Zeros and amoebas of partition functions

Angelelli, Mario; Konopelchenko, B. G.

doi:10.1142/s0129055x18500150

Cited by 10 publications

(20 citation statements)

References 71 publications

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“…In physical terms, the assumption (2.3), which replaces some variables with associated first moments, is valid under certain conditions that often involve the characteristic time scales of the model (e.g., thermalization time). Hence, blocks at g / ∈ {1, n} represent a new approach to deal with the notion of metastability also discussed in a different framework in [1,2].…”

Section: Discussionmentioning

confidence: 99%

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Streaming generalized cross entropy

2019

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We propose a new method to combine adaptive processes with a class of entropy estimators for the case of streams of data.Starting from a first estimation obtained from a batch of initial data, at each step the parameters of the model are estimated combining the prior knowledge and the new observation (or a block of observations). This allows extending the maximum entropy technique to a dynamical setting distinguishing between entropic contributions of the signal and the error. Furthermore, it gives a suitable approximation of standard GME problems when exact solutions are hard to evaluate.We test this method performing numerical simulations at various sample sizes and batch dimensions. Moreover, we explore intermediate cases between streaming GCE and standard GCE, namely, when the update of estimations involves blocks of observations of different sizes, and we include collinearity effects. Finally, we discuss the results to highlight the main characteristics of this method, the range of application, and future perspectives.

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Section: Discussionmentioning

confidence: 99%

“…respectively. The sample standard deviation s y = 2 was used in (5.4) in accordance to the 3-sigma rule [26,17], in order to make the scale of support compatible with s y .…”

Section: Simulationmentioning

confidence: 99%

Streaming generalized cross entropy

2019

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“…[20]). The importance of filters on finite sets also lies in its connections with the statistical amoeba formalism developed in [55]. The instability domain for a statistical amoeba is the locus of points x in the parameter space R n where the family…”

Section: The Case Of Finite Setsmentioning

confidence: 99%

“…These quantities were introduced in order to study real points where the partition function becomes singular and explore the associated metastability. In particular, the results in [55] mean that N k (x) is induced by an ultrafilter if and only if x belongs to the instability domain D k− .…”

Section: The Case Of Finite Setsmentioning

confidence: 99%

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Tropical limit and a micro-macro correspondence in statistical physics

Angelelli¹

2017

J. Phys. A: Math. Theor.

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Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituent (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Main attention is paid to asymmetry and duality between max-and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated.

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Representations of epistemic uncertainty and awareness in data-driven strategies

Angelelli,

Gervasi,

Ciavolino

2024

Soft Comput

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The diffusion of AI and big data is reshaping decision-making processes by increasing the amount of information that supports decisions, while reducing direct interaction with data and empirical evidence. This paradigm shift introduces new sources of uncertainty, as limited data observability results in ambiguity and a lack of interpretability. The need for the proper analysis of data-driven strategies motivates the search for new models that can describe this type of bounded access to knowledge.This contribution presents a novel theoretical model for uncertainty in knowledge representation and its transfer mediated by agents. We provide a dynamical description of knowledge states by endowing our model with a structure to compare and combine them. Specifically, an update is represented through combinations, and its explainability is based on its consistency in different dimensional representations. We look at inequivalent knowledge representations in terms of multiplicity of inferences, preference relations, and information measures. Furthermore, we define a formal analogy with two scenarios that illustrate non-classical uncertainty in terms of ambiguity (Ellsberg’s model) and reasoning about knowledge mediated by other agents observing data (Wigner’s Friend). Finally, we discuss some implications of the proposed model for data-driven strategies, with special attention to reasoning under uncertainty about business value dimensions and the design of measurement tools for their assessment.

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Zeros and amoebas of partition functions

Cited by 10 publications

References 71 publications

Streaming generalized cross entropy

Streaming generalized cross entropy

Tropical limit and a micro-macro correspondence in statistical physics

Representations of epistemic uncertainty and awareness in data-driven strategies

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