3,172 research outputs found
Unified formalism for higher-order non-autonomous dynamical systems
This work is devoted to giving a geometric framework for describing
higher-order non-autonomous mechanical systems. The starting point is to extend
the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these
kinds of systems, generalizing previous developments for higher-order
autonomous mechanical systems and first-order non-autonomous mechanical
systems. Then, we use this unified formulation to derive the standard
Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map
and the Euler-Lagrange and the Hamilton equations, both for regular and
singular systems. As applications of our model, two examples of regular and
singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions
2 and 3. A remark is added after Proposition
Physical qubits from charged particles: IR divergences in quantum information
We consider soft photons effects (IR structure of QED) on the construction of
physical qubits. Soft-photons appear when we build charged qubits from the
asymptotic states of QED. This construction is necessary in order to include
the effect of soft photons on entanglement measures. The nonexistence of free
charged particles (due to the long range of QED interactions) lead us to
question the sense of the very concept of free charged qubit. In this letter,
using the "dressing" formalism, we build physical charged qubits from dressed
fields which have the correct asymptotic behavior, are gauge invariant, their
propagators have a particle pole structure and are free from infrared
divergences. Finally, we discuss the impact of the soft corrections on the
entanglement measures.Comment: 4 pages, 2 figures, RevTeX. Version 2: Some references update
Pandemic effects in the Solow growth model
We show how diseases can affect economic growth in a Solow growth model, with population growth and no technical progress, but modified to include a saving rate that depends on the individual health status. We successively insert this model into the SIS (susceptible–infected–susceptible) and SIR (susceptible–infected–recovered) models of disease spreading. In these two models, the spread of the infection proceeds according to the so-called basic reproductive number. This number determines in which of the two possible equilibria, the disease-free or the pandemic equilibrium, the economy ends. We show that output per capita is always lower in the pandemic steady state, which implies a contraction in the economy's production possibilities frontier.Julio Carmona acknowledges the financial support from the Spanish Ministerio de Economía y Competitividad, through the project ECO2016-77200-P. Ángel León acknowledges the financial support from the Spanish Ministerio de Economía y Competitividad, through grant PID2021-124860NB-I00
Investment option under CIR interest rates
We analyze extensively the characteristics of the solution to an irreversible investment decision when the only source of uncertainty comes from interest rates. They are assumed to be driven by the popular Cox–Ingersoll–Ross (CIR) stochastic process. Particular attention is paid to the impact that both CIR parameters and risk aversion have on the threshold rate.Financial support from the Spanish Ministry of Education and Science through the grant SEJ 2005-09372 (Leon) and SEJ 2004-05815 (Carmona) is gratefully acknowledged
Radiative corrections to the Dalitz plot of K_{l3}^\pm decays
We calculate the model-independent radiative corrections to the Dalitz plot
of K_{l3}^\pm decays to order (\alpha/\pi)(q/M_1), where q is the momentum
transfer and M_1 is the mass of the kaon. The final results are presented,
first, with the triple integration over the variables of the bremsstrahlung
photon ready to be performed numerically and, second, in an analytical form.
