J. W. Clark

On the controllability of quantum‐mechanical systems

The systems‐theoretic concept of controllability is elaborated for quantum‐mechanical systems, sufficient conditions being sought under which the state vector ψ can be guided in time to a chosen point in the Hilbert space H of the system. The Schrodinger equation for a quantum object influenced by adjustable external fields provides a state‐evolution equation which is linear in ψ and linear in the external controls (thus a bilinear control system). For such systems the existence of a dense analytic domain Dω in the sense of Nelson, together with the assumption that the Lie algebra associated with the system dynamics gives rise to a tangent space of constant finite dimension, permits the adaptation of the geometric approach developed for finite‐dimensional bilinear and nonlinear control systems. Conditions are derived for global controllability on the intersection of Dω with a suitably defined finite‐dimensional submanifold of the unit sphere SH in H. Several soluble examples are presented to illuminate th...

Detecting network communities by propagating labels under constraints

We investigate the recently proposed label-propagation algorithm (LPA) for identifying network communities. We reformulate the LPA as an equivalent optimization problem, giving an objective function whose maxima correspond to community solutions. By considering properties of the objective function, we identify conceptual and practical drawbacks of the label-propagation approach, most importantly the disparity between increasing the value of the objective function and improving the quality of communities found. To address the drawbacks, we modify the objective function in the optimization problem, producing a variety of algorithms that propagate labels subject to constraints; of particular interest is a variant that maximizes the modularity measure of community quality. Performance properties and implementation details of the proposed algorithms are discussed. Bipartite as well as unipartite networks are considered.

Relation between regional myocardial uptake of rubidium-82 and perfusion: absolute reduction of cation uptake in ischemia.

Experiments were undertaken using rubidium-82 and position tomography to examine the relation between myocardial perfusion and cation uptake during acute ischemia. Rubidium-82 was repeatedly eluted from a strontium-82-rubidium-82 generator. In six dogs emission tomograms were used to measure the delivered arterial and myocardial concentrations at rest and after coronary stenosis, stress and ischemia. There was a poor overall relation between regional myocardial uptake and flow measured by microspheres and a large individual variability. Extraction of rubidium-82 was inversely related to flow. Significant regional reduction of cation uptake was detected in the tomograms when regional flow decreased by more than 35 percent. This reduction was significantly greater when ischemia was present. A small but significantly greater when ischemia was present. A small but significant decrease (33.0 +/- 9.1 percent, mean +/- standard deviation) in the myocardial uptake of rubidium-82 was detected only when flow was increased by more than 120 percent in relation to a control area after administration of dypiridamole. The technique using rubidum-82 and tomography was applied in five volunteers and five patients with angina pectoris and coronary artery disease. Myocardial tomograms recorded at rest and after exercise in the volunteers showed homogeneous uptake of cation in reproducible and repeatable scans. In contrast, the patients with coronary artery disease showed an absolute mean decrease of 36 +/- 14 percent in regional myocardial uptake of rubidium-82 after exercise. These abnormalities persisted in serial tomograms for more than 20 minutes after the symptoms and electrocardiographic signs of ischemia.

Femoral Neck Length and Hip Fracture Risk

To determine whether there are differences in femoral skeletal geometry in fracture‐prone subjects when size, positioning diagnosis, and age are controlled, we compared femoral measurements made from the uninvolved hip on 119 plane anteroposterior pelvis radiographs of women without fracture to those of the contralateral hip in a group of 43 female patients with hip fractures (neck, 23; intertrochanteric, 20). The hip was imaged in a standardized position of rotation and adduction. Race, age, and musculoskeletal diagnosis were known. Subjects were grouped by diagnosis of the opposite hip condition (rheumatoid arthritis, osteoarthritis, and normal) and compared. Measurements were also analyzed as ratios to head diameter (HD), neck diameter (ND), and pelvic width. Femoral neck length (NL) was measured from skeletal preparations and imaged in controlled positions of abduction and external rotation. No differences were found between the neck and intertrochanteric fracture groups. The differences between the fracture group and the controls were a thinner femoral cortex (measured at a point one head radius below the lesser trochanter) a larger femoral head, and a larger femoral ND in the fracture group (p < 0.025). The difference in cortical thickness was still significant when scaled by size, but the ratio of HD to ND was equivalent in fractures and controls. No difference in femoral NL could be demonstrated. The experimental measurements showed that apparent NL is significantly position sensitive and this may explain previously reported differences in fracture‐prone groups.

The relationship of the glenohumeral joint capsule to the rotator cuff

The glenohumeral joint capsules of 23 shoulders in which the rotator cuff was not torn were studied by gross dissection and histologic methods. The cuff tendons were resected, leaving the intact capsule attached to the bones. This dissection method provided a unique overview of the capsule in situ and allowed the areas of cuff tendon and muscle attachment to be mapped. The capsule was found to be a continuous cylinder between humerus and glenoid. On approximately one-third of the capsule (the portion adjacent to the humeral tuberosities), tight insertions of cuff tendons were noted. The superior segment between subscapularis and supraspinatus contained the coracohumeral ligament. This segment appeared to reinforce the cuff through a transversely oriented band similar to the glenohumeral ligaments.

Chaos in neural systems

Abstract The occurence of chaos in continuous-time neural network models is demonstrated through two examples, (i) a single neuron with an unusual kind of periodic input and (ii) a randomly connected network of 26 neurons with 7 incoming synapses per neuron, half the neurons being subject to a steady external stimulus. The former case is susceptible to exhaustive analysis, while the latter, discovered by computer simulation, is more attuned to neurobiological reality.

