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Publication Metadata only Consistent treatment of quantum systems with a time-dependent Hilbert space(MDPI, 2024) Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of SciencesWe consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product. © 2024 by the author.Publication Metadata only Quantitative analysis of structural alterations in the choroid of patients with active Behçet uveitis(Lippincott Williams and Wilkins (LWW), 2018) Oray, Merih; Herbort, Carl P.; Akman, Mehmet; Tugal-Tutkun, Ilknur; Department of Mathematics; N/A; N/A; N/A; N/A; Mengi, Emre; Önal, Sumru; Uludağ, Günay; Metin, Mustafa Mert; Akbay, Aylin Koç; Faculty Member; Other; Doctor; Undergraduate Student; Doctor; Department of Mathematics; College of Sciences; School of Medicine; N/A; School of Medicine; N/A; N/A; N/A; Koç University Hospital; N/A; Koç University Hospital; 113760; 52359; N/A; N/A; N/APurpose: To quantitatively analyze in vivo morphology of subfoveal choroid during an acute attack of Behcet uveitis. Methods: In this prospective study, 28 patients with Behcet uveitis of <= 4-year duration, and 28 control subjects underwent enhanced depth imaging optical coherence tomography. A novel custom software was used to calculate choroidal stroma-to-choroidal vessel lumen ratio. Subfoveal choroidal thickness was measured at fovea and 750 mu m nasal, temporal, superior, and inferior to fovea. Patients underwent fluorescein angiography and indocyanine green angiography. Receiver operating characteristic curve and area under the curve were computed for central foveal thickness. The eye with a higher Behcet disease ocular attack score 24 was studied. The main outcome measures were choroidal stromato-choroidal vessel lumen ratio and choroidal thickness. Results: The mean total Behcet disease ocular attack score 24, fluorescein angiography, and indocyanine green angiography scores were 7.42 +/- 4.10, 17.42 +/- 6.03, and 0.66 +/- 0.73, respectively. Choroidal stroma-to-choroidal vessel lumen ratio was significantly higher in patients (0.413 +/- 0.056 vs. 0.351 +/- 0.063, P = 0.003). There were no significant differences in subfoveal choroidal thickness between patients and control subjects. Choroidal stroma-tochoroidal vessel lumen ratio correlated with retinal vascular staining and leakage score of fluorescein angiography (r = 0.300, P = 0.036). Central foveal thickness was significantly increased in patients (352.750 +/- 107.134 mu m vs. 263.500 +/- 20.819 p.m, P < 0.001). Central foveal thickness showed significant correlations with logarithm of minimum angle of resolution vision, Behcet disease ocular attack score 24, total fluorescein angiography score, retinal vascular staining and/or leakage and capillary leakage scores of fluorescein angiography, and total indocyanine green angiography score. At 275 mu m cutoff, diagnostic sensitivity and specificity of central foveal thickness for acute Behcet uveitis were 89% and 72%, respectively (area under the curve = 0.902; 95% CI = 0.826-0.978, P < 0.001). Conclusion: There was choroidal stromal expansion which was not associated with thickening of the choroid. Central foveal thickness may be used as a noninvasive measure to assess inflammatory activity in early Behcet uveitis.Publication Metadata only Segregation indices for disease clustering(Wiley-Blackwell, 2014) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ASpatial clustering has important implications in various fields. In particular, disease clustering is of major public concern in epidemiology. In this article, we propose the use of two distance-based segregation indices to test the significance of disease clustering among subjects whose locations are from a homogeneous or an inhomogeneous population. We derive the asymptotic distributions of the segregation indices and compare them with other distance-based disease clustering tests in terms of empirical size and power by extensive Monte Carlo simulations. The null pattern we consider is the random labeling (RL) of cases and controls to the given locations. Along this line, we investigate the sensitivity of the size of these tests to the underlying background pattern (e.g., clustered or homogenous) on which the RL is applied, the level of clustering and number of clusters, or to differences in relative abundances of the classes. We demonstrate that differences in relative abundances have the highest influence on the empirical sizes of the tests. We also propose various non-RL patterns as alternatives to the RL pattern and assess the empirical power performances of the tests under these alternatives. We observe that the empirical size of one of the indices is more robust to the differences in relative abundances, and this index performs comparable with the best performers in literature in terms of power. We illustrate the methods on two real-life examples from epidemiology. Copyright (c) 2013 John Wiley & Sons, Ltd.Publication Metadata only Modeling reflex asymmetries with implicit delay differential equations(Elsevier, 1998) Mallet-Paret, J; Department of Mathematics; Atay, Fatihcan; Faculty Member; Department of Mathematics; College of Sciences; 253074Neuromuscular reflexes with time-delayed negative feedback, such as the pupil light reflex, have different rates depending on the direction of movement. This asymmetry is modeled by an implicit first-order delay differential equation in which the value of the rate constant depends on the direction of movement. Stability analyses are presented for the cases when the rate is: (1) an increasing and (2) a decreasing function of the direction of movement. It