These two forms are useful to crosscheck on one another and with other
calculations. This paper is organized to make it accessible and reliable in the
analysis of the Dalitz plot of precision experiments and is not compromised to
fixing the form factors at predetermined values. It is assumed that the real
photons are kinematically discriminated. Otherwise, our results have a general
model-independent applicability.Comment: RevTex4, 38 pages, 5 figures, 5 tables; some typos corrected;
discussion extended to compare with other result
U and Th speciation in river sediments
A study of the distribution of some natural radionuclides in different chemical fractions of river bottom sediments has been carried out. The study has shown that the majority of the total U in sediments is located in the non-residual fractions, while Th is more likely to be present in the residual ones. This difference between U and Th reflects largely a much higher mobility of U relative to Th in surface and near-surface environments. Coprecipitation with amorphous ferromanganese oxyhydroxides is the main process of U and Th incorporation from the water column into the soil particles. Moreover, the distribution of the radionuclides and the analysis of the Th/U mass ratios in different chemical fractions of sediments has made an unequivocal connection between the enhanced U content in river sediments and the wastes discharged into the rivers by the operation of fertilizer industries
Higher-order Mechanics: Variational Principles and other topics
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the
Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we
state a unified geometrical version of the Variational Principles which allows
us to derive the Lagrangian and Hamiltonian equations for these kinds of
systems. Then, the standard Lagrangian and Hamiltonian formulations of these
principles and the corresponding dynamical equations are recovered from this
unified framework.Comment: New version of the paper "Variational principles for higher-order
dynamical systems", which was presented in the "III Iberoamerican Meeting on
Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A
detailed review is added. Sections containing results about variational
principles are enlarged with additional comments, diagrams and summarizing
results. Bibliography is update
Pricing executive stock optons under employment shocks
We obtain explicit expressions for the subjective, objective and market value of perpetual executive stock options (ESOs) under exogenous employment shocks driven by an independent Poisson process. Previously, we obtain the executive's optimal exercise policy from the subjective valuation that is necessary for the objective one, or fair value. The perpetual ESO is compared with the true finite maturity ESO finding that the approximation is reasonably good. To illustrate the usefulness of the objective valuation for accounting purposes, we analyze the statistical distribution of the fair value when there is uncertainty about the employment shock intensity. Finally, the role of ESOs in the design of executives’ incentives is also discussed.Spanish Ministry for Science and Innovation through the Grant SEJ 2004-05815; Spanish Ministry for Science and Innovation through the Grant ECO2008-02599/ECO; Spanish Ministry for Science and Innovation through the Grant ECO2010-18567
Does stock return predictability affect ESO fair value?
Executive Stock Options (ESOs) are modified American options that cannot be valued using standard methods. With a few exceptions, the literature has discussed the ESO fair value by assuming unpredictable stock returns which are not supported by the available empirical evidence. In this paper we obtain the fair value of American ESOs when stock returns are predictable and, specifically, driven by the trending Ornstein–Uhlenbeck process of Lo and Wang (1995). We solve the executive’s portfolio allocation problem for a simple buy-and-hold strategy when his wealth can be distributed between a risk-free asset and a market portfolio. This problem is jointly solved with the executive’s optimal exercise policy. We find that executives tend to wait longer the higher the predictability, independently of the composition of executive’s asset menu. We have also analyzed the implications under the FAS123R proposals for the ESO fair value and found that, even for low autocorrelations, there is a meaningful mispricing when unpredictable returns are erroneously assumed.Angel León and Antoni Vaello-Sebastiá acknowledge the financial support from the Spanish Ministry for Science and Innovation through the Grants ECO2011-29751 and ECO2010-18567 respectively
CAR T cells for T-cell leukemias: Insights from mathematical models
Immunotherapy has the potential to change the way all cancer types are
treated and cured. Cancer immunotherapies use elements of the patient immune
system to attack tumor cells. One of the most successful types of immunotherapy
is CAR-T cells. This treatment works by extracting patient's T-cells and adding
to them an antigen receptor allowing tumor cells to be recognized and targeted.
These new cells are called CAR-T cells and are re-infused back into the patient
after expansion in-vitro. This approach has been successfully used to treat
B-cell malignancies (B-cell leukemias and lymphomas). However, its application
to the treatment of T-cell leukemias faces several problems. One of these is
fratricide, since the CAR-T cells target both tumor and other CAR-T cells. This
leads to nonlinear dynamical phenomena amenable to mathematical modeling. In
this paper we construct a mathematical model describing the competition of
CAR-T, tumor and normal T-cells and studied some basic properties of the model
and its practical implications. Specifically, we found that the model
reproduced the observed difficulties for in-vitro expansion of the therapeutic
cells found in the laboratory. The mathematical model predicted that CAR-T cell
expansion in the patient would be possible due to the initial presence of a
large number of targets. We also show that, in the context of our mathematical
approach, CAR-T cells could control tumor growth but not eradicate the disease
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