We present a novel tractable generative model that extends Sum-Product Networks (SPNs) and significantly boosts their power. We call it Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate conditional distributions into the model by direct computation using quotient nodes, e.g. P (A|B)= (A,B) P (B) . We provide sufficient conditions for the tractability of SPQNs that gene...

Let X be a smooth projective curve over C which admits a finite group G of automorphisms. Then G×G acts on the product surface Y = X ×X, and so for each subgroup H ≤ G×G, the quotient Z = H\Y is a normal algebraic surface. Here we shall restrict attention to the case that the subgroup H is the graph of a group automorphism α ∈ Aut(G) of G, i.e. H = ∆α = {(g, α(g)) : g ∈ G}; we propose to call t...

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

in this research, we investigated the glottal wave of persian vowels, using electroglottography. in the first level, the properties of vowels glottal wave were analyzed. in the second level, the glottal wave between male and female speakers were  compared. contact quotient is the glottal wave parameter which was analyzed. data included six persian vowels and the glottal wave recorded using elec...

The purpose of this paper is to draw attention to the widespread occurrence of quotient spaces in statistical work. Quotient spaces are intrinsic to probability distributions, residuals and interaction in linear models, covariance functions and variograms of stochastic processes, etc. The theme is that explicit recognition of the quotient space can offer surprising conceptual simplification. Th...

Let the special linear group G := SL 2 act regularly on a Q-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U/ /N with a divisorial quotient space, then the intersection W (U) of all translates g·U is open in X and admits a good quotient W (U) → W (U)/ /G with a divisorial quotien...

Motion planning problems can be simplified by admissible projections of the configuration space to sequences lower-dimensional quotient-spaces, called sequential simplifications. To exploit simplifications, we present Quotient-space Rapidly-exploring Random Trees (QRRT) algorithm. QRRT takes as input a start and goal configuration, sequence quotient-spaces. The algorithm grows trees on quotient...

The aim of this paper is to analyze and compare two time–domain parameterization methods of the glottal flow waveform on a large intensity range. The first parameter is the classical closing quotient which indicates the portion of a period where the glottis is closing. The second parameter is the recently developed normalized amplitude quotient which is defined using the ratio between the maxim...