A Mathematical Model for Optimum Error-Reject Trade-Off for Learning of Secure Classification Models in the Presence of Label Noise During Training

2020 ◽  
pp. 547-554
Author(s):  
Seyedfakhredin Musavishavazi ◽  
Mehrdad Mohannazadeh Bakhtiari ◽  
Thomas Villmann
Keyword(s):  
Mathematical Model ◽  
Classification Models ◽  
Label Noise ◽  
Trade Off

scholarly journals Optimization of Stochastic Lossy Transport Networks and Applications to Power Grids

2021 ◽  
Author(s):  
Alessandro Zocca ◽  
Bert Zwart
Keyword(s):  
Mathematical Model ◽  
Renewable Energy ◽  
Smart Grids ◽  
Transport Network ◽  
Power Grids ◽  
Performance Gain ◽  
Power Losses ◽  
Transport Networks ◽  
Trade Off ◽  
Stochastic Load

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty, and the network structure.

scholarly journals Detection, not mortality, constrains the evolution of virulence

2021 ◽  
Author(s):  
David A Kennedy
Keyword(s):  
Mathematical Model ◽  
Disease Severity ◽  
Behavioral Change ◽  
Scientific Literature ◽  
Empirical Support ◽  
Infectious Period ◽  
Trade Off ◽  
Evolution Of Virulence ◽  
Host Mortality

Why would a pathogen evolve to kill its hosts when killing a host ends a pathogen's own opportunity for transmission? A vast body of scientific literature has attempted to answer this question using "trade-off theory," which posits that host mortality persists due to its cost being balanced by benefits of other traits that correlate with host mortality. The most commonly invoked trade-off is the mortality-transmission trade-off, where increasingly harmful pathogens are assumed to transmit at higher rates from hosts while the hosts are alive, but the pathogens truncate their infectious period by killing their hosts. Here I show that costs of mortality are too small to plausibly constrain the evolution of disease severity except in systems where survival is rare. I alternatively propose that disease severity can be much more readily constrained by a cost of behavioral change due to the detection of infection, whereby increasingly harmful pathogens have increasing likelihood of detection and behavioral change following detection, thereby limiting opportunities for transmission. Using a mathematical model, I show the conditions under which detection can limit disease severity. Ultimately, this argument may explain why empirical support for trade-off theory has been limited and mixed.

scholarly journals Boredom begets creativity: a solution to the exploitation-exploration trade-off in predictive coding

2017 ◽  
Author(s):  
Jaime Gomez-Ramirez ◽  
Tommaso Costa
Keyword(s):  
Mathematical Model ◽  
Prediction Error ◽  
Predictive Coding ◽  
Error Minimization ◽  
Trade Off ◽  
Black Scholes ◽  
Intelligent Behavior ◽  
Prediction Error Minimization ◽  
Key Drivers ◽  
Technical Systems

AbstractHere, we investigate whether systems that minimize prediction error e.g. predictive coding, can also show creativity, or on the contrary, prediction error minimization unqualifies for the design of systems that respond in creative ways to non recurrent problems. We argue that there is a key ingredient that has been overlooked by researchers that needs to be incorporated to understand intelligent behavior in biological and technical systems. This ingredient is boredom. We propose a mathematical model based on the Black-Scholes-Merton equation which provides mechanistic insights into the interplay between boredom and prediction pleasure as the key drivers of behavior.

scholarly journals A Label Noise Robust Stacked Auto-Encoder Algorithm for Inaccurate Supervised Classification Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Zi-yang Wang ◽  
Xiao-yi Luo ◽  
Jun Liang
Keyword(s):  
Supervised Classification ◽  
Cross Validation ◽  
Training Dataset ◽  
Classification Models ◽  
Classification Problems ◽  
Noise Sources ◽  
Label Noise ◽  
Noise Robust ◽  
Fold Cross Validation ◽  
New Framework

In real applications, label noise and feature noise are two main noise sources. Similar to feature noise, label noise imposes great detriment on training classification models. Motivated by successful application of deep learning method in normal classification problems, this paper proposes a new framework called LNC-SDAE to handle those datasets corrupted with label noise, or so-called inaccurate supervision problems. The LNC-SDAE framework contains a preliminary label noise cleansing part and a stacked denoising auto-encoder. In preliminary label noise cleansing part, the K-fold cross-validation thought is applied for detecting and relabeling those mislabeled samples. After being preprocessed by label noise cleansing part, the cleansed training dataset is then input into the stacked denoising auto-encoder to learn robust representation for classification. A corrupted UCI standard dataset and a corrupted real industrial dataset are used for test, both of which contain a certain proportion of label noise (the ratio changes from 0% to 30%). The experiment results prove the effectiveness of LNC-SDAE, the representation learnt by which is shown robust.

A Decision Support Model for Salary Structure Design

2020 ◽  
Vol 52 (3) ◽  
pp. 109-120
Author(s):  
Biniyam Asmare Kassa
Keyword(s):  
Mathematical Model ◽  
Decision Support ◽  
Structure Design ◽  
Simple Mathematical Model ◽  
Decision Support Model ◽  
External Market ◽  
Trade Off ◽  
Actual Application ◽  
Salary Structure ◽  
Market Competitiveness

This article presents a simple mathematical model for salary structure design that enhances clarity and allows for reasonable trade-off between internal equity and external market competitiveness considerations in salary structure design. Practical use of the model is illustrated with an actual application in one organization.

