1,419 research outputs found
Bipolynomial Hilbert functions
Let X be a closed subscheme and let HF(X,-) and hp(X,-) denote, respectively,
the Hilbert function and the Hilbert polynomial of X. We say that X has
bipolynomial Hilbert function if HF(X,d)=min{hp(P^n,d),hp(X,d)} for every
non-negative integer d. We show that if X consists of a plane and generic
lines, then X has bipolynomial Hilbert function. We also conjecture that
generic configurations of non-intersecting linear spaces have bipolynomial
Hilbert function
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
A Risk-Based Model Predictive Control Approach to Adaptive Interventions in Behavioral Health
This brief examines how control engineering and risk management techniques can be applied in the field of behavioral health through their use in the design and implementation of adaptive behavioral interventions. Adaptive interventions are gaining increasing acceptance as a means to improve prevention and treatment of chronic, relapsing disorders, such as abuse of alcohol, tobacco, and other drugs, mental illness, and obesity. A risk-based model predictive control (MPC) algorithm is developed for a hypothetical intervention inspired by Fast Track, a real-life program whose long-term goal is the prevention of conduct disorders in at-risk children. The MPC-based algorithm decides on the appropriate frequency of counselor home visits, mentoring sessions, and the availability of after-school recreation activities by relying on a model that includes identifiable risks, their costs, and the cost/benefit assessment of mitigating actions. MPC is particularly suited for the problem because of its constraint-handling capabilities, and its ability to scale to interventions involving multiple tailoring variables. By systematically accounting for risks and adapting treatment components over time, an MPC approach as described in this brief can increase intervention effectiveness and adherence while reducing waste, resulting in advantages over conventional fixed treatment. A series of simulations are conducted under varying conditions to demonstrate the effectiveness of the algorithm
Down-Hole Heat Exchangers: Modelling of a Low-Enthalpy Geothermal System for District Heating
In order to face the growing energy demands, renewable energy sources can provide an alternative to fossil fuels. Thus, low-enthalpy geothermal plants may play a fundamental role in those areas—such as the Province of Viterbo—where shallow groundwater basins occur and conventional geothermal plants cannot be developed. This may lead to being fuelled by locally available sources. The aim of the present paper is to exploit the heat coming from a low-enthalpy geothermal system. The experimental plant consists in a down-hole heat exchanger for civil purposes and can supply thermal needs by district heating. An implementation in MATLAB environment is provided in order to develop a mathematical model. As a consequence, the amount of withdrawable heat can be successfully calculated
Hilbert functions of schemes of double and reduced points
It remains an open problem to classify the Hilbert functions of double points in P2. Given a valid Hilbert function Hof a zero-dimensional scheme in P2, we show how to construct a set of fat points Z⊆P2of double and reduced points such that HZ, the Hilbert function of Z, is the same as H. In other words, we show that any valid Hilbert function Hof a zero-dimensional scheme is the Hilbert function of a set a positive number of double points and some reduced points. Fo r some families of valid Hilbert functions, we are also able to show that His the Hilbert function of only double points. In addition, we give necessary and sufficient conditions for the Hilbert function of a scheme of a double points, or double points plus one additional reduced point, to be the Hilbert function of points with support on a star configuration of lines
Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
We give analytical solutions for the time-optimal synthesis of entangling
gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three
qubits subject to an Ising Hamiltonian interaction with equal coupling plus
a local magnetic field acting on the intermediate qubit. The energy available
is fixed, but we relax the standard assumption of instantaneous unitary
operations acting on single qubits. The time required for performing an
entangling gate which is equivalent, modulo local unitary operations, to the
between the indirectly coupled qubits 1 and 3 is
, i.e. faster than a previous estimate based on a similar
Hamiltonian and the assumption of local unitaries with zero time cost.
Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space
of qubit 3 shows that the time-optimal synthesis of the (which acts as the identity when the control qubit 1 is in the state
, while if the control qubit is in the state the target
qubit 3 is flipped as ) also requires the same
time .Comment: 9 pages; minor modification
An adaptive POD approximation method for the control of advection-diffusion equations
We present an algorithm for the approximation of a finite horizon optimal
control problem for advection-diffusion equations. The method is based on the
coupling between an adaptive POD representation of the solution and a Dynamic
Programming approximation scheme for the corresponding evolutive
Hamilton-Jacobi equation. We discuss several features regarding the adaptivity
of the method, the role of error estimate indicators to choose a time
subdivision of the problem and the computation of the basis functions. Some
test problems are presented to illustrate the method.Comment: 17 pages, 18 figure
Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background
The effective potential for a dynamical Wick field (dynamical signature)
induced by the quantum effects of massive fields on a topologically non-trivial
dimensional background is considered. It is shown that when the radius of
the compactified dimension is very small compared with (where
is a proper-time cutoff), a flat metric with Lorentzian signature is
preferred on . When the compactification radius
becomes larger a careful analysis of the 1-loop effective potential indicates
that a Lorentzian signature is preferred in both and and that these
results are relatively stable under metrical perturbations
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