Deterministic Sequences Research Articles

Carbon Mineral Evolution

The discovery of the extreme antiquity of specific minerals through radiometric dating (e.g., Strutt 1910), coupled with Norman L. Bowen’s recognition of a deterministic evolutionary sequence of silicate minerals in igneous rocks (Bowen 1915, 1928), implies that Earth’s crustal mineralogy has changed dramatically through more than 4.5 billion years of planetary history. Detailed examination of the mineralogical record has led to a growing realization that varied physical, chemical, and biological processes have resulted in a sequential increase in diversification of the mineral kingdom. This diversification has been accompanied by significant changes in the near-surface distribution, compositional range (including minor and trace elements), size, and morphology of minerals (Ronov et al. 1969; Nash et al. 1981; Zhabin 1981; Meyer 1985; Wenk and Bulakh 2004; Hazen et al. 2008, 2009, 2011). Variation in Earth’s mineralogical character thus reflects the tectonic, geochemical, and biological evolution of Earth’s near-surface environment (Bartley and Kah 2004; Hazen et al. 2009, 2012; Grew and Hazen 2010a,b; McMillan et al. 2010; Krivovichev 2010; Grew et al. 2011; Tkachev 2011). The mineral kingdom’s evolutionary narrative shares many features with the increased complexity inherent within other evolving systems, including the nucleosynthesis of elements and isotopes, the prebiotic synthesis of organic molecules, biological evolution through Dar-winian natural selection, and the evolution of social and material culture (Hazen and Eldredge 2010). In particular, well-known biological phenomena such as diversification, punctuation, and extinction appear to be common traits within a wide range of complex, evolving systems. Perhaps more than any other element, carbon exemplifies these processes of “mineral evolution.” Four episodes outline major events in the mineral evolution of carbon: (1) the synthesis of the first mineral, likely diamond, and perhaps a dozen other “ur-minerals” …

Impaired implicit sequence learning in Parkinson's disease patients with freezing of gait.

Freezing of gait (FOG) in Parkinson's disease (PD) may involve specific impairments in acquiring automaticity under working memory load. This study examined whether implicit sequence learning, with or without a secondary task, is impaired in patients with FOG. Fourteen freezers (FRs), 14 nonfreezers (nFRs), and 14 matched healthy controls (HCs) performed a serial reaction time (SRT) task with a deterministic stimulus sequence under single-task (ST) and dual-task (DT) conditions. The increase in reaction times (RTs) for random compared with sequenced blocks was used as a measure of implicit sequence learning. Neuropsychological tests assessing global cognitive functioning and executive dysfunction were administered in order to investigate their relation to sequence learning. nFRs and HCs showed significant implicit sequence learning effects (p < 0.001). FRs demonstrated a tendency to learn sequence-specific information in the SRT-ST task (p = 0.07) but not in the SRT-DT task (p = 0.69). Severity of FOG, however, correlated positively with SRT-DT task performance (r = -0.56; p < 0.05). The present results suggest that PD patients suffering from FOG pathology exhibit a specific impairment in the acquisition of automaticity. When working memory capacity is supplementarily loaded by adding a DT, sequence learning in FRs becomes increasingly impaired. These findings indicate that therapies should focus on extensive training in acquiring novel motor activities and reducing working memory load to improve learning in FOG.

Minimal model of associative learning for cross-situational lexicon acquisition

An explanation for the acquisition of word–object mappings is the associative learning in a cross-situational scenario. Here we present analytical results of the performance of a simple associative learning algorithm for acquiring a one-to-one mapping between N objects and N words based solely on the co-occurrence between objects and words. In particular, a learning trial in our learning scenario consists of the presentation of C+1<N objects together with a target word, which refers to one of the objects in the context. We find that the learning times are distributed exponentially and the learning rates are given by ln[N(N−1)C+(N−1)2] in the case the N target words are sampled randomly and by 1Nln[N−1C] in the case they follow a deterministic presentation sequence. This learning performance is much superior to those exhibited by humans and more realistic learning algorithms in cross-situational experiments. We show that introduction of discrimination limitations using Weber’s law and forgetting reduce the performance of the associative algorithm to the human level.

Convolutional Compressed Sensing Using Deterministic Sequences

In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the \textit{m}-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.

