scholarly journals Achieving Fairness in the Stochastic Multi-Armed Bandit Problem

2020 ◽  
Vol 34 (04) ◽  
pp. 5379-5386
Author(s):  
Vishakha Patil ◽  
Ganesh Ghalme ◽  
Vineet Nair ◽  
Y. Narahari
Keyword(s):  
Learning Algorithm ◽  
Complete Characterization ◽  
Bandit Problem ◽  
Fairness Constraints ◽  
Two Parameters ◽  
The Cost ◽  
Primary Contribution ◽  
Theoretical Results ◽  
Natural Way

We study an interesting variant of the stochastic multi-armed bandit problem, which we call the Fair-MAB problem, where, in addition to the objective of maximizing the sum of expected rewards, the algorithm also needs to ensure that at any time, each arm is pulled at least a pre-specified fraction of times. We investigate the interplay between learning and fairness in terms of a pre-specified vector denoting the fractions of guaranteed pulls. We define a fairness-aware regret, which we call r-Regret, that takes into account the above fairness constraints and extends the conventional notion of regret in a natural way. Our primary contribution is to obtain a complete characterization of a class of Fair-MAB algorithms via two parameters: the unfairness tolerance and the learning algorithm used as a black-box. For this class of algorithms, we provide a fairness guarantee that holds uniformly over time, irrespective of the choice of the learning algorithm. Further, when the learning algorithm is UCB1, we show that our algorithm achieves constant r-Regret for a large enough time horizon. Finally, we analyze the cost of fairness in terms of the conventional notion of regret. We conclude by experimentally validating our theoretical results.

A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XII: PERIOD-3, PERIOD-6, AND PERMUTIVE RULES

2009 ◽  
Vol 19 (12) ◽  
pp. 3887-4038 ◽  
Author(s):  
LEON O. CHUA ◽  
GIOVANNI E. PAZIENZA
Keyword(s):  
Nonlinear Dynamics ◽  
Cellular Automata ◽  
Complete Characterization ◽  
The Third ◽  
Arbitrary Choice ◽  
The One ◽  
Theoretical Results ◽  
Science Part

This 12th part of our Nonlinear Dynamics Perspective of Cellular Automata concludes a series of three articles devoted to CA local rules having robust periodic ω-limit orbits. Here, we consider only the two rules, [Formula: see text] and [Formula: see text], constituting the third of the six groups in which we classified the 1D binary Cellular Automata. Among the numerous theoretical results contained in this article, we emphasize the complete characterization of the ω-limit orbits, both robust and nonrobust, of these two rules and the proof that period-3 and period-6 ω-limit orbits are dense for [Formula: see text] and [Formula: see text], respectively. Furthermore, we will also introduce the fundamental concepts of perfect period-T orbitsets and riddled basins, and see how they emerge in rule [Formula: see text]. As stated in the title, we also focus on permutive rules, which have been introduced in a previous installment of our series but never thoroughly studied. Indeed, we will review some of the well-known properties of such rules, like the surjectivity, examining their implications for finite and bi-infinite Cellular Automata. Finally, we propose a new list of the 88 globally-independent local rules, which is slightly different from the one we have used so far but has the great advantage of being selected via a rigorous methodology and not an arbitrary choice. For the sake of completeness, we display in the appendix the basin tree diagrams and the portraits of the ω-limit orbits of the rules from this refined table which have not yet been reported in our previous articles.

scholarly journals Numerical and analytical results for the two discs capacitor problem

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160792 ◽  
Author(s):  
Giampiero Paffuti
Keyword(s):  
Numerical Calculation ◽  
Contact Zone ◽  
Complete Characterization ◽  
Unusual Behaviour ◽  
Analytical Results ◽  
Theoretical Results

In this paper, we study the two discs capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms the theoretical results. The study shows the existence of a hierarchy in the divergent behaviour of the capacitance coefficients and this implies some unusual behaviour of the forces, strictly related to the dimensionality of the near-contact zone between electrodes.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

scholarly journals Complete characterization of spin chains with two Ising symmetries

2019 ◽  
Vol 125 (1) ◽  
pp. 10008 ◽  
Author(s):  
Bat-el Friedman ◽  
Atanu Rajak ◽  
Emanuele G. Dalla Torre
Keyword(s):  
Complete Characterization ◽  
Spin Chains

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Protein complex formation in methionine chain-elongation and leucine biosynthesis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Li-Qun Chen ◽  
Shweta Chhajed ◽  
Tong Zhang ◽  
Joseph M. Collins ◽  
Qiuying Pang ◽  
...  
Keyword(s):  
Protein Complexes ◽  
Complete Characterization ◽  
Bimolecular Fluorescence Complementation ◽  
Chain Elongation ◽  
Substrate Channeling ◽  
Leucine Biosynthesis ◽  
Protein Complex Formation ◽  
Genes Encoding ◽  
Isopropylmalate Dehydrogenase

