The repulsion between localization centers in the Anderson model

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together

Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

Additive Manufacturing of Biomechanically Tailored Meshes for Compliant Wearable and Implantable Devices

Additive manufacturing (AM) of medical devices such as orthopedic implants and hearing aids is highly attractive because of AM’s potential to match the complex form and mechanics of individual human bodies. Externally worn and implantable tissue-support devices, such as ankle or knee braces, and hernia repair mesh, offer a new opportunity for AM to mimic tissue-like mechanics and improve both patient outcomes and comfort. Here, it is demonstrated how explicit programming of the toolpath in an extrusion AM process can enable new, flexible mesh materials having digitally tailored mechanical properties and geometry. Meshes are fabricated by extrusion of thermoplastics, optionally with continuous fiber reinforcement, using a continuous toolpath that tailors the elasticity of unit cells of the mesh via incorporation of slack and modulation of filament-filament bonding. It is shown how the tensile mesh mechanics can be engineered to match the nonlinear response of muscle, incorporate printed mesh into an ankle brace with directionally specific inversion stiffness, and present further concepts for tailoring their 3D geometry for medical applications.Financial support was provided by a National Science Foundation Science, Engineering, and Education for Sustainability postdoctoral fellowship (Award number: 1415129) to S.W.P.; a Samsung Scholarship to J.L; the School of Engineering and Sciences from Tecnologico de Monterrey to R.R.; the Manufacturing Demonstration Facility, Oak Ridge National Laboratory, the Department of Energy, UT-Batelle, Oak Ridge Associated Universities, the DOE’s Advanced Manufacturing Office to G.D.; the German Academic Exchange Service (DAAD) to C.M.; and the Eric P. and Evelyn E. Newman Fund and NSF-CRCNS-1724135 to N.H

Quantum site percolation on amenable graphs

We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.Comment: 10 pages, LaTeX 2e, to appear in "Applied Mathematics and Scientific Computing", Brijuni, June 23-27, 2003. by Kluwer publisher

New characterizations of the region of complete localization for random Schr\"odinger operators

We study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity

Remote monitoring and follow-up of cardiovascular implantable electronic devices in the Netherlands: An expert consensus report of the Netherlands Society of Cardiology

Remote monitoring of cardiac implanted electronic devices (CIED: pacemaker, cardiac resynchronisation therapy device and implantable cardioverter defibrillator) has been developed for technical control and follow-up using transtelephonic data transmission. In addition, automatic or patient-triggered alerts are sent to the cardiologist or allied professional who can respond if necessary with various interventions. The advantage of remote monitoring appears obvious in impending CIED failures and suspected symptoms but is less likely in routine follow-up of CIED. For this follow-up the indications, quality of care, cost-effectiveneness and patient satisfaction have to be determined before remote CIED monitoring can be applied in daily practice. Nevertheless remote CIED monitoring is expanding rapidly in the Netherlands without professional agreements about methodology, responsibilities of all the parties involved and that of the device patient, and reimbursement. The purpose of this consensus document on remote CIED monitoring and follow-up is to lay the base for a nationwide, uniform implementation in the Netherlands. This report describes the technical communication, current indications, benefits and limitations of remote CIED monitoring and follow-up, the role of the patient and device manufacturer, and costs and reimbursement. The view of cardiology experts and of other disciplines in conjunction with literature was incorporated in a preliminary series of recommendations. In addition, an overview of the questions related to remote CIED monitoring that need to be answered is given. This consensus document can be used for future guidelines for the Dutch profession

Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.Comment: 94 pages, v2: a revision of Sec. 5; v3: an error in Sec. 7 is corrected, major revisions of Sec. 7 and Appendix E, Sec. 7 is enlarged to Secs. 7-12, minor corrections; v4: major revisions, accepted for publication in Journal of Statistical Physics; v5: minor corrections, accepted versio

Telecardiology and Remote Monitoring of Implanted Electrical Devices: The Potential for Fresh Clinical Care Perspectives

Telecardiology may help confront the growing burden of monitoring the reliability of implantable defibrillators/pacemakers. Herein, we suggest that the evolving capabilities of implanted devices to monitor patients’ status (heart rhythm, fluid overload, right ventricular pressure, oximetry, etc.) may imply a shift from strictly device-centered follow-up to perspectives centered on the patient (and patient-device interactions). Such approaches could provide improvements in health care delivery and clinical outcomes, especially in the field of heart failure. Major professional, policy, and ethical issues will have to be overcome to enable real-world implementation. This challenge may be relevant for the evolution of our health care systems