350 research outputs found
k-Part splittings and operator parameter overrelaxation
AbstractThis paper proceeds in two directions of attack for finding (iteratively) solutions for linear systems on Hilbert space. First, we consider scalar-dependent Overrelaxation as a special case of operator-dependent overrelaxations. Secondly, we study “finer” splittings than the conventional two-part splittings and show where, in some cases, these new splittings can either accelerate convergence of approximating sequences derived from two-part splittings or else turn divergent sequences into convergent ones
Filter Cleaning Using Gas Injection
A filter cleaning process using gas injection is considered. An estimate for the minimum mass flow rate out of the gas injector and the corresponding injector/filter geometry is found. The estimates are based on a similarity solution for a free turbulent jet. The minimum mass flow rate and geometry is worked out for a specific example
Hawaiian Identity and Collectivism Predict the \u27Ideal Virtual Team Personality\u27
Previous studies have linked trust with virtual team performance. In turn, trust is predicted by high levels of extraversion, agreeableness, and conscientiousness. Previous research indicates that individuals high in these three traits are ideal virtual team members due to the higher levels of trust and consequent performance they display in virtual teams. In the present study we set out to determine predictors of this “ideal virtual team personality” in a multicultural setting, the University of Hawaii at Hilo. Our results show that the higher an individual is in Collectivism and Hawaiian Identity, the more likely they will possess the “ideal virtual team personality” profile that leads to better trust and performance in virtual teams
A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach
We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations
Structured Near-Optimal Channel-Adapted Quantum Error Correction
We present a class of numerical algorithms which adapt a quantum error
correction scheme to a channel model. Given an encoding and a channel model, it
was previously shown that the quantum operation that maximizes the average
entanglement fidelity may be calculated by a semidefinite program (SDP), which
is a convex optimization. While optimal, this recovery operation is
computationally difficult for long codes. Furthermore, the optimal recovery
operation has no structure beyond the completely positive trace preserving
(CPTP) constraint. We derive methods to generate structured channel-adapted
error recovery operations. Specifically, each recovery operation begins with a
projective error syndrome measurement. The algorithms to compute the structured
recovery operations are more scalable than the SDP and yield recovery
operations with an intuitive physical form. Using Lagrange duality, we derive
performance bounds to certify near-optimality.Comment: 18 pages, 13 figures Update: typos corrected in Appendi
Single-shot discrimination of quantum unitary processes
We formulate minimum-error and unambiguous discrimination problems for
quantum processes in the language of process positive operator valued measures
(PPOVM). In this framework we present the known solution for minimum-error
discrimination of unitary channels. We derive a "fidelity-like" lower bound on
the failure probability of the unambiguous discrimination of arbitrary quantum
processes. This bound is saturated (in a certain range of apriori
probabilities) in the case of unambiguous discrimination of unitary channels.
Surprisingly, the optimal solution for both tasks is based on the optimization
of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur
Teaching Time Savers: Is Homework Grading on Your Nerves?
You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework
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