Sparse Sequence Research Articles

Bit-level composite signal design for simultaneous ranging and communication

As the complexity of space exploration missions augments, how to enhance the overall performance of communication, ranging or other functions has become a challengeable problem. Considering the integration of communication and ranging, we present a bit-level composite signal for simultaneous ranging and communication. In this composite method, through a specially designed mapping scheme using low-weight codewords, the information sequence is converted to a sparse sequence which is then superimposed on the ranging code. For ranging, the correlation characteristics of the ranging code component can be maintained to calculate the transmitter-receiver distance. For communications, the sparse sequence can be extracted without interference by eliminating the ranging code component. Simulation results show that the proposed composite signal can support communication and ranging simultaneously with limited sacrifice of ranging performance, and the performance loss of ranging can be controlled and minimized by lowering the density of information sequences using different sparsification encoding methods.

Comment on "Ancient origins of allosteric activation in a Ser-Thr kinase".

Hadzipasic et al (Reports, 21 February 2020, p. 912) used ancestral sequence reconstruction to identify historical sequence substitutions that putatively caused Aurora kinases to evolve allosteric regulation. We show that their results arise from using an implausible phylogeny and sparse sequence sampling. Addressing either problem reverses their inferences: Allostery and the amino acids that confer it were not gained during the diversification of eukaryotes but were lost in a subgroup of Fungi.

Comparability of compressed sensing-based gradient echo perfusion sequence SPARSE and conventional gradient echo sequence in assessment of myocardial ischemia

PurposeStress perfusion imaging plays a major role in non-invasive detection of coronary artery disease.We compared a compressed sensing-based and a conventional gradient echo perfusion sequence with regard to image quality and diagnostic performance. MethodPatients sent for coronary angiography due to pathologic stress perfusion CMR were recruited. All patients underwent two adenosine stress CMR using conventional TurboFLASH and prototype SPARSE sequence as well as quantitative coronary angiography with fractional flow reserve (FFR) within 6 weeks. Coronary angiography was considered gold standard with FFR < 0.75 or visual stenosis >90 % for identification of myocardial ischemia. Diagnostic performance of perfusion imaging was assessed in basal, mid-ventricular and apical slices by quantification of myocardial perfusion reserve (MPR) analysis utilizing the signal upslope method and a deconvolution technique using the fermi function model. Results23 patients with mean age of 69.6 ± 8.9 years were enrolled. 46 % were female.Image quality was similar in conventional TurboFLASH sequence and SPARSE sequence (2.9 ± 0.5 vs 3.1 ± 0.7, p = 0,06). SPARSE sequence showed higher contrast-to-noise ratio (52.1 ± 27.4 vs 40.5 ± 17.6, p < 0.01) and signal-to-noise ratio (15.6 ± 6.2 vs 13.2 ± 4.2, p < 0.01) than TurboFLASH sequence. Dark-rim artifacts occurred less often with SPARSE (9 % of segments) than with TurboFLASH (23 %).In visual assessment of perfusion defects, SPARSE sequence detected less false-positive perfusion defects (n = 1) than TurboFLASH sequence (n = 3).Quantitative perfusion analysis on segment basis showed equal detection of perfusion defects for TurboFLASH and SPARSE with both upslope MPR analysis (TurboFLASH 0.88 ± 0.18; SPARSE 0.77 ± 0.26; p = 0.06) and fermi function model (TurboFLASH 0.85 ± 0.24; SPARSE 0.76 ± 0.30; p = 0.13). ConclusionsCompressed sensing perfusion imaging using SPARSE sequence allows reliable detection of myocardial ischemia.

Paludicola gen. nov. and Revision of the Species Formerly in Batrachospermum Section Turfosa (Batrachospermales, Rhodophyta)

Since the first phylogenetic study of the order Batrachospermales, Batrachospermum was shown to be paraphyletic. Subsequently, sections of the genus have been methodically investigated using DNA sequences and morphology in order to propose new genera and delineate species. Batrachospermum section Turfosa is the last section with multiple species yet to be examined. New sequence data of specimens from Europe and the United States were combined with the sparse sequence data already available. Phylogenetic analyses using rbcL and COI-5P sequences showed this section to be a well-supported clade, distinct from Batrachospermum section Batrachospermum and its segregate genera. SectionTurfosa is raised to the generic rank as Paludicola gen. nov. Substantial genetic variation within the genus was discovered and 12 species are recognized based on DNA sequence data as well as morphological characters and geographic distribution. The following morphological characters were applied to distinguish species: branching pattern (pseudodichotomous or irregular), whorl size (reduced or well developed), primary fascicles (curved or straight), spermatangia origin (primary or secondary fascicles), and carposporophyte arrangement (loose or dense). Previously published species were transferred to the new genus: P.turfosa, P.keratophyta, P.orthosticha, P.phangiae, and P.periploca. Seven new species are proposed as follows: P.groenbladii from Europe; P.communis, P.johnhallii, and P.leafensis from North America; and P.aquanigra, P.diamantinensis, and P.turfosiformis from Brazil. In addition, three unsequenced species in the section, P.bakarensis, P.gombakensis, and P.tapirensis, were transferred to the new genus.

