The Discrete Type-II Half-Logistic Exponential Distribution with Applications to COVID-19 Data

We propose a new two-parameter discrete model, called discrete Type-II half-logistics exponential (DTIIHLE) distribution using the survival discretization approach. The DTIIHLE distribution can be utilized to model COVID-19 data. The model parameters are estimated using the maximum likelihood method. A simulation study is conducted to evaluate the performance of the maximum likelihood estimators. The usefulness of the proposed distribution is evaluated using two real-life COVID-19 data sets. The DTIIHLE distribution provides a superior fit to COVID-19 data as compared with competitive discrete models including the discrete-Pareto, discrete Burr-XII, discrete log-logistic, discrete-Lindley, discrete-Rayleigh, discrete inverse-Rayleigh, and natural discrete-Lindley.

A Note on Variational Principle of Subsets for Nonautonomous Dynamical Systems

In this paper, we introduce measure-theoretic for Borel probability measures to characterize upper and lower Katok measure-theoretic entropies in discrete type and the measure-theoretic entropy for arbitrary Borel probability measure in nonautonomous case. Then we establish new variational principles for Bowen topological entropy for nonautonomous dynamical systems. JEL classification numbers: 37A35. Keywords: Nonautonomous, Measure-theoretical entropies, Variational principles.

Intercultural Dialogue via Music: Translating the Beatles’ Legacy into Contemporary Pop Culture

Cultural translation phenomena are per se an intercultural product. Exchange and interaction take place every day in our globalized world. Especially with respect to music, a translational perspective can broaden the horizon of research projects in a very fruitful way. Music always combines elements from different cultures, periods and styles and can, in that way, serve as a medium of intercultural dialogue, which affects the participants of the dialogue not only on a rational, but also on an emotional level – and helps to cross borders and build bridges between different cultures. In my analysis, I take a look at the legacy of the Beatles and how it is performatively unfolded by the Spanish-Chilean band the Recalls, based in Germany. Different cultures intermingle in such appropriation and show a joyful (postmodern) handling to create a very special, discrete type of music and self-staging. Thus, music as a product of intercultural dialogue can become a chance for a successful interaction between different cultures.

Multidimensional sampling theorems for multivariate discrete transforms

This paper is devoted to the establishment of two-dimensional sampling theorems for discrete transforms, whose kernels arise from second order partial difference equations. We define a discrete type partial difference operator and investigate its spectral properties. Green’s function is constructed and kernels that generate orthonormal basis of eigenvectors are defined. A discrete Kramer-type lemma is introduced and two sampling theorems of Lagrange interpolation type are proved. Several illustrative examples are depicted. The theory is extendible to higher order settings.

Bacinella, a discrete type of Mesozoic calcimicrobial structure

The controversy surrounding Bacinella irregularis Radoičić, 1959, and Lithocodium aggregatum Elliott, 1956, has involved both sedimentologists and paleontologists. Arguments to exclude them from the Codiaceae are reviewed. The same arguments may be advanced to exclude their ascription to most other organisms. The only hypothesis resisting all elements of disproof is that of a consortium involving microbial communities. Accordingly, these structures are treated here as biosedimentary structures, namely bacinella structures, and not as taxa. One of the features specific to the organisms that built these structures is their strong corroding ability, as shown by the examples of fossils partly or fully cannibalized. This represents one state of corrosion beyond surficial etching and borings. Besides their capacity to corrode calcareous substrates, these microbial organisms formed nodules or oncoids and even built biostromes, which, depending on their stage of development, may have formed soft, firm or even hard substrates. However, to our knowledge, microbial communities contributing to bacinella structures never built up any bioherm. To complete this summary review, a building-block model that coherently takes into account most architectural variations is presented in the form of a figure sketch. The endolithic foraminifer Troglotella incrustans, which is commonly found associated with bacinella structures, is not an encruster or a borer. Lastly, contrary to certain erroneous hypotheses, no major bacinella episode has been ever found coeval with any significant Oceanic Anoxic Event.

Limitations of Incentive Compatibility on Discrete Type Spaces

In the design of incentive compatible mechanisms, a common approach is to enforce incentive compatibility as constraints in programs that optimize over feasible mechanisms. Such constraints are often imposed on sparsified representations of the type spaces, such as their discretizations or samples, in order for the program to be manageable. In this work, we explore limitations of this approach, by studying whether all dominant strategy incentive compatible mechanisms on a set T of discrete types can be extended to the convex hull of T.Dobzinski, Fu and Kleinberg (2015) answered the question affirmatively for all settings where types are single dimensional. It is not difficult to show that the same holds when the set of feasible outcomes is downward closed. In this work we show that the question has a negative answer for certain non-downward-closed settings with multi-dimensional types. This result should call for caution in the use of the said approach to enforcing incentive compatibility beyond single-dimensional preferences and downward closed feasible outcomes.