7,777 research outputs found
Ideals of general forms and the ubiquity of the Weak Lefschetz property
Let be positive integers and let be an
ideal generated by general forms of degrees , respectively, in a
polynomial ring with variables. When all the degrees are the same we
give a result that says, roughly, that they have as few first syzygies as
possible. In the general case, the Hilbert function of has been
conjectured by Fr\"oberg. In a previous work the authors showed that in many
situations the minimal free resolution of must have redundant terms which
are not forced by Koszul (first or higher) syzygies among the (and hence
could not be predicted from the Hilbert function), but the only examples came
when . Our second main set of results in this paper show that further
examples can be obtained when . We also show that if
Fr\"oberg's conjecture on the Hilbert function is true then any such redundant
terms in the minimal free resolution must occur in the top two possible degrees
of the free module. Related to the Fr\"oberg conjecture is the notion of Weak
Lefschetz property. We continue the description of the ubiquity of this
property. We show that any ideal of general forms in has
it. Then we show that for certain choices of degrees, any complete intersection
has it and any almost complete intersection has it. Finally, we show that most
of the time Artinian ``hypersurface sections'' of zeroschemes have it.Comment: 24 page
state generation of three Josephson qubits in presence of bosonic baths
We analyze an entangling protocol to generate tripartite
Greenberger-Horne-Zeilinger states in a system consisting of three
superconducting qubits with pairwise coupling. The dynamics of the open quantum
system is investigated by taking into account the interaction of each qubit
with an independent bosonic bath with an ohmic spectral structure. To this end
a microscopic master equation is constructed and exactly solved. We find that
the protocol here discussed is stable against decoherence and dissipation due
to the presence of the external baths.Comment: 16 pages and 4 figure
TRAIL, DR5 and Caspase 3-dependent Apoptosis in Vessels of Diseased Human Temporomandibular Joint Disc. An Immunohistochemical Study
To evaluate the apoptosis involvement in the angiogenesis as a self-limiting process in patients with temporomandibular joint (TMJ) degenerated disc vessels, we assessed, by immunohistochemistry, the detection of TRAIL, its death receptor DR5 and caspase 3. TRAIL, its death receptor DR5 and caspase 3 expression were studied by immunohistochemistry in 15 TMJ discs displaced without reduction and in 4 unaffected discs. These apoptosis molecules were detected in the intima and media layers of newly formed vessels affected discs. In conclusion, vessels apoptosis activation in TMJ disc with ID could be regarded as a self-limiting process that try to leads to vessel regression; in this way an inhibition of angiogenic vessels may prove a key strategy in limiting pathological angiogenesis, by cutting off blood supply to tumors, or by reducing harmful inflammation
Non-Markovian dissipative dynamics of two coupled qubits in independent reservoirs: a comparison between exact solutions and master equation approaches
The reduced dynamics of two interacting qubits coupled to two independent
bosonic baths is investigated. The one-excitation dynamics is derived and
compared with that based on the resolution of appropriate non-Markovian master
equations. The Nakajima-Zwanzig and the time-convolutionless projection
operator techniques are exploited to provide a description of the non-Markovian
features of the dynamics of the two-qubits system. The validity of such
approximate methods and their range of validity in correspondence to different
choices of the parameters describing the system are brought to light.Comment: 6 pages, 3 figures. Submitted to PR
On the shape of a pure O-sequence
An order ideal is a finite poset X of (monic) monomials such that, whenever M
is in X and N divides M, then N is in X. If all, say t, maximal monomials of X
have the same degree, then X is pure (of type t). A pure O-sequence is the
vector, h=(1,h_1,...,h_e), counting the monomials of X in each degree.
