Martin H. Krieger’s research while affiliated with University of Southern California and other places

What is this page?


This page lists works of an author who doesn't have a ResearchGate profile or hasn't added the works to their profile yet. It is automatically generated from public (personal) data to further our legitimate goal of comprehensive and accurate scientific recordkeeping. If you are this author and want this page removed, please let us know.

Publications (33)


Learning from Newton
  • Chapter

February 2024

·

2 Reads

Martin H. Krieger

Newton's work on mathematics, alchemy, and theology it would seem are of a piece.


Why Mathematical Physics?

February 2024

·

17 Reads

The 2022 Prizes from the International Mathematical Union featured two focusing on mathematical physics: a Fields Medal to Hugo Duminil-Copin, and the Carl Friedrich Gauss Prize for Applications of Mathematics to Elliott H. Lieb. Duminil-Copin (and his teacher, Stanislav Smirnov, 2010 Fields Medal) developed rigorous ways of thinking of a lattice at its critical local connection probability that leads to a path through the lattice (Fig. 2.1). They employed a discrete complex analysis. Then, they develop ingenious ways of describing that lattice at the critical point, ways amenable to rigorous mathematical proof. In a lifetime of work, Lieb has employed mathematics as the usual physicists’ starting point to reveal the physics. For example, Lieb and collaborators (1964) showed how that Ising lattice might be thought of as a quantum field theory (with annihilation and creation operators). Themes are: Technique is physical. Rigor is revealing. Tricks are physical. And, mathematical physics often leads to deep mathematics.


Mathematical Physics

February 2024

·

3 Reads

The practice of mathematics applied to physics, more particularly mathematical physics, leads to demands for explicitness and rigor. The features of this practice are in effect unavoidable—although derivations of the same fact may go by different routes. Rigor matters substantively.



Legerdemain in Mathematical Physics: Structure, “Tricks,” and Lacunae in Derivations of the Partition Function of the Two-Dimensional Ising Model and in Proofs of The Stability of Matter

February 2024

·

1 Read

Many mathematical or physical paper would seem to magically go from one line to the next, the reader unable to figure out the logic of the transition. Such legerdemain, whether it be magical or in doing physics, is no less impressive if you know how it is done, for you yourself would have to train extensively to actually perform these sleights of hand. What you might have ignored turns out to have needed informed careful attention. Yet, to be struck by legerdemain you must have actually read the paper, so that the device or method would stop you cold. Where did that come from? How do you get from line A to line A + 1? (I should note that much of the discussion below will benefit from having those papers in front of you.)


So Far and in Prospect

February 2024

Kinship and Particles; Primes and Particles; Effective Field Theory; Packaging Functions Connecting Spectra to Symmetries; Multiples Ways of Computing Partition Functions; Algebraic, Arithmetic, Analytic; The Right Particles or Parts.



Primes and Particles

February 2024

·

7 Reads

Mathematics and physics have been borrowing notions from each other for a very long time. Some mathematical object or construction provides a superb model of the physical world. Some physical account instantiates a more general mathematical object or construction, avant la lettre, that mathematical notion only then discovered. Abstract mathematical constructions are found to be useful by physicists, sometimes decades after the mathematicians have lost interest in them. Physical theories develop as they will, while across town, there is mathematics that will enlighten the physicist—but by chance such enlightenment may take place, if it does, decades later than would be ideal.



Ising Matter as Bulky: An Identity Described by Many Models

September 2020

·

2 Reads

The two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear to analogize with the mathematical threefold analogy of analysis, algebra, and arithmetic, due to R. Dedekind and H. Weber, 1882, and more recently described by A. Weil.


Citations (12)


... For an insurance company, the insurance clerk not only needs to master the coverage and amount of each type of insurance but also requires the insurance clerk to master each customer's purchase of insurance. rough these professional knowledge and situations, insurance salesmen need to do their best to sell insurance [5][6][7]. It can be seen from the above description that the data of insurance business is numerous, multisource, and complex, which is a difficult task for insurance business, that consumes a lot of human and material resources [8]. ...

Reference:

Evaluation and Selection of Insurance Marketing Schemes Driven by Multisource Big Data
Options and Insurance for Planning
  • Citing Article
  • April 2018

Journal of Planning Education and Research

... Trahan's attitude is close to the way that mathematicians treat long proofs. By the 1980s, according to Krieger (2004), a variety of rigorous proofs were provided of various fundamental facts about our world, many of them lengthy and complex and involving much calculation (Krieger, 2004): ...

