Bounded Abstract Effects

Effect systems have been a subject of active research for nearly four decades, with the most notable practical example being checked exceptions in programming languages such as Java. While many exception systems support abstraction, aggregation, and hierarchy (e.g., via class declaration and subclassing mechanisms), it is rare to see such expressive power in more generic effect systems. We designed an effect system around the idea of protecting system resources and incorporated our effect system into the Wyvern programming language. Similar to type members, a Wyvern object can have effect members that can abstract lower-level effects, allow for aggregation, and have both lower and upper bounds, providing for a granular effect hierarchy. We argue that Wyvern’s effects capture the right balance of expressiveness and power from the programming language design perspective. We present a full formalization of our effect-system design, showing that it allows reasoning about authority and attenuation. Our approach is evaluated through a security-related case study.

Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian

We provide bounds for the sequence of eigenvalues { λ i ⁢ ( Ω ) } i {\{\lambda_{i}(\Omega)\}_{i}} of the Dirichlet problem L Δ ⁢ u = λ ⁢ u ⁢ in ⁢ Ω , u = 0 ⁢ in ⁢ ℝ N ∖ Ω , L_{\Delta}u=\lambda u\text{ in }\Omega,\quad u=0\text{ in }\mathbb{R}^{N}% \setminus\Omega, where L Δ {L_{\Delta}} is the logarithmic Laplacian operator with Fourier transform symbol 2 ⁢ ln ⁡ | ζ | {2\ln\lvert\zeta\rvert} . The logarithmic Laplacian operator is not positively defined if the volume of the domain is large enough. In this article, we obtain the upper and lower bounds for the sum of the first k eigenvalues by extending the Li–Yau method and Kröger’s method, respectively. Moreover, we show the limit of the quotient of the sum of the first k eigenvalues by k ⁢ ln ⁡ k {k\ln k} is independent of the volume of the domain. Finally, we discuss the lower and upper bounds of the k-th principle eigenvalue, and the asymptotic behavior of the limit of eigenvalues.

Communicating Uncertainty in National Security Intelligence: Expert and Non-expert Interpretations of and Preferences for Verbal and Numeric Formats

Organizations in several domains including national security intelligence communicate judgments under uncertainty using verbal probabilities (e.g., likely) instead of numeric probabilities (e.g., 75% chance), despite research indicating that the former have variable meanings across individuals. In the intelligence domain, uncertainty is also communicated using terms such as low, moderate, or high to describe the analyst’s confidence level. However, little research has examined how intelligence professionals interpret these terms and whether they prefer them to numeric uncertainty quantifiers. In two experiments (N = 481 and 624, respectively), uncertainty communication preferences of expert (n = 41 intelligence analysts inExperiment 1) and non-expert intelligence consumers were elicited. We examined which format participants judged to be more informative and simpler to process. We further tested whether participants treated probability and confidence as independent constructs and whether participants provided coherent numeric probability translations of verbal probabilities. Results showed that whereas most non-experts favored the numeric format, experts were about equally split, and most participants in both samples regarded the numeric format as more informative.Experts and non-experts consistently conflated probability and confidence. For instance, confidence intervals inferred from verbal confidence terms had a greater effect on the location of the estimate than the width of the estimate, contrary to normative expectation. Approximately ¼ of experts and over ½ of non-experts provided incoherent numeric probability translations of best estimates and lower and upper bounds when elicitations were spaced by intervening tasks.

Estimating vertex-degree-based energies

Introduction/purpose: In the current literature, several dozens of vertex-degree-based (VDB) graph invariants are being studied. To each such invariant, a matrix can be associated. The VDB energy is the energy (= sum of the absolute values of the eigenvalues) of the respective VDB matrix. The paper examines some general properties of the VDB energy of bipartite graphs. Results: Estimates (lower and upper bounds) are established for the VDB energy of bipartite graphs in which there are no cycles of size divisible by 4, in terms of ordinary graph energy. Conclusion: The results of the paper contribute to the spectral theory of VDB matrices, especially to the general theory of VDB energy.

