Search results for "Logarithm"
showing 10 items of 182 documents
Surface effects on kinetics of ordering
1992
We study the effects of surfaces on the kinetics of phase changes in Ising-type systems. If the surface effects can be modelled by a field which couples linearly to the local order parameter, the growth of wetting or drying layers occurs. The numerical solution of the corresponding time-dependent Ginzburg-Landau equation yields a temporally logarithmic growth for the thickness of a wetting (drying) layer growing from an unstable dry (wet) state. On the other hand, if one starts off with a metastable state, the radius of a supercritical plug (wet or dry) grows linearly in time, in accordance with recent experimental results.
Algebraic models of the Euclidean plane
2018
We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic to $\mathbb{R}^2$, but which are pairwise not birationally diffeomorphic. There are thus infinitely many non-trivial models of the euclidean plane, contrary to the compact case.
Matrix Shuffle- Exchange Networks for Hard 2D Tasks
2021
Convolutional neural networks have become the main tools for processing two-dimensional data. They work well for images, yet convolutions have a limited receptive field that prevents its applications to more complex 2D tasks. We propose a new neural model, called Matrix Shuffle-Exchange network, that can efficiently exploit long-range dependencies in 2D data and has comparable speed to a convolutional neural network. It is derived from Neural Shuffle-Exchange network and has O(log N) layers and O(N ^ 2 log N) total time and O(N^2) space complexity for processing a NxN data matrix. We show that the Matrix Shuffle-Exchange network is well-suited for algorithmic and logical reasoning tasks on …
TOPS-MODE approach for the prediction of blood-brain barrier permeation.
2004
The blood-brain barrier permeation has been investigated by using a topological substructural molecular design approach (TOPS-MODE). A linear regression model was developed to predict the in vivo blood-brain partitioning coefficient on a data set of 119 compounds, treated as the logarithm of the blood-brain concentration ratio. The final model explained the 70% of the variance and it was validated through the use of an external validation set (33 compounds of the 119, MAE = 0.33), a leave-one-out crossvalidation (q(2) = 0.65, S(press) = 0.43), fivefold full crossvalidation (removing 28 compounds in each cycle, MAE = 33, RMSE = 0.43) and the prediction of +/- values for an external test set …
FIR Kramers–Kronig transformers for relaxation data conversion
2006
It is shown that relaxation data conversion by the Kramers-Kronig (KK) relations can be treated as a filtering problem of band-unlimited relaxation signals in the Mellin transform domain. Based on this concept, KK relations are implemented in the form of FIR filters with the logarithmic sampling. It is demonstrated that KK transformers have sampling rate dependent impulse and frequency responses and only calculation of the imaginary part from the real part can be implemented by a computationally realisable filter. The performance of different types of transformers is studied.Approximately inversely proportional relationship is established between the error and the frequency range of input s…
Random telegraph signal transients in active logarithmic continuous-time vision sensors
2015
Abstract Random Telegraph Signal (RTS) is a well-known source of noise in current submicron circuits. Its static effects have been widely studied and its noise levels are in the order of other noise sources, especially for moderate submicron transistors. Nevertheless, RTS events may produce transients many times larger than the RTS itself, and this problem seems to have not yet been addressed. In this article we present results on the transients produced by RTS events in a smart vision sensor. RTS transients in closed-loop amplifiers can be many times greater than static RTS. The duration of the RTS transient may last for several milliseconds, and can be considered almost stationary for som…
A Nondifferentiable Optimization Approach to Ratio-Cut Partitioning
2003
We propose a new method for finding the minimum ratio-cut of a graph. Ratio-cut is NP-hard problem for which the best previously known algorithm gives an O(log n)-factor approximation by solving its dually related maximum concurrent flow problem.We formulate the minimum ratio-cut as a certain nondifferentiable optimization problem, and show that the global minimum of the optimization problem is equal to the minimum ratio-cut. Moreover, we provide strong symbolic computation based evidence that any strict local minimum gives an approximation by a factor of 2. We also give an efficient heuristic algorithm for finding a local minimum of the proposed optimization problem based on standard nondi…
Formal Analysis and Model Checking of a Group Authentication Protocol by Scyther
2016
Scyther [1] is designed to check the security and vulnerabilities of security protocols. In this paper, we use Scyther to analyze two discrete logarithm problem (DLP) based group authentication protocols proposed in [2]. These two protocols are claimed to satisfy several security requirements, but only part of them have been checked because of the properties and limitations of Scyther. Some positive results have been gained and show that the protocols provide mutual authentication and implicit key authentication and are secure against impersonation attack. An important innovation in this paper is that we have extended the expressing ability of Scyther by giving some reasonable assumption du…
Measuring frequency domain granger causality for multiple blocks of interacting time series
2011
In the past years, several frequency-domain causality measures based on vector autoregressive time series modeling have been suggested to assess directional connectivity in neural systems. The most followed approaches are based on representing the considered set of multiple time series as a realization of two or three vector-valued processes, yielding the so-called Geweke linear feedback measures, or as a realization of multiple scalar-valued processes, yielding popular measures like the directed coherence (DC) and the partial DC (PDC). In the present study, these two approaches are unified and generalized by proposing novel frequency-domain causality measures which extend the existing meas…
Scalar particle contribution to Higgs production via gluon fusion at NLO
2007
22 pages, 5 figures.-- ISI Article Identifier: 000252243700095.-- ArXiv pre-print available at: http://arxiv.org/abs/0709.4227