On the structure of covariant phase observables

We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant trace-preserving operations. Covariant generalized operator measures are defined by structure matrices which form a W*-algebra with phase matrices as its subset. The properties of the Radon-Nikodym derivatives of phase probability measures are studied.Comment: 11 page

Comparison of energy and greenhouse gas balances of biogas with other transport biofuel options based on domestic agricultural biomass in Finland

Biofuels have been promoted as a way to reduce greenhouse gas (GHG) emissions, but it is questionable whether they indeed do so. The study compared energy and GHG balances of transport biofuels produced in Finnish conditions. Energy and GHG balances were calculated from a life cycle perspective for biogas when timothy-clover and reed canary grass silages and green manure of an organic farm were used as a raw material. The results were compared with published data on barley-based ethanol, rape methyl ester (biodiesel) and biowaste-based biogas. The energy input for biogas was 22–37% of the output depending on the raw material. The GHG emissions from field-based biogas were 21–36% of emissions from fossil-based fuels. The largest energy input was used in the processing of the biofuels while most of the greenhouse gases were emitted during farming. The GHG emissions of the field-based biogas were emitted mainly from fuels of farming machinery, nitrous oxide (N2O) emissions of the soil and the production of ensiling additives. The energy efficiency was most sensitive to the methane yield, and GHG emissions to the N2O emissions. Biogas had clearly lower energy input and GHG emissions per unit energy output than domestic barley-based ethanol and biodiesel

Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane

We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane (also known as noncommutative flat space). We also include a detailed comparison of our cut-off regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R^4 still holds if one replaces all pointwise products by the noncommutative Moyal product.Comment: 37 pages, v2 contains an improved treatment of the theta function in Appendix A.

Let's Ask Students About Their Programs, Automatically

Students sometimes produce code that works but that its author does not comprehend. For example, a student may apply a poorly-understood code template, stumble upon a working solution through trial and error, or plagiarize. Similarly, passing an automated functional assessment does not guarantee that the student understands their code. One way to tackle these issues is to probe students' comprehension by asking them questions about their own programs. We propose an approach to automatically generate questions about student-written program code. We moreover propose a use case for such questions in the context of automatic assessment systems: after a student's program passes unit tests, the system poses questions to the student about the code. We suggest that these questions can enhance assessment systems, deepen student learning by acting as self-explanation prompts, and provide a window into students' program comprehension. This discussion paper sets an agenda for future technical development and empirical research on the topic

Conserved currents of massless fields of spin s>0

A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s>0 in four dimensional flat spacetime. These results generalize the recent classification in the spin s=1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s>0 analogs of the well-known electromagnetic stress-energy tensor and Lipkin's zilch tensor, as well as a spin s>0 analog of a novel chiral tensor found in the spin s=1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e., a phase rotation) on the spin s field, in contrast to the even parity of the stress-energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s>0 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated to the stress-energy, zilch, and chiral tensors, and higher derivative extensions of these currents in which the spin s field is replaced by its repeated conformally-weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct, unified characterization in terms of Killing spinors. The cases s=2, s=1/2 and s=3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e., linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.Comment: 26 pages; final version with minor changes, accepted in Proc. Roy. Soc. A (London

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

Landau-Zener Problem for Trilinear Hamiltonians

We consider a nonlinear version of the Landau-Zener problem, focusing on photoassociation of a Bose-Einstein condensate as a specific example. Contrary to the exponential rate dependence obtained for the linear problem, a series expansion technique indicates that, when the resonance is crossed slowly, the probability for failure of adiabaticity is directly proportional to the rate at which the resonance is crossed.Comment: 4.5 pages, 1 figure, transferred to PRA; v2 adds discussion, clarification, and explicit numbers for Na and 87R

Stability of topological solitons in modified two-component Ginzburg-Landau model

We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D66, 041701(R) (2002)] that certain modification of the ordinary model results in system which supports stable topological solitons (Hopfions) for some values of the parameters of the model. We expand the search for stability into previously uninvestigated region of the parameter space, charting an approximate shape for the stable/unstable boundary and find that, within the accuracy of the numerical methods used, the energy of the stable knot at the boundary is independent of the parameters.Comment: v4: Fixed some citations and acknowledgements; 6 pages, 4 figures; to be published in Phys. Rev.

