Determining All Universal Tilers

A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.Comment: 18 pages, 12 figure

Excision for simplicial sheaves on the Stein site and Gromov's Oka principle

A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion \Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to $X$ are given the compact-open topology. Gromov's Oka principle states that if $X$ has a spray, then it has the Oka-Grauert property. The purpose of this paper is to investigate the Oka-Grauert property using homotopical algebra. We embed the category of complex manifolds into the model category of simplicial sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert property is equivalent to $X$ representing a finite homotopy sheaf on the Stein site. This expresses the Oka-Grauert property in purely holomorphic terms, without reference to continuous maps.Comment: Version 3 contains a few very minor improvement

What makes men leak? An investigation of objective and self-report measures of urinary incontinence early after radical prostatectomy

AimsPelvic floor muscle training for patients having radical prostatectomy promotes contraction of these muscles in anticipation of activities that may provoke urine leakage. The aims of this study were: to determine the contribution of the individual activities comprising a standardised 1-hour pad test (1HPT) to overall urine leakage early after radical prostatectomy; and to investigate relationships between the 1HPT, 24-hour pad test (24HPT) and the International Consultation on Incontinence QuestionnaireShort Form (ICIQ-SF) early after radical prostatectomy. MethodsA prospective analysis of patients having radical prostatectomy and receiving pelvic floor muscle training (n=33). Participants completed the 1HPT, 24HPT and ICIQ-SF at 3 and 6 weeks postoperatively. Participants wore a separate, pre-weighed continence pad for each of the seven activities comprising the 1HPT; pads were weighed separately and together to calculate activity-related and overall urine leakage. ResultsWalking at a comfortable speed and drinking while sitting were the two activities contributing most to overall urine leakage, albeit these activities also comprised 75% of 1HPT time. All component activities contributed a minimum 75% of overall urine leakage. There were significant and strong to very strong correlations between all of the 1HPT, 24HPT, and ICIQ-SF at 3 weeks postoperatively. There were significant decreases in 24HPT (P=0.032) and ICIQ-SF (P=0.001) but no significant change in 1HPT from 3 to 6 weeks postoperatively. ConclusionsPelvic floor muscle training should include contraction of these muscles in sedentary and walking postures. The 1HPT correlates well with the 24HPT, but may not be sensitive to early postoperative improvements in urinary leakage. Neurourol. Urodynam. 35:225-229, 2016. (c) 2014 Wiley Periodicals, Inc

The homotopy theory of simplicial props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat

Clinical mentorship to improve pediatric quality of care at the health centers in rural Rwanda: a qualitative study of perceptions and acceptability of health care workers

Background: Despite evidence supporting Integrated Management of Childhood Illness (IMCI) as a strategy to improve pediatric care in countries with high child mortality, its implementation faces challenges related to lack of or poor post-didactic training supervision and gaps in necessary supporting systems. These constraints lead to health care workers’ inability to consistently translate IMCI knowledge and skills into practice. A program providing mentoring and enhanced supervision at health centers (MESH), focusing on clinical and systems improvement was implemented in rural Rwanda as a strategy to address these issues, with the ultimate goal of improving the quality of pediatric care at rural health centers. We explored perceptions of MESH from the perspective of IMCI clinical mentors, mentees, and district clinical leadership. Methods: We conducted focus group discussions with 40 health care workers from 21 MESH-supported health centers. Two FGDs in each district were carried out, including one for nurses and one for director of health centers. District medical directors and clinical mentors had individual in-depth interviews. We performed a hermeneutic analysis using Atlas.ti v5.2. Results: Study participants highlighted program components in five key areas that contributed to acceptability and impact, including: 1) Interactive, collaborative capacity-building, 2) active listening and relationships, 3) supporting not policing, 4) systems improvement, and 5) real-time feedback. Staff turn-over, stock-outs, and other facility/systems gaps were identified as barriers to MESH and IMCI implementation. Conclusion: Health care workers reported high acceptance and positive perceptions of the MESH model as an effective strategy to build their capacity, bridge the gap between knowledge and practice in pediatric care, and address facility and systems issues. This approach also improved relationships between the district supervisory team and health center-based care providers. Despite some challenges, many perceived a strong benefit on clinical performance and outcomes. This study can inform program implementers and policy makers of key components needed for developing similar health facility-based mentorship interventions and potential barriers and resistance which can be proactively addressed to ensure success

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

Small world effect in an epidemiological model

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered systems, there is a fluctuating endemic state of low infection. At a finite value of the disorder of the network, we find a transition to self-sustained oscillations in the size of the infected subpopulation

DG-algebras and derived A-infinity algebras

A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A-infinity algebra. Such a minimal derived A-infinity algebra model for A is a k-projective resolution of the homology algebra of A together with a family of maps satisfying appropriate relations. As in the case of A-infinity algebras, it is possible to recover the dga up to quasi-isomorphism from a minimal derived A-infinity algebra model. Hence the structure we are describing provides a complete description of the quasi-isomorphism type of the dga.Comment: v3: 27 pages. Minor corrections, to appear in Crelle's Journa