41,488 research outputs found
A Coding Theoretic Study on MLL proof nets
Coding theory is very useful for real world applications. A notable example
is digital television. Basically, coding theory is to study a way of detecting
and/or correcting data that may be true or false. Moreover coding theory is an
area of mathematics, in which there is an interplay between many branches of
mathematics, e.g., abstract algebra, combinatorics, discrete geometry,
information theory, etc. In this paper we propose a novel approach for
analyzing proof nets of Multiplicative Linear Logic (MLL) by coding theory. We
define families of proof structures and introduce a metric space for each
family. In each family, 1. an MLL proof net is a true code element; 2. a proof
structure that is not an MLL proof net is a false (or corrupted) code element.
The definition of our metrics reflects the duality of the multiplicative
connectives elegantly. In this paper we show that in the framework one
error-detecting is possible but one error-correcting not. Our proof of the
impossibility of one error-correcting is interesting in the sense that a proof
theoretical property is proved using a graph theoretical argument. In addition,
we show that affine logic and MLL + MIX are not appropriate for this framework.
That explains why MLL is better than such similar logics.Comment: minor modification
Low-Complexity Quantized Switching Controllers using Approximate Bisimulation
In this paper, we consider the problem of synthesizing low-complexity
controllers for incrementally stable switched systems. For that purpose, we
establish a new approximation result for the computation of symbolic models
that are approximately bisimilar to a given switched system. The main advantage
over existing results is that it allows us to design naturally quantized
switching controllers for safety or reachability specifications; these can be
pre-computed offline and therefore the online execution time is reduced. Then,
we present a technique to reduce the memory needed to store the control law by
borrowing ideas from algebraic decision diagrams for compact function
representation and by exploiting the non-determinism of the synthesized
controllers. We show the merits of our approach by applying it to a simple
model of temperature regulation in a building
On a combinatorial problem of Erdos, Kleitman and Lemke
In this paper, we study a combinatorial problem originating in the following
conjecture of Erdos and Lemke: given any sequence of n divisors of n,
repetitions being allowed, there exists a subsequence the elements of which are
summing to n. This conjecture was proved by Kleitman and Lemke, who then
extended the original question to a problem on a zero-sum invariant in the
framework of finite Abelian groups. Building among others on earlier works by
Alon and Dubiner and by the author, our main theorem gives a new upper bound
for this invariant in the general case, and provides its right order of
magnitude.Comment: 15 page
On the existence of zero-sum subsequences of distinct lengths
In this paper, we obtain a characterization of short normal sequences over a
finite Abelian p-group, thus answering positively a conjecture of Gao for a
variety of such groups. Our main result is deduced from a theorem of Alon,
Friedland and Kalai, originally proved so as to study the existence of regular
subgraphs in almost regular graphs. In the special case of elementary p-groups,
Gao's conjecture is solved using Alon's Combinatorial Nullstellensatz. To
conclude, we show that, assuming every integer satisfies Property B, this
conjecture holds in the case of finite Abelian groups of rank two.Comment: 10 pages, to appear in Rocky Mountain Journal of Mathematic
Plugin procedure in segmentation and application to hyperspectral image segmentation
In this article we give our contribution to the problem of segmentation with
plug-in procedures. We give general sufficient conditions under which plug in
procedure are efficient. We also give an algorithm that satisfy these
conditions. We give an application of the used algorithm to hyperspectral
images segmentation. Hyperspectral images are images that have both spatial and
spectral coherence with thousands of spectral bands on each pixel. In the
proposed procedure we combine a reduction dimension technique and a spatial
regularisation technique. This regularisation is based on the mixlet
modelisation of Kolaczyck and Al
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and NLogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is inspired from
proof theory and more specifically linear logic and Geometry of Interaction.
We show how unification can be used to build a model of computation by means
of specific subalgebras associated to finite permutations groups. We then prove
that whether an observation (the algebraic counterpart of a program) accepts a
word can be decided within logarithmic space. We also show that the
construction can naturally represent pointer machines, an intuitive way of
understanding logarithmic space computing
Reducing Unlawful Prescription Drug Promotion: Is the Public Health Being Served by an Enforcement Approach that Focuses on Punishment?
Despite the imposition of increasingly substantial fines and recently successful efforts to impose individual liability on corporate executives under the Park doctrine, punishing pharmaceutical companies and their executives for unlawful promotional activities has not been as successful in achieving compliance with the Federal Food, Drug, and Cosmetic Act (FD&C Act) as the protection of the public health demands. Over the past decade, the Food and Drug Administration (FDA) and the Department of Justice (DOJ) have shifted their focus from correction and compliance to a more punitive model when it comes to allegedly unlawful promotion of pharmaceuticals. The shift initially focused on imposing monetary penalties and was arguably justified by the expectation that financial punishment would achieve a level of compliance that would reduce the need for correction. By exacting enormous fines from companies, the agencies presumably hoped that the costs associated with unlawful promotion would be too high to justify the monetary benefits of non-compliance. Unfortunately, however, that approach has not been entirely successful. Despite the growth in settlements and penalties, and the recent efforts to hold individual executives liable for corporate misbehavior, the intended impact of substantially increased compliance has only partially materialized. The upward spiraling of settlement amounts and the trend toward prosecuting repeat offenders indicate that a change in approach is necessary.
This article argues that FDA and DOJ cannot justify a continued emphasis on punishment without more demonstrable improvement in compliance and corporate accountability.
The article goes on to describe several proposals to refocus the agencies’ efforts to effectively address the impact of unlawful promotion on public health by returning to an approach that emphasizes the more traditional goals of correction and compliance. It also argues that any meaningful protection of the public health ultimately requires a broader public understanding of the issues surrounding unlawful promotion of pharmaceutical products and greater participation by patients; physicians; health care professionals; and others with an interest in, and the opportunity to, impact this area. Increasing the public’s ability and interest in monitoring companies’ promotional activities at every level will reinforce the benefits of compliance, which will better serve the public health goals of the FD&C Act
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