Enhancing performance of failure-prone clusters by adaptive provisioning of cloud resources

In this paper, we investigate Cloud computing resource provisioning to extend the computing capacity of local clusters in the presence of failures. We consider three steps in the resource provisioning including resource brokering, dispatch sequences, and scheduling. The proposed brokering strategy is based on the stochastic analysis of routing in distributed parallel queues and takes into account the response time of the Cloud provider and the local cluster while considering computing cost of both sides. Moreover, we propose dispatching with probabilistic and deterministic sequences to redirect requests to the resource providers. We also incorporate checkpointing in some well-known scheduling algorithms to provide a fault-tolerant environment. We propose two cost-aware and failure-aware provisioning policies that can be utilized by an organization that operates a cluster managed by virtual machine technology, and seeks to use resources from a public Cloud provider. Simulation results demonstrate that the proposed policies improve the response time of users' requests by a factor of 4.10 under a moderate load with a limited cost on a public Cloud.

Limit Theory for Moderate Deviations from a Unit Root Under Innovations with a Possibly Infinite Variance

An asymptotic theory was given by Phillips and Magdalinos (J Econom 136(1):115–130, 2007) for autoregressive time series Yt = ρYt−1 + ut, t = 1,...,n, with ρ = ρn = 1 + c/kn, under (2 + δ)-order moment condition for the innovations ut, where δ > 0 when c 0, {ut} is a sequence of independent and identically distributed random variables, and (kn)n ∈ ℕ is a deterministic sequence increasing to infinity at a rate slower than n. In the present paper, we established similar results when the truncated second moment of the innovations \(l(x)=\textsf{E} [u_1^2I\{|u_1|\le x\}]\) is a slowly varying function at ∞, which may tend to infinity as x → ∞. More interestingly, we proposed a new pivotal for the coefficient ρ in case c < 0, and formally proved that it has an asymptotically standard normal distribution and is nuisance parameter free. Our numerical simulation results show that the distribution of this pivotal approximates the standard normal distribution well under normal innovations.

Implicit sequence learning in dyslexia: a within-sequence comparison of first- and higher-order information

The present study examines implicit sequence learning in adult dyslexics with a focus on comparing sequence transitions with different statistical complexities. Learning of a 12-item deterministic sequence was assessed in 12 dyslexic and 12 non-dyslexic university students. Both groups showed equivalent standard reaction time increments when the sequence was unexpectedly changed, suggesting that learning of the sequence took place. However, a novel analysis comparing transitions of differing complexity within the learning blocks indicated that dyslexic participants were impaired only for higher-order but not first-order sequence learning. No difference was found in the explicit awareness contribution between the two groups and this was found not to correlate with reaction time performance. This result suggests that statistical complexity of the sequence may account for intact and impaired learning performance in dyslexia.

Progressive Screening: Long-Term Contracting with a Privately Known Stochastic Process

We examine a model of long-term contracting in which the buyer is privately informed about the stochastic process by which her value for a good evolves. In addition, the realized values are also private information. We characterize a class of environments in which the profit-maximizing long-term contract offered by a monopolist takes an especially simple structure: we derive sufficient conditions on primitives under which the optimal contract consists of a menu of deterministic sequences of static contracts. Within each sequence, higher realized values lead to greater quantity provision; however, an increasing proportion of buyer types are excluded over time, eventually leading to inefficiently early termination of the relationship. Moreover, the menu choices differ by future generosity, with more costly (up front) plans guaranteeing greater quantity provision in the future. Thus, the seller screens process information in the initial period and then progressively screens across realized values so as to reduce the information rents paid in future periods. Copyright , Oxford University Press.

Visuospatial Perceptual Sequence Learning and Eye Movements

We examined perceptual sequence learning by means of an adapted serial reaction time task in which eye movements were unnecessary for performing the sequence learning task. Participants had to respond to the identity of a target letter pair ("OX" or "XO") appearing in one of four locations. On the other locations, similar distractor letter pairs ("QY" or "YQ") were shown. While target identity changed randomly, target location was structured according to a deterministic sequence. To render eye movements superfluous, (1) stimulus letter pairs appeared around a fixation cross with a visual angle of 0.63°, which means that they appeared within the foveal visual area and (2) the letter pairs were presented for only 100 ms, a period too short to allow proper eye movements. Reliable sequence knowledge was acquired under these conditions, as responses were both slower and less accurate when the trained sequence was replaced by an untrained sequence. These results support the notion that perceptual sequence learning can be based on shifts of attention without overt oculomotor movements.

