Opentask sep 2026 (4 risultati)

Taschenbuch. Condizione: Neu. Neuware - This pocket-size book introduces set theory and its applications to computing, data, and engineering. We start with basic concepts such as membership, equality, subsets, relations, and functions. We then consider equivalence, order, cardinality, induction, and recursion. We also discuss infinite sets and the axioms of set theory, along with their consequences for representation and computation.The applications include Boolean logic, relational databases, programming collections and types, formal specification with Z, B, and Alloy, combinatorial counting, probability, and graphs. The same mathematical concepts apply across contexts. For example, the distinction between sets and multisets helps explain how SQL handles duplicates. Relations model dependencies and connectivity. Different independence assumptions lead to different conclusions about collision probabilities. We also consider fuzzy sets, rough sets, and multisets as generalizations that require separate examination of their operations and laws.We use definitions, theorems, and worked examples throughout. We pay particular attention to the assumptions behind mathematical results and the differences between abstract models and their software implementations.The book is intended for software developers, data analysts, engineers, and students interested in the mathematical foundations of their work. A notation reference, an annotated bibliography, and an index are included for further study and practical reference.…

Taschenbuch. Condizione: Neu. Neuware - This book is AI-synthesized from our published work, including bits and pieces of CT applied to software diagnostics and debugging from 10-15 years ago.Software diagnostics usually involves analyzing and transforming several execution artifacts. We filter and join logs, reconstruct call stacks from memory dumps, compare traces, and combine observations from different tools. Such operations preserve some information and may discard relationships needed for diagnosis.In this book, we develop an Applied Category Theory approach to software diagnostics, observability, and debugging. We consider software behavior, execution artifacts, analysis patterns, and diagnostic hypotheses as related structures. Categories, functors, natural transformations, presheaves, and sheaves help us describe these relationships and specify what should be preserved. For example, two different analysis paths may be expected to produce the same result. A discrepancy then becomes a diagnostic indicator that requires further investigation.The book develops our earlier work on pattern-oriented software diagnostics, Software Codiagnostics, and trace and log analysis patterns. We introduce the Categorical Invariant Violation analysis pattern and connect categorical constructions to practical checks for distributed systems, memory analysis, observability drift, and agentic AI workflows. Worked examples include the analysis of a real HTTP log artifact. We also consider diagnostic applications of toposes and explain the relationship between established mathematics and our proposed constructions.Separate appendices introduce the mathematical prerequisites and category theory, assuming only school mathematics, and review established categorical applications. The book includes references, a glossary, and an index, and is intended for software developers, support engineers, SREs, software diagnosticians, and researchers.…

Taschenbuch. Condizione: Neu. Neuware - Mathematical concepts provide additional viewpoints for software diagnostics and software data analysis. We can consider a trace as a sequence of messages, a collection of activities, or a structure of relationships. Changing the viewpoint allows us to ask different questions about the same software evidence.In Mathematical Concepts in Software Diagnostics and Software Data Analysis, we introduce 85 concepts and explore their diagnostic interpretations. These range from graphs, equivalence relations, and partially ordered sets to sheaves, category theory, and ideas from mathematical physics. We consider how such concepts help us describe software behavior, compare execution structures, organize observations, and reason about incomplete evidence.Each concept is explained at three levels: an intuitive explanation requiring no mathematical knowledge, an undergraduate treatment, and a graduate perspective. Every two-page entry includes an illustration, explanations of terminology, readings of formulas in ordinary language, and a discussion of practical value and applicability. Readers can begin with a concrete software example and return to the mathematical details as their understanding develops.The concepts are arranged alphabetically for reference. Appendices provide mathematical foundations, classify the concepts, and connect them to their origins in analysis patterns and theoretical software diagnostics. Throughout the book, we distinguish formal constructions, structural analogies, and heuristic metaphors.This guide is intended for software diagnosticians, developers, and researchers who want to extend their mathematical vocabulary and explore its use in pattern-oriented software data analysis.…

Taschenbuch. Condizione: Neu. Neuware - We can think of optimization as choosing among alternatives under constraints. Similar structures appear in different disciplines, although the objects, criteria, and meanings may differ. For example, allocating computing resources, selecting a medical intervention, and revising a musical composition involve different interpretations of what constitutes an improvement.In Optimization Across Disciplines, we examine these connections across mathematics, computing, engineering, living systems, society, and creative work. We begin with fundamental concepts and proceed to methods and worked examples. These include black-box optimization, where we evaluate candidate solutions without direct access to the objective's internal structure. We also use category theory to examine composition and the conditions under which a relationship can be carried from one domain to another.The book includes illustrations, method cards, a glossary, an index, and references for further study. A mathematics companion develops the prerequisites from school foundations to advanced topics. An equation atlas connects the formulas in the main text with explanations of their symbols and meaning.Throughout the book, we consider how objectives are chosen, what evidence supports a result, and what a model leaves out. We also examine situations where further optimization is inappropriate, including when goals change, measurements distort behavior, or important values cannot be represented by a single score.In a bonus article, we consider optimization in software diagnostics, observability, memory dump analysis, trace and log analysis, and debugging. Optimization applies to both software behavior and the process used to explain it. We may collect more data, run additional debugger commands, or introduce another measurement, but each action has a cost. Its usefulness depends on the diagnostic question and the decision it may change.Using analysis patterns, we examine evidence selection, competing mechanisms, and controlled intervention. Memory dumps and execution traces provide different projections of software execution, and their combined evidence may answer questions that either artifact leaves unresolved. We introduce a formal model based on expected decision loss and value of information, then relate it to practical choices about instrumentation, sampling, artifact acquisition, and analysis.A worked latency example follows the process from initial hypotheses to a reversible software change. We also consider incomplete evidence, measurement effects, reduced failure reproductions, and conditions for stopping an investigation. Throughout the article, we retain the assumptions and uncertainty behind each conclusion and specify what a proposed improvement must preserve.…