Single and multiple recurrence along non-polynomial sequences

We establish new recurrence and multiple recurrence results for a rather large family F of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth.In particular, we show that, somewhat surprisingly (and in the contrast to the multiple recurrence along polynomials), the sets of return times along functions from F are thick, i.e., contain arbitrarily long intervals. A major component of our paper is a new result about equidistribution of sparse sequences on nilmanifolds, whose proof borrows ideas from the work of Green and Tao [26].Among other things, we show that for any f∈F, any invertible probability measure preserving system (X,B,μ,T), any A∈B with μ(A)>0, and any ε>0, the sets of returns{n∈N:μ(A∩T−⌊f(n)⌋A)>μ2(A)−ε}{n∈N:μ(A∩T−⌊f(n)⌋A∩T−⌊f(n+1)⌋A∩⋯∩T−⌊f(n+k)⌋A)>0} are thick.Our recurrence theorems imply, via Furstenberg's correspondence principle, some new combinatorial results. For example, we show that given a set E⊂N with positive upper density, for every k∈N there are a,n∈N such that{a,a+⌊f(n)⌋,⋯,a+⌊f(n+k)⌋}⊂E. When f(n)=nc, with c>0 non-integer, this result provides a positive answer to a question posed by Frantzikinakis [16, Problem 23].

Reusing Preconditioners in Projection Based Model Order Reduction Algorithms

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the MOR algorithms require solving large sparse sequences of linear systems. Since using direct methods for solving such systems does not scale well in time with respect to the increase in the input dimension, efficient preconditioned iterative methods are commonly used. In one of our previous works, we have shown substantial improvements by reusing preconditioners for the parametric MOR (Singh et al. 2019). Here, we had proposed techniques for both, the non-parametric and the parametric cases, but had applied them only to the latter. We have three main contributions here. First, we demonstrate that preconditioners can be reused more effectively in the non-parametric case as compared to the parametric one. Second, we show that reusing preconditioners is an art via detailed algorithmic implementations in multiple MOR algorithms. Third and final, we demonstrate that reusing preconditioners for reducing a real-life industrial problem (of size 1.2 million), leads to relative savings of up to 64 % in the total computation time (in absolute terms a saving of 5 days).

Needles and straw in a haystack: Robust confidence for possibly sparse sequences

In the general signal$+$noise (allowing non-normal, non-independent observations) model, we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which gives rise to a new slicing of the entire space that is suitable for uncertainty quantification. Under EBR and some mild exchangeable exponential moment condition on the noise, we establish the local (oracle) optimality of the proposed confidence ball. Without EBR, we propose another confidence ball of full coverage, but its radius contains an additional $\sigma n^{1/4}$-term. In passing, we also get the local optimal results for estimation, posterior contraction problems, and the problem of weak recovery of sparsity structure. Adaptive minimax results (also for the estimation and posterior contraction problems) over various sparsity classes follow from our local results.

The Expansion and Diversification of Pentatricopeptide Repeat RNA-Editing Factors in Plants

The RNA-binding pentatricopeptide repeat (PPR) family comprises hundreds to thousands of genes in most plants, but only a few dozen in algae, indicating massive gene expansions during land plant evolution. The nature and timing of these expansions has not been well defined due to the sparse sequence data available from early-diverging land plant lineages. In this study, we exploit the comprehensive OneKP datasets of over 1000 transcriptomes from diverse plants and algae toward establishing a clear picture of the evolution of this massive gene family, focusing on the proteins typically associated with RNA editing, which show the most spectacular variation in numbers and domain composition across the plant kingdom. We characterize over 2 250 000 PPR motifs in over 400 000 proteins. In lycophytes, polypod ferns, and hornworts, nearly 10% of expressed protein-coding genes encode putative PPR editing factors, whereas they are absent from algae and complex-thalloid liverworts. We show that rather than a single expansion, most land plant lineages with high numbers of editing factors have continued to generate novel sequence diversity. We identify sequence variations that imply functional differences between PPR proteins in seed plants versus non-seed plants and variations we propose to be linked to seed-plant-specific editing co-factors. Finally, using the sequence variations across the datasets, we develop a structural model of the catalytic DYW domain associated with C-to-U editing and identify a clade of unique DYW variants that are strong candidates as U-to-C RNA-editing factors, given their phylogenetic distribution and sequence characteristics.

