23 papers · ranked by Valyu relevance
Ri-Xiang Chen
Throughout this paper S = k[x1, x2, . . . , xn] denotes the polynomial ring in n variables over a field k. Let f1, f2, . . . , fn be some homogeneous polynomials in S of degrees a1, a2, . . . , an with 1 ≤ a1 ≤ a2 ≤ · · · ≤ an. It is well-known that the following statements are equivalent:
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
For an integer $q\ge 2$, a q-recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of q. In this article, q-recursive sequences are studied and the asymptotic behavior of their summatory functions is analyzed. It is shown that every q-recursive sequence is q-regular in the…
Shakov, Anton
We introduce the 2-regular integer sequence A383066 = (s(n))n≥1, which begins 0, 1, 1, 2, 3, 3, 2, . . .. We prove that the number of occurrences of an integer m ≥ 0 in this sequence is equal to τ (m2+1), the number of divisors of m2+1. Using this fact, we give a generating function for τ (m 2 + 1). We also discuss…
Alice Milne, Sijia Zhao, Christina Tampakaki, Gabriela Bury + 1 more
The brain is highly sensitive to auditory regularities and exploits the predictable order of sounds in many situations, from parsing complex auditory scenes, to the acquisition of language. To understand the impact of stimulus predictability on perception, it is important to determine how the detection of predictable…
Rosy Southwell, Candida Tufo, Maria Chait
In classical studies of auditory pattern learning, neuronal responses exhibit repetition suppression, where sequences of repeated tones show a reduced evoked response. This may be due in part to adaptation, but is also hypothesized to indicate suppression of expected stimuli. Repetition suppression is thought to form a…
Richard A. Moy, David Rolnick
Given a set of integers with no three in arithmetic progression, we construct a Stanley sequence by adding integers greedily so that no arithmetic progression is formed. This paper offers two main contributions to the theory of Stanley sequences. First, we characterize well-structured Stanley sequences as solutions to…
Nadir Murru, Carlo Sanna
For integers k ≥ 2 and n 6= 0, let νk(n) denotes the greatest nonnegative integer e such that k e divides n. Moreover, let (un)n≥0 be a nondegenerate Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 +bun, for some integers a and b. Shu and Yao showed that for any prime number p the sequence νp(un+1)n≥0 is…
Victor Vergnieux, Rufin Vogels
Animals of several species, including primates, learn the statistical regularities of their environment. In particular, they learn the temporal regularities that occur in streams of visual images. Previous human neuroimaging studies reported discrepant effects of such statistical learning, ranging from stronger…
Katarina C. Poole, Maria Chait, Jennifer K. Bizley
Acoustic sequences that transition from random to regularly repeating tones are increasingly used to study how the auditory system detects structure. Humans can identify such regularities rapidly, often within a single cycle. To test whether this ability is unique to humans, we trained ferrets (n = 6) to detect…
Francesco Rubino, Marcella Attimonelli
Background One of the most frequent uses of bioinformatics tools concerns functional characterization of a newly produced nucleotide sequence (a query sequence) by applying Blast or FASTA against a set of sequences (the subject sequences). However, in some specific contexts, it is useful to compare the query sequence…
Jean‐Paul Allouche, Han Guo, Harald Niederreiter
Sequences with perfect linear complexity profile were defined more than thirty years ago in the study of measures of randomness for binary sequences. More recently apwenian sequences, first with values ±1 , then with values in {0, 1}, were introduced in the study of Hankel determinants of automatic sequences. We…
Javier Jiménez-Garrido, Ignacio Miguel-Cantero, Javier Sanz, Gerhard Schindl
We prove several improved versions of the Borel-Ritt theorem about the surjectivity of the asymptotic Borel mapping in classes of functions with M-uniform asymptotic expansion on an unbounded sector of the Riemann surface of the logarithm. While in previous results the weight sequence M of positive numbers is supposed…
Hanna Ringer, Erich Schröger, Sabine Grimm
Detection of repeating patterns within continuous sound streams is crucial for efficient auditory perception. Previous studies demonstrated a remarkable sensitivity of the human auditory system to periodic repetitions in randomly generated sounds. Automatic repetition detection was reflected in different EEG markers…
Giorgio Gronchi, Steven A. Sloman
The overalternating bias is that people rate sequences with an excess of alternation as more random than prescribed by information theory. There are two main explanations: the representativeness heuristic (Kahneman & Tversky Cognitive Psychology, 3, 430-454, [19]) and the implicit encoding hypothesis (Falk & Konold…
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi + 1 more
'Raghavendra Tripathi' 'Ruimin Zhang'] Abstract. We investigate a method of generating a graph G = (V, E) out of an ordered list of n distinct real numbers a1, . . . , an. These graphs can be used to test for the presence of combinatorial structure in the sequence. We describe sequences exhibiting intricate hidden…
Sabine Schwager, Dennis Rünger, Robert Gaschler, Peter A. Frensch
for the generation of explicit sequence knowledge? Authors: ['Sabine Schwager' 'Dennis Rünger' 'Robert Gaschler' 'Peter A. Frensch'] In incidental sequence learning situations, there is often a number of participants who can report the task-inherent sequential regularity after training. Two kinds of mechanisms for the…
Yiren Ren, Grace Leslie, Thackery Brown, Thiago P. Fernandes
Music is omnipresent in daily life and may interact with critical cognitive processes including memory. Despite music’s presence during diverse daily activities including studying, commuting, or working, existing literature has yielded mixed results as to whether music improves or impairs memory for information…
Laura Fernández-Merino, Mikel Lizarazu, Nicola Molinaro, Marina Kalashnikova
Long and short-term musical training has been proposed to improve efficiency of cortical tracking of speech, the mechanism through which brain oscillations synchronize to the acoustic temporal structure of external stimuli. Here, we study how different rhythm structures of the musical signal can guide the temporal…
Authors not listed
Sequence is the critical determinant of macromolecular function, yet current polymer design approaches often optimize monomer composition and ratios while ignoring sequence. This creates poorly defined design spaces for active learning that miss the vast combinatorial landscape of sequence possibilities. We introduce…
Angshuman R. Goswami
In this paper, we present an alternative proof of Fekete's Lemma. We demonstrate that for any subadditive sequence, it is possible to construct a subadditive function that exactly interpolates the sequence. Using this result, along with Hille's theorem on subadditive functions, we naturally arrive at Fekete's Lemma.…
Babu Bassa
In this communication the author describes a software tool named "ChameleonSort". The software program, developed by the present author is useful in the sorting of biological sequence variants like those accumulating mutations while diverging from the common ancestors. Examples include viral protein variants, protein…
Christoph Aistleitner
By a classical result of Weyl, for any increasing sequence (nk)k≥1 of integers the sequence of fractional parts ({nkx})k≥1 is uniformly distributed modulo 1 for almost all x ∈ [0, 1]. Except for a few special cases, e.g. when nk = k, k ≥ 1, the exceptional set cannot be described explicitly. The exact asymptotic order…
Nicholas Tjahjono, Evgeni Penev, Boris Yakobson
Programmable self-assembly provides a promising avenue to improve upon traditional synthesis and create multi-component materials with emergent properties and arbitrary nanoscale complexity. However, its most successful realizations utilizing DNA often use complicated arduous procedures that result in low yields. Here…