On ergodic two-armed bandits

A device has two arms with unknown deterministic payoffs and the aim is to asymptotically identify the best one without spending too much time on the other. The Narendra algorithm offers a stochastic procedure to this end. We show under weak ergodic assumptions on these deterministic payoffs that the procedure eventually chooses the best arm (i.e., with greatest Cesaro limit) with probability one for appropriate step sequences of the algorithm. In the case of i.i.d. payoffs, this implies a “quenched” version of the “annealed” result of Lamberton, Pagès and Tarrès [Ann. Appl. Probab. 14 (2004) 1424–1454] by the law of iterated logarithm, thus generalizing it. More precisely, if (ηℓ,i)i∈ℕ ∈ {0, 1}ℕ, ℓ ∈ {A, B}, are the deterministic reward sequences we would get if we played at time i, we obtain infallibility with the same assumption on nonincreasing step sequences on the payoffs as in Lamberton, Pagès and Tarrès [Ann. Appl. Probab. 14 (2004) 1424–1454], replacing the i.i.d. assumption by the hypothesis that the empirical averages ∑i=1nηA,i / n and ∑i=1nηB,i / n converge, as n tends to infinity, respectively, to θA and θB, with rate at least 1/(log n)1+ε, for some ε > 0. We also show a fallibility result, that is, convergence with positive probability to the choice of the wrong arm, which implies the corresponding result of Lamberton, Pagès and Tarrès [Ann. Appl. Probab. 14 (2004) 1424–1454] in the i.i.d. case.

Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method

In practice, reliability analysis of structures is often performed on the basis of limited data. Under this circumstance, there are practical difficulties in identifying unique distributions as input for a probabilistic analysis. But the selection of realistic probabilistic input is critical for the quality of the results of the reliability analysis. This problem can be addressed using an entire set of plausible distribution functions rather than one single distribution for random variables based on limited data. The uncertain nature of the available information is then reflected in the probabilistic input. An imprecise probability distribution can be modeled by a probability box, i.e., the bounds of the cumulative distribution function for the random variable. Sampling-based methods have been proposed to perform reliability analysis with probability boxes. However, direct sampling of probability boxes requires a large number of samples. The computational cost can be very high as each simulation involves an interval analysis (a range-finding problem). This study proposes an interval quasi-Monte Carlo simulation methodology to efficiently compute the bounds of structure failure probabilities. The methodology is based on deterministic low-discrepancy sequences, which are distributed more regularly than the (pseudo) random points in direct Monte Carlo simulation. The efficiency and accuracy of the present method is illustrated using two examples. The reliability implications of different approaches for construction of probability boxes are also investigated through the example.

Physical Portrayal of Computational Complexity

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because information requires physical representations and because many natural processes complete in nondeterministic polynomial time (NP). The irreversible process with three or more degrees of freedom is found intractable when, in terms of physics, flows of energy are inseparable from their driving forces. In computational terms, when solving a problem in the class NP, decisions among alternatives will affect subsequently available sets of decisions. Thus the state space of a nondeterministic finite automaton is evolving due to the computation itself, hence it cannot be efficiently contracted using a deterministic finite automaton. Conversely when solving problems in the class P, the set of states does not depend on computational history, hence it can be efficiently contracted to the accepting state by a deterministic sequence of dissipative transformations. Thus it is concluded that the state set of class P is inherently smaller than the state set of class NP. Since the computational time needed to contract a given set is proportional to dissipation, the computational complexity class P is a proper (strict) subset of NP.

Non-Systematic Complex Number RS Coded OFDM by Unique Word Prefix

In this paper, we expand our recently introduced concept of unique word orthogonal frequency division multiplexing (UW-OFDM). In UW-OFDM the cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called unique words (UWs). The UWs are generated by appropriately loading a set of redundant subcarriers. By that a systematic complex number Reed-Solomon (RS) code construction is introduced in a quite natural way, because an RS code may be defined as the set of vectors, for which a block of successive zeros occurs in the other domain w.r.t. a discrete Fourier transform. (For a fixed block different to zero, i.e., a UW, a coset code of an RS code is generated.) A remaining problem in the original systematic coded UW-OFDM concept is the fact that the redundant subcarrier symbols disproportionately contribute to the mean OFDM symbol energy. In this paper we introduce the concept of non-systematic coded UW-OFDM, where the redundancy is no longer allocated to dedicated subcarriers, but distributed over all subcarriers. We derive optimum complex valued code generator matrices matched to the best linear unbiased estimator (BLUE) and to the linear minimum mean square error (LMMSE) data estimator, respectively. With the help of simulations we highlight the advantageous spectral properties and the superior bit error ratio (BER) performance of non-systematic coded UW-OFDM compared to systematic coded UW-OFDM and to CP-OFDM in additive white Gaussian noise (AWGN ) as well as in frequency selective environments.

Classical and Bayesian Linear Data Estimators for Unique Word OFDM

Unique word - orthogonal frequency division multiplexing (UW-OFDM) is a novel OFDM signaling concept, where the guard interval is built of a deterministic sequence - the so-called unique word - instead of the conventional random cyclic prefix. In contrast to previous attempts with deterministic sequences in the guard interval the addressed UW-OFDM signaling approach introduces correlations between the subcarrier symbols, which can be exploited by the receiver in order to improve the bit error ratio performance. In this paper we develop several linear data estimators specifically designed for UW-OFDM, some based on classical and some based on Bayesian estimation theory. Furthermore, we derive complexity optimized versions of these estimators, and we study their individual complex multiplication count in detail. Finally, we evaluate the estimators' performance for the additive white Gaussian noise channel as well as for selected indoor multipath channel scenarios.

