pinecone/core-2020-05-10-deduplication huggingface dataset:
Need Polynomial Systems be Doubly-exponential?

Polynomial Systems, or at least their algorithms, have the reputation of
being doubly-exponential in the number of variables [Mayr and Mayer, 1982],
[Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that
number of zeros of a zero-dimensional system is singly-exponential in the
number of variables. How should this contradiction be reconciled?
  We first note that [Mayr and Ritscher, 2013] shows that the doubly
exponential nature of Gr\"{o}bner bases is with respect to the dimension of the
ideal, not the number of variables. This inspires us to consider what can be
done for Cylindrical Algebraic Decomposition which produces a
doubly-exponential number of polynomials of doubly-exponential degree.
  We review work from ISSAC 2015 which showed the number of polynomials could
be restricted to doubly-exponential in the (complex) dimension using McCallum's
theory of reduced projection in the presence of equational constraints. We then
discuss preliminary results showing the same for the degree of those
polynomials. The results are under primitivity assumptions whose importance we
illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text
  overlap with arXiv:1605.0249
Recursive double-size fixed precision arithmetic

International audienceThis work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture)
On the computation of confluent hypergeometric functions for large imaginary part of parameters b and z

The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-42432-3_30We present an efficient algorithm for the confluent hypergeometric functions when the imaginary part of b and z is large. The algorithm is based on the steepest descent method, applied to a suitable representation of the confluent hypergeometric functions as a highly oscillatory integral, which is then integrated by using various quadrature methods. The performance of the algorithm is compared with open-source and commercial software solutions with arbitrary precision, and for many cases the algorithm achieves high accuracy in both the real and imaginary parts. Our motivation comes from the need for accurate computation of the characteristic function of the Arcsine distribution or the Beta distribution; the latter being required in several financial applications, for example, modeling the loss given default in the context of portfolio credit risk.Peer ReviewedPostprint (author's final draft
Linking Mathematical Software in Web Archives

The Web is our primary source of all kinds of information today. This
includes information about software as well as associated materials, like
source code, documentation, related publications and change logs. Such data is
of particular importance in research in order to conduct, comprehend and
reconstruct scientific experiments that involve software. swMATH, a
mathematical software directory, attempts to identify software mentions in
scientific articles and provides additional information as well as links to the
Web. However, just like software itself, the Web is dynamic and most likely the
information on the Web has changed since it was referenced in a scientific
publication. Therefore, it is crucial to preserve the resources of a software
on the Web to capture its states over time.
  We found that around 40% of the websites in swMATH are already included in an
existing Web archive. Out of these, 60% of contain some kind of documentation
and around 45% even provide downloads of software artifacts. Hence, already
today links can be established based on the publication dates of corresponding
articles. The contained data enable enriching existing information with a
temporal dimension. In the future, specialized infrastructure will improve the
coverage of software resources and allow explicit references in scientific
publications.Comment: ICMS 2016, Berlin, German
A primer on quantum fluids

This book introduces the theoretical description and properties of quantum
fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a
minor extent, superfluid helium, but the underlying concepts are relevant to
other forms of quantum fluids such as polariton and photonic condensates. The
book is pitched at the level of advanced undergraduates and early postgraduate
students, aiming to provide the reader with the knowledge and skills to develop
their own research project on quantum fluids. Indeed, the content for this book
grew from introductory notes provided to our own research students. It is
assumed that the reader has prior knowledge of undergraduate mathematics and/or
physics; otherwise, the concepts are introduced from scratch, often with
references for directed further reading.Comment: 132 pages. Published as SpringerBriefs in Physics book. Typos
  corrected in this versio
Mathematical Theory Exploration in Theorema: Reduction Rings

In this paper we present the first-ever computer formalization of the theory
of Gr\"obner bases in reduction rings, which is an important theory in
computational commutative algebra, in Theorema. Not only the formalization, but
also the formal verification of all results has already been fully completed by
now; this, in particular, includes the generic implementation and correctness
proof of Buchberger's algorithm in reduction rings. Thanks to the seamless
integration of proving and computing in Theorema, this implementation can now
be used to compute Gr\"obner bases in various different domains directly within
the system. Moreover, a substantial part of our formalization is made up solely
by "elementary theories" such as sets, numbers and tuples that are themselves
independent of reduction rings and may therefore be used as the foundations of
future theory explorations in Theorema.
  In addition, we also report on two general-purpose Theorema tools we
developed for an efficient and convenient exploration of mathematical theories:
an interactive proving strategy and a "theory analyzer" that already proved
extremely useful when creating large structured knowledge bases.Comment: submitted to CICM 2015 (Conference on Intelligent Computer
  Mathematics
Satisfiability Checking meets Symbolic Computation (Project Paper)

