Equitable coloring of planar graphs with maximum degree at least eight

The Chen-Lih-Wu Conjecture states that each connected graph with maximum degree $\Delta\geq 3$ that is not the complete graph $K_{\Delta+1}$ or the complete bipartite graph $K_{\Delta,\Delta}$ admits an equitable coloring with $\Delta$ colors. For planar graphs, the conjecture has been confirmed for $\Delta\geq 13$ by Yap and Zhang and for $9\leq \Delta\leq 12$ by Nakprasit. In this paper, we present a proof that confirms the conjecture for graphs embeddable into a surface with non-negative Euler characteristic with maximum degree $\Delta\geq 9$ and for planar graphs with maximum degree $\Delta\geq 8$.Comment: 19 pages, 3 figure

Regular Abstractions for Array Systems

Verifying safety and liveness over array systems is a highly challenging problem. Array systems naturally capture parameterized systems such as distributed protocols with an unbounded number of processes. Such distributed protocols often exploit process IDs during their computation, resulting in array systems whose element values range over an infinite domain. In this paper, we develop a novel framework for proving safety and liveness over array systems. The crux of the framework is to overapproximate an array system as a string rewriting system (i.e. over a finite alphabet) by means of a new predicate abstraction that exploits the so-called indexed predicates. This allows us to tap into powerful verification methods for string rewriting systems that have been heavily developed in the last few decades (e.g. regular model checking). We demonstrate how our method yields simple, automatically verifiable proofs of safety and liveness properties for challenging examples, including Dijkstra's self-stabilizing protocol and the Chang-Roberts leader election protocol

A High-Performance Triple Patterning Layout Decomposer with Balanced Density

Triple patterning lithography (TPL) has received more and more attentions from industry as one of the leading candidate for 14nm/11nm nodes. In this paper, we propose a high performance layout decomposer for TPL. Density balancing is seamlessly integrated into all key steps in our TPL layout decomposition, including density-balanced semi-definite programming (SDP), density-based mapping, and density-balanced graph simplification. Our new TPL decomposer can obtain high performance even compared to previous state-of-the-art layout decomposers which are not balanced-density aware, e.g., by Yu et al. (ICCAD'11), Fang et al. (DAC'12), and Kuang et al. (DAC'13). Furthermore, the balanced-density version of our decomposer can provide more balanced density which leads to less edge placement error (EPE), while the conflict and stitch numbers are still very comparable to our non-balanced-density baseline

Extramedullary versus intramedullary tibial alignment technique in total knee arthroplasty: A meta-analysis of randomized controlled trials

The aim of this study was to establish whether the use of an extramedullary or intramedullary tibial cutting guide leads to superior mechanical leg axis and implant positioning. A meta-analysis of six randomized controlled trials including 350 knees was performed. For the mechanical axis, frontal tibial component angle and tibial slope, there were no significant differences in the mean values or the number of outliers (±3°) between the extramedullary and intramedullary groups. A reduced tourniquet time was associated with the intramedullary guide. No significant difference in the complication rate was noted between the two groups. Neither extramedullary nor intramedullary tibial alignment was more accurate in facilitating the tibial cut. Use of an intramedullary guide results in a shorter tourniquet time and exhibits a similar complication rate as the extramedullary guide

CSS Minification via Constraint Solving

Minification is a widely-accepted technique which aims at reducing the size of the code transmitted over the web. We study the problem of minifying Cascading Style Sheets (CSS) --- the de facto language for styling web documents. Traditionally, CSS minifiers focus on simple syntactic transformations (e.g. shortening colour names). In this paper, we propose a new minification method based on merging similar rules in a CSS file. We consider safe transformations of CSS files, which preserve the semantics of the CSS file. The semantics of CSS files are sensitive to the ordering of rules in the file. To automatically identify a rule merging opportunity that best minimises file size, we reduce the rule-merging problem to a problem on CSS-graphs, i.e., node-weighted bipartite graphs with a dependency ordering on the edges, where weights capture the number of characters (e.g. in a selector or in a property declaration). Roughly speaking, the corresponding CSS-graph problem concerns minimising the total weight of a sequence of bicliques (complete bipartite subgraphs) that covers the CSS-graph and respects the edge order. We provide the first full formalisation of CSS3 selectors and reduce dependency detection to satisfiability of quantifier-free integer linear arithmetic, for which highly-optimised SMT-solvers are available. To solve the above NP-hard graph optimisation problem, we show how Max-SAT solvers can be effectively employed. We have implemented our algorithms using Max-SAT and SMT-solvers as backends, and tested against approximately 70 real-world examples (including the top 20 most popular websites). In our benchmarks, our tool yields larger savings than six well-known minifiers (which do not perform rule-merging, but support many other optimisations). Our experiments also suggest that better savings can be achieved in combination with one of these six minifiers

Monadic Decomposability of Regular Relations

Monadic decomposibility - the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas - is a powerful tool for devising a decision procedure for a given logical theory. In this paper, we revisit a classical decision problem in automata theory: given a regular (a.k.a. synchronized rational) relation, determine whether it is recognizable, i.e., it has a monadic decomposition (that is, a representation as a boolean combination of cartesian products of regular languages). Regular relations are expressive formalisms which, using an appropriate string encoding, can capture relations definable in Presburger Arithmetic. In fact, their expressive power coincide with relations definable in a universal automatic structure; equivalently, those definable by finite set interpretations in WS1S (Weak Second Order Theory of One Successor). Determining whether a regular relation admits a recognizable relation was known to be decidable (and in exponential time for binary relations), but its precise complexity still hitherto remains open. Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp. NFA) representations of regular relations is shown to be NLOGSPACE-complete (resp. PSPACE-complete)

Regulation of subcellular location and activity of Cdc2-cyclinb1 is involved in bendamustine-induced G2 arrest

Bendamustine is a multifunctional alkylating agent for the treatment of multiple myeloma, with the G2/M arrest-induction ability in human multiple myeloma RPMI-8226 cells, but the mechanism remains ambiguous. In this study, we found bendamustine caused the G2 arrest in 24 h, regulated the phosphorylation status of Cdc2, and blocked the nuclear import of Cdc2-CyclinB1 complex. Pretreatment with ATM/ATR inhibitor caffeine or p38 MAPK inhibitor SB203580 suppressed the phosphorylation of Cdc2 at Thr14/Tyr15 or attenuate the blockade of nuclear import, respectively; however, neither of these two inhibitors nor the combination imposed significant effects on Bendamustine-triggered G2 arrest. Bendamustine-induced blockade of the nuclear translocation dissipated after 48 h, after which, the G2 arrest was maintained through the inhibitory phosphorylation of Cdc2. Taken together, our research suggested that two or more pathways and mechanisms which regulated the cell cycle in a time-dependent manner were involved in the G2 arrest invoked by bendamustine.Colegio de Farmacéuticos de la Provincia de Buenos Aire