Complexity Of Function Research Articles

Towards ultra-efficient QCA reversible circuits

Nanotechnologies, remarkably Quantum-dot Cellular Automata (QCA), offer an attractive perspective for future computing technologies. In this paper, QCA is investigated as an implementation method for reversible logic. A novel XOR gate and also a new approach to implement 2:1 multiplexer are presented. Moreover, an efficient and potent universal reversible gate based on the proposed XOR gate is designed. The proposed reversible gate has a superb performance in implementing the QCA standard benchmark combinational functions in terms of area, complexity, power consumption, and cost function in comparison to the other reversible gates. The gate achieves the lowest overall cost among the most cost-efficient designs presented so far, with a reduction of 24%. In order to employ the merits of reversibility, the proposed reversible gate is leveraged to design the four common latches (D latch, T latch, JK latch, and SR latch). Specialized structures of the proposed circuits could be used as building blocks in designing sequential and combinational circuits in QCA architectures.

Symbolic complexity for nucleotide sequences: a sign of the genome structure

We introduce a method for estimating the complexity function (which counts the number of observable words of a given length) of a finite symbolic sequence, which we use to estimate the complexity function of coding DNA sequences for several species of the Hominidae family. In all cases, the obtained symbolic complexities show the same characteristic behavior: exponential growth for small word lengths, followed by linear growth for larger word lengths. The symbolic complexities of the species we consider exhibit a systematic trend in correspondence with the phylogenetic tree. Using our method, we estimate the complexity function of sequences obtained by some known evolution models, and in some cases we observe the characteristic exponential-linear growth of the Hominidae coding DNA complexity. Analysis of the symbolic complexity of sequences obtained from a specific evolution model points to the following conclusion: linear growth arises from the random duplication of large segments during the evolution of the genome, while the decrease in the overall complexity from one species to another is due to a difference in the speed of accumulation of point mutations.

On asymptotic gate complexity and depth of reversible circuits without additional memory

In the paper we study reversible logic circuits, which consist of NOT, CNOT and C2NOT gates. We consider a set F(n,q) of all transformations Bn→Bn that can be realized by reversible circuits with (n+q) inputs. We define the Shannon gate complexity function L(n,q) and the depth function D(n,q) as functions of n and the number of additional inputs q. We prove general lower bounds for these functions. We introduce a new group-theory-based synthesis algorithm that can produce a reversible circuit S without additional inputs and with the gate complexity L(S)≤3n2n+4(1+o(1))/log2⁡n in the worst case.

Cyclic complexity of words

We introduce and study a complexity function on words cx(n), called cyclic complexity, which counts the number of conjugacy classes of factors of length n of an infinite word x. We extend the well-known Morse–Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if x is a Sturmian word and y is a word having the same cyclic complexity of x, then up to renaming letters, x and y have the same set of factors. In particular, y is also Sturmian of slope equal to that of x. Since cx(n)=1 for some n≥1 implies x is periodic, it is natural to consider the quantity liminfn→∞cx(n). We show that if x is a Sturmian word, then liminfn→∞cx(n)=2. We prove however that this is not a characterization of Sturmian words by exhibiting a restricted class of Toeplitz words, including the period-doubling word, which also verify this same condition on the limit infimum. In contrast we show that, for the Thue–Morse word t, liminfn→∞ct(n)=+∞.

Abelian Complexity and Frequencies of Letters in Infinite Words

Abelian complexity in infinite words is a combinatorial tool which developed essentially during the last five years. In this paper, we undertake to establish connections between abelian complexity and uniform frequencies in infinite words. In particular, we focus on the binary case to link uniform equi-frequency with abelian complexity. We also provide various examples of infinite words to illustrate the absence of connection between usual complexity and abelian complexity. Some properties involving uniform recurrence are also given.

Computing abelian complexity of binary uniform morphic words

Although a lot of research has been done on the factor complexity (also called subword complexity) of morphic words obtained as fixed points of iterated morphisms, there has been little development in exploring algorithms that can efficiently compute their abelian complexity. The factor complexity counts the number of factors of a given length n, while the abelian complexity counts that number up to letter permutation. We propose and analyze a simple O(n) algorithm for quickly computing the exact abelian complexities for all indices from 1 up to n, when considering binary uniform morphisms. Using our algorithm we also analyze the structure in the abelian complexity for that class of morphisms. Our main result implies, in particular, that the infinite word over the alphabet {−1,0,1} constructed from the consecutive forward differences of the abelian complexity of a fixed point of a binary uniform morphism is in fact an automatic sequence with the same morphic length. Since the proof produces morphisms that typically contain many redundant letters, we present an efficient algorithm to eliminate them in order to simplify the morphisms and to see the patterns produced more clearly.

