10,051 research outputs found
The Church Problem for Countable Ordinals
A fundamental theorem of Buchi and Landweber shows that the Church synthesis
problem is computable. Buchi and Landweber reduced the Church Problem to
problems about ω-games and used the determinacy of such games as one of
the main tools to show its computability. We consider a natural generalization
of the Church problem to countable ordinals and investigate games of arbitrary
countable length. We prove that determinacy and decidability parts of the
Bu}chi and Landweber theorem hold for all countable ordinals and that its full
extension holds for all ordinals < \omega\^\omega
A Mathematical Analysis of the Axial Anomaly
As is well known to physicists, the axial anomaly of the massless free
fermion in Euclidean signature is given by the index of the corresponding Dirac
operator. We use the Batalin-Vilkovisky (BV) formalism and the methods of
equivariant quantization of Costello and Gwilliam to produce a new,
mathematical derivation of this result. Using these methods, we formalize two
conventional interpretations of the axial anomaly, the first as a violation of
current conservation at the quantum level and the second as the obstruction to
the existence of a well-defined fermionic partition function. Moreover, in the
formalism of Costello and Gwilliam, anomalies are measured by cohomology
classes in a certain obstruction-deformation complex. Our main result shows
that---in the case of the axial symmetry---the relevant complex is
quasi-isomorphic to the complex of de Rham forms of the spacetime manifold and
that the anomaly corresponds to a top-degree cohomology class which is trivial
if and only if the index of the corresponding Dirac operator is zero.Comment: Version 3 differs from version 2 only in the metadata. The title and
abstract in the metadata have been corrected to match those appearing in the
document itsel
A Proof of Stavi's Theorem
Kamp's theorem established the expressive equivalence of the temporal logic
with Until and Since and the First-Order Monadic Logic of Order (FOMLO) over
the Dedekind-complete time flows. However, this temporal logic is not
expressively complete for FOMLO over the rationals. Stavi introduced two
additional modalities and proved that the temporal logic with Until, Since and
Stavi's modalities is expressively equivalent to FOMLO over all linear orders.
We present a simple proof of Stavi's theorem.Comment: arXiv admin note: text overlap with arXiv:1401.258
Ecological niche modelling in triatomines–abusus non tollit usum: A reply to gutiérrez (2016)
Fil: Rabinovich, Jorge Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Estudios Parasitológicos y de Vectores. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. Centro de Estudios Parasitológicos y de Vectores; Argentin
Escaping the Shadow of Malpractice Law
Abinovich-Einy addresses several constituencies operating at the meeting point of alternative dispute resolution (ADR), communication theory, healthcare policy, and medical-malpractice doctrine. From an ADR perspective, the need for, and barriers to, addressing non-litigable disputes, for which the alternative route is the only one, is explored. It is shown that ADR mechanisms may not take root when introduced into an environment that is resistant to collaborative and open discourse without additional incentives and measures being adopted
Finite Volume Spaces and Sparsification
We introduce and study finite -volumes - the high dimensional
generalization of finite metric spaces. Having developed a suitable
combinatorial machinery, we define -volumes and show that they contain
Euclidean volumes and hypertree volumes. We show that they can approximate any
-volume with multiplicative distortion. On the other hand, contrary
to Bourgain's theorem for , there exists a -volume that on vertices
that cannot be approximated by any -volume with distortion smaller than
.
We further address the problem of -dimension reduction in the context
of volumes, and show that this phenomenon does occur, although not to
the same striking degree as it does for Euclidean metrics and volumes. In
particular, we show that any metric on points can be -approximated by a sum of cut metrics, improving
over the best previously known bound of due to Schechtman.
In order to deal with dimension reduction, we extend the techniques and ideas
introduced by Karger and Bencz{\'u}r, and Spielman et al.~in the context of
graph Sparsification, and develop general methods with a wide range of
applications.Comment: previous revision was the wrong file: the new revision: changed
(extended considerably) the treatment of finite volumes (see revised
abstract). Inserted new applications for the sparsification technique
Time-Frequency Integrals and the Stationary Phase Method in Problems of Waves Propagation from Moving Sources
The time-frequency integrals and the two-dimensional stationary phase method
are applied to study the electromagnetic waves radiated by moving modulated
sources in dispersive media. We show that such unified approach leads to
explicit expressions for the field amplitudes and simple relations for the
field eigenfrequencies and the retardation time that become the coupled
variables. The main features of the technique are illustrated by examples of
the moving source fields in the plasma and the Cherenkov radiation. It is
emphasized that the deeper insight to the wave effects in dispersive case
already requires the explicit formulation of the dispersive material model. As
the advanced application we have considered the Doppler frequency shift in a
complex single-resonant dispersive metamaterial (Lorenz) model where in some
frequency ranges the negativity of the real part of the refraction index can be
reached. We have demonstrated that in dispersive case the Doppler frequency
shift acquires a nonlinear dependence on the modulating frequency of the
radiated particle. The detailed frequency dependence of such a shift and
spectral behavior of phase and group velocities (that have the opposite
directions) are studied numerically
The Church Synthesis Problem with Parameters
For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the
Church Synthesis Problem concerns the existence and construction of an operator
Y=F(X) such that ψ(X,F(X)) is universally valid over Nat.
B\"{u}chi and Landweber proved that the Church synthesis problem is
decidable; moreover, they showed that if there is an operator F that solves the
Church Synthesis Problem, then it can also be solved by an operator defined by
a finite state automaton or equivalently by an MLO formula. We investigate a
parameterized version of the Church synthesis problem. In this version ψ
might contain as a parameter a unary predicate P. We show that the Church
synthesis problem for P is computable if and only if the monadic theory of
is decidable. We prove that the B\"{u}chi-Landweber theorem can be
extended only to ultimately periodic parameters. However, the MLO-definability
part of the B\"{u}chi-Landweber theorem holds for the parameterized version of
the Church synthesis problem
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