Dimensional Consistency Analysis in Complex Algebraic Models

Relations in complex algebraic models include numerous variables and parameter that capture the physical dimensions of the objects represented in models (such as "mass", or "volume" of an object). A model developer must ensure the semantic correctness of the model, which includes consistency across physical dimensions and their units of measure in the model relations. Such dimensional consistency analysis is the subject of the research described in this paper. We propose a new methodological framework for this type of analysis which comprises: - a two-level structure for representing knowledge about physical dimensions and units of measure; and - the dimensional analysis algorithm that uses this structured knowledge for the verification of consistency. The proposed methodology allows us to resolve issues related to handling complex non-decomposable units of measure and the situation when instances of the same physical dimension are associated with different physical quantities. We illustrate the proposed methodological framework using mathematical relations from a comprehensive environmental model developed at IIASA

Quark-Gluon Plasma/Black Hole duality from Gauge/Gravity Correspondence

The Quark-Gluon Plasma (QGP) is the QCD phase of matter expected to be formed at small proper-times in the collision of heavy-ions at high energy. Experimental observations seem to favor a strongly coupled QCD plasma with the hydrodynamic properties of a quasi-perfect fluid, i.e. rapid thermalization (or isotropization) and small viscosity. The theoretical investigation of such properties is not obvious, due to the the strong coupling. The Gauge/Gravity correspondence provides a stimulating framework to explore the strong coupling regime of gauge theories using the dual string description. After a brief introduction to Gauge/Gravity duality, and among various existing studies, we focus on challenging problems of QGP hydrodynamics, such as viscosity and thermalization, in terms of gravitational duals of both the static and relativistically evolving plasma. We show how a Black Hole geometry arises naturally from the dual properties of a nearly perfect fluid and explore the lessons and prospects one may draw for actual heavy ion collisions from the Gauge/Gravity duality approach.Comment: 6 pages, 4 figures, invited talk at the EPS HEP 2007 Conference, Manchester (UK), and at the ``Deuxiemes rencontres PQG-France'', Etretat (2007); reference adde

Naturalistic stimuli reveal a dominant role for agentic action in visual representation

Abstract Naturalistic, dynamic movies evoke strong, consistent, and information-rich patterns of activity over a broad expanse of cortex and engage multiple perceptual and cognitive systems in parallel. The use of naturalistic stimuli enables functional brain imaging research to explore cognitive domains that are poorly sampled in highly-controlled experiments. These domains include perception and understanding of agentic action, which plays a larger role in visual representation than was appreciated from experiments using static, controlled stimuli

Running anti-de Sitter radius from QCD-like strings

We consider renormalization effects for a bosonic QCD-like string, whose partons have $1/p^{2}$ propagators instead of Gaussian. Classically this model resembles (the bosonic part of) the projective light-cone (zero-radius) limit of a string on an AdS${}_5$ background, where Schwinger parameters give rise to the fifth dimension. Quantum effects generate dynamics for this dimension, producing an AdS${}_5$ background with a running radius. The projective light-cone is the high-energy limit: Holography is enforced dynamically.Comment: 12 page

Neural Responses to Naturalistic Clips of Behaving Animals Under Two Different Task Contexts

The human brain rapidly deploys semantic information during perception to facilitate our interaction with the world. These semantic representations are encoded in the activity of distributed populations of neurons (Haxby et al., 2001; McClelland and Rogers, 2003; Kriegeskorte et al., 2008b) and command widespread cortical real estate (Binder et al., 2009; Huth et al., 2012). The neural representation of a stimulus can be described as a location (i.e., response vector) in a high-dimensional neural representational space (Kriegeskorte and Kievit, 2013; Haxby et al., 2014). This resonates with behavioral and theoretical work describing mental representations of objects and actions as being organized in a multidimensional psychological space (Attneave, 1950; Shepard, 1958, 1987; Edelman, 1998; Gärdenfors and Warglien, 2012). Current applications of this framework to neural representation (e.g., Kriegeskorte et al., 2008b) often implicitly assume that these neural representational spaces are relatively fixed and context-invariant. In contrast, earlier work emphasized the importance of attention and task demands in actively reshaping representational space (Shepard, 1964; Tversky, 1977; Nosofsky, 1986; Kruschke, 1992). A growing body of work in both electrophysiology (e.g., Sigala and Logothetis, 2002; Sigala, 2004; Cohen and Maunsell, 2009; Reynolds and Heeger, 2009) and human neuroimaging (e.g., Hon et al., 2009; Jehee et al., 2011; Brouwer and Heeger, 2013; Çukur et al., 2013; Sprague and Serences, 2013; Harel et al., 2014; Erez and Duncan, 2015; Nastase et al., 2017) has suggested mechanisms by which behavioral goals dynamically alter neural representation

Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry

To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z$_2$ gauge invariance $\psi \to -\psi$, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) in order that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z$_2$ gauge invariance identifies two seemingly distinct `vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated $\omega \sim 0$ solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure

Modeling Semantic Encoding in a Common Neural Representational Space

Encoding models for mapping voxelwise semantic tuning are typically estimated separately for each individual, limiting their generalizability. In the current report, we develop a method for estimating semantic encoding models that generalize across individuals. Functional MRI was used to measure brain responses while participants freely viewed a naturalistic audiovisual movie. Word embeddings capturing agent-, action-, object-, and scene-related semantic content were assigned to each imaging volume based on an annotation of the film. We constructed both conventional within-subject semantic encoding models and between-subject models where the model was trained on a subset of participants and validated on a left-out participant. Between-subject models were trained using cortical surface-based anatomical normalization or surface-based whole-cortex hyperalignment. We used hyperalignment to project group data into an individual’s unique anatomical space via a common representational space, thus leveraging a larger volume of data for out-of-sample prediction while preserving the individual’s fine-grained functional–anatomical idiosyncrasies. Our findings demonstrate that anatomical normalization degrades the spatial specificity of between-subject encoding models relative to within-subject models. Hyperalignment, on the other hand, recovers the spatial specificity of semantic tuning lost during anatomical normalization, and yields model performance exceeding that of within-subject models