Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Primrose syndrome: Characterization of the phenotype in 42 patients

Primrose syndrome (PS; MIM# 259050) is characterized by intellectual disability (ID), macrocephaly, unusual facial features (frontal bossing, deeply set eyes, down-slanting palpebral fissures), calcified external ears, sparse body hair and distal muscle wasting. The syndrome is caused by de novo heterozygous missense variants in ZBTB20. Most of the 29 published patients are adults as characteristics appear more recognizable with age. We present 13 hitherto unpublished individuals and summarize the clinical and molecular findings in all 42 patients. Several signs and symptoms of PS develop during childhood, but the cardinal features, such as calcification of the external ears, cystic bone lesions, muscle wasting, and contractures typically develop between 10 and 16 years of age. Biochemically, anemia and increased alpha-fetoprotein levels are often present. Two adult males with PS developed a testicular tumor. Although PS should be regarded as a progressive entity, there are no indications that cognition becomes more impaired with age. No obvious genotype-phenotype correlation is present. A subgroup of patients with ZBTB20 variants may be associated with mild, nonspecific ID. Metabolic investigations suggest a disturbed mitochondrial fatty acid oxidation. We suggest a regular surveillance in all adult males with PS until it is clear whether or not there is a truly elevated risk of testicular cancer.This article is freely available via Open Access. Click on the Publisher URL to access it via the publisher's site.published version, accepted version (12 month embargo) submitted versio

Cavity-enhanced direct frequency comb spectroscopy

Cavity-enhanced direct frequency comb spectroscopy combines broad spectral bandwidth, high spectral resolution, precise frequency calibration, and ultrahigh detection sensitivity, all in one experimental platform based on an optical frequency comb interacting with a high-finesse optical cavity. Precise control of the optical frequency comb allows highly efficient, coherent coupling of individual comb components with corresponding resonant modes of the high-finesse cavity. The long cavity lifetime dramatically enhances the effective interaction between the light field and intracavity matter, increasing the sensitivity for measurement of optical losses by a factor that is on the order of the cavity finesse. The use of low-dispersion mirrors permits almost the entire spectral bandwidth of the frequency comb to be employed for detection, covering a range of ~10% of the actual optical frequency. The light transmitted from the cavity is spectrally resolved to provide a multitude of detection channels with spectral resolutions ranging from a several gigahertz to hundreds of kilohertz. In this review we will discuss the principle of cavity-enhanced direct frequency comb spectroscopy and the various implementations of such systems. In particular, we discuss several types of UV, optical, and IR frequency comb sources and optical cavity designs that can be used for specific spectroscopic applications. We present several cavity-comb coupling methods to take advantage of the broad spectral bandwidth and narrow spectral components of a frequency comb. Finally, we present a series of experimental measurements on trace gas detections, human breath analysis, and characterization of cold molecular beams.Comment: 36 pages, 27 figure

Governing urban accessibility: moving beyond transport and mobility

Access to people, goods, ideas and services is the basis of economic development in cities. The better this access, the greater the economic benefits through economies of scale, agglomeration effects and networking advantages. The way in which cities facilitate accessibility also impacts directly on other key aspects of human development, social inclusion and well-being. Accessibility is created through a complex interplay of urban form and transport systems. Thus, governing urban accessibility requires moving beyond conventional urban transport considerations linked to mobility and movement. Such a re-framing implies a far greater recognition of urban form characteristics like land use, distribution of densities and urban design, in addition to transport characteristics like infrastructures, service levels and travel speeds. A new interface between these characteristics has emerged as a result of shared mobility systems, putting additional pressure on city governments to act as system integrators. Based on a literature review, empirical insights from a global survey and the case-study cities of London, NYC and Berlin, this paper explores the institutional capacities of shifting from governing urban transport to urban accessibility. The evidence shows that there are entrenched misalignments which may impact negatively on the capacity to pair planning and policies essential for delivering better accessibility. Furthermore, it is clear that “hierarchies” and “networks” are not mutually exclusive when it comes to integrated governance of accessibility. The findings also suggest that cities may be better equipped to integrate shared mobility and consider mobility as a service than to pursue more wide-ranging metropolitan accessibility policies

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo

Calculated angular distribution of fragment ions from polyatomic-ion collisions

The angular distribution of ion fragments from dissociation collisions of ions with molecular ions is discussed, and results are given for the fragments of nitromethane molecular ion. (WHK