is shown that the stability of equilibria in these dynamical systems depends on whether the rate constant is a decreasing or increasing function. In particular, when the asymmetry has the shape of an increasing step function, it is possible to have stability which is independent of the value of the time delay or the steepness (i.e., gain) of the negative feedback. (C) 1998 Society for Mathematical Biology.Publication Metadata only Unidirectional invisibility and non-reciprocal transmission in two and three dimensions(Royal Soc Chemistry, 2016) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations and discuss its three-dimensional generalization. In particular, we construct an infinite class of unidirectionally invisible optical potentials that describe the scattering of normally incident transverse electric waves by an infinite planar slab with refractive-index modulations along both the normal directions to the electric field. A by-product of this investigation is a demonstration of non-reciprocal transmission in two dimensions. To elucidate this phenomenon, we state and prove a general reciprocity theorem that applies to quantum scattering theory of real and complex potentials in two and three dimensions.Publication Metadata only Quantization and analysis of hippocampal morphometric changes due to dementia of alzheimer type using metric distances based on large deformation diffeomorphic metric mapping(Elsevier, 2011) Beg, Mirza Faisal; Ceritoglu, Can; Wang, Lei; Morris, John C.; Csernansky, John G.; Miller, Michael I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe metric distance obtained from the large deformation diffeomorphic metric mapping (LDDMM) algorithm is used to quantize changes in morphometry of brain structures due to neuropsychiatric diseases. For illustrative purposes we consider changes in hippocampal morphometry (shape and size) due to very mild dementia of the Alzheimer type (DAT). LDDMM, which was previously used to calculate dense one-to-one correspondence vector fields between hippocampal shapes, measures the morphometric differences with respect to a template hippocampus by assigning metric distances on the space of anatomical images thereby allowing for direct comparison of morphometric differences. We characterize what information the metric distances provide in terms of size and shape given the hippocampal, brain and intracranial volumes. We demonstrate that metric distance is a measure of morphometry (i.e., shape and size) but mostly a measure of shape, while volume is mostly a measure of size. Moreover, we show how metric distances can be used in cross-sectional, longitudinal analysis, as well as left-right asymmetry comparisons, and provide how the metric distances can serve as a discriminative tool using logistic regression. Thus, we show that metric distances with respect to a template computed via LDDMM can be a powerful tool in detecting differences in shape. (C) 2011 Elsevier Ltd. All rights reserved.Publication Metadata only Quantitative analysis of immunogold labeling for basic fibroblast growth factor according to the activational stages of mast cells(Sci Printers & Publ Inc, 2013) Kayton, Robert J.; N/A; Department of Mathematics; N/A; Aktaş, Ranan Gülhan; Çağlar, Mine; Oktayer, Adviye Gözde; Faculty Member; Faculty Member; Master Student; Department of Mathematics; School of Medicine; College of Sciences; Graduate School of Health Sciences; 137519; 105131; N/AOBJECTIVE: To analyze whether immunogold labeling density for basic fibroblastic growth factor in granules is compatible with the activation stage of mast cells. STUDY DESIGN: Cytoplasmic features and granules of 46 mast cells were examined at the ultrastructural level. The cells were classified according to their activation stage, namely, whether resting, initially activated, fully degranulated or piecemeal degranulated. Granules were classified as electron lucent, moderate or dense granules. Gold particles per secretory granules in the cells were counted. Recently described quantitative analysis techniques were used for evaluation. RESULTS: There is a statistically meaningful relationship between the activation stage of mast cells and their immunogold labeling density. The number of different types of granules encountered in a cell depends on the type of the cell. The distribution of gold particles among the secretory granules depends upon the cell. The type of granule does not have an individual effect on the number of particles, as indicated by an overall statistical analysis of granules, cells and their interaction effects. CONCLUSION: A count of gold particles in the cells can be used as a strong biological indicator. Therefore the number of gold particles might be very useful for comparative studies related to the secretion of this growth factor under different conditions.Publication Metadata only The role of base excision repair in major depressive disorder and bipolar disorder(Elsevier, 2022) Küçüker, Mehmet Utku; Özerdem, Ayşegül; Cabello Arreola, Alejandra; Ho, Ada M. C.; Joseph, Boney; Webb, Lauren M.; Croarkin, Paul E.; Frye, Mark A.; Veldic, Marin; Department of Mathematics; Ceylan, Deniz; Faculty Member; Department of Mathematics; College of Sciences; 137755Background: In vivo and in vitro studies suggest that inflammation and oxidative damage may contribute to the pathogenesis of major depressive disorder (MDD) and bipolar disorder (BD). Imbalance between DNA damage and repair is an emerging research area examining pathophysiological mechanisms of these major mood disorders. This systematic review sought to review DNA repair enzymes, with emphasis on the base excision repair (BER), in mood disorders.Methods: We conducted a comprehensive literature search of Ovid MEDLINE (R) Epub Ahead of Print, Ovid MEDLINE (R) In-Process & Other Non-Indexed Citations, Ovid MEDLINE (R) Daily, EMBASE (1947), and PsycINFO for studies investigating the alterations in base excision repair in patients with MDD or BD.Results: A total of 1364 records were identified. 