By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffmans double $t$-values and Kaneko-Tsumuras double $T$-values, and establish several s
ymmetric extensions of the Kaneko-Tsumura conjecture. Some special cases are discussed in detail to determine the coefficients of involved mathematical constants in the evaluations. In particular, it can be found that several general convolution identities on the classical Bernoulli numbers and Genocchi numbers are required in this study, and they are verified by the derivative polynomials of hyperbolic tangent.
Despite the great progress achieved in unsupervised feature embedding, existing contrastive learning methods typically pursue view-invariant representations through attracting positive sample pairs and repelling negative sample pairs in the embedding
space, while neglecting to systematically explore instance relations. In this paper, we explore instance relations including intra-instance multi-view relation and inter-instance interpolation relation for unsupervised feature embedding. Specifically, we embed intra-instance multi-view relation by aligning the distribution of the distance between an instances different augmented samples and negative samples. We explore inter-instance interpolation relation by transferring the ratio of information for image sample interpolation from pixel space to feature embedding space. The proposed approach, referred to as EIR, is simple-yet-effective and can be easily inserted into existing view-invariant contrastive learning based methods. Experiments conducted on public benchmarks for image classification and retrieval report state-of-the-art or comparable performance.
In this paper, we study the alternating Euler $T$-sums and $S$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions. By using the method of residue co
mputations, we establish the explicit formulas for the (alternating) linear and quadratic Euler $T$-sums and $S$-sums, from which, the parity theorems of Hoffmans double and triple $t$-values and Kaneko-Tsumuras double and triple $T$-values are further obtained. As supplements, we also show that the linear $T$-sums and $S$-sums are expressible in terms of colored multiple zeta values. Some interesting consequences and illustrative examples are presented.
Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the smallest n
umber of nodes whose failure leads to the unrecoverable loss of the stored file. We consider upper bounds on the minimum distance and present several families of explicit FR codes attaining these bounds. The optimal constructions are derived from regular graphs and combinatorial designs, respectively.
In this paper, we study the alternating Euler $T$-sums and related sums by using the method of contour integration. We establish the explicit formulas for all linear and quadratic Euler $T$-sums and related sums. Some interesting new consequences and illustrative examples are considered.
In this paper, we study some Euler-Apery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and alternating multiple z
eta values. Based on these formulas, we further show that some other series are reducible to ln(2), zeta values, and alternating multiple zeta values by considering the contour integrals related to gamma functions, polygamma functions and trigonometric functions. The evaluations of a large number of special Euler-Apery-type series are presented as examples.
The prevailing net-centric environment demands and enables modeling and simulation to combine efforts from numerous disciplines. Software techniques and methodology, in particular service-oriented architecture, provide such an opportunity. Service-or
iented simulation has been an emerging paradigm following on from object- and process-oriented methods. However, the ad-hoc frameworks proposed so far generally focus on specific domains or systems and each has its pros and cons. They are capable of addressing different issues within service-oriented simulation from different viewpoints. It is increasingly important to describe and evaluate the progress of numerous frameworks. In this paper, we propose a novel three-dimensional reference model for a service-oriented simulation paradigm. The model can be used as a guideline or an analytic means to find the potential and possible future directions of the current simulation frameworks. In particular, the model inspects the crossover between the disciplines of modeling and simulation, service-orientation, and software/systems engineering. Based on the model, we present a comprehensive survey on several classical service-oriented simulation frameworks, including formalism-based, model-driven, interoperability protocol based, eXtensible Modeling and Simulation Framework (XMSF), and Open Grid Services Architecture (OGSA) based frameworks etc. The comparison of these frameworks is also performed. Finally the significance both in academia and practice are presented and future directions are pointed out.
This paper describes the use of the Levels of Conceptual Interoperability Model (LCIM) as a framework for conceptual modeling and its descriptive and prescriptive uses. LCIM is applied to show its potential and shortcomings in the current simulation
interoperability approaches, in particular the High Level Architecture (HLA) and Base Object Models (BOM). It emphasizes the need to apply rigorous engineering methods and principles and replace ad-hoc approaches.
