Scrutinizing the Monotonicity Assumption in IV and fuzzy RD designs*

2021 ◽  
Author(s):  
Mario Fiorini ◽  
Katrien Stevens
Keyword(s):  
Monotonicity Assumption

scholarly journals Wegner estimate for discrete Schrödinger operators with Gaussian random potentials

2019 ◽  
Vol 27 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Martin Tautenhahn
Keyword(s):  
Conditional Distribution ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Gaussian Random Process ◽  
Random Potentials ◽  
Wegner Estimate ◽  
Compactly Supported ◽  
Covariance Functions ◽  
Monotonicity Assumption ◽  
Discrete Schrödinger Operators

Abstract We prove a Wegner estimate for discrete Schrödinger operators with a potential given by a Gaussian random process. The only assumption is that the covariance function decays exponentially; no monotonicity assumption is required. This improves earlier results where abstract conditions on the conditional distribution, compactly supported and non-negative, or compactly supported covariance functions with positive mean are considered.

scholarly journals ON UNIQUENESS OF MILD SOLUTIONS FOR DISSIPATIVE STOCHASTIC EVOLUTION EQUATIONS

2010 ◽  
Vol 13 (03) ◽  
pp. 363-376 ◽  
Author(s):  
CARLO MARINELLI ◽  
MICHAEL RÖCKNER
Keyword(s):  
Evolution Equations ◽  
Broad Class ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Fundamental Issue ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Monotonicity Assumption ◽  
Semigroup Approach

In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried out in a formal way, without really justifying why and how one can do that. We provide sufficient conditions for uniqueness of mild solutions to a broad class of semilinear stochastic evolution equations with coefficients satisfying a monotonicity assumption.

scholarly journals Uniqueness issues for evolution equations with density constraints

2016 ◽  
Vol 26 (09) ◽  
pp. 1761-1783 ◽  
Author(s):  
Simone Di Marino ◽  
Alpár Richárd Mészáros
Keyword(s):  
Velocity Field ◽  
Evolution Equations ◽  
Planck Equation ◽  
Wasserstein Distance ◽  
First Order ◽  
Uniqueness Results ◽  
Monotonicity Assumption ◽  
Crowd Motion ◽  
The Given ◽  
Uniqueness Of A Solution

In this paper, we present some basic uniqueness results for evolution equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monotonicity assumption: we prove the uniqueness of a solution for first-order systems modeling crowd motion with hard congestion effects, introduced recently by Maury et al. The monotonicity of the velocity field implies that the [Formula: see text]-Wasserstein distance along two solutions is [Formula: see text]-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an [Formula: see text]-contraction property. In this case, by the regularization effect of the nondegenerate diffusion, the result follows even if the given velocity field is only [Formula: see text] as in the standard Fokker–Planck equation.

scholarly journals New Insights into Approaches to Evaluating Intention and Path for Network Multistep Attacks

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Hao Hu ◽  
Yuling Liu ◽  
Yingjie Yang ◽  
Hongqi Zhang ◽  
Yuchen Zhang
Keyword(s):  
Success Probability ◽  
Security Policies ◽  
Attack Graph ◽  
The Public ◽  
Absorbing Markov Chain ◽  
Monotonicity Assumption ◽  
Attack Path ◽  
Security Evaluations ◽  
Public Datasets ◽  
Evaluation Approaches

The attack graph (AG) is an abstraction technique that reveals the ways an attacker can use to leverage vulnerabilities in a given network to violate security policies. The analyses developed to extract security-relevant properties are referred to as AG-based security evaluations. In recent years, many evaluation approaches have been explored. However, they are generally limited to the attacker’s “monotonicity” assumption, which needs further improvements to overcome the limitation. To address this issue, the stochastic mathematical model called absorbing Markov chain (AMC) is applied over the AG to give some new insights, namely, the expected success probability of attack intention (EAIP) and the expected attack path length (EAPL). Our evaluations provide the preferred mitigating target hosts and the vulnerabilities patching prioritization of middle hosts. Tests on the public datasets DARPA2000 and Defcon’s CTF23 both verify that our evaluations are available and reliable.

