Primary decomposition and the fractal nature of knot concordance

For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S^3, such a sequence of polynomials arises naturally as the orders of certain submodules of the sequence of higher-order Alexander modules of K. These group series yield new filtrations of the knot concordance group that refine the (n)-solvable filtration of Cochran-Orr-Teichner. We show that the quotients of successive terms of these refined filtrations have infinite rank. These results also suggest higher-order analogues of the p(t)-primary decomposition of the algebraic concordance group. We use these techniques to give evidence that the set of smooth concordance classes of knots is a fractal set. We also show that no Cochran-Orr-Teichner knot is concordant to any Cochran-Harvey-Leidy knot.Comment: 60 pages, added 4 pages to introduction, minor corrections otherwise; Math. Annalen 201

Nature of the quantum phase transitions in the two-dimensional hardcore boson model

We use two Quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near ($V_1$) and next near ($V_2$) neighbor repulsion. At half filling we find three phases: Superfluid (SF), checkerboard solid and striped solid depending on the relative values of $V_1$, $V_2$ and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases co-exist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: Co-existence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the $V_2$ interaction.Comment: 10 pages, 14 eps figures, include

Finite Temperature Properties of Quantum Antiferromagnets in a Uniform Magnetic Field in One and Two Dimensions

Consider a $d$-dimensional antiferromagnet with a quantum disordered ground state and a gap to bosonic excitations with non-zero spin. In a finite external magnetic field, this antiferromagnet will undergo a phase transition to a ground state with non-zero magnetization, describable as the condensation of a dilute gas of bosons. The finite temperature properties of the Bose gas in the vicinity of this transition are argued to obey a hypothesis of ZERO SCALE-FACTOR UNIVERSALITY for $d < 2$, with logarithmic violations in $d=2$. Scaling properties of various experimental observables are computed in an expansion in $\epsilon=2-d$, and exactly in $d=1$.Comment: 27 pages, REVTEX 3.0, 8 Postscript figures appended, YCTP-xyz

Machine learning for prediction of sustained opioid prescription after anterior cervical discectomy and fusion

Scientific Assessment and Innovation in Neurosurgical Treatment Strategie

A proposed set of metrics for standardized outcome reporting in the management of low back pain

Background and purpose - Outcome measurement has been shown to improve performance in several fields of healthcare. This understanding has driven a growing interest in value-based healthcare, where value is defined as outcomes achieved per money spent. While low back pain (LBP) constitutes an enormous burden of disease, no universal set of metrics has yet been accepted to measure and compare outcomes. Here, we aim to define such a set. Patients and methods - An international group of 22 specialists in several disciplines of spine care was assembled to review literature and select LBP outcome metrics through a 6-round modified Delphi process. The scope of the outcome set was degenerative lumbar conditions. Results - Patient-reported metrics include numerical pain scales, lumbar-related function using the Oswestry disability index, health-related quality of life using the EQ-5D-3L questionnaire, and questions assessing work status and analgesic use. Specific common and serious complications are included. Recommended follow-up intervals include 6, 12, and 24 months after initiating treatment, with optional follow-up at 3 months and 5 years. Metrics for risk stratification are selected based on preexisting tools. Interpretation - The outcome measures recommended here are structured around specific etiologies of LBP, span a patient's entire cycle of care, and allow for risk adjustment. Thus, when implemented, this set can be expected to facilitate meaningful comparisons and ultimately provide a continuous feedback loop, enabling ongoing improvements in quality of care. Much work lies ahead in implementation, revision, and validation of this set, but it is an essential first step toward establishing a community of LBP providers focused on maximizing the value of the care we deliver