Some of what mathematicians do
  • Citing Article
  • November 2004

Notices of the American Mathematical Society

... The proposed CAS theory has provided new ideas for people to recognize, control, and manage complex systems, and is widely used in economic systems, ecosystems, and social systems (Auyang, 1999a(Auyang, , 1999bGuo, 2017;Krieger, 2001). The study of complexity is also valued by Chinese scholars, whose research on the science of complexity mainly covers the three aspects of methodology, mathematical theory, and application, and involves many subjects including geography, economics, biology, physics, management and philosophy (Comfort, 1999;Song, 2005). ...

Foundations of Complex-Systems Theories
  • Citing Article
  • March 2001

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

... Representations are human inventions/constructs that stand in for the phenomena (Morgan and Morrison, 1999;Giere, 2005;Frigg and Hartmann, 2006;Windschitl et al., 2008;Schwarz et al., 2009). In physics, common types of representations include graphs, vector diagrams, equations, simulations, words, and pictures (Krieger, 1987). From the MI perspective, this means that instruction should focus on helping students to identify, use, and interpret representational tools that are useful in describing physical systems. ...

The physicist's toolkit
  • Citing Article
  • November 1987

American Journal of Physics

... Buck-Morss argues that the sensorium can be understood as a "form of cognition, achieved through taste, touch, hearing, seeing, smell-the whole corporeal sensorium" (Buck-Morss, 1992, p. 6). The idea of the urban sensorium, therefore, is fairly straightforward and is drawn from an understanding of developing a sense of the city through the five senses: sight, sound, smell, taste and touch (Krieger & Holman, 2007). Here, we restrict ourselves to an understanding of primarily the corporeality of the sensorium as a pedagogic mode rather than the more often associated category of the aesthetic. ...

A Dozen "Tamales!": Documenting the Aural Urban Sensorium
  • Citing Article
  • December 2007

Journal of Planning Education and Research

... This optimistic tone about the use of photography is echoed by others in planning, geography and sociology. Martin Krieger (2004) states that planners, in particular, are in a strong position to document cities through photography. He encourages systematic photography of particular places or phenomena that then could become the basis of archives upon which future students and scholars can draw. ...

Taking Pictures in the City
  • Citing Article
  • December 2004

Journal of Planning Education and Research

... Whereas the complexity of coordination in spatial planning increased with the centralization of the state and later its democratization (involving more actors), the history of spatial design is also tied to state development, but more indirectly, through the increase of patronage. Complex cities produced rich citizens and proud city governments that could engage in private and public works that were the product of a design philosophy, with the sum of city space given higher consideration than the separate parts (Braunfels, 1990;Rios, 2008;Krieger, 2000;Mumford, 1961). ...

Planning and Design as the Manufacture of Transcendence
  • Citing Article
  • March 2000

Journal of Planning Education and Research

... One of the major implications of this analysis is that literary fiction and narratology, and more generally public humanities, should enter the toolbox of urban planners on a permanent basis, and possibly also become part of their educational curricula (Dakin 1993;Krieger 1995). We see this perspective as particularly promising if properly framed within the emerging paradigm of the Narrative Policy Framework (Jones 2018), that systematizes the role of narrative in the policy process in cognitive, pragmatic and strategic terms. ...

What Does Jerusalem Have to Do With Athens?: Roles for the Humanities in Planning
  • Citing Article
  • April 1995

Journal of Planning Education and Research

... Our research also complements papers that have used online user-generated content to extract time-series data about consumer behavior ( [16]), health ( [17]; [18]), or finance ( [19]), or to obtain cross-sectional socioeconomic data ( [20]). A growing literature in urban tomography ( [21]) is demonstrating that adding geographical identification to such methods can improve research and practice in urban planning, urban sciences, environmental science or psychology, and architecture. For example, [22] shows the conditions under which user-generated opinions can be deemed reliable for planning decisions. ...

Urban Tomography
  • Citing Article
  • August 2010

Journal of Urban Technology

Martin H. Krieger

·

·

·

[...]

·

... Abdelzaher et al. [1] conclude the primary participatory sensing applications deeply. A number of early participatory sensing prototype systems have been built such as BikeNet [2], SoundSense [3], CenceMe [4,5], MetroSense [6], Bubble-Sensing [7], Urban Tomography [8,9], CarTel [10], Darwin [11], and Microblog [12] at the same time. These participatory sensing prototype systems lay the foundation of human sensing. ...

Commentary: Pervasive Urban Media Documentation
  • Citing Article
  • September 2009

Journal of Planning Education and Research