scholarly journals A variant of the Recoil Growth algorithm to generate multi-polymer systems

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Florian Simatos
Keyword(s):  
Lower Bound ◽  
Simple Proof ◽  
Efficient Algorithm ◽  
Computational Cost ◽  
Polymer System ◽  
Specific Class ◽  
Trade Off ◽  
Polymer Systems ◽  
Original Algorithm ◽  
International Audience

International audience The Recoil Growth algorithm, proposed in 1999 by Consta $\textit{et al.}$, is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well.

scholarly journals A note on domino treewidth

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Hans L. Bodlaender
Keyword(s):  
Lower Bound ◽  
Simple Proof ◽  
Maximum Degree ◽  
International Audience

International audience In [DO95], Ding and Oporowski proved that for every k, and d, there exists a constant c_k,d, such that every graph with treewidth at most k and maximum degree at most d has domino treewidth at most c_k,d. This note gives a new simple proof of this fact, with a better bound for c_k,d, namely (9k+7)d(d+1) -1. It is also shown that a lower bound of Ω (kd) holds: there are graphs with domino treewidth at least 1/12 × kd-1, treewidth at most k, and maximum degree at most d, for many values k and d. The domino treewidth of a tree is at most its maximum degree.

scholarly journals Lumáwig: An Efficient Algorithm for Dimension Zero Bottleneck Distance Computation in Topological Data Analysis

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 291
Author(s):  
Paul Samuel Ignacio ◽  
Jay-Anne Bulauan ◽  
David Uminsky
Keyword(s):  
Data Analysis ◽  
Efficient Algorithm ◽  
Computational Cost ◽  
Topological Data Analysis ◽  
Real World Data ◽  
Matching Problem ◽  
Original Algorithm ◽  
Dimension Zero ◽  
Topological Data ◽  
Persistence Diagrams

Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck distance which entails matching points between diagrams. Instances of use of this metric in practical studies have, however, been few and sparingly far between because of the computational obstruction, especially in dimension zero where the computational cost explodes with the growth of data size. We present a novel efficient algorithm to compute dimension zero bottleneck distance between two persistent diagrams of a specific kind which runs significantly faster and provides significantly sharper approximates with respect to the output of the original algorithm than any other available algorithm. We bypass the overwhelming matching problem in previous implementations of the bottleneck distance, and prove that the zero dimensional bottleneck distance can be recovered from a very small number of matching cases. Partly in keeping with nomenclature traditions in this area of TDA, we name this algorithm Lumáwig as a nod to a deity in the northern Philippines, where the algorithm was developed. We show that Lumáwig generally enjoys linear complexity as shown by empirical tests. We also present an application that leverages dimension zero persistence diagrams and the bottleneck distance to produce features for classification tasks.

Sky Segmentation for Enhanced Depth Reconstruction and Bokeh Rendering with Efficient Architectures

2020 ◽  
Vol 2020 (14) ◽  
pp. 378-1-378-7
Author(s):  
Tyler Nuanes ◽  
Matt Elsey ◽  
Radek Grzeszczuk ◽  
John Paul Shen
Keyword(s):  
Real Time ◽  
Mobile Device ◽  
Computational Cost ◽  
False Positives ◽  
Compact Model ◽  
High Quality ◽  
False Negatives ◽  
Trade Off ◽  
Depth Reconstruction ◽  
Binary Classifiers

We present a high-quality sky segmentation model for depth refinement and investigate residual architecture performance to inform optimally shrinking the network. We describe a model that runs in near real-time on mobile device, present a new, highquality dataset, and detail a unique weighing to trade off false positives and false negatives in binary classifiers. We show how the optimizations improve bokeh rendering by correcting stereo depth misprediction in sky regions. We detail techniques used to preserve edges, reject false positives, and ensure generalization to the diversity of sky scenes. Finally, we present a compact model and compare performance of four popular residual architectures (ShuffleNet, MobileNetV2, Resnet-101, and Resnet-34-like) at constant computational cost.

scholarly journals A mechanism for fire retardancy realized by a combination of biofillers and ammonium polyphosphate in various polymer systems

Cellulose ◽  
2021 ◽  
Author(s):  
Koki Matsumoto ◽  
Tatsuya Tanaka ◽  
Masahiro Sasada ◽  
Noriyuki Sano ◽  
Kenta Masuyama
Keyword(s):  
Polymer Matrix ◽  
Synergetic Effect ◽  
Polymer System ◽  
Ammonium Polyphosphate ◽  
Fire Retardancy ◽  
Polymer Systems ◽  
Thermal Decomposition Behavior ◽  
Burning Behavior ◽  
The Matrix ◽  
Decomposition Behavior