Symbolic Computation and Satisfiability Checking are two research areas, both
having their individual scientific focus but sharing also common interests in
the development, implementation and application of decision procedures for
arithmetic theories. Despite their commonalities, the two communities are
rather weakly connected. The aim of our newly accepted SC-square project
(H2020-FETOPEN-CSA) is to strengthen the connection between these communities
by creating common platforms, initiating interaction and exchange, identifying
common challenges, and developing a common roadmap from theory along the way to
tools and (industrial) applications. In this paper we report on the aims and on
the first activities of this project, and formalise some relevant challenges
for the unified SC-square community
On the Power of Simple Reductions for the Maximum Independent Set
  Problem

Reductions---rules that reduce input size while maintaining the ability to
compute an optimal solution---are critical for developing efficient maximum
independent set algorithms in both theory and practice. While several simple
reductions have previously been shown to make small domain-specific instances
tractable in practice, it was only recently shown that advanced reductions (in
a measure-and-conquer approach) can be used to solve real-world networks on
millions of vertices [Akiba and Iwata, TCS 2016]. In this paper we compare
these state-of-the-art reductions against a small suite of simple reductions,
and come to two conclusions: just two simple reductions---vertex folding and
isolated vertex removal---are sufficient for many real-world instances, and
further, the power of the advanced rules comes largely from their initial
application (i.e., kernelization), and not their repeated application during
branch-and-bound. As a part of our comparison, we give the first experimental
evaluation of a reduction based on maximum critical independent sets, and show
it is highly effective in practice for medium-sized networks.Comment: 13 pages; 1 figure; 3 tables; Appeared at the 22nd International
  Conference on Computing and Combinatorics (COCOON 2016
From Preemptive to Non-preemptive Scheduling Using Rejections

International audienceWe study the classical problem of scheduling a set of independent jobs with release dates on a single machine. There exists a huge literature on the preemptive version of the problem, where the jobs can be interrupted at any moment. However, we focus here on the non-preemptive case, which is harder, but more relevant in practice. For instance, the jobs submitted to actual high performance platforms cannot be interrupted or migrated once they start their execution (due to prohibitive management overhead). We target on the minimization of the total stretch objective, defined as the ratio of the total time a job stays in the system (waiting time plus execution time), normalized by its processing time. Stretch captures the quality of service of a job and the minimum total stretch reflects the fairness between the jobs. So far, there have been only few studies about this problem, especially for the non-preemptive case. Our approach is based to the usage of the classical and efficient for the preemptive case shortest remaining processing time (SRPT) policy as a lower bound. We investigate the (offline) transformation of the SRPT schedule to a non-preemptive schedule subject to a recently introduced resource augmentation model, namely the rejection model according to which we are allowed to reject a small fraction of jobs. Specifically, we propose a 2 ǫ-approximation algorithm for the total stretch minimization problem if we allow to reject an ǫ-fraction of the jobs, for any ǫ > 0. This result shows that the rejection model is more powerful than the other resource augmentations models studied in the literature, like speed augmentation or machine augmentation, for which non-polynomial or non-scalable results are known. As a byproduct, we present a O(1)-approximation algorithm for the total flow-time minimization problem which also rejects at most an \epsilon-fraction of jobs
Combinatorial Scoring of Phylogenetic Networks

Construction of phylogenetic trees and networks for extant species from their
characters represents one of the key problems in phylogenomics. While solution
to this problem is not always uniquely defined and there exist multiple methods
for tree/network construction, it becomes important to measure how well the
constructed networks capture the given character relationship across the
species.
  In the current study, we propose a novel method for measuring the specificity
of a given phylogenetic network in terms of the total number of distributions
of character states at the leaves that the network may impose. While for binary
phylogenetic trees, this number has an exact formula and depends only on the
number of leaves and character states but not on the tree topology, the
situation is much more complicated for non-binary trees or networks.
Nevertheless, we develop an algorithm for combinatorial enumeration of such
distributions, which is applicable for arbitrary trees and networks under some
reasonable assumptions.Comment: 12 pages; 3 figure
A Parameterized Algorithm for Bounded-Degree Vertex Deletion

