Mixing Property Tester: A General Framework for Evaluating the Mixing Properties of Initialization of Stream Ciphers

2019 ◽  
pp. 570-582
Author(s):  
Lin Ding ◽  
Dawu Gu ◽  
Lei Wang
Keyword(s):  
General Framework ◽  
Stream Ciphers ◽  
Mixing Properties ◽  
Mixing Property

scholarly journals Complete characterization of mixing time for the continuous quantum walk on the hypercube with Markovian decoherence model

2009 ◽  
Vol 9 (9&10) ◽  
pp. 856-878
Author(s):  
M. Drezgich ◽  
A.P. Hines ◽  
M. Sarovar ◽  
S. Sastry
Keyword(s):  
Degrees Of Freedom ◽  
Mixing Time ◽  
Quantum Walk ◽  
Complete Characterization ◽  
Arbitrary Direction ◽  
Bloch Sphere ◽  
Quantum Random Walk ◽  
Mixing Properties ◽  
Mixing Property

The n-dimensional hypercube quantum random walk (QRW) is a particularily appealing example of a quantum walk because it has a natural implementation on a register on n qubits. However, any real implementation will encounter decoherence effects due to interactions with uncontrollable degrees of freedom. We present a complete characterization of the mixing properties of the hypercube QRW under a physically relevant Markovian decoherence model. In the local decoherence model considered the non-unitary dynamics are modeled as a sum of projections on individual qubits to an arbitrary direction on the Bloch sphere. We prove that there is always classical (asymptotic) mixing in this model and specify the conditions under which instantaneous mixing always exists. And we show that the latter mixing property, as well as the classical mixing time, depend heavily on the exact environmental interaction and its strength. Therefore, algorithmic applications of the QRW on the hypercube, if they intend to employ mixing properties, need to consider both the walk dynamics and the precise decoherence model.

scholarly journals Mixing properties for STIT tessellations

2011 ◽  
Vol 43 (01) ◽  
pp. 40-48 ◽  
Author(s):  
R. Lachièze-Rey
Keyword(s):  
Decay Rate ◽  
Translation Operator ◽  
Mixing Properties ◽  
Connected Sets ◽  
Stit Tessellation ◽  
Mixing Property

The so-called STIT tessellations form a class of homogeneous (spatially stationary) tessellations inRdwhich are stable under the nesting/iteration operation. In this paper we establish the mixing property for these tessellations and give the decay rate of P(A∩M= ∅,ThB∩M= ∅) / P(A∩Y= ∅)P(B∩Y= ∅) − 1, whereAandBare both compact connected sets,his a vector ofRd,This the corresponding translation operator, andMis a STIT tessellation.

scholarly journals Mixing properties for STIT tessellations

2011 ◽  
Vol 43 (1) ◽  
pp. 40-48 ◽  
Author(s):  
R. Lachièze-Rey
Keyword(s):  
Decay Rate ◽  
Translation Operator ◽  
Mixing Properties ◽  
Connected Sets ◽  
Stit Tessellation ◽  
Mixing Property

The so-called STIT tessellations form a class of homogeneous (spatially stationary) tessellations in Rd which are stable under the nesting/iteration operation. In this paper we establish the mixing property for these tessellations and give the decay rate of P(A ∩ M = ∅, ThB ∩ M = ∅) / P(A ∩ Y = ∅)P(B ∩ Y = ∅) − 1, where A and B are both compact connected sets, h is a vector of Rd, Th is the corresponding translation operator, and M is a STIT tessellation.

scholarly journals MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS

2013 ◽  
Vol 1 ◽  
Author(s):  
TERENCE TAO
Keyword(s):  
Finite Field ◽  
Error Term ◽  
Schwarz Inequality ◽  
Partial Result ◽  
Strong Mixing ◽  
Mixing Properties ◽  
Polynomial Bounds ◽  
Mixing Property ◽  
Weil Bound ◽  
Nonabelian Groups

AbstractWe study the mixing properties of progressions $(x, xg, x{g}^{2} )$, $(x, xg, x{g}^{2} , x{g}^{3} )$ of length three and four in a model class of finite nonabelian groups, namely the special linear groups ${\mathrm{SL} }_{d} (F)$ over a finite field $F$, with $d$ bounded. For length three progressions $(x, xg, x{g}^{2} )$, we establish a strong mixing property (with an error term that decays polynomially in the order $\vert F\vert $ of $F$), which among other things counts the number of such progressions in any given dense subset $A$ of ${\mathrm{SL} }_{d} (F)$, answering a question of Gowers for this class of groups. For length four progressions $(x, xg, x{g}^{2} , x{g}^{3} )$, we establish a partial result in the $d= 2$ case if the shift $g$ is restricted to be diagonalizable over $F$, although in this case we do not recover polynomial bounds in the error term. Our methods include the use of the Cauchy–Schwarz inequality, the abelian Fourier transform, the Lang–Weil bound for the number of points in an algebraic variety over a finite field, some algebraic geometry, and (in the case of length four progressions) the multidimensional Szemerédi theorem.

Phonologically conditioned allomorphy in the morphology of Surmiran (Rumantsch)

2008 ◽  
Vol 1 (2) ◽  
pp. 109-134 ◽  
Author(s):  
Stephen R. Anderson
Keyword(s):  
Optimality Theory ◽  
General Framework ◽  
Great Majority ◽  
Historical Change ◽  
Romance Languages ◽  
Morphological Properties ◽  
Entire System ◽  
Verbal System ◽  
Extended Sense ◽  
Phonological Rule

Alternations between allomorphs that are not directly related by phonological rule, but whose selection is governed by phonological properties of the environment, have attracted the sporadic attention of phonologists and morphologists. Such phenomena are commonly limited to rather small corners of a language's structure, however, and as a result have not been a major theoretical focus. This paper examines a set of alternations in Surmiran, a Swiss Rumantsch language, that have this character and that pervade the entire system of the language. It is shown that the alternations in question, best attested in the verbal system, are not conditioned by any coherent set of morphological properties (either straightforwardly or in the extended sense of ‘morphomes’ explored in other Romance languages by Maiden). These alternations are, however, straightforwardly aligned with the location of stress in words, and an analysis is proposed within the general framework of Optimality Theory to express this. The resulting system of phonologically conditioned allomorphy turns out to include the great majority of patterning which one might be tempted to treat as productive phonology, but which has been rendered opaque (and subsequently morphologized) as a result of the working of historical change.

More's usage of Latin verbal predicates: the particular case of fio

Moreana ◽  
2019 ◽  
Vol 56 (Number 211) (1) ◽  
pp. 97-120
Author(s):  
Concepción Cabrillana
Keyword(s):  
General Framework ◽  
Medieval Latin ◽  
Lexical Semantic ◽  
Syntactic Features ◽  
Comparative Review ◽  
Poetic Text

This article addresses Thomas More's use of an especially complex Latin predicate, fio, as a means of examining the degree of classicism in this aspect of his writing. To this end, the main lexical-semantic and syntactic features of the verb in Classical Latin are presented, and a comparative review is made of More's use of the predicate—and also its use in texts contemporaneous to More, as well as in Late and Medieval Latin—in both prose and poetry. The analysis shows that he works within a general framework of classicism, although he introduces some of his own idiosyncrasies, these essentially relating to the meaning of the verb that he employs in a preferential way and to the variety of verbal forms that occur in his poetic text.

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