Statistics of Largest Loops in a Random Walk

We report further findings on the size distribution of the largest neutral segments in a sequence of N randomly charged monomers [D. Ertas and Y. Kantor, Phys. Rev. E53, 846 (1996); cond-mat/9507005]. Upon mapping to one--dimensional random walks (RWs), this corresponds to finding the probability distribution for the size L of the largest segment that returns to its starting position in an N--step RW. We primarily focus on the large N, \ell = L/N << 1 limit, which exhibits an essential singularity. We establish analytical upper and lower bounds on the probability distribution, and numerically probe the distribution down to \ell \approx 0.04 (corresponding to probabilities as low as 10^{-15}) using a recursive Monte Carlo algorithm. We also investigate the possibility of singularities at \ell=1/k for integer k.Comment: 5 pages and 4 eps figures, requires RevTeX, epsf and multicol. Postscript file also available at http://cmtw.harvard.edu/~deniz/publications.htm

Examination of foramen tympanicum: an anatomical study using cone-beam computed tomography

Background: The foramen tympanicum (FT) is an osseous dehiscence of the temporal bone and usually closes by the age of 5 years. The foramen is located posteromedial to the temporomandibular joint and anteroinferior of the external auditory canal. The aim of this study is to define the prevalence, location and size of the foramen. Materials and methods: We retrospectively examined 200 cone-beam computed tomography (CBCT) images (400 ears). We used a CBCT dental imaging system (GALILEOS, Sirona Dental Systems, Bensheim, Germany) working at 15–30 mA and 98 kV. We noted size and location (unilateral and bilateral) of the present FT. Results: Foramen tympanicum was determined in 11.5% of 200 patients (they had FT at least on one side of the head). This was bilateral in 5 (2.5%) patients. Prevalence of the FT was significintly higher in females (8%) than in males (3.5%). FT was found more frequently on the left side (7.5%) than on the right side (4%). Mean axial diameter was 1.13 mm (range 0.23–4.43 mm), and mean sagittal diameter was 1.44 mm (range 0.22–3.99 mm). Conclusions: Considering that FT was present in 11.75% of patients, radiologists and clinicians should be aware of the possible presence of this defect. It is known that this developmental dehiscence may cause herniation of temporomandibular joint, formation of salivary otorrhea, and spread of tumour or infection to the infratemporal fossa from external auditory canal. This study showed that CBCT may be preferred for imaging these conditions. (Folia Morphol 2018; 77, 2: 335–339

Dinamik Geometri Yazılımlarındaki Sürükleme ve Çeşitlerinin Geometri Öğretimindeki Rolü

Geometrideki tümdengelimli ve tümevarımsal muhakeme arasındaki etkileşimli süreç içerisinde,dinamik geometri yazılımlarının en temel ve ayırt edici özelliği olan sürükleme anahtarbir role sahiptir. Sürüklemenin bu anahtar rolünün ortaya çıkarılmasında ise eğitimcilere ve araştırmacılara önemli görevler düşmektedir. Bu doğrultuda bu çalışmadadinamik geometri yazılımlarının sürükleme özelliğinin farklı kullanım amaçlarıaçıklanmış, sürükleme çeşitleri tanıtılmış ve eğitimcilerin bu süreçteki rolü tartışılmıştır. Kuramsal olarak desenlenen bu çalışmanın Türkiye’deki literatüre katkı sağlayacağı düşünülmektedir. Çalışmada öncelikle sürüklemenin kısa tarihçesine ve geometri öğretimindeki önemine değinilmiş, ardından sürükleme çeşitlerinin “kurama geçiş” ve “algıya geçiş” sürecindeki rolü açıklanmıştır.Bu sürükleme çeşitleri parabol konusuna ilişkin örnek bir problem durumu üzerinde tanıtılmış ve süreç içinde öğrencilerde gerçekleşebilecek muhakemeler tartışılmışt

Probabilistic Seismic Loss Estimation for Eskisehir, Turkey

Stochastic methods are utilized for the assessment of seismic hazard for the Eskisehir region. A comprehensive earthquake catalog, in which earthquakes in different scales are converted to a common scale, is compiled. Seismic source zones near the region with revised boundaries and various attenuation relationships are employed. Uncertainties related to the seismicity parameters and different assumptions are taken into consideration by using the logic tree procedure. Seismic hazard maps in terms of peak ground acceleration and MSK intensity, corresponding to a return period of 475 years are developed for Eskisehir. At the end of the study, the expected earthquake damage is estimated for the 31 districts located in Odunpazari, which is a municipality of Eskisehir

Randomly Charged Polymers, Random Walks, and Their Extremal Properties

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe

Vancomycin-resistant enterococci colonization in patients with hematological malignancies: screening and its cost-effectiveness

Background and objective: We evaluated the rates of vancomycin-resistant enterococci (VRE) colonization and VRE related bacteremia in patients with hematological malignancies in terms of routine screening culture and its cost-effectiveness.Materials and Methods: All patients of the hematology department who were older than 14 years of age and who developed at least one febrile neutropenia episode during chemotherapy for hematological cancers between November 2010 and November 2012 were evaluated retrospectively.Results: We retrospectively analyzed 282 febrile episodes in 126 neutropenic patients during a two-year study period. The study included 65 cases in the first study-year and 78 cases in the second study-year. The numbers of colonization days and colonized patient were 748 days of colonization in 29 patients (44%) in the first study-year and 547 colonization days in 21 patients (26%) in the second study-year, respectively. Routine screening culture for VRE cost $4516,4 (427 cultures) in the first study-year,$5082,7 (504 cultures) in the second study-year depending on the number of patients and their length of stay.Conclusion: In line with our study results, routine screening of hematological patients for VRE colonization is not costeffective. Routine surveillance culture for VRE should be considered with respect to the conditions of health care setting.Keywords: Hematological patients, febrile neutropenia, vancomycin-resistant enterococci, vancomycin-sensitive enterococci, bacteremia, colonization

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Three-dimensional racetrack memory devices designed from freestanding magnetic heterostructures

The fabrication of three-dimensional nanostructures is key to the development of next-generation nanoelectronic devices with a low device footprint. Magnetic racetrack memory encodes data in a series of magnetic domain walls that are moved by current pulses along magnetic nanowires. To date, most studies have focused on two-dimensional racetracks. Here we introduce a lift-off and transfer method to fabricate three-dimensional racetracks from freestanding magnetic heterostructures grown on a water-soluble sacrificial release layer. First, we create two-dimensional racetracks from freestanding films transferred onto sapphire substrates and show that they have nearly identical characteristics compared with the films before transfer. Second, we design three-dimensional racetracks by covering protrusions patterned on a sapphire wafer with freestanding magnetic heterostructures. We demonstrate current-induced domain-wall motion for synthetic antiferromagnetic three-dimensional racetracks with protrusions of up to 900 nm in height. Freestanding magnetic layers, as demonstrated here, may enable future spintronic devices with high packing density and low energy consumption