Research Outputs

Permanent URI for this communityhttps://hdl.handle.net/20.500.14288/2

Browse

Filters

Advanced Search

Filter by

Settings

Department: search.filters.department.Department of MathematicsIndexed at: search.filters.indexed.PubMed

Search Results

Now showing 1 - 10 of 22
  • Thumbnail Image
    PublicationOpen Access
    Anti-icing properties on surfaces through a functional composite: effect of ionic salts
    (American Chemical Society (ACS), 2018) Department of Mathematics; Aydın, Derya; Akolpoğlu, Mükrime Birgül; Kızılel, Rıza; Kızılel, Seda; Researcher; Master Student; Researcher; Faculty Member; Department of Mathematics; Koç University Tüpraş Energy Center (KUTEM) / Koç Üniversitesi Tüpraş Enerji Merkezi (KÜTEM); College of Engineering; Graduate School of Sciences and Engineering; College of Sciences; N/A; N/A; N/A; 28376
    This study reports the potential of a unique functional composite for anti-icing applications. To date, various ionic salt formulations have been applied to prevent ice accumulation on surfaces. However, salt can be removed by external factors and large amounts must be used to attain anti-icing properties. Incorporating hydrophilic salts into hydrophobic mediums and controlled release of specific agents can provide effective solution to reduce ice accumulation on surfaces. Here, we developed functional polymer composites with salt pockets of altered ionic salts consisting of potassium formate (KCOOH), sodium chloride (NaCl), or magnesium chloride (MgCl2). We dissolved ionic salts in hydrophilic gel domains and dispersed in a hydrophobic styrene-butadiene-styrene polymer matrix. Na+ and Cl- ions delayed ice formation by 42.6 min at -2 degrees C compared to that for unmodified surfaces. Functional composites prepared with the NaCl ionic salt exhibited better anti-icing behavior at -2 degrees C because of their high concentration compared to that of the composites prepared with KCOOH and MgCl2 ionic salts. We also characterized the release of ionic salts from composite-modified hydrophobic medium separately up to 118 days. Furthermore, we monitored freezing of water on composite-incorporated or composite-coated hydrophobic surfaces in a camera-integrated cold chamber with a uniform temperature (-2 degrees C). The results demonstrated significant increases in the delay of freezing on composite-incorporated or composite-coated surfaces compared to that on controls. We observed altered effects of each ionic salt on the mechanical, morphological, and functional properties of the composite-incorporated or composite-coated hydrophobic surfaces. Our results suggested that the efficiency of a polymer composite to promote anti-icing behavior on a surface is directly related to the type and concentration of the particular ionic salt incorporation into the composite. This approach is promising and demonstrates significant potential of the ionic salt embedded within polymer composite-modified hydrophobic surfaces to attain delayed icing function.
  • Thumbnail Image
    PublicationOpen Access
    Censoring distances based on labeled cortical distance maps in cortical morphometry
    (Frontiers, 2013) Nishino, Tomoyuki; Alexopolous, Dimitrios; Todd, Richard D.; Botteron, Kelly N.; Miller, Michael I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    It has been demonstrated that shape differences in cortical structures may be manifested in neuropsychiatric disorders. Such morphometric differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed/labeled distances of gray matter (GM) voxels with respect to GM/white matter (VW) surface. Volumes and other summary measures for each subject and the pooled distances can help determine the morphometric differences between diagnostic groups, however they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the pooled distances is introduced for each diagnostic group where the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, the distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances but also provide information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC in MDD and HR subjects is observed compared to Ctrl subjects. Moreover, the GM LCDM distances (i.e., locations with respect to the GM/WM surface) for which these differences start to occur are determined. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.
  • Placeholder
    PublicationMetadata only
    Consistent treatment of quantum systems with a time-dependent Hilbert space
    (MDPI, 2024) Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of Sciences
    We 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.
  • Placeholder
    PublicationMetadata 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/A
    Background: 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.
  • Thumbnail Image
    PublicationOpen Access
    Metric distances between hippocampal shapes indicate different rates of change over time in nondemented and demented subjects
