Dimension Distortion by Right Coset Projections in the Heisenberg Group

We study the family of vertical projections whose fibers are right cosets of horizontal planes in the Heisenberg group, $\mathbb{H}^n$. We prove lower bounds for Hausdorff dimension distortion of sets under these mappings, with respect to the Euclidean metric and also the natural quotient metric which we show behaves like the Euclidean metric in this context. Our bounds are sharp in a large part of the dimension range, and we give conjectural sharp lower bounds for the remaining range. Our approach also lets us improve the known almost sure lower bound for the standard family of vertical projections in $\mathbb{H}^n$ for $n \geq 2$

Ground state fidelity from tensor network representations

For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well-defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.Comment: 4 pages, 2 figures. Published version in Physical Review Letter

Growth and growth hormone secretion in children with cancer treated with chemotherapy

To evaluate the effect of chemotherapy on growth and growth hormone (GH) secretion. METHODS: We analyzed growth and GH secretion in 60 children in complete remission after treatment by chemotherapy and surgery for malignant solid tumors. None of them received cranial radiotherapy. Growth hormone reserve was assessed by at least two stimulation tests (clonidine, L-dopa, growth hormone-releasing hormone). In 12 children the reserve of GH pretreatment was also evaluated. RESULTS: Growth hormone deficiency (GHD) was observed in 27 of 60 patients (45%). At diagnosis, mean standing height was +0.23 +/- 0.11 standard deviation score (SDS) in the GHD group and +0.16 +/- 0.10 SDS in the non-GHD group. After chemotherapy, mean standing height in the GHD group was -0.28 +/- 0.15 SDS and -0.14 +/- 0.11 in the non-GHD group (p < 0.05), and the growth rate was +0.13 +/- 0.07 SDS in the GHD group and +0.22 +/- 0.18 SDS in the non-GHD group. For a mean follow-up of 30 months, the mean standing height was -0.46 +/- 0.29 SDS in the GHD group and -0.24 +/- 0.16 SDS for the non-GHD group (p < 0.05), and the growth rate was -0.27 +/- 0.19 SDS in the GHD group and -0.16 +/- 0.12 SDS in the non-GHD group (p < 0.05). The GH response to clonidine was significantly less than that found with the other stimuli. There was correlation between the dose intensity of some drugs and the subsequent GH response to stimulation tests. The GHD group was found to have received significantly higher doses of actinomycin D than the non-GHD group (p < 0.05). Growth impairment and GHD were not found to be correlated with duration of treatment and follow-up, tumor type, sex, or age. CONCLUSIONS: Chemotherapy as the sole form of treatment in children with cancer interferes with growth. The observed impairment of growth depends, at least in part, on a GHD related to chemotherapy. The growth rate in conjunction with the GH response to clonidine provides a sensitive measure of GHD associated with chemotherapy

Overview of methods used to evaluate the adequacy of nutrient intakes for individuals and populations

The objective of the present paper is to review the methods of measuring micronutrient intake adequacy for individuals and for populations in order to ascertain best practice. A systematic review was conducted to locate studies on the methodological aspects of measuring nutrient adequacy. The results showed that for individuals, qualitative methods (to find probability of adequacy) and quantitative methods (to find confidence of adequacy) have been proposed for micronutrients where there is enough data to set an average nutrient requirement (ANR). If micronutrients do not have ANR, an adequate intake (AI) is often defined and can be used to assess adequacy, provided the distribution of daily intake over a number of days is known. The probability of an individual's intake being excessive can also be compared with the upper level of safe intake and the confidence of this estimate determined in a similar way. At the population level, adequacy can be judged from the ANR using the probability approach or its short cut – the estimated average requirement cut-point method. If the micronutrient does not have an ANR, adequacy cannot be determined from the average intake and must be expressed differently. The upper level of safe intake can be used for populations in a similar way to that of individuals. All of the methodological studies reviewed were from the American continent and all used the methodology described in the Institute of Medicine publications. The present methodology should now be adapted for use in Europe

Exact symmetry breaking ground states for quantum spin chains

We introduce a family of spin-1/2 quantum chains, and show that their exact ground states break the rotational and translational symmetries of the original Hamiltonian. We also show how one can use projection to construct a spin-3/2 quantum chain with nearest neighbor interaction, whose exact ground states break the rotational symmetry of the Hamiltonian. Correlation functions of both models are determined in closed form. Although we confine ourselves to examples, the method can easily be adapted to encompass more general models.Comment: 4 pages, RevTex. 4 figures, minor changes, new reference

Chronological control and centennial-scale climatic subdivisions of the Last Glacial Termination in the western Mediterranean region

The Last Glacial Termination is marked by changing environmental conditions affected by abrupt and rapid climate oscillations, such as Heinrich Stadial 1 (HS1), which is characterized by extremely low sea surface temperatures (SST) and significant changes in northern hemisphere terrestrial landscape (e.g., vegetation) and human dispersion. Previous studies show that overall cold/dry conditions occurred during HS1, but the lack of high-resolution records precludes whether climate was stable or instead characterized by instability. A high-resolution paleoclimatic record from the Padul wetland (southern Iberian Peninsula), supported by a high-resolution chronology and contrasted with other records from southern Europe and the Mediterranean region, shows 1) that the age boundaries of HS1 in this area occurred at similar to 18.0 kyr BP (median age = 17,970 cal yr BP; mean age = 18,030 +/- 330 cal yr BP) and similar to 15.2 kyr BP (median age = 15,210 cal yr BP; mean age = 15,200 +/- 420 cal yr BP) and 2) that climate during HS1 was non-stationary and centennial-scale variability in moisture is superimposed on this overall cold climatic period. In this study, we improve the pollen sampling resolution with respect to previous studies on the same Padul-15-05 sedimentary core and suggest a novel subdivision of HS1 in 7 sub-phases, including: i) 3 sub-phases (a.1-a.3) during an arid early phase (HS1a; similar to 18.4-17.2 kyr BP), ii) a relatively humid middle phase (HS1b; similar to 17.2-16.9 kyr BP), and iii) 3 sub-phases (c.1-c.3) during an arid late phase (HS1c; similar to 16.9-15.7 kyr BP). This climatic subdivision is regionally supported by SST oscillations from the Mediterranean Sea, suggesting a strong land-sea coupling. A cyclostratigraphic analysis of pollen data between 20 and 11 kyr BP indicates that the climate variability and the proposed subdivisions characterized by similar to 2000 and similar to 800-yr periodicities could be related to solar forcing controlling climate in this area. (C) 2021 Elsevier Ltd. All rights reserved.Peer reviewe

Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.Comment: 40 pages, 16 figure