The discrete spherical averages over a family of sparse sequences

We initiate the study of the ℓp(ℤd)-boundedness of the arithmetic spherical maximal function over sparse sequences. We state a folklore conjecture for lacunary sequences, a key example of Zienkiewicz and prove new bounds for a family of sparse sequences that achieves the endpoint of the Magyar-Stein-Wainger theorem for the full discrete spherical maximal function in [MSW02]. Perhaps our most interesting result is the boundedness of a discrete spherical maximal function in ℤ4 over an infinite, albeit sparse, set of radii. Our methods include the Kloosterman refinement for the Fourier transform of the spherical measure (introduced in [Mag07]) and Weil bounds for Kloosterman sums which are utilized by a new further decomposition of spherical measure.

희소하고 긴 시계열 데이터의 동적 시간 워핑 거리 상계값 개선

희소하고 긴 시계열 데이터의 동적 시간 워핑 거리 상계값 개선

Variation in sequence dynamics improves maintenance of stereotyped behavior in an example from bird song

Performing a stereotyped behavior successfully over time requires both maintaining performance quality and adapting efficiently to environmental or physical changes affecting performance. The bird song system is a paradigmatic example of learning a stereotyped behavior and therefore is a good place to study the interaction of these two goals. Through a model of bird song learning, we show how instability in neural representation of stable behavior confers advantages for adaptation and maintenance with minimal cost to performance quality. A precise, temporally sparse sequence from the premotor nucleus HVC is crucial to the performance of song in songbirds. We find that learning in the presence of sequence variations facilitates rapid relearning after shifts in the target song or muscle structure and results in decreased error with neuron loss. This robustness is due to the prevention of the buildup of correlations in the learned connectivity. In the absence of sequence variations, these correlations grow, due to the relatively low dimensionality of the exploratory variation in comparison with the number of plastic synapses. Our results suggest one would expect to see variability in neural systems executing stereotyped behaviors, and this variability is an advantageous feature rather than a challenge to overcome.

A map-matching algorithm dealing with sparse cellular fingerprint observations

ABSTRACT The widespread availability of mobile communication makes mobile devices a resource for the collection of data about mobile infrastructures and user mobility. In these contexts, the problem of reconstructing the most likely trajectory of a device on the road network on the basis of the sequence of observed locations (map-matching problem) turns out to be particularly relevant. Different contributions have demonstrated that the reconstruction of the trajectory of a device with good accuracy is technically feasible even when only a sparse set of GNSS positions is available. In this paper, we face the problem of coping with sparse sequences of cellular fingerprints. Compared to GNSS positions, cellular fingerprints provide coarser spatial information, but they work even when a device is missing GNSS positions or is operating in an energy saving mode. We devise a new map-matching algorithm, that exploits the well-known Hidden Markov Model and Random Forests to successfully deal with noisy and sparse cellular observations. The performance of the proposed solution has been tested over a medium-sized Italian city urban environment by varying both the sampling of the observations and the density of the fingerprint map as well as by including some GPS positions into the sequence of fingerprint observations.

Integer part independent polynomial averages and applications along primes

Exploiting the equidistribution properties of polynomial sequences, following the methods developed by Leibman (Pointwise Convergence of ergodic averages for polynomial sequences of translations on a nilmanifold. Ergodic Theory Dynam. Systems, 25 (2005) no. 1, 201-213) and Frantzikinakis (Multiple recurrence and convergence for Hardy field sequences of polynomial growth. Journal d'Analyse Mathematique, 112 (2010), 79-135 and Equidistribution of sparse sequences on nilmanifolds. Journal d'Analyse Mathematique, 109 (2009), 353-395) we show that the ergodic averages with iterates given by the integer part of real-valued strongly independent polynomials, converge in the mean to the right-expected limit. These results have, via Furstenberg's correspondence principle, immediate combinatorial applications while combining these results with methods from The polynomial multidimensional Szemeredi theorem along shifted primes. Israel J. Math., 194 (2013), no. 1, 331-348 and Closest integer polynomial multiple recurrence along shifted primes. Ergodic Theory Dynam. Systems, 1-20. doi:10.1017/etds.2016.40 we get the respective right limits and combinatorial results for multiple averages for a single sequence as well as for several sequences along prime numbers.

A positive-charged patch and stabilized hydrophobic core are essential for avirulence function of AvrPib in the rice blast fungus.

