105 research outputs found
Erratum: Robust disruptions in electroencephalogram cortical oscillations and large-scale functional networks in autism
Criteria for flatness and injectivity
Let be a commutative Noetherian ring. We give criteria for flatness of
-modules in terms of associated primes and torsion-freeness of certain
tensor products. This allows us to develop a criterion for regularity if
has characteristic , or more generally if it has a locally contracting
endomorphism. Dualizing, we give criteria for injectivity of -modules in
terms of coassociated primes and (h-)divisibility of certain \Hom-modules.
Along the way, we develop tools to achieve such a dual result. These include a
careful analysis of the notions of divisibility and h-divisibility (including a
localization result), a theorem on coassociated primes across a \Hom-module
base change, and a local criterion for injectivity.Comment: 19 page
Reconstructing nonlinear plasma wakefields using a generalized temporally encoded spectral shifting analysis
We generalize the temporally encoded spectral shifting (TESS) analysis for measuring plasma wakefields using spectral interferometry to dissimilar probe pulses of arbitrary spectral profile and to measuring nonlinear wakefields. We demonstrate that the Gaussian approximation used up until now results in a substantial miscalculation of the wakefield amplitude, by a factor of up to two. A method to accurately measure higher amplitude quasilinear and nonlinear wakefields is suggested, using an extension to the TESS procedure, and we place some limits on its accuracy in these regimes. These extensions and improvements to the analysis demonstrate its potential for rapid and accurate on-shot diagnosis of plasma wakefields, even at low plasma densities
The amalgamated duplication of a ring along a multiplicative-canonical ideal
After recalling briefly the main properties of the amalgamated duplication of
a ring along an ideal , denoted by R\JoinI, we restrict our attention
to the study of the properties of R\JoinI, when is a multiplicative
canonical ideal of \cite{hhp}. In particular, we study when every regular
fractional ideal of is divisorial
Almost clean rings and arithmetical rings
It is shown that a commutative B\'ezout ring with compact minimal prime
spectrum is an elementary divisor ring if and only if so is for each
minimal prime ideal . This result is obtained by using the quotient space
of the prime spectrum of the ring modulo the equivalence
generated by the inclusion. When every prime ideal contains only one minimal
prime, for instance if is arithmetical, is Hausdorff and
there is a bijection between this quotient space and the minimal prime spectrum
, which is a homeomorphism if and only if is
compact. If is a closed point of , there is a pure ideal
such that . If is almost clean, i.e. each element is the
sum of a regular element with an idempotent, it is shown that is totally disconnected and, , is
almost clean; the converse holds if every principal ideal is finitely
presented. Some questions posed by Facchini and Faith at the second
International Fez Conference on Commutative Ring Theory in 1995, are also
investigated. If is a commutative ring for which the ring of
quotients of is an IF-ring for each proper ideal , it is proved that
is a strongly discrete valuation ring for each maximal ideal and
is semicoherent for each proper ideal
Perverse coherent t-structures through torsion theories
Bezrukavnikov (later together with Arinkin) recovered the work of Deligne
defining perverse -structures for the derived category of coherent sheaves
on a projective variety. In this text we prove that these -structures can be
obtained through tilting torsion theories as in the work of Happel, Reiten and
Smal\o. This approach proves to be slightly more general as it allows us to
define, in the quasi-coherent setting, similar perverse -structures for
certain noncommutative projective planes.Comment: New revised version with important correction
On Albanese torsors and the elementary obstruction
We show that the elementary obstruction to the existence of 0-cycles of
degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed
in terms of the Albanese 1-motives associated with dense open subsets of X.
Arithmetic applications are given
Ultrafast Diagnostics for Electron Beams from Laser Plasma Accelerators
We present an overview of diagnostic techniques for measuring key parameters of electron bunches from Laser Plasma Accelerators (LPAs). The diagnostics presented here were chosen because they highlight the unique advantages (e.g., diverse forms of electromagnetic emission) and difficulties (e.g., shot-to-shot variability) associated with LPAs. Non destructiveness and high resolution (in space and time and energy) are key attributes that enable the formation of a comprehensive suite of simultaneous diagnostics which are necessary for the full characterization of the ultrashort, but highly-variable electron bunches from LPAs
Algebraic entropy in locally linearly compact vector spaces
We introduce algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as a natural extension of the algebraic entropy for endomorphisms of discrete vector spaces studied in Giordano Bruno and Salce (Arab J Math 1:69\u201387, 2012). We show that the main properties continue to hold in the general context of locally linearly compact vector spaces, in particular we extend the Addition Theorem
On the production of flat electron bunches for laser wake field acceleration
We suggest a novel method for injection of electrons into the acceleration
phase of particle accelerators, producing low emittance beams appropriate even
for the demanding high energy Linear Collider specifications. In this paper we
work out the injection into the acceleration phase of the wake field in a
plasma behind a high intensity laser pulse, taking advantage of the laser
polarization and focusing. With the aid of catastrophe theory we categorize the
injection dynamics. The scheme uses the structurally stable regime of
transverse wake wave breaking, when electron trajectory self-intersection leads
to the formation of a flat electron bunch. As shown in three-dimensional
particle-in-cell simulations of the interaction of a laser pulse in a
line-focus with an underdense plasma, the electrons, injected via the
transverse wake wave breaking and accelerated by the wake wave, perform
betatron oscillations with different amplitudes and frequencies along the two
transverse coordinates. The polarization and focusing geometry lead to a way to
produce relativistic electron bunches with asymmetric emittance (flat beam). An
approach for generating flat laser accelerated ion beams is briefly discussed.Comment: 29 pages, 5 figure
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