Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in [8, 44, 39, 9]. On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m = n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables – variables with the same value in all the solutions of an instance– and hardness of GSP.

The impact of balancing on problem hardness in a highly structured domain

Random problem distributions have played a key role in the study and design of algorithms for constraint satisfaction and Boolean satisfiability, as well as in ourunderstanding of problem hardness, beyond standard worst-case complexity. We consider random problem distributions from a highly structured problem domain that generalizes the Quasigroup Completion problem (QCP) and Quasigroup with Holes (QWH), a widely used domain that captures the structure underlying a range of real-world applications. Our problem domain is also a generalization of the well-known Sudoku puz- zle: we consider Sudoku instances of arbitrary order, with the additional generalization that the block regions can have rectangular shape, in addition to the standard square shape. We evaluate the computational hardness of Generalized Sudoku instances, for different parameter settings. Our experimental hardness results show that we can generate instances that are considerably harder than QCP/QWH instances of the same size. More interestingly, we show the impact of different balancing strategies on problem hardness. We also provide insights into backbone variables in Generalized Sudoku instances and how they correlate to problem hardness.

Completion of the isomorphous Ln(trensal) series

The CeIII, PrIII, NdIII, GdIII and YbIII complexes of the heptadentate ligand 2,2´,2´´-tris(salicylideneimino) triethylamine, H3trensal (in its trianionic form), have been synthesized and characterized structurally by X-ray crystallography. These five [Ln(trensal)] structures complete a rare isomorphous and isostructural series of lanthanoid complexes in the trigonal P–3c1 space group with a ≈ 13.1 and c ≈ 16.5 Å

A comparative study of telephone versus onsite completion of the WOMAC 3.0 Osteoarthritis Index

Objective. Outcome assessment in clinical trials using the Western Ontario and McMaster University (WOMAC 3.0) Osteoarthritis Index is traditionally achieved through self-administration of the Index. However, in other areas of clinical measurement, telephone administration has been shown to be a reliable method of acquiring data that are both accurate and complete. To address this issue in knee osteoarthritis (OA), we conducted a comparative study of telephone administration by interviewer of WOMAC LK3.0 versus onsite self-completion at the hospital. Methods. Fifty consenting patients with knee OA were randomized to complete the WOMAC LK3.0 Index by telephone interview one day, followed by onsite completion the following day, or vice versa. Neither patients nor interviewers had access to any prior scores. Results. The mean age of the 50 patients was 66.3 years (range 44-82); 34 (68%) were female and 16 (32%) male. There was excellent agreement between the mean office and telephone scores, with mean differences for the WOMAC LK3.0 pain, stiffness, and function subscale scores and total score of 0.09, 0.12, 0.78, and 0.98, respectively. These differences were well within the respective protocol defined equivalence criteria of +/- 1.7, +/- 0.9, +/- 6.4, and +/- 9.1, and represented differences from office scores of 0.9, 2.6, 2.4, and 2.2%, respectively. Conclusion. The use of telephone interviews for the WOMAC LK3.0 Index is a valid method of obtaining OA outcome measurements. These observations have important implications for designing data acquisition strategies for future OA clinical trials and for longterm observational studies.

Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

An integer programming framework for sequencing cutting patterns based on interval graph completion

We derived a framework in integer programming, based on the properties of a linear ordering of the vertices in interval graphs, that acts as an edge completion model for obtaining interval graphs. This model can be applied to problems of sequencing cutting patterns, namely the minimization of open stacks problem (MOSP). By making small modifications in the objective function and using only some of the inequalities, the MOSP model is applied to another pattern sequencing problem that aims to minimize, not only the number of stacks, but also the order spread (the minimization of the stack occupation problem), and the model is tested.

An integer programming model for the minimum interval graph completion problem

The minimum interval graph completion problem consists of, given a graph G = ( V, E ), finding a supergraph H = ( V, E ∪ F ) that is an interval graph, while adding the least number of edges |F| . We present an integer programming formulation for solving the minimum interval graph completion problem recurring to a characteri- zation of interval graphs that produces a linear ordering of the maximal cliques of the solution graph.

Setting boundaries: brain dynamics of modal and amodal illusory shape completion in humans.

