The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Energy versus information based estimations of dissipation using a pair of magnetic colloidal particles

Using the framework of stochastic thermodynamics, we present an experimental study of a doublet of magnetic colloidal particles which is manipulated by a time-dependent magnetic field. Due to hydrodynamic interactions, each bead experiences a state-dependent friction, which we characterize using a hydrodynamic model. In this work, we compare two estimates of the dissipation in this system: the first one is energy based since it relies on the measured interaction potential, while the second one is information based since it uses only the information content of the trajectories. While the latter only offers a lower bound of the former, we find it to be simple to implement and of general applicability to more complex systems.Comment: Main text: 5 pages, 4 figures. Supplementary material: 5 pages, 5 figure

Weakly coupled neutral gauge bosons at future linear colliders

A weakly coupled new neutral gauge boson forms a narrow resonance that is hard to discover directly in e+e- collisions. However, if the gauge boson mass is below the center-of-mass energy, it can be produced through processes where the effective energy is reduced due to initial-state radiation and beamstrahlung. It is shown that at a high-luminosity linear collider, such a gauge boson can be searched for with very high sensitivity, leading to a substantial improvement compared to existing limits from the Tevatron and also extending beyond the expected reach of the LHC in most models. If a new vector boson is discovered either at the Tevatron Run II, the LHC or the linear collider, its properties can be determined at the linear collider with high precision, thus helping to reveal origin of the new boson.Comment: 21 p

Low and High Energy Phenomenology of Quark-Lepton Complementarity Scenarios

We conduct a detailed analysis of the phenomenology of two predictive see-saw scenarios leading to Quark-Lepton Complementarity. In both cases we discuss the neutrino mixing observables and their correlations, neutrinoless double beta decay and lepton flavor violating decays such as mu -> e gamma. We also comment on leptogenesis. The first scenario is disfavored on the level of one to two standard deviations, in particular due to its prediction for U_{e3}. There can be resonant leptogenesis with quasi-degenerate heavy and light neutrinos, which would imply sizable cancellations in neutrinoless double beta decay. The decays mu -> e gamma and tau -> mu gamma are typically observable unless the SUSY masses approach the TeV scale. In the second scenario leptogenesis is impossible. It is however in perfect agreement with all oscillation data. The prediction for mu -> e gamma is in general too large, unless the SUSY masses are in the range of several TeV. In this case tau -> e gamma and tau -> mu gamma are unobservable.Comment: 32 pages, 9 figures. Discussion on leptogenesis changed due to inclusion of flavor effects. To appear in PR

Four-path interference and uncertainty principle in photodetachment microscopy

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.Comment: submitted to Europhysics Letter

Generalized Spring Tensor Model: A New Improved Load Balancing Method in Cloud Computing

Significant characteristics of cloud computing such as elasticity, scalability and payment model attract businesses to replace their legacy infrastructure with the newly offered cloud technologies. As the number of the cloud users is growing rapidly, extensive load volume will affect performance and operation of the cloud. Therefore, it is essential to develop smarter load management methods to ensure effective task scheduling and efficient management of resources. In order to reach these goals, varieties of algorithms have been explored and tested by many researchers. But so far, not many operational load balancing algorithms have been proposed that are capable of forecasting the future load patterns in cloud-based systems. The aim of this research is to design an effective load management tool, characterized by collective behavior of the workflow tasks and jobs that is able to predict various dynamic load patterns occurring in cloud networks. The results show that the proposed new load balancing algorithm can visualize the network load by projecting the existing relationships among submitted tasks and jobs. The visualization can be particularly useful in terms of monitoring the robustness and stability of the cloud systems. © Springer International Publishing Switzerland 2015

Percutaneous management of thoracolumbar burst fractures: Evolution of techniques and strategy

SummaryIntroductionA number of techniques have been described in the management of thoracolumbar spinal fractures, testimony to the absence of consensus on their treatment. For the past few years, minimally invasive techniques have been developed to limit surgery-related iatrogenic injury. The objective of this study was to report the results of percutaneous management of these lesions and the technical progress made based on our experience.Patients and methodsTwenty-nine patients presenting an A3 fracture, with a mean age of 51 years, were included in this study. All had a balloon kyphoplasty and percutaneous osteosynthesis. Of the first 22 cases, kyphoplasty was the initial procedure performed associated with reduction maneuvers using distraction. Assessment was clinical (neurological status and pain intensity) and radiological (implant positioning, cement leakage, restoration of local kyphosis and any loss of correction).ResultsIn the overall series, the mean local kyphosis correction was 11° with a 2° angle loss at the last follow-up. Pain assessment showed significant improvement, decreasing from 6/10 to 1/10 on discharge. The mean hospital stay lasted 4 days. On the follow-up radiological exams, no cases of extrapedicular screw migration were noted; in two cases, lateral cement leakage was found. The results were equivalent in terms of correction no matter which procedure was performed first, although for the second part of the series the technology was available to bend the spinal fixation rod to the desired curve.DiscussionThe results of this study support the growing interest in minimally invasive techniques in the management of spinal injuries with no neurological deficit. In addition, the evolving material makes it possible to come close to conventional techniques, including reduction maneuvers, while limiting muscle injury by using a purely percutaneous approach. Rigorous patient selection is necessary and the time to learn the procedure must be taken into account. Studies with a longer follow-up are required to confirm the stability of the correction over time.Level of evidenceLevel IV. Retrospective observational study