17,903 research outputs found
Quantum Mechanics Lecture Notes. Selected Chapters
These are extended lecture notes of the quantum mechanics course which I am
teaching in the Weizmann Institute of Science graduate physics program. They
cover the topics listed below. The first four chapter are posted here. Their
content is detailed on the next page. The other chapters are planned to be
added in the coming months.
1. Motion in External Electromagnetic Field. Gauge Fields in Quantum
Mechanics.
2. Quantum Mechanics of Electromagnetic Field
3. Photon-Matter Interactions
4. Quantization of the Schr\"odinger Field (The Second Quantization)
5. Open Systems. Density Matrix
6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation
7. Mean Field Approaches for Many Body Systems -- Fermions and Boson
Fair Grading Algorithms for Randomized Exams
This paper studies grading algorithms for randomized exams. In a randomized
exam, each student is asked a small number of random questions from a large
question bank. The predominant grading rule is simple averaging, i.e.,
calculating grades by averaging scores on the questions each student is asked,
which is fair ex-ante, over the randomized questions, but not fair ex-post, on
the realized questions. The fair grading problem is to estimate the average
grade of each student on the full question bank. The maximum-likelihood
estimator for the Bradley-Terry-Luce model on the bipartite student-question
graph is shown to be consistent with high probability when the number of
questions asked to each student is at least the cubed-logarithm of the number
of students. In an empirical study on exam data and in simulations, our
algorithm based on the maximum-likelihood estimator significantly outperforms
simple averaging in prediction accuracy and ex-post fairness even with a small
class and exam size
Geometry of Rounding: Near Optimal Bounds and a New Neighborhood Sperner's Lemma
A partition of is called a
-secluded partition if, for every ,
the ball intersects at most
members of . A goal in designing such secluded partitions is to
minimize while making as large as possible. This partition
problem has connections to a diverse range of topics, including deterministic
rounding schemes, pseudodeterminism, replicability, as well as Sperner/KKM-type
results.
In this work, we establish near-optimal relationships between and
. We show that, for any bounded measure partitions and for any
, it must be that . Thus, when is
restricted to , it follows that . This bound is tight up to log factors, as it is
known that there exist secluded partitions with and
. We also provide new constructions of secluded
partitions that work for a broad spectrum of and
parameters. Specifically, we prove that, for any
, there is a secluded partition with
and
. These new partitions are optimal up to
factors for various choices of and . Based
on the lower bound result, we establish a new neighborhood version of Sperner's
lemma over hypercubes, which is of independent interest. In addition, we prove
a no-free-lunch theorem about the limitations of rounding schemes in the
context of pseudodeterministic/replicable algorithms
PrivLava: Synthesizing Relational Data with Foreign Keys under Differential Privacy
Answering database queries while preserving privacy is an important problem
that has attracted considerable research attention in recent years. A canonical
approach to this problem is to use synthetic data. That is, we replace the
input database R with a synthetic database R* that preserves the
characteristics of R, and use R* to answer queries. Existing solutions for
relational data synthesis, however, either fail to provide strong privacy
protection, or assume that R contains a single relation. In addition, it is
challenging to extend the existing single-relation solutions to the case of
multiple relations, because they are unable to model the complex correlations
induced by the foreign keys. Therefore, multi-relational data synthesis with
strong privacy guarantees is an open problem. In this paper, we address the
above open problem by proposing PrivLava, the first solution for synthesizing
relational data with foreign keys under differential privacy, a rigorous
privacy framework widely adopted in both academia and industry. The key idea of
PrivLava is to model the data distribution in R using graphical models, with
latent variables included to capture the inter-relational correlations caused
by foreign keys. We show that PrivLava supports arbitrary foreign key
references that form a directed acyclic graph, and is able to tackle the common
case when R contains a mixture of public and private relations. Extensive
experiments on census data sets and the TPC-H benchmark demonstrate that
PrivLava significantly outperforms its competitors in terms of the accuracy of
aggregate queries processed on the synthetic data.Comment: This is an extended version of a SIGMOD 2023 pape
Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective
This paper introduces a comprehensive, multi-stage machine learning
methodology that effectively integrates information systems and artificial
intelligence to enhance decision-making processes within the domain of
operations research. The proposed framework adeptly addresses common
limitations of existing solutions, such as the neglect of data-driven
estimation for vital production parameters, exclusive generation of point
forecasts without considering model uncertainty, and lacking explanations
regarding the sources of such uncertainty. Our approach employs Quantile
Regression Forests for generating interval predictions, alongside both local
and global variants of SHapley Additive Explanations for the examined
predictive process monitoring problem. The practical applicability of the
proposed methodology is substantiated through a real-world production planning
case study, emphasizing the potential of prescriptive analytics in refining
decision-making procedures. This paper accentuates the imperative of addressing
these challenges to fully harness the extensive and rich data resources
accessible for well-informed decision-making
Tonelli Approach to Lebesgue Integration
Leonida Tonelli devised an interesting and efficient method to introduce the
Lebesgue integral. The details of this method can only be found in the original
Tonelli paper and in an old italian course and solely for the case of the
functions of one variable. We believe that it is woth knowing this method and
here we present a complete account for functions of every number of variables
Construction of radon chamber to expose active and passive detectors
In this research and development, we present the design and manufacture of a radon chamber
(PUCP radon chamber), a necessary tool for the calibration of passive detectors, verification
of the operation of active radon monitors as well as diffusion chamber calibration used in
radon measurements in air, and soils. The first chapter is an introduction to describe radon
gas and national levels of radon concentration given by many organizations. Parameters that
influence the calibration factor of the LR 115 type 2 film detector are studied, such as the
energy window, critical angle, and effective volumes. Those are strongly related to the etching
processes and counting of tracks all seen from a semi-empirical approach studied in the second
chapter. The third chapter presents a review of some radon chambers that have been reported
in the literature, based on their size and mode of operation as well as the radon source they use.