1352 records remained after duplicates were removed. 24 records were selected for full-text screening and a remaining 12 articles were included in the qualitative synthesis. SNPs (single nucleotide polymorphisms) of several BER genes have been shown to be associated with MDD and BD. However, it was difficult to draw conclusions from BER gene expression studies due to conflicting findings and the small number of studies. Limitations: All studies were correlational so it was not possible to draw conclusions regarding causality.Conclusion: Future studies comparing DNA repair during the manic or depressive episode to remission will give us a better insight regarding the role of DNA repair in mood disorders. These alterations might be utilized as diagnostic and prognostic biomarkers as well as measuring treatment response.Publication Metadata only Statistical analysis of cortical morphometrics using pooled distances based on labeled cortical distance maps(Springer, 2011) Hosakere, M.; Nishino, T.; Alexopoulos, J.; Todd, R. D.; Botteron, K. N.; Miller, M. I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ANeuropsychiatric disorders have been demonstrated to manifest shape differences in cortical structures. Labeled Cortical Distance Mapping (LCDM) is a powerful tool in quantifying such morphometric differences and characterizes the morphometry of the laminar cortical mantle of cortical structures. Specifically, LCDM data are distances of labeled gray matter (GM) voxels with respect to the gray/white matter cortical surface. Volumes and descriptive measures (such as means and variances for each subject) based on LCDM distances provide descriptive summary information on some of the shape characteristics. However, additional morphometrics are contained in the data and their analysis may provide additional clues to underlying differences in cortical characteristics. To use more of this information, we pool (merge) LCDM distances from subjects in the same group. These pooled distances can help detect morphometric differences between groups, but do not provide information about the locations of such differences in the tissue in question. In this article, we check for the influence of the assumption violations on the analysis of pooled LCDM distances. We demonstrate that the classical parametric tests are robust to the non-normality and within sample dependence of LCDM distances and nonparametric tests are robust to within sample dependence of LCDM distances. We specify the types of alternatives for which the tests are more sensitive. We also show that the pooled LCDM distances provide powerful results for group differences in distribution of LCDM distances. As an illustrative example, we use GM in the ventral medial prefrontal cortex (VMPFC) in subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy subjects. Significant morphometric differences were found in VMPFC due to MDD or being at HR. In particular, the analysis indicated that distances in left and right VMPFCs tend to decrease due to MDD or being at HR, possibly as a result of thinning. The methodology can also be applied to other cortical structures.Publication Metadata only Frequency of nerve root sleeve cysts in autosomal dominant polycystic kidney disease(Galenos Publ House, 2016) Asik, Murat; Tufan, Fatih; Akpinar, Timur Selcuk; Akalin, Nilgul; Tunc, Necmeddin; Hasiloglu, Zehra Isik; Altiparmak, Mehmet Riza; Ecder, Tevfik; Albayram, Sait; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ABackground: There is sporadic data about the occurrence of spinal meningeal cysts in patients with autosomal dominant polycystic kidney disease ( ADPKD). We suggest that there is a relationship with the frequency and size of spinal meningeal cysts and headache, intracranial aneurysms, and cerebrospinal fluid leakage in patients with ADPKD. Aim: To investigate the relationship with spinal meningeal cyst, cerebrospinal fluid leakage, and headache in patients with ADPKD. Study Design: Cross-sectional study. Methods: We enrolled 50 patients with ADPKD and 37 healthy volunteers. This cross-sectional study included patients with ADPKD and matched healthy volunteers. Magnetic resonance imaging myelography was performed using the 3D-T2 HASTE technique in an MRI scanner. We questioned our subjects regarding presence of headache and evaluated headache severity using a visual analog scale. The relationship between the number and size of spinal men-ingeal cysts with headache, intracranial aneurysms, and liver cysts was also investigated. Results: Spinal meningeal cysts were more numerous and larger in patients than in controls (14.8 +/- 11.6 vs. 6.4 +/- 4.6 cysts respectively, p<0.001, 68.3 +/- 49.3 vs. 25.4 +/- 20.1 mm, p<0.001, respectively). Spinal cyst number and size were similar in APDKD patients with or without intracranial aneurysms. Headache score was correlated with the size and number of spinal meningeal cysts. This was valid only in patients with ADPKD. Conclusion: Abnormality involving the vessel wall in ADPKD may explain the increased number of spinal meningeal cysts in ADPKD. Moreover, leakage of cerebrospinal fluid secondary to spinal meningeal cyst may be responsible for recurrent severe headache by causing spontaneous intracranial hypotension in these patients.