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A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a…
The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the…
Using standard methods (due to Janson, Stein-Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects ${\cal A}$ being "covered" by at most one…
We consider the problem of optimizing expensive black-box functions over discrete spaces (e.g., sets, sequences, graphs). The key challenge is to select a sequence of combinatorial structures to evaluate, in order to identify…
Ensuring the effectiveness of search queries while protecting user privacy remains an open issue. When an Information Retrieval System (IRS) does not protect the privacy of its users, sensitive information may be disclosed through the…
In the 1980s a new, extraordinarily productive way of reasoning about algorithms emerged. In this paper, we introduce the term "outcome reasoning" to refer to this form of reasoning. Though outcome reasoning has come to dominate areas of…
This paper studies an open question in the warehouse problem where a merchant trading a commodity tries to find an optimal inventory-trading policy to decide on purchase and sale quantities during a fixed time horizon in order to maximize…
With the rapid development of recommender systems, accuracy is no longer the only golden criterion for evaluating whether the recommendation results are satisfying or not. In recent years, diversity has gained tremendous attention in…
Document retrieval is one of the best established information retrieval activities since the sixties, pervading all search engines. Its aim is to obtain, from a collection of text documents, those most relevant to a pattern query. Current…
The prediction of the N-box paradox, that whichever box is opened will contain the record of the particle having passed through it, is traced to a failure to specify whether the other boxes are distinguishable or indistinguishable. These…
Topic taxonomy discovery aims at uncovering topics of different abstraction levels and constructing hierarchical relations between them. Unfortunately, most of prior work can hardly model semantic scopes of words and topics by holding the…
Wormholes are intriguing classical solutions in General Relativity, that have fascinated theoretical physicists for decades. In recent years, especially in Holography, gravitationalWormhole geometries have found a new life in many…
Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries.…
Cuckoo search (CS) is a relatively new algorithm, developed by Yang and Deb in 2009, and CS is efficient in solving global optimization problems. In this paper, we review the fundamental ideas of cuckoo search and the latest developments as…
We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them.…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…