    (Bentham Science, 2013) Beg, M. F.; Ceritoglu, C.; Wang, L.; Morris, J. C.; Csernansky, J. G.; Miller, M. I.; Ratnanather, J. T.; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    In this article, we use longitudinal morphometry (shape and size) measures of hippocampus in subjects with mild dementia of Alzheimer type (DAT) and nondemented controls in logistic discrimination. The morphometric measures we use are volume and metric distance measures at baseline and follow-up (two years apart from baseline). Morphometric differences with respect to a template hippocampus were measured by the metric distance obtained from the large deformation diffeomorphic metric mapping (LDDMM) algorithm. LDDMM assigns metric distances on the space of anatomical images, thereby allowing for the direct comparison and quantization of morphometric changes. We also apply principal component analysis (PCA) on volume and metric distance measures to obtain principal components that capture some salient aspect of morphometry. We construct classifiers based on logistic regression to distinguish diseased and healthy hippocampi (hence potentially diagnose the mild form of DAT). We consider logistic classifiers based on volume and metric distance change over time (from baseline to follow-up), on the raw volumes and metric distances, and on principal components from various types of PCA analysis. We provide a detailed comparison of the performance of these classifiers and guidelines for their practical use. Moreover, combining the information conveyed by volume and metric distance measures by PCA can provide a better biomarker for detection of dementia compared to volume, metric distance, or both.
  • Placeholder
    PublicationMetadata 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; 253074
    Neuromuscular 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.
  • Thumbnail Image
    PublicationOpen Access
    Morphometric differences in planum temporale in schizophrenia and bipolar disorder revealed by statistical analysis of labeled cortical depth maps
    (Frontiers, 2015) Ratnanather, J. Tilak; Cebron, Shannon; Postell, Elizabeth; Pisano, Dominic V.; Poynton, Clare B.; Crocker, Britni; Honeycutt, Nancy A.; Mahon, Pamela B.; Barta, Patrick E.; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    Differences in cortical thickness in the lateral temporal lobe, including the planum temporale (PT), have been reported in MRI studies of schizophrenia (SCZ) and bipolar disorder (BPD) patients. Most of these studies have used a single-valued global or local measure for thickness. However, additional and complementary information can be obtained by generating labeled cortical distance maps (LCDMs), which are distances of labeled gray matter (GM) voxels from the nearest point on the GM/white matter (WM) (inner) cortical surface. Statistical analyses of pooled and censored LCDM distances reveal subtle differences in PT between SCZ and BPD groups from data generated by Ratnanather et al. (Schizophrenia Research, https://dx.doi.org/10.1016/j.schres.2013.08.014). These results confirm that the left planum temporale (LPT) is more sensitive than the right PT in distinguishing between SCZ, BPD, and healthy controls. Also confirmed is a strong gender effect, with a thicker PT seen in males than in females. The differences between groups at smaller distances in the LPT revealed by pooled and censored LCDM analysis suggest that SCZ and BPD have different effects on the cortical mantle close to the GM/WM surface. This is consistent with reported subtle changes in the cortical mantle observed in post-mortem studies.
  • Thumbnail Image
    PublicationOpen Access
    Nonlinear spectral singularities for confined nonlinearities
    (American Physical Society (APS), 2013) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrodinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex delta-function potential that is subject to a general confined nonlinearity.
  • Thumbnail Image
    PublicationOpen Access
    Prediction and control of number of cells in microdroplets by stochastic modeling
    (Royal Society of Chemistry (RSC), 2012) Xu, Feng; Gürkan, Umut Atakan; Emre, Almet Emrehan; Turalı, Emine Sümeyra; El Assal, Rami; Açıkgenc, Ali; Wu, Chung-an Max; Demirci, Utkan; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    Manipulation and encapsulation of cells in microdroplets has found many applications in various fields such as clinical diagnostics, pharmaceutical research, and regenerative medicine. The control over the number of cells in individual droplets is important especially for microfluidic and bioprinting applications. There is a growing need for modeling approaches that enable control over a number of cells within individual droplets. In this study, we developed statistical models based on negative binomial regression to determine the dependence of number of cells per droplet on three main factors: cell concentration in the ejection fluid, droplet size, and cell size. These models were based on experimental data obtained by using a microdroplet generator, where the presented statistical models estimated the number of cells encapsulated in droplets. We also propose a stochastic model for the total volume of cells per droplet. The statistical and stochastic models introduced in this study are adaptable to various cell types and cell encapsulation technologies such as microfluidic and acoustic methods that require reliable control over number of cells per droplet provided that settings and interaction of the variables is similar.
  • Thumbnail Image
    PublicationOpen Access
    Pseudo-Hermitian quantum mechanics with unbounded metric operators
    (The Royal Society, 2013) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    I extend the formulation of pseudo-Hermitian quantum mechanics to eta(+)-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta(+). In particular, I give the details of the construction of the physical Hilbert space, observables and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of eta(+) and consequently root eta(+).