Spectral Polarization and Spectral Phase Control of Time and Energy Entangled Photons

We demonstrate a scheme to spectrally manipulate a collinear, continuous stream of time and energy entangled photons to generate beamlike, bandwidth-limited fuxes of polarization-entangled photons with nearly-degenerate wavelengths. Utilizing an ultrashort-pulse shaper to control the spectral phase and polarization of the photon pairs, we tailor the shape of the Hong-Ou-Mandel interference pattern, demonstrating the rules that govern the dependence of this interference pattern on the spectral phases of the photons. We then use the pulse shaper to generate all four polarization Bell states. The singlet state generated by this scheme forms a very robust decoherence-free subspace, extremely suitable for long distance fiber-optics based quantum communication.Comment: 5 pages, 3 figure

Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral

An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and plunge. The plunge trajectory from the innermost stable circular orbit (ISCO) is special (somewhat independent of initial conditions). We write an expression for its solution in closed-form and for the emitted waveform. In particular we extract an expression for the associated black-hole ringdown amplitudes, and evaluate them numerically.Comment: 21 pages, 5 figures. v4: added section with numerical evaluation of the ringdown amplitude

A quantitative metric of pioneer activity reveals that HNF4A has stronger in vivo pioneer activity than FOXA1

BACKGROUND: We and others have suggested that pioneer activity - a transcription factor\u27s (TF\u27s) ability to bind and open inaccessible loci - is not a qualitative trait limited to a select class of pioneer TFs. We hypothesize that most TFs display pioneering activity that depends on the TF concentration and the motif content at their target loci. RESULTS: Here, we present a quantitative in vivo measure of pioneer activity that captures the relative difference in a TF\u27s ability to bind accessible versus inaccessible DNA. The metric is based on experiments that use CUT&Tag to measure the binding of doxycycline-inducible TFs. For each location across the genome, we determine the concentration of doxycycline required for a TF to reach half-maximal occupancy; lower concentrations reflect higher affinity. We propose that the relative difference in a TF\u27s affinity between ATAC-seq labeled accessible and inaccessible binding sites is a measure of its pioneer activity. We estimate binding affinities at tens of thousands of genomic loci for the endodermal TFs FOXA1 and HNF4A and show that HNF4A has stronger pioneer activity than FOXA1. We show that both FOXA1 and HNF4A display higher binding affinity at inaccessible sites with more copies of their respective motifs. The quantitative analysis of binding suggests different modes of binding for FOXA1, including an anti-cooperative mode of binding at certain accessible loci. CONCLUSIONS: Our results suggest that relative binding affinities are reasonable measures of pioneer activity and support the model wherein most TFs have some degree of context-dependent pioneer activity

Drosophila Cdi4 is a p21/p27/p57-like cyclin-dependent kinase inhibitor with specificity for cyclin E complexes.

The eukaryotic cell cycle is controlled by a network of interacting regulatory proteins. We used an interaction mating two-hybrid assay to identify connections within the cell cycle regulatory network in Drosophila. We tested interactions between Drosophila cyclins and a panel of hundreds of previously identified proteins. One of the connections we identified was the interaction between cyclin E and a novel Drosophila protein, Cdi4. Because Cdi4 was originally identified by its ability to interact with a Drosophila cyclin-dependent kinase, the finding that it interacts with cyclin E strengthened the notion that it functions in cell cycle regulation. We show that Cdi4 can inhibit cyclin E function both in a yeast assay and in vitro. In light of these results, our sequence analysis revealed that Cdi4 is a unique member of the p21/p27/p57 family of Cdk inhibitors. Our results demonstrate that interaction mating assays using large informative panels of proteins can aid the analysis of regulatory networks by generating and constraining hypotheses that guide further work

Templates for stellar mass black holes falling into supermassive black holes

The spin modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes tumbling and inspiralling into massive black holes have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this article we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just three or four, much smaller than what has hitherto been thought to be about nine or ten. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte-Carlo simulations to test the predictions made in this paper.Comment: 12 pages, 4 Tables, 4th LISA symposium, submitted to CQ

Quality of internal representation shapes learning performance in feedback neural networks

A fundamental feature of complex biological systems is the ability to form feedback interactions with their environment. A prominent model for studying such interactions is reservoir computing, where learning acts on low-dimensional bottlenecks. Despite the simplicity of this learning scheme, the factors contributing to or hindering the success of training in reservoir networks are in general not well understood. In this work, we study non-linear feedback networks trained to generate a sinusoidal signal, and analyze how learning performance is shaped by the interplay between internal network dynamics and target properties. By performing exact mathematical analysis of linearized networks, we predict that learning performance is maximized when the target is characterized by an optimal, intermediate frequency which monotonically decreases with the strength of the internal reservoir connectivity. At the optimal frequency, the reservoir representation of the target signal is high-dimensional, de-synchronized, and thus maximally robust to noise. We show that our predictions successfully capture the qualitative behaviour of performance in non-linear networks. Moreover, we find that the relationship between internal representations and performance can be further exploited in trained non-linear networks to explain behaviours which do not have a linear counterpart. Our results indicate that a major determinant of learning success is the quality of the internal representation of the target, which in turn is shaped by an interplay between parameters controlling the internal network and those defining the task

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

Peritoneal mesothelioma in a young woman: Case report of radiopathologic findings and review of the literature

Peritoneal mesothelioma is a rare diagnosis most often seen in middle-aged men and exceedingly rarely in individuals in their teens and twenties. Diagnosis is often delayed secondary to nonspecific presenting symptoms and a misconception that there must be a history of asbestos exposure to garner such a diagnosis. Here, we present the case of a 21 year-old female with a histologically confirmed diagnosis of peritoneal mesothelioma and review the key radiologic and histologic findings of this rare diagnosis