a program of visual training? Will reading performance increase as a result of more efficient eye movement patterns? It is the intent of this review to explore these relationships and to show that there is indeed a correlation between eye movements and reading performance. This review examines and asks several questions: (1) Where should the focus of a remedial effort be focused for those persons exhibiting poor reading ability and concurrently demonstrating inefficient eye movement skills? (2) What are the possible causes of deficient eye movements and/or reading ability? (3) Background physiological information about eye movements and their recording systems are presented. (4) Several studies dealing with the modification of eye movements are reviewed. (5) Finally, concluding remarks are offered as to what inferences and conclusions can be drawn from the available literature

"Almost stable" matchings in the Roommates problem

An instance of the classical Stable Roommates problem (SR) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an SR instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within n^{\frac{1}{2}-\varepsilon}, for any \varepsilon>0, unless P=NP. If the preference lists contain ties, we improve this result to n^{1-\varepsilon}. Also, we show that, given an integer K and an SR instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an SR instance I

Financial Markets in the Face of the Apocalypse

This paper brings together two strands of the literature: Quantifying the impact of apocalyptic risk on capital markets, and the correct computation of the equity risk premium. For the former, we use events in four countries during the Second World War to discern markets' incorporation of information regarding the probability of an Armageddon for each country. We then turn to analyzing the impact of a political col- lapse on the correct computation of the equity risk premium. Arguing that past computations did not properly account for the nancial implications of political collapse on prop- erty/civil/human rights, we argue past calculations overstated the equity risk premium. We provide a correct estimate of the equity risk premium, demonstrating the important changes in this estimate over time

The Hospitals/Residents Problem with Couples: complexity and integer programming models

The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc

Ventricular tachycardia in infants with structurally normal heart: A benign disorder

We evaluated the presentation, treatment, and outcome of infants who present with ventricular tachycardia in the first year of life. Seventy-six infants were admitted to our institution with a diagnosis of ventricular tachycardia between January, 1987 and May, 2006. Forty-five infants were excluded from the study because of additional confounding diagnoses including accelerated idioventricular rhythm, Wolff– Parkinson–White syndrome, supraventricular tachycardia with aberrancy, long QT syndrome, cardiac rhabdomyoma, myocarditis, congenital lesions, or incomplete data. The remaining 31 included infants who had a median age at presentation of 1 day, with a range from 1 to 255 days, and a mean ventricular tachycardia rate of 213 beats per minute, with a range from 171 to 280, at presentation. The infants were treated chronically with propranolol (38.7%), amiodarone (12.9%), mexiletine (3.2%), propranolol and mexiletine (9.7%), or propranolol and procainamide (6.5%). The median duration of treatment was 13 months, with a range from 3 to 105 months. Ventricular tachycardia resolved spontaneously in all infants. No patient died, or received catheter ablation or device therapy. Median age at last ventricular tachycardia was 59 days, with a range from 1 to 836 days. Mean follow-up was 45 months, with a range from 5 to 164 months, with a mean ventricular tachycardia-free period of 40 months. Infants with asymptomatic ventricular tachycardia, a structurally normal heart, and no additional electrophysiological diagnosis all had spontaneous resolution of tachycardia. Furthermore, log-rank analysis of the time to ventricular tachycardia resolution showed no difference between children who received chronic outpatient anti-arrhythmic treatment and those who had no such therapy. While indications for therapy cannot be determined from this study, lack of symptoms or myocardial dysfunction suggests that therapy may not be necessary

The hospitals/residents problem

No abstract available

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201