Unimodality ≈ Unimodality
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Unimodality, Log-concavity, Real-rootedness And Beyond Open
Theorem 7.5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 7.10 Historical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476Re…
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Rethinking Bias-Variance Trade-off for Generalization of Neural Networks Open
The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models,…
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Gamma-positivity in combinatorics and geometry Open
Gamma-positivity is an elementary property that polynomials with symmetric coefficients may have, which directly implies their unimodality. The idea behind it stems from work of Foata, Schützenberger and Strehl on the Eulerian polynomials;…
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Stochastic Model Predictive Control for Linear Systems Using Probabilistic Reachable Sets Open
In this paper we propose a stochastic model predictive control (MPC)\nalgorithm for linear discrete-time systems affected by possibly unbounded\nadditive disturbances and subject to probabilistic constraints. Constraints are\ntreated in an…
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Optimal testing for properties of distributions Open
Given samples from an unknown discrete distribution p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C? This fundamental question has received tremendous atte…
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Optimal Testing for Properties of Distributions Open
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has rec…
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Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions Open
In the paper, the author establishes inequalities, monotonicity, convexity,\nand unimodality for functions concerning the modified Bessel functions of the\nfirst kind and compute the completely monotonic degrees of differences between\nthe…
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Fast Learning for Dynamic Resource Allocation in AI-Enabled Radio Networks Open
Artificial Intelligence (AI)-enabled radios are expected to enhance the spectral efficiency of 5th generation (5G) millimeter wave (mmWave) networks by learning to optimize network resources. However, allocating resources over the mmWave b…
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On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means Open
The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence b…
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Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions Open
In general, although some random variables such as wind speed, temperature, and load are known to have multimodal distributions, input or output random variables are considered to follow unimodal distributions without assessing the unimoda…
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A Novel Online and Non-Parametric Approach for Drift Detection in Big Data Open
A sizable amount of current literature on online drift detection tools thrive on unrealistic parametric strictures such as normality or on non-parametric methods whose power performance is questionable. Using minimal realistic assumptions …
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Lattice Points and Simultaneous Core Partitions Open
We apply lattice point techniques to the study of simultaneous core partitions. Our central observation is that for $a$ and $b$ relatively prime, the abacus construction identifies the set of simultaneous $(a,b)$-core partitions with latti…
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Truncated Weibull-G More Flexible and More Reliable than Beta-G Distribution Open
Our purpose in this study includes introducing a new family of distributions as an alternative to beta-G (B-G) distribution with flexible hazard rate and greater reliability which we call Truncated Weibull-G (TW-G) distribution. We shall d…
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Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets Open
In this paper, we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in anal…
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From multiline queues to Macdonald polynomials via the exclusion process Open
Recently James Martin introduced multiline queues, and used them to give a\ncombinatorial formula for the stationary distribution of the multispecies\nasymmetric simple exclusion exclusion process (ASEP) on a circle. The ASEP is a\nmodel o…
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The Influence of Crystal Size Distributions on the Rheology of Magmas: New Insights From Analog Experiments Open
This study examines the influence of particle‐size distributions on the rheology of particle suspensions by using analog experiments with spherical glass beads in silicone oil as a magma equivalent. The analyses of 274 individual particle‐…
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Stationary moments, distribution conjugation and phenotypic regions in stochastic gene transcription Open
Transcription is a pivotal step in gene expression yet a complex biochemical process. It occurs often in a bursty manner, leading to cell-to-cell variability important for the cells surviving in complex environments. Quantitative experimen…
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UniS-MMC: Multimodal Classification via Unimodality-supervised Multimodal Contrastive Learning Open
Multimodal learning aims to imitate human beings to acquire complementary information from multiple modalities for various downstream tasks. However, traditional aggregation-based multimodal fusion methods ignore the inter-modality relatio…
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Domain-Structured Chaos in a Hopfield Neural Network Open
In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic r…
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The Discrete Poisson-Akash Distribution Open
A Poisson-Akash distribution has been obtained by compounding Poisson distribution with Akash distribution introduced by Shanker (2015). A general expression for the th factorial moment has been derived and hence the first four moments abo…
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A Comparison of Statistical Tools for Identifying Modality in Body Mass Distributions Open
The assessment of modality or \bumps in distributions is of in- terest to scientists in many areas. We compare the performance of four statistical methods to test for departures from unimodality in simulations, and further illustrate the f…
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From multiline queues to Macdonald polynomials via the exclusion process Open
Recently James Martin introduced multiline queues, and used them to give a combinatorial formula for the stationary distribution of the multispecies asymmetric simple exclusion exclusion process (ASEP) on a circle. The ASEP is a model of p…
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Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution Open
In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This M…
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What causes the test error? Going beyond bias-variance via ANOVA Open
Modern machine learning methods are often overparametrized, allowing adaptation to the data at a fine level. This can seem puzzling; in the worst case, such models do not need to generalize. This puzzle inspired a great amount of work, arg…
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Zeilberger’s KOH theorem and the strict unimodality of $q$-binomial coefficients Open
A recent nice result due to I. Pak and G. Panova is the strict unimodality of the -binomial coefficients . Since their proof used representation theory and Kronecker coefficients, the authors also asked for an argument that would employ Ze…
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Are your data gathered? Open
International audience
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Research of Image Sharpness Assessment Algorithm for Autofocus Open
With the wide application of imaging system in security monitoring, aerospace, medical image and other fields, how to capture the clear image of the target in real time and automatically is particularly important. Image sharpness evaluatio…
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Active Target Localization using Low-Rank Matrix Completion and Unimodal Regression Open
The detection and localization of a target from samples of its generated field is a problem of interest in a broad range of applications. Often, the target field admits structural properties that enable the design of lower sample detection…
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Moldboard Surface Universalization of the Ploughshare Operating Unit Open
This paper deals with a way of universalizing of ploughshare-moldboard surfaces (PMS) due to spatial rotation to work on different soil types and at various speeds. The paper presents a newly developed way to compare the topology of two pl…
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A Bimodal Discrete Shifted Poisson Distribution. A Case Study of Tourists’ Length of Stay Open
Although the Poisson distribution is appropriate for modelling equi-dispersed distributions, it reflects bimodality less well. In this paper, we propose a distribution which is more suitable for the latter purpose. It can be fitted to both…