The design and construction of the radon chamber are presented, use of uranium ore (autunite)
as a chamber source is also discussed. In chapter fourth, radon chamber characterization
is presented through leakage lambda, homogeneity of radon concentration, regimes-operation
modes, and the saturation concentrations that can be reached. Procedures and methodology
used in this work are contained in the fifth chapter and also some uses and applications of the
PUCP radon chamber are presented; the calibration of cylindrical metallic diffusion chamber
based on CR-39 chips detectors taking into account overlapping effect; transmission factors of
gaps and pinhole for the same diffusion chambers are determined; permeability of glass fiber
filter for 222Rn is obtained after reach equilibrium through Ramachandran model and taking
into account a partition function as the rate of track density. The results of this research have
been published in indexed journals. Finally, the conclusion and recommendations that reflect
the fulfillment aims of this thesis are presented
A study of uncertainty quantification in overparametrized high-dimensional models
Uncertainty quantification is a central challenge in reliable and trustworthy
machine learning. Naive measures such as last-layer scores are well-known to
yield overconfident estimates in the context of overparametrized neural
networks. Several methods, ranging from temperature scaling to different
Bayesian treatments of neural networks, have been proposed to mitigate
overconfidence, most often supported by the numerical observation that they
yield better calibrated uncertainty measures. In this work, we provide a sharp
comparison between popular uncertainty measures for binary classification in a
mathematically tractable model for overparametrized neural networks: the random
features model. We discuss a trade-off between classification accuracy and
calibration, unveiling a double descent like behavior in the calibration curve
of optimally regularized estimators as a function of overparametrization. This
is in contrast with the empirical Bayes method, which we show to be well
calibrated in our setting despite the higher generalization error and
overparametrization
Recommended from our members
The Epidemiology and Genetic Architecture of Vitamin D Deficiency in African Children
Vitamin D deficiency is a common public health problem worldwide. However, little is known about the epidemiology of vitamin D deficiency in Africa. In this thesis, I aimed to determine: 1) the prevalence of and risk factors associated with vitamin D deficiency in studies conducted in Africa; 2) the prevalence and predictors of vitamin D deficiency in African children; 3) the association between vitamin D and iron deficiency in African children; and 4) genetic variants that influence vitamin D status in Africans.
In a systematic review and meta-analyses of previous vitamin D studies in Africa, the average prevalence of low vitamin D status was 18.5%, 34.2% and 59.5% using cut-offs of 25-hydroxyvitamin D (25(OH)D) levels of <30 nmol/L, <50 nmol/L and <75 nmol/L, respectively. Populations at risk of vitamin D deficiency included newborns, women, and people living in high latitudes or urban areas.
In an epidemiological study of young children living in Africa, the prevalence of low vitamin D status was 0.6%, 7.8% and 44.5% using cut-offs of 25(OH)D levels of GC2 variant of the group-specific component (GC) gene, which encodes vitamin D binding protein.
Vitamin D deficiency was also associated with 80% higher odds of iron deficiency in these children. Adjusted regression models revealed that vitamin D deficiency was associated with higher ferritin and hepcidin levels suggesting lower iron status, and reduced sTfR and transferrin levels and increased TSAT and serum iron levels suggesting improved iron status.
Genome-wide association study (GWAS) in Africans revealed genetic variants that influence vitamin D status in vitamin D metabolism genes: DHCR7/NADSYN1, CYP2R1 and GC. However, the majority of SNPs from previous European GWASs did not replicate in the current GWAS.
Findings from this thesis indicate that vitamin D deficiency is prevalent in many African populations and should be considered in public health strategies in Africa
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