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We show that given a graph G we can CMSO-transduce its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who gave such transductions using order-invariant MSO, a strictly more expressive logic than CMSO. Our methods more generally yield C2MSO-transductions of the canonical decomposition of weakly-partitive set systems and weakly-bipartitive systems of bipartitions.

The development of deep neural networks is witnessing fast growth in network size, which requires novel hardware computing platforms with large bandwidth and low energy consumption. Optical computing has been a potential candidate for next-generation computing systems. Specifically, wavelength-division multiplexing (WDM) has been widely adopted in optical neural network architecture to increase the computation bandwidth. Although existing WDM neural networks architectures have shown promise, they face challenges in the integration of light sources and further increase of the computing bandwidth. To overcome these issues, we introduce a mode-division multiplexing (MDM) strategy, offering a new degree of freedom in optical computing within the micro-ring resonator platform. We propose a MDM approach for small-scale networks and a multi-dimensional architecture for large-scale applications, supplementing WDM with MDM to enhance channel capacity for computations. In this work, we design and experimentally demonstrate key components for the MDM computing system, i.e., a multimode beam splitter, a thermo-optical tuner for the high-order mode, and a multimode waveguide bend. We further show a 2-by-2 matrix multiplexing system fabricated in a foundry that works for both MDM and MDM-WDM computing, which confirms that our approach successfully increases the input vector size for computing and ensures compatibility with existing WDM networks., Comment: 6 pages, 4 figures

Beam steering involves the calibration of the angle and position at which a particle accelerator's electron beam is incident upon the x-ray target with respect to the rotation axis of the collimator. Beam Steering is an essential task for light sources. The Linac To Undulator is very difficult to steer and aim due to the changes of each use of the accelerator there must be re-calibration of magnets. However with each use of the Beamline its current method of steering runs into issues when faced with calibrating angles and positions. Human operators spend a substantial amount of time and resources on the task. We developed multiple different feed-forward-neural networks with varying hyper-parameters, inputs, and outputs, seeking to compare their performance. Specifically, our smaller models with 33 inputs and 13 outputs outperformed the larger models with 73 inputs and 50 outputs. We propose the following explanations for this lack of performance in larger models. First, a lack of training time and computational power limited the ability of our models to mature. Given more time, our models would outperform SVD. Second, when the input size of the model increases the noise increases as well. In this case more inputs corresponded to a greater length upon the LINAC accelerator. Less specific and larger models that seek to make more predictions will inherently perform worse than SVD.

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a class of $2D$ models generalizing recent experiments on photonic systems. We explore two kinds of localization that emerge in these models: Anderson localization by disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. We find localization properties to depend on the symmetry class within a family of amorphized kagom\'{e} tight-binding models, set by a tunable synthetic magnetic field. The flat-band-like degeneracy innate to kagom\'{e} lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. For particular values of the field, such states emerge in the amorphous system that were not present on the kagom\'{e} lattice in the same field. For generic states, the standard paradigm of Anderson localization is found to apply as expected for systems with particle-hole symmetry (class D), while a similar interpretation does not extend to our results in the general unitary case (class A). The structure of amorphous graphs, which arise in current photonics experiments, allows exact statements about flat-band-like states, including such states that only exist in amorphous systems, and demonstrates how the qualitative behavior of a disordered system can be tuned at fixed graph topology.

Lettericity is a graph parameter responsible for many attractive structural properties. In particular, graphs of bounded lettericity have bounded linear clique-width and they are well-quasi-ordered by induced subgraphs. The latter property implies that any hereditary class of graphs of bounded lettericity can be described by finitely many forbidden induced subgraphs. This, in turn, implies, in a non-constructive way, polynomial-time recognition of such classes. However, no constructive algorithms and no specific bounds on the size of forbidden graphs are available up to date. In the present paper, we develop an algorithm that recognizes $n$-vertex graphs of lettericity at most $k$ in time $f(k)n^3$ and show that any minimal graph of lettericity more than $k$ has at most $2^{O(k^2\log k)}$ vertices., Comment: 16pages + 3pages appendix. Submitted to a journal

Beam steering is the process involving the calibration of the angle and position at which a particle accelerator's electron beam is incident upon the x-ray target with respect to the rotation axis of the collimator. Beam Steering is an essential task for light sources. In the case under study, the LINAC To Undulator (LTU) section of the beamline is difficult to aim. Each use of the accelerator requires re-calibration of the magnets in this section. This involves a substantial amount of time and effort from human operators, while reducing scientific throughput of the light source. We investigate the use of deep neural networks to assist in this task. The deep learning models are trained on archival data and then validated on simulation data. The performance of the deep learning model is contrasted against that of trained human operators.

