scholarly journals SIPE: Small Integer Plus Exponent

2013 ◽  
Author(s):  
V. Lefevre
Keyword(s):  
Small Integer

scholarly journals A biological rationale for musical consonance

2015 ◽  
Vol 112 (36) ◽  
pp. 11155-11160 ◽  
Author(s):  
Daniel L. Bowling ◽  
Dale Purves
Keyword(s):  
Central Issue ◽  
Small Integer

The basis of musical consonance has been debated for centuries without resolution. Three interpretations have been considered: (i) that consonance derives from the mathematical simplicity of small integer ratios; (ii) that consonance derives from the physical absence of interference between harmonic spectra; and (iii) that consonance derives from the advantages of recognizing biological vocalization and human vocalization in particular. Whereas the mathematical and physical explanations are at odds with the evidence that has now accumulated, biology provides a plausible explanation for this central issue in music and audition.

scholarly journals Message Integration Authentication in the Internet-of-Things via Lattice-Based Batch Signatures

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 4056 ◽  
Author(s):  
Xiuhua Lu ◽  
Wei Yin ◽  
Qiaoyan Wen ◽  
Kaitai Liang ◽  
Liqun Chen ◽  
...  
Keyword(s):  
Internet Of Things ◽  
Processing Speed ◽  
Quantum Computer ◽  
The Internet ◽  
Small Integer ◽  
Computer Attacks ◽  
Intersection Method ◽  
Small Integer Solution Problem ◽  
The Internet Of Things ◽  
Batch Signature

The internet-of-things (also known as IoT) connects a large number of information-sensing devices to the Internet to collect all kinds of information needed in real time. The reliability of the source of a large number of accessed information tests the processing speed of signatures. Batch signature allows a signer to sign a group of messages at one time, and signatures’ verification can be completed individually and independently. Therefore, batch signature is suitable for data integration authentication in IoT. An outstanding advantage of batch signature is that a signer is able to sign as many messages as possible at one time without worrying about the size of signed messages. To reduce complexity yielded by multiple message signing, a binary tree is usually leveraged in the construction of batch signature. However, this structure requires a batch residue, making the size of a batch signature (for a group of messages) even longer than the sum of single signatures. In this paper, we make use of the intersection method from lattice to propose a novel generic method for batch signature. We further combine our method with hash-and-sign paradigm and Fiat–Shamir transformation to propose new batch signature schemes. In our constructions, a batch signature does not need a batch residue, so that the size of the signature is relatively smaller. Our schemes are securely proved to be existential unforgeability against adaptive chosen message attacks under the small integer solution problem, which shows great potential resisting quantum computer attacks.

scholarly journals Optimal Bounds for the k -cut Problem

2022 ◽  
Vol 69 (1) ◽  
pp. 1-18
Author(s):  
Anupam Gupta ◽  
David G. Harris ◽  
Euiwoong Lee ◽  
Jason Li
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Connected Components ◽  
Small Integer ◽  
Main Ingredient ◽  
Fine Grained ◽  
Optimal Bounds ◽  
Sunflower Lemma ◽  
General Graphs ◽  
New Algorithms

In the k -cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into k connected components. Algorithms of Karger and Stein can solve this in roughly O ( n 2k ) time. However, lower bounds from conjectures about the k -clique problem imply that Ω ( n (1- o (1)) k ) time is likely needed. Recent results of Gupta, Lee, and Li have given new algorithms for general k -cut in n 1.98k + O(1) time, as well as specialized algorithms with better performance for certain classes of graphs (e.g., for small integer edge weights). In this work, we resolve the problem for general graphs. We show that the Contraction Algorithm of Karger outputs any fixed k -cut of weight α λ k with probability Ω k ( n - α k ), where λ k denotes the minimum k -cut weight. This also gives an extremal bound of O k ( n k ) on the number of minimum k -cuts and an algorithm to compute λ k with roughly n k polylog( n ) runtime. Both are tight up to lower-order factors, with the algorithmic lower bound assuming hardness of max-weight k -clique. The first main ingredient in our result is an extremal bound on the number of cuts of weight less than 2 λ k / k , using the Sunflower lemma. The second ingredient is a fine-grained analysis of how the graph shrinks—and how the average degree evolves—in the Karger process.

