Weak generalized self-shrinking generators

The security of certain classes of the generalized self-shrinking sequence （GSS） generators is analyzed. Firstly, it is shown that the security of these GSS generators is equivalent to the security of the GSS generators of the class-1, after which two effective key recovery attacks on the GSS generators of the class-1 are developed to evaluate their security.

Next Generation Sequencing in Oncological Diagnostics: Hype or Hope?

The understanding of how genetic and epigenetic factors influence tumorigenesis, progression and invasion, is vastly growing since new technologies allow the analysis of the functional genome namely the exome, the transcriptome and the epigenome, besides enabling genome-wide assessment of genetic variations. With the advent of new drugs that are indicated tissue agnostic, depending on certain mutations, there is a growing demand for fast and cost-effective genetic diagnosis. The method in focus that already became an indispensable tool in viral diagnosis is next-generation sequencing (NGS). This approach allows sequencing of literally every DNA molecule in the sample and can either be used to assess numerous genetic markers of one patient at a time, or to assess fewer markers of many patients in parallel, which reduces costs. We submitted 23 samples of different tumor entities to four diagnostic companies with different analysis profiles. The results as disclosed and discussed in this report indicate that so far, the main application of NGS is rather in cancer research than in diagnosis, as none of the reports had a real impact on the therapeutic scheme. We are perfectly aware that such a small cohort cannot be generalized, but considering the costs vs. benefits, NGS should be engaged upon a very stringent evaluation only. However, in cases where obtaining a tissue biopsy is impossible or unfavorable, analysis of liquid biopsy by NGS provides a vital alternative.

Linear complexity of Ding generalized cyclotomic sequences

Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.

Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.

Generalized Harmonic Numbers Hn,k,r (α,β) with Combinatorial Sequences

In this paper, we observe the generalized Harmonic numbers Hn,k,r (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers Hn,k,r (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.

Ordered Generalized Sequence Spaces and their Duals

ＯｒｄｅｒｅｄＧｅｎｅｒａｌｉｚｅｄＳｅｑｕｅｎｃｅＳｐａｃｅｓａｎｄｔｈｅｉｒＤｕａｌｓＭａｎｊｕｌＧｕｐｔａ；ＫａｌｉｋａＫａｕｓｈａｌ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｄｉａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｋａｎｐｕｒ－...

Linear Complexity of New Generalized Cyclotomic Sequences of Length 2pq

The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.

DNA Sequences with Forbidden Words and the Generalized Cantor Set

In this work, we establish relations between DNA sequences with missing subsequences (the forbidden words) and the generalized Cantor sets. Various examples associated with some generalized Cantor sets, including Hao’s frame representation and the generalized Sierpinski Set, along with their fractal graphs, are also presented in this work.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

SELECTION OF THE LINEAR COMBINING VECTOR G OF THE GENERALIZED SELF-SHRINKING GENERATORS

Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking (GSS) sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial of L GSS sequences and the comparison of their degrees, an algorithm for selecting the linear com-bining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2L?1 linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.

Digital chaotic sequence generator based on coupled chaotic systems

Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2^128＊2^128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array （FPGA） implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can he applied to the real-time video image encryption.

THE HAUSDORFF DIMENSION OF THE SPECTRUM OF A CLASS OF GENERALIZED THUE-MORSE HAMILTONIANS

Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.

Cross-domain sequence labelling using language modelling and parameter generating

Sequence labelling(SL)tasks are currently widely studied in the field of natural language processing.Most sequence labelling methods are developed on a large amount of labelled training data via supervised learning,which is time-consuming and expensive.As an alternative,domain adaptation is proposed to train a deep-learning model for sequence labelling in a target domain by exploiting existing labelled training data in related source domains.To this end,the authors propose a Bi-LSTM model to extract more-related knowledge from multi-source domains and learn specific context from the target domain.Further,the language modelling training is also applied to cross-domain adaptability facilitating.The proposed model is extensively evaluated with the named entity recognition and part-of-speech tagging tasks.The empirical results demonstrate the effectiveness of the cross-domain adaption.Our model outperforms the state-of-the-art methods used in both cross-domain tasks and crowd annotation tasks.

A general result on precise asymptotics for linear processes of positively associated sequences

Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.

A RANDOM SEQUENCE GENERATOR BASED ON CHAOTIC CIRCUITS

In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.

Generating functions for powers of second-order recurrence sequences

For the sequences satisfying the recurrence relation of the second order,the generating functions for the products of the powers of these sequences are established.This study was from Carlita and Riordan who began a study on closed form of generating functions for powers of second-order recurrence sequences.This investigation was completed by Stnica.Inspired by the recent work of Istva＇n about the non-closed generating functions of the products of the powers of the second-order sequences,the authors give several extensions of Istva＇n＇s results in this paper.

HIERACHICAL STRUCTURES FOR GENERATING PSEUDO-RANDOM SEQUENCES AND ARRAYS

This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.

Design of Digital Hybrid Chaotic Sequence Generator

The feasibility of the hybrid chaotic sequences as the spreading codes in code divided multiple access(CDMA) system is analyzed. The design and realization of the digital hybrid chaotic sequence generator by very high speed integrated circuit hardware description language(VHDL) are described. A valid hazard canceledl method is presented. Computer simulations show that the stable digital sequence waveforms can be produced. The correlations of the digital hybrid chaotic sequences are compared with those of m-sequences. The results show that the correlations of the digital hybrid chaotic sequences are almost as good as those of m-sequences. The works in this paper explored a road for the practical applications of chaos.

Minimal-Length Interoperability Test Sequences Generation via Genetic Algorithm

A novel interoperability test sequences optimization scheme is proposed in which the genetic algorithm （GA） is used to obtain the minimal-length interoperability test sequences. During our work, the basic interoperability test sequences are generated based on the minimal-complete-coverage criterion, which removes the redundancy from conformance test sequences. Then interoperability sequences minimization problem can be considered as an instance of the set covering problem, and the GA is applied to remove redundancy in interoperability transitions. The results show that compared to conventional algorithm, the proposed algorithm is more practical to avoid the state space explosion problem, for it can reduce the length of the test sequences and maintain the same transition coverage.