scholarly journals Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree

2019 ◽  
Vol 33 (1) ◽  
pp. 327-345 ◽  
Author(s):  
Fedor V. Fomin ◽  
Petteri Kaski ◽  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh
Keyword(s):  
Steiner Tree ◽  
Polynomial Space ◽  
Exponential Time ◽  
Single Exponential

scholarly journals Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree

2015 ◽  
pp. 494-505 ◽  
Author(s):  
Fedor V. Fomin ◽  
Petteri Kaski ◽  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh
Keyword(s):  
Steiner Tree ◽  
Polynomial Space ◽  
Exponential Time ◽  
Single Exponential

Voltage-clamp analysis of the ionic conductances in a leech neuron with a purely calcium-dependent action potential

1987 ◽  
Vol 58 (6) ◽  
pp. 1468-1484 ◽  
Author(s):  
J. Johansen ◽  
J. Yang ◽  
A. L. Kleinhaus
Keyword(s):  
Steady State ◽  
Action Potential ◽  
Time Course ◽  
Outward Current ◽  
Time Constants ◽  
Exponential Time ◽  
Calcium Dependent ◽  
Voltage Dependent ◽  
Ca Currents ◽  
Single Exponential

1. The purely calcium-dependent action potential of the anterior lateral giant (ALG) cell in the leech Haementeria was examined under voltage clamp. 2. Analysis with ion substitutions showed that the ALG cell action potential is generated by only two time- and voltage-dependent conductance systems, an inward Ca-dependent current (ICa) and an outward Ca-dependent K current IK(Ca). 3. The kinetic properties of the inward current were examined both in Cs-loaded neurons with Ca as the current carrier as well as in Ba-containing Ringer solutions with Ba as the current carrier, since Ba effectively blocked all time- and voltage-dependent outward current. 4. During a maintained depolarization, Ba and Ca currents activated with a time constant tau m, they then inactivated with the decay following a single exponential time course with a time constant tau h. The time constants for decay of both Ba and Ca currents were comparable, suggesting that the mechanism of inactivation of ICa in the ALG cell is largely voltage dependent. In the range of potentials from 5 to 45 mV, tau m varied from 8 to 2 ms and tau h varied from 250 to 125 ms. 5. The activation of currents carried by Ba, after correction for inactivation, could be described reasonably well by the expression I'Ba = I'Ba(infinity) [1--exp(-t/tau m)]. 6. The steady-state activation of the Ba-conductance mBa(infinity) increased sigmoidally with voltage and was approximated by the equation mBa(infinity) = (1 + exp[(Vh-6)/3])-1. The steady-state inactivation hBa(infinity) varied with holding potential and could be described by the equation hBa(infinity) = [1 + exp(Vh + 10/7)]-1. Recovery from inactivation of IBa was best described by the sum of two exponential time courses with time constants of 300 ms and 1.75 s, respectively. 7. The outward current IK(Ca) developed very slowly (0.5–1 s to half-maximal amplitude) and did not inactivate during a 20-s depolarizing command pulse. Tail current decay of IK(Ca) followed a single exponential time course with voltage-dependent time constants of between 360 and 960 ms. The steady-state activation n infinity of IK(Ca) increased sigmoidally with depolarization as described by the equation n infinity = [1 + exp(Vh-13.5)/-8)]-1. 8. The reversal potentials of IK(Ca) tail currents were close to the expected equilibrium potential for potassium and they varied linearly with log [K]o with a slope of 51 mV. These results suggest a high selectivity of the conductance for K ions.(ABSTRACT TRUNCATED AT 400 WORDS)

APPROXIMATING ASYMMETRIC TSP IN EXPONENTIAL TIME

2014 ◽  
Vol 25 (01) ◽  
pp. 89-99 ◽  
Author(s):  
ALEXANDER GOLOVNEV
Keyword(s):  
Traveling Salesman Problem ◽  
Directed Graph ◽  
Short Note ◽  
Simple Algorithm ◽  
Computable Function ◽  
Traveling Salesman ◽  
Polynomial Space ◽  
Exponential Time ◽  
Running Time ◽  
Polynomial Factor

