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1. Network Restructuring Control for Conic Invariance with Application to Neural Networks

   https://doi.org/10.1109/CDC.2018.8618729  

   Singh, Matthew F.; Ching, ShiNung (December 2018, Conference on Decision and Control)

   Recent advances in the study of artificial and biological neural networks support the power of dynamic representations-computing with information stored as nontrivial limit-sets rather than fixed-point attractors. Understanding and manipulating these computations in nonlinear networks requires a theory of control for abstract objective functions. Towards this end, we consider two properties of limit-sets: their topological dimension and orientation (covariance) in phase space and combine these abstract properties into a single well-defined objective: conic control-invariant sets in the derivative space (i.e., the vector field). Real-world applications, such as neural-medicine, constrain which control laws are feasible with less-invasive controllers being preferable. To this end, we derive a feedback control-law for conic invariance which corresponds to constrained restructuring of the network connections as might occur with pharmacological intervention (as opposed to a physically separate control unit). We demonstrate the ease and efficacy of the technique in controlling the orientation and dimension of limit sets in high-dimensional neural networks. 

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2. Correlation consistent basis sets designed for density functional theory: Third-row atoms (Ga–Br)

   https://doi.org/10.1063/5.0176964  

   Determan, John J; Wilson, Angela K (February 2024, The Journal of Chemical Physics)

   The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga–Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn–Sham limit is improved relative to other basis sets where convergence to the Kohn–Sham limit is typically not observed. 

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3. Independent sets of a given size and structure in the hypercube

   https://doi.org/10.1017/S0963548321000559  

   Jenssen, Matthew; Perkins, Will; Potukuchi, Aditya (January 2022, Combinatorics, Probability and Computing)

   Abstract We determine the asymptotics of the number of independent sets of size $$\lfloor \beta 2^{d-1} \rfloor$$ in the discrete hypercube $$Q_d = \{0,1\}^d$$ for any fixed $$\beta \in (0,1)$$ as $$d \to \infty$$ , extending a result of Galvin for $$\beta \in (1-1/\sqrt{2},1)$$ . Moreover, we prove a multivariate local central limit theorem for structural features of independent sets in $$Q_d$$ drawn according to the hard-core model at any fixed fugacity $$\lambda>0$$ . In proving these results we develop several general tools for performing combinatorial enumeration using polymer models and the cluster expansion from statistical physics along with local central limit theorems. 

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4. Gravitational-wave Statistics for Pulsar Timing Arrays: Examining Bias from Using a Finite Number of Pulsars

   https://doi.org/10.3847/1538-4357/ac6f5e  

   Johnson, Aaron D.; Vigeland, Sarah J.; Siemens, Xavier; Taylor, Stephen R. (June 2022, The Astrophysical Journal)

   Abstract Recently, many different pulsar timing array (PTA) collaborations have reported strong evidence for a common stochastic process in their data sets. The reported amplitudes are in tension with previously computed upper limits. In this paper, we investigate how using a subset of a set of pulsars biases Bayesian upper limit recovery. We generate 500 simulated PTA data sets, based on the NANOGrav 11 yr data set with an injected stochastic gravitational-wave background (GWB). We then compute the upper limits by sampling the individual pulsar likelihoods, and combine them through a factorized version of the PTA likelihood to obtain upper limits on the GWB amplitude, using different numbers of pulsars. We find that it is possible to recover an upper limit (95% credible interval) below the injected value, and that it is significantly more likely for this to occur when using a subset of pulsars to compute the upper limit. When picking pulsars to induce the maximum possible bias, we find that the 95% Bayesian upper limit recovered is below the injected value in 10.6% of the realizations (53 of 500). Further, we find that if we choose a subset of pulsars in order to obtain a lower upper limit than when using the full set of pulsars, the distribution of the upper limits obtained from these 500 realizations is shifted to lower-amplitude values. 

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5. Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers

   https://doi.org/10.1364/OE.480092  

   Goodsell, Jeremy; Xiong, Pei; Nikolov, Daniel_K; Vamivakas, A_Nick; Rolland, Jannick_P (January 2023, Optics Express)

   Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays. 

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