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Twenty years ago Breiman (2001) called to our attention a significant cultural division in modeling and data analysis between the stochastic data models and the algorithmic models. Out of his deep concern that the statistical community was…
We present an explicit bijection between finite-decimal real numbers and natural numbers ($\mathbb{N} = \{1, 2, 3, ...\}$) using a systematic 4-tuple parametrization with closed-form mathematical formulas for enumeration. Our enumeration…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
Distributed ledger technology offers several advantages for banking and finance industry, including efficient transaction processing and cross-party transaction reconciliation. The key challenges for adoption of this technology in financial…
Protecting an individual's privacy when releasing their data is inherently an exercise in relativity, regardless of how privacy is qualified or quantified. This is because we can only limit the gain in information about an individual…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted…
Discrete Euclidian Spaces (DESs) are the starting point in the study of the major fields of the Isodimensional Discrete Mathematics (IDM). The isodimensional analysis is not an exception, being particularly interesting and fruitful the…
Data sharing is crucial for open science and reproducible research, but the legal sharing of clinical data requires the removal of protected health information from electronic health records. This process, known as de-identification, is…
Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data…
ICD(International Classification of Diseases) coding involves assigning ICD codes to patients visit based on their medical notes. Considering ICD coding as a multi-label text classification task, researchers have developed sophisticated…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
Text de-identification techniques are often used to mask personally identifiable information (PII) from documents. Their ability to conceal the identity of the individuals mentioned in a text is, however, hard to measure. Recent work has…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
In this survey we discuss a wide variety of aspects related to Lie group integrators. These numerical integration schemes for differential equations on manifolds have been studied in a general and systematic manner since the 1990s and the…
Differential Privacy (DP) provides an elegant mathematical framework for defining a provable disclosure risk in the presence of arbitrary adversaries; it guarantees that whether an individual is in a database or not, the results of a DP…
In distributed differential privacy, multiple parties collaborate to analyze their combined data while each party protects the confidentiality of its data from the others. Interestingly, for certain fundamental two-party functions, such as…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
International Classification of Diseases (ICD) are the de facto codes used globally for clinical coding. These codes enable healthcare providers to claim reimbursement and facilitate efficient storage and retrieval of diagnostic…