989 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!
Drawings of Complete Multipartite Graphs up to Triangle Flips
For a drawing of a labeled graph, the rotation of a vertex or crossing is the cyclic order of its incident edges, represented by the labels of their other endpoints. The extended rotation system (ERS) of the drawing is the collection of the rotations of all vertices and crossings. A drawing is simple if each pair of edges has at most one common point. Gioan's Theorem states that for any two simple drawings of the complete graph Kn with the same crossing edge pairs, one drawing can be transformed into the other by a sequence of triangle flips (a.k.a. Reidemeister moves of Type 3). This operation refers to the act of moving one edge of a triangular cell formed by three pairwise crossing edges over the opposite crossing of the cell, via a local transformation. We investigate to what extent Gioan-type theorems can be obtained for wider classes of graphs. A necessary (but in general not sufficient) condition for two drawings of a graph to be transformable into each other by a sequence of triangle flips is that they have the same ERS. As our main result, we show that for the large class of complete multipartite graphs, this necessary condition is in fact also sufficient. We present two different proofs of this result, one of which is shorter, while the other one yields a polynomial time algorithm for which the number of needed triangle flips for graphs on n vertices is bounded by O(n16). The latter proof uses a Carathéodory-type theorem for simple drawings of complete multipartite graphs, which we believe to be of independent interest. Moreover, we show that our Gioan-type theorem for complete multipartite graphs is essentially tight in the following sense: For the complete bipartite graph Km, n minus two edges and Km, n plus one edge for any m, n ≥ 4, as well as Kn minus a 4-cycle for any n ≥ 5, there exist two simple drawings with the same ERS that cannot be transformed into each other using triangle flips. So having the same ERS does not remain sufficient when removing or adding very few edges
Behavior quantification as the missing link between fields: Tools for digital psychiatry and their role in the future of neurobiology
The great behavioral heterogeneity observed between individuals with the same
psychiatric disorder and even within one individual over time complicates both
clinical practice and biomedical research. However, modern technologies are an
exciting opportunity to improve behavioral characterization. Existing
psychiatry methods that are qualitative or unscalable, such as patient surveys
or clinical interviews, can now be collected at a greater capacity and analyzed
to produce new quantitative measures. Furthermore, recent capabilities for
continuous collection of passive sensor streams, such as phone GPS or
smartwatch accelerometer, open avenues of novel questioning that were
previously entirely unrealistic. Their temporally dense nature enables a
cohesive study of real-time neural and behavioral signals.
To develop comprehensive neurobiological models of psychiatric disease, it
will be critical to first develop strong methods for behavioral quantification.
There is huge potential in what can theoretically be captured by current
technologies, but this in itself presents a large computational challenge --
one that will necessitate new data processing tools, new machine learning
techniques, and ultimately a shift in how interdisciplinary work is conducted.
In my thesis, I detail research projects that take different perspectives on
digital psychiatry, subsequently tying ideas together with a concluding
discussion on the future of the field. I also provide software infrastructure
where relevant, with extensive documentation.
Major contributions include scientific arguments and proof of concept results
for daily free-form audio journals as an underappreciated psychiatry research
datatype, as well as novel stability theorems and pilot empirical success for a
proposed multi-area recurrent neural network architecture.Comment: PhD thesis cop
- …