Fungal avirulence effectors, a key weapon utilized by pathogens to promote their infection, are recognized by immune receptors to boost host R gene-mediated resistance. Many avirulence effectors share sparse sequence homology to proteins with known functions, and their molecular and biochemical functions together with the evolutionary relationship among different members remain largely unknown. Here, the crystal structure of AvrPib, an avirulence effector from Magnaporthe oryzae, was determined and showed a high degree of similarity to the M.oryzae Avrs and ToxB (MAX) effectors. Compared with other MAX effectors, AvrPib has a distinct positive-charge patch formed by five positive-charged residues (K29, K30, R50, K52 and K70) on the surface. These five key residues were essential to avirulence function of AvrPib and affected its nuclear localization into host cells. Moreover, residues V39 and V58, which locate in the hydrophobic core of the structure, cause loss of function of AvrPib by single-point mutation in natural isolates. In comparison with the wild-type AvrPib, the V39A or V58A mutations resulted in a partial or entire loss of secondary structure elements. Taken together, our results suggest that differences in the surface charge distribution of avirulence proteins could be one of the major bases for the variation in effector-receptor specificity, and that destabilization of the hydrophobic core is one of the major mechanisms employed by AvrPib for the fungus to evade recognition by resistance factors in the host cell.

A note on signs of Fourier coefficients of two cusp forms

Kohnen and Sengupta (Proc. Am. Math. Soc. 137(11) (2009) 3563–3567) showed that if two Hecke eigencusp forms of weight $$k_1$$ and $$k_2$$ respectively, with $$1<k_1<k_2$$ over $$\Gamma _0({N})$$ , have totally real algebraic Fourier coefficients $$\lbrace a(n) \rbrace $$ and $$\lbrace b(n) \rbrace $$ respectively for $$n \ge 1$$ with $$a(1)=1=b(1)$$ , then there exists an element $$\sigma $$ of the absolute Galois group $$\mathrm{Gal}({\bar{\mathbb {Q}}}/{\mathbb {Q}})$$ such that $$a(n)^{\sigma } b(n)^{\sigma } < 0$$ for infinitely many n. Later Gun et al. (Arch. Math. (Basel) 105(5) (2015) 413–424) extended their result by showing that if two Hecke eigen cusp forms, with $$1<k_1<k_2$$ , have real Fourier-coefficients $$\lbrace a(n)\rbrace $$ and $$\lbrace b(n)\rbrace $$ for $$n \ge 1$$ and $$a(1)b(1) \ne 0$$ , then there exists infinitely many n such that $$a(n)b(n) > 0$$ and infinitely many n such that $$a(n)b(n) < 0$$ . When $$k_1=k_2$$ , the simultaneous sign changes of Fourier coefficients of two normalized Hecke eigen cusp forms follow from an earlier work of Ram Murty (Math. Ann. 262 (1983) 431–446). In this note, we compare the signs of the Fourier coefficients of two cusp forms simultaneously for the congruence subgroup $$\Gamma _0({N})$$ where the coefficients lie in an arithmetic progression. Next, we consider an analogous question for the particular sparse sequences of Fourier coefficients of normalized Hecke eigencusp forms for the full modular group.

Elliptic curves in isogeny classes

We show that the distribution of elliptic curves in isogeny classes of curves with a given value of the Frobenius trace t becomes close to uniform even when t is averaged over very short intervals inside the Hasse–Weil interval. This result is based on a new form of the large sieve inequality for sparse sequences.

The Effect of Local Decodability Constraints on Variable-Length Compression

We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$ -sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most $d$ codeword bits. We consider both adaptive and non-adaptive access models, and derive upper and lower bounds that often coincide up to constant factors. Such a characterization for the fixed-blocklength analog of our problem, known as the bit probe complexity of static membership, remains unknown despite considerable attention from researchers over the last few decades. We also show that locally decodable schemes for sparse sequences are able to decode 0s (frequent source symbols) of the source with far fewer probes on average than they can decode 1s (infrequent source symbols), thus rigorizing the notion that infrequent symbols require high probe complexity, even on average. Connections to the fixed-blocklength model and to communication complexity are also briefly discussed.

Waring–Goldbach Problem with Piatetski-Shapiro Primes

In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of Piatetski-Shapiro primes, thereby establishing a variant of Waring–Goldbach problem with primes from a sparse sequence.

DotAligner: identification and clustering of RNA structure motifs

The diversity of processed transcripts in eukaryotic genomes poses a challenge for the classification of their biological functions. Sparse sequence conservation in non-coding sequences and the unreliable nature of RNA structure predictions further exacerbate this conundrum. Here, we describe a computational method, DotAligner, for the unsupervised discovery and classification of homologous RNA structure motifs from a set of sequences of interest. Our approach outperforms comparable algorithms at clustering known RNA structure families, both in speed and accuracy. It identifies clusters of known and novel structure motifs from ENCODE immunoprecipitation data for 44 RNA-binding proteins.

On the exponential large sieve inequality for sparse sequences modulo primes

We complement the argument of M. Z. Garaev (2009) [9] with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form λsn. In particular, we obtain a result which is non-trivial for monotonically increasing sequences S={sn}n=1∞ provided sn⩽n2+o(1), whereas the original argument of M. Z. Garaev requires sn⩽n15/14+o(1) in the same setting. We also give an application of our result to arithmetic properties of integers with almost all digits prescribed.