International trade and emerging markets: the importance of managing the key strategy drivers

Purpose This paper aims to review the latest management developments across the globe and pinpoint practical implications from cutting-edge research and case studies. Design/methodology/approach This briefing is prepared by an independent writer who adds their own impartial comments and places the articles in context. Findings Any discussion about change in the business environment usually results in some reference to globalization. In many ways, it has proved to be a positive force. Markets are more efficient and competition has intensified to an extent that no firm can rest easily on its laurels. In addition, wealth imbalance across the world has also been addressed to a point. On the flip side, many people believe that richer nations benefit most from global trade. Erosion of cultural diversity is another issue, while environmental groups also voice concerns. International trading companies have been affected more than most. Their operating environment has greatly increased in its complexity and many established functions associated with international distribution are no longer applicable in their original form. Practical implications The paper provides strategic insights and practical thinking that have influenced some of the world’s leading organizations. Originality/value The briefing saves busy executives and researchers hours of reading time by selecting only the very best, most pertinent information and presenting it in a condensed and easy-to-digest format.

Automation of Algorithmic Tasks for Virtual Laboratories Based on Automata Theory

In the work a description of an automata model of standard algorithm for constructing a correct solution of algorithmic tests is given. The described model allows a formal determination of the variant complexity of algorithmic test and serves as a basis for determining the complexity functions, incl

Initial non-repetitive complexity of infinite words

The initial non-repetitive complexity function of an infinite word x (first introduced by Moothathu) is the function of n that counts the number of distinct factors of length n that appear at the beginning of x prior to the first repetition of a length-n factor. We examine general properties of the initial non-repetitive complexity function, as well as obtain formulas for the initial non-repetitive complexity of the Thue–Morse word, the Fibonacci word and the Tribonacci word.

Longitudinal studies of gender differences in cognitional process in dream content

We assessed the longitudinal effects of a cognitive processing variable (automated count of words indicating cognitive processing in a dream narrative) on other dream content variables in dream series collected from 37 men and 46 women over a two year period. Dreams were obtained from the online dream posting website dreamboard.com . Using mixed effects regression modeling for longitudinal data we found that on a month by month basis cognitive processing is significantly associated with markers of grammatical complexity (verbs and function words), the personal pronoun I, social processes, health and emotion (both negative and positive). All but the perceptual processes variables had a significantly different effect on cognitive processing for men vs women with men having a greater association to processing resources with these matters than women. Men exhibited a significantly positive rate of change in cognitive processing on a monthly basis, while women did not show a significant rate of change over time. These results suggest that people use dreams to “work through” or cognitively process selected types of emotional information and the rate at which they do so appears to increase, at least for men.

Newton–Okounkov bodies and complexity functions

We show that quite universally the holonomicity of the complexity function of a divisor does not predict whether the Newton–Okounkov body is polyhedral for every choice of a flag.

Abstract PR04: The role of long noncoding RNA HIF1A-AS2 in hypoxic environment of glioblastoma

