19,114 research outputs found

### Multi-Shift de Bruijn Sequence

A (non-circular) de Bruijn sequence w of order n is a word such that every
word of length n appears exactly once in w as a factor. In this paper, we
generalize the concept to a multi-shift setting: a multi-shift de Bruijn
sequence tau(m,n) of shift m and order n is a word such that every word of
length n appears exactly once in w as a factor that starts at index im+1 for
some integer i>=0. We show the number of the multi-shift de Bruijn sequence
tau(m,n) is (a^n)!a^{(m-n)(a^n-1)} for 1<=n<=m and is (a^m!)^{a^{n-m}} for
1<=m<=n, where a=|Sigma|. We provide two algorithms for generating a tau(m,n).
The multi-shift de Bruijn sequence is important in solving the Frobenius
problem in a free monoid.Comment: 9 page

### A new characterization of the Clifford torus via scalar curvature pinching

Let $M^n$ be a compact hypersurface with constant mean curvature $H$ in
$\mathbb{S}^{n+1}$. Denote by $S$ the squared norm of the second fundamental
form of $M$. We prove that there exists a positive constant $\gamma(n)$
depending only on $n$ such that if $|H|\leq\gamma(n)$ and $\beta(n,H)\leq
S\leq\beta(n,H)+\frac{n}{23}$, then $S\equiv\beta(n,H)$ and $M$ is one of the
following cases: (i) $\mathbb{S}^{k}(\sqrt{\frac{k}{n}})\times
\mathbb{S}^{n-k}(\sqrt{\frac{n-k}{n}})$, $\,1\le k\le n-1$; (ii)
$\mathbb{S}^{1}(\frac{1}{\sqrt{1+\mu^2}})\times
\mathbb{S}^{n-1}(\frac{\mu}{\sqrt{1+\mu^2}})$. Here
$\beta(n,H)=n+\frac{n^3}{2(n-1)}H^2+\frac{n(n-2)}{2(n-1)}\sqrt{n^2H^4+4(n-1)H^2}$
and $\mu=\frac{n|H|+\sqrt{n^2H^2+4(n-1)}}{2}$. This provides a new
characterization of the Clifford torus.Comment: 25 page

### An NP-hardness Result on the Monoid Frobenius Problem

The following problem is NP-hard: given a regular expression $E$, decide if
$E^*$ is not co-finite.Comment: 2 pages, working paper; an error in Problem 5 is correcte

### Frequency Principle in Deep Learning with General Loss Functions and Its Potential Application

Previous studies have shown that deep neural networks (DNNs) with common
settings often capture target functions from low to high frequency, which is
called Frequency Principle (F-Principle). It has also been shown that
F-Principle can provide an understanding to the often observed good
generalization ability of DNNs. However, previous studies focused on the loss
function of mean square error, while various loss functions are used in
practice. In this work, we show that the F-Principle holds for a general loss
function (e.g., mean square error, cross entropy, etc.). In addition, DNN's
F-Principle may be applied to develop numerical schemes for solving various
problems which would benefit from a fast converging of low frequency. As an
example of the potential usage of F-Principle, we apply DNN in solving
differential equations, in which conventional methods (e.g., Jacobi method) is
usually slow in solving problems due to the convergence from high to low
frequency.Comment: 8 pages, 4 figure

### Microscopic analysis of octupole shape transitions in neutron-rich actinides with relativistic energy density functional

Quadrupole and octupole deformation energy surfaces, low-energy excitation
spectra, and electric transition rates in eight neutron-rich isotopic chains --
Ra, Th, U, Pu, Cm, Cf, Fm, and No -- are systematically analyzed using a
quadrupole-octupole collective Hamiltonian model, with parameters determined by
constrained reflection-asymmetric and axially-symmetric relativistic mean-field
calculations based on the PC-PK1 energy density functional. The theoretical
results of low-lying negative-parity bands, odd-even staggering, average
octupole deformations $\langle\beta_3\rangle$, and $B(E3; 3^-_1\to 0^+_1)$ show
evidence of a shape transition from nearly spherical to stable
octupole-deformed, and finally octupole-soft equilibrium shapes in the
neutron-rich actinides. A microscopic mechanism for the onset of stable
octupole deformation is also discussed in terms of the evolution of
single-nucleon orbitals with deformation.Comment: 13 pages, 10 figures, Accepted for Publication in Chinese Physics C.
arXiv admin note: substantial text overlap with arXiv:1710.08230; text
overlap with arXiv:1402.6102 by other author

