Model bicategories and their homotopy bicategories

We give the definitions of model bicategory and $w$-homotopy, which are natural generalizations of the notions of model category and homotopy to the context of bicategories. For any model bicategory $\mathcal{C}$, denote by $\mathcal{C}_{fc}$ the full sub-bicategory of the fibrant-cofibrant objects. We prove that the 2-dimensional localization of $\mathcal{C}$ at the weak equivalences can be computed as a bicategory \mathcal{H}\mbox{o}(\mathcal{C}) whose objects and arrows are those of $\mathcal{C}_{fc}$ and whose 2-cells are classes of $w$-homotopies up to an equivalence relation. The pseudofunctor \mathcal{C} \stackrel{r}{\longrightarrow} \mathcal{H}\mbox{o}(\mathcal{C}) which yields the localization is constructed by using a notion of fibrant-cofibrant replacement in this context. When considered for a model category, the results in this article give in particular a bicategory whose reflection into categories is the usual homotopy category constructed by Quillen.Comment: 37 pages, many elevator calculus diagrams. This is a "preliminary version

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Pre-torsors and Galois comodules over mixed distributive laws

We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions $(N_A,R_A)$ and $(N_B,R_B)$ on one hand, and the category of regular comonad arrows $(R_A,\xi)$ from some equalizer preserving comonad ${\mathbb C}$ to $N_BR_B$ on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras.Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad ${\mathbb D}$ and a co-regular comonad arrow from ${\mathbb D}$ to $N_A R_A$, such that the comodule categories of ${\mathbb C}$ and ${\mathbb D}$ are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte

Synchronizing automata with a letter of deficiency 2

AbstractWe present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of Černý’s construction

Slowly synchronizing automata and digraphs

We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

The eSMAF: a software for the assessment and follow-up of functional autonomy in geriatrics

BACKGROUND: Functional status or disability forms the core of most assessment instruments used to identify mix and level of resources and services needed by older adults who possess common characteristics. The Functional Autonomy Measurement System (SMAF) is a 29-item scale measuring functional ability in five different areas. It has been recommended for use for home care, for allocation of chronic beds, for developing care plans in institutional settings and for epidemiological and evaluative studies. The SMAF can also be used with a case-mix classification system (Iso-SMAF) to allocate resources based on patients' functional autonomy characteristics. The objective of this project was to develop a software version of the SMAF to facilitate the evaluation of the functional status of older adults in health services research and to optimize the clinical decision-making process. RESULTS: The eSMAF was developed over an 24-month period using a modified waterfall software engineering process. Requirements and functional specifications were determined using focus groups of stakeholders. Different versions of the software were iteratively field-tested in clinical and research environments and software adaptations made accordingly. User documentation and online help were created to assist the deployment of the software. The software is available in French or English versions under a 30-day unregistered demonstration license or a free restricted registered academic license. It can be used locally on a Windows-based PC or over a network to input SMAF data into a database, search and aggregate client data according to clinical and/or administrative criteria, and generate summary or detailed reports of selected data sets for print or export to another database. CONCLUSION: In the last year, the software has been successfully deployed in the clinical workflow of different institutions in research and clinical applications. The software performed relatively well in terms of stability and performance. Barriers to implementation included antiquated computer hardware, low computer literacy and access to IT support. Key factors for the deployment of the software included standardization of the workflow, user training and support

Discovery of the Optical Transient of the Gamma Ray Burst 990308

The optical transient of the faint Gamma Ray Burst 990308 was detected by the QUEST camera on the Venezuelan 1-m Schmidt telescope starting 3.28 hours after the burst. Our photometry gives $V = 18.32 \pm 0.07$, $R = 18.14 \pm 0.06$, $B = 18.65 \pm 0.23$, and $R = 18.22 \pm 0.05$ for times ranging from 3.28 to 3.47 hours after the burst. The colors correspond to a spectral slope of close to $f_{\nu} \propto \nu^{1/3}$. Within the standard synchrotron fireball model, this requires that the external medium be less dense than $10^{4} cm^{-3}$, the electrons contain $> 20$ of the shock energy, and the magnetic field energy must be less than 24% of the energy in the electrons for normal interstellar or circumstellar densities. We also report upper limits of $V > 12.0$ at 132 s (with LOTIS), $V > 13.4$ from 132-1029s (with LOTIS), $V > 15.3$ at 28.2 min (with Super-LOTIS), and a 8.5 GHz flux of $< 114 \mu Jy$ at 110 days (with the Very Large Array). WIYN 3.5-m and Keck 10-m telescopes reveal this location to be empty of any host galaxy to $R > 25.7$ and $K > 23.3$. The lack of a host galaxy likely implies that it is either substantially subluminous or more distant than a red shift of $\sim 1.2$.Comment: ApJ Lett submitted, 5 pages, 2 figures, no space for 12 coauthor