Normal visual perception requires differentiating foreground from background objects. Differences in physical attributes sometimes determine this relationship. Often such differences must instead be inferred, as when two objects or their parts have the same luminance. Modal completion refers to such perceptual "filling-in" of object borders that are accompanied by concurrent brightness enhancement, in turn termed illusory contours (ICs). Amodal completion is filling-in without concurrent brightness enhancement. Presently there are controversies regarding whether both completion processes use a common neural mechanism and whether perceptual filling-in is a bottom-up, feedforward process initiating at the lowest levels of the cortical visual pathway or commences at higher-tier regions. We previously examined modal completion (Murray et al., 2002) and provided evidence that the earliest modal IC sensitivity occurs within higher-tier object recognition areas of the lateral occipital complex (LOC). We further proposed that previous observations of IC sensitivity in lower-tier regions likely reflect feedback modulation from the LOC. The present study tested these proposals, examining the commonality between modal and amodal completion mechanisms with high-density electrical mapping, spatiotemporal topographic analyses, and the local autoregressive average distributed linear inverse source estimation. A common initial mechanism for both types of completion processes (140 msec) that manifested as a modulation in response strength within higher-tier visual areas, including the LOC and parietal structures, is demonstrated, whereas differential mechanisms were evident only at a subsequent time period (240 msec), with amodal completion relying on continued strong responses in these structures.

Detection of Mycobacterium leprae DNA by polymerase chain reaction in the blood of individuals, eight years after completion of anti-leprosy therapy

Thirty eight patients with indeterminate leprosy (HI), at least 4 to 6 years after discharge from multibacillary (MB) or paucibacillary (PB) schemes of anti leprosy multidrug therapy (MDT), were submitted to traditional diagnostic procedures for leprosy and to polymerase chain reaction (PCR) analysis of different clinical samples for detection of Mycobacterium leprae DNA. No significant difference was observed for any of the parameters analyzed between PB or MB schemes of treatment and no indications were found for more efficient outcome of HI using the MB scheme. Remarkably, 18 (54.5%) of the individuals were PCR positive in at least one of the samples: positivity of PCR was highest in blood samples and four individuals were PCR positive in blood and some other sample. Upon comparison of PCR results with clinical and histopathological parameters, no correlation was found between PCR-positivity and eventual relapse. This is the first report on detection of M. leprae DNA in PB patients, more than half a decade after completion of MDT, suggesting that live bacilli are present and circulating much longer than expected, although reinfection of the individuals can not be excluded. Overall, we feel that because of the high sensitivity of the assay, extreme care should be taken about association of PCR results, efficacy of treatment and disease status.

Review Of The Circumstances Surrounding The Elapse Of Time In Bringing To Completion The Western Health Board Inquiry Into Allegations Of Abuse In The Brothers Of Charity Services, Galway

Review Of The CircumstancesSurrounding The Elapse Of TimeIn Bringing To CompletionThe Western Health Board Inquiry IntoAllegations Of Abuse In The BrothersOf Charity Services, Galway Click here to download PDF 104kb

Strategic Review of Medical Training and Career Structures Report on Medical Career Structures and Pathways following completion of Specialist Training

The Minister for Health decided, in July 2013, to establish a Working Group, chaired by Professor Brian MacCraith, President of DCU, to carry out a strategic review of medical training and career structure. The Working Group will examine and make high-level recommendations relating to training and career pathways for doctors with a view to: From January-April 2014, the Working Group prioritised work on career structures and pathways following completion of specialist training in order to report to the Minister for Health on these issues in this report. Download the Report (PDF, 800 kb)  

Determinants of acquisition completion: a relational perspective

The strategic literature on relatedness in the context of mergers and acquisitions (M&As) is extensive, yet we know little about whether or how relatedness has an influence on the announcement to completion stage of the M&A process. Drawing on research on intra-industry competition and relational capabilities, we seek to shed light on the relatedness debate by examining the strategic forces that affect the completion of an announced related M&A, accounting for financial and organizational factors. We also explore additional strategic forces that might amplify or attenuate the negative effect of relatedness on deal completion. We test and find support for our hypotheses using longitudinal data from a sample of the largest M&A announcements in the world from 1991 to 2001.