How Fast Can We Multiply Large Integers on an Actual Computer?

We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like multiplication of long integers. The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices. An interesting outcome is that the proposed refined complexity measures do not rank the well known multiplication algorithms the same way as the Turing machine model.Comment: To appear in the proceedings of Latin 2014. Springer LNCS 839

Consistent histories, the quantum Zeno effect, and time of arrival

We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view

Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation

We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schr\"odinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schr\"odinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects.Comment: 29 pages in RevTeX, Added Note, references adde

Comparative effectiveness of dual vs. single-action antidepressants on HIV clinical outcomes in HIV-infected people with depression

Objective: Depression is highly prevalent among people living with HIV/AIDS (PLWHA) and has deleterious effects on HIV clinical outcomes. We examined changes in depression symptoms, viral suppression, and CD4 + T cells/μl among PLWHA diagnosed with depression who initiated antidepressant treatment during routine care, and compared the effectiveness of dual-action and single-action antidepressants for improving those outcomes. Design: Comparative effectiveness study of new user dual-action or single-action antidepressant treatment episodes occurring from 2004 to 2014 obtained from the Center for AIDS Research Network of Integrated Clinical Systems. Methods: We identified new user treatment episodes with no antidepressant use in the preceding 90 days. We completed intent-to-treat and per protocol evaluations for the main analysis. Primary outcomes, were viral suppression (HIV viral load <200 copies/ml) and CD4 + T cells/μl. In a secondary analysis, we used the Patient Health Questionnaire-9 (PHQ-9) to evaluate changes in depression symptoms and remission (PHQ <5). Generalized estimating equations with inverse probability of treatment weights were fitted to estimate treatment effects. Results: In weighted intent-to-treat analyses, the probability of viral suppression increased 16% after initiating antidepressants [95% confidence interval=(1.12, 1.20)]. We observed an increase of 39 CD4 + T cells/μl after initiating antidepressants (30, 48). Both the frequency of remission from depression and PHQ-9 scores improved after antidepressant initiation. Comparative effectiveness estimates were null in all models. Conclusion: Initiating antidepressant treatment was associated with improvements in depression, viral suppression, and CD4 + T cells/μl, highlighting the health benefits of treating depression in PLWHA. Dual and single-action antidepressants had comparable effectiveness

A direct path to dependable software

What would it take to make software more dependable? Until now, most approaches have been indirect: some practices – processes, tools or techniques – are used that are believed to yield dependable software, and the argument for dependability rests on the extent to which the developers have adhered to them. This article argues instead that developers should produce direct evidence that the software satisfies its dependability claims. The potential advantages of this approach are greater credibility (since the argument is not contingent on the effectiveness of the practices) and reduced cost (since development resources can be focused where they have the most impact)

Long-term perturbations due to a disturbing body in elliptic inclined orbit

In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68\degree is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure

Symbolic Model Checking of Concurrent Programs Using Partial Orders and On-the-Fly Transactions

Abstract. The state explosion problem is one of the core bottlenecks in the model checking of concurrent software. We show how to ameliorate the problem by combining the ability of partial order techniques to reduce the state space of the concurrent program with the power of symbolic model checking to explore large state spaces. Our new verification methodology involves translating the given concurrent program into a circuit-based model which gives us the flexibility to then employ any model checking technique of choice – either SAT or BDD-based – for verifying a broad range of linear time properties, not just safety. The reduction in the explored state-space is obtained by statically augmenting the symbolic encoding of the program by additional constraints. These constraints restrict the scheduler to choose from a minimal conditional stubborn set of transitions at each state. Another key contribution of the paper, is a new method for detecting transactions on-the-fly which takes into account patterns of lock acquisition and yields better reductions than existing methods which rely on a lockset based analysis. Moreover unlike existing techniques, identifying on-the-fly transactions does not require the program to follow a lock discipline in accessing shared variables. We have applied our techniques to the Daisy test bench and shown the existence of several bugs.