Power-law energy level-spacing distributions in fractals

In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise linear functions. We propose that such a behaviour is a general feature of fractals, which can not be described properly by random matrix theory. Several other arguments for the power-law behaviour of the energy level-spacing distributions are proposed

Linearized spectral decimation in fractals

In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it numerically. Our approach provides qualitative explanations for various spectral properties of self-similar graphs within the theory of dynamical systems, including power-law level-spacing distribution, smooth density of states and effective chaotic regime

Hall conductivity of Sierpinski carpet

We calculate the Hall conductivity of a Sierpinski carpet using Kubo-Bastin formula. The quantization of Hall conductivity disappears when we increase the depth of the fractal. The Hall conductivity is no more proportional to the Chern number. Nevertheless, these quantities behave in a similar way showing some reminiscence of a topological nature of the Hall conductivity. We also study numerically the bulk-edge correspondence and find that the edge states become less manifested when the depth of Sierpinski carpet is increased

Strong enhancement of superconductivity in finitely ramified fractal lattices

Using the Sierpinski gasket (triangle) and carpet (square) lattices as examples, we theoretically study the properties of fractal superconductors. For that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard model with attractive on-site potential and employ the Bogoliubov-de Gennes approach and the theory of superfluid stiffness. For the case of the Sierpinski gasket, we demonstrate that fractal geometry of the underlying crystalline lattice can be strongly beneficial for superconductivity, not only leading to a considerable increase of the critical temperature $T_c$ as compared to the regular triangular lattice but also supporting macroscopic phase coherence of the Cooper pairs. In contrast, the Sierpinski carpet geometry does not lead to pronounced effects, and we find no substantial difference as compared with the regular square lattice. We conjecture that the qualitative difference between these cases is caused by different ramification properties of the fractals.Comment: 9 pages, 6 figure

Peran Sequence Paracoronal T2FSE Pada Informasi Citra Magnetic Resonance Imaging (MRI) Pelvis Pada Kasus Fistula

The Role Of The T2FSE Paracoronal Sequence On Pelvic Magnetic Resonance Imaging (MRI) Image Information In Fistula Pelvic MRI is the most ideal part to be examined using Magnetic Resonance Imaging because it is very suitable for detecting abnormalities in the pelvis which most of the organs consist of soft tissue can be seen using MRI techniques . A fistula is an abnormal connection between two epithelial sites. A fistula is one that connects the anus with the skin around the anus or with other organs such as the vagina. One or more fistula bones are visible on the surface of the skin, which can become pus or feces during bowel movements. This study aims to determine the role of pelvic MRI examination with clinical fistula and to find out paracoronal sequence information can establish the clinical diagnosis of fistula. This study uses qualitative descriptive with a case study approach, the subject consists of one patient who will indeed perform a pelvic MRI examination with clinical fistula, the subject is carried out a 1.5 Tesla MRI examination to find out the sequence and procedure and sequence information used. The results of the study were obtained according to theory using sagittal sequences SE / FSE T2, axial SE / FSE T2, axial SE / FSE T1, coronal SE / FSE T2, and coronal GRE / SE / FSE T1, while in the field using sequences axial T2, axial Fat Sat, coronal T1, coronal T2, coronal T2 Fat Sat, sagittal T1 and sagittal T2 Fat Sat

EFFECT OF RENNIN INHIBITORS AND ANGIOTENSIN II RECEPTOR ANTAGONISTS ON LEFT VENTRICULAR HYPERTROPHY IN RENOVASCULAR HYPERTENSIVE RATS

