Edoardo Bassini is considered the father of modern surgery. His early
results revealed a 2.7% recurrence rate. Earl Shouldice, his true successor,
has improved the results to less than 1%. These results were produced by
several well-known surgeons from 1970-2000 and well published. The need for
mesh was meant for a small segment of the surgical patient population. What has
happened? Generally, recurrence rates with mesh have not come down; instead,
pain has become the bane of hernia repair as we begin the 21st century. A pain
which makes the patient wish that he had a recurrence instead!

Abstract:
Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-1/2 BECs due to an Sz1 Sz2 interaction. The states that are generated show a remarkably rich structure showing fractal characteristics. In the limit of large particle number N, the entanglement shows a strong dependence upon whether the entangling gate times are a rational or irrational multiple of pi/4. We discuss the robustness of various states under decoherence and show that despite the large number of particles in a typical BEC, entanglement on a macroscopic scale should be observable as long as the gate times are less than hbar/J sqrt[N], where J is the effective BEC-BEC coupling energy. Such states are anticipated to be useful for various quantum information applications such as quantum teleportation and quantum algorithms.

Abstract:
We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our original problem is reduced to a sequence of submodular maximization problems. We characterize a class of submodular functions, which when maximized in the subproblems, lead the algorithm to converge to a global maximizer of f-g. Two "natural" members of this class are analyzed; the first yields polynomially-solvable subproblems, the second, which requires less branching, yields NP-hard subproblems but is amenable to a polynomial-time approximation algorithm. These results are extended to problems where the solution is constrained to be a member of a subset system. Structural properties of the maximizer of f-g are also proved.

Abstract:
Chronic fatiguing illness remains a poorly understood syndrome of unknown pathogenesis. We attempted to identify biomarkers for chronic fatiguing illness using microarrays to query the transcriptome in peripheral blood leukocytes.

Abstract:
We analyse models of inflation in which isocurvature perturbations present during inflation are converted into the primordial curvature perturbation during instant preheating. This can be due to an asymmetry between the fields present either during inflation or during preheating. We consider all the constraints that the model must satisfy in order to be theoretically valid and to satisfy observations. We show that the constraints are very tight in all of the models proposed and special initial conditions are required for the models to work. In the case where the symmetry is strongly broken during inflation the non-Gaussianity parameter f_NL is generally large and negative.

Abstract:
As a species, we are on the cusp of being able to alter that which makes us uniquely human, our genome. Two new genetic technologies, embryo selection and germline engineering, are either in use today or may be developed in the future. Embryo selection acts to alter the human gene pool, reducing genetic diversity, while germline engineering will have the ability to alter directly the genomes of engineered individuals. Our genome has come to be what it is through an evolutionary process extending over millions of years, a process that has involved exceedingly complex and unpredictable interactions between ourselves or our ancestors and myriad other life forms within Earth's biosphere. In this paper, the ecological imperativ e, which states that we must not alter the human genome or the collective human genetic inheritance, will be introduced. It will be argued based on ecological principles that embryo selection and germline engineering are unethical and unwise because they will diminish our survivability as a species, will disrupt our relationship with the natural world, and will destroy the very basis of that which makes us human.

Abstract:
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a particular state is found to have a linear dependence with the total number of lattice sites. The number of qubit operations required for performing the time evolution corresponding to the Hamiltonian is found to be between a linear to quadratic function of the number of lattice sites, depending on the arrangement of qubits in the quantum computer. We remark that our results may also be easily generalized to higher SU(N) gauge theories.

Abstract:
We introduce a quantum teleportation scheme that can transfer a macroscopic spin coherent state between two locations. In the scheme a large number of copies of a qubit, such as realized in a coherent two-component Bose-Einstein condensate, is teleported onto a distant macroscopic spin coherent state using only elementary operations and measurements. We analyze the error of the protocol with the number of particles N in the spin coherent state under decoherence and find that it scales favorably with N.

Abstract:
We consider maximizing a continuous convex function over the assignment polytope. Such problems arise in Graph Matching (the optimization version of Graph Isomorphism) and Quadratic Assignment problems. In the typical case of maximizing a convex function over a polytope the problem can be solved by using a simplicial algorithm such as Tuy's method or the Falk-Hoffman method, but these algorithms require that the underlying polytope be non-degenerate, which is not the case for the assignment polytope. In this note we show how a simple perturbation scheme can be used to create a "surrogate problem" that is both non-degenerate and combinatorially equivalent to the original problem. We further provide an explicit construction of a surrogate problem that is non-degenerate and combinatorially equivalent to the Graph Matching problem, when the latter is posed as a convex maximization problem. By constructing a surrogate problem that is known a priori to be non-degenerate and combinatorially equivalent to Graph Matching we resolve an "open issue" of solving Graph Matching via convex maximization first raised by Maciel.

Abstract:
We study the non-Gaussianity generated during multiple-field inflation. We provide an exact expression for the bispectrum parameter f_NL which is valid beyond the slow-roll regime, valid for certain classes of inflationary models. We then study a new, exact multi-field inflationary model considering a case where the bispectrum grows to observable values at the end of inflation. We show that in this case the trispectrum is also large and may even provide the dominant signal of non-Gaussianity.