A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor

Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles}. A {\em partition oracle} is a procedure that, given access to the incidence lists representation of a bounded-degree graph $G= (V,E)$ and a parameter \eps, when queried on a vertex $v\in V$, returns the part (subset of vertices) which $v$ belongs to in a partition of all graph vertices. The partition should be such that all parts are small, each part is connected, and if the graph has certain properties, the total number of edges between parts is at most \eps |V|. In this work we give a partition oracle for graphs with excluded minors whose query complexity is quasi-polynomial in 1/\eps, thus improving on the result of Hassidim et al. ({\em Proceedings of FOCS 2009}) who gave a partition oracle with query complexity exponential in 1/\eps. This improvement implies corresponding improvements in the complexity of testing planarity and other properties that are characterized by excluded minors as well as sublinear-time approximation algorithms that work under the promise that the graph has an excluded minor.Comment: 13 pages, 1 figur

Testing bounded arboricity

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs with bounded treewidth) and randomly generated preferential attachment graphs. Graphs with bounded arboricity have been studied extensively in the past, in particular since for many problems they allow for much more efficient algorithms and/or better approximation ratios. We present a tolerant tester in the sparse-graphs model. The sparse-graphs model allows access to degree queries and neighbor queries, and the distance is defined with respect to the actual number of edges. More specifically, our algorithm distinguishes between graphs that are $\epsilon$-close to having arboricity $\alpha$ and graphs that $c \cdot \epsilon$-far from having arboricity $3\alpha$, where $c$ is an absolute small constant. The query complexity and running time of the algorithm are $\tilde{O}\left(\frac{n}{\sqrt{m}}\cdot \frac{\log(1/\epsilon)}{\epsilon} + \frac{n\cdot \alpha}{m} \cdot \left(\frac{1}{\epsilon}\right)^{O(\log(1/\epsilon))}\right)$ where $n$ denotes the number of vertices and $m$ denotes the number of edges. In terms of the dependence on $n$ and $m$ this bound is optimal up to poly-logarithmic factors since $\Omega(n/\sqrt{m})$ queries are necessary (and $\alpha = O(\sqrt{m}))$. We leave it as an open question whether the dependence on $1/\epsilon$ can be improved from quasi-polynomial to polynomial. Our techniques include an efficient local simulation for approximating the outcome of a global (almost) forest-decomposition algorithm as well as a tailored procedure of edge sampling

A Local Algorithm for Constructing Spanners in Minor-Free Graphs

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider this problem in the setting of local algorithms: one wants to quickly determine whether a given edge $e$ is in a specific spanning tree, without computing the whole spanning tree, but rather by inspecting the local neighborhood of $e$. The challenge is to maintain consistency. That is, to answer queries about different edges according to the same spanning tree. Since it is known that this problem cannot be solved without essentially viewing all the graph, we consider the relaxed version of finding a spanning subgraph with $(1+\epsilon)n$ edges (where $n$ is the number of vertices and $\epsilon$ is a given sparsity parameter). It is known that this relaxed problem requires inspecting $\Omega(\sqrt{n})$ edges in general graphs, which motivates the study of natural restricted families of graphs. One such family is the family of graphs with an excluded minor. For this family there is an algorithm that achieves constant success probability, and inspects $(d/\epsilon)^{poly(h)\log(1/\epsilon)}$ edges (for each edge it is queried on), where $d$ is the maximum degree in the graph and $h$ is the size of the excluded minor. The distances between pairs of vertices in the spanning subgraph $G'$ are at most a factor of $poly(d, 1/\epsilon, h)$ larger than in $G$. In this work, we show that for an input graph that is $H$-minor free for any $H$ of size $h$, this task can be performed by inspecting only $poly(d, 1/\epsilon, h)$ edges. The distances between pairs of vertices in the spanning subgraph $G'$ are at most a factor of $\tilde{O}(h\log(d)/\epsilon)$ larger than in $G$. Furthermore, the error probability of the new algorithm is significantly improved to $\Theta(1/n)$. This algorithm can also be easily adapted to yield an efficient algorithm for the distributed setting

A catalog of stability-associated sequence elements in 3' UTRs of yeast mRNAs

BACKGROUND: In recent years, intensive computational efforts have been directed towards the discovery of promoter motifs that correlate with mRNA expression profiles. Nevertheless, it is still not always possible to predict steady-state mRNA expression levels based on promoter signals alone, suggesting that other factors may be involved. Other genic regions, in particular 3' UTRs, which are known to exert regulatory effects especially through controlling RNA stability and localization, were less comprehensively investigated, and deciphering regulatory motifs within them is thus crucial. RESULTS: By analyzing 3' UTR sequences and mRNA decay profiles of Saccharomyces cerevisiae genes, we derived a catalog of 53 sequence motifs that may be implicated in stabilization or destabilization of mRNAs. Some of the motifs correspond to known RNA-binding protein sites, and one of them may act in destabilization of ribosome biogenesis genes during stress response. In addition, we present for the first time a catalog of 23 motifs associated with subcellular localization. A significant proportion of the 3' UTR motifs is highly conserved in orthologous yeast genes, and some of the motifs are strikingly similar to recently published mammalian 3' UTR motifs. We classified all genes into those regulated only at transcription initiation level, only at degradation level, and those regulated by a combination of both. Interestingly, different biological functionalities and expression patterns correspond to such classification. CONCLUSION: The present motif catalogs are a first step towards the understanding of the regulation of mRNA degradation and subcellular localization, two important processes which - together with transcription regulation - determine the cell transcriptome

A simple online competitive adaptation of Lempel-Ziv compression with efficient random access support

We present a simple adaptation of the Lempel Ziv 78' (LZ78) compression scheme ({\em IEEE Transactions on Information Theory, 1978}) that supports efficient random access to the input string. Namely, given query access to the compressed string, it is possible to efficiently recover any symbol of the input string. The compression algorithm is given as input a parameter \eps >0, and with very high probability increases the length of the compressed string by at most a factor of (1+\eps). The access time is O(\log n + 1/\eps^2) in expectation, and O(\log n/\eps^2) with high probability. The scheme relies on sparse transitive-closure spanners. Any (consecutive) substring of the input string can be retrieved at an additional additive cost in the running time of the length of the substring. We also formally establish the necessity of modifying LZ78 so as to allow efficient random access. Specifically, we construct a family of strings for which $\Omega(n/\log n)$ queries to the LZ78-compressed string are required in order to recover a single symbol in the input string. The main benefit of the proposed scheme is that it preserves the online nature and simplicity of LZ78, and that for {\em every} input string, the length of the compressed string is only a small factor larger than that obtained by running LZ78

Local Algorithms for Sparse Spanning Graphs

We initiate the study of the problem of designing sublinear-time (local) algorithms that, given an edge (u,v) in a connected graph G=(V,E), decide whether (u,v) belongs to a sparse spanning graph G\u27 = (V,E\u27) of G. Namely, G\u27 should be connected and |E\u27| should be upper bounded by (1+epsilon)|V| for a given parameter epsilon > 0. To this end the algorithms may query the incidence relation of the graph G, and we seek algorithms whose query complexity and running time (per given edge (u,v)) is as small as possible. Such an algorithm may be randomized but (for a fixed choice of its random coins) its decision on different edges in the graph should be consistent with the same spanning graph G\u27 and independent of the order of queries. We first show that for general (bounded-degree) graphs, the query complexity of any such algorithm must be Omega(sqrt{|V|}). This lower bound holds for graphs that have high expansion. We then turn to design and analyze algorithms both for graphs with high expansion (obtaining a result that roughly matches the lower bound) and for graphs that are (strongly) non-expanding (obtaining results in which the complexity does not depend on |V|). The complexity of the problem for graphs that do not fall into these two categories is left as an open question

Human Muscle Progenitor Cells Overexpressing Neurotrophic Factors Improve Neuronal Regeneration in a Sciatic Nerve Injury Mouse Model

