Related papers: Pretentiously detecting power cancellation
Let $A$ be a commutative Noetherian ring of characteristic $p>0$, such that $\dim(A)=d$. Let $P$ be a projective $A[T_1,...,T_n]$-module of rank $d$. We show that $P$ is cancellative if and only if $P/<T_1,...,T_n>P$ is cancellative. We…
Deep models have been widely and successfully used in image manipulation detection, which aims to classify tampered images and localize tampered regions. Most existing methods mainly focus on extracting global features from tampered images,…
We embed the somewhat unusual multiplicative function, which was serendipitously discovered in 2010 during a study of mutually unbiased bases in the Hilbert space of quantum physics, into two families of multiplicative functions that we…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
Calculating the primordial bispectrum predicted by a model of inflation and comparing it to what we see in the sky is very computationally intensive, necessitating layers of approximations and limiting the models which can be constrained.…
Previous researches have shown that learning multiple representations for polysemous words can improve the performance of word embeddings on many tasks. However, this leads to another problem. Several vectors of a word may actually point to…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering…
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors' new proof of Halasz's theorem on mean values to this simpler setting. Several of the technical difficulties that arise over…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
Science consists on conceiving hypotheses, confronting them with empirical evidence, and keeping only hypotheses which have not yet been falsified. Under deductive reasoning they are conceived in view of a theory and confronted with…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
Theories with both electric and magnetic charges ("mutually non-local" theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent,…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…