Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2^n) and compute the fractional hypertree-width of H in time O(m*1.734601^n).Comment: 12 pages, 1 figur

Apartment House: Wolff, Cage, ‘Performing Indeterminacy’, University of Leeds, 1 July 2017

At the beginning of July, the University of Leeds played host to the ‘Performing Indeterminacy’ conference: a series of talks, panels and concerts that are part of a research project on John Cage's Concert for Piano and Orchestra (1957–58), led by Philip Thomas and Martin Iddon. In the middle of all this, Apartment House presented what many consider the pinnacle of Cage's indeterminate work alongside a new commission from Christian Wolff, the last surviving member of the New York School composers. Resistance (2016–17), Wolff's new work ‘for 10 or more players and a pianist’, was written in response to Cage's Concert, sharing elements of its instrumentation and schema. In Leeds’ Clothworkers Hall, Apartment House – led by Anton Lukoszevieze – premiered the new piece alongside its progenitor, composed some 59 years apart. At the heart of both pieces in this concert is Philip Thomas at the piano. The conscientiousness and exactitude that Thomas brings to the music of both Cage and Wolff (having worked closely with the latter over the past 15 years) make him, perhaps, the ideal soloist for this programme. Quite simply, it is a line-up that could not have come about through chance procedure

Naturalistic neuroscience and virtual reality

Virtual reality (VR) is one of the techniques that became particularly popular in neuroscience over the past few decades. VR experiments feature a closed-loop between sensory stimulation and behavior. Participants interact with the stimuli and not just passively perceive them. Several senses can be stimulated at once, large-scale environments can be simulated as well as social interactions. All of this makes VR experiences more natural than those in traditional lab paradigms. Compared to the situation in field research, a VR simulation is highly controllable and reproducible, as required of a laboratory technique used in the search for neural correlates of perception and behavior. VR is therefore considered a middle ground between ecological validity and experimental control. In this review, I explore the potential of VR in eliciting naturalistic perception and behavior in humans and non-human animals. In this context, I give an overview of recent virtual reality approaches used in neuroscientific research

Modeling Cell-to-Cell Communication Networks Using Response-Time Distributions.

Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes, such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as "black boxes" with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps

An Approximation Algorithm for #k-SAT

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >= 3 within a running time that is not only non-trivial, but also significantly better than that of the currently fastest exact algorithms for the problem. More precisely, our algorithm is a randomized approximation scheme whose running time depends polynomially on the error tolerance and is mildly exponential in the number n of variables of the input formula. For example, even stipulating sub-exponentially small error tolerance, the number of solutions to 3-CNF input formulas can be approximated in time O(1.5366^n). For 4-CNF input the bound increases to O(1.6155^n). We further show how to obtain upper and lower bounds on the number of solutions to a CNF formula in a controllable way. Relaxing the requirements on the quality of the approximation, on k-CNF input we obtain significantly reduced running times in comparison to the above bounds