Nonlocal Operational Calculi for Dunkl Operators

The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found

A guided network propagation approach to identify disease genes that combines prior and new information

A major challenge in biomedical data science is to identify the causal genes underlying complex genetic diseases. Despite the massive influx of genome sequencing data, identifying disease-relevant genes remains difficult as individuals with the same disease may share very few, if any, genetic variants. Protein-protein interaction networks provide a means to tackle this heterogeneity, as genes causing the same disease tend to be proximal within networks. Previously, network propagation approaches have spread signal across the network from either known disease genes or genes that are newly putatively implicated in the disease (e.g., found to be mutated in exome studies or linked via genome-wide association studies). Here we introduce a general framework that considers both sources of data within a network context. Specifically, we use prior knowledge of disease-associated genes to guide random walks initiated from genes that are newly identified as perhaps disease-relevant. In large-scale testing across 24 cancer types, we demonstrate that our approach for integrating both prior and new information not only better identifies cancer driver genes than using either source of information alone but also readily outperforms other state-of-the-art network-based approaches. To demonstrate the versatility of our approach, we also apply it to genome-wide association data to identify genes functionally relevant for several complex diseases. Overall, our work suggests that guided network propagation approaches that utilize both prior and new data are a powerful means to identify disease genes.Comment: RECOMB202

Optimal Monetary Policy in a Monetary Union with Housing and Credit Market Heterogeneity

This paper develops a two-country DSGE model for a monetary union in which each country is populated by two types of households - savers and borrowers - and two types of production sectors - a consumption goods sector and a housing sector. Households trade nominal private debt in equilibrium, with the borrowers being subject to a collateral constraint, which is tied to the value of the stock of housing. The analysis focuses on the implications of housing and credit market heterogeneities for the design of optimal monetary policy of a common central bank. The results indicate that as long as the only heterogeneity between the two countries is the degree of nominal rigidity, the Benigno (2004) result according to which the common central bank puts a higher weight on stabilizing inflation in the country with a higher degree of nominal rigidity continues to hold. However, due to the introduction of collateralized household debt and borrowing constraints the effects of cross-country disparities in the degree of price rigidities on the volatility of inflation are amplified. While the volatility of inflation in the economy with a higher degree of price rigidity is almost as low as in the model without borrowers, inflation in the economy with more flexible prices becomes much more volatile. As a result, under optimal policy the central bank allows union-wide inflation to fluctuate more in response to productivity shocks than in an economy without credit constrained borrowers. In addition we find that housing and credit market heterogeneities have an impact on the central bank's goal to stabilize inflation. Finally, the paper shows that even in the presence of a common productivity shock already small deviations of some of the credit market parameters from the symmetry assumption are sufficient to create sizeable reductions in the cross-country correlation of inflation rates

Data Parallel Hypersweeps for in Situ Topological Analysis

The contour tree is a tool for understanding the topological structure of a scalar field. Recent work has built efficient contour tree algorithms for shared memory parallel computation, driven by the need to analyze large data sets in situ while the simulation is running. Unfortunately, methods for using the contour tree for practical data analysis are still primarily serial, including single isocontour extraction, branch decomposition and simplification. We report data parallel methods for these tasks using a data structure called the hyperstructure and a general purpose approach called a hypersweep. We implement and integrate these methods with a Cinema database that stores features as depth images and with a web server that reconstructs the features for direct visualization

BEHAVIOR FACTOR EVALUATION BASED ON SDOF SYSTEM PRESENTATION AND ENERGY APPROACH

Rectangular steel frames are considered and subjected to strong ground motion. Their behavior factor is numerically evaluated using nonlinear time history analysis and different ground acceleration records. The behavior factor is determined assuming severe collapse mechanism occurs throughout the time history. The system of equations is transformed into single equation end then the energy balance concept is applied. The expression for the behavior factor is derived and its application to four story two bays steel frame is illustrated and the corresponding results are discussed

Radiation Characteristics of 3D Resonant Cavity Antenna with Grid-Oscillator Integrated Inside

A three-dimensional (3D) rectangular cavity antenna with an aperture size of 80 mm × 80 mm and a length of 16 mm, integrated with a four-MESFET transistor grid-oscillator, is designed and studied experimentally. It is found that the use of 3D antenna resonant cavity in case of small or medium gain microwave active cavity antenna leads to effective and stable power combining and radiation. The lack of lateral cavity diffraction and radiation helps in producing a directive gain of about 17 dB and radiation aperture efficiency bigger than 75% at a resonance frequency of 8.62 GHz. Good DC to RF oscillator efficiency of 26%, effective isotropic radiated power (EIRP) of 5.2 W, and SSB spectral power density of −82 dBc/Hz are found from the measured data. The 3D antenna cavity serves also as a strong metal container for the solid-state oscillator circuitry

