Upper and Lower Bounds for Weak Backdoor Set Detection

We obtain upper and lower bounds for running times of exponential time algorithms for the detection of weak backdoor sets of 3CNF formulas, considering various base classes. These results include (omitting polynomial factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas. These bounds improve an earlier known bound of 6^k. We also prove a 2^k lower bound for these problems, subject to the Strong Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th International Conference on Theory and Applications of Satisfiability Testin

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

Backdoors to q-Horn

The class q-Horn, introduced by Boros, Crama and Hammer in 1990, is one of the largest known classes of propositional CNF formulas for which satisfiability can be decided in polynomial time. This class properly contains the fundamental classes of Horn and Krom formulas as well as the class of renamable (or disguised) Horn formulas. In this paper we extend this class so that its favorable algorithmic properties can be made accessible to formulas that are outside but "close"\u27 to this class. We show that deciding satisfiability is fixed-parameter tractable parameterized by the distance of the given formula from q-Horn. The distance is measured by the smallest number of variables that we need to delete from the formula in order to get a q-Horn formula, i.e., the size of a smallest deletion backdoor set into the class q-Horn. This result generalizes known fixed-parameter tractability results for satisfiability decision with respect to the parameters distance from Horn, Krom, and renamable Horn

A General Reduction Theorem with Applications to Pathwidth and the Complexity of MAX 2-CSP

We prove a general reduction theorem which allows us to extend bounds for certain graph parameters on cubic graphs to bounds for general graphs taking into account the individual vertex degrees. As applications, we give an algorithm for Max 2 -CSP whose complexity matches the algorithm of Scott and Sorkin in the case of d -regular graphs, d=5 , but is otherwise faster. It also improves on the previously fastest known algorithm in terms of the average degree, given by Golovnev and Kutzkov. Also from the general theorem, we derive a bound for the pathwidth of a general graph which equals that of Fomin et al. and Gaspers for graphs of degree at most 6 , but is smaller otherwise, and use this to give an improved exponential-space algorithm for Max 2 -CSP. Finally we use the general result to give a faster algorithm for Max 2 -CSP on claw-free graphs

On the Two q-Analogue Logarithmic Functions

There is a simple, multi-sheet Riemann surface associated with e_q(z)'s inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be defined. However, the topology of the Riemann surface for ln_q(w) changes each time "q" increases above the collision point of a pair of the turning points of e_q(x). There is also a power series representation for ln_q(1+w). An infinite-product representation for e_q(z) is used to obtain the ordinary natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power series in terms of values of these sum rules. The values of the sum rules for the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General. Some explict formulas added, and to update the reference

The parameterized complexity of positional games

We study the parameterized complexity of several positional games. Our main result is that Short Generalized Hex is W[1]-complete parameterized by the number of moves. This solves an open problem from Downey and Fellows’ influential list of open problems from 1999. Previously, the problem was thought of as a natural candidate for AW[*]-completeness. Our main tool is a new fragment of first-order logic where universally quantified variables only occur in inequalities. We show that model-checking on arbitrary relational structures for a formula in this fragment is W[1]-complete when parameterized by formula size. We also consider a general framework where a positional game is represented as a hypergraph and two players alternately pick vertices. In a Maker-Maker game, the first player to have picked all the vertices of some hyperedge wins the game. In a Maker-Breaker game, the first player wins if she picks all the vertices of some hyperedge, and the second player wins otherwise. In an Enforcer-Avoider game, the first player wins if the second player picks all the vertices of some hyperedge, and the second player wins otherwise. Short Maker-Maker, Short Maker-Breaker, and Short Enforcer-Avoider are respectively AW[*]-, W[1]-, and co-W[1]-complete parameterized by the number of moves. This suggests a rough parameterized complexity categorization into positional games that are complete for the first level of the W-hierarchy when the winning condition only depends on which vertices one player has been able to pick, but AW[*]-complete when it depends on which vertices both players have picked. However, some positional games with highly structured board and winning configurations are fixed-parameter tractable. We give another example of such a game, Short k-Connect, which is fixed-parameter tractable when parameterized by the number of moves

Separate, measure and conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, such as Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for an improved running time analysis. We illustrate the method with improved algorithms for Max (r,2) -CSP and #Dominating Set. For Max (r,2) -CSP instances with domain size r and m constraints, the running time improves from r m/6 to r m/7.5 for cubic instances and from r 0.19⋅m to r 0.18⋅m for general instances, omitting subexponential factors. For #Dominating Set instances with n vertices, the running time improves from 1.4143 n to 1.2458 n for cubic instances and from 1.5673 n to 1.5183 n for general instances. It is likely that other algorithms relying on local transformations can be improved using our method, which exploits a non-local property of graphs

Engineering Phi29‐DNAP Variants for Customized DNA Hydrogel Materials

DNA hydrogels, which hold potential for use in medicine, biosensors, and tissue engineering, can be produced through enzymatic rolling circle amplification (RCA) using phi29 DNA polymerase (DNAP). This paper introduces new DNAP variants designed for RCA-based DNA hydrogel production, featuring enzymes with modified DNA binding, enhanced thermostability, reduced exonuclease activity, and protein tags for fluorescence detection or specific immobilization. We evaluated these enzymes by quantifying DNA output via quantitative PCR (qPCR) and assessing hydrogel mechanical properties through micromechanical indentation. The results showed that most variants generated similar DNA amounts and hydrogels with comparable mechanical properties. Additionally, all variants successfully incorporated non-natural nucleotides, such as base-modified dGTP derivatives and 2′fluoro-dGTP, during RCA. This study\u27s robust analytical approach offers a strong foundation for selecting new enzymes and producing DNA hydrogels with tailored material properties

Bax affects intracellular Ca2+ stores and induces Ca2+ wave propagation

In the present study, we evaluated proapoptotic protein Bax on mitochondria and Ca2+ homeostasis in primary cultured astrocytes. We found that recombinant Bax (rBax, 10 and 100 ng/ml) induces a loss in mitochondrial membrane potential (DeltaPsi(m)). This effect might be related to the inhibition of respiratory rates and a partial release of cytochrome c, which may change mitochondrial morphology. the loss of DeltaPsi(m) and a selective permeabilization of mitochondrial membranes contribute to the release of Ca2+ from the mitochondria. This was inhibited by cyclosporin A (5 muM) and Ruthenium Red (1 mug/ml), indicating the involvement of mitochondrial Ca2+ transport mechanisms. Bax-induced mitochondrial Ca2+ release evokes Ca2+ waves and wave propagation between cells. Our results show that Bax induces mitochondrial alteration that affects Ca2+ homeostasis and signaling. These changes show that Ca2+ signals might be correlated with the proapoptotic activities of Bax.Universidade Federal de São Paulo, UNIFESP, INFAR, Dept Pharmacol, BR-04044020 São Paulo, BrazilNINDS, Biochem Sect, NIH, Bethesda, MD 20892 USAUniv São Paulo, Inst Quim, Dept Biochem, São Paulo, BrazilUniversidade Federal de São Paulo, UNIFESP, INFAR, Dept Pharmacol, BR-04044020 São Paulo, BrazilWeb of Scienc