164 research outputs found
Most secant varieties of tangential varieties to Veronese varieties are nondefective
We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002,
which claims that the secant varieties of tangential varieties to the th
Veronese embedding of the projective -space have the expected
dimension, modulo a few well-known exceptions. As Bernardi, Catalisano,
Gimigliano, and Id\'a demonstrated that the proof of this conjecture may be
reduced to the case of cubics, i.e., , the main contribution of this work
is the resolution of this base case. The proposed proof proceeds by induction
on the dimension of the projective space via a specialization argument.
This reduces the proof to a large number of initial cases for the induction,
which were settled using a computer-assisted proof. The individual base cases
were computationally challenging problems. Indeed, the largest base case
required us to deal with the tangential variety to the third Veronese embedding
of in .Comment: 25 pages, 2 figures, extended the introduction, and added a C++ code
as an ancillary fil
Projector - a partially typed language for querying XML
We describe Projector, a language that can be used to perform a mixture of typed and untyped computation against data represented in XML. For some problems, notably when the data is unstructured or semistructured, the most desirable programming model is against the tree structure underlying the document. When this tree structure has been used to model regular data structures, then these regular structures themselves are a more desirable programming model. The language Projector, described here in outline, gives both models within a single partially typed algebra and is well suited for hybrid applications, for example when fragments of a known structure are embedded in a document whose overall structure is unknown. Projector is an extension of ECMA-262 (aka JavaScript), and therefore inherits an untyped DOM interface. To this has been added some static typing and a dynamic projection primitive, which can be used to assert the presence of a regular structure modelled within the XML. If this structure does exist, the data is extracted and presented as a typed value within the programming language
Functional relations for elliptic polylogarithms
Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities
Bigraphical Logics for XML
Bigraphs have been recently proposed as a meta-model for global computing resources; they are built orthogonally on two structures: a hierarchical ‘place’ graph for locations and a ‘link’ (hyper-)graph for connections. XML is now the standard meta-language for the data exchange and storage on the web. In this paper we address the similarities between bigraphs and XML and we propose bigraphs as a rich model for XML (and XML contexts). Building on this idea we proceed by investigating how the recently proposed logic of BiLog can be instantiated to describe, query and reason about web data (and web contexts)
Spin Measurements in Cascade Decays at the LHC
We systematically study the possibility of determining the spin of new
particles after their discovery at the LHC. We concentrate on angular
correlations in cascade decays. Motivated by constraints of electroweak
precision tests and the potential of providing a Cold Dark Matter candidate, we
focus on scenarios of new physics in which some discrete symmetry guarantees
the existence of stable neutral particles which escape the detector. More
specifically, we compare supersymmetry with another generic scenario in which
new physics particles have the same spin as their Standard Model partners. A
survey of possibilities of observing spin correlations in a broad range of
decay channels is carried out, with interesting ones identified. Rather than
confining ourselves to one "collider friendly" benchmark point (such as SPS1a),
we describe the parameter region in which any particular decay channel is
effective. We conduct a more detailed study of chargino's spin determination in
the decay channel . A scan
over the chargino and neutralino masses is performed. We find that as long as
the spectrum is not too degenerate the prospects for spin determination in this
channel are rather good.Comment: 36 pages, references added, 1 figure modifie
Web and Semantic Web Query Languages
A number of techniques have been developed to facilitate
powerful data retrieval on the Web and Semantic Web. Three categories
of Web query languages can be distinguished, according to the format
of the data they can retrieve: XML, RDF and Topic Maps. This article
introduces the spectrum of languages falling into these categories
and summarises their salient aspects. The languages are introduced using
common sample data and query types. Key aspects of the query
languages considered are stressed in a conclusion
STRUCTURED DOCUMENT LOGIC
This paper describes some practical and theoretical foundations of
Structured Document Logic (SDL),
which is a logical methodology for analyzing
properties of Web documents, like XML or HTML. SDL can make benefits in
searching of HTML pages, or in defining filters for web documents. Both
syntax and semantics of SDL are described, and an efficient evaluation
algorithm is also introduced
Exploration via Cost-Aware Subgoal Design
The problem of exploration in unknown environments continues to pose a
challenge for reinforcement learning algorithms, as interactions with the
environment are usually expensive or limited. The technique of setting subgoals
with an intrinsic reward allows for the use of supplemental feedback to aid
agent in environment with sparse and delayed rewards. In fact, it can be an
effective tool in directing the exploration behavior of the agent toward useful
parts of the state space. In this paper, we consider problems where an agent
faces an unknown task in the future and is given prior opportunities to
``practice'' on related tasks where the interactions are still expensive. We
propose a one-step Bayes-optimal algorithm for selecting subgoal designs, along
with the number of episodes and the episode length, to efficiently maximize the
expected performance of an agent. We demonstrate its excellent performance on a
variety of tasks and also prove an asymptotic optimality guarantee.Comment: Presented at TARL, ICLR 2019 worksho
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