AbstractDuring the past two decades, glucosinolate (GLS) metabolic pathways have been under extensive studies because of the importance of the specialized metabolites in plant defense against herbivores and pathogens. The studies have led to a nearly complete characterization of biosynthetic genes in the reference plant Arabidopsis thaliana. Before methionine incorporation into the core structure of aliphatic GLS, it undergoes chain-elongation through an iterative three-step process recruited from leucine biosynthesis. Although enzymes catalyzing each step of the reaction have been characterized, the regulatory mode is largely unknown. In this study, using three independent approaches, yeast two-hybrid (Y2H), coimmunoprecipitation (Co-IP) and bimolecular fluorescence complementation (BiFC), we uncovered the presence of protein complexes consisting of isopropylmalate isomerase (IPMI) and isopropylmalate dehydrogenase (IPMDH). In addition, simultaneous decreases in both IPMI and IPMDH activities in a leuc:ipmdh1 double mutants resulted in aggregated changes of GLS profiles compared to either leuc or ipmdh1 single mutants. Although the biological importance of the formation of IPMI and IPMDH protein complexes has not been documented in any organisms, these complexes may represent a new regulatory mechanism of substrate channeling in GLS and/or leucine biosynthesis. Since genes encoding the two enzymes are widely distributed in eukaryotic and prokaryotic genomes, such complexes may have universal significance in the regulation of leucine biosynthesis.

scholarly journals AB1062 LIPODERMATOSCLEROSIS AS A TYPE OF LOBULAR PANNICULITIS: THE EFFECTIVENESS OF NON-PHARMACOLOGICAL TREATMENT METHODS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1821.1-1821
Author(s):  
M. Sukhareva ◽  
O. Egorova ◽  
B. Belov
Keyword(s):  
Subcutaneous Fat ◽  
Lymphatic Drainage ◽  
Normal Body Mass Index ◽  
Positive Trend ◽  
Group I ◽  
Positive Clinical Effect ◽  
Group Ii ◽  
The Cost ◽  
Lobular Panniculitis

Background:In medical practice lobular panniculitis-lipodermatosclerosis (LDS) is becoming more and more common. It is manifested by degenerative-dystrophic changes in subcutaneous fat (SCF) and occurs more often in middle-aged women affected by chronic venous insufficiency.Objectives:to evaluate the effectiveness of mesotherapy (MT) and shockwave ultrasound therapy (UST) for LDSMethods:among 539 patients referred to the V.A. Nasonova Research Institute of Rheumatology with the referral diagnoses of erythema nodosum or panniculitis 8.5% (46) of patients (44 women, 2 men) aged 18 to 82 with overweight (32) LDS with the disease duration of 11,8±6.4 months was verified. Patients were randomized into two groups of 23 patients each: group I received daily MT (10 sessions) therapy with drugs that have antioxidant, anti-inflammatory, lymphatic drainage and lipolytic effects, and 3 MHz UST of the node area twice a week (5 sessions). In group II MT was performed daily with 9% Natrii chloridum solution at a dose comparable to group I. The control methods included general clinical examination (characterization of induration on the lower legs with an assessment of the effect of pain pressing according to visual analogue scale (VAS pain), general blood and urine tests and ultrasound with elastography (USE) of the compaction. The main stages of control: initial (T0), after 14 days (T1), 1 month (T2) and 3 months (T3).Results:before treatment 38 patients with LDS demonstrated asymmetric (83%) inflammation of SCF of the lower legs (100%) on its medial surface (91%). LDS regressed faster with normal body mass index (p = 0,04). In all patients of group I, after a course of physiotherapy a positive trend was registered, that is a decrease in VAS pain intensity (T0 50±18 mm; T1 35±11 mm), decrease in diameter (T0 6±2.2 cm; T1 4.5±1, 7 mm) and color intensity of the node (p<0.002), SCF thickening which results in “lumping” with macrovascularization according to USE, and decrease in ESR and CRP. In 44% of cases the treatment effect increased to T2 (p <0.05). After 3 months of observation, 15 patients required a second course of physiotherapy. In group II a positive clinical effect was registered for T2 in 14 patients (60.8%) and for T3 in 19 patients (83%) (p<0.05). Over the entire observation period LDS recurrence was registered in 19 patients (41%), the median of recurrence was 3 [1; 6] months, mainly in patients of group I. Recurrence was associated with node fusion into conglomerates (OR 4.33, 95% CI 1.05-17.8; p = 0.037). MT and UST were tolerated well, no side effects were detected.Conclusion:the use of MT with 9% Natrii chloridum solution allowed us to achieve positive dynamics in patients with LDS, which significantly reduced the cost of treatment. Further studies are needed to evaluate the significance of these techniques.Disclosure of Interests:None declared

scholarly journals Topological Approach to Mathematical Programs with Switching Constraints

2021 ◽  
Author(s):  
Vladimir Shikhman
Keyword(s):  
Stationary Point ◽  
Mountain Pass Theorem ◽  
Strong Stability ◽  
Complete Characterization ◽  
Stationary Points ◽  
Mathematical Programs ◽  
Linear Independence Constraint Qualification ◽  
Point Set ◽  
Stationary Level

AbstractWe study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

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