Alternate Lucas Cubes

2021 ◽  
pp. 1-29
Author(s):  
Ömer Eğecioğlu ◽  
Elif Saygı ◽  
Zülfükar Saygı
Keyword(s):  
Interconnection Networks ◽  
Recursive Structure ◽  
Metric Properties ◽  
New Family ◽  
Representation Of Integers ◽  
The One ◽  
Binary Strings

We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes. The vertices of alternate Lucas cubes are constructed from binary strings that are encodings of Lucas representation of integers. As well as ordinary hypercubes, Fibonacci cubes and Lucas cubes, alternate Lucas cubes have several interesting structural and enumerative properties. In this paper we study some of these properties. Specifically, we give the fundamental decomposition giving the recursive structure, determine the number of edges, number of vertices by weight, the distribution of the degrees; as well as the properties of induced hypercubes, [Formula: see text]-cube polynomials and maximal hypercube polynomials. We also obtain the irregularity polynomials of this family of graphs, determine the conditions for Hamiltonicity, and calculate metric properties such as the radius, diameter, and the center.

scholarly journals DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS

2006 ◽  
Vol 16 (04) ◽  
pp. 887-910 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
BRUNO ROSSETTO
Keyword(s):  
Differential Geometry ◽  
Dynamical Systems ◽  
Slow Manifold ◽  
Van Der Pol ◽  
New Approach ◽  
Metric Properties ◽  
Chaotic Dynamical Systems ◽  
Mechanics Concepts ◽  
The One ◽  
Curvature And Torsion

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical expression of the slow manifold equation of slow-fast autonomous dynamical systems starting from kinematics variables (velocity, acceleration and over-acceleration or jerk). The attractivity of the slow manifold will be characterized thanks to a criterion proposed by Henri Poincaré. Moreover, the specific use of acceleration will make it possible on the one hand to define slow and fast domains of the phase space and on the other hand, to provide an analytical equation of the slow manifold towards which all the trajectories converge. The attractive slow manifold constitutes a part of these dynamical systems attractor. So, in order to propose a description of the geometrical structure of attractor, a new manifold called singular manifold will be introduced. Various applications of this new approach to the models of Van der Pol, cubic-Chua, Lorenz, and Volterra–Gause are proposed.

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

2007 ◽  
Vol 62 (7-8) ◽  
pp. 368-372
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Landau Equation ◽  
Model Parameters ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Paraxial Ray Approximation ◽  
New Family ◽  
Ginzburg Landau Equation ◽  
The Stability ◽  
The One ◽  
Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals Exploring Efficient Neural Architectures for Linguistic–Acoustic Mapping in Text-To-Speech

2019 ◽  
Vol 9 (16) ◽  
pp. 3391 ◽  
Author(s):  
Santiago Pascual ◽  
Joan Serrà ◽  
Antonio Bonafonte
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Recurrent Neural Network ◽  
Recurrent Neural Networks ◽  
Affine Transformations ◽  
Text To Speech ◽  
Recursive Structure ◽  
The One ◽  
Acoustic Mapping ◽  
Symbol Sequences

Conversion from text to speech relies on the accurate mapping from linguistic to acoustic symbol sequences, for which current practice employs recurrent statistical models such as recurrent neural networks. Despite the good performance of such models (in terms of low distortion in the generated speech), their recursive structure with intermediate affine transformations tends to make them slow to train and to sample from. In this work, we explore two different mechanisms that enhance the operational efficiency of recurrent neural networks, and study their performance–speed trade-off. The first mechanism is based on the quasi-recurrent neural network, where expensive affine transformations are removed from temporal connections and placed only on feed-forward computational directions. The second mechanism includes a module based on the transformer decoder network, designed without recurrent connections but emulating them with attention and positioning codes. Our results show that the proposed decoder networks are competitive in terms of distortion when compared to a recurrent baseline, whilst being significantly faster in terms of CPU and GPU inference time. The best performing model is the one based on the quasi-recurrent mechanism, reaching the same level of naturalness as the recurrent neural network based model with a speedup of 11.2 on CPU and 3.3 on GPU.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (3) ◽  
pp. 714-716 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals On the Transport Properties of Li-TFSI Water-in-Salt Electrolytes