Compressibility of Deterministic and Random Infinite Sequences

We introduce a definition of the notion of compressibility for infinite deterministic and i.i.d. random sequences which is based on the asymptotic behavior of truncated subsequences. For this purpose, we use asymptotic results regarding the distribution of order statistics for heavy-tail distributions and their link with α -stable laws for 1 <; α <; 2 . In many cases, our proposed definition of compressibility coincides with intuition. In particular, we prove that heavy-tail (polynomial decaying) distributions fulfill the requirements of compressibility. On the other hand, exponential decaying distributions like Laplace and Gaussian do not. The results are such that two compressible distributions can be compared with each other in terms of their degree of compressibility.

The proteoglycan bikunin has a defined sequence

Proteoglycans are complex glycoconjugates that regulate critical biological pathways in all higher organisms. Bikunin, the simplest proteoglycan having a single glycosaminoglycan chain, is a serine protease inhibitor used to treat acute pancreatitis. Unlike the template driven synthesis of nucleic acids and proteins, Golgi synthesized glycosaminoglycans are not believed to have predictable or deterministic sequence. Bikunin peptidoglycosaminoglycans were prepared and fractionated to obtain a collection of size similar and charge similar chains. Fourier transform mass spectral analysis identified a small number of parent molecular-ions corresponding to mono-compositional peptidoglycosaminoglycans. Fragmentation using collision induced dissociation surprisingly afforded a single sequence for each mono-compositional parent-ion, unequivocally demonstrating the presence of a defined sequence. The common biosynthetic pathway for all proteoglycans suggests that even more structurally complex proteoglycans, such as heparan sulfate, may have defined sequences, requiring a readjustment of our understanding of information storage in complex glycans.

Inequalities for martingale transforms and related characterizations of Hilbert spaces

Suppose that f is a martingale taking values in a Banach space B and g is its transform by a deterministic sequence of numbers in { − 1 , 1 } , such that sup n ‖ g n ‖ ≥ 1 almost surely. We show that a certain family of Φ -estimates for f holds true if and only B is a Hilbert space.

Sequential decision problems on isolated time domains

In this paper, we shall study the deterministic dynamic sequence problem on isolated time domains. After introducing the Euler equations and the transversality condition, we shall prove that the Euler equations and transversality condition are sufficient for the existence of the optimal solution. We shall also introduce the Bellman equation on isolated time scales. This equation will generalize the well-known Bellman equation in the theory of dynamic programming. As an application in financial economics, we shall optimize a sequence problem of growth model on isolated time domains.

Spectrum of Non-Hermitian Heavy Tailed Random Matrices

Let (X jk ) j,k ≥ 1 be i.i.d. complex random variables such that |X jk | is in the domain of attraction of an α-stable law, with 0 < α < 2. Our main result is a heavy tailed counterpart of Girko’s circular law. Namely, under some additional smoothness assumptions on the law of X jk , we prove that there exist a deterministic sequence a n ~ n 1/α and a probability measure μ α on $${\mathbb{C}}$$ depending only on α such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix $${(a_n^{-1}X_{jk})_{1\leq j,k\leq n}}$$ converges weakly to μ α as n → ∞. Our approach combines Aldous & Steele’s objective method with Girko’s Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous’ Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of μ α . In contrast with the Hermitian case, we find that μ α is not heavy tailed.

Experimental investigation of random loading sequence effect on fatigue crack growth

An experimental study is proposed to investigate the effect of random loading sequence effect on the fatigue crack growth behavior of Al 7075-T6. The testing matrix includes different overload cycle percentage, overload ratios, and deterministic and random loading sequences in the current investigation. Multiple specimen tests and statistical data analysis are performed to show the effect of random loading sequence on the median and scatter behavior of fatigue crack growth. The proposed experimental study suggests that extreme value distribution is a good approximation of fatigue life distribution. It is observed that the effect of uncertain loading is different under different loading spectrums. For high overload cycle percentage spectrums, the random loading sequence has no major impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions. For low overload cycle percentage spectrums, the random loading sequence has huge impact on the probabilistic crack growth behavior compared to the deterministic loading sequence with identical load cycle distributions, for both the median and the scatter of the fatigue crack length curves. Finally, all experimental observations are reported in table format in Appendix A for future numerical model development and validation for interested readers.