BICEP3: a 95GHz refracting telescope for degree-scale CMB polarization

Bicep3 is a 550 mm-aperture refracting telescope for polarimetry of radiation in the cosmic microwave background at 95 GHz. It adopts the methodology of Bicep1, Bicep2 and the Keck Array experiments | it possesses sufficient resolution to search for signatures of the inflation-induced cosmic gravitational-wave background while utilizing a compact design for ease of construction and to facilitate the characterization and mitigation of systematics. However, Bicep3 represents a significant breakthrough in per-receiver sensitivity, with a focal plane area 5x larger than a Bicep2/Keck Array receiver and faster optics (f=1:6 vs. f=2:4). Large-aperture infrared-reflective metal-mesh filters and infrared-absorptive cold alumina filters and lenses were developed and implemented for its optics. The camera consists of 1280 dual-polarization pixels; each is a pair of orthogonal antenna arrays coupled to transition-edge sensor bolometers and read out by multiplexed SQUIDs. Upon deployment at the South Pole during the 2014-15 season, Bicep3 will have survey speed comparable to Keck Array 150 GHz (2013), and will signifcantly enhance spectral separation of primordial B-mode power from that of possible galactic dust contamination in the Bicep2 observation patch

Modelling of pedagogical patterns through e-learning objects

Програмні платформи для електронного навчання підтримують різні варіанти подання навчального контенту. Одним із способів для його організації та структурування є так звані педагогічні моделі. Вони є методом для відображення і розповсюдження отриманих знань та практичного досвіду. Педагогічні моделі використовуються для опису педагогічних ситуацій, які неодноразово виникають під час навчання. У контексті систем електронного навчання існують різні підходи до цифровізації педагогічних моделей. Мета роботи – показати, як побудувати педагогічні моделі, використовуючи педагогічні об’єкти електронного навчання, які можна легко та зручно впровадити як моделі в адаптивному середовищі електронного навчання. Педагогічний об’єкт електронного навчання – це абстрактне поняття, яке може бути представлено в конкретній формі об’єкта електронного навчання, методичного об’єкта електронного навчання, об’єкта електронного навчання для моніторингу та діагностики чи об’єкта електронного навчання з результатами навчання. Ці об'єкти є базовими блоками для побудови педагогічних моделей. У даній роботі детально розглянуто питання створення педагогічних моделей з використанням чотирьох типів педагогічних об’єктів електронного навчання. Представлений приклад педагогічної моделі призначений для досягнення певних освітніх цілей. Приклади моделей, створених з використанням певних об’єктів електронного навчання, представляють навчальні блоки, які використовуються залежно від контексту певної педагогічної ситуації. Педагогічні об’єкти електронного навчання та педагогічні моделі, призначені для їх застосування як засоби навчання в адаптивному середовищі електронного навчання, застосовуються в Moodle LMS відповідно до тенденції програмного забезпечення з метою допомоги викладачу або заміни деяких його функцій, а роль викладача піднімається на більш високий організаційний, педагогічний та методичний рівень. За допомогою педагогічних об’єктів електронного навчання створено три приклади педагогічних моделей: «Ранній зворотний зв’язок», «Сендвіч - метод зворотного зв’язку» та «Послідовна метафора» в LMS Moodle, які були апробовані в навчальному курсі «Моделювання навчальних курсів у Moodle» під час осіннього триместру 2021/2022 навчального року на факультеті математики та інформатики Пловдивського університету “Паїсій Хілендарський”, Болгарія.Software platforms for e-learning support various options for presenting educational content. One of the ways to organize and structure it is via so-called pedagogical patterns. They are a method for describing and sharing knowledge and practical experience. Pedagogical patterns are used to describe pedagogical situations that occur repeatedly in the learning process. In the context of e-learning systems, there are various approaches to digitalization of pedagogical patterns. The purpose of the paper is to show how to build instances of pedagogical patterns using e-learning pedagogical objects, which can be easily and conveniently used as models in an adaptive e-learning environment. An e-learning pedagogical object is an abstract concept that can be presented in the concrete form of an e-learning object, an e-learning methodological object, an e-learning object for monitoring and diagnostics or an e-learning object with learning outcomes. These objects are building blocks for constructing instances of pedagogical patterns. This paper thoroughly discusses the issue of creating instances of pedagogical patterns of the four types of e-learning pedagogical objects. The instance of a pedagogical pattern is meant to serve to create subsections of educational topics. The instances of the patterns built of e-learning objects are learning units that are used depending on the context of a particular pedagogical situation. The e-learning pedagogical objects and the pedagogical pattern instances are intended to be applied in an adaptive e-learning environment as teaching aids. Their theoretical models are applied in Moodle LMS in line with the tendency for software to assist and replace some of the teacher functions, while the teacher’s role is raised to a higher organizational, pedagogical and methodological level. Three instances of pedagogical patterns have been created through e-learning pedagogical objects: “Early Feedback”, “Feedback Sandwich” and “Consistent Metaphor” in LMS Moodle, which have been tested in the training course “Modeling of training courses in Moodle” during the autumn trimester of the academic year 2021/2022 at the Faculty of Mathematics and Informatics of Paisii Hilendarski University of Plovdiv, Bulgaria