A graph $G$ contains a graph $H$ as a pivot-minor if $H$ can be obtained from $G$ by applying a sequence of vertex deletions and edge pivots. Pivot-minors play an important role in the study of rank-width. Pivot-minors have mainly been studied from a structural perspective. In this paper we perform the first systematic computational complexity study of pivot-minors. We first prove that the Pivot-Minor problem, which asks if a given graph $G$ contains a pivot-minor isomorphic to a given graph $H$, is NP-complete. If $H$ is not part of the input, we denote the problem by $H$-Pivot-Minor. We give a certifying polynomial-time algorithm for $H$-Pivot-Minor when (1) $H$ is an induced subgraph of $P_3+tP_1$ for some integer $t\geq 0$, (2) $H=K_{1,t}$ for some integer $t\geq 1$, or (3) $|V(H)|\leq 4$ except when $H \in \{K_4,C_3+ P_1\}$. Let ${\cal F}_H$ be the set of induced-subgraph-minimal graphs that contain a pivot-minor isomorphic to $H$. To prove the above statement, we either show that there is an integer $c_H$ such that all graphs in ${\cal F}_H$ have at most $c_H$ vertices, or we determine ${\cal F}_H$ precisely, for each of the above cases., Comment: 33 pages, 9 figures. An extended abstract appeared in the proceedings of WG2018

Inverse design is a powerful tool in wave-physics and in particular in photonics for compact, high-performance devices. To date, applications have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the "black box" nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at 1.1MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

Silicon-based quantum emitters are candidates for large-scale qubit integration due to their single-photon emission properties and potential for spin-photon interfaces with long spin coherence times. Here, we demonstrate local writing and erasing of selected light-emitting defects using fs laser pulses in combination with hydrogen-based defect activation and passivation. By selecting forming gas (N2/H2) during thermal annealing of carbon-implanted silicon, we form Ci centers while passivating the more common G-centers. The Ci center is a telecom S-band emitter with very promising spin properties that consists of a single interstitial carbon atom in the silicon lattice. Density functional theory calculations show that the Ci center brightness is enhanced by several orders of magnitude in the presence of hydrogen. Fs-laser pulses locally affect the passivation or activation of quantum emitters with hydrogen and enable programmable quantum emitter formation in a qubit-by-design paradigm.

Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition's width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms which achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width alone. Motivated by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth (sd). Here, sd is a bounded-depth analogue of cliquewidth, in the same way as td is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. Precisely, we prove that on $n$-vertex graphs equipped with a tree-model (a decomposition notion underlying sd) of depth $d$ and using $k$ labels, we can solve - Independent Set in time $2^{O(dk)}\cdot n^{O(1)}$ using $O(dk^2\log n)$ space; - Max Cut in time $n^{O(dk)}$ using $O(dk\log n)$ space; and - Dominating Set in time $2^{O(dk)}\cdot n^{O(1)}$ using $n^{O(1)}$ space via a randomized algorithm. We also establish a lower bound, conditional on a certain assumption about the complexity of Longest Common Subsequence, which shows that at least in the case of IS the exponent of the parametric factor in the time complexity has to grow with $d$ if one wishes to keep the space complexity polynomial., Comment: Conference version to appear at the European Symposium on Algorithms (ESA 2023)

Solid-state point defects are attracting increasing attention in the field of quantum information science, because their localized states can act as a spin-photon interface in devices that store and transfer quantum information, which have been used for applications in quantum computing, sensing, and networking. In this work we have performed high-throughput calculations of over 50,000 point defects in various semiconductors including diamond, silicon carbide, and silicon. Focusing on quantum applications, we characterize the relevant optical and electronic properties of these defects, including formation energies, spin characteristics, transition dipole moments, zero-phonon lines. We find 2331 composite defects which are stable in intrinsic silicon, which are then filtered to identify many new optically bright telecom spin qubit candidates and single-photon sources. All computed results and relaxed defect structures are made publicly available online at quantumdefects.com, a living database of defect characteristics which will be continually expanded with new defects and properties, and will enable researchers to select defects tailored to their applications., Comment: 12 pages, 3 figures

Near infrared color centers in silicon are emerging candidates for on-chip integrated quantum emitters, optical access quantum memories and sensing. We access ensemble G color center formation dynamics and radiation-induced atomic disorder in silicon for a series of MeV proton flux conditions. Photoluminescence results reveal that the G-centers are formed more efficiently by pulsed proton irradiation than continuous wave proton irradiation. The enhanced transient excitations and dynamic annealing within nanoseconds allows optimizing the ratio of G-center formation to nonradiative defect accumulation. The G-centers preserve narrow linewidths of about 0.1 nm when they are generated by moderate pulsed proton fluences, while the linewidth broadens significantly as the pulsed proton fluence increases. This implies vacancy/interstitial clustering by overlapping collision cascades. Tracking G-center properties for a series of irradiation conditions enables sensitive probing of atomic disorder, serving as a complimentary analytical method for sensing damage accumulation. Aided by ${\it ab}$ ${\it initio}$ electronic structure calculations, we provide insight into the atomic disorder-induced inhomogeneous broadening by introducing vacancies and silicon interstitials in the vicinity of a G-center. A vacancy leads to a tensile strain and can result in either a redshift or blueshift of the G-center emission, depending on its position relative to the G-center. Meanwhile, Si interstitials lead to compressive strain, which results in a monotonic redshift. High flux and tunable ion pulses enable the exploration of fundamental dynamics of radiation-induced defects as well as methods for defect engineering and qubit synthesis for quantum information processing., Comment: 9 pages, 7 figures

Silicon is the most scalable optoelectronic material, and it has revolutionized our lives in many ways. The prospect of quantum optics in silicon is an exciting avenue because it has the potential to address the scaling and integration challenges, the most pressing questions facing quantum science and technology. We report the first all-silicon quantum light source based on a single atomic emissive center embedded in a silicon-based nanophotonic cavity. We observe a more than 30-fold enhancement of luminescence, a near unity atom-cavity coupling efficiency, and an 8-fold acceleration of the emission from the quantum center. Our work opens avenues for large-scale integrated all-silicon cavity quantum electrodynamics and quantum photon interfaces with applications in quantum communication, sensing, imaging, and computing.

Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to preserve the response of systems in the presence of disorder. We propose and demonstrate topological structurally disordered systems with a modal structure that enhances nonlinear phenomena in the topological channels by inhibiting the ultrafast leakage of energy from edge modes to bulk modes. We present the construction of the graph and show that its dynamics enhances the topologically protected photon pair generation rate by an order of magnitude. Disordered nonlinear topological graphs will enable advanced quantum interconnects, efficient nonlinear sources, and light-based information processing for artificial intelligence., Comment: Main Text: 7 pages, 4 figures. Supplementary Information: 5 pages, 6 figures. With respect to version 1 we've carried out a minor revision of the document

Incoherent light is ubiquitous, yet designing optical devices that can handle its random nature is very challenging, since directly averaging over many incoherent incident beams can require a huge number of scattering calculations. We show how to instead solve this problem with a reciprocity technique which leads to three orders of magnitude speedup: one Maxwell solve (using any numerical technique) instead of thousands. This improvement enables us to perform efficient inverse design, large scale optimization of the metasurface for applications such as light collimators and concentrators. We show the impact of the angular distribution of incident light on the resulting performance, and show especially promising designs for the case of "annular" beams distributed only over nonzero angles.

The study of defect centers in silicon has been recently reinvigorated by their potential applications in optical quantum information processing. A number of silicon defect centers emit single photons in the telecommunication $O$-band, making them promising building blocks for quantum networks between computing nodes. The two-carbon G-center, self-interstitial W-center, and spin-$1/2$ T-center are the most intensively studied silicon defect centers, yet despite this, there is no consensus on the precise configurations of defect atoms in these centers, and their electronic structures remain ambiguous. Here we employ \textit{ab initio} density functional theory to characterize these defect centers, providing insight into the relaxed structures, bandstructures, and photoluminescence spectra, which are compared to experimental results. Motivation is provided for how these properties are intimately related to the localization of electronic states in the defect centers. In particular, we present the calculation of the zero-field splitting for the excited triplet state of the G-center defect as the structure is transformed from the A-configuration to the B-configuration, showing a sudden increase in the magnitude of the $D_{zz}$ component of the zero-field splitting tensor. By performing projections onto the local orbital states of the defect, we analyze this transition in terms of the symmetry and bonding character of the G-center defect which sheds light on its potential application as a spin-photon interface., Comment: 11 pages, 6 figures

Defect engineering is foundational to classical electronic device development and for emerging quantum devices. Here, we report on defect engineering of silicon single crystals with ion pulses from a laser accelerator with ion flux levels up to 10^22 ions/cm^2/s. Low energy ions from plasma expansion of the laser-foil target are implanted near the surface and then diffuse into silicon samples that were locally pre-heated by high energy ions. We observe low energy ion fluences of ~10^16 cm^-2, about four orders of magnitude higher than the fluence of high energy (MeV) ions. In the areas of highest energy deposition, silicon crystals exfoliate from single ion pulses. Color centers, predominantly W and G-centers, form directly in response to ion pulses without a subsequent annealing step. We find that the linewidth of G-centers increase in areas with high ion flux much more than the linewidth of W-centers, consistent with density functional theory calculations of their electronic structure. Laser ion acceleration generates aligned pulses of high and low energy ions that expand the parameter range for defect engineering and doping of semiconductors with tunable balances of ion flux, damage rates and local heating.

The scaling of electromagnetic apertures is a long-standing question that has been investigated for at least six decades but has still not been resolved [1-5]. The size of single aperture cavities, bounded by the existence of higher-order transverse modes, fundamentally limits the power emitted by single-mode lasers or the brightness of quantum light sources. The free-spectral range of existing electromagnetic apertures goes to zero when the size of the aperture increases, and the demonstration of scale-invariant apertures or lasers has remained elusive. Here, we report open-Dirac electromagnetic apertures that exploit a subtle cavity-mode-dependent scaling of losses in reciprocal space. For cavities with a quadratic dispersion, the complex frequencies of modes converge towards each other with the size of cavities, making cavities invariably multimode. Surprisingly, for a class of cavities with linear dispersion, we discover that, while the convergence of the real parts of cavity modes towards each other is delayed (it still quickly goes to zero), the normalized complex free-spectral range converge towards a constant governed by the loss rate of distinct Bloch bands. We show that this unconventional scaling of the complex frequency of cavity modes in open-Dirac electromagnetic apertures guarantees single-mode operation of large cavities. We experimentally demonstrate that single-mode lasing of such cavities is maintained when the cavity is scale up in size. We name such sources Berkeley Surface Emitting Lasers (BerkSELs). We further show that the far-field emitted by the proposed single-mode BerkSELs corresponds to a topological singularity of charge two, in full agreement with our theory. Open-Dirac apertures open new avenues for light-matter interaction and basic science in open-wave systems with applications in classical and quantum communications, sensing, and imaging.

Light-actuated motors, vehicles, and even space sails have drawn tremendous attention for basic science and applications in space, biomedical, and sensing domains. Optical bound states in the continuum (BIC) are topological singularities of the scattering matrix, known for their unique light trapping capability and enhanced light-matter interaction. We show that BIC modes enable the generation of enhanced and tunable optical forces and torques. A sharp and controllable lineshape is observed in forces and torques spectra when approaching high-Q resonance BIC modes. Wavelength and polarization tunability are presented as an effective method to control the forces on BIC enclosed structures. Finally Finite-size simulations are performed to evaluate the practical application for a BIC assisted metavehicle.

Researchers have turned to various disciplines in search for theories that can contribute in different ways towards Information privacy. The data collection instrument (questionnaire) of these theories is in English. Nevertheless, issues related to Social Network Sites are meant for various groups with different cultural background. Therefore, cross-cultural and international studies are used in majority to address issues facing these platforms. Henceforth, there is a need to translate these instruments into other languages such as French. In this paper, we produced a mixed method for English instrument translation into French using different techniques from different approaches, the B-TAMBiT.

Every minor-closed class of matroids of bounded branch-width can be characterized by a list of excluded minors, but unlike graphs, this list may need to be infinite in general. However, for each fixed finite field $\mathbb F$, the list needs to contain only finitely many $\mathbb F$-representable matroids, due to the well-quasi-ordering of $\mathbb F$-representable matroids of bounded branch-width under taking matroid minors [J. F. Geelen, A. M. H. Gerards, and G. Whittle (2002)]. But this proof is non-constructive and does not provide any algorithm for computing these $\mathbb F$-representable excluded minors in general. We consider the class of matroids of path-width at most $k$ for fixed $k$. We prove that for a finite field $\mathbb F$, every $\mathbb F$-representable excluded minor for the class of matroids of path-width at most $k$ has at most $2^{|\mathbb{F}|^{O(k^2)}}$ elements. We can therefore compute, for any integer $k$ and a fixed finite field $\mathbb F$, the set of $\mathbb F$-representable excluded minors for the class of matroids of path-width $k$, and this gives as a corollary a polynomial-time algorithm for checking whether the path-width of an $\mathbb F$-represented matroid is at most $k$. We also prove that every excluded pivot-minor for the class of graphs having linear rank-width at most $k$ has at most $2^{2^{O(k^2)}}$ vertices, which also results in a similar algorithmic consequence for linear rank-width of graphs., Comment: 19 pages; slightly revised

We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of their respective classes of objects. We prove that these notions are equivalent in the sense that a permutation class is geometrically griddable if and only if the corresponding class of inversion graphs has bounded lettericity.