136 research outputs found
The computation of expected values and moments of special polynomials via characteristic and generating functions
No full textAn approach to revealing clinically relevant subgroups across the mood spectrum
No full textBackground Individuals diagnosed with bipolar 1 disorder (BP1), bipolar 2 disorder (BP2), or major depressive disorder (MDD) experience varying levels of depressive and (hypo)manic symptoms. Clarifying symptom heterogeneity is meaningful, as even subthreshold symptoms may impact quality of life and treatment outcome. The MOODS Lifetime self-report instrument was designed to capture the full range of depressive and (hypo)manic characteristics. Methods This study applied clustering methods to 347 currently depressed adults with MDD, BP2, or BP1 to reveal naturally occurring MOODS subgroups. Subgroups were then compared on baseline clinical and demographic characteristics and as well as depressive and (hypo)manic symptoms over twenty weeks of treatment. Results Four subgroups were identified: (1) high depressive and (hypo)manic symptoms (N=77, 22%), (2) moderate depressive and (hypo)manic symptoms (N=115, 33%), (3) low depressive and moderate (hypo)manic symptoms (N=82, 24%), and (4) low depressive and (hypo)manic symptoms (N=73, 21%). Individuals in the low depressive/moderate (hypo)manic subgroup had poorer quality of life and greater depressive symptoms over the course of treatment. Individuals in the high and moderate severity subgroups had greater substance use, longer duration of illness, and greater (hypo)manic symptoms throughout treatment. Treatment outcomes were primarily driven by individuals diagnosed with MDD. Limitations The sample was drawn from three randomized clinical trials. Validation is required for this exploratory study. Conclusions After validation, these subgroups may inform classification and personalized treatment beyond categorical diagnosis
Topology of soft cone metric spaces
No full textInternational Conference on Functional Analysis in Interdisciplinary Applications (FAIA) -- OCT 02-05, 2017 -- Astana, KAZAKHSTANIn Simsek's paper it was introduced a concept of soft cone metric space via soft elements and some fixed point theorems in soft cone metric space were provided. In this work, we examine topological structures such as open ball, soft neighbourhood and soft open set in soft metric spaces and their some properties, and prove that every soft cone metric space under some condition is a soft topological space according to elementary operations on soft sets.Kyrgyz Turkish Manas University [KTMUBAP-2016.FBE.12]This work is supported by Kyrgyz Turkish Manas University in the framework of Scientific Research Projects (KTMUBAP-2016.FBE.12)
APPLICATIONS OF POINT PROCESS MODELS TO IMAGING AND BIOLOGY
No full textThis dissertation deals with point process models and their applications to imaging and messenger RNA (mRNA) transcription. We address three problems. The first problem arises in two-photon laser scanning microscopy. We model the process by which photons are counted by a detector which suffers from a dead period upon registration of a photon. In this model, we assume that there are a Poisson (α) number of excited molecules, with exponentially distributed waiting times for the emissions of photons. We derive the exact distribution of all observed counts, rather than grouped counts which were used earlier. We use it to get improved estimates of the Poisson intensity, which leads to images with higher signal-to-noise ratio. This improvement is because grouping of count data results in loss of information. We illustrate this improvement on imaging data of paper fibers. Next, we study two variants of this model: the first uses a finite time horizon and the second considers gamma waiting times for the emissions.
The second problem concerns the Conway-Maxwell-Poisson distribution for count data. This family has been proposed as a generalization of the Poisson for handling overdispersion and underdisperson. Because the normalizing constant of this family is hard to compute, good approximations for it are needed. We provide a statistical approach to derive an existing approximation more simply. However, this approximation does not perform well across all the parameter ranges. Therefore, we introduce correction terms to improve its performance. For other parts of the parameter space, we use the geometric and Bernoulli distributions, with correction terms based on Taylor expansions. Using numerical examples, we show that our approximations are much better than earlier proposed methods.
In the last problem, we present a new application for Conway-Maxwell-Poisson family.
We use the generalized linear model setting of this family to study mRNA counts. We then compare its performance with the existing methods used for modeling mRNAs, such as the negative binomial. This empirical model can be a good modeling tool for dispersed mRNA count data when a biophysically based model is not available
Extention of the distribution of photon counts with censoring in two-photon laser scanning microscopy
No full textON CERTAIN MATHEMATICAL PROBLEMS IN TWO-PHOTON LASER SCANNING MICROSCOPY
No full textIn an earlier paper, we derived the distribution of the number of photons detected in two-photon laser scanning microscopy when the counter has a dead period. We assumed a Poisson number of emissions, exponential waiting times, and an infinite time horizon, and used an equivalent inhomogeneous Poisson process formulation. We then used that result to improve image quality as measured by the signal-to-noise ratio. Here, we extend that study in two directions. First, we treat the finite-horizon case to assess the accuracy of the simpler infinite-horizon approximation. Second, we use a direct approach by conditioning on the Poisson count for the infinite-horizon case to derive several polynomial identities.</jats:p
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
No full textThe aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson−Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution
New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms
No full textSimsek, Burcin/0000-0003-2857-6629; KUCUKOGLU, IREM/0000-0001-9100-2252The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the Catalan-type numbers and polynomials with their plots under the special conditions. We also give some derivative formulas for these polynomials. Applying the Riemann integral, contour integral, Volkenborn (bosonic p-adic) integral and fermionic p-adic integral to these polynomials, we also derive some integral formulas. With the help of these integral formulas, we give some identities and relations associated with some classes of special numbers and also the Cauchy-type numbers.Scientific Research Project Administration of Akdeniz UniversityAkdeniz University [FBA-2020-5299]The third author of the present paper was supported by the Scientific Research Project Administration of Akdeniz University (with Project ID No: FBA-2020-5299)
- …