Forward–backward stochastic partial differential equations with non-monotonic coefficients

2016 ◽  
Vol 16 (06) ◽  
pp. 1650025
Author(s):  
Hong Yin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Evolution Equations ◽  
Common Belief ◽  
Partial Differential ◽  
Diffusion Term ◽  
Monotonicity Assumption ◽  
The Common ◽  
Fully Coupled

In this paper we study the solvability of a class of fully-coupled forward–backward stochastic partial differential equations (FBSPDEs) with non-monotonic coefficients. These FBSPDEs cannot be put into the framework of stochastic evolution equations in general, and the usual decoupling methods for the Markovian forward–backward SDEs are difficult to apply. We prove the well-posedness of such FBSPDEs by using the method of continuation. Contrary to the common belief, we show that the usual monotonicity assumption can be removed by a change of the diffusion term.

scholarly journals Dataset Sensitive Autotuning of Multi-versioned Code Based on Monotonic Properties

2021 ◽  
pp. 3-23
Author(s):  
Philip Munksgaard ◽  
Svend Lund Breddam ◽  
Troels Henriksen ◽  
Fabian Cristian Gieseke ◽  
Cosmin Oancea
Keyword(s):  
Optimal Solution ◽  
Black Box ◽  
Stochastic Search ◽  
Effective Solution ◽  
Tuning Time ◽  
Monotonicity Assumption ◽  
Optimized Code ◽  
Tuning Strategy ◽  
Monotonic Properties ◽  
Rule Systems

AbstractFunctional languages allow rewrite-rule systems that aggressively generate a multitude of semantically-equivalent but differently-optimized code versions. In the context of GPGPU execution, this paper addresses the important question of how to compose these code versions into a single program that (near-)optimally discriminates them across different datasets. Rather than aiming at a general autotuning framework reliant on stochastic search, we argue that in some cases, a more effective solution can be obtained by customizing the tuning strategy for the compiler transformation producing the code versions.We present a simple and highly-composable strategy which requires that the (dynamic) program property used to discriminate between code versions conforms with a certain monotonicity assumption. Assuming the monotonicity assumption holds, our strategy guarantees that if an optimal solution exists it will be found. If an optimal solution doesn’t exist, our strategy produces human tractable and deterministic results that provide insights into what went wrong and how it can be fixed.We apply our tuning strategy to the incremental-flattening transformation supported by the publicly-available Futhark compiler and compare with a previous black-box tuning solution that uses the popular OpenTuner library. We demonstrate the feasibility of our solution on a set of standard datasets of real-world applications and public benchmark suites, such as Rodinia and FinPar. We show that our approach shortens the tuning time by a factor of $$6\times $$ 6 × on average, and more importantly, in five out of eleven cases, it produces programs that are (as high as $$10\times $$ 10 × ) faster than the ones produced by the OpenTuner-based technique.

scholarly journals Latent class instrumental variables and the monotonicity assumption

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Stuart G. Baker
Keyword(s):  
Instrumental Variables ◽  
Latent Class ◽  
Monotonicity Assumption

Alternative Monotonicity Assumptions for Improving Bounds on Natural Direct Effects

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Yasutaka Chiba ◽  
Masataka Taguri
Keyword(s):  
Coronary Heart Disease ◽  
Linear Programming ◽  
Heart Disease ◽  
Clinical Research ◽  
Randomized Trial ◽  
Direct Effect ◽  
Outcome Variable ◽  
Direct Effects ◽  
Additional Advantage ◽  
Monotonicity Assumption

AbstractEstimating the direct effect of a treatment on an outcome is often the focus of epidemiological and clinical research, when the treatment has more than one specified pathway to the defined outcome. Even if the total effect is unconfounded, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables. Therefore, bounds on direct effects have been presented via linear programming under two common definitions of direct effects: controlled and natural. Here, we propose bounds on natural direct effects without using linear programming, because such bounds on controlled direct effects have already been proposed. To derive narrow bounds, we introduce two monotonicity assumptions that are weaker than those in previous studies and another monotonicity assumption. Furthermore, we do not assume that an outcome variable is binary, whereas previous studies have made that assumption. An additional advantage of our bounds is that the bounding formulas are extremely simple. The proposed bounds are illustrated using a randomized trial for coronary heart disease.

scholarly journals Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1999
Author(s):  
Hongpeng Guo ◽  
Zhiming Guo
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Local Reaction ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Birth Function ◽  
Wave Solutions ◽  
Monotonicity Assumption ◽  
Non Local

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

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