A Comparison of Continuously Controlled and Controlled K-theory

We define an unreduced version of the e-controlled lower $K$-theoretic groups of Ranicki and Yamasaki, and Quinn. We show that the reduced versions of our groups coincide (in the inverse limit and its first derived, $\lim^1$) with those of Ranicki and Yamasaki. We also relate the controlled groups to the continuously controlled groups of Anderson and Munkholm, and to the Quinn homology groups of Quinn

Some neutron and gamma radiation characteristics of plutonium cermet fuel for isotopic power sources

Gamma and neutron measurements on various types of plutonium sources are presented in order to show the effects of O-17, O-18 F-19, Pu-236, age of the fuel, and size of the source on the gamma and neutron spectra. Analysis of the radiation measurements shows that fluorine is the main contributor to the neutron yields from present plutonium-molybdenum cermet fuel, while both fluorine and Pu-236 daughters contribute significantly to the gamma ray intensities

Gaussian pulse dynamics in gain media with Kerr nonlinearity

Using the Kantorovitch method in combination with a Gaussian ansatz, we derive the equations of motion for spatial, temporal and spatiotemporal optical propagation in a dispersive Kerr medium with a general transverse and spectral gain profile. By rewriting the variational equations as differential equations for the temporal and spatial Gaussian q parameters, optical ABCD matrices for the Kerr effect, a general transverse gain profile and nonparabolic spectral gain filtering are obtained. Further effects can easily be taken into account by adding the corresponding ABCD matrices. Applications include the temporal pulse dynamics in gain fibers and the beam propagation or spatiotemporal pulse evolution in bulk gain media. As an example, the steady-state spatiotemporal Gaussian pulse dynamics in a Kerr-lens mode-locked laser resonator is studied

Exotic order in simple models of bosonic systems

We show that simple Bose Hubbard models with unfrustrated hopping and short range two-body repulsive interactions can support stable fractionalized phases in two and higher dimensions, and in zero magnetic field. The simplicity of the constructed models advances the possibility of a controlled experimental realization and novel applications of such unconventional states.Comment: 4 pages, 4 figure

A Divergent Synthetic Route to the Vallesamidine and Schizozygine Alkaloids: Total Synthesis of (+)‐Vallesamidine and (+)‐14,15‐Dehydrostrempeliopine

The total synthesis of representative members of the schizozygine alkaloids, (+)‐vallesamidine and (+)‐14,15‐dehydrostrempeliopine, were completed from a late‐stage divergent intermediate. The synthesis took advantage of efficient nitro‐group reactions with the A/B/C ring skeleton constructed concisely on a gram scale through an asymmetric Michael addition, nitro‐Mannich/lactamisation, Tsuji–Trost allylation, and intramolecular C−N coupling reaction. Other key features of the synthesis are a novel [1,4] hydride transfer/Mannich‐type cyclisation to build ring E and a diastereoselective ring‐closing metathesis reaction to construct ring D. This approach gave access to a late‐stage C14,C15 alkene divergent intermediate that could be simply transformed into (+)‐vallesamidine, (+)‐14,15‐dehydrostrempeliopine, and potentially other schizozygine alkaloids and unnatural derivatives

A Divergent Synthetic Route to the Vallesamidine, Strempeliopine and Schizozygine Alkaloids: Total Synthesis of (+)-Vallesamidine and (+)-14,15-Dehydrostrempeliopine

The total synthesis of representative members of the schizozygine alkaloids, (+)‐vallesamidine and (+)‐14,15‐dehydrostrempeliopine, were completed from a late‐stage divergent intermediate. The synthesis took advantage of efficient nitro‐group reactions with the A/B/C ring skeleton constructed concisely on a gram scale through an asymmetric Michael addition, nitro‐Mannich/lactamisation, Tsuji–Trost allylation, and intramolecular C−N coupling reaction. Other key features of the synthesis are a novel [1,4] hydride transfer/Mannich‐type cyclisation to build ring E and a diastereoselective ring‐closing metathesis reaction to construct ring D. This approach gave access to a late‐stage C14,C15 alkene divergent intermediate that could be simply transformed into (+)‐vallesamidine, (+)‐14,15‐dehydrostrempeliopine, and potentially other schizozygine alkaloids and unnatural derivatives

Non-unique factorization of polynomials over residue class rings of the integers

We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring arbitrary non-zero polynomials into irreducibles to the problem of factoring monic polynomials into monic irreducibles. The multiplicative monoid of monic polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to irreducible polynomials in Z_p[x], and we show that each of these monoids has infinite elasticity. Moreover, for every positive integer m, there exists in each of these monoids a product of 2 irreducibles that can also be represented as a product of m irreducibles.Comment: 11 page

Three-Dimensional Spin-Orbit Coupling in a Trap

We investigate the properties of an atom under the influence of a synthetic three-dimensional spin-orbit coupling (Weyl coupling) in the presence of a harmonic trap. The conservation of total angular momentum provides a numerically efficient scheme for finding the spectrum and eigenfunctions of the system. We show that at large spin-orbit coupling the system undergoes dimensional reduction from three to one dimension at low energies, and the spectrum is approximately Landau level-like. At high energies, the spectrum is approximately given by the three-dimensional isotropic harmonic oscillator. We explore the properties of the ground state in both position and momentum space. We find the ground state has spin textures with oscillations set by the spin-orbit length scale

Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance

We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a quantum phase transition. This continuation takes local operators into local operators, while approximately preserving the ground state expectation values. We apply this continuation to the problem of gauge theories coupled to matter, and propose a new distinction, perimeter law versus "zero law" to identify confinement. We also apply the continuation to local bosonic models with emergent gauge theories. We show that local gauge invariance is topological and cannot be broken by any local perturbations in the bosonic models in either continuous or discrete gauge groups. We show that the ground state degeneracy in emergent discrete gauge theories is a robust property of the bosonic model, and we argue that the robustness of local gauge invariance in the continuous case protects the gapless gauge boson.Comment: 15 pages, 6 figure

Schema Independent Relational Learning

Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions