We review several occurrences of poly-Bernoulli numbers in various contexts, and discuss in particular some aspects of relations of poly-Bernoulli numbers and special values of certain zeta functions, notably multiple zeta values.

In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those functions in terms of Bernoulli functions.

In this paper we consider a discrete version of the Bernoulli convolution problem traditionally studied via functional analysis. We develop an algorithm which bounds the Bernoulli sequences, and we give a significant improvement on the best known bound.

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

PrQcedures are exhibited and analyzed for converting a sequence of iid Bernoulli variables with unknown mean p into a Bernoulli variable with mean 1/2. The efficiency of several procedures is studied.

あらまし 深層学習の重要な一要素として,レイヤーワイズの pre-trainingがある.レイヤーワイズの pre-trainingの 一つとして制約つきBoltzmannマシン (RBM)が有名である.RBMにはBernoulli-Bernoulli型とGaussian-Bernoulli 型があり,従来法の学習アルゴリズムとしてContrastive Divergence法が有名である.本発表ではBernoulli-Bernoulli 型,Gaussian-Bernoulli型の両方の最尤学習アルゴリズムと,最適化規準として新たに最大再構築確率を導入し,そ の学習アルゴリズムに焦点を当て,経験的に高速で安定に収束する補助関数法による新たな更新アルゴリズムの導出 を行う.そして,人工データによる収束性能の比較実験を行い,その挙動に対して議論する. キーワード 深層学習,制約付き B...

In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determi...