Contributions of Computed Tomography in the Staging and Management of Malignant Lymphoma

Pretreatment staging is considered essential in the management of patients with malignant lymphoma, particularly nodular sclerosing Hodgkin disease. The results of CT examination of 33 patients with malignant lymphoma are correlated with the results of lymphangiography, nuclide images of the liver and spleen, gallium citrate57 images of lymphoid tissue, and nuclide bone images. CT is least effective in the early clinical stages of malignant lymphoma because normal or minimally enlarged nodes are difficult to detect; CT is probably reliable enough to replace lymphangiography of gallium57 imaging in patients with advanced disease.

Pairing gaps in nucleonic superfluids

Abstract Singlet S-wave nucleonic superfluids are studied within a microscopic many-body theory that incorporates explicit spatial correlations due to strong short-range repulsive forces as well as the momentum-space pairing correlations of BCS theory. The theory is formulated within the method of correlated basis functions (CBF). Within this scheme, there results a nonlinear problem for the superfluid energy gap that is identical in form to the gap problem of conventional BCS theory. However, the input single-particle energies and pairing matrix elements are dressed by the short-range spatial correlations and accordingly incorporate an important class of medium corrections. The effective pairing force of the theory is finite even if the bare two-nucleon potential contains an infinitely hard core; both the pairing matrix elements and single-particle energies are to be constructed from normal-state CBF matrix elements and may be evaluated by cluster-expansion techniques. The theory is explicated and applied at a variational level that is equivalent to the leading order of a CBF superstate perturbation theory. New results are presented for the 1 s 0 pairing gap Δ k F in pure neutron matter at densities relevant to the inner crust of a neutron star, based on a simplified version of the Reid soft-core interaction and spin-dependent spatial correlations optimized in the correlated normal state. Careful consideration is given to the treatment of the gap equation at large intermediate-state momenta, correcting quantitative defects of earlier calculations. The variational gap function evaluated at the Fermi surface, Δ F , which serves as a critical input to models of the cooling and internal dynamics of neutron stars, is found to be larger than predicted in earlier work. Estimates of the suppression of the gap due to polarization processes (and other particle-particle and hole-hole irreducible medium effects of higher order within CBF superstate perturbation theory) yield values for Δ k F that are generally compatible with results from the semi-empirical polarization-potential approach, except at higher densities where the gap is closing. Updated solutions of the gap problem at the variational-CBF level are also given for 1 S 0 proton pairing in the quantum fluid interior of a neutron star and for 1 S 0 like-nucleon pairing in symmetrical nuclear matter at densities typical of the nuclear surface.

Solution of the gap equation in neutron matter

Abstract The problem of solving the gap equation for S-wave pairing in pure neutron matter is considered for the case that the pairing matrix elements V ( p , p ′) are calculated directly from a realistic bare neutron-neutron potential containing a strong short-range repulsion. The original gap equation is replaced identically by a coupled set of equations: a non-singular quasilinear integral equation for the dimensionless gap function χ ( p ) defined by Δ ( p ) = Δ F χ ( p ) and a non-linear algebraic equation for the gap magnitude Δ F = Δ ( p F ) at the Fermi surface. This reformulation admits a robust and rapidly convergent iteration procedure for the determination of the gap function. The treatment may be extended to singlet or triplet pairing in non-zero angular momentum states. S-wave pairing is investigated numerically for the Reid-soft-core interaction. Although the pairing matrix elements of this potential are everywhere positive, non-trivial solutions of the gap equation are obtained on the range 0 p F p c = 1.7496… fm −1 of Fermi momenta, with the gap parameter Δ F reaching a maximum of some 3 MeV near p F = 0.85 fm −1 . Numerical results are also provided for the highly realistic Argonne υ 14 and υ 18 interactions. Within the context of the new computational scheme, a condition for closure of the gap is derived in terms of the first zero p 0 of the gap function Δ ( p ). It is shown that Δ F vanishes exponentially not only in the low-density limit p F → 0, but also as the Fermi momentum rises and approaches the upper critical value p c specified by p F = p 0 ( p F ), beyond which there exists no non-trivial solution of the gap equation. The numerical results for the function Δ ( p ) in neutron matter display a remarkable universality of structure, visible especially in the stability of p 0 under variation of density. Upon renormalizing the gap equation in terms of the vacuum S-wave scattering amplitude, this behavior is seen to be a manifestation of the resonant nature of the neutron-neutron interaction at low energy, which leads to a scattering amplitude of nearly separable form.

Invertibility of quantum-mechanical control systems

This is the first of two papers concerned with the formulation of a continuous-time quantum-mechanical filter. Efforts focus on a quantum system with Hamiltonian of the formH0+u(t)H1, whereH0 is the Hamiltonian of the undisturbed system,H1 is a system observable which couples to an external classical field, andu(t) represents the time-varying signal impressed by this field. An important problem is to determine when and how the signalu(t) can be extracted from the time-development of the measured value of a suitable system observableC (invertibility problem). There exist certain quasiclassical observables such that the expected value and the measured value can be made to coincide. These are called quantum nondemolition observables. The invertibility problem is posed and solved for such observables. Since the physical quantum-mechanical system must be modelled as aninfinite-dimensional bilinear system, the domain issue for the operatorsH0,H1, andC becomes nontrivial. This technical matter is dealt with by invoking the concept of an analytic domain. An additional complication is that the output observableC is in general time-dependent.