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Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 683 (1 self)
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problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability
The Retinoblastoma Protein and CellCycle Control
 Cell
, 1995
"... pRB, the product of the retinoblastoma tumor suppressor gene, operates in the midst of the cell cycle clock apparatus. Its main role is to act as a signal transducer connecting the cell cycle clock with the transcriptional machinery. In this role, pRB allows the clock to control the expression of b ..."
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Cited by 429 (5 self)
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of banks of genes that mediate advance of the cell through a critical phase of its growth cycle. Loss of pRB function deprives the clock and thus the cell of an important mechanism for braking cell proliferation through modulation of gene expression. pRB and the G1 Restriction Point pRB exerts most
Critical points in coupled Potts models and critical phases in coupled loop models
"... We show how to couple two critical Qstate Potts models to yield a new selfdual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new criti ..."
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Cited by 4 (2 self)
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We show how to couple two critical Qstate Potts models to yield a new selfdual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new
Rigidity of the critical phases on a Cayley tree
 Moscow Mathematical Journal
, 2001
"... We discuss statistical mechanics on nonamenable graphs, and we study the features of the phase transition, which are due to nonamenability. For the Ising model on the usual lattice it is known that uctuations of magnetization are much less likely in the states with nonzero magnetic eld than in th ..."
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Cited by 13 (0 self)
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We discuss statistical mechanics on nonamenable graphs, and we study the features of the phase transition, which are due to nonamenability. For the Ising model on the usual lattice it is known that uctuations of magnetization are much less likely in the states with nonzero magnetic eld than
Lack of Critical Phase Points and Exponentially Faint Illumination
"... Abstract. The Stationary Phase Principle (S.P.P.) states that in the computation of oscillatory integrals, the contributions of non stationary points of the phase are smaller than any power n of 1/k, for k → ∞. Unfortunately, S.P.P. says nothing about the possible growth in the constants in the esti ..."
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Abstract. The Stationary Phase Principle (S.P.P.) states that in the computation of oscillatory integrals, the contributions of non stationary points of the phase are smaller than any power n of 1/k, for k → ∞. Unfortunately, S.P.P. says nothing about the possible growth in the constants
Extended Criticality, Phase Spaces and Enablement in Biology
"... This paper analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given. We argue that one major aspect of biological evolution is the continual change of the pertinent ph ..."
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This paper analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given. We argue that one major aspect of biological evolution is the continual change of the pertinent
On the Critical Phase Transition Time of Wireless Multihop Networks with Random Failures
"... In this paper, we study the critical phase transition time of largescale wireless multihop networks when the network topology experiences a partition due to increasing random node failures. We first define two new metrics, namely the last connection time and first partition time. The former is the ..."
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Cited by 12 (4 self)
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In this paper, we study the critical phase transition time of largescale wireless multihop networks when the network topology experiences a partition due to increasing random node failures. We first define two new metrics, namely the last connection time and first partition time. The former
Modular invariance of finite size corrections and a vortex critical phase
, 2008
"... We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods L0 and L1 where the spins carry a representation of the fundamental group of the torus labeled by phases u0 and u1. We find the exact finite size and lattice corrections, to the partition function Z, for arbit ..."
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Cited by 5 (1 self)
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, for arbitrary mass m and phases ui. Summing Z −1/2 over phases gives the corresponding result for the Ising model. The limits m → 0 and u i → 0 do not commute. With m = 0 the model exhibits a vortex critical phase when at least one of the ui is nonzero. In the continuum or scaling limit, for arbitrary m
IASSNSHEP95/62 Statistics Of The Burst Model At Supercritical Phase
, 2008
"... We investigate the statistics of a model of typeI Xray burst [Phys. Rev. E, 51, 3045 (1995)] in its supercritical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time evolution ..."
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We investigate the statistics of a model of typeI Xray burst [Phys. Rev. E, 51, 3045 (1995)] in its supercritical phase. The time evolution of the burnable clusters, places where fire can pass through, is studied using simple statistical arguments. We offer a simple picture for the time
Results 1  10
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539,111