相关论文: Phoneme discrimination using KS algebra I
In this paper we establish some (presumably new) interesting expressions for the composition of some well known fractional integral operators $ I^{\mu}_{a+}, D^{\mu}_{a+} $,$ I^{\gamma , \mu}_{a+}$ and also derive an integral operator…
Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
Four problems related to information divergence measures defined on finite alphabets are considered. In three of the cases we consider, we illustrate a contrast which arises between the binary-alphabet and larger-alphabet settings. This is…
We study refinements between spectral resolutions in an arbitrary II$_1$ factor $\M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an…
In the classical theory of formal languages, finite state automata allow to recognize the words of a rational subset of $\Sigma^*$ where $\Sigma$ is a set of symbols (or the alphabet). Now, given a semiring $(\K,+,.)$, one can construct…
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on…
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…
This paper presents a method to automatically synthesize the structure of an operational amplifier. It is positioned between approaches with fixed design plans and a small search space of structures and approaches with generic structural…
Recent advances in machine learning and the availability of articulatory datasets allow vocal tract synthesis to be conditioned on phonetic sequences, a primary task of articulatory speech synthesis. However, quality assessment needs a…
We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.
The central topic of this work is the categories of modules over unital quantales. The main categorical properties are established and a special class of operators, called Q-module transforms, is defined. Such operators - that turn out to…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…
The purpose of this paper is to study the algorithm FCM and some of its famous innovations, analyse and discover the method of applying hedge algebra theory that uses algebra to represent linguistic-valued variables, to FCM. Then, this…
We propose an approach for learning critical articulators for phonemes through a machine learning approach. We formulate the learning with three models trained end to end. First, we use Acoustic to Articulatory Inversion (AAI) to predict…
We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and…
We consider the Weyl algebra A (=A_n(k)) and its Rees algebra B with respect to the Bernstein filtration. The homogenisation of a differential operator in A is an element in B. In this paper we establish the validity of the division theorem…
New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer $m$. The eigenstates of the Hamiltonian…
Divided difference operators are degree-reducing operators on the cohomology of flag varieties that are used to compute algebraic invariants of the ring (for instance, structure constants). We identify divided difference operators on the…