### Beam Splitter Entangler for Light Fields

We propose an experimentally feasible scheme to generate various types of
entangled states of light fields by using beam splitters and single-photon
detectors. Two light fields are incident on two beam splitters and are split
into strong and weak output modes respectively. A conditional joint measurement
on both weak output modes may result in an entanglement between the two strong
output modes. The conditions for the maximal entanglement are discussed based
on the concurrence. Several specific examples are also examined.Comment: 5 pages, 1 figur

### Triangular Self-Assembly

We discuss the self-assembly system of triangular tiles instead of square
tiles, in particular right triangular tiles and equilateral triangular tiles.
We show that the triangular tile assembly system, either deterministic or
non-deterministic, has the same power to the square tile assembly system in
computation, which is Turing universal. By providing counter-examples, we show
that the triangular tile assembly system and the square tile assembly system
are not comparable in general. More precisely, there exists square tile
assembly system S such that no triangular tile assembly system is a division of
S and produces the same shape; there exists triangular tile assembly system T
such that no square tile assembly system produces the same compatible shape
with border glues. We also discuss the assembly of triangles by triangular
tiles and obtain results similar to the assembly of squares, that is to
assemble a triangular of size O(N^2), the minimal number of tiles required is
in O(log N/log log N)

### Edge Intelligence: On-Demand Deep Learning Model Co-Inference with Device-Edge Synergy

As the backbone technology of machine learning, deep neural networks (DNNs)
have have quickly ascended to the spotlight. Running DNNs on
resource-constrained mobile devices is, however, by no means trivial, since it
incurs high performance and energy overhead. While offloading DNNs to the cloud
for execution suffers unpredictable performance, due to the uncontrolled long
wide-area network latency. To address these challenges, in this paper, we
propose Edgent, a collaborative and on-demand DNN co-inference framework with
device-edge synergy. Edgent pursues two design knobs: (1) DNN partitioning that
adaptively partitions DNN computation between device and edge, in order to
leverage hybrid computation resources in proximity for real-time DNN inference.
(2) DNN right-sizing that accelerates DNN inference through early-exit at a
proper intermediate DNN layer to further reduce the computation latency. The
prototype implementation and extensive evaluations based on Raspberry Pi
demonstrate Edgent's effectiveness in enabling on-demand low-latency edge
intelligence.Comment: ACM SIGCOMM Workshop on Mobile Edge Communications, Budapest,
Hungary, August 21-23, 2018. https://dl.acm.org/authorize?N66547

### Pseudo-Power Avoidance

Repetition avoidance has been studied since Thue's work. In this paper, we
considered another type of repetition, which is called pseudo-power. This
concept is inspired by Watson-Crick complementarity in DNA sequence and is
defined over an antimorphic involution $\phi$. We first classify the alphabet
$\Sigma$ and the antimorphic involution $\phi$, under which there exists
sufficiently long pseudo-$k$th-power-free words. Then we present algorithms to
test whether a finite word $w$ is pseudo-$k$th-power-free

### Optimal segmentation of directed graph and the minimum number of feedback arcs

The minimum feedback arc set problem asks to delete a minimum number of arcs
(directed edges) from a digraph (directed graph) to make it free of any
directed cycles. In this work we approach this fundamental cycle-constrained
optimization problem by considering a generalized task of dividing the digraph
into D layers of equal size. We solve the D-segmentation problem by the
replica-symmetric mean field theory and belief-propagation heuristic
algorithms. The minimum feedback arc density of a given random digraph ensemble
is then obtained by extrapolating the theoretical results to the limit of large
D. A divide-and-conquer algorithm (nested-BPR) is devised to solve the minimum
feedback arc set problem with very good performance and high efficiency.Comment: 14 page

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