242 research outputs found
Higher homotopy commutativity and cohomology of finite H-spaces
We study connected mod p finite A_p-spaces admitting AC_n-space structures
with n<p for an odd prime p. Our result shows that if n is greator than
(p-1)/2, then the mod p Steenrod algebra acts on the mod p cohomology of such a
space in a systematic way. Moreover, we consider A_p-spaces which are mod p
homotopy equivalent to product spaces of odd dimensional spheres. Then we
determine the largest integer n for which such a space admits an AC_n-space
structure compatible with the A_p-space structure.Comment: This is the version published by Geometry & Topology Monographs on 29
January 200
An Epistemic Approach to the Formal Specification of Statistical Machine Learning
We propose an epistemic approach to formalizing statistical properties of
machine learning. Specifically, we introduce a formal model for supervised
learning based on a Kripke model where each possible world corresponds to a
possible dataset and modal operators are interpreted as transformation and
testing on datasets. Then we formalize various notions of the classification
performance, robustness, and fairness of statistical classifiers by using our
extension of statistical epistemic logic (StatEL). In this formalization, we
show relationships among properties of classifiers, and relevance between
classification performance and robustness. As far as we know, this is the first
work that uses epistemic models and logical formulas to express statistical
properties of machine learning, and would be a starting point to develop
theories of formal specification of machine learning.Comment: Accepted in Software and Systems Modeling https://rdcu.be/b7ssR This
paper is the journal version of the SEFM'19 conference paper arxiv:1907.1032
Local Distribution Obfuscation via Probability Coupling
We introduce a general model for the local obfuscation of probability
distributions by probabilistic perturbation, e.g., by adding differentially
private noise, and investigate its theoretical properties. Specifically, we
relax a notion of distribution privacy (DistP) by generalizing it to
divergence, and propose local obfuscation mechanisms that provide divergence
distribution privacy. To provide f-divergence distribution privacy, we prove
that probabilistic perturbation noise should be added proportionally to the
Earth mover's distance between the probability distributions that we want to
make indistinguishable. Furthermore, we introduce a local obfuscation
mechanism, which we call a coupling mechanism, that provides divergence
distribution privacy while optimizing the utility of obfuscated data by using
exact/approximate auxiliary information on the input distributions we want to
protect.Comment: Full version of Allerton 2019 paper (This paper extends some part of
the unpublished v3 of arXiv:1812.00939, while v4 of arXiv:1812.00939 extends
the other part and is published in ESORICS'19.
Formalizing Statistical Causality via Modal Logic
We propose a formal language for describing and explaining statistical
causality. Concretely, we define Statistical Causality Language (StaCL) for
expressing causal effects and specifying the requirements for causal inference.
StaCL incorporates modal operators for interventions to express causal
properties between probability distributions in different possible worlds in a
Kripke model. We formalize axioms for probability distributions, interventions,
and causal predicates using StaCL formulas. These axioms are expressive enough
to derive the rules of Pearl's do-calculus. Finally, we demonstrate by examples
that StaCL can be used to specify and explain the correctness of statistical
causal inference
Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs
We propose a new approach to formally describing the requirement for
statistical inference and checking whether a program uses the statistical
method appropriately. Specifically, we define belief Hoare logic (BHL) for
formalizing and reasoning about the statistical beliefs acquired via hypothesis
testing. This program logic is sound and relatively complete with respect to a
Kripke model for hypothesis tests. We demonstrate by examples that BHL is
useful for reasoning about practical issues in hypothesis testing. In our
framework, we clarify the importance of prior beliefs in acquiring statistical
beliefs through hypothesis testing, and discuss the whole picture of the
justification of statistical inference inside and outside the program logic
Theme Aspect Argumentation Model for Handling Fallacies
From daily discussions to marketing ads to political statements, information
manipulation is rife. It is increasingly more important that we have the right
set of tools to defend ourselves from manipulative rhetoric, or fallacies.
Suitable techniques to automatically identify fallacies are being investigated
in natural language processing research. However, a fallacy in one context may
not be a fallacy in another context, so there is also a need to explain how and
why it has come to be judged a fallacy. For the explainable fallacy
identification, we present a novel approach to characterising fallacies through
formal constraints, as a viable alternative to more traditional fallacy
classifications by informal criteria. To achieve this objective, we introduce a
novel context-aware argumentation model, the theme aspect argumentation model,
which can do both: the modelling of a given argumentation as it is expressed
(rhetorical modelling); and a deeper semantic analysis of the rhetorical
argumentation model. By identifying fallacies with formal constraints, it
becomes possible to tell whether a fallacy lurks in the modelled rhetoric with
a formal rigour. We present core formal constraints for the theme aspect
argumentation model and then more formal constraints that improve its fallacy
identification capability. We show and prove the consequences of these formal
constraints. We then analyse the computational complexities of deciding the
satisfiability of the constraints
INFLUENCE OF TURN RADIUS OF RUNNING ON TORSIONAL LOADING OF THE TIBIA
The purpose of this study was to investigate influence of turn radius of running on the torsional loading of the tibia. Six male subjects ran on a straightway and anti-clockwise corners with different turn radiuses (R=15m and 5m). Data were collected using two high-speed cameras and force platforms. The torsional stresses acting on the inner tibias of runners were compared among each running condition. At beginning, net torsional moments at both ends of the lower leg were calculated. Then, the tibial torsional stresses were estimated, based on equilibrium of those moments. Much larger torsional stress acted on the tibia in later portion of the stance phase of sharper cornering compared to other two running conditions. Mean value of the maximum stress in sharper cornering was also significantly larger (
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