Related papers: Conservation theorems on semi-classical arithmetic

In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

In the paper we introduce a weak set theory $\mathsf{H}_{<\omega}$ . A formalization of arithmetic on finite von Neumann ordinals gives an embedding of arithmetical language into this theory. We show that $\mathsf{H}_{<\omega}$ proves a…

In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…

We prove that the NTP$_1$ property of a geometric theory $T$ is inherited by theories of lovely pairs and $H$-structures associated to $T$. We also provide a class of examples of nonsimple geometric NTP$_1$ theories.

The set theory KP$\Pi_{N+1}$ for $\Pi_{N+1}$-reflecting universes is shown to be $\Pi_{N+1}$-conservative over iterations of $\Pi_{N}$-recursively Mahlo operations for each $N\geq 2$.

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…

Under conditions of clean flow we compute the leading term in the STF when the set of periods of the energy surface is discrete. Comparing to the case of non-degenerate periodic orbits, we obtain a supplementary term which is given in terms…

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for…

In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

We study when a sound arithmetic theory $\mathcal S{\supseteq}S^1_2$ with polynomial-time decidable axioms efficiently proves the bounded consistency statements $Con_{\mathcal S{+}\phi}(n)$ for a true sentence $\phi$. Equivalently, we ask…

In much discussed work Artemov has recently shown that, for $\mathrm{PA}$, the consistency schema admits a form of uniform verification via selector proofs, despite the unprovability of the corresponding uniform consistency sentence…

In this paper, we introduce a hierarchy dividing the set $\{\sigma \in \Pi^1_2 : \Pi^1_1$-$\mathsf{CA}_0 \vdash \sigma\}$. Then, we give some characterizations of this set using weaker variants of some principles equivalent to…

The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…

We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…

This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…

We provide a general and syntactically-defined family of sequent calculi, called \emph{semi-analytic}, to formalize the informal notion of a "nice" sequent calculus. We show that any sufficiently strong (multimodal) substructural logic with…

Let $\mathsf{M}$ be the set theory obtained from $\mathsf{ZF}$ by removing the collection scheme, restricting separation to $\Delta_0$-formulae and adding an axiom asserting that every set is contained in a transitive set. Let…