Equivalently, in the language of commutative algebra, pure O-sequences are the
h-vectors of monomial Artinian level algebras. Pure O-sequences had their
origin in one of Richard Stanley's early works in this area, and have since
played a significant role in at least three disciplines: the study of
simplicial complexes and their f-vectors, level algebras, and matroids. This
monograph is intended to be the first systematic study of the theory of pure
O-sequences. Our work, making an extensive use of algebraic and combinatorial
techniques, includes: (i) A characterization of the first half of a pure
O-sequence, which gives the exact converse to an algebraic g-theorem of Hausel;
(ii) A study of (the failing of) the unimodality property; (iii) The problem of
enumerating pure O-sequences, including a proof that almost all O-sequences are
pure, and the asymptotic enumeration of socle degree 3 pure O-sequences of type
t; (iv) The Interval Conjecture for Pure O-sequences (ICP), which represents
perhaps the strongest possible structural result short of an (impossible?)
characterization; (v) A pithy connection of the ICP with Stanley's matroid
h-vector conjecture; (vi) A specific study of pure O-sequences of type 2,
including a proof of the Weak Lefschetz Property in codimension 3 in
characteristic zero. As a corollary, pure O-sequences of codimension 3 and type
2 are unimodal (over any field); (vii) An analysis of the extent to which the
Weak and Strong Lefschetz Properties can fail for monomial algebras; (viii)
Some observations about pure f-vectors, an important special case of pure
O-sequences.Comment: iii + 77 pages monograph, to appear as an AMS Memoir. Several, mostly
minor revisions with respect to last year's versio
Asymptotic Entanglement Dynamics and Geometry of Quantum States
A given dynamics for a composite quantum system can exhibit several distinct
properties for the asymptotic entanglement behavior, like entanglement sudden
death, asymptotic death of entanglement, sudden birth of entanglement, etc. A
classification of the possible situations was given in [M. O. Terra Cunha,
{\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no
known examples. In this work we give a better classification for the possibile
relaxing dynamics at the light of the geometry of their set of asymptotic
states and give explicit examples for all the classes. Although the
classification is completely general, in the search of examples it is
sufficient to use two qubits with dynamics given by differential equations in
Lindblad form (some of them non-autonomous). We also investigate, in each case,
the probabilities to find each possible behavior for random initial states.Comment: 9 pages, 2 figures; revised version accepted for publication in J.
Phys. A: Math. Theo
Resonant effects in a SQUID qubit subjected to non adiabatic changes
By quickly modifying the shape of the effective potential of a double SQUID
flux qubit from a single-well to a double-well condition, we experimentally
observe an anomalous behavior, namely an alternance of resonance peaks, in the
probability to find the qubit in a given flux state. The occurrence of
Landau-Zener transitions as well as resonant tunneling between degenerate
levels in the two wells may be invoked to partially justify the experimental
results. A quantum simulation of the time evolution of the system indeed
suggests that the observed anomalous behavior can be imputable to quantum
coherence effects. The interplay among all these mechanisms has a practical
implication for quantum computing purposes, giving a direct measurement of the
limits on the sweeping rates possible for a correct manipulation of the qubit
state by means of fast flux pulses, avoiding transitions to non-computational
states.Comment: 6 pages and 6 figures. The paper, as it is, has been accepted for
publication on PRB on March 201
Master equations for two qubits coupled via a nonlinear mode
A microscopic master equation describing the dynamics of two qubits coupled via a nonlinear mediator is constructed supposing that the two qubits, as well as the nonlinear mode, interact, each with its own independent bosonic bath. Generally speaking the master equation derived in this way represents a more appropriate tool for studying the dynamics of open quantum systems. Indeed we showthat it is more complex than the phenomenological master equation, constructed simply adding ad hoc dissipative terms
Dissipation and entanglement dynamics for two interacting qubits coupled to independent reservoirs
We derive the master equation of a system of two coupled qubits by taking
into account their interaction with two independent bosonic baths. Important
features of the dynamics are brought to light, such as the structure of the
stationary state at general temperatures and the behaviour of the entanglement
at zero temperature, showing the phenomena of sudden death and sudden birth as
well as the presence of stationary entanglement for long times. The model here
presented is quite versatile and can be of interest in the study of both
Josephson junction architectures and cavity-QED.Comment: 14 pages, 3 figures, submitted to Journal of Physics A: Mathematical
and Theoretica
On the validity of non-Markovian master equation approaches for the entanglement dynamics of two-qubit systems
In the framework of the dissipative dynamics of coupled qubits interacting with independent reservoirs, a comparison between non-Markovian master equation techniques and an exact solution is presented here. We study various regimes in order to find the limits of validity of the Nakajima\u2013Zwanzig and the time-convolutionless master equations in the description of the
entanglement dynamics. A comparison between the performances of the concurrence and the
negativity as entanglement measures for the system under study is also presented
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