Sampling and Approximation of Bandlimited Volumetric Data

We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is based on expanding the given function in the basis of generalized prolate spheroidal wavefunctions, with the expansion coefficients given by weighted dot products between the samples of the function and the samples of the basis functions. As numerical implementations require all expansions to be finite, we present a truncation rule for the expansions. Finally, we derive a bound on the overall approximation error in terms of the assumed space/frequency concentration

Decimated Prony's Method for Stable Super-resolution

We study recovery of amplitudes and nodes of a finite impulse train from a limited number of equispaced noisy frequency samples. This problem is known as super-resolution (SR) under sparsity constraints and has numerous applications, including direction of arrival and finite rate of innovation sampling. Prony's method is an algebraic technique which fully recovers the signal parameters in the absence of measurement noise. In the presence of noise, Prony's method may experience significant loss of accuracy, especially when the separation between Dirac pulses is smaller than the Nyquist-Shannon-Rayleigh (NSR) limit. In this work we combine Prony's method with a recently established decimation technique for analyzing the SR problem in the regime where the distance between two or more pulses is much smaller than the NSR limit. We show that our approach attains optimal asymptotic stability in the presence of noise. Our result challenges the conventional belief that Prony-type methods tend to be highly numerically unstable.Comment: 5 pages, 10 figure

Calabi-Yau Spaces and Five Dimensional Field Theories with Exceptional Gauge Symmetry

Five dimensional field theories with exceptional gauge groups are engineered from degenerations of Calabi-Yau threefolds. The structure of the Coulomb branch is analyzed in terms of relative K\"ahler cones. For low number of flavors, the geometric construction leads to new five dimensional fixed points.Comment: Harvmac, 42 pages, 21 Postscript figure

On the gain of entrainment in a class of weakly contractive bilinear control systems with applications to the master equation and the ribosome flow model

We consider a class of bilinear weakly contractive systems that entrain to periodic excitations. Entrainment is important in many natural and artificial processes. For example, in order to function properly synchronous generators must entrain to the frequency of the electrical grid, and biological organisms must entrain to the 24h solar day. A dynamical system has a positive gain of entrainment (GOE) if entrainment also yields a larger output, on average. This property is important in many applications from the periodic operation of bioreactors to the periodic production of proteins during the cell cycle division process. We derive a closed-form formula for the GOE to first-order in the control perturbation. This is used to show that in the class of systems that we consider the GOE is always a higher-order phenomenon. We demonstrate the theoretical results using two applications: the master equation and a model from systems biology called the ribosome flow model, both with time-varying and periodic transition rates

Who’s afraid of the predicate theory of names?

This essay is devoted to an analysis of the semantic significance of a fashionable view of proper names, the Predicate Theory of names (PT), typically developed in the direction of the Metalinguistic Theory of names (MT). According to MT, ‘syntactic evidence supports the conclusion that a name such as ‘Kennedy’ is analyzable in terms of the predicate (general term) ‘individual named ‘Kennedy’’. This analysis is in turn alleged to support a descriptivist treatment of proper names in designative position, presumably in contrast with theories of names as ‘directly referring rigid designators’. The main aim of this essay is that of questioning the significance of PT and MT as theories of designation: even granting for the argument’s sake that names are analyzable as (metalinguistic) predicates, their designative occurrences may be interpreted in consonance with the dictates of Direct Reference—indeed, in consonance with the radically anti-descriptivist version of Direct Reference I call Millianism

Atomic Multi-Channel Updates with Constant Collateral in Bitcoin-Compatible Payment-Channel Networks

Current cryptocurrencies provide a heavily limited transaction throughput that is clearly insufficient to cater their growing adoption. Payment-channel networks (PCNs) have emerged as an interesting solution to the scalability issue and are currently deployed by popular cryptocurrencies such as Bitcoin and Ethereum. While PCNs do increase the transaction throughput by processing payments off-chain and using the blockchain only as a dispute arbitrator, they unfortunately require high collateral (i.e., they lock coins for a non-constant time along the payment path) and are restricted to payments in a path from sender to receiver. These issues have severe consequences in practice. The high collateral enables denial-of-service attacks that hamper the throughput and utility of the PCN. Moreover, the limited functionality hinders the applicability of current PCNs in many important application scenarios. Unfortunately, current proposals do not solve either of these issues, or they require Turing-complete language support, which severely limit their applicability. In this work, we present AMCU, the first protocol for atomic multi-channel updates and reduced collateral that is compatible with Bitcoin (and other cryptocurrencies with reduced scripting capabilities). We provide a formal model in the Universal Composability framework and show that AMCU realizes it, thus demonstrating that AMCU achieves atomicity and value privacy. Moreover, the reduced collateral mitigates the consequences of griefing attacks in PCNs while the (multi-payment) atomicity achieved by AMCU opens the door to new applications such as credit rebalancing and crowdfunding that are not possible otherwise. Moreover, our evaluation results demonstrate that AMCU has a performance in line with that of the Lightning Network (the most widely deployed PCN) and thus is ready to be deployed in practice

MHC class II–restricted antigen presentation by plasmacytoid dendritic cells inhibits T cell–mediated autoimmunity

Although plasmacytoid dendritic cells (pDCs) express major histocompatibility complex class II (MHCII) molecules, and can capture, process, and present antigens (Ags), direct demonstrations that they function as professional Ag-presenting cells (APCs) in vivo during ongoing immune responses remain lacking. We demonstrate that mice exhibiting a selective abrogation of MHCII expression by pDCs develop exacerbated experimental autoimmune encephalomyelitis (EAE) as a consequence of enhanced priming of encephalitogenic CD4+ T cell responses in secondary lymphoid tissues. After EAE induction, pDCs are recruited to lymph nodes and establish MHCII-dependent myelin-Ag–specific contacts with CD4+ T cells. These interactions promote the selective expansion of myelin-Ag–specific natural regulatory T cells that dampen the autoimmune T cell response. pDCs thus function as APCs during the course of EAE and confer a natural protection against autoimmune disease development that is mediated directly by their ability to present of Ags to CD4+ T cells in vivo