Related papers: First-Order Tests for Toricity

We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of…

We study real steady state varieties of the dynamics of chemical reaction networks. The dynamics are derived using mass action kinetics with parametric reaction rates. The models studied are not inherently parametric in nature. Rather, our…

We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed…

We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…

We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called Chemical Organization Theory (COT) sheds new light on the longstanding complexity-stability debate. Namely, COT…

Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…

We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials…

We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…

<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…

We study the problem of checking whether an existential sentence (that is, a first-order sentence in prefix form built using existential quantifiers and all Boolean connectives) is true in a finite partially ordered set (in short, a poset).…

Toric posets are cyclic analogues of finite posets. They can be viewed combinatorially as equivalence classes of acyclic orientations generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane…

Many existing algorithms for model checking of infinite-state systems operate on constraints which are used to represent (potentially infinite) sets of states. A general powerful technique which can be employed for proving termination of…

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…

In this paper we present the first goal-driven query answering technique for first- and second-order dependencies with equality. Our technique transforms the input dependencies so that applying the chase to the output avoids many inferences…

Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…

Text corpora are widely used resources for measuring societal biases and stereotypes. The common approach to measuring such biases using a corpus is by calculating the similarities between the embedding vector of a word (like nurse) and the…

In the logical framework introduced by Grohe and Tur\'an (TOCS 2004) for Boolean classification problems, the instances to classify are tuples from a logical structure, and Boolean classifiers are described by parametric models based on…

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…

Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…