Related papers: Pretentiously detecting power cancellation
Feature selection has attracted significant attention in data mining and machine learning in the past decades. Many existing feature selection methods eliminate redundancy by measuring pairwise inter-correlation of features, whereas the…
We start to investigate how small changes on the definition of ordinary means affect their properties. Especially the property of being a mean. In that direction we are looking for weakenings of the basic defining property of means. Hence…
The notion of distortion in social choice problems has been defined to measure the loss in efficiency -- typically measured by the utilitarian social welfare, the sum of utilities of the participating agents -- due to having access only to…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…
Anomalous cancellation of fractions is a mathematically inaccurate method where cancelling the common digits of the numerator and denominator correctly reduces it. While it appears to be accidentally successful, the property of anomalous…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…
We shed doubt on a commonly used manipulation in computing the partition function for a matrix valued operator together with its attendant invocation of the multiplicative anomaly.
We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is "pretentious". This leads to applications in the circle method, and a natural interpretation of the local-global…
A choice of optimization objective is immensely pivotal in the design of a recommender system as it affects the general modeling process of a user's intent from previous interactions. Existing approaches mainly adhere to three categories of…
In this paper, by using a general result on the monotonicity of quotients of power series, our aim is to prove some monotonicity and convexity results for the modified Struve functions. Moreover, as consequences of the above mentioned…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by…
The first-order theory of MALL (multiplicative, additive linear logic) over only equalities is an interesting but weak logic since it cannot capture unbounded (infinite) behavior. Instead of accounting for unbounded behavior via the…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Let $\pi$ be an irreducible unitary representation of a finitely generated nonabelian free group $\Gamma$; suppose $\pi$ is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a…
Let $f:\mathbb{N}\to \mathbb{D}$ be a multiplicative function. Under the merely necessary assumption that $f$ is non-pretentious (in the sense of Granville and Soundararajan), we show that for any pair of distinct integer shifts $h_1,h_2$…
It is quite well-known from Kurt Godel's (1931) ground-breaking result on the Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are…