84,500 research outputs found
On Exponential Time Lower Bound of Knapsack under Backtracking
M.Aleknovich et al. have recently proposed a model of algorithms, called BT
model, which generalizes both the priority model of Borodin, Nielson and
Rackoff, as well as a simple dynamic programming model by Woeginger. BT model
can be further divided into three kinds of fixed, adaptive and fully adaptive
ones. They have proved exponential time lower bounds of exact and approximation
algorithms under adaptive BT model for Knapsack problem. Their exact lower
bound is , in this paper, we slightly improve the
exact lower bound to about , by the same technique,
with related parameters optimized.Comment: This paper supersedes the result of arXiv:cs/060606
Virasoro Constraints For Quantum Cohomology
Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition
function of topological sigma model coupled to gravity is annihilated by
infinitely many differential operators which form half branch of the Virasoro
algebra. In this paper, we give a proof to this conjecture for the genus 0
part.Comment: LaTex, 38 pages. Corrected some typos and minor mistakes in the first
version of this paper posted on June 7, 199
Weinstein Conjecture and GW Invariants
In this paper, we establish a general relationship between the nonvanishing
of GW invariants with the existence of the closed orbits of a Hamiltonian
system. As an application, we completely solved the stabilized Weinstein
conjecture
Conservation laws and symmetries of Hunter-Saxton equation: revisited
Through a reciprocal transformation induced by the
conservation law , the Hunter-Saxton
(HS) equation is shown to possess conserved
densities involving arbitrary smooth functions, which have their roots in
infinitesimal symmetries of , the counterpart of the HS equation
under . Hierarchies of commuting symmetries of the HS equation
are studied under appropriate changes of variables initiated by
, and two of these are linearized while the other is identical
to the hierarchy of commuting symmetries admitted by the potential modified
Korteweg-de Vries equation. A fifth order symmetry of the HS equation is
endowed with a sixth order hereditary recursion operator by its connection with
the Fordy-Gibbons equation. These results reveal the origin for the rich and
remarkable structures of the HS equation and partially answer the questions
raised by Wang [{\it Nonlinearity} {\bf 23}(2010) 2009].Comment: 18 page
Family Seiberg-Witten invariants and wall crossing formulas
In this paper we set up the family Seiberg-Witten theory. It can be applied
to the counting of nodal pseudo-holomorphic curves in a symplectic 4-manifold
(especially a Kahler surface). A new feature in this theory is that the chamber
structure plays a more prominent role. We derive some wall crossing formulas
measuring how the family Seiberg-Witten invariants change from one chamber to
another.Comment: 46 pages Typos corrected, references updated, Theorem 2.2 made more
precis
An Improved Decision Procedure for Linear Time Mu-Calculus
An improved Present Future form (PF form) for linear time -calculus
(TL) is presented in this paper. In particular, the future part of the new
version turns into the conjunction of elements in the closure of a formula. We
show that every closed TL formula can be transformed into the new PF form.
Additionally, based on the PF form, an algorithm for constructing Present
Future form Graph (PFG), which can be utilized to describe models of a formula,
is given. Further, an intuitive and efficient decision procedure for checking
satisfiability of the guarded fragment of TL formulas based on PFG is
proposed and implemented in C++. The new decision procedure has the best time
complexity over the existing ones despite the cost of exponential space.
Finally, a PFG-based model checking approach for TL is discussed where a
counterexample can be obtained visually when a model violates a property
DNS Study on Vorticity Structures in Late Flow Transition
Vorticity and vortex are two different but related concepts. This paper
focuses on the investigation of vorticity generation and development, and
vorticity structure inside/ outside the vortex. Vortex is a region where the
vorticity overtakes deformation. Vortex cannot be directly represented by the
vorticity. Except for those vorticity lines which come from and end at side
boundaries, another type of vorticity, self-closed vorticity lines named
vorticity rings, is numerously generated inside the domain during flow
transition. These new vorticity rings are found around the hairpin vortex heads
and legs. The generation and growth of vorticity rings are produced by the
buildup of the vortices according to the vorticity transport equation. On the
other hand, vortex buildup is a consequence of vorticity line stretching,
tilting and twisting. Both new vorticity and new vortices are generated during
the flow transition. According to the Helmholtz vorticity flux conservation
law, vorticity line cannot be interrupted, started, or ended inside the flow
field, the newly produced vorticity has only one form which is the vorticity
rings. In addition, an interesting finding is that a single hairpin vortex
consists of several types of vorticity lines which could come from the side
boundaries, whole vorticity rings and part of vorticity rings
Super-pixel cloud detection using Hierarchical Fusion CNN
Cloud detection plays a very important role in the process of remote sensing
images. This paper designs a super-pixel level cloud detection method based on
convolutional neural network (CNN) and deep forest. Firstly, remote sensing
images are segmented into super-pixels through the combination of SLIC and
SEEDS. Structured forests is carried out to compute edge probability of each
pixel, based on which super-pixels are segmented more precisely. Segmented
super-pixels compose a super-pixel level remote sensing database. Though cloud
detection is essentially a binary classification problem, our database is
labeled into four categories: thick cloud, cirrus cloud, building and other
culture, to improve the generalization ability of our proposed models.
Secondly, super-pixel level database is used to train our cloud detection
models based on CNN and deep forest. Considering super-pixel level remote
sensing images contain less semantic information compared with general object
classification database, we propose a Hierarchical Fusion CNN (HFCNN). It takes
full advantage of low-level features like color and texture information and is
more applicable to cloud detection task. In test phase, every super-pixel in
remote sensing images is classified by our proposed models and then combined to
recover final binary mask by our proposed distance metric, which is used to
determine ambiguous super-pixels. Experimental results show that, compared with
conventional methods, HFCNN can achieve better precision and recall
On some properties of a class of fractional stochastic heat equations
We consider nonlinear parabolic stochastic equations of the form \partial_t
u=\sL u + \lambda \sigma(u)\dot \xi on the ball , where
denotes some Gaussian noise and is Lipschitz continuous. Here \sL
corresponds to an -stable process killed upon exiting . We
will consider two types of noise; space-time white noise and spatially
correlated noise. Under a linear growth condition on , we study growth
properties of the second moment of the solutions
Critical points of solutions for mean curvature equation in strictly convex and nonconvex domains
In this paper, we mainly investigate the set of critical points associated to
solutions of mean curvature equation with zero Dirichlet boundary condition in
a strictly convex domain and a nonconvex domain respectively. Firstly, we
deduce that mean curvature equation has exactly one nondegenerate critical
point in a smooth, bounded and strictly convex domain of
. Secondly, we study the geometric structure about the
critical set of solutions for the constant mean curvature equation in a
concentric (respectively an eccentric) spherical annulus domain of
, and deduce that exists (respectively does not
exist) a rotationally symmetric critical closed surface . In fact, in an
eccentric spherical annulus domain, is made up of finitely many isolated
critical points () on an axis and finitely many
rotationally symmetric critical Jordan curves () with
respect to an axis.Comment: 13 pages, 5 figure
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