Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

General relativistic Sagnac formula revised

The Sagnac effect is a time or phase shift observed between two beams of light traveling in opposite directions in a rotating interferometer. We show that the standard description of this effect within the framework of general relativity misses the effect of deflection of light due to rotational inertial forces. We derive the necessary modification and demonstrate it through a detailed analysis of the square Sagnac interferometer rotating about its symmetry axis in Minkowski space-time. The role of the time shift in a Sagnac interferometer in the synchronization procedure of remote clocks as well as its analogy with the Aharanov-Bohm effect are revised.Comment: 11 pages, 3 figure

On the thermal sunset diagram for scalar field theories

We study the so-called `` sunset diagram'', which is one of two-loop self-energy diagrams, for scalar field theories at finite temperature. For this purpose, we first find the complete expression of the bubble diagram, the one-loop subdiagram of the sunset diagram, for arbitrary momentum. We calculate the temperature independent part and dependent part of the sunset diagram separately. For the former, we obtain the discontinuous part first and the finite continuous part next using a twice-subtracted dispersion relation. For the latter, we express it as a one-dimensional integral in terms of the bubble diagram. We also study the structure of the discontinuous part of the sunset diagram. Physical processes, which are responsible for it, are identified. Processes due to the scattering with particles in the heat bath exist only at finite temperature and generate discontinuity for arbitrary momentum, which is a remarkable feature of the two-loop diagrams at finite temperature. As an application of our result, we study the effect of the diagram on the spectral function of the sigma meson at finite temperature in the linear sigma model, which was obtained at one-loop order previously. At high temperature where the decay $\sigma\to\pi\pi$ is forbidden, sigma acquires a finite width of the order of $10 {\rm MeV}$ while within the one-loop calculation its width vanishes. At low temperature, the spectrum does not deviate much from that at one-loop order. Possible consequences with including other two-loop diagrams are discussed.Comment: 30 page

Mountain maple and balsam fir early response to partial and clear-cut harvesting under aspen stands of northern Quebec

This study is a component of the Sylviculture et am

The experience of being a partner to a spinal cord injured person: A phenomenological-hermeneutic study

This qualitative focuses on the personal experiences of partners to a spinal cord injured person. Using a Ricoeurian phenomenological-hermeneutic approach, we analysed seven partners’ narratives 1 and 2 years after their partner's injury. The study revealed how the injury was experienced from the partners’ perspective through the aftermath. In the acute phase after the injury, partners also felt harmed, and support was needed in relation to their own daily activities, eating, resting, and managing distress. During the institutionalized rehabilitation, partners felt torn between supporting the injured partner and the demanding tasks of everyday life outside the institution. After discharge, partners struggled for the injured partner to regain a well-functioning everyday life and for reestablishing life as a couple. The partner struggled to manage the overwhelming amount of everyday tasks. Some sought to reestablish their usual functions outside the family, whereas others focused on establishing a new life together. The partners experienced much distress and appreciated the support they got, but felt that they were mainly left to manage the difficult process on their own