The peripheral nervous system has an intrinsic ability to regenerate after injury. However, this process is slow, incomplete, and often accompanied by disturbing motor and sensory consequences. Sciatic nerve injury (SNI), which is the most common model for studying peripheral nerve injury, is characterized by damage to both motor and sensory fibers. The main goal of this study is to examine the feasibility of administration of human muscle progenitor cells (hMPCs) overexpressing neurotrophic factor (NTF) genes, known to protect peripheral neurons and enhance axon regeneration and functional recovery, to ameliorate motoric and sensory deficits in SNI mouse model. To this end, hMPCs were isolated from a human muscle biopsy, and manipulated to ectopically express brain-derived neurotrophic factor (BDNF), glial-cell-line-derived neurotrophic factor (GDNF), vascular endothelial growth factor (VEGF), and insulin-like growth factor (IGF-1). These hMPC-NTF were transplanted into the gastrocnemius muscle of mice after SNI, and motor and sensory functions of the mice were assessed using the CatWalk XT system and the hot plate test. ELISA analysis showed that genetically manipulated hMPC-NTF express significant amounts of BDNF, GDNF, VEGF, or IGF-1. Transplantation of 3 × 106 hMPC-NTF was shown to improve motor function and gait pattern in mice following SNI surgery, as indicated by the CatWalk XT system 7 days post-surgery. Moreover, using the hot-plate test, performed 6 days after surgery, the treated mice showed less sensory deficits, indicating a palliative effect of the treatment. ELISA analysis following transplantation demonstrated increased NTF expression levels in the gastrocnemius muscle of the treated mice, reinforcing the hypothesis that the observed positive effect was due to the transplantation of the genetically manipulated hMPC-NTF. These results show that genetically modified hMPC can alleviate both motoric and sensory deficits of SNI. The use of hMPC-NTF demonstrates the feasibility of a treatment paradigm, which may lead to rapid, high-quality healing of damaged peripheral nerves due to administration of hMPC. Our approach suggests a possible clinical application for the treatment of peripheral nerve injury

Evaluation of integrated care services in Catalonia:population-based and service-based real-life deployment protocols

BackgroundComprehensive assessment of integrated care deployment constitutes a major challenge to ensure quality, sustainability and transferability of both healthcare policies and services in the transition toward a coordinated service delivery scenario. To this end, the manuscript articulates four different protocols aiming at assessing large-scale implementation of integrated care, which are being developed within the umbrella of the regional project Nextcare (2016-2019), undertaken to foster innovation in technologically-supported services for chronic multimorbid patients in Catalonia (ES) (7.5M inhabitants).Whereas one of the assessment protocols is designed to evaluate population-based deployment of care coordination at regional level during the period 2011-2017, the other three are service-based protocols addressing: i) Home hospitalization; ii) Prehabilitation for major surgery; and, iii) Community-based interventions for frail elderly chronic patients. All three services have demonstrated efficacy and potential for health value generation. They reflect different implementation maturity levels. While full coverage of the entire urban health district of Barcelona-Esquerra (520k inhabitants) is the main aim of home hospitalization, demonstration of sustainability at Hospital Clinic of Barcelona constitutes the core goal of the prehabilitation service. Likewise, full coverage of integrated care services addressed to frail chronic patients is aimed at the city of Badalona (216k inhabitants).MethodsThe population-based analysis, as well as the three service-based protocols, follow observational and experimental study designs using a non-randomized intervention group (integrated care) compared with a control group (usual care) with a propensity score matching method. Evaluation of cost-effectiveness of the interventions using a Quadruple aim approach is a central outcome in all protocols. Moreover, multi-criteria decision analysis is explored as an innovative method for health delivery assessment. The following additional dimensions will also be addressed: i) Determinants of sustainability and scalability of the services; ii) Assessment of the technological support; iii) Enhanced health risk assessment; and, iv) Factors modulating service transferability.DiscussionThe current study offers a unique opportunity to undertake a comprehensive assessment of integrated care fostering deployment of services at regional level. The study outcomes will contribute refining service workflows, improving health risk assessment and generating recommendations for service selection.Trials registrationNCT03130283 (date released 04/06/2018), NCT03768050 (date released 12/05/2018), NCT03767387 (date released 12/05/2018).</p