Related papers: Dream of a Christmas lecture
The reference links to the modern classical umbral calculus before that known as blissardian symbolic method are numerous. Rota founded and then extended finite operator calculus has links to references which are plenty numerous. The…
Computability logic (CoL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently introduced semantical platform and ambitious program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth…
This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…
As quantum theory celebrates its 100th birthday, spectacular successes are mixed with outstanding puzzles and promises of new technologies. This article reviews both the successes of quantum theory and the ongoing debate about its…
We review some approaches and philosophies of causal inference coming from sociology, economics, computer science, cognitive science, and statistics
The UDC (Universal Decimal Classification) is not only a classification language with a long history; it also presents a complex cognitive system worthy of the attention of complexity theory. The elements of the UDC: classes, auxiliaries,…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…
Reinforcement learning (RL) often faces the challenges of uninformed search problems where the agent should explore without access to the domain knowledge such as characteristics of the environment or external rewards. To tackle these…
Duality is the heart of advanced microeconomics. It exists everywhere throughout advanced microeconomics, from the beginning of consumer theory to the end of production theory. The complex, circular relationships among various theoretical…
Continual learning requires learning incremental tasks with dynamic data distributions. So far, it has been observed that employing a combination of contrastive loss and distillation loss for training in continual learning yields strong…
We introduce derivative sensitivity, an analogue to local sensitivity for continuous functions. We use this notion in an analysis that determines the amount of noise to be added to the result of a database query in order to obtain a certain…
The prescriptions of our two most prominent strands of decision theory, evidential and causal, differ in a general class of problems known as Newcomb problems. In these, evidential decision theory prescribes choosing a dominated act.…
In an earlier experiment, participants played a perfect information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in each game,…
The sound of our speech is influenced by the places we come from. Great Britain contains a wide variety of distinctive accents which are of interest to linguistics. In particular, the "a" vowel in words like "class" is pronounced…
The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…