Abstract Purpose: While multiple protein-coding genes are known to play a crucial role in the formation and progression of glioblastoma multiforme (GBM), the role of long-non-coding RNAs (lncRNAs) in these cascades remains to be fully characterized. Considering the fundamental roles of hypoxia in the cellular and microenvironmental complexity and unexplored function of lncRNAs in GBM pathobiology, the identification of novel lncRNAs and their target pathways that drive the adaptation to hypoxic niche is crucial for better understanding of the development and progression of this highly heterogeneous brain tumor. Transcriptome profiling of GBM have revealed the presence of four clearly distinguishable subtypes, variably expressed in individual cells within a tumor. This finding may have potential clinical implications, including subtype-specific rearrangements of transcriptional programs related to oncogenic signaling, growth and hypoxia. However, the subtype-specific role of lncRNAs in tumorigenic potential of GBM subtypes remains largely unknown. Materials and Methods: The brain tissue samples including GBM tumors and non-pathological tissue adjacent to the tumor were collected. GBM-derived primary stem cells (GSCs) classified by transcriptome analysis as proneural (P) and mesenchymal (M), were collected and exposed to hypoxic conditions. Using custom designed Nanostring platform analysis followed by qPCR, the expression patterns of 70 cancer-related lncRNAs were characterized. The in situ hybridization and qPCR analysis was used to validate sub-cellular localization of selected lncRNA. RNA immunoprecipitation (RIP) and mass-spectroscopy (MS) was performed to map RNA-protein interaction and identified targets were validated by Western blotting. The global GSC transcriptome profiling upon lncRNA de-regulation was performed using Pan Cancer Nanostring platform. The knock-down and overexpression strategies in GSC were used to characterize cellular and molecular phenotypes in vitro and in in vivo intracranial GBM model. Results: We identified lncRNA HIF1A-AS2 (Hypoxia Inducible Factor 1 alpha - antisense 2) as one of the most deregulated in GBM comparing to the matched adjacent tissue. Despite lack of difference in the hypoxia-dependent activation of HIF1A protein between P and M GSC, HIF1A-AS2 was specifically upregulated in M GSC in vitro and in vivo. The deregulation of expression of HIF1A-AS2 had a broad effect on autophagy-related signaling network regulated in response to hypoxia in M but not P GSC. The IGF2BP2 and DHX9 were identified as direct protein partners of this lncRNA. The deregulation of HIF1A-AS2 affected the recruitment of IGF2BP2 to its mRNA targets (e.g. HMG1) and stability of DHX9 protein (but not mRNA), resulting in deregulation of its target genes (e.g FOSL1). Downregulation of HIF1A-AS2 in vivo led to de-regulation of its downstream effectors and resulted in survival benefit of mice bearing M GSC-originated tumors. Conclusion: P and M GSC respond differently to hypoxic stress by induction of autophagy to maintain their homeostasis and viability and this mechanism is controlled by HIF1A-AS2. This abstract is also presented as Poster A16. Citation Format: Marco Mineo, Franz Ricklefs, Shawn S. Lyons, Pavel Ivanov, E. Antonio Chiocca, Jakub Godlewski, Agnieszka Bronisz. The role of long noncoding RNA HIF1A-AS2 in hypoxic environment of glioblastoma. [abstract]. In: Proceedings of the AACR Special Conference on Noncoding RNAs and Cancer: Mechanisms to Medicines ; 2015 Dec 4-7; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2016;76(6 Suppl):Abstract nr PR04.

Automation of Algorithmic Tasks for Virtual Laboratories Based on Automata Theory

In the work a description of an automata model of standard algorithm for constructing a correct solution of algorithmic tests is given. The described model allows a formal determination of the variant complexity of algorithmic test and serves as a basis for determining the complexity functions, including the collision concept – the situation of uncertainty, when a choice must be made upon fulfilling the task between the alternatives with various priorities. The influence of collisions on the automata model and its inner structure is described. The model and complexity functions are applied for virtual laboratories upon designing the algorithms of constructing variant with a predetermined complexity in real time and algorithms of the estimation procedures of students’ solution with respect to collisions. The results of the work are applied to the development of virtual laboratories, which are used in the practical part of massive online course on graph theory.

Computing automorphism groups of shifts using atypical equivalence classes

Computing automorphism groups of shifts, using atypical equivalence classes, Discrete Analysis 2016:3, 24 pp. Symbolic dynamics is about dynamical systems of the following type. Let $A$ be an alphabet, and let $\sigma$ be the left shift map from $A^{\mathbb Z}$ to itself. Giving $A$ the discrete topology and $A^{\mathbb Z}$ the product topology, if $X$ is a closed $\sigma$-invariant subset of $A^{\mathbb Z}$, then $(X,\sigma)$ is a dynamical system. Of particular interest are _minimal_ systems of this type: that is, systems where $X$ is the closure of the set of all shifts of a single doubly infinite word $(a_n)_{n\in\mathbb{Z}}$ in $A$. The properties of the word turn out to be interestingly related to properties of the dynamical system. A key parameter for such a system is the _complexity function_ $p:\mathbb{N}\to\mathbb{N}$, where for each positive integer $n$, $p(n)$ is defined to be the number of distinct subwords of the form $(a_m,a_{m+1},\dots,a_{m+n-1})$. In particular, the rate of growth of this function is important. An _automorphism_ of a dynamical system $(X,\sigma)$ is a continuous bijection from $X$ to $X$ that commutes with $\sigma$. A trivial example of an automorphism is $\sigma$ itself, or indeed any power of $\sigma$. In the past few years, there has been a lot of work on showing that dynamical systems $(X,\sigma)$ for which the complexity function grows slowly have automorphism groups that are in some sense small. However, even in the lowest nontrivial complexity (that of nonconstant, sublinear complexity), we do not have a complete understanding of the automorphism group, and in general there is no method that gives a complete characterization of this group. In this paper, the authors focus on the particular class of substitution systems of constant length, which are the systems whose infinite words are obtained by iterating a substitution infinitely many times on some letter in the alphabet. An interesting result in the paper is an algorithm to compute the automorphism group in this situation, along with the use of this algorithm to compute all conjugacies between two shifts generated by constant length substitutions. The proof uses dynamical methods to reduce the problem to combinatorial arguments. Another result is that for a minimal system with complexity that grows at most linearly the quotient of the automorphism group by the group generated by $\sigma$ is finite. It is not clear whether the techniques used in this paper can be generalized to a significantly wider class of systems. However, the difficulty of computing the automorphism group in general is such that any new non-trivial examples are useful and instructive.

