1,563 research outputs found
Information complexity of the AND function in the two-Party, and multiparty settings
In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O.
Weinstein, From information to exact communication, STOC'13] Braverman et al.
developed a local characterization for the zero-error information complexity in
the two party model, and used it to compute the exact internal and external
information complexity of the 2-bit AND function, which was then applied to
determine the exact asymptotic of randomized communication complexity of the
set disjointness problem.
In this article, we extend their results on AND function to the multi-party
number-in-hand model by proving that the generalization of their protocol has
optimal internal and external information cost for certain distributions. Our
proof has new components, and in particular it fixes some minor gaps in the
proof of Braverman et al
Corporal Punishment - Schools and School Districts - Constitutional Law
The United States District Court for the Western District of Pennsylvania has held that the infliction of corporal punishment on a child by school authorities against the expressed wishes of a parent is violative of a fundamental right of parental liberty.
Glaser v. Marietta, 351 F. Supp. 555 (W.D. Pa. 1972)
Surface Operators in N=2 Abelian Gauge Theory
We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly
prove that for any embedding of surface operators in a general, twisted N=2
pure abelian theory on an arbitrary four-manifold, the parameters transform
naturally under the SL(2,Z) duality of the theory. However, for
nontrivially-embedded surface operators, exact S-duality holds if and only if
the "quantum" parameter effectively vanishes, while the overall SL(2,Z) duality
holds up to a c-number at most, regardless. Nevertheless, this observation sets
the stage for a physical proof of a remarkable mathematical result by
Kronheimer and Mrowka--that expresses a "ramified" analog of the Donaldson
invariants solely in terms of the ordinary Donaldson invariants--which, will
appear, among other things, in forthcoming work. As a prelude to that, the
effective interaction on the corresponding u-plane will be computed. In
addition, the dependence on second Stiefel-Whitney classes and the appearance
of a Spin^c structure in the associated low-energy Seiberg-Witten theory with
surface operators, will also be demonstrated. In the process, we will stumble
upon an interesting phase factor that is otherwise absent in the "unramified"
case.Comment: 46 pages. Minor refinemen
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Relation between two properties of linear difference equations with infinite
delay is investigated: (i) exponential stability, (ii) \l^p-input
\l^q-state stability (sometimes is called Perron's property). The latter
means that solutions of the non-homogeneous equation with zero initial data
belong to \l^q when non-homogeneous terms are in \l^p. It is assumed that
at each moment the prehistory (the sequence of preceding states) belongs to
some weighted \l^r-space with an exponentially fading weight (the phase
space). Our main result states that (i) (ii) whenever and a certain boundedness condition on coefficients is
fulfilled. This condition is sharp and ensures that, to some extent,
exponential and \l^p-input \l^q-state stabilities does not depend on the
choice of a phase space and parameters and , respectively. \l^1-input
\l^\infty-state stability corresponds to uniform stability. We provide some
evidence that similar criteria should not be expected for non-fading memory
spaces.Comment: To be published in Journal of Difference Equations and Application
Spatial and temporal characterization of a Bessel beam produced using a conical mirror
We experimentally analyze a Bessel beam produced with a conical mirror,
paying particular attention to its superluminal and diffraction-free
properties. We spatially characterized the beam in the radial and on-axis
dimensions, and verified that the central peak does not spread over a
propagation distance of 73 cm. In addition, we measured the superluminal phase
and group velocities of the beam in free space. Both spatial and temporal
measurements show good agreement with the theoretical predictions.Comment: 5 pages, 6 figure
Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs
We give sufficient conditions for essential self-adjointness of magnetic
Schr\"odinger operators on locally finite graphs. Two of the main theorems of
the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as
follows: the ordering of presentation has been modified in several places,
more details have been provided in several places, some notations have been
changed, two examples have been added, and several new references have been
inserted. The final version of this preprint will appear in Integral
Equations and Operator Theor
On the six-dimensional origin of the AGT correspondence
We argue that the six-dimensional (2,0) superconformal theory defined on M
\times C, with M being a four-manifold and C a Riemann surface, can be twisted
in a way that makes it topological on M and holomorphic on C. Assuming the
existence of such a twisted theory, we show that its chiral algebra contains a
W-algebra when M = R^4, possibly in the presence of a codimension-two defect
operator supported on R^2 \times C \subset M \times C. We expect this structure
to survive the \Omega-deformation.Comment: References added. 14 page
Mesoscopic Superconducting Disc with Short-Range Columnar Defects
Short-range columnar defects essentially influence the magnetic properties of
a mesoscopic superconducting disc.They help the penetration of vortices into
the sample, thereby decrease the sample magnetization and reduce the upper
critical field. Even the presence of weak defects split a giant vortex state
(usually appearing in a clean disc in the vicinity of the transition to a
normal state) into a number of vortices with smaller topological charges. In a
disc with a sufficient number of strong enough defects vortices are always
placed onto defects. The presence of defects lead to the appearance of
additional magnetization jumps related to the redistribution of vortices which
are already present on the defects and not to the penetration of new vortices.Comment: 14 pgs. RevTex, typos and figures corrected. Submitted to Phys. Rev.
Surface Operators in Abelian Gauge Theory
We consider arbitrary embeddings of surface operators in a pure,
non-supersymmetric abelian gauge theory on spin (non-spin) four-manifolds. For
any surface operator with a priori simultaneously non-vanishing parameters, we
explicitly show that the parameters transform naturally under an SL(2, Z) (or a
congruence subgroup thereof) duality of the theory. However, for
non-trivially-embedded surface operators, exact S-duality holds only if the
quantum parameter effectively vanishes, while the overall SL(2, Z) (or a
congruence subgroup thereof) duality holds up to a c-number at most,
regardless. Via the formalism of duality walls, we furnish an alternative
derivation of the transformation of parameters - found also to be consistent
with a switch from Wilson to 't Hooft loop operators under S-duality. With any
background embedding of surface operators, the partition function and the
correlation functions of non-singular, gauge-invariant local operators on any
curved four-manifold, are found to transform like modular forms under the
respective duality groups.Comment: 30 pages. Minor refinemen
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