AbstractThis study focused on realizing fire retardancy for polymer composites by using a cellulosic biofiller and ammonium polyphosphate (APP). The motivation of this study was based on revealing the mechanism of the synergetic effect of a cellulosic biofiller and APP and determining the parameters required for achieving a V-0 rating in UL94 standard regardless of the kind of polymer system used. As for the polymer matrix, polypropylene and polylactic acid were used. The flammability, burning behavior and thermal decomposition behavior of the composites were investigated through a burning test according to the UL-94 standard, cone calorimetric test and thermogravimetric analysis. As a result, the incorporation of a high amount of cellulose enabled a V-0 rating to be achieved with only a small amount of APP despite the variation of the optimum cellulose loading between the matrix polymers. Through analysis, the results indicated that APP decreased the dehydration temperature of cellulose. Furthermore, APP promoted the generation of enough water as a nonflammable gas and formed enough char until the degradation of the polymer matrix was complete. The conditions required to achieve the V-0 rating were suggested against composites incorporating APP and biofillers. Furthermore, the suggested conditions were validated by using polyoxymethylene as a highly flammable polymer.

scholarly journals On Greedy Trie Execution

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Zbigniew Gołębiewski ◽  
Filip Zagórski
Keyword(s):  
Lower Bound ◽  
Greedy Algorithm ◽  
International Audience ◽  
The Greedy Algorithm

International audience In the paper "How to select a looser'' Prodinger was analyzing an algorithm where $n$ participants are selecting a leader by flipping <underline>fair</underline> coins, where recursively, the 0-party (those who i.e. have tossed heads) continues until the leader is chosen. We give an answer to the question stated in the Prodinger's paper – what happens if not a 0-party is recursively looking for a leader but always a party with a smaller cardinality. We show the lower bound on the number of rounds of the greedy algorithm (for <underline>fair</underline> coin).

An Efficient Algorithm to Construct an Orthonormal Basis for the Extended Krylov Subspace

2014 ◽  
Vol 4 (3) ◽  
pp. 267-282
Author(s):  
Akira Imakura
Keyword(s):  
Efficient Algorithm ◽  
Orthonormal Basis ◽  
Krylov Subspace ◽  
Computational Cost ◽  
Projection Methods ◽  
Matrix Equations ◽  
Subspace Projection ◽  
Matrix Computations ◽  
Large Matrix ◽  
Traditional Algorithm

AbstractSubspace projection methods based on the Krylov subspace using powers of a matrix A have often been standard for solving large matrix computations in many areas of application. Recently, projection methods based on the extended Krylov subspace using powers of A and A−1 have attracted attention, particularly for functions of a matrix times a vector and matrix equations. In this article, we propose an efficient algorithm for constructing an orthonormal basis for the extended Krylov subspace. Numerical experiments indicate that this algorithm has less computational cost and approximately the same accuracy as the traditional algorithm.

scholarly journals Cauchy's interlace theorem and lower bounds for the spectral radius

2000 ◽  
Vol 23 (8) ◽  
pp. 563-566 ◽  
Author(s):  
A. McD. Mercer ◽  
Peter R. Mercer
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Lower Bounds ◽  
Simple Proof ◽  
Symmetric Matrix ◽  
Real Symmetric Matrix

We present a short and simple proof of the well-known Cauchy interlace theorem. We use the theorem to improve some lower bound estimates for the spectral radius of a real symmetric matrix.

scholarly journals Lower bounds and the asymptotic behaviour of positive operator semigroups

2017 ◽  
Vol 38 (8) ◽  
pp. 3012-3041 ◽  
Author(s):  
MORITZ GERLACH ◽  
JOCHEN GLÜCK
Keyword(s):  
Lower Bound ◽  
Asymptotic Behaviour ◽  
Lower Bounds ◽  
Simple Proof ◽  
Continuous Operator ◽  
Banach Lattices ◽  
Operator Semigroups ◽  
Markov Operators ◽  
Discrete Semigroups ◽  
Analytical Tools

If $(T_{t})$ is a semigroup of Markov operators on an $L^{1}$-space that admits a non-trivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as $t\rightarrow \infty$. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius–Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.

A Novel Parameter Estimation Method for Boltzmann Machines

2015 ◽  
Vol 27 (11) ◽  
pp. 2423-2446
Author(s):  
Takashi Takenouchi
Keyword(s):  
Probabilistic Models ◽  
Risk Function ◽  
Computational Cost ◽  
Estimation Method ◽  
Estimating Function ◽  
Specific Class ◽  
Normalization Constant ◽  
Boltzmann Machines ◽  
Comparable Performance ◽  
Discrete Spaces

We propose a novel estimator for a specific class of probabilistic models on discrete spaces such as the Boltzmann machine. The proposed estimator is derived from minimization of a convex risk function and can be constructed without calculating the normalization constant, whose computational cost is exponential order. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality in the framework of the estimating function. Small experiments show that the proposed estimator can attain comparable performance to the maximum likelihood expectation at a much lower computational cost and is applicable to high-dimensional data.

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