8,785 research outputs found
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
First Law, Counterterms and Kerr-AdS_5 Black Holes
We apply the counterterm subtraction technique to calculate the action and
other quantities for the Kerr--AdS black hole in five dimensions using two
boundary metrics; the Einstein universe and rotating Einstein universe with
arbitrary angular velocity. In both cases, the resulting thermodynamic
quantities satisfy the first law of thermodynamics. We point out that the
reason for the violation of the first law in previous calculations is that the
rotating Einstein universe, used as a boundary metric, was rotating with an
angular velocity that depends on the black hole rotation parameter. Using a new
coordinate system with a boundary metric that has an arbitrary angular
velocity, one can show that the resulting physical quantities satisfy the first
law.Comment: 19 pages, 1 figur
Positivity of energy for asymptotically locally AdS spacetimes
We derive necessary conditions for the spinorial Witten-Nester energy to be
well-defined for asymptotically locally AdS spacetimes. We find that the
conformal boundary should admit a spinor satisfying certain differential
conditions and in odd dimensions the boundary metric should be conformally
Einstein. We show that these conditions are satisfied by asymptotically AdS
spacetimes. The gravitational energy (obtained using the holographic stress
energy tensor) and the spinorial energy are equal in even dimensions and differ
by a bounded quantity related to the conformal anomaly in odd dimensions.Comment: 36 pages, 1 figure; minor corrections, JHEP versio
Holographic Renormalization of general dilaton-axion gravity
We consider a very general dilaton-axion system coupled to Einstein-Hilbert
gravity in arbitrary dimension and we carry out holographic renormalization for
any dimension up to and including five dimensions. This is achieved by
developing a new systematic algorithm for iteratively solving the radial
Hamilton-Jacobi equation in a derivative expansion. The boundary term derived
is valid not only for asymptotically AdS backgrounds, but also for more general
asymptotics, including non-conformal branes and Improved Holographic QCD. In
the second half of the paper, we apply the general result to Improved
Holographic QCD with arbitrary dilaton potential. In particular, we derive the
generalized Fefferman-Graham asymptotic expansions and provide a proof of the
holographic Ward identities.Comment: 42 pages. v2: two references added. Version published in JHEP. v3:
fixed minor typos in eqs. (1.6), (2.3), (3.20), (A.3), (B.8), (B.12) and
(B.22
Tetris is Hard, Even to Approximate
In the popular computer game of Tetris, the player is given a sequence of
tetromino pieces and must pack them into a rectangular gameboard initially
occupied by a given configuration of filled squares; any completely filled row
of the gameboard is cleared and all pieces above it drop by one row. We prove
that in the offline version of Tetris, it is NP-complete to maximize the number
of cleared rows, maximize the number of tetrises (quadruples of rows
simultaneously filled and cleared), minimize the maximum height of an occupied
square, or maximize the number of pieces placed before the game ends. We
furthermore show the extreme inapproximability of the first and last of these
objectives to within a factor of p^(1-epsilon), when given a sequence of p
pieces, and the inapproximability of the third objective to within a factor of
(2 - epsilon), for any epsilon>0. Our results hold under several variations on
the rules of Tetris, including different models of rotation, limitations on
player agility, and restricted piece sets.Comment: 56 pages, 11 figure
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
High-Performance Bioinstrumentation for Real-Time Neuroelectrochemical Traumatic Brain Injury Monitoring
Traumatic brain injury (TBI) has been identified as an important cause of death and severe disability in all age groups and particularly in children and young adults. Central to TBIs devastation is a delayed secondary injury that occurs in 30–40% of TBI patients each year, while they are in the hospital Intensive Care Unit (ICU). Secondary injuries reduce survival rate after TBI and usually occur within 7 days post-injury. State-of-art monitoring of secondary brain injuries benefits from the acquisition of high-quality and time-aligned electrical data i.e., ElectroCorticoGraphy (ECoG) recorded by means of strip electrodes placed on the brains surface, and neurochemical data obtained via rapid sampling microdialysis and microfluidics-based biosensors measuring brain tissue levels of glucose, lactate and potassium. This article progresses the field of multi-modal monitoring of the injured human brain by presenting the design and realization of a new, compact, medical-grade amperometry, potentiometry and ECoG recording bioinstrumentation. Our combined TBI instrument enables the high-precision, real-time neuroelectrochemical monitoring of TBI patients, who have undergone craniotomy neurosurgery and are treated sedated in the ICU. Electrical and neurochemical test measurements are presented, confirming the high-performance of the reported TBI bioinstrumentation
Ab-initio No-Core Gamow Shell Model calculations with realistic interactions
No-Core Gamow Shell Model (NCGSM) is applied for the first time to study
selected well-bound and unbound states of helium isotopes. This model is
formulated on the complex energy plane and, by using a complete Berggren
ensemble, treats bound, resonant, and scattering states on equal footing. We
use the Density Matrix Renormalization Group method to solve the many-body
Schr\"{o}dinger equation. To test the validity of our approach, we benchmarked
the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for
H and He nuclei. We also performed {\textit ab initio} NCGSM
calculations for the unstable nucleus He and determined the ground state
energy and decay width, starting from a realistic NLO chiral interaction.Comment: 17 pages, 14 figures. Revised version. Discussion on microscopic
overlap functions, SFs and ANCs is added. Added references. Accepted for
publication at PR
A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs
The Capacitated Vehicle Routing problem is to find a minimum-cost set of
tours that collectively cover clients in a graph, such that each tour starts
and ends at a specified depot and is subject to a capacity bound on the number
of clients it can serve. In this paper, we present a polynomial-time
approximation scheme (PTAS) for instances in which the input graph is planar
and the capacity is bounded. Previously, only a quasipolynomial-time
approximation scheme was known for these instances. To obtain this result, we
show how to embed planar graphs into bounded-treewidth graphs while preserving,
in expectation, the client-to-client distances up to a small additive error
proportional to client distances to the depot
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