Forecasting Model to Predict the Spreading of the COVID-19 Outbreak in Turkey

This study aimed to forecast the future of the COVID-19 outbreak parameters such as spreading, case fatality, and case recovery values based on the publicly available epidemiological data for Turkey. We first performed different forecasting methods including Facebook's Prophet, ARIMA and Decision Tree. Based on the metrics of MAPE and MAE, Facebook's Prophet has the most effective forecasting model. Then, using Facebook's Prophet, we generated a forecast model for the evolution of the outbreak in Turkey fifteen-days-ahead. Based on the reported confirmed cases, the simulations suggest that the total number of infected people could reach 4328083 (with lower and upper bounds of 3854261 and 4888611, respectively) by April 23, 2021. Simulation forecast shows that death toll could reach 35656 with lower and upper bounds of 34806 and 36246, respectively. Besides, our findings suggest that although more than 86.38% growth in recovered cases might be possible, the future active cases will also significantly increase compared to the current active cases. This time series analysis indicates an increase trend of the COVID-19 outbreak in Turkey in the near future. Altogether, the present study highlights the importance of an efficient data-driven forecast model analysis for the simulation of the pandemic transmission and hence for further implementation of essential interventions for COVID-19 outbreak.

Limit Cycles Appearing From Piecewise Smooth Perturbations to a Reversible Nonlinear Center

This paper deals with the limit cycle bifurcation from a reversible differential center of degree [Formula: see text] due to small piecewise smooth homogeneous polynomial perturbations. By using the averaging theory for discontinuous systems and the complex method based on the Argument Principle, we obtain lower and upper bounds for the maximum number of limit cycles bifurcating from the period annulus around the center of the unperturbed system.

Regarding Two Conjectures on Clique and Biclique Partitions

For a graph $G$, let $cp(G)$ denote the minimum number of cliques of $G$ needed to cover the edges of $G$ exactly once. Similarly, let $bp_k(G)$ denote the minimum number of bicliques (i.e. complete bipartite subgraphs of $G$) needed to cover each edge of $G$ exactly $k$ times. We consider two conjectures – one regarding the maximum possible value of $cp(G) + cp(\overline{G})$ (due to de Caen, Erdős, Pullman and Wormald) and the other regarding $bp_k(K_n)$ (due to de Caen, Gregory and Pritikin). We disprove the first, obtaining improved lower and upper bounds on $\max_G cp(G) + cp(\overline{G})$, and we prove an asymptotic version of the second, showing that $bp_k(K_n) = (1+o(1))n$.

The probability of joint monophyly of all species in an arbitrary species tree.

Monophyly is a feature of a set of genetic lineages in which every lineage in the set is more closely related to all other members of the set than it is to any lineage outside the set. Multiple sets of lineages that are separately monophyletic are said to be reciprocally monophyletic, or jointly monophyletic. The prevalence of reciprocal monophyly, or joint monophyly, has been used to evaluate phylogenetic and phylogeographic hypotheses, as well as to delimit species. These applications often make use of a probability of joint monophyly under models of gene lineage evolution. Studies in coalescent theory have computed this joint monophyly probability for small numbers of separate groups in arbitrary species trees, and for arbitrary numbers of separate groups in trivial species trees. Here, generalizing existing results on monophyly probabilities under the multispecies coalescent, we derive the probability of joint monophyly for arbitrary numbers of separate groups in arbitrary species trees. We illustrate how our result collapses to previously examined cases. We also study the effect of tree height, sample size, and number of species on the probability of joint monophyly. The result also enables computation of relatively simple lower and upper bounds on the joint monophyly probability. Our results expand the scope of joint monophyly calculations beyond small numbers of species, subsuming past formulas that have been used in simpler cases.

Inequalities for Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal Type f–Divergences

In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.