Extending the Coordination of Cognitive and Social Perspectives

Cognitive analyses are typically used to study individuals, whereas social analyses are typically used to study groups. In this article, I make a distinction between what one is looking with?one’s theoretical lens?and what one is looking at?e.g., an individual or a group?. By emphasizing the former, I discuss social analyses of individuals and cognitive analyses of groups, additional analyses that can enhance mathematics education research. I give examples of each and raise questions about the appropriateness of such analyses

A Joint Intensity and Depth Co-Sparse Analysis Model for Depth Map Super-Resolution

High-resolution depth maps can be inferred from low-resolution depth measurements and an additional high-resolution intensity image of the same scene. To that end, we introduce a bimodal co-sparse analysis model, which is able to capture the interdependency of registered intensity and depth information. This model is based on the assumption that the co-supports of corresponding bimodal image structures are aligned when computed by a suitable pair of analysis operators. No analytic form of such operators exist and we propose a method for learning them from a set of registered training signals. This learning process is done offline and returns a bimodal analysis operator that is universally applicable to natural scenes. We use this to exploit the bimodal co-sparse analysis model as a prior for solving inverse problems, which leads to an efficient algorithm for depth map super-resolution.Comment: 13 pages, 4 figure

Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. III. Factorized asymptotics

In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic Calogero-Moser type. We focused on the first steps of the scheme in Part I, and on the cases $N=2$ and $N=3$ in Part II. In this paper, we determine the dominant asymptotics of a similarity transformed function \rE_N(b;x,y) for $y_j-y_{j+1}\to\infty$, $j=1,\ldots, N-1$, and thereby confirm the long standing conjecture that the particles in the hyperbolic relativistic Calogero-Moser system exhibit soliton scattering. This result generalizes a main result in Part II to all particle numbers $N>3$.Comment: 21 page

Are the Ultra-Faint Dwarf Galaxies Just Cusps?

We develop a technique to investigate the possibility that some of the recently discovered ultra-faint dwarf satellites of the Milky Way might be cusp caustics rather than gravitationally self-bound systems. Such cusps can form when a stream of stars folds, creating a region where the projected 2-D surface density is enhanced. In this work, we construct a Poisson maximum likelihood test to compare the cusp and exponential models of any substructure on an equal footing. We apply the test to the Hercules dwarf (d ~ 113 kpc, M_V ~ -6.2, e ~ 0.67). The flattened exponential model is strongly favored over the cusp model in the case of Hercules, ruling out at high confidence that Hercules is a cusp catastrophe. This test can be applied to any of the Milky Way dwarfs, and more generally to the entire stellar halo population, to search for the cusp catastrophes that might be expected in an accreted stellar halo.Comment: Accepted for publication in ApJ Letters. Minor revisions from version

Self-, other-, and joint monitoring using forward models

In the psychology of language, most accounts of self-monitoring assume that it is based on comprehension. Here we outline and develop the alternative account proposed by Pickering and Garrod (2013), in which speakers construct forward models of their upcoming utterances and compare them with the utterance as they produce them. We propose that speakers compute inverse models derived from the discrepancy (error) between the utterance and the predicted utterance and use that to modify their production command or (occasionally) begin anew. We then propose that comprehenders monitor other people’s speech by simulating their utterances using covert imitation and forward models, and then comparing those forward models with what they hear. They use the discrepancy to compute inverse models and modify their representation of the speaker’s production command, or realize that their representation is incorrect and may develop a new production command. We then discuss monitoring in dialogue, paying attention to sequential contributions, concurrent feedback, and the relationship between monitoring and alignment

Tailored Source Code Transformations to Synthesize Computationally Diverse Program Variants

The predictability of program execution provides attackers a rich source of knowledge who can exploit it to spy or remotely control the program. Moving target defense addresses this issue by constantly switching between many diverse variants of a program, which reduces the certainty that an attacker can have about the program execution. The effectiveness of this approach relies on the availability of a large number of software variants that exhibit different executions. However, current approaches rely on the natural diversity provided by off-the-shelf components, which is very limited. In this paper, we explore the automatic synthesis of large sets of program variants, called sosies. Sosies provide the same expected functionality as the original program, while exhibiting different executions. They are said to be computationally diverse. This work addresses two objectives: comparing different transformations for increasing the likelihood of sosie synthesis (densifying the search space for sosies); demonstrating computation diversity in synthesized sosies. We synthesized 30184 sosies in total, for 9 large, real-world, open source applications. For all these programs we identified one type of program analysis that systematically increases the density of sosies; we measured computation diversity for sosies of 3 programs and found diversity in method calls or data in more than 40% of sosies. This is a step towards controlled massive unpredictability of software

On the descriptional complexity of operations on semilinear sets

We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by con- stant and period vectors. The interesting parameters of a semilinear set are: (i) the maximal value that appears in the vectors of periods and constants and (ii) the number of such sets of periods and constants necessary to describe the semilinear set under consideration. More precisely, we prove upper bounds on the union, intersection, complementation, and inverse homomorphism. In particular, our result on the complementation upper bound answers an open problem from [G. J. Lavado, G. Pighizzini, S. Seki: Operational State Complexity of Parikh Equivalence, 2014]