2019 ◽  
Author(s):  
Zhujie Li ◽  
Roza Bouchal ◽  
Trinidad Mendez-Morales ◽  
Anne-Laure Rollet ◽  
Cecile Rizzi ◽  
...  
Keyword(s):  
Force Field ◽  
Transport Properties ◽  
Transport Number ◽  
Lithium Ion ◽  
Ionic Species ◽  
Self Diffusion ◽  
New Family ◽  
The One ◽  
Dynamics Simulations ◽  
Percolating Network

Water-in-salts are a new family of electrolytes that may allow the development of aqueous Li-ion batteries. They have a structure which is reminiscent of the one of ionic liquids, and they are characterized by a large concentration of ionic species. In this work we study their transport properties and how they evolve with concentration by using molecular dynamics simulations. We first focus on the choice of the force field. By comparing the simulated viscosities and self diffusion coefficients with experimental measurements, we select a set of parameters that reproduces well the transport properties. We then use the selected force field to study in detail the variations of the self and collective diffusivities of all the species as well as the transport number of the lithium ion. We show that correlation between ions and water play an important role over the whole concentration range. In the water-in-salt regime, the anions form a percolating network which reduces the cation-anion correlations and leads to rather large values for the transport number compared to other standard electrolytes.

Family Frames as Exile Photography

2019 ◽  
Vol 64 (1) ◽  
pp. 5-17
Author(s):  
Talila Kosh-Zohar
Keyword(s):  
The Other ◽  
The Past ◽  
New Family ◽  
The Holocaust ◽  
Family Photographs ◽  
The One

Abstract This article examines five family photographs. The first of these family frames was taken in Czechoslovakia during the early 1930s and was found after the Holocaust, the one and only surviving photograph of my father’s exterminated family. The other four are family frames taken in Israel, the land of rebirth, where the survivors tried to start over from scratch, forget the past, and create a new family. All five frames are discussed as ‘exile photographs’—images of absence, alienation, and nostalgia; images of emotions like anxiety, sadness, and loneliness, all of which are inherent to the condition of exile. The article argues that the new family frames, which are supposed to represent new (personal and national) beginnings, continue to authenticate the traumatic past. Their testimony bears witness not to revival and reconstruction, but to forced exile from one’s birthplace, a devastated home and family, a condition of terminal loss.

Invariants of Translation (May 29, 1970)

2020 ◽  
pp. 99-114
Author(s):  
Cameron Domenico Kirk-Giannini ◽  
Ernie Lepore
Keyword(s):  
Natural Language ◽  
The Other ◽  
Object Language ◽  
Recursive Structure ◽  
Other Hand ◽  
The World ◽  
The One

In his final lecture, Davidson turns away from the project of providing semantic analyses for particular natural language constructions. He outlines his theory of radical translation—that is, his theory of how one can come to know that a candidate T-theory for a given object language is correct. By assuming (on the one hand) that whenever an object-language speaker accepts a sentence, that sentence is true, and (on the other hand) that we as theoreticians generally have correct beliefs about the world, Davidson argues that we can arrive at a correct T-theory for an object language. He concludes with some reflections on the fact that this procedure seems to make it inevitable that we will discover the recursive structure of our own language in the languages of others, as well as the preponderance of our beliefs in the minds of our peers.

A new family of salts for lithium Secondary batteries

1999 ◽  
Vol 575 ◽  
Author(s):  
D. Baril ◽  
S. Brranger ◽  
N. Ravet ◽  
C. Michot ◽  
M. Armand
Keyword(s):  
Large Scale ◽  
Lithium Perchlorate ◽  
Solid Polymer ◽  
Calorimetric Analysis ◽  
Lithium Secondary Batteries ◽  
New Family ◽  
Poly Ethylene Oxide ◽  
Poly Ethylene ◽  
The One ◽  
Battery Application

ABSTRACTA novel family of salts suitable for lithium battery application was synthesized and characterized. These salts have a large delocalized anion whose charge is spread over a single SO2and a phenyl ring. Remarkable properties were obtained for the lithium N-(3-trifluoromethyl phenyl) trifluoromethanesulfonamide salt or LiTFPTS. The electrochemical stability window is around 4.0 V and its conductivity in solid poly(ethylene oxide) or PEO is close to the one of the lithium perchlorate salt. Calorimetric analysis also showed that LiTFPTS behaves as a plasticizer since it hinders, to a certain extent, the PEO crystallization when it is used in a solid polymer matrix. Above all, its synthesis is quite straightforward and leads to potentially inexpensive salts as the starting amines are made commercially on a large scale.

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