Rhythmic inhibition allows neural networks to search for maximally consistent states

Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits yet its computational role still remains elusive. We show that a model of Gamma-band rhythmic inhibition allows networks of coupled cortical circuit motifs to search for network configurations that best reconcile external inputs with an internal consistency model encoded in the network connectivity. We show that Hebbian plasticity allows the networks to learn the consistency model by example. The search dynamics driven by rhythmic inhibition enable the described networks to solve difficult constraint satisfaction problems without making assumptions about the form of stochastic fluctuations in the network. We show that the search dynamics are well approximated by a stochastic sampling process. We use the described networks to reproduce perceptual multi-stability phenomena with switching times that are a good match to experimental data and show that they provide a general neural framework which can be used to model other 'perceptual inference' phenomena

Time lower bounds for nonadaptive turnstile streaming algorithms

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds

The Meltdown of the Global Economy: A Keynes-Minsky Episode?

The enormity and pervasiveness of the global economic crisis that began in 2008 makes it relevant to analyze the circumstances that can explain this catastrophe. This will also provide clues to the appropriate remedial measures needed to prevent future occurrences of similar developments. The paper begins with some theoretical concerns relating to factors that could trigger a similar crisis. The first of these concerns relates to the deregulated financial institutions and the growing uncertainty that can be witnessed in these liberalized financial markets. The secondrelates to financial engineering with innovations in these markets, simultaneously providing cushions against risks while generating flows of liquidity that remain beyond the conventional sources of bank credit. Interpreting the role of uncertainty, one can observe the connections between investment and finance, both of which are subject to changes in the state of expectations. The initial formulation can be traced back to John Maynard Keynes's General Theory (1936), where liquidity preference is linked to asset prices and new investments. The Keynesian analysis of the impact of uncertainty related expectations was reformulated in 1986 by Hyman P. Minsky, who introduced the possibility of sourcing external finance through debt, which further adds to the impact of uncertainty. Minsky's characterization of deregulated financial markets considers the newfangled sources of nonbank credit, especially with the involvement of banks in the securities market under the universal banking model. As for the institutional arrangements that provide for profits on transactions, financial assets bought and sold in the primary market as initial public offerings of stocks are usually transacted later, in the secondary market, where these are no longer backed by physical assets.In the upswing, finance creates a myriad of financial claims and liabilities, and thus becomes increasingly remote from the real economy, while innovations to hedge and insulate assets continue to proliferate in the financial market, especially in the presence of uncertainty. The paper dwells on an account of the pattern of the financial crisis and its spread in the United States. This is appended by a stylized account of the turn of events in terms of a theoretical model that highlights the role of uncertainty in the process

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

Testing (subclasses of) halfspaces

We address the problem of testing whether a Boolean-valued function f is a halfspace, i.e. a function of the form f(x) = sgn(w . x − θ). We consider halfspaces over the continuous domain R n (endowed with the standard multivariate Gaussian distribution) as well as halfspaces over the Boolean cube { − 1,1} n (endowed with the uniform distribution). In both cases we give an algorithm that distinguishes halfspaces from functions that are ε-far from any halfspace using only poly(1) queries, independent of the dimension n. In contrast to the case of general halfspaces, we show that testing natural subclasses of halfspaces can be markedly harder; for the class of { − 1,1}-weight halfspaces, we show that a tester must make at least Ω(logn) queries. We complement this lower bound with an upper bound showing that O(√n) queries suffice.National Basic Research Program of China (grant 2007CB807900)National Basic Research Program of China (grant 2007CB807901)National Natural Science Foundation (China) (grant 60553001

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

The social cognition of medical knowledge, with special reference to childhood epilepsy

This paper arose out of an engagement in medical communication courses at a Gulf university. It deploys a theoretical framework derived from a (critical) sociocognitive approach to discourse analysis in order to investigate three aspects of medical discourse relating to childhood epilepsy: the cognitive processes that are entailed in relating different types of medical knowledge to their communicative context; the types of medical knowledge that are constituted in the three different text types analysed; and the relationship between these different types of medical knowledge and the discursive features of each text type. The paper argues that there is a cognitive dimension to the human experience of understanding and talking about one specialized from of medical knowledge. It recommends that texts be studied in medical communication courses not just in terms of their discrete formal features but also critically, in terms of the knowledge which they produce, transmit and reproduce