The Trade-Off Mechanism in Mammalian Circadian Clock Model with Two Time Delays

2017 ◽  
Vol 27 (09) ◽  
pp. 1750147
Author(s):  
Jie Yan ◽  
Xiaxia Kang ◽  
Ling Yang
Keyword(s):  
Mathematical Model ◽  
Circadian Clock ◽  
Time Delays ◽  
Feedback Loop ◽  
Sustained Oscillation ◽  
System Delay ◽  
Trade Off ◽  
Biological Oscillators ◽  
Delay Dependent ◽  
Theoretical Analyses

Circadian clock is an autonomous oscillator which orchestrates the daily rhythms of physiology and behaviors. This study is devoted to explore how a positive feedback loop affects the dynamics of mammalian circadian clock. We simplify an experimentally validated mathematical model in our previous work, to a nonlinear differential equation with two time delays. This simplified mathematical model incorporates the pacemaker of mammalian circadian clock, a negative primary feedback loop, and a critical positive auxiliary feedback loop, [Formula: see text] loop. We perform analytical studies of the system. Delay-dependent conditions for the asymptotic stability of the nontrivial positive steady state of the model are investigated. We also prove the existence of Hopf bifurcation, which leads to self-sustained oscillation of mammalian circadian clock. Our theoretical analyses show that the oscillatory regime is reduced upon the participation of the delayed positive auxiliary loop. However, further simulations reveal that the auxiliary loop can enable the circadian clock gain widely adjustable amplitudes and robust period. Thus, the positive auxiliary feedback loop may provide a trade-off mechanism, to use the small loss in the robustness of oscillation in exchange for adaptable flexibility in mammalian circadian clock. The results obtained from the model may gain new insights into the dynamics of biological oscillators with interlocked feedback loops.

scholarly journals Model of Construction Subcontractors Selection with Time Windows for their Availability

2019 ◽  
Vol 65 (4) ◽  
pp. 295-307
Author(s):  
S. Biruk ◽  
P. Jaskowski ◽  
M. Krzemiński
Keyword(s):  
Mathematical Model ◽  
Resource Availability ◽  
Construction Projects ◽  
Programming Model ◽  
Time Windows ◽  
Mixed Integer ◽  
Time Cost ◽  
Trade Off ◽  
Availability Constraints ◽  
The Cost

AbstractMost construction projects involve subcontracting some work packages. A subcontractor is employed on the basis of their bid as well as according to their availability. A viable schedule must account for resource availability constraints. These resources (e.g. crews, subcontractors) engage in many projects, so they become at the disposal for a new project only in certain periods. One of the key tasks of a planner is thus synchronizing the work of resources between concurrent projects. The paper presents a mathematical model of the problem of selecting subcontractors or general contractor’s crews for a time-constrained project that accounts for the availability of contractors, as well as for the cost of subcontracting works. The proposed mixed integer-binary linear programming model enables the user to perform the time/cost trade-off analysis.

scholarly journals Variability of the mechanical properties of bone, and its evolutionary consequences

2006 ◽  
Vol 4 (12) ◽  
pp. 127-135 ◽  
Author(s):  
John D Currey ◽  
Jonathan W Pitchford ◽  
Paul D Baxter
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Mineral Content ◽  
Optimal Allocation ◽  
Compact Bone ◽  
Simple Mathematical Model ◽  
Trade Off ◽  
Evolutionary Consequences ◽  
Insight Into ◽  
Mechanical Phenomena

The relative variabilities (coefficient of variation (CV)) of 10 different mechanical properties of compact bone were determined from 2166 measurements. All measures of variability were made on a minimum of four specimens from any bone. Three pre-yield properties had a CV of about 12%. Six post-yield properties had CVs varying from 24 to 46%. Pre-yield properties increase as a function of mineral content, whereas post-yield properties decrease. These differences give insight into mechanical phenomena occurring at different stages during loading. Furthermore, the fact that some properties are more tightly determined than others has implications for the optimum values set by natural selection. This assertion is made more rigorous using a simple mathematical model for the evolutionarily optimal allocation in a trade-off where one property is imprecisely determined. It is argued that in general the optimum will be biased in favour of the more tightly determined properties than would be the case if all properties had the same CV.

scholarly journals Affect enhances object-background associations: Evidence from behavior and mathematical modeling

2019 ◽  
Author(s):  
Christopher R Madan ◽  
Aubrey Knight ◽  
Elizabeth Kensinger ◽  
Katherine Mickley Steinmetz
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Recognition Memory ◽  
Recall Performance ◽  
Cued Recall ◽  
Trade Off ◽  
Primary Driver ◽  
The Cost ◽  
Better Than ◽  
Emotional Scenes

In recognition memory paradigms, emotional details are often recognized better than neutral ones, but at the cost of memory for peripheral details. We previously provided evidence that, when peripheral details must be recalled using central details as cues, peripheral details from emotional scenes are at least as likely to be recalled as those from neutral scenes. Here we replicated and explicated this result by implementing a mathematical modeling approach to disambiguate the influence of target type, scene emotionality, scene valence, and their interactions. After incidentally encoding scenes that included neutral backgrounds with a positive, negative, or neutral foreground objects, participants showed equal or better cued recall of components from emotional scenes compared to neutral scenes. There was no evidence of emotion-based impairment in cued recall in either of two experiments, including one in which we replicated the emotion-induced memory trade-off in recognition. Mathematical model fits indicated that the emotionality of the encoded scene was the primary driver of improved cued-recall performance. Thus, even when emotion impairs recognition of peripheral components of scenes, it can preserve the ability to recall which scene components were studied together.

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