Objective: Left ventricular (LV) hypertrophy involves numerous structural adaptations that may lead to ventricular dysfunction and eventually, heart failure. Particular emphasis is placed on the molecular mechanisms that govern the development of hypertrophy and may lead to maladaptive structural changes resulting in adverse cardiac events. This study investigates the effectiveness of Valsartan (Val) which is an angiotensinII receptor antagonist and Aliskiren (Ali) which is a direct rennin inhibitor in the treatment of cardiac remodeling resulted from renovascular hypertension, particularly left ventricular hypertrophy, and to address the molecular mechanisms underlying them.Methods: 24 male albino rats were randomly divided into 4 main groups (n=6 each), normal control rats (N), hypertensive control rats (HC), Val treated hypertensive rats (Val, 8 mg/kg/day orally) and Ali treated hypertensive rats (Ali, 25 mg/kg/day orally).Results: At the end of 4 weeks HC rats showed enhanced hypertrophic response (higher heart weight/body weight ratio) and dyslipidemia (lower high density lipoprotein "HDL-c" and higher triacyl glycerol "TAG") and a significant deletion of antioxidant enzymes in comparison with N group. The β myosin heavy chain "βMHC", regulator of calcineurin-1 "RCAN1", nuclear factor kappa B "NFκB" and inducible nitric oxide synthase "iNOS" was markedly elevated. While, α myosin heavy chain "αMHC" was markedly decreased as compared with N group. On the other hand Val treated hypertensive rats and Ali treated hypertensive rats showed a significant decrease in heart weight/body weight ratio, improved lipogram pattern and higher levels of antioxidant enzymes. While, cardiac β-MHC, RCAN-1, NFκB and iNOS were significantly decreased as compared with HC group. Both Val treated hypertensive rats and Ali treated hypertensive rats showed a significant increase in α-MHC, compared with HC groupConclusion: The results reported in this study suggested that chronic untreated hypertension induced a pathological hypertrophy. Administration of the Val or Ali individually exerted beneficial effects regarding the improved lipogram pattern and anti-oxidant enzymes levels, as well as cardiac hypertrophy and highlights the role of Val and Ali as a promising therapeutic strategy for hypertension and LV hypertrophy.Â

Association between periodontitis and systemic medication intake: A case- control study

BackgroundTo investigate the frequency of systemic drugs taken by elderly patients with or without periodontitis and the possible association between medication consumption and the severity of periodontitis.MethodsA total of 1221 patients, including 608 with generalized moderate to severe periodontitis (periodontitis group) and 613 age- and gender- matched individuals with healthy periodontium (healthy group) were selected. Systemic conditions, medications and periodontal status were recorded. Medication intake frequency (%) was compared using unconditional logistic regression.ResultsThe top three most common medications were angiotensin- converting enzyme (ACE) inhibitors (17.9%), antidepressants (17.8%), and lipid- lowering medications (16.5%). Both ACE inhibitors and antidepressants showed statistically higher intake frequency in the periodontitis group relative to healthy controls (21.5% versus 14.4%; odds ratio [OR] = 1.64), (21.1% versus 14.5%, OR = 1.57) (P < 0.01). Additionally, intake of oral hypoglycemic agents, calcium channel blockers (CCB), insulin, and diuretics were significantly higher in the periodontitis group with OR = 2.49, 2.32, 2.08 and 1.79, respectively (P < 0.05). Several medications demonstrated a disease severity- dependent association comparing generalized severe periodontitis with moderate periodontitis and healthy group: oral hypoglycemic agents (17.4% versus 16.8% versus 8.0%), CCB (14.8% versus 14.4% versus 8.0%) and anticonvulsants (13.4% versus 7.7% versus 6.4%) with OR of 2.43, 1.99, and 2.28 (severe periodontitis versus healthy group), respectively.ConclusionThere was a significantly higher frequency of medication intake related to cardiovascular disease and diabetes in patients with periodontitis. A disease severity- dependence with medication intake frequency was also noted. This study provides indirect evidence for the possible relationship between systemic diseases and periodontitis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163409/2/jper10532_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163409/1/jper10532.pd

Level-spectra Statistics in Planar Fractal Tight-Binding Models

In this communication, we study the level-spectra statistics when a noninteracting electron gas is confined in \textit{Sierpi\'{n}ski Carpet} (\textit{SC}) lattices. These \textit{SC} lattices are constructed under two representative patterns of the $self$ and $gene$ patterns, and classified into two subclass lattices by the area-perimeter scaling law. By the singularly continuous spectra and critical traits using two level-statistic tools\iffalse the nearest spacing distribution and alternative gap-ratio distribution\fi, we ascertain that both obey the critical phase due to broken translation symmetry and the long-range order of scaling symmetry. The Wigner-like conjecture is confirmed numerically since both belong to the Gaussian orthogonal ensemble. An analogy was observed in a quasiperiodic lattice~\cite{Zhong1998Level}. In addition, this critical phase isolates the crucial behavior near the metal-insulator transition edge in Anderson model. The lattice topology of the self-similarity feature can induce level clustering behavior.Comment: 11 pages, 6 figures, 2 Table

Local quenches in fracton field theory: non-causal dynamics and fractal excitation patterns

We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green function, $\langle \phi^2\rangle$ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension, and argue that this phenomenon cannot be explained by a simple self-interference effect.Comment: v1: 25 pages, 7 figures; v2: 25 pages, 7 figures, references added, minor correction