Let G be a complete directed graph with n vertices and integer edge weights in range [0,M]. It is well known that an optimal Traveling Salesman Problem (TSP) in G can be solved in 2n time and space (all bounds are given within a polynomial factor of the input length, i.e., poly(n, log M)) and this is still the fastest known algorithm. If we allow a polynomial space only, then the best known algorithm has running time 4nnlog n. For TSP with bounded weights there is an algorithm with 1.657n · M running time. It is a big challenge to develop an algorithm with 2n time and polynomial space. Also, it is well-known that TSP cannot be approximated within any polynomial time computable function unless P=NP. In this short note we propose a very simple algorithm that, for any 0 < ε < 1, finds (1+ε)-approximation to asymmetric TSP in 2nε−1 time and ε−1 · poly(n, log M) space. Thereby, for any fixed ε, the algorithm needs 2n steps and polynomial space to compute (1 + ε)-approximation.

scholarly journals Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time

2011 ◽  
Author(s):  
Marek Cygan ◽  
Jesper Nederlof ◽  
Marcin Pilipczuk ◽  
Michal Pilipczuk ◽  
Joham M.M. van Rooij ◽  
...  
Keyword(s):  
Exponential Time ◽  
Single Exponential

Modulation of high-threshold transmission between heart interneurons of the medicinal leech by FMRF-NH2

1994 ◽  
Vol 71 (2) ◽  
pp. 454-466 ◽  
Author(s):  
T. W. Simon ◽  
J. Schmidt ◽  
R. L. Calabrese
Keyword(s):  
Synaptic Transmission ◽  
Time Course ◽  
High Threshold ◽  
Presynaptic Neuron ◽  
Voltage Step ◽  
Exponential Time ◽  
Time To Peak ◽  
Postsynaptic Currents ◽  
Bath Application ◽  
Single Exponential

1. We examined high-threshold synaptic transmission between oscillatory pairs of leech heart interneurons. Inhibitory postsynaptic currents (IPSCs) could be reliably evoked by depolarizing the presynaptic neuron in voltage clamp from a holding potential of -35 mV. At this presynaptic potential, the Ca2+ currents underlying graded transmission are completely inactivated, and we conclude that a high-threshold Ca2+ current is extant in heart interneurons. Further evidence for this was that inhibitory postsynaptic currents were blocked when Co2+ replaced Ca2+ in the saline and thus high-threshold transmission was dependent on the presence of external Ca2+. 2. When IPSCs were evoked by a 200-ms duration voltage step from a holding potential of -35 mV in the presynaptic neuron, the time course of turn-on of the IPSC consisted of a fast (time-to-peak = 17.5 +/- 1.93 (SE) ms [n = 7]) and a slow (time-to-peak = 250 +/- 28.5 ms [n = 8]) component. FMRF-NH2 reduced the amplitude of the fast component but did not affect the slow component. When the presynaptic voltage step was ended the IPSC turned off with a single exponential time course. FMRF-NH2 slowed the time course of turn-off of the IPSC. 3. When IPSCs were evoked by a 1500-ms duration voltage step from a holding potential of -35 mV in the presynaptic neuron, these IPSCs peaked around 300 ms. Following the peak, the IPSC decayed with a single exponential time course. FMRF-NH2 accelerated the time course of this decay. At potentials of 0 mV and +5 mV, FMRF-NH2 produced a significant decrease in the peak current and at potentials of -5 mV and 0 mV, produced a significant decrease in the current integral. 4. High-threshold IPSCs could also be evoked by a spike in the presynaptic neuron. Bath application of 1 microM FMRF-NH2 decreased the amplitude of the spike-evoked IPSC and slowed the time course of its falling phase. 5. We examined the effect of FMRF-NH2 on the quantal synaptic transmission. Bath-application of FMRF-NH2 increased binomial p, the probability of release, and decreased binomial n, the number of units available for release. FMRF-NH2 had no effect on q, the unit size, when calculated from the distributions of PSPs, and increased the coefficient of variation (CV). 6. The lack of a change in q and the increase in CV suggested that FMRF-NH2 acted at a presynaptic location.(ABSTRACT TRUNCATED AT 400 WORDS)

An FPT algorithm in polynomial space for the Directed Steiner Tree problem with Limited number of Diffusing nodes

2015 ◽  
Vol 115 (2) ◽  
pp. 275-279 ◽  
Author(s):  
Dimitri Watel ◽  
Marc-Antoine Weisser ◽  
Cédric Bentz ◽  
Dominique Barth
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Polynomial Space ◽  
Fpt Algorithm
Sign in / Sign up

Export Citation Format

Share Document