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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

A trigraph is a graph where each pair of vertices is labelled either 0 (a non-arc), 1 (an arc) or $\star$ (both an arc and a non-arc). In a series of papers, Hell and co-authors proposed to study the complexity of homomorphisms from graphs to trigraphs, called Matrix Partition Problems, where arcs and non-arcs can be both mapped to $\star$-arcs, while a non-arc cannot be mapped to an arc, and vice-versa. Even though Matrix Partition Problems are generalisations of CSPs, they share with them the property of being ``intrinsically'' combinatorial. So, the question of a possible P-time vs NP-complete dichotomy is a very natural one and was raised in Hell et al.'s papers. We propose a generalisation of Matrix Partitions to relational structures and study them with respect to the question of a dichotomy. We first show that trigraph homomorphisms and Matrix Partitions are P-time equivalent, and then prove that one can also restrict (with respect to having a dichotomy) to relational structures with a single relation. Failing in proving that Matrix Partitions on directed graphs are not P-time equivalent to Matrix Partitions on relational structures, we give some evidence that it might be unlikely by formalising the reductions used in the case of CSPs and by showing that such reductions cannot work for the case of Matrix Partitions. We then turn our attention to Matrix Partitions that can be described by finite sets of (induced-subgraph) obstructions. We show, in particular, that any such problem has finitely many minimal obstructions if and only if it has finite duality. We conclude by showing that on trees (seen as trigraphs) it is NP-complete to decide whether a given tree has a homomorphism to another input trigraph. The latter shows a notable difference on tractability between CSP and Matrix Partitions as it is well-known that CSP is tractable on the class of trees.

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.

Tree-width and its linear variant path-width play a central role for the graph minor relation. In particular, Robertson and Seymour (1983) proved that for every tree~$T$, the class of graphs that do not contain $T$ as a minor has bounded path-width. For the pivot-minor relation, rank-width and linear rank-width take over the role from tree-width and path-width. As such, it is natural to examine if for every tree~$T$, the class of graphs that do not contain $T$ as a pivot-minor has bounded linear rank-width. We first prove that this statement is false whenever $T$ is a tree that is not a caterpillar. We conjecture that the statement is true if $T$ is a caterpillar. We are also able to give partial confirmation of this conjecture by proving: (1) for every tree $T$, the class of $T$-pivot-minor-free distance-hereditary graphs has bounded linear rank-width if and only if $T$ is a caterpillar; (2) for every caterpillar $T$ on at most four vertices, the class of $T$-pivot-minor-free graphs has bounded linear rank-width. To prove our second result, we only need to consider $T=P_4$ and $T=K_{1,3}$, but we follow a general strategy: first we show that the class of $T$-pivot-minor-free graphs is contained in some class of $(H_1,H_2)$-free graphs, which we then show to have bounded linear rank-width. In particular, we prove that the class of $(K_3,S_{1,2,2})$-free graphs has bounded linear rank-width, which strengthens a known result that this graph class has bounded rank-width., Comment: 26 pages, 5 figures; accepted to SIAM Journal on Discrete Mathematics

The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels that is contaminated by some infectious substance and we are looking for a search strategy that, at each step, either places a searcher on a vertex or removes a searcher from a vertex and where an edge is cleaned when both endpoints are simultaneously occupied by searchers. It was proved that the minimum number of searchers required for a successful cleaning strategy is equal to the pathwidth of the graph plus one. Two desired characteristics for a cleaning strategy is to be monotone (no recontamination occurs) and connected (clean territories always remain connected). Under these two demands, the number of searchers is equivalent to a variant of pathwidth called {\em connected pathwidth}. We prove that connected pathwidth is fixed parameter tractable, in particular we design a $2^{O(k^2)}\cdot n$ time algorithm that checks whether the connected pathwidth of $G$ is at most $k.$ This resolves an open question by [Dereniowski, Osula, and Rz{\k{a}}{\.{z}}ewski, Finding small-width connected path-decompositions in polynomial time. Theor. Comput. Sci., 794:85-100, 2019]. For our algorithm, we enrich the typical sequence technique that is able to deal with the connectivity demand. Typical sequences have been introduced in [Bodlaender and Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358-402, 1996] for the design of linear parameterized algorithms for treewidth and pathwidth. The proposed extension is based on an encoding of the connectivity property that is quite versatile and may be adapted so to deliver linear parameterized algorithms for the connected variants of other width parameters as well.

Topological photonics has emerged as a novel route to engineer the flow of light. Topologically-protected photonic edge modes, which are supported at the perimeters of topologically-nontrivial insulating bulk structures, have been of particular interest as they may enable low-loss optical waveguides immune to structural disorder. Very recently, there is a sharp rise of interest in introducing gain materials into such topological photonic structures, primarily aiming at revolu-tionizing semiconductor lasers with the aid of physical mechanisms existing in topological physics. Examples of re-markable realizations are topological lasers with unidirectional light output under time-reversal symmetry breaking and topologically-protected polariton and micro/nano-cavity lasers. Moreover, the introduction of gain and loss provides a fascinating playground to explore novel topological phases, which are in close relevance to non-Hermitian and parity-time symmetric quantum physics and are in general difficult to access using fermionic condensed matter systems. Here, we review the cutting-edge research on active topological photonics, in which optical gain plays a pivotal role. We discuss recent realizations of topological lasers of various kinds, together with the underlying physics explaining the emergence of topological edge modes. In such demonstrations, the optical modes of the topological lasers are deter-mined by the dielectric structures and support lasing oscillation with the help of optical gain. We also address recent researches on topological photonic systems in which gain and loss themselves essentially influence on topological prop-erties of the bulk systems. We believe that active topological photonics provides powerful means to advance mi-cro/nanophotonics systems for diverse applications and topological physics itself as well., Comment: 23 pages, 11 figures, review paper to appear in Nanophotonics

Vortices are topologically stable singularities at the center of a swirl of energy. Optical vortices are conventionally formed using diffractive optics or by bespoke optical elements. We report room temperature integrated lasers directly generating and multiplexing coherent beams carrying arbitrarily large orbital angular momenta (OAM). The OAM beams are created using two-dimensional topological-rings formed by circular boundaries between topologically distinct photonic materials that naturally radiate vortices in the third dimension. We also demonstrate the planar multiplexing of OAM beams using concentric lasers. Our experimental demonstration reveals a subtle connection between topological matter and topological light and provides opportunities in microscopy, metrology, high-capacity communications, and quantum information processing.

In the past few years, carpet cloaking attracted interests because of its feasibility at optical frequencies and potential in stealth technologies. Metasurfaces have been proposed as a method to engineer ultra-thin carpet cloaking surfaces due to their abilities to manipulate wavefronts, polarization, and phase at subwavelength scale. However, achieving broadband carpet cloaking with a significant bandwidth is one of the key remaining challenges for metasurface designs. To date, broadband carpet cloaking based on metasurfaces has not been achieved and cloaking is limited to discrete wavelengths. Here, we propose and numerically demonstrate a novel metasurface design for broadband carpet cloaking with linear polarization at visible wavelengths from 650 nm to 800 nm. Our proposed method is a promising approach for broadband structured interfaces.

Non-Hermitian singularities known as exceptional-points (EPs) have been shown to exhibit increased sensitivities but the observation of EPs has so far been limited to wavelength scaled systems subject to diffraction limit. We propose a novel approach to EPs and report their first observation in plasmonics at room temperature. The plasmonic EPs are based on the hybridization of detuned resonances in multilayered plasmonic crystals to reach a critical complex coupling rate between nanoantennas arrays, and, resulting in the simultaneous coalescence of the resonances and loss rates. Because plasmons shrink the wavelength of light to make it compatible with biological relevant substances, enhanced sensing of anti-Immunoglobulin G, the most common antibody found in blood circulation, is observed. Our work opens the way to novel class of nanoscale devices, sensors, and imagers based on topological polaritonic effects.

With exponential increase in the availability oftelemetry / streaming / real-time data, understanding contextualbehavior changes is a vital functionality in order to deliverunrivalled customer experience and build high performance andhigh availability systems. Real-time behavior change detectionfinds a use case in number of domains such as social networks,network traffic monitoring, ad exchange metrics etc. In streamingdata, behavior change is an implausible observation that does notfit in with the distribution of rest of the data. A timely and preciserevelation of such behavior changes can give us substantialinformation about the system in critical situations which can bea driving factor for vital decisions. Detecting behavior changes instreaming fashion is a difficult task as the system needs to processhigh speed real-time data and continuously learn from data alongwith detecting anomalies in a single pass of data. In this paperwe introduce a novel algorithm called Accountable BehaviorChange Detection (VEDAR) which can detect and elucidate thebehavior changes in real-time and operates in a fashion similarto human perception. We have bench marked our algorithmon open source anomaly detection datasets. We have benchmarked our algorithm by comparing its performance on opensource anomaly datasets against industry standard algorithmslike Numenta HTM and Twitter AdVec (SH-ESD). Our algorithmoutperforms above mentioned algorithms for behaviour changedetection, efficacy is given in section V., Comment: 10 pages, 12 figures, 1 table

Miniature semiconductor lasers have attracted a large amount of interest owing to their potential as highly integrated components in photonic circuits or in sensors. Particularly, microdisk lasers exploiting whispering gallery modes have been regarded as an important candidate because of their relatively small footprint and low threshold. However, it has been challenging for microdisk to operate under single mode operation and to lase in a preselected mode. We report subwavelength microdisk resonators suspended in air with connecting bridges and propose a simple method using the number and symmetry of bridges to enhance or reduce wave confinement in the whispering gallery cavity. Moreover, a suitable choice of bridges increases the quality factor of microdisks compared to microdisks resonator without bridges. Using this method, we demonstrate single mode lasing of preselected modes at telecommunication wavelength.

Random media introduce large degrees of freedom in device design and can thus address challenges in manipulating optical waves. Wave shaping with metasurfaces has mainly utilized periodic or quasi-periodic grids, and, the potential of random arrangement of particles for devices has only come under investigation recently. The main difficulty in pursuing random metasurfaces is the identification of the degrees of freedom that optimize their efficiencies and functions. They can also encode information using the statistics of particles distribution. We propose a phase-map that accounts for the statistical nature of random media. The method takes into account effects of random near-field couplings that introduce phase errors by affecting the phase shift of elements. The proposed approach increases the efficiency of our random metasurface devices by up to ~20%. This work paves the way towards the efficient design of random metasurfaces with potential applications in highly secure optical cryptography and information encoding., Comment: 10 pages, 4 figures, 1 table

We prove that one can count in polynomial time the number of minimal transversals of $\beta$-acyclic hypergraphs. In consequence, we can count in polynomial time the number of minimal dominating sets of strongly chordal graphs, continuing the line of research initiated in [M.M. Kant\'e and T. Uno, Counting Minimal Dominating Sets, TAMC'17].

In this paper, we design a framework to obtain efficient algorithms for several problems with a global constraint (acyclicity or connectivity) such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. We design a meta-algorithm that solves all these problems and whose running time is upper bounded by $2^{O(k)}\cdot n^{O(1)}$, $2^{O(k \log(k))}\cdot n^{O(1)}$, $2^{O(k^2)}\cdot n^{O(1)}$ and $n^{O(k)}$ where $k$ is respectively the clique-width, $\mathbf{Q}$-rank-width, rank-width and maximum induced matching width of a given decomposition. Our approach simplifies and unifies the known algorithms for each of the parameters and its running time matches asymptotically also the running times of the best known algorithms for basic NP-hard problems such as Vertex Cover and Dominating Set. Our framework is based on the $d$-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013] and the rank-based approach introduced in [Bodlaender, Cygan, Kratsch and Nederlof, ICALP 2013]. The results we obtain highlight the importance of the $d$-neighbor equivalence relation on the algorithmic applications of width measures. We also prove that our framework could be useful for $W[1]$-hard problems parameterized by clique-width such as Max Cut and Maximum Minimal Cut. For these latter problems, we obtain $n^{O(k)}$, $n^{O(k)}$ and $n^{2^{O(k)}}$ time algorithms where $k$ is respectively the clique-width, the $\mathbf{Q}$-rank-width and the rank-width of the input graph.

Conventional optical components have been proposed to realize high-quality line focusing with uniform intensity distribution such as cylindrical lenses, segmented wedge-arrays, or a combination of prisms and spherical mirrors. However, numerous factors such as the manufacturing tolerances of conventional lenses or the need for precise alignment of the lenses cause wavefront aberrations that impact the performance of optical systems. These aforementioned limitations of conventional optical components affect the uniformity of the intensity distribution. Here, we numerically and experimentally demonstrate an integrable planar all-dielectric cylindrical lens for uniform line focusing. The lens has a NA of 0.247 and a measured uniformity of 0.92% at 800 nm.

Metasurfaces are generally designed by placing scatterers in periodic or pseudo-periodic grids. We propose and discuss design rules for functional metasurfaces with randomly placed anisotropic elements. By analyzing the focusing performance of random metasurface lenses as a function of their density and the density of the phase-maps used to design them, we find that the performance of 1D metasurfaces is mostly governed by their density while 2D metasurfaces strongly depend on both the density and the near-field coupling configuration of the surface. The proposed approach is used to design all-polarization random metalenses at near infrared frequencies. Challenges, as well as opportunities of random metasurfaces compared to periodic ones are discussed. Our results pave the way to new approaches in the design of nanophotonic structures and devices from lenses to solar energy concentrators., Comment: 13 pages 6 figures. arXiv admin note: substantial text overlap with arXiv:1708.07865

Metasurfaces are generally designed by placing scatterers in a periodic grid. We propose and discuss design rules for efficient random and functional metasurfaces with anisotropic elements. We investigate the impact of the elements density on the performance of metasurfaces in both periodic and random cases. Using numerical simulations, we apply our approach to the design of all-polarization random metalenses at near infrared frequencies. The results will open a new paradigm in the design of metamaterial and metasurface devices from lenses to solar energy concentrators., Comment: 8 pages, 5 figures

Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex Cover. We also propose a $2^{O(k)}\cdot n$ time algorithm for Feedback Vertex Set. The best running times for all the considered cases were either $2^{O(k\cdot \log(k))}\cdot n^{O(1)}$ or worse.