Related papers: When is Existential Quantification Conservative?
Previous work of the author [39] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures. In this paper, we give a new proof of this result via a…
Assuming that quantum states, including pure states, represent subjective degrees of belief rather than objective properties of systems, the question of what other elements of the quantum formalism must also be taken as subjective is…
We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the…
Categories can be identified -- up to isomorphism -- with polynomial comonads on Set. The left Kan extension of a functor along itself is always a comonad -- called the density comonad -- so it defines a category when its carrier is…
We study locally constant coefficients. We first study the theory of homotopy Kan extensions with locally constant coefficients in model categories, and explain how it characterizes the homotopy theory of small categories. We explain how to…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
Let $K$ be a number field, let $L$ be an algebraic (possibly infinite degree) extension of $K$, and let $O_K$ $\subset$ $O_L$ be their rings of integers. Suppose $A$ is an abelian variety defined over $K$ such that $A(K)$ is infinite and…
We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…
We describe necessary and sufficient conditions for the hereditarity of the category algebra of an infinite EI category satisfying certain combinatorial assumptions. More generally, we discuss conditions such that the left global dimension…
It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions…
This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the case of an arbitrary sequence $(q_k)$.
Using the language of double categories we generalise a classical result on finite-product-preserving left Kan extensions, by Ad\'amek and Rosick\'y, to one on left Kan extensions that preserve algebraic structures defined by `suitable'…
The capability to quantitatively distinguish quantum states is of great importance for a variety of tasks, and has recently played an important role in the study of quantum reduced dynamics and their characterization in terms of memory…
We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining…
A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising…
We discuss necessary and sufficient conditions for an auto-encoder to define a conservative vector field, in which case it is associated with an energy function akin to the unnormalized log-probability of the data. We show that the…
We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditions for induction functors associated to simple current…
It is well known that the classic {\L}o\'s-Tarski preservation theorem fails in the finite: there are first-order definable classes of finite structures closed under extensions which are not definable (in the finite) in the existential…
Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which $\hbar >0$ throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action…