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.

The capacity defines the ultimate fidelity limits of information transmission by any system. We derive the capacity of parallel Poisson process channels to judge the relative effectiveness of neural population structures. Because the Poisson process is equivalent to a Bernoulli process having small event probabilities, we infer the capacity of multi-channel Poisson models from their Bernoulli s...

This paper analyzes an optical switch with centralized partial wavelength conversion by means of a mean field model. The model can be used to approximate the behavior of a switch with a large number of output wavelengths, and it becomes more accurate as the number of wavelengths increases. At each wavelength packets arrive according to a Markovian arrival process, and their size follows a gener...

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...