相关论文: Achievement sets of conditionally convergent serie…

We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.

Conditional modeling x \to y is a central problem in machine learning. A substantial research effort is devoted to such modeling when x is high dimensional. We consider, instead, the case of a high dimensional y, where x is either low…

Every conditionally convergent series of real numbers has a divergent subseries. How many subsets of the natural numbers are needed so that every conditionally convergent series diverges on the subseries corresponding to one of these sets?…

We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely,…

We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…

Machine learning algorithms generally suffer from a problem of explainability. Given a classification result from a model, it is typically hard to determine what caused the decision to be made, and to give an informative explanation. We…

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…

We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…

A backdoor set is a set of variables of a propositional formula such that fixing the truth values of the variables in the backdoor set moves the formula into some polynomial-time decidable class. If we know a small backdoor set we can…

Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…

Sequence transformations accomplish an acceleration of convergence or a summation in the case of divergence by detecting and utilizing regularities of the elements of the sequence to be transformed. For sufficiently large indices, certain…

We give simple characterizations of the category PAsm(A) of partitioned assemblies, and of the realizability topos RT(A) over a partial combinatory algebra A. This answers the question for an 'extensional characterization' of realizability…

We study realizations of Lie algebras by vector fields. A correspondence between classification of transitive local realizations and classification of subalgebras is generalized to the case of regular local realizations. A reasonable…

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…

We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be…

We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…

Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…