Eigenvalue estimates for non-selfadjoint Dirac operators on the real line

We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials.

Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Bounded Seas: Island Parsing Without Shipwrecks

Imprecise manipulation of source code (semi-parsing) is useful for tasks such as robust parsing, error recovery, lexical analysis, and rapid development of parsers for data extraction. An island grammar precisely defines only a subset of a language syntax (islands), while the rest of the syntax (water) is defined imprecisely. Usually, water is defined as the negation of islands. Albeit simple, such a definition of water is naive and impedes composition of islands. When developing an island grammar, sooner or later a programmer has to create water tailored to each individual island. Such an approach is fragile, however, because water can change with any change of a grammar. It is time-consuming, because water is defined manually by a programmer and not automatically. Finally, an island surrounded by water cannot be reused because water has to be defined for every grammar individually. In this paper we propose a new technique of island parsing - bounded seas. Bounded seas are composable, robust, reusable and easy to use because island-specific water is created automatically. We integrated bounded seas into a parser combinator framework as a demonstration of their composability and reusability.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

SMARTnet: A Sensor for Monitoring the Geostationary Ring

As the number of space debris is increasing in the geostationary ring, it becomes mandatory for any satellite operator to avoid any collisions. Space debris in geosynchronous orbits may be observed with optical telescopes. Other than radar, that requires very large dishes and transmission powers for sensing high-altitude objects, optical observations do not depend on active illumination from ground and may be performed with notably smaller apertures. The detection size of an object depends on the aperture of the telescope, sky background and exposure time. With a telescope of 50 cm aperture, objects down to approximately 50 cm may be observed. This size is regarded as a threshold for the identification of hazardous objects and the prevention of potentially catastrophic collisions in geostationary orbits. In collaboration with the Astronomical Institute of the University of Bern (AIUB), the German Space Operations Center (GSOC) is building a small aperture telescope to demonstrate the feasibility of optical surveillance of the geostationary ring. The telescope will be located in the southern hemisphere and complement an existing telescope in the northern hemisphere already operated by AIUB. These two telescopes provide an optimum coverage of European GEO satellites and enable a continuous monitoring independent of seasonal limitations. The telescope will be operated completely automatically. The automated operations should be demonstrated covering the full range of activities including scheduling of observations, telescope and camera control as well as data processing.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

Percutaneous screw fixation of the iliosacral joint: optimal screw pathways are frequently not completely intraosseous

INTRODUCTION In iliosacral screw fixation, the dimensions of solely intraosseous (secure) pathways, perpendicular to the ilio-sacral articulation (optimal) with corresponding entry (EP) and aiming points (AP) on lateral fluoroscopic projections, and the factors (demographic, anatomic) influencing these have not yet been described. METHODS In 100 CTs of normal pelvises, the height and width of the secure and optimal pathways were measured on axial and coronal views bilaterally (total measurements: n=200). Corresponding EP and AP were defined as either the location of the screw head or tip at the crossing of lateral innominate bones' cortices (EP) and sacral midlines (AP) within the centre of the pathway, respectively. EP and AP were transferred to the sagittal pelvic view using a coordinate system with the zero-point in the centre of the posterior cortex of the S1 vertebral body (x-axis parallel to upper S1 endplate). Distances are expressed in relation to the anteroposterior distance of the S1 upper endplate (in %). The influence of demographic (age, gender, side) and/or anatomic (PIA=pelvic incidence angle; TCA=transversal curvature angle, PID-Index=pelvic incidence distance-index; USW=unilateral sacral width-index) parameters on pathway dimensions and positions of EP and AP were assessed (multivariate analysis). RESULTS The width, height or both factors of the pathways were at least 7mm or more in 32% and 53% or 20%, respectively. The EP was on average 14±24% behind the centre of the posterior S1 cortex and 41±14% below it. The AP was on average 53±7% in the front of the centre of the posterior S1 cortex and 11±7% above it. PIA influenced the width, TCA, PID-Index the height of the pathways. PIA, PID-Index, and USW-Index significantly influenced EP and AP. Age, gender, and TCA significantly influenced EP. CONCLUSION Secure and optimal placement of screws of at least 7mm in diameter will be unfeasible in the majority of patients. Thoughtful preoperative planning of screw placement on CT scans is advisable to identify secure pathways with an optimal direction. For this purpose, the presented methodology of determining and transferring EPs and APs of corresponding pathways to the sagittal pelvic view using a coordinate system may be useful.

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin-0 and spin- 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed. Read More: http://www.worldscientific.com/doi/10.1142/S0217732315500996

A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.

Operator and replicability bias in comparative taphonomic studies

The operator effect is a well-known methodological bias already quantified in some taphonomic studies. However, the replicability effect, i.e., the use of taphonomic attributes as a replicable scientific method, has not been taken into account to the present. Here, we quantified for the first time this replicability bias using different multivariate statistical techniques, testing if the operator effect is related to the replicability effect. We analyzed the results reported by 15 operators working on the same dataset. Each operator analyzed 30 biological remains (bivalve shells) from five different sites, considering the attributes fragmentation, edge rounding, corrasion, bioerosion and secondary color. The operator effect followed the same pattern reported in previous studies, characterized by a worse correspondence for those attributes having more than two levels of damage categories. However, the effect did not appear to have relation with the replicability effect, because nearly all operators found differences among sites. Despite the binary attribute bioerosion exhibited 83% of correspondence among operators it was the taphonomic attributes that showed the highest dispersion among operators (28%). Therefore, we conclude that binary attributes (despite showing a reduction of the operator effect) diminish replicability, resulting in different interpretations of concordant data. We found that a variance value of nearly 8% among operators, was enough to generate a different taphonomic interpretation, in a Q-mode cluster analysis. The results reported here showed that the statistical method employed influences the level of replicability and comparability of a study and that the availability of results may be a valid alternative to reduce bias.