How to compute the Chow form of an unmixed polynomial ideal in single exponential time

1990 ◽  
Vol 1 (1) ◽  
pp. 25-41 ◽  
Author(s):  
Leandro Caniglia
Keyword(s):  
Polynomial Ideal ◽  
Exponential Time ◽  
Chow Form ◽  
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)

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)

scholarly journals Voting and Bribing in Single-Exponential Time

2020 ◽  
Vol 8 (3) ◽  
pp. 1-28 ◽  
Author(s):  
Dušan Knop ◽  
Martin Koutecký ◽  
Matthias Mnich
Keyword(s):  
Exponential Time ◽  
Single Exponential

scholarly journals Fine-Grained Complexity of Temporal Problems

2020 ◽  
Author(s):  
Konrad K. Dabrowski ◽  
Peter Jonsson ◽  
Sebastian Ordyniak ◽  
George Osipov
Keyword(s):  
Time Complexity ◽  
Unit Length ◽  
Solution Space ◽  
Worst Case ◽  
Exponential Time ◽  
Fine Grained ◽  
Novel Algorithms ◽  
Open Question ◽  
Special Case ◽  
Single Exponential

Expressive temporal reasoning formalisms are essential for AI. One family of such formalisms consists of disjunctive extensions of the simple temporal problem (STP). Such extensions are well studied in the literature and they have many important applications. It is known that deciding satisfiability of disjunctive STPs is NP-hard, while the fine-grained complexity of such problems is virtually unexplored. We present novel algorithms that exploit structural properties of the solution space and prove, assuming the Exponential-Time Hypothesis, that their worst-case time complexity is close to optimal. Among other things, we make progress towards resolving a long-open question concerning whether Allen's interval algebra can be solved in single-exponential time, by giving a 2^{O(nloglog(n))} algorithm for the special case of unit-length intervals.

An ExpTime Upper Bound for ALC with Integers

2020 ◽  
Author(s):  
Nadia Labai ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Upper Bound ◽  
Description Logics ◽  
Upper Bounds ◽  
Worst Case ◽  
Exponential Time ◽  
Functional Roles ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Concrete Domains ◽  
Single Exponential

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called ω-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of ALC with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of ALC with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard ALC. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

scholarly journals Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth

2015 ◽  
Vol 243 ◽  
pp. 86-111 ◽  
Author(s):  
Hans L. Bodlaender ◽  
Marek Cygan ◽  
Stefan Kratsch ◽  
Jesper Nederlof
Keyword(s):  
Exponential Time ◽  
Exponential Time Algorithms ◽  
Single Exponential

scholarly journals Matching cut: Kernelization, single-exponential time FPT, and exact exponential algorithms

2020 ◽  
Vol 283 ◽  
pp. 44-58 ◽  
Author(s):  
Christian Komusiewicz ◽  
Dieter Kratsch ◽  
Van Bang Le
Keyword(s):  
Exponential Time ◽  
Exact Exponential Algorithms ◽  
Single Exponential
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