140 research outputs found
On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory
We prove a non-smooth generalization of the global implicit function theorem.
More precisely we use the non-smooth local implicit function theorem and the
non-smooth critical point theory in order to prove a non-smooth global implicit
function theorem for locally Lipschitz functions. A comparison between several
global inversion theorems is discussed
Family Abuse Against Minors
This study is a general analysis of data included in the statistics of the General Directorate of Romanian Penitentiaries with respect to violent crimes, sexual crimes and crimes related to deviations from social cohabitation rules in 2007. The study assesses, for this purpose the distribution, according to various indicators (sex, age, original environment, the relationship with the aggressor), of the victims of the abovementioned crimes, and also emphasizes the main risk factors which impact on, or cause, victimization rates
Suicide in Europe in the Context of the Global Economic Crisis
Starting from Durkheim's hypothesis according to which crisis periods cause a significant increase in the number of suicides, the author examines several variables associated with the recent economic crisis and the extent to which they influence suicide rates in Europe, including Romania. In this respect, an assessment is made of the findings of theoretical studies and empirical surveys conducted in several European countries, according to which the increase of unemployment rates, the decline of welfare standards and the deterioration of health conditions (including those related to mental health) are among the main factors associated with the increase of suicide rates in different countries
International and National Legislative Regulations Aiming at Preventing Sexual Abuse against Children, as Well as the Protection of Children
This article presents a short “history” of the evolution over time of internationallegal regulations concerning child rights and the protection of children against any actof physical, emotional or sexual abuse. The concerns of European bodies in this respectare also highlighted, as are the objectives of the legislation in different countries, whichare mainly aimed at sanctioning abuses committed against children and, in particular,the punishment of acts of sexual abuse
On Nash Equilibria in Normal-Form Games With Vectorial Payoffs
We provide an in-depth study of Nash equilibria in multi-objective normal
form games (MONFGs), i.e., normal form games with vectorial payoffs. Taking a
utility-based approach, we assume that each player's utility can be modelled
with a utility function that maps a vector to a scalar utility. In the case of
a mixed strategy, it is meaningful to apply such a scalarisation both before
calculating the expectation of the payoff vector as well as after. This
distinction leads to two optimisation criteria. With the first criterion,
players aim to optimise the expected value of their utility function applied to
the payoff vectors obtained in the game. With the second criterion, players aim
to optimise the utility of expected payoff vectors given a joint strategy.
Under this latter criterion, it was shown that Nash equilibria need not exist.
Our first contribution is to provide a sufficient condition under which Nash
equilibria are guaranteed to exist. Secondly, we show that when Nash equilibria
do exist under both criteria, no equilibrium needs to be shared between the two
criteria, and even the number of equilibria can differ. Thirdly, we contribute
a study of pure strategy Nash equilibria under both criteria. We show that when
assuming quasiconvex utility functions for players, the sets of pure strategy
Nash equilibria under both optimisation criteria are equivalent. This result is
further extended to games in which players adhere to different optimisation
criteria. Finally, given these theoretical results, we construct an algorithm
to compute all pure strategy Nash equilibria in MONFGs where players have a
quasiconvex utility function
Opponent Learning Awareness and Modelling in Multi-Objective Normal Form Games
Many real-world multi-agent interactions consider multiple distinct criteria,
i.e. the payoffs are multi-objective in nature. However, the same
multi-objective payoff vector may lead to different utilities for each
participant. Therefore, it is essential for an agent to learn about the
behaviour of other agents in the system. In this work, we present the first
study of the effects of such opponent modelling on multi-objective multi-agent
interactions with non-linear utilities. Specifically, we consider two-player
multi-objective normal form games with non-linear utility functions under the
scalarised expected returns optimisation criterion. We contribute novel
actor-critic and policy gradient formulations to allow reinforcement learning
of mixed strategies in this setting, along with extensions that incorporate
opponent policy reconstruction and learning with opponent learning awareness
(i.e., learning while considering the impact of one's policy when anticipating
the opponent's learning step). Empirical results in five different MONFGs
demonstrate that opponent learning awareness and modelling can drastically
alter the learning dynamics in this setting. When equilibria are present,
opponent modelling can confer significant benefits on agents that implement it.
When there are no Nash equilibria, opponent learning awareness and modelling
allows agents to still converge to meaningful solutions that approximate
equilibria.Comment: Under review since 14 November 202
On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
We are concerned with the long time behaviour of solutions to the fractional
porous medium equation with a variable spatial density. We prove that if the
density decays slowly at infinity, then the solution approaches the
Barenblatt-type solution of a proper singular fractional problem. If, on the
contrary, the density decays rapidly at infinity, we show that the minimal
solution multiplied by a suitable power of the time variable converges to the
minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-
A Practical Guide to Multi-Objective Reinforcement Learning and Planning
Real-world decision-making tasks are generally complex, requiring trade-offs
between multiple, often conflicting, objectives. Despite this, the majority of
research in reinforcement learning and decision-theoretic planning either
assumes only a single objective, or that multiple objectives can be adequately
handled via a simple linear combination. Such approaches may oversimplify the
underlying problem and hence produce suboptimal results. This paper serves as a
guide to the application of multi-objective methods to difficult problems, and
is aimed at researchers who are already familiar with single-objective
reinforcement learning and planning methods who wish to adopt a multi-objective
perspective on their research, as well as practitioners who encounter
multi-objective decision problems in practice. It identifies the factors that
may influence the nature of the desired solution, and illustrates by example
how these influence the design of multi-objective decision-making systems for
complex problems
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