In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable representations of quivers with generic superpotential in terms of a set of invariants associated to ‘single-centered’ or ‘pure-Higgs’ states. The distinguishing fe...

We study the problem of the interpretability of arithmetic in the r.e. degrees in models of fragments of Peano arithmetic. The main result states that there is an interpretation φ 7→ φ∗ such that every formula φ of Peano arithmetic corresponds to a formula φ∗ in the language of the partial ordering of r.e. degrees such that for every model N of Σ4-induction, N |= φ if and only if RN |= φ∗, wher...

The rules of formation of a logistic system are by definition1) such that the notion of formula, well-formed formula or sentence, determined by these rules, is effectively decidable. However, I am not convinced that the arguments brought forth by Church2) to the effect that sentencehood has to be an effectively decidable notion for any system that may be used for communication purposes are conc...

There exists a model in a countable language having a unique element which is not definable in Lω1,ω. We answer problem 10.12 from the updated version of Arnie Miller’s problem list, [3]. Definition For a structure M and a ∈ M, we say that a is definable over Lω1,ω if there is a formul ψ ∈ Lω1,ω such that for all b ∈ M a = b ⇔ M |= ψ(b). Theorem 0.1 There is a countable language L and a model M...

We give an exposition of Dwork’s construction Frobenius structures associated to generalized hypergeometric equations via the interpretation latter due Gelfand–Kapranov–Zelevinsky in language A A</mm...

This paper presents a high-level compiler that generates hardware implementations of the discrete Fourier transform (DFT) from mathematical specifications. The matrix formula input language captures not only the DFT calculation but also the implementation options at the algorithmic and architectural levels. By selecting the appropriate formula, the resulting hardware implementations (described ...

We present a technique that enables the use of finite model finding to check the satisfiability of certain formulas whose intended models are infinite. Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which rea...

Modeling abstract behavior is essential for intelligent agents under incomplete and uncertain environments. In this paper, we extend Propositional Dynamic Logic (PDL) to Propositional Abstract Dynamic Logic (PADL) for modeling abstract behavior in two aspects. On the one hand, we treat the task of finding a plan to achieve a certain formula as an abstract action. On the other hand, we explicitl...

In this paper, we present some ideas about possible directions of a new interpretation of the Okapi BM25 ranking formula. In particular, we have focused on a full bayesian approach for deriving a smoothed formula that takes into account a-priori knowledge on the probability of terms. In fact, most of the efforts in improving the BM25 were done in capturing the language model (frequencies, lengt...