The Most Influential Paper Gerard Salton Never Wrote

Gerard Salton is often credited with developing the vector space model (VSM) for information retrieval (IR). Citations to Salton give the impression that the VSM must have been articulated as an IR model sometime between 1970 and 1975. However, the VSM as it is understood today evolved over a longer time period than is usually acknowledged, and an articulation of the model and its assumptions did not appear in print until several years after those assumptions had been criticized and alternative models proposed. An often cited overview paper titled ???A Vector Space Model for Information Retrieval??? (alleged to have been published in 1975) does not exist, and citations to it represent a confusion of two 1975 articles, neither of which were overviews of the VSM as a model of information retrieval. Until the late 1970s, Salton did not present vector spaces as models of IR generally but rather as models of specifi c computations. Citations to the phantom paper refl ect an apparently widely held misconception that the operational features and explanatory devices now associated with the VSM must have been introduced at the same time it was fi rst proposed as an IR model.published or submitted for publicatio

The Zeroth Law of Thermodynamics and Volume-Preserving Conservative Dynamics with Equilibrium Stochastic Damping

We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase space while in equilibrium with a heat bath. The theory generalizes underdamped mechanical equilibrium: $dx=gdt+\{-D\nabla\phi dt+\sqrt{2D}dB(t)\}$, with $\nabla\cdot g=0$ and $\{\cdots\}$ respectively representing phase-volume preserving dynamics and stochastic damping. The zeroth law implies stationary distribution $u^{ss}(x)=e^{-\phi(x)}$. We find an orthogonality $\nabla\phi\cdot g=0$ as a hallmark of the system. Stochastic thermodynamics based on time reversal $\big(t,\phi,g\big)\rightarrow\big(-t,\phi,-g\big)$ is formulated: entropy production $e_p^{\#}(t)=-dF(t)/dt$; generalized "heat" $h_d^{\#}(t)=-dU(t)/dt$, $U(t)=\int_{\mathbb{R}^n} \phi(x)u(x,t)dx$ being "internal energy", and "free energy" $F(t)=U(t)+\int_{\mathbb{R}^n} u(x,t)\ln u(x,t)dx$ never increases. Entropy follows $\frac{dS}{dt}=e_p^{\#}-h_d^{\#}$. Our formulation is shown to be consistent with an earlier theory of P. Ao. Its contradistinctions to other theories, potential-flux decomposition, stochastic Hamiltonian system with even and odd variables, Klein-Kramers equation, Freidlin-Wentzell's theory, and GENERIC, are discussed.Comment: 25 page

Two variable deformations of the Chebyshev measure

We construct one and two parameter deformations of the two dimensional Chebyshev polynomials with simple recurrence coefficients, following the algorithm in [3]. Using inverse scattering techniques, we compute the corresponding orthogonality measures.Comment: 16 page