Generation of navigation graphs for indoor space

This article proposes a comprehensive approach to computing a navigation graph for an indoor space. It focuses on a single floor, but the work is easily extensible to multi-level spaces. The approach proceeds by using a formal model, based on the combinatorial map but enhanced with geometric and semantic information. The process is almost fully automatic, taking as input the building plans providing the geometric structure of the floors and semantics of the building, such as functions of interior spaces, portals, etc. One of the novel aspects in this work was the use of combinatorial maps and their duals to provide a compact formal description of the topology and connectivity of the indoor structure represented by a connected, embedded graph. While making use of existing libraries for the more routine computational geometry involved, the research develops several new algorithms, including one for computing the local kernel of a region. The process is evaluated by means of a case study using part of a university building

Distribution and density of the partition function zeros for the diamond-decorated Ising model

Exact renormalization map of temperature between two successive decorated lattices is given, and the distribution of the partition function zeros in the complex temperature plane is obtained for any decoration-level. The rule governing the variation of the distribution pattern as the decoration-level changes is given. The densities of the zeros for the first two decoration-levels are calculated explicitly, and the qualitative features about the densities of higher decoration-levels are given by conjecture. The Julia set associated with the renormalization map is contained in the distribution of the zeros in the limit of infinite decoration level, and the formation of the Julia set in the course of increasing the decoration-level is given in terms of the variations of the zero density.Comment: 8 pages,8figure

A classical explanation of quantization

In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck's constant h is shown to be indicative of a particle's "zitterbewegung" and thus of a fundamental angular momentum. The latter is identified with quantum mechanical spin, a residue of which is thus present even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic

Recognizing basal cell carcinoma on smartphone‐captured digital histopathology images with a deep neural network

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154530/1/bjd18026.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154530/2/bjd18026_am.pd

Non-Markovian dynamics in a spin star system: The failure of thermalization

In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non- Markovian. A direct consequence is that the final state of the central spin is not the thermal state equilibrium with the bath, but a steady state which depends on its initial state.Comment: 8 page

Prospective Registry Trial Assessing the Use of Magnetic Seeds to Locate Clipped Nodes After Neoadjuvant Chemotherapy for Breast Cancer Patients

Background Targeted axillary dissection (TAD) involves locating and removing both clipped nodes and sentinel nodes for assessment of the axillary response to neoadjuvant chemotherapy (NAC) by clinically node-positive breast cancer patients. Initial reports described radioactive seeds used for localization, which makes the technique difficult to implement in some settings. This trial was performed to determine whether magnetic seeds can be used to locate clipped axillary lymph nodes for removal. Methods This prospective registry trial enrolled patients who had biopsy-proven node-positive disease with a clip placed in the node and treatment with NAC. A magnetic seed was placed under ultrasound guidance in the clipped node after NAC. All the patients underwent TAD. Results Magnetic seeds were placed in 50 patients by 17 breast radiologists. All the patients had successful seed placement at the first attempt (mean time for localization was 6.1 min; range 1-30 min). The final position of the magnetic seed was within the node (n = 44, 88%), in the cortex (n = 3, 6%), less than 3 mm from the node (n = 2, 4%), or by the clip when the node could not be adequately visualized (n = 1, 2%). The magnetic seed was retrieved at surgery from all the patients. In 49 (98%) of the 50 cases, the clip and magnetic seed were retrieved from the same node. Surgeons rated the transcutaneous and intraoperative localization as easy for 43 (86%) of the 50 cases. No device-related adverse events occurred. Conclusions Localization and selective removal of clipped nodes can be accomplished safely and effectively using magnetic seeds

Block bond-order potential as a convergent moments-based method

The theory of a novel bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of sigma and pi bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent O(N) method we apply the block bond-order potential to the large scale simulation of the deformation of a carbon nanotube.Comment: revtex, 43 pages, 11 figures, submitted to Phys. Rev.

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial

We derive some new structural results for the transfer matrix of square-lattice Potts models with free and cylindrical boundary conditions. In particular, we obtain explicit closed-form expressions for the dominant (at large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as the solution of a special one-dimensional polymer model. We also obtain the large-q expansion of the bulk and surface (resp. corner) free energies for the zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47} (resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <= m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19 Postscript figures. Also included are Mathematica files data_CYL.m and data_FREE.m. Many changes from version 1: new material on series expansions and their analysis, and several proofs of previously conjectured results. Final version to be published in J. Stat. Phy

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio