On the Multidimensional Stable Marriage Problem

We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural way and present so called elemental and compound algorithms to generate matchings for a problem instance. We demonstrate the stability of matchings generated by both algorithms, as well as show that the former runs in $O(pn^2)$ time.Comment: 8 page

Performance Comparisons of Greedy Algorithms in Compressed Sensing

Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recovery the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large scale empirical investigation into the behavior of three of the state of the art greedy algorithms: NIHT, HTP, and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recovery the sparsest solution is accurately determined, and throughout this region additional performance characteristics are presented. Contrasting the recovery regions and average computational time for each algorithm we present algorithm selection maps which indicate, for each problem size, which algorithm is able to reliably recovery the sparsest vector in the least amount of time. Though no one algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise and for a variety of problem classes. The algorithm selection maps presented here are the first of their kind for compressed sensing

Sequential Changes of Plasma C-Reactive Protein, Erythrocyte Sedimentation Rate and White Blood Cell Count in Spine Surgery : Comparison between Lumbar Open Discectomy and Posterior Lumbar Interbody Fusion.

ObjectiveC-reactive protein (CRP) and erythrocyte sedimentation rate (ESR) are often utilized to evaluate for postoperative infection. Abnormal values may be detected after surgery even in case of non-infection because of muscle injury, transfusion, which disturbed prompt perioperative management. The purpose of this study was to evaluate and compare the perioperative CRP, ESR, and white blood cell (WBC) counts after spine surgery, which was proved to be non-infection.MethodsTwenty patients of lumbar open discectomy (LOD) and 20 patients of posterior lumbar interbody fusion (PLIF) were enrolled in this study. Preoperative and postoperative prophylactic antibiotics were administered routinely for 7 days. Blood samples were obtained one day before surgery and postoperative day (POD) 1, POD3, and POD7. Using repeated measures ANOVA, changes in effect measures over time and between groups over time were assessed. All data analysis was conducted using SAS v.9.1.ResultsChanges in CRP, within treatment groups over time and between treatment groups over time were both statistically significant F(3,120)=5.05, p=0.003 and F(1,39)=7.46, p=0.01, respectively. Most dramatic changes were decreases in the LOD group on POD3 and POD7. Changes in ESR, within treatment groups over time and between treatment groups over time were also found to be statistically significant, F(3,120)=6.67, p=0.0003 and F(1,39)=3.99, p=0.01, respectively. Changes in WBC values also were be statistically significant within groups over time, F(3,120)=40.52, p<0.001, however, no significant difference was found in between groups WBC levels over time, F(1,39)=0.02, p=0.89.ConclusionWe found that, dramatic decrease of CRP was detected on POD3 and POD7 in LOD group of non-infection and dramatic increase of ESR on POD3 and POD7 in PLIF group of non-infection. We also assumed that CRP would be more effective and sensitive parameter especially in LOD than PLIF for early detection of infectious complications. Awareness of the typical pattern of CRP, ESR, and WBC may help to evaluate the early postoperative course

The Synthesis and Characterization of New, Robust Titanium (IV) Scorpionate Complexes

Titanium complexes possessing sterically encumbered ligands have allowed for the preparation of reactive moieties (imido, alkylidene and alkylidyne species) relevant to reactions such as olefin polymerization and alkyne hydroamination. For this reason, we have targeted robust scorpionate ancillary ligands to support reactive titanium centers. Thus, a series of titanium complexes were synthesized using an achiral oxazoline-based scorpionate ligand, tris(4,4-dimethyl-2-oxazolinyl)phenyl borate [To^M^]^-^ as well as the related chiral ligand, tris(4-isopropyl-2-oxazolinyl)phenyl borate [To^P^]^-^. The complex [Ti(κ^3^- To^M^)Cl~3~] was prepared in moderate yield (43%) by the rapid (<1 min at room temperature) reaction of Li[To^M^] and TiCl~4~ in methylene chloride; this new compound was characterized by ^1^H NMR spectroscopy as the expected C~3v~-symmetric species. One route to Ti (IV) alkyls involves salt metathesis; accordingly, syntheses of [To^M^]Ti alkyl complexes by interaction of [Ti(κ^3^-To^M^)Cl~3~] and one or three equivalents of alkylating agents, such as benzyl potassium (KCH~2~C~6~H~5~), trimethylsilylmethyl
lithium (LiCH~2~Si(CH~3~) ~3~), or neopentyl lithium (LiCH~2~C(CH~3~)~3~) are currently under investigation. The complexes [Ti(=NBut) (κ~3~-To^M^)(Cl)(Bu^t^py)] (Bu^t^py=4 tert-butylpyridine) and [Ti(=NBu^t^) (κ~3~-To^P^)(Cl)(Bu^t^py)] were synthesized by reaction of the known Ti imido [Ti(=NBu^t^)(Cl)~2~(Bu^t^py)~2~] with Li[To^M^] or Li[To^P^], respectively, by stirring overnight in methylene chloride at ambient temperature. The complexes were identified using ^1^H NMR spectroscopy, ^1^H-^13^C HMQC and ^1^H-^15^N HMBC correlation experiments