Testing Equid Body Mass Estimate Equations on Modern Zebras-With Implications to Understanding the Relationship of Body Size, Diet, and Habitats of Equus in the Pleistocene of Europe

The monodactyl horses of the genus Equus originated in North America during the Pliocene, and from the beginning of the Pleistocene, they have been an essential part of the large ungulate communities of Europe, North America and Africa. Understanding how body size of Equus species evolved and varied in relation to changes in environments and diet thus forms an important part of understanding the dynamics of ungulate body size variation in relation to Pleistocene paleoenvironmental changes. Here we test previously published body mass estimation equations for the family Equidae by investigating how accurately different skeletal and dental measurements estimate the mean body mass (and body mass range) reported for extant Grevy's zebra (Equus grevyi) and Burchell's zebra (Equus quagga). Based on these tests and information on how frequently skeletal elements occur in the fossil record, we construct a hierarchy of best practices for the selection of body mass estimation equations in Equus. As a case study, we explore body size variation in Pleistocene European Equus paleopopulations in relation to diet and vegetation structure in their paleoenvironments. We show a relationship between diet and body size in Equus: very large-sized species tend to have more browse-dominated diets than small and medium-sized species, and paleovegetation proxies indicate on average more open and grass-rich paleoenvironments for small-sized, grazing species of Equus. When more than one species of Equus co-occur sympatrically, the larger species tend to be less abundant and have more browse-dominated diets than the smaller species. We suggest that body size variation in Pleistocene Equus was driven by a combined effect of resource quality and availability, partitioning of habitats and resources between species, and the effect of environmental openness and group size on the body size of individuals.Peer reviewe

Dual Role of a Viral Polymerase in Viral Genome Replication and Particle Self-Assembly

Double-stranded RNA (dsRNA) viruses package several RNA-dependent RNA polymerases (RdRp) together with their dsRNA genome into an icosahedral protein capsid known as the polymerase complex. This structure is highly conserved among dsRNA viruses but is not found in any other virus group. RdRp subunits typically interact directly with the main capsid proteins, close to the 5-fold symmetric axes, and perform viral genome replication and transcription within the icosahedral protein shell. In this study, we utilized Pseudomonas phage Phi 6, a well-established virus self-assembly model, to probe the potential roles of the RdRp in dsRNA virus assembly. We demonstrated that Phi 6 RdRp accelerates the polymerase complex self-assembly process and contributes to its conformational stability and integrity. We highlight the role of specific amino acid residues on the surface of the RdRp in its incorporation during the self-assembly reaction. Substitutions of these residues reduce RdRp incorporation into the polymerase complex during the self-assembly reaction. Furthermore, we determined that the overall transcription efficiency of the Phi 6 polymerase complex increased when the number of RdRp subunits exceeded the number of genome segments. These results suggest a mechanism for RdRp recruitment in the polymerase complex and highlight its novel role in virion assembly, in addition to the canonical RNA transcription and replication functions. IMPORTANCE Double-stranded RNA viruses infect a wide spectrum of hosts, including animals, plants, fungi, and bacteria. Yet genome replication mechanisms of these viruses are conserved. During the infection cycle, a proteinaceous capsid, the polymerase complex, is formed. An essential component of this capsid is the viral RNA polymerase that replicates and transcribes the enclosed viral genome. The polymerase complex structure is well characterized for many double-stranded RNA viruses. However, much less is known about the hierarchical molecular interactions that take place in building up such complexes. Using the bacteriophage Phi 6 self-assembly system, we obtained novel insights into the processes that mediate polymerase subunit incorporation into the polymerase complex for generation of functional structures. The results presented pave the way for the exploitation and engineering of viral self-assembly processes for biomedical and synthetic biology applications. An understanding of viral assembly processes at the molecular level may also facilitate the development of antivirals that target viral capsid assembly.Peer reviewe