DECOMPOSITION OF PARTIALLY OCCLUDED STRINGS IN THE PRESENCE OF ERRORS

2001 ◽  
Vol 15 (07) ◽  
pp. 1129-1142 ◽  
Author(s):  
COSTAS S. ILIOPOULOS ◽  
JAMES F. REID
Keyword(s):  
Edit Distance ◽  
Theoretical Study ◽  
Unit Cost ◽  
Input Image ◽  
Equal Length ◽  
Sequential Algorithm ◽  
Small Integer ◽  
One Dimensional ◽  
Dimensional Image ◽  
Partially Occluded

A partially occluded scene in an image consists of a number of objects that are partially obstructed by others. By validating a partially occluded image one aims to generate a sequence of concatenated and possibly overlapping objects that corresponds to the input image. This is a theoretical study of partially occluded strings (considered as one-dimensional images) allowing for the presence of errors in each occluded object appearing in the input. Using the unit cost edit distance as our measure of errors, for some small integer k ≥ 0, we present a sequential algorithm for validating a k-approximate one-dimensional image x of length n over a dictionary [Formula: see text] of m objects each having equal length τ in O(nd) time where d = mτ is the size of the dictionary.

scholarly journals Cross-frequency coupling explains the preference for simple ratios in rhythmic behaviour and the relative stability across non-synchronous patterns

2021 ◽  
Vol 376 (1835) ◽  
pp. 20200333 ◽  
Author(s):  
Dobromir Dotov ◽  
Laurel J. Trainor
Keyword(s):  
Phase Synchronization ◽  
Scaling Law ◽  
Small Integer ◽  
Circle Map ◽  
Repetitive Nature ◽  
Farey Tree ◽  
Frequency Coupling ◽  
Complex Forms ◽  
Musical Rhythms ◽  
Cross Frequency Coupling

Rhythms are important for understanding coordinated behaviours in ecological systems. The repetitive nature of rhythms affords prediction, planning of movements and coordination of processes within and between individuals. A major challenge is to understand complex forms of coordination when they differ from complete synchronization. By expressing phase as ratio of a cycle, we adapted levels of the Farey tree as a metric of complexity mapped to the range between in-phase and anti-phase synchronization. In a bimanual tapping task, this revealed an increase of variability with ratio complexity, a range of hidden and unstable yet measurable modes, and a rank-frequency scaling law across these modes. We use the phase-attractive circle map to propose an interpretation of these findings in terms of hierarchical cross-frequency coupling (CFC). We also consider the tendency for small-integer attractors in the single-hand repeated tapping of three-interval rhythms reported in the literature. The phase-attractive circle map has wider basins of attractions for such ratios. This work motivates the question whether CFC intrinsic to neural dynamics implements low-level priors for timing and coordination and thus becomes involved in phenomena as diverse as attractor states in bimanual coordination and the cross-cultural tendency for musical rhythms to have simple interval ratios. This article is part of the theme issue ‘Synchrony and rhythm interaction: from the brain to behavioural ecology’.

scholarly journals Provably Secure Lattice-Based Self-Certified Signature Scheme

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qiang Yang ◽  
Daofeng Li
Keyword(s):  
Computational Cost ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Public Key ◽  
Communication Overhead ◽  
Small Integer ◽  
Signature Scheme ◽  
Signature Schemes ◽  
The Public ◽  
Security Technologies

Digital signatures are crucial network security technologies. However, in traditional public key signature schemes, the certificate management is complicated and the schemes are vulnerable to public key replacement attacks. In order to solve the problems, in this paper, we propose a self-certified signature scheme over lattice. Using the self-certified public key, our scheme allows a user to certify the public key without an extra certificate. It can reduce the communication overhead and computational cost of the signature scheme. Moreover, the lattice helps prevent quantum computing attacks. Then, based on the small integer solution problem, our scheme is provable secure in the random oracle model. Furthermore, compared with the previous self-certified signature schemes, our scheme is more secure.

scholarly journals Automatic comparison of human music, speech, and bird song suggests uniqueness of human scales

2019 ◽  
Author(s):  
Jiei Kuroyanagi ◽  
Shoichiro Sato ◽  
Meng-Jou Ho ◽  
Gakuto Chiba ◽  
Joren Six ◽  
...  
Keyword(s):  
Group Performance ◽  
Bird Song ◽  
Small Integer ◽  
Scale Analysis ◽  
Bird Songs ◽  
Analysis Algorithm ◽  
Human Speech ◽  
The World ◽  
Human Tendency ◽  
Automatic Comparison

The uniqueness of human music relative to speech and animal song has been extensively debated, but never directly measured. To address this, we applied an automated scale analysis algorithm to a sample of 86 recordings of human music, human speech, and bird songs from around the world. We found that human music throughout the world uniquely emphasized scales with small-integer ratios, particularly a perfect 5th (3:2 ratio), while human speech and bird song showed no clear evidence of scale-like tuning. We speculate that the uniquely human tendency toward scales with small-integer ratios may have resulted from the evolution of synchronized group performance among humans.

scholarly journals Hardware Division by Small Integer Constants

2017 ◽  
Vol 66 (12) ◽  
pp. 2097-2110 ◽  
Author(s):  
H. Fatih Ugurdag ◽  
Florent de Dinechin ◽  
Y. Serhan Gener ◽  
Sezer Goren ◽  
Laurent-Stephane Didier
Keyword(s):  
Small Integer
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