On non-linear lower bounds in computational complexity

1975 ◽  
Author(s):  
Leslie G. Valiant
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Non Linear

scholarly journals Non-ohmic tissue conduction in cardiac electrophysiology: upscaling the non-linear voltage-dependent conductance of gap junctions

2019 ◽  
Author(s):  
Daniel E. Hurtado ◽  
Javiera Jilberto ◽  
Grigory Panasenko
Keyword(s):  
Computational Complexity ◽  
Gap Junctions ◽  
Cardiac Tissue ◽  
Tissue Level ◽  
Cardiac Conduction ◽  
Non Linear ◽  
Voltage Dependent ◽  
Junctional Coupling ◽  
Organ Level ◽  
Electrical Propagation

AbstractGap junctions are key mediators of the intercellular communication in cardiac tissue, and their function is vital to sustain normal cardiac electrical activity. Conduction through gap junctions strongly depends on the hemichannel arrangement and transjunctional voltage, rendering the intercellular conductance highly non-Ohmic. Despite this marked non-linear behavior, current tissue-level models of cardiac conduction are rooted on the assumption that gap-junctions conductance is constant (Ohmic), which results in inaccurate predictions of electrical propagation, particularly in the low junctional-coupling regime observed under pathological conditions. In this work, we present a novel non-Ohmic multiscale (NOM) model of cardiac conduction that is suitable for tissue-level simulations. Using non-linear homogenization theory, we develop a conductivity model that seamlessly upscales the voltage-dependent conductance of gap junctions, without the need of explicitly modeling gap junctions. The NOM model allows for the simulation of electrical propagation in tissue-level cardiac domains that accurately resemble that of cell-based microscopic models for a wide range of junctional coupling scenarios, recovering key conduction features at a fraction of the computational complexity. A unique feature of the NOM model is the possibility of upscaling the response of non-symmetric gap-junction conductance distributions, which result in conduction velocities that strongly depend on the direction of propagation, thus allowing to model the normal and retrograde conduction observed in certain regions of the heart. We envision that the NOM model will enable organ-level simulations that are informed by sub- and inter-cellular mechanisms, delivering an accurate and predictive in-silico tool for understanding the heart function.Author summaryThe heart relies on the propagation of electrical impulses that are mediated gap junctions, whose conduction properties vary depending on the transjunctional voltage. Despite this non-linear feature, current mathematical models assume that cardiac tissue behaves like an Ohmic (linear) material, thus delivering inaccurate results when simulated in a computer. Here we present a novel mathematical multiscale model that explicitly includes the non-Ohmic response of gap junctions in its predictions. Our results show that the proposed model recovers important conduction features modulated by gap junctions at a fraction of the computational complexity. This contribution represents an important step towards constructing computer models of a whole heart that can predict organ-level behavior in reasonable computing times.

scholarly journals Novel Low Complexity BP Decoding Algorithms for Polar Codes: Simplifying on Non-Linear Operations

Electronics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Yuhuan Wang ◽  
Jianguo Li ◽  
Neng Ye ◽  
Xiangyuan Bu
Keyword(s):  
Computational Complexity ◽  
Hardware Implementation ◽  
Low Complexity ◽  
Bp Algorithm ◽  
Polar Codes ◽  
Decoding Algorithm ◽  
Hyperbolic Tangent ◽  
Decoding Algorithms ◽  
Tangent Function ◽  
Non Linear

The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introduces high-complexity non-linear operations in the iterative messages update process, this paper proposes to simplify these operations and develops two novel low complexity BP decoding algorithms, namely, exponential BP (Exp-BP) decoding algorithm and quantization function BP (QF-BP) decoding algorithm. The proposed algorithms simplify the compound hyperbolic tangent function by using probability distribution fitting techniques. Specifically, the Exp-BP algorithm simplifies two types of non-linear operations into single non-linear operation using the piece-wise exponential model function, which can approximate the hyperbolic tangent function in the updating formula. The QF-BP algorithm eliminates non-linear operations using the non-uniform quantization in the updating formula, which is effective in reducing computational complexity. According to the simulation results, the proposed algorithms can reduce the computational complexity up to 50% in each iteration with a loss of less than 0.1 dB compared with the BP decoding algorithm, which can facilitate the hardware implementation.

scholarly journals The Complexity of Finite Memory Programs with Recursion

1976 ◽  
Vol 5 (68) ◽  
Author(s):  
Neil D. Jones ◽  
Steven S. Muchnick
Keyword(s):  
Computational Complexity ◽  
Programming Language ◽  
Lower Bounds ◽  
Equivalence Problem ◽  
Theoretical Interest ◽  
Exponential Time ◽  
Sophisticated Model ◽  
Finite Memory ◽  
Pushdown Automata ◽  
Exponential Space

<p>In an earlier paper (JACM, 1976) we studied the computational complexity of a number of questions of both programming and theoretical interest (e.g. halting, looping, equivalence) concerning the behaviour of programs written in an extremely simple programming language. These finite memory programs or fmps model the behaviour of FORTRAN-like programs with a finite memory whose size can be determined by examination of the program itself.</p><p>The present paper is a continuation in which we extend the analysis to include ALGOL-like programs (called fmp^(rec) s) with the finite memory augmented by an implicit pushdown stack used to support recursion.</p><p>Our major results are the following. First, we show that at least deterministic exponential time is required to determine whether a program in the basic fmpr~C model accepts a nonempty set. Then we show that a model with a limited version of call-by-name requires exponential space to determine acceptance of a nonempty set, and that a more sophisticated model with rewritable conditional formal parametershas an undecidable halting problem. The same lower bounds apply to the equivalence problem, which in contrast to the situation for the basic fmp model is not known to be decidable (since it is not known whether equivalence of deterministic pushdown automata is decidable).</p>

scholarly journals Simplified group activity selection with group size constraints

2021 ◽  
Author(s):  
Andreas Darmann ◽  
Janosch Döcker ◽  
Britta Dorn ◽  
Sebastian Schneckenburger
Keyword(s):  
Computational Complexity ◽  
Simple Model ◽  
Lower Bounds ◽  
Group Activity ◽  
Core Stability ◽  
Upper And Lower Bounds ◽  
Size Constraints ◽  
Broad Variety ◽  
Special Case ◽  
Additional Constraints

AbstractSeveral real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

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