8,267 research outputs found
First-order transition in small-world networks
The small-world transition is a first-order transition at zero density of
shortcuts, whereby the normalized shortest-path distance undergoes a
discontinuity in the thermodynamic limit. On finite systems the apparent
transition is shifted by . Equivalently a ``persistence
size'' can be defined in connection with finite-size
effects. Assuming , simple rescaling arguments imply that
. We confirm this result by extensive numerical simulation in one to
four dimensions, and argue that implies that this transition is
first-order.Comment: 4 pages, 3 figures, To appear in Europhysics Letter
Incremental Recompilation of Knowledge
Approximating a general formula from above and below by Horn formulas (its
Horn envelope and Horn core, respectively) was proposed by Selman and Kautz
(1991, 1996) as a form of ``knowledge compilation,'' supporting rapid
approximate reasoning; on the negative side, this scheme is static in that it
supports no updates, and has certain complexity drawbacks pointed out by
Kavvadias, Papadimitriou and Sideri (1993). On the other hand, the many
frameworks and schemes proposed in the literature for theory update and
revision are plagued by serious complexity-theoretic impediments, even in the
Horn case, as was pointed out by Eiter and Gottlob (1992), and is further
demonstrated in the present paper. More fundamentally, these schemes are not
inductive, in that they may lose in a single update any positive properties of
the represented sets of formulas (small size, Horn structure, etc.). In this
paper we propose a new scheme, incremental recompilation, which combines Horn
approximation and model-based updates; this scheme is inductive and very
efficient, free of the problems facing its constituents. A set of formulas is
represented by an upper and lower Horn approximation. To update, we replace the
upper Horn formula by the Horn envelope of its minimum-change update, and
similarly the lower one by the Horn core of its update; the key fact which
enables this scheme is that Horn envelopes and cores are easy to compute when
the underlying formula is the result of a minimum-change update of a Horn
formula by a clause. We conjecture that efficient algorithms are possible for
more complex updates.Comment: See http://www.jair.org/ for any accompanying file
Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
We consider quantum computations comprising only commuting gates, known as
IQP computations, and provide compelling evidence that the task of sampling
their output probability distributions is unlikely to be achievable by any
efficient classical means. More specifically we introduce the class post-IQP of
languages decided with bounded error by uniform families of IQP circuits with
post-selection, and prove first that post-IQP equals the classical class PP.
Using this result we show that if the output distributions of uniform IQP
circuit families could be classically efficiently sampled, even up to 41%
multiplicative error in the probabilities, then the infinite tower of classical
complexity classes known as the polynomial hierarchy, would collapse to its
third level. We mention some further results on the classical simulation
properties of IQP circuit families, in particular showing that if the output
distribution results from measurements on only O(log n) lines then it may in
fact be classically efficiently sampled.Comment: 13 page
System Identification of Constructed Facilities: Challenges and Opportunities Across Hazards
The motivation, success and prevalence of full-scale monitoring of constructed buildings vary
considerably across the hazard of concern (earthquakes, strong winds, etc.), due in part to various
fiscal and life safety motivators. Yet while the challenges of successful deployment and
operation of large-scale monitoring initiatives are significant, they are perhaps dwarfed by the
challenges of data management, interrogation and ultimately system identification. Practical
constraints on everything from sensor density to the availability of measured input has driven the
development of a wide array of system identification and damage detection techniques, which in
many cases become hazard-specific. In this study, the authors share their experiences in fullscale monitoring of buildings across hazards and the associated challenges of system
identification. The study will conclude with a brief agenda for next generation research in the
area of system identification of constructed facilities
Spin-injection Hall effect in a planar photovoltaic cell
Successful incorporation of the spin degree of freedom in semiconductor
technology requires the development of a new paradigm allowing for a scalable,
non-destructive electrical detection of the spin-polarization of injected
charge carriers as they propagate along the semiconducting channel. In this
paper we report the observation of a spin-injection Hall effect (SIHE) which
exploits the quantum-relativistic nature of spin-charge transport and which
meets all these key requirements on the spin detection. The two-dimensional
electron-hole gas photo-voltaic cell we designed to observe the SIHE allows us
to develop a quantitative microscopic theory of the phenomenon and to
demonstrate its direct application in optoelectronics. We report an
experimental realization of a non-magnetic spin-photovoltaic effect via the
SIHE, rendering our device an electrical polarimeter which directly converts
the degree of circular polarization of light to a voltage signal.Comment: 14 pages, 4 figure
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
Biased random satisfiability problems: From easy to hard instances
In this paper we study biased random K-SAT problems in which each logical
variable is negated with probability . This generalization provides us a
crossover from easy to hard problems and would help us in a better
understanding of the typical complexity of random K-SAT problems. The exact
solution of 1-SAT case is given. The critical point of K-SAT problems and
results of replica method are derived in the replica symmetry framework. It is
found that in this approximation for .
Solving numerically the survey propagation equations for K=3 we find that for
there is no replica symmetry breaking and still the SAT-UNSAT
transition is discontinuous.Comment: 17 pages, 8 figure
Quantum annealing and the Schr\"odinger-Langevin-Kostin equation
We show, in the context of quantum combinatorial optimization, or quantum
annealing, how the nonlinear Schr\"odinger-Langevin-Kostin equation can
dynamically drive the system toward its ground state. We illustrate, moreover,
how a frictional force of Kostin type can prevent the appearance of genuinely
quantum problems such as Bloch oscillations and Anderson localization which
would hinder an exhaustive search.Comment: 5 pages, 4 figures. To appear on Physical Review
Euclidean TSP with few inner points in linear space
Given a set of points in the Euclidean plane, such that just points
are strictly inside the convex hull of the whole set, we want to find the
shortest tour visiting every point. The fastest known algorithm for the version
when is significantly smaller than , i.e., when there are just few inner
points, works in time [Knauer and Spillner,
WG 2006], but also requires space of order . The best
linear space algorithm takes time [Deineko, Hoffmann, Okamoto,
Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space
time algorithm. The new insight is extending the
known divide-and-conquer method based on planar separators with a
matching-based argument to shrink the instance in every recursive call. This
argument also shows that the problem admits a quadratic bikernel.Comment: under submissio
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