The $d$-bounded-degree vertex deletion problem, to delete at most $k$
vertices in a given graph to make the maximum degree of the remaining graph at
most $d$, finds applications in computational biology, social network analysis
and some others. It can be regarded as a special case of the $(d+2)$-hitting
set problem and generates the famous vertex cover problem. The
$d$-bounded-degree vertex deletion problem is NP-hard for each fixed $d\geq 0$.
In terms of parameterized complexity, the problem parameterized by $k$ is
W[2]-hard for unbounded $d$ and fixed-parameter tractable for each fixed $d\geq
0$. Previously, (randomized) parameterized algorithms for this problem with
running time bound $O^*((d+1)^k)$ are only known for $d\leq2$. In this paper,
we give a uniform parameterized algorithm deterministically solving this
problem in $O^*((d+1)^k)$ time for each $d\geq 3$. Note that it is an open
problem whether the $d'$-hitting set problem can be solved in $O^*((d'-1)^k)$
time for $d'\geq 3$. Our result answers this challenging open problem
affirmatively for a special case. Furthermore, our algorithm also gets a
running time bound of $O^*(3.0645^k)$ for the case that $d=2$, improving the
previous deterministic bound of $O^*(3.24^k)$
Locality-Sensitive Hashing without False Negatives for l_p

In this paper, we show a construction of locality-sensitive hash functions
without false negatives, i.e., which ensure collision for every pair of points
within a given radius $R$ in $d$ dimensional space equipped with $l_p$ norm
when $p \in [1,\infty]$. Furthermore, we show how to use these hash functions
to solve the $c$-approximate nearest neighbor search problem without false
negatives. Namely, if there is a point at distance $R$, we will certainly
report it and points at distance greater than $cR$ will not be reported for
$c=\Omega(\sqrt{d},d^{1-\frac{1}{p}})$. The constructed algorithms work: - with
preprocessing time $\mathcal{O}(n \log(n))$ and sublinear expected query time,
- with preprocessing time $\mathcal{O}(\mathrm{poly}(n))$ and expected query
time $\mathcal{O}(\log(n))$. Our paper reports progress on answering the open
problem presented by Pagh [8] who considered the nearest neighbor search
without false negatives for the Hamming distance.Comment: 11 pages, 2 figures, COCOON 201
Specialized review selection using topic models

Online reviews and comments about a product or service are an invaluable source of information for users to assist them in making purchase decisions. In recent years, the research in review selection has attracted considerable attention. Many of the existing works attempted to identify a number of statistical features related to review text such as word count (Mudambi and Schuff 2010) and hidden relations between these features and review quality by using supervised learning methods such as classification techniques. However, one significant drawback of these works is that they do not take the review content into consideration. A recent work has been proposed to find specialized reviews that focus on a specific feature based on similar words to the feature (Long et al. 2014). In this paper, we propose a topic model based method which selects reviews by considering both similar words and related words from a topic model such as LDA model. The conducted experiment has proven that those related words generated from LDA have a great contribution to the task of finding helpful reviews on a specified feature
The experience-driven perspective

Ultimately, content is generated for the player. But so far, our algorithms\ud
have not taken specific players into account. Creating computational models of a\ud
player’s behaviour, preferences, or skills is called player modelling. With a model\ud
of the player, we can create algorithms that create content specifically tailored to\ud
that player. The experience-driven perspective on procedural content generation provides\ud
a framework for content generation based on player modelling; one of the most\ud
important ways of doing this is to use a player model in the evaluation function for\ud
search-based PCG. This chapter discusses different ways of collecting and encoding\ud
data about the player, primarily player experience, and ways of modelling this data.\ud
It also gives examples of different ways in which such models can be used.peer-reviewe
Evaluating content generators

Evaluating your content generator is a very important task, but difficult to\ud
do well. Creating a game content generator in general is much easier than creating\ud
a good game content generator—but what is a “good” content generator? That depends\ud
very much on what you are trying to create and why. This chapter discusses\ud
the importance and the challenges of evaluating content generators, and more generally\ud
understanding a generator’s strengths and weaknesses and suitability for your\ud
goals. In particular, we discuss two different approaches to evaluating content generators:\ud
visualizing the expressive range of generators, and using questionnaires to\ud
understand the impact of your generator on the player. These methods could broadly\ud
be called top-down and bottom-up methods for evaluating generators.peer-reviewe
Complex symbolic sequence clustering and multiple classifiers for predictive process monitoring

This paper addresses the following predictive business process monitoring problem: Given the execution trace of an ongoing case,and given a set of traces of historical (completed) cases, predict the most likely outcome of the ongoing case. In this context, a trace refers to a sequence of events with corresponding payloads, where a payload consists of a set of attribute-value pairs. Meanwhile, an outcome refers to a label associated to completed cases, like, for example, a label indicating that a given case completed “on time” (with respect to a given desired duration) or “late”, or a label indicating that a given case led to a customer complaint or not. The paper tackles this problem via a two-phased approach. In the first phase, prefixes of historical cases are encoded using complex symbolic sequences and clustered. In the second phase, a classifier is built for each of the clusters. To predict the outcome of an ongoing case at runtime given its (uncompleted) trace, we select the closest cluster(s) to the trace in question and apply the  respective classifier(s), taking into account the Euclidean distance of the trace from the center of the clusters. We consider two families of clustering algorithms – hierarchical clustering and k-medoids – and use random forests for classification. The approach was evaluated on four real-life datasets
The Maximum Scatter TSP on a Regular Grid

In the maximum scatter traveling salesman problem the objective is to find a
tour that maximizes the shortest distance between any two consecutive nodes.
This model can be applied to manufacturing processes, particularly laser
melting processes. We extend an algorithm by Arkin et al. that yields optimal
solutions for nodes on a line to a regular $m \times n$-grid. The new algorithm
$\textsc{Weave}(m,n)$ takes linear time to compute an optimal tour in some
cases. It is asymptotically optimal and a $\frac{\sqrt{10}}{5}$-approximation
for the $3\times 4$-grid, which is the worst case.Comment: 6 pages, 2 figures; to appear in OR Proceedings 201
Local Search with Noisy Strategy for Minimum Vertex Cover in Massive Graphs

Finding minimum vertex covers (MinVC) for simple undirected graphs is a well-known NP-hard problem. In the literature there have been many heuristics for obtaining good vertex covers. However, most of them focus on solving this problem in relatively small graphs. Recently, a local search solver called FastVC is designed to solve the MinVC problem on real-world massive graphs. Since the traditional best-picking heuristic was believed to be of high complexity, FastVC replaces it with an approximate best-picking strategy. However, since best-picking has been proved to be powerful for a wide range of problems, abandoning it may be a great sacrifice. In this paper we have developed a local search MinVC solver which utilizes best-picking with noise to remove vertices. Experiments conducted on a broad range of real-world massive graphs show that our proposed method finds better vertex covers than state-of-the-art local search algorithms on many graphs.Griffith Sciences, School of Information and Communication TechnologyFull Tex
Robust Fuzzy Clustering via Trimming and Constraints

Producción CientíficaA methodology for robust fuzzy clustering is proposed. This
methodology can be widely applied in very different statistical problems given
that it is based on probability likelihoods. Robustness is achieved by trimming
a fixed proportion of “most outlying” observations which are indeed
self-determined by the data set at hand. Constraints on the clusters’ scatters
are also needed to get mathematically well-defined problems and to avoid the
detection of non-interesting spurious clusters. The main lines for computationally
feasible algorithms are provided and some simple guidelines about
how to choose tuning parameters are briefly outlined. The proposed methodology
is illustrated through two applications. The first one is aimed at heterogeneously
clustering under multivariate normal assumptions and the second
one migh be useful in fuzzy clusterwise linear regression problems.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13
Fuzzy Clustering Throug Robust Factor Analyzers

Producción CientíficaIn fuzzy clustering, data elements can belong to more than one cluster , and membership levels are associated with each element, to indicate the strength of the association between that data element and a particular cluster. Unfortunately, fuzzy clustering is not robust, while in real applications the data is contaminated by outliers and noise, and the assumed underlying Gaussian distributions could be unrealistic. Here we propose a robust fuzzy estimator for clustering through Factor Analyzers, by introducing the joint usage of trimming and of constrained estimation of noise matrices in the classic Maximum Likelihood approach
Lexicographic choice functions without archimedeanicity

We investigate the connection between choice functions and lexicographic probabilities, by means of the convexity axiom considered by Seidenfeld, Schervisch and Kadane (2010) but without imposing any Archimedean condition. We show that lexicographic probabilities are related to a particular type of sets of desirable gambles, and investigate the properties of the coherent choice function this induces via maximality. Finally, we show that the convexity axiom is necessary but not sufficient for a coherent choice function to be the infimum of a class of lexicographic ones
A norm-aware multi-agent system for social simulations in a river basin

Wastewater management is a complex task involving a wide range of technical environmental and social factors. Furthermore, it typically requires the coordination of a heterogeneous society of actors with different goals. Regulations and protocols can be effectively used to tackle this complexity. In this chapter we present a norm-aware multi-agent system for social simulations in a river basin. The norms we present are inspired in European policies for wastewater management and they can evolve through time.Peer ReviewedPostprint (author's final draft