A note on the complexity function and entropy of pseudogroups

We examine the connections between complexity of a pseudogroup, its equicontinuity, the mixing property and entropy. We prove that the entropy of a pseudogroup can be (under some additional assumptions) computed using a continuous and dynamically generating pseudometric.

О сложности обратимых схем, состоящих из функциональных элементов NOT, CNOT и 2-CNOT

Рассматривается вопрос о сложности обратимых схем, состоящих из функциональных элементов NOT, CNOT и 2-CNOT. Определяется функция Шеннонa $L(n, q)$ сложности обратимой схемы, реализующей отображение $f\colon \mathbb Z_2^n \to \mathbb Z_2^n$, как функция от $n$ и количества $q$ дополнительных входов схемы. Установлены нижняя оценка сложности обратимой схемы $L(n,q) \geqslant \frac{2^n(n-2)}{3\log_2(n+q)} - \frac{n}{3}$, верхняя оценка сложности $L(n,0) \leqslant 48n2^n(1+o(1)) \mathop / \log_2n$ в случае отсутствия дополнительных входов, асимптотическая верхняя оценка сложности $L(n,q_0) \lesssim 2^n$ в случае использования $q_0 \sim n2^{n-o(n)}$ дополнительных входов.

Complexity of short rectangles and periodicity

The Morse–Hedlund Theorem states that a bi-infinite sequence η in a finite alphabet is periodic if and only if there exists n∈N such that the block complexity function Pη(n) satisfies Pη(n)≤n. In dimension two, Nivat conjectured that if there exist n,k∈N such that the n×k rectangular complexity Pη(n,k) satisfies Pη(n,k)≤nk, then η is periodic. Sander and Tijdeman showed that this holds for k≤2. We generalize their result, showing that Nivat’s Conjecture holds for k≤3. The method involves translating the combinatorial problem to a question about the nonexpansive subspaces of a certain Z2 dynamical system, and then analyzing the resulting system.

Sequential memory: Binding dynamics.

Temporal order memories are critical for everyday animal and human functioning. Experiments and our own experience show that the binding or association of various features of an event together and the maintaining of multimodality events in sequential order are the key components of any sequential memories-episodic, semantic, working, etc. We study a robustness of binding sequential dynamics based on our previously introduced model in the form of generalized Lotka-Volterra equations. In the phase space of the model, there exists a multi-dimensional binding heteroclinic network consisting of saddle equilibrium points and heteroclinic trajectories joining them. We prove here the robustness of the binding sequential dynamics, i.e., the feasibility phenomenon for coupled heteroclinic networks: for each collection of successive heteroclinic trajectories inside the unified networks, there is an open set of initial points such that the trajectory going through each of them follows the prescribed collection staying in a small neighborhood of it. We show also that the symbolic complexity function of the system restricted to this neighborhood is a polynomial of degree L - 1, where L is the number of modalities.

Complexity functions of varieties of Leibniz algebras with nilpotent commutator subalgebra

Complexity functions of varieties of Leibniz algebras with nilpotent commutator subalgebra

State Complexity of Boundary of Prefix-Free Regular Languages

Recently, researchers studied the state complexity of boundary — [Formula: see text] — of regular languages L motivated from the famous Kuratowski’s 14-theorem. Prefix codes — a set of languages — play an important role in several applications. We consider prefix-free regular languages and investigate the state complexity of two operations, [Formula: see text] and [Formula: see text] for prefix-free regular languages. Based on the unique structural properties of a prefix-free minimal DFA, we compute the precise state complexity of [Formula: see text] and [Formula: see text]. We then present the tight bound over a quaternary alphabet for [Formula: see text] and [Formula: see text]. Our results are